diff options
Diffstat (limited to 'lib/hcrypto')
316 files changed, 45239 insertions, 13828 deletions
diff --git a/lib/hcrypto/Makefile.am b/lib/hcrypto/Makefile.am index a9c688d28f21..878525c17d06 100644 --- a/lib/hcrypto/Makefile.am +++ b/lib/hcrypto/Makefile.am @@ -9,12 +9,19 @@ AM_CPPFLAGS += $(INCLUDE_openssl_crypto) endif AM_CPPFLAGS += -I$(top_srcdir)/lib/hx509 \ - -I$(srcdir)/libtommath -DUSE_HCRYPTO_LTM=1 + -I$(srcdir)/libtommath -DUSE_HCRYPTO_LTM=1 \ + -I$(srcdir)/x25519 \ + -I$(srcdir)/.. + +WFLAGS += $(WFLAGS_LITE) -Wno-error=unused-function +# XXX: Make these not necessary: +WFLAGS += -Wno-error=unused-result -Wno-error=deprecated-declarations +WFLAGS += $(WFLAGS_UNUSED_BUT_SET_VAR) lib_LTLIBRARIES = libhcrypto.la check_LTLIBRARIES = libhctest.la -libhcrypto_la_LDFLAGS = -version-info 5:0:1 +libhcrypto_la_LDFLAGS = -version-info 5:0:0 libhcrypto_la_LIBADD = \ $(top_builddir)/lib/asn1/libasn1.la \ $(LIB_dlopen) \ @@ -55,7 +62,7 @@ hcryptoinclude_HEADERS = \ ui.h \ undef.h -install-build-headers:: $(hcryptoinclude_HEADERS) +install-build-headers:: $(hcryptoinclude_HEADERS) $(x25519include_HEADERS) @foo='$(hcryptoinclude_HEADERS)'; \ for f in $$foo; do \ f=`basename $$f`; \ @@ -95,6 +102,22 @@ SCRIPT_TESTS = \ noinst_PROGRAMS = test_rand +noinst_HEADERS = \ + x25519/ed25519_ref10_fe_51.h \ + x25519/ed25519_ref10_fe_25_5.h \ + x25519/ed25519_ref10.h \ + x25519/fe_25_5/base.h \ + x25519/fe_25_5/base2.h \ + x25519/fe_25_5/constants.h \ + x25519/fe_25_5/fe.h \ + x25519/fe_51/base.h \ + x25519/fe_51/base2.h \ + x25519/fe_51/constants.h \ + x25519/fe_51/fe.h \ + x25519/align.h \ + x25519_ref10.h + + check_PROGRAMS = $(PROGRAM_TESTS) test_rsa test_dh example_evp_cipher check_SCRIPTS = $(SCRIPT_TESTS) @@ -105,6 +128,7 @@ test_rand_LDADD = $(LDADD) -lm libhcrypto_la_SOURCES = \ $(ltmsources) \ + $(x25519sources)\ aes.c \ aes.h \ bn.c \ @@ -168,131 +192,172 @@ libhcrypto_la_SOURCES = \ undef.h ltmsources = \ - libtommath/tommath.h \ - libtommath/tommath_class.h \ - libtommath/tommath_superclass.h \ - libtommath/bncore.c \ - libtommath/bn_mp_init.c \ + libtommath/bn_cutoffs.c \ + libtommath/bn_deprecated.c \ + libtommath/bn_mp_2expt.c \ + libtommath/bn_mp_abs.c \ + libtommath/bn_mp_add.c \ + libtommath/bn_mp_add_d.c \ + libtommath/bn_mp_addmod.c \ + libtommath/bn_mp_and.c \ + libtommath/bn_mp_clamp.c \ libtommath/bn_mp_clear.c \ + libtommath/bn_mp_clear_multi.c \ + libtommath/bn_mp_cmp.c \ + libtommath/bn_mp_cmp_d.c \ + libtommath/bn_mp_cmp_mag.c \ + libtommath/bn_mp_cnt_lsb.c \ + libtommath/bn_mp_complement.c \ + libtommath/bn_mp_copy.c \ + libtommath/bn_mp_count_bits.c \ + libtommath/bn_mp_decr.c \ + libtommath/bn_mp_div.c \ + libtommath/bn_mp_div_2.c \ + libtommath/bn_mp_div_2d.c \ + libtommath/bn_mp_div_3.c \ + libtommath/bn_mp_div_d.c \ + libtommath/bn_mp_dr_is_modulus.c \ + libtommath/bn_mp_dr_reduce.c \ + libtommath/bn_mp_dr_setup.c \ + libtommath/bn_mp_error_to_string.c \ libtommath/bn_mp_exch.c \ + libtommath/bn_mp_expt_u32.c \ + libtommath/bn_mp_exptmod.c \ + libtommath/bn_mp_exteuclid.c \ + libtommath/bn_mp_fread.c \ + libtommath/bn_mp_from_sbin.c \ + libtommath/bn_mp_from_ubin.c \ + libtommath/bn_mp_fwrite.c \ + libtommath/bn_mp_gcd.c \ + libtommath/bn_mp_get_double.c \ + libtommath/bn_mp_get_i32.c \ + libtommath/bn_mp_get_i64.c \ + libtommath/bn_mp_get_l.c \ + libtommath/bn_mp_get_ll.c \ + libtommath/bn_mp_get_mag_u32.c \ + libtommath/bn_mp_get_mag_u64.c \ + libtommath/bn_mp_get_mag_ul.c \ + libtommath/bn_mp_get_mag_ull.c \ libtommath/bn_mp_grow.c \ - libtommath/bn_mp_shrink.c \ - libtommath/bn_mp_clamp.c \ - libtommath/bn_mp_zero.c \ - libtommath/bn_mp_zero_multi.c \ - libtommath/bn_mp_set.c \ - libtommath/bn_mp_set_int.c \ - libtommath/bn_mp_init_size.c \ - libtommath/bn_mp_copy.c \ + libtommath/bn_mp_incr.c \ + libtommath/bn_mp_init.c \ libtommath/bn_mp_init_copy.c \ - libtommath/bn_mp_abs.c \ - libtommath/bn_mp_neg.c \ - libtommath/bn_mp_cmp_mag.c \ - libtommath/bn_mp_cmp.c \ - libtommath/bn_mp_cmp_d.c \ - libtommath/bn_mp_rshd.c \ + libtommath/bn_mp_init_i32.c \ + libtommath/bn_mp_init_i64.c \ + libtommath/bn_mp_init_l.c \ + libtommath/bn_mp_init_ll.c \ + libtommath/bn_mp_init_multi.c \ + libtommath/bn_mp_init_set.c \ + libtommath/bn_mp_init_size.c \ + libtommath/bn_mp_init_u32.c \ + libtommath/bn_mp_init_u64.c \ + libtommath/bn_mp_init_ul.c \ + libtommath/bn_mp_init_ull.c \ + libtommath/bn_mp_invmod.c \ + libtommath/bn_mp_is_square.c \ + libtommath/bn_mp_iseven.c \ + libtommath/bn_mp_isodd.c \ + libtommath/bn_mp_kronecker.c \ + libtommath/bn_mp_lcm.c \ + libtommath/bn_mp_log_u32.c \ libtommath/bn_mp_lshd.c \ + libtommath/bn_mp_mod.c \ libtommath/bn_mp_mod_2d.c \ - libtommath/bn_mp_div_2d.c \ - libtommath/bn_mp_mul_2d.c \ - libtommath/bn_mp_div_2.c \ - libtommath/bn_mp_mul_2.c \ - libtommath/bn_s_mp_add.c \ - libtommath/bn_s_mp_sub.c \ - libtommath/bn_fast_s_mp_mul_digs.c \ - libtommath/bn_s_mp_mul_digs.c \ - libtommath/bn_fast_s_mp_mul_high_digs.c \ - libtommath/bn_s_mp_mul_high_digs.c \ - libtommath/bn_fast_s_mp_sqr.c \ - libtommath/bn_s_mp_sqr.c \ - libtommath/bn_mp_add.c \ - libtommath/bn_mp_sub.c \ - libtommath/bn_mp_karatsuba_mul.c \ + libtommath/bn_mp_mod_d.c \ + libtommath/bn_mp_montgomery_calc_normalization.c \ + libtommath/bn_mp_montgomery_reduce.c \ + libtommath/bn_mp_montgomery_setup.c \ libtommath/bn_mp_mul.c \ - libtommath/bn_mp_karatsuba_sqr.c \ - libtommath/bn_mp_sqr.c \ - libtommath/bn_mp_div.c \ - libtommath/bn_mp_mod.c \ - libtommath/bn_mp_add_d.c \ - libtommath/bn_mp_sub_d.c \ + libtommath/bn_mp_mul_2.c \ + libtommath/bn_mp_mul_2d.c \ libtommath/bn_mp_mul_d.c \ - libtommath/bn_mp_div_d.c \ - libtommath/bn_mp_mod_d.c \ - libtommath/bn_mp_expt_d.c \ - libtommath/bn_mp_addmod.c \ - libtommath/bn_mp_submod.c \ libtommath/bn_mp_mulmod.c \ - libtommath/bn_mp_sqrmod.c \ - libtommath/bn_mp_gcd.c \ - libtommath/bn_mp_lcm.c \ - libtommath/bn_fast_mp_invmod.c \ - libtommath/bn_mp_invmod.c \ - libtommath/bn_mp_reduce.c \ - libtommath/bn_mp_montgomery_setup.c \ - libtommath/bn_fast_mp_montgomery_reduce.c \ - libtommath/bn_mp_montgomery_reduce.c \ - libtommath/bn_mp_exptmod_fast.c \ - libtommath/bn_mp_exptmod.c \ - libtommath/bn_mp_2expt.c \ - libtommath/bn_mp_n_root.c \ - libtommath/bn_mp_jacobi.c \ - libtommath/bn_reverse.c \ - libtommath/bn_mp_count_bits.c \ - libtommath/bn_mp_read_unsigned_bin.c \ - libtommath/bn_mp_read_signed_bin.c \ - libtommath/bn_mp_to_unsigned_bin.c \ - libtommath/bn_mp_to_signed_bin.c \ - libtommath/bn_mp_unsigned_bin_size.c \ - libtommath/bn_mp_signed_bin_size.c \ - libtommath/bn_mp_xor.c \ - libtommath/bn_mp_and.c \ + libtommath/bn_mp_neg.c \ libtommath/bn_mp_or.c \ - libtommath/bn_mp_rand.c \ - libtommath/bn_mp_montgomery_calc_normalization.c \ - libtommath/bn_mp_prime_is_divisible.c \ - libtommath/bn_prime_tab.c \ + libtommath/bn_mp_pack.c \ + libtommath/bn_mp_pack_count.c \ libtommath/bn_mp_prime_fermat.c \ - libtommath/bn_mp_prime_miller_rabin.c \ + libtommath/bn_mp_prime_frobenius_underwood.c \ libtommath/bn_mp_prime_is_prime.c \ + libtommath/bn_mp_prime_miller_rabin.c \ libtommath/bn_mp_prime_next_prime.c \ - libtommath/bn_mp_find_prime.c \ - libtommath/bn_mp_dr_reduce.c \ - libtommath/bn_mp_dr_is_modulus.c \ - libtommath/bn_mp_dr_setup.c \ - libtommath/bn_mp_reduce_setup.c \ - libtommath/bn_mp_toom_mul.c \ - libtommath/bn_mp_toom_sqr.c \ - libtommath/bn_mp_div_3.c \ - libtommath/bn_s_mp_exptmod.c \ + libtommath/bn_mp_prime_rabin_miller_trials.c \ + libtommath/bn_mp_prime_rand.c \ + libtommath/bn_mp_prime_strong_lucas_selfridge.c \ + libtommath/bn_mp_radix_size.c \ + libtommath/bn_mp_radix_smap.c \ + libtommath/bn_mp_rand.c \ + libtommath/bn_mp_read_radix.c \ + libtommath/bn_mp_reduce.c \ libtommath/bn_mp_reduce_2k.c \ - libtommath/bn_mp_reduce_is_2k.c \ - libtommath/bn_mp_reduce_2k_setup.c \ libtommath/bn_mp_reduce_2k_l.c \ - libtommath/bn_mp_reduce_is_2k_l.c \ + libtommath/bn_mp_reduce_2k_setup.c \ libtommath/bn_mp_reduce_2k_setup_l.c \ - libtommath/bn_mp_radix_smap.c \ - libtommath/bn_mp_read_radix.c \ - libtommath/bn_mp_toradix.c \ - libtommath/bn_mp_radix_size.c \ - libtommath/bn_mp_fread.c \ - libtommath/bn_mp_fwrite.c \ - libtommath/bn_mp_cnt_lsb.c \ - libtommath/bn_error.c \ - libtommath/bn_mp_init_multi.c \ - libtommath/bn_mp_clear_multi.c \ - libtommath/bn_mp_exteuclid.c \ - libtommath/bn_mp_toradix_n.c \ - libtommath/bn_mp_prime_random_ex.c \ - libtommath/bn_mp_get_int.c \ + libtommath/bn_mp_reduce_is_2k.c \ + libtommath/bn_mp_reduce_is_2k_l.c \ + libtommath/bn_mp_reduce_setup.c \ + libtommath/bn_mp_root_u32.c \ + libtommath/bn_mp_rshd.c \ + libtommath/bn_mp_sbin_size.c \ + libtommath/bn_mp_set.c \ + libtommath/bn_mp_set_double.c \ + libtommath/bn_mp_set_i32.c \ + libtommath/bn_mp_set_i64.c \ + libtommath/bn_mp_set_l.c \ + libtommath/bn_mp_set_ll.c \ + libtommath/bn_mp_set_u32.c \ + libtommath/bn_mp_set_u64.c \ + libtommath/bn_mp_set_ul.c \ + libtommath/bn_mp_set_ull.c \ + libtommath/bn_mp_shrink.c \ + libtommath/bn_mp_signed_rsh.c \ + libtommath/bn_mp_sqr.c \ + libtommath/bn_mp_sqrmod.c \ libtommath/bn_mp_sqrt.c \ - libtommath/bn_mp_is_square.c \ - libtommath/bn_mp_init_set.c \ - libtommath/bn_mp_init_set_int.c \ - libtommath/bn_mp_invmod_slow.c \ - libtommath/bn_mp_prime_rabin_miller_trials.c \ - libtommath/bn_mp_to_signed_bin_n.c \ - libtommath/bn_mp_to_unsigned_bin_n.c + libtommath/bn_mp_sqrtmod_prime.c \ + libtommath/bn_mp_sub.c \ + libtommath/bn_mp_sub_d.c \ + libtommath/bn_mp_submod.c \ + libtommath/bn_mp_to_radix.c \ + libtommath/bn_mp_to_sbin.c \ + libtommath/bn_mp_to_ubin.c \ + libtommath/bn_mp_ubin_size.c \ + libtommath/bn_mp_unpack.c \ + libtommath/bn_mp_xor.c \ + libtommath/bn_mp_zero.c \ + libtommath/bn_prime_tab.c \ + libtommath/bn_s_mp_add.c \ + libtommath/bn_s_mp_balance_mul.c \ + libtommath/bn_s_mp_exptmod.c \ + libtommath/bn_s_mp_exptmod_fast.c \ + libtommath/bn_s_mp_get_bit.c \ + libtommath/bn_s_mp_invmod_fast.c \ + libtommath/bn_s_mp_invmod_slow.c \ + libtommath/bn_s_mp_karatsuba_mul.c \ + libtommath/bn_s_mp_karatsuba_sqr.c \ + libtommath/bn_s_mp_montgomery_reduce_fast.c \ + libtommath/bn_s_mp_mul_digs.c \ + libtommath/bn_s_mp_mul_digs_fast.c \ + libtommath/bn_s_mp_mul_high_digs.c \ + libtommath/bn_s_mp_mul_high_digs_fast.c \ + libtommath/bn_s_mp_prime_is_divisible.c \ + libtommath/bn_s_mp_rand_jenkins.c \ + libtommath/bn_s_mp_rand_platform.c \ + libtommath/bn_s_mp_reverse.c \ + libtommath/bn_s_mp_sqr.c \ + libtommath/bn_s_mp_sqr_fast.c \ + libtommath/bn_s_mp_sub.c \ + libtommath/bn_s_mp_toom_mul.c \ + libtommath/bn_s_mp_toom_sqr.c \ + libtommath/tommath_private.h \ + libtommath/tommath_cutoffs.h \ + libtommath/tommath_superclass.h \ + libtommath/tommath_class.h \ + libtommath/tommath.h +x25519sources = \ + x25519/ed25519_ref10.c \ + x25519/x25519_ref10.c $(libhcrypto_la_OBJECTS) $(test_rand_OBJECTS): hcrypto-link diff --git a/lib/hcrypto/Makefile.in b/lib/hcrypto/Makefile.in deleted file mode 100644 index 85b5196df582..000000000000 --- a/lib/hcrypto/Makefile.in +++ /dev/null @@ -1,4280 +0,0 @@ -# Makefile.in generated by automake 1.16.5 from Makefile.am. -# @configure_input@ - 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int i, len; + if (bn == NULL) + return 0; + for (num2 = num, i = 0; num2 > 0; i++) num2 = num2 >> 8; diff --git a/lib/hcrypto/camellia-ntt.h b/lib/hcrypto/camellia-ntt.h index 31db336dbb6e..5edd8a82e755 100644 --- a/lib/hcrypto/camellia-ntt.h +++ b/lib/hcrypto/camellia-ntt.h @@ -32,6 +32,11 @@ extern "C" { #endif +/* symbol renaming */ +#define Camellia_DecryptBlock hc_Camellia_DecryptBlock +#define Camellia_Ekeygen hc_Camellia_Ekeygen +#define Camellia_EncryptBlock hc_Camellia_EncryptBlock + #define CAMELLIA_BLOCK_SIZE 16 #define CAMELLIA_TABLE_BYTE_LEN 272 #define CAMELLIA_TABLE_WORD_LEN (CAMELLIA_TABLE_BYTE_LEN / 4) diff --git a/lib/hcrypto/des.c b/lib/hcrypto/des.c index ad15c67be8b4..cb9cac74b6c6 100644 --- a/lib/hcrypto/des.c +++ b/lib/hcrypto/des.c @@ -225,8 +225,14 @@ DES_set_key_unchecked(DES_cblock *key, DES_key_schedule *ks) uint32_t *k = &ks->ks[0]; int i; - t1 = (uint32_t)(*key)[0] << 24 | (*key)[1] << 16 | (*key)[2] << 8 | (*key)[3]; - t2 = (uint32_t)(*key)[4] << 24 | (*key)[5] << 16 | (*key)[6] << 8 | (*key)[7]; + t1 = (uint32_t)((*key)[0]) << 24 + | (uint32_t)((*key)[1]) << 16 + | (uint32_t)((*key)[2]) << 8 + | (*key)[3]; + t2 = (uint32_t)((*key)[4]) << 24 + | (uint32_t)((*key)[5]) << 16 + | (uint32_t)((*key)[6]) << 8 + | (*key)[7]; c = (pc1_c_3[(t1 >> (5 )) & 0x7] << 3) | (pc1_c_3[(t1 >> (5 + 8 )) & 0x7] << 2) @@ -325,14 +331,14 @@ DES_key_sched(DES_cblock *key, DES_key_schedule *ks) static void load(const unsigned char *b, uint32_t v[2]) { - v[0] = (uint32_t)b[0] << 24U; - v[0] |= b[1] << 16U; - v[0] |= b[2] << 8U; - v[0] |= b[3] << 0U; - v[1] = (uint32_t)b[4] << 24U; - v[1] |= b[5] << 16U; - v[1] |= b[6] << 8U; - v[1] |= b[7] << 0U; + v[0] = (uint32_t)(b[0]) << 24; + v[0] |= (uint32_t)(b[1]) << 16; + v[0] |= (uint32_t)(b[2]) << 8; + v[0] |= b[3]; + v[1] = (uint32_t)(b[4]) << 24; + v[1] |= (uint32_t)(b[5]) << 16; + v[1] |= (uint32_t)(b[6]) << 8; + v[1] |= b[7]; } static void @@ -722,6 +728,7 @@ DES_cfb64_encrypt(const void *in, void *out, int i = *num; unsigned char c; + memset(tmp, 0, DES_CBLOCK_LEN); while (length > 0) { if (i == 0) { DES_encrypt(uiv, ks, 1); @@ -844,7 +851,7 @@ DES_string_to_key(const char *str, DES_cblock *key) k[7] ^= 0xF0; DES_set_key(key, &ks); DES_cbc_cksum(s, key, len, &ks, key); - memset(&ks, 0, sizeof(ks)); + memset_s(&ks, sizeof(ks), 0, sizeof(ks)); DES_set_odd_parity(key); if (DES_is_weak_key(key)) k[7] ^= 0xF0; diff --git a/lib/hcrypto/dh-ltm.c b/lib/hcrypto/dh-ltm.c index 774f0e1176ab..720662199f99 100644 --- a/lib/hcrypto/dh-ltm.c +++ b/lib/hcrypto/dh-ltm.c @@ -40,7 +40,7 @@ #include "tommath.h" -static void +static int BN2mpz(mp_int *s, const BIGNUM *bn) { size_t len; @@ -49,8 +49,12 @@ BN2mpz(mp_int *s, const BIGNUM *bn) len = BN_num_bytes(bn); p = malloc(len); BN_bn2bin(bn, p); - mp_read_unsigned_bin(s, p, len); + if (mp_from_ubin(s, p, len) != MP_OKAY) { + free(p); + return -1; + } free(p); + return 0; } @@ -61,11 +65,14 @@ mpz2BN(mp_int *s) BIGNUM *bn; void *p; - size = mp_unsigned_bin_size(s); + size = mp_ubin_size(s); p = malloc(size); - if (p == NULL && size != 0) + if (p == NULL) + return NULL; + if (mp_to_ubin(s, p, SIZE_MAX, NULL) != MP_OKAY) { + free(p); return NULL; - mp_to_unsigned_bin(s, p); + }; bn = BN_bin2bn(p, size, NULL); free(p); @@ -110,11 +117,17 @@ ltm_dh_generate_key(DH *dh) dh->pub_key = NULL; } - mp_init_multi(&pub, &priv_key, &g, &p, NULL); + if (mp_init_multi(&pub, &priv_key, &g, &p, NULL) != MP_OKAY) + continue; - BN2mpz(&priv_key, dh->priv_key); - BN2mpz(&g, dh->g); - BN2mpz(&p, dh->p); + if (BN2mpz(&priv_key, dh->priv_key) != 0) + continue; + + if (BN2mpz(&g, dh->g) != 0) + continue; + + if (BN2mpz(&p, dh->p) != 0) + continue; res = mp_exptmod(&g, &priv_key, &p, &pub); @@ -157,9 +170,18 @@ ltm_dh_compute_key(unsigned char *shared, const BIGNUM * pub, DH *dh) if (dh->pub_key == NULL || dh->g == NULL || dh->priv_key == NULL) return -1; - mp_init_multi(&s, &priv_key, &p, &peer_pub, NULL); - BN2mpz(&p, dh->p); - BN2mpz(&peer_pub, pub); + if (mp_init_multi(&s, &priv_key, &p, &peer_pub, NULL) != MP_OKAY) + return -1; + + if (BN2mpz(&p, dh->p) != 0) { + ret = -1; + goto out; + } + + if (BN2mpz(&peer_pub, pub) != 0) { + ret = 1; + goto out; + } /* check if peers pubkey is reasonable */ if (mp_isneg(&peer_pub) @@ -170,17 +192,20 @@ ltm_dh_compute_key(unsigned char *shared, const BIGNUM * pub, DH *dh) goto out; } - BN2mpz(&priv_key, dh->priv_key); + if (BN2mpz(&priv_key, dh->priv_key) != 0) { + ret = -1; + goto out; + } ret = mp_exptmod(&peer_pub, &priv_key, &p, &s); - if (ret != 0) { ret = -1; goto out; } - ret = mp_unsigned_bin_size(&s); - mp_to_unsigned_bin(&s, shared); + ret = mp_ubin_size(&s); + if (mp_to_ubin(&s, shared, SIZE_MAX, NULL) != MP_OKAY) + ret = -1; out: mp_clear_multi(&s, &priv_key, &p, &peer_pub, NULL); diff --git a/lib/hcrypto/dh.c b/lib/hcrypto/dh.c index 0447c4f48384..b3b25e5186d1 100644 --- a/lib/hcrypto/dh.c +++ b/lib/hcrypto/dh.c @@ -98,7 +98,7 @@ DH_new_method(ENGINE *engine) if (dh->engine) { dh->meth = ENGINE_get_DH(dh->engine); if (dh->meth == NULL) { - ENGINE_finish(engine); + ENGINE_finish(dh->engine); free(dh); return 0; } @@ -145,7 +145,7 @@ DH_free(DH *dh) free_if(dh->counter); #undef free_if - memset(dh, 0, sizeof(*dh)); + memset_s(dh, sizeof(*dh), 0, sizeof(*dh)); free(dh); } diff --git a/lib/hcrypto/dsa.c b/lib/hcrypto/dsa.c index bbb34601c31f..eac0ae6498ec 100644 --- a/lib/hcrypto/dsa.c +++ b/lib/hcrypto/dsa.c @@ -70,7 +70,7 @@ DSA_free(DSA *dsa) free_if(dsa->r); #undef free_if - memset(dsa, 0, sizeof(*dsa)); + memset_s(dsa, sizeof(*dsa), 0, sizeof(*dsa)); free(dsa); } diff --git a/lib/hcrypto/ec.c b/lib/hcrypto/ec.c new file mode 100644 index 000000000000..5a5c3c7d52b2 --- /dev/null +++ b/lib/hcrypto/ec.c @@ -0,0 +1,178 @@ +/* + * Copyright (c) 2009 Kungliga Tekniska Högskolan + * (Royal Institute of Technology, Stockholm, Sweden). + * All rights reserved. + * + * Redistribution and use in source and binary forms, with or without + * modification, are permitted provided that the following conditions + * are met: + * + * 1. Redistributions of source code must retain the above copyright + * notice, this list of conditions and the following disclaimer. + * + * 2. Redistributions in binary form must reproduce the above copyright + * notice, this list of conditions and the following disclaimer in the + * documentation and/or other materials provided with the distribution. + * + * 3. Neither the name of the Institute nor the names of its contributors + * may be used to endorse or promote products derived from this software + * without specific prior written permission. + * + * THIS SOFTWARE IS PROVIDED BY THE INSTITUTE AND CONTRIBUTORS ``AS IS'' AND + * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE + * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE + * ARE DISCLAIMED. IN NO EVENT SHALL THE INSTITUTE OR CONTRIBUTORS BE LIABLE + * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL + * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS + * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) + * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT + * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY + * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF + * SUCH DAMAGE. + */ + +#include <config.h> +#include <roken.h> + +#include "ec.h" + +struct EC_POINT { + int inf; + mp_int x; + mp_int y; + mp_int z; +}; + +struct EC_GROUP { + size_t size; + mp_int prime; + mp_int order; + mp_int Gx; + mp_int Gy; +}; + +struct EC_KEY { + int type; + EC_GROUP *group; + EC_POINT *pubkey; + mp_int privkey; +}; + + +unsigned long +EC_GROUP_get_degree(EC_GROUP *) +{ +} + +EC_GROUP * +EC_KEY_get0_group(EC_KEY *) +{ +} + +int +EC_GROUP_get_order(EC_GROUP *, BIGNUM *, BN_CTX *) +{ +} + +EC_KEY * +o2i_ECPublicKey(EC_KEY **key, unsigned char **, size_t) +{ +} + +void +EC_KEY_free(EC_KEY *) +{ + +} + +EC_GROUP * +EC_GROUP_new_by_curve_name(int nid) +{ +} + +EC_KEY * +EC_KEY_new_by_curve_name(EC_GROUP_ID nid) +{ + EC_KEY *key; + + key = calloc(1, sizeof(*key)); + return key; +} + +void +EC_POINT_free(EC_POINT *p) +{ + mp_clear_multi(&p->x, p->y, p->z, NULL); + free(p); +} + +static int +ec_point_mul(EC_POINT *res, const EC_GROUP *group, const mp_int *point) +{ +} + +EC_POINT * +EC_POINT_new(void) +{ + EC_POINT *p; + + p = calloc(1, sizeof(*p)); + + if (mp_init_multi(&p->x, &p->y, &p->z, NULL) != 0) { + EC_POINT_free(p); + return NULL; + } + + return p; +} + +int +EC_KEY_generate_key(EC_KEY *key) +{ + int ret = 0; + + if (key->group == NULL) + return 0; + + do { + random(key->privkey, key->group->size); + } while(mp_cmp(key->privkey, key->group->order) >= 0); + + if (key->pubkey == NULL) + key->pubkey = EC_POINT_new(); + + if (ec_point_mul(&key->pubkey, key->group, key->privkey) != 1) + goto error; + + ret = 1; + error: + ECPOINT_free(&base); + + return ret; +} + +void +EC_KEY_set_group(EC_KEY *, EC_GROUP *) +{ + +} + +void +EC_GROUP_free(EC_GROUP *) +{ +} + +int +EC_KEY_check_key(const EC_KEY *) +{ +} + +const BIGNUM * +EC_KEY_get0_private_key(const EC_KEY *key) +{ +} + +int +EC_KEY_set_private_key(EC_KEY *key, const BIGNUM *bn) +{ +} diff --git a/lib/hcrypto/ec.h b/lib/hcrypto/ec.h index 726deec6169f..8fa4d11d623a 100644 --- a/lib/hcrypto/ec.h +++ b/lib/hcrypto/ec.h @@ -1,5 +1,5 @@ /* - * Copyright (c) 2009-2016 Kungliga Tekniska Högskolan + * Copyright (c) 2009-2016 Kungliga Tekniska Högskolan * (Royal Institute of Technology, Stockholm, Sweden). * All rights reserved. * diff --git a/lib/hcrypto/ecdh.h b/lib/hcrypto/ecdh.h index 4dda28499c60..f224afdb15e2 100644 --- a/lib/hcrypto/ecdh.h +++ b/lib/hcrypto/ecdh.h @@ -1,5 +1,5 @@ /* - * Copyright (c) 2009 Kungliga Tekniska Högskolan + * Copyright (c) 2009 Kungliga Tekniska Högskolan * (Royal Institute of Technology, Stockholm, Sweden). * All rights reserved. * diff --git a/lib/hcrypto/ecdsa.h b/lib/hcrypto/ecdsa.h index 84886f4078fe..ffae17bc6cc1 100644 --- a/lib/hcrypto/ecdsa.h +++ b/lib/hcrypto/ecdsa.h @@ -1,5 +1,5 @@ /* - * Copyright (c) 2009 Kungliga Tekniska Högskolan + * Copyright (c) 2009 Kungliga Tekniska Högskolan * (Royal Institute of Technology, Stockholm, Sweden). * All rights reserved. * diff --git a/lib/hcrypto/engine.c b/lib/hcrypto/engine.c index 04ba6b645f66..6a79b7c99079 100644 --- a/lib/hcrypto/engine.c +++ b/lib/hcrypto/engine.c @@ -36,13 +36,6 @@ #include <engine.h> -#ifdef HAVE_DLFCN_H -#include <dlfcn.h> -#ifndef RTLD_NOW -#define RTLD_NOW 0 -#endif -#endif - struct hc_engine { int references; char *name; @@ -51,15 +44,22 @@ struct hc_engine { const RSA_METHOD *rsa; const DH_METHOD *dh; const RAND_METHOD *rand; + void *dso_handle; }; -ENGINE * +ENGINE * ENGINE_new(void) { ENGINE *engine; engine = calloc(1, sizeof(*engine)); + if (engine == NULL) + return NULL; engine->references = 1; + engine->destroy = 0; + engine->dh = 0; + engine->rand = 0; + engine->dso_handle = 0; return engine; } @@ -84,8 +84,10 @@ ENGINE_finish(ENGINE *engine) free(engine->id); if(engine->destroy) (*engine->destroy)(engine); + if (engine->dso_handle) + dlclose(engine->dso_handle); - memset(engine, 0, sizeof(*engine)); + memset_s(engine, sizeof(*engine), 0, sizeof(*engine)); engine->references = -1; @@ -306,15 +308,17 @@ ENGINE_by_dso(const char *path, const char *id) { #ifdef HAVE_DLOPEN ENGINE *engine; - void *handle; int ret; engine = calloc(1, sizeof(*engine)); if (engine == NULL) return NULL; - - handle = dlopen(path, RTLD_NOW); - if (handle == NULL) { + engine->references = 0; /* ref will be added below */ + engine->destroy = 0; + engine->dh = 0; + engine->rand = 0; + engine->dso_handle = dlopen(path, RTLD_NOW | RTLD_LOCAL | RTLD_GROUP); + if (engine->dso_handle == NULL) { /* printf("error: %s\n", dlerror()); */ free(engine); return NULL; @@ -324,16 +328,16 @@ ENGINE_by_dso(const char *path, const char *id) unsigned long version; openssl_v_check v_check; - v_check = (openssl_v_check)dlsym(handle, "v_check"); + v_check = (openssl_v_check)dlsym(engine->dso_handle, "v_check"); if (v_check == NULL) { - dlclose(handle); + dlclose(engine->dso_handle); free(engine); return NULL; } version = (*v_check)(OPENSSL_DYNAMIC_VERSION); if (version == 0) { - dlclose(handle); + dlclose(engine->dso_handle); free(engine); return NULL; } @@ -342,16 +346,17 @@ ENGINE_by_dso(const char *path, const char *id) { openssl_bind_engine bind_engine; - bind_engine = (openssl_bind_engine)dlsym(handle, "bind_engine"); + bind_engine = + (openssl_bind_engine)dlsym(engine->dso_handle, "bind_engine"); if (bind_engine == NULL) { - dlclose(handle); + dlclose(engine->dso_handle); free(engine); return NULL; } ret = (*bind_engine)(engine, id, NULL); /* XXX fix third arg */ if (ret != 1) { - dlclose(handle); + dlclose(engine->dso_handle); free(engine); return NULL; } @@ -361,7 +366,6 @@ ENGINE_by_dso(const char *path, const char *id) ret = add_engine(engine); if (ret != 1) { - dlclose(handle); ENGINE_finish(engine); return NULL; } diff --git a/lib/hcrypto/evp-openssl.c b/lib/hcrypto/evp-openssl.c index ae38e27c0092..f6cf687b98b6 100644 --- a/lib/hcrypto/evp-openssl.c +++ b/lib/hcrypto/evp-openssl.c @@ -80,6 +80,24 @@ #define EVP_MD_CTX_free EVP_MD_CTX_destroy #endif +#if defined(HAVE_OPENSSL_FIPS_H) || defined(HAVE_OPENSSL_FIPS_MODE_SET_API) +int _heim_openssl_fips_enabled(void); +int +_heim_openssl_fips_enabled(void) +{ + static int fips_enabled_res = -1; + + if (fips_enabled_res != -1) + return fips_enabled_res; + +#ifdef HAVE_OPENSSL_30 + return fips_enabled_res = !!EVP_default_properties_is_fips_enabled(NULL); +#else + return fips_enabled_res = !!FIPS_mode(); +#endif +} +#endif + /* A HEIM_BASE_ONCE argument struct for per-EVP one-time initialization */ struct once_init_cipher_ctx { const hc_EVP_CIPHER **hc_memoizep; @@ -158,7 +176,7 @@ cipher_do_cipher(hc_EVP_CIPHER_CTX *ctx, unsigned char *out, struct ossl_cipher_ctx *ossl_ctx = ctx->cipher_data; assert(ossl_ctx != NULL); - return EVP_Cipher(ossl_ctx->ossl_cipher_ctx, out, in, len); + return EVP_Cipher(ossl_ctx->ossl_cipher_ctx, out, in, len) == 0 ? 0 : 1; } static int @@ -204,7 +222,7 @@ get_EVP_CIPHER_once_cb(void *d) */ ossl_evp = EVP_get_cipherbynid(arg->nid); if (ossl_evp == NULL) { - (void) memset(hc_evp, 0, sizeof(*hc_evp)); + (void) memset_s(hc_evp, sizeof(*hc_evp), 0, sizeof(*hc_evp)); #if HCRYPTO_FALLBACK *arg->hc_memoizep = arg->fallback; #endif @@ -348,7 +366,7 @@ get_EVP_MD_once_cb(void *d) *arg->ossl_memoizep = ossl_evp = EVP_get_digestbynid(arg->nid); if (ossl_evp == NULL) { - (void) memset(hc_evp, 0, sizeof(*hc_evp)); + (void) memset_s(hc_evp, sizeof(*hc_evp), 0, sizeof(*hc_evp)); #if HCRYPTO_FALLBACK *arg->hc_memoizep = arg->fallback; #endif @@ -438,7 +456,9 @@ OSSL_CIPHER_ALGORITHM(des_ede3_cbc, hc_EVP_CIPH_CBC_MODE) * * @ingroup hcrypto_evp */ +#ifndef HAVE_OPENSSL_30 OSSL_CIPHER_ALGORITHM(des_cbc, hc_EVP_CIPH_CBC_MODE) +#endif /** * The AES-128 cipher type (OpenSSL provider) @@ -494,6 +514,7 @@ OSSL_CIPHER_ALGORITHM(aes_192_cfb8, hc_EVP_CIPH_CFB8_MODE) */ OSSL_CIPHER_ALGORITHM(aes_256_cfb8, hc_EVP_CIPH_CFB8_MODE) +#ifndef HAVE_OPENSSL_30 /* * RC2 is only needed for tests of PKCS#12 support, which currently uses * the RC2 PBE. So no RC2 -> tests fail. @@ -530,6 +551,7 @@ OSSL_CIPHER_ALGORITHM(rc2_40_cbc, OSSL_CIPHER_ALGORITHM(rc2_64_cbc, hc_EVP_CIPH_CBC_MODE | hc_EVP_CIPH_VARIABLE_LENGTH) +#endif /** * The Camellia-128 cipher type - OpenSSL @@ -558,6 +580,7 @@ OSSL_CIPHER_ALGORITHM(camellia_192_cbc, hc_EVP_CIPH_CBC_MODE) */ OSSL_CIPHER_ALGORITHM(camellia_256_cbc, hc_EVP_CIPH_CBC_MODE) +#ifndef HAVE_OPENSSL_30 /** * The RC4 cipher type (OpenSSL provider) * @@ -588,6 +611,7 @@ OSSL_CIPHER_ALGORITHM(rc4_40, * @ingroup hcrypto_evp */ OSSL_MD_ALGORITHM(md4) +#endif /** * The MD5 hash algorithm (OpenSSL provider) diff --git a/lib/hcrypto/evp-pkcs11.c b/lib/hcrypto/evp-pkcs11.c index 522c036fb926..90e2b91be4b8 100644 --- a/lib/hcrypto/evp-pkcs11.c +++ b/lib/hcrypto/evp-pkcs11.c @@ -33,21 +33,8 @@ #include <config.h> #include <roken.h> #include <assert.h> -#ifdef HAVE_DLFCN_H -#include <dlfcn.h> -#ifndef RTLD_LAZY -#define RTLD_LAZY 0 -#endif -#ifndef RTLD_LOCAL -#define RTLD_LOCAL 0 -#endif -#ifndef RTLD_GROUP -#define RTLD_GROUP 0 -#endif -#ifndef RTLD_NODELETE -#define RTLD_NODELETE 0 -#endif -#else + +#ifndef HAVE_DLFCN_H #error PKCS11 support requires dlfcn.h #endif @@ -100,18 +87,16 @@ p11_module_load(CK_FUNCTION_LIST_PTR_PTR ppFunctionList) { CK_RV rv; CK_RV (*C_GetFunctionList_fn)(CK_FUNCTION_LIST_PTR_PTR); - - *ppFunctionList = NULL; - - if (!issuid()) { - char *pkcs11ModulePath = getenv("PKCS11_MODULE_PATH"); - if (pkcs11ModulePath != NULL) { - pkcs11_module_handle = - dlopen(pkcs11ModulePath, - RTLD_LAZY | RTLD_LOCAL | RTLD_GROUP | RTLD_NODELETE); - if (pkcs11_module_handle == NULL) - fprintf(stderr, "p11_module_load(%s): %s\n", pkcs11ModulePath, dlerror()); - } + char *pkcs11ModulePath = secure_getenv("PKCS11_MODULE_PATH"); + + *ppFunctionList = NULL; + + if (pkcs11ModulePath != NULL) { + pkcs11_module_handle = + dlopen(pkcs11ModulePath, + RTLD_LAZY | RTLD_LOCAL | RTLD_GROUP | RTLD_NODELETE); + if (pkcs11_module_handle == NULL) + fprintf(stderr, "p11_module_load(%s): %s\n", pkcs11ModulePath, dlerror()); } #ifdef PKCS11_MODULE_PATH if (pkcs11_module_handle == NULL) { diff --git a/lib/hcrypto/evp-wincng.c b/lib/hcrypto/evp-wincng.c index bd498d58faa1..34ac3b32459e 100644 --- a/lib/hcrypto/evp-wincng.c +++ b/lib/hcrypto/evp-wincng.c @@ -33,12 +33,17 @@ #include <config.h> #include <roken.h> #include <assert.h> +#include <versionsupport.h> #include <evp.h> #include <evp-wincng.h> #include <bcrypt.h> +#ifndef BCRYPT_HASH_REUSABLE_FLAG +#define BCRYPT_HASH_REUSABLE_FLAG 0x00000020 +#endif + /* * CNG cipher provider */ @@ -96,8 +101,10 @@ wincng_cleanup(EVP_CIPHER_CTX *ctx) { struct wincng_key *cng = ctx->cipher_data; - if (cng->hKey) + if (cng->hKey) { BCryptDestroyKey(cng->hKey); + cng->hKey = (BCRYPT_KEY_HANDLE)0; + } SecureZeroMemory(cng->rgbKeyObject, WINCNG_KEY_OBJECT_SIZE(ctx)); return 1; @@ -196,10 +203,7 @@ wincng_key_init(EVP_CIPHER_CTX *ctx, if (ctx->cipher->app_data == NULL) return 0; - if (cng->hKey) { - BCryptDestroyKey(cng->hKey); /* allow reinitialization */ - cng->hKey = (BCRYPT_KEY_HANDLE)0; - } + wincng_cleanup(ctx); /* * Note: ctx->key_len not EVP_CIPHER_CTX_key_length() for @@ -568,17 +572,23 @@ wincng_md_algorithm_init(EVP_MD *md, } static int +wincng_md_cleanup(EVP_MD_CTX *ctx); + +static int wincng_md_hash_init(BCRYPT_ALG_HANDLE hAlgorithm, EVP_MD_CTX *ctx) { struct wincng_md_ctx *cng = (struct wincng_md_ctx *)ctx; NTSTATUS status; - ULONG cbData; + ULONG cbData, dwFlags = 0; - if (cng->hHash) { - BCryptDestroyHash(cng->hHash); /* allow reinitialization */ - cng->hHash = (BCRYPT_HASH_HANDLE)0; - } + if (IsWindows8OrGreaterCached()) { + if (cng->hHash) + return 1; + else + dwFlags |= BCRYPT_HASH_REUSABLE_FLAG; + } else + wincng_md_cleanup(ctx); status = BCryptGetProperty(hAlgorithm, BCRYPT_OBJECT_LENGTH, @@ -595,7 +605,7 @@ wincng_md_hash_init(BCRYPT_ALG_HANDLE hAlgorithm, cng->cbHashObject, NULL, 0, - 0); + dwFlags); return BCRYPT_SUCCESS(status); } @@ -643,8 +653,10 @@ wincng_md_cleanup(EVP_MD_CTX *ctx) { struct wincng_md_ctx *cng = (struct wincng_md_ctx *)ctx; - if (cng->hHash) + if (cng->hHash) { BCryptDestroyHash(cng->hHash); + cng->hHash = (BCRYPT_HASH_HANDLE)0; + } SecureZeroMemory(cng->rgbHashObject, cng->cbHashObject); return 1; diff --git a/lib/hcrypto/evp.c b/lib/hcrypto/evp.c index 06935449e47b..3874179c0298 100644 --- a/lib/hcrypto/evp.c +++ b/lib/hcrypto/evp.c @@ -59,6 +59,7 @@ # define HCRYPTO_DEF_PROVIDER pkcs11_hcrypto # elif HAVE_HCRYPTO_W_OPENSSL # define HCRYPTO_DEF_PROVIDER ossl +# define HCRYPTO_DEF_PROVIDER_IS_OPENSSL # else # define HCRYPTO_DEF_PROVIDER hcrypto # endif @@ -69,6 +70,11 @@ #define EVP_DEF_OP(_prov,_op) HC_CONCAT4(EVP_,_prov,_,_op)() +#if defined(HAVE_OPENSSL_FIPS_H) || defined(HAVE_OPENSSL_FIPS_MODE_SET_API) +extern int _heim_openssl_fips_enabled(void); +#endif + + /** * @page page_evp EVP - generic crypto interface * @@ -189,12 +195,12 @@ EVP_MD_CTX_cleanup(EVP_MD_CTX *ctx) HC_DEPRECATED if (!ret) return ret; } else if (ctx->md) { - memset(ctx->ptr, 0, ctx->md->ctx_size); + memset_s(ctx->ptr, ctx->md->ctx_size, 0, ctx->md->ctx_size); } ctx->md = NULL; ctx->engine = NULL; free(ctx->ptr); - memset(ctx, 0, sizeof(*ctx)); + memset_s(ctx, sizeof(*ctx), 0, sizeof(*ctx)); return 1; } @@ -463,6 +469,13 @@ const EVP_MD * EVP_md4(void) HC_DEPRECATED_CRYPTO { hcrypto_validate(); +#if defined(HCRYPTO_DEF_PROVIDER_IS_OPENSSL) && defined(HAVE_OPENSSL_30) +#if defined(HAVE_OPENSSL_FIPS_H) || defined(HAVE_OPENSSL_FIPS_MODE_SET_API) + if (_heim_openssl_fips_enabled()) + return NULL; +#endif + return EVP_DEF_OP(hcrypto, md4); +#endif return EVP_DEF_OP(HCRYPTO_DEF_PROVIDER, md4); } @@ -473,17 +486,17 @@ EVP_md4(void) HC_DEPRECATED_CRYPTO static int null_Init (void *m) { - return -1; + return 1; } static int null_Update (void *m, const void * data, size_t size) { - return -1; + return 1; } static int null_Final(void *res, void *m) { - return -1; + return 1; } /** @@ -592,7 +605,7 @@ EVP_CIPHER_CTX_cleanup(EVP_CIPHER_CTX *c) } if (c->cipher_data) { if (c->cipher) - memset(c->cipher_data, 0, c->cipher->ctx_size); + memset_s(c->cipher_data, c->cipher->ctx_size, 0, c->cipher->ctx_size); free(c->cipher_data); c->cipher_data = NULL; } @@ -857,40 +870,37 @@ EVP_CipherUpdate(EVP_CIPHER_CTX *ctx, void *out, int *outlen, *outlen = 0; - /** - * If there in no spare bytes in the left from last Update and the - * input length is on the block boundery, the EVP_CipherUpdate() - * function can take a shortcut (and preformance gain) and - * directly encrypt the data, otherwise we hav to fix it up and - * store extra it the EVP_CIPHER_CTX. + /* + * If there in no bytes left over from the last Update and the + * input length is on a block boundary, then we can take a + * shortcut (and preformance gain) and directly encrypt the + * data. */ - if (ctx->buf_len == 0 && (inlen & ctx->block_mask) == 0) { + if (ctx->buf_len == 0 && inlen && (inlen & ctx->block_mask) == 0) { ret = (*ctx->cipher->do_cipher)(ctx, out, in, inlen); if (ret == 1) *outlen = inlen; - else + else *outlen = 0; return ret; } - blocksize = EVP_CIPHER_CTX_block_size(ctx); left = blocksize - ctx->buf_len; assert(left > 0); if (ctx->buf_len) { - - /* if total buffer is smaller then input, store locally */ + /* If we can't fill one block in the buffer, save the input there */ if (inlen < left) { memcpy(ctx->buf + ctx->buf_len, in, inlen); ctx->buf_len += inlen; return 1; } - /* fill in local buffer and encrypt */ + /* Fill the buffer and encrypt */ memcpy(ctx->buf + ctx->buf_len, in, left); ret = (*ctx->cipher->do_cipher)(ctx, out, ctx->buf, blocksize); - memset(ctx->buf, 0, blocksize); + memset_s(ctx->buf, blocksize, 0, blocksize); if (ret != 1) return ret; @@ -905,12 +915,16 @@ EVP_CipherUpdate(EVP_CIPHER_CTX *ctx, void *out, int *outlen, ctx->buf_len = (inlen & ctx->block_mask); inlen &= ~ctx->block_mask; - ret = (*ctx->cipher->do_cipher)(ctx, out, in, inlen); - if (ret != 1) - return ret; + if (inlen) { + /* Encrypt all the whole blocks of input that we have */ + ret = (*ctx->cipher->do_cipher)(ctx, out, in, inlen); + if (ret != 1) + return ret; + } *outlen += inlen; + /* Save the tail of the input, if any */ in = ((unsigned char *)in) + inlen; memcpy(ctx->buf, in, ctx->buf_len); } @@ -951,7 +965,7 @@ EVP_CipherFinal_ex(EVP_CIPHER_CTX *ctx, void *out, int *outlen) /* zero fill local buffer */ memset(ctx->buf + ctx->buf_len, 0, left); ret = (*ctx->cipher->do_cipher)(ctx, out, ctx->buf, blocksize); - memset(ctx->buf, 0, blocksize); + memset_s(ctx->buf, blocksize, 0, blocksize); if (ret != 1) return ret; @@ -969,7 +983,7 @@ EVP_CipherFinal_ex(EVP_CIPHER_CTX *ctx, void *out, int *outlen) * @param in in data to the operation. * @param size length of data. * - * @return 1 on success. + * @return bytes encrypted on success, zero on failure. */ int @@ -1048,6 +1062,13 @@ const EVP_CIPHER * EVP_rc2_cbc(void) { hcrypto_validate(); +#if defined(HCRYPTO_DEF_PROVIDER_IS_OPENSSL) && defined(HAVE_OPENSSL_30) +#if defined(HAVE_OPENSSL_FIPS_H) || defined(HAVE_OPENSSL_FIPS_MODE_SET_API) + if (_heim_openssl_fips_enabled()) + return NULL; +#endif + return EVP_DEF_OP(hcrypto, rc2_cbc); +#endif return EVP_DEF_OP(HCRYPTO_DEF_PROVIDER, rc2_cbc); } @@ -1063,6 +1084,13 @@ const EVP_CIPHER * EVP_rc2_40_cbc(void) { hcrypto_validate(); +#if defined(HCRYPTO_DEF_PROVIDER_IS_OPENSSL) && defined(HAVE_OPENSSL_30) +#if defined(HAVE_OPENSSL_FIPS_H) || defined(HAVE_OPENSSL_FIPS_MODE_SET_API) + if (_heim_openssl_fips_enabled()) + return NULL; +#endif + return EVP_DEF_OP(hcrypto, rc2_40_cbc); +#endif return EVP_DEF_OP(HCRYPTO_DEF_PROVIDER, rc2_40_cbc); } @@ -1078,6 +1106,13 @@ const EVP_CIPHER * EVP_rc2_64_cbc(void) { hcrypto_validate(); +#if defined(HCRYPTO_DEF_PROVIDER_IS_OPENSSL) && defined(HAVE_OPENSSL_30) +#if defined(HAVE_OPENSSL_FIPS_H) || defined(HAVE_OPENSSL_FIPS_MODE_SET_API) + if (_heim_openssl_fips_enabled()) + return NULL; +#endif + return EVP_DEF_OP(hcrypto, rc2_64_cbc); +#endif return EVP_DEF_OP(HCRYPTO_DEF_PROVIDER, rc2_64_cbc); } @@ -1093,6 +1128,13 @@ const EVP_CIPHER * EVP_rc4(void) { hcrypto_validate(); +#if defined(HCRYPTO_DEF_PROVIDER_IS_OPENSSL) && defined(HAVE_OPENSSL_30) +#if defined(HAVE_OPENSSL_FIPS_H) || defined(HAVE_OPENSSL_FIPS_MODE_SET_API) + if (_heim_openssl_fips_enabled()) + return NULL; +#endif + return EVP_DEF_OP(hcrypto, rc4); +#endif return EVP_DEF_OP(HCRYPTO_DEF_PROVIDER, rc4); } @@ -1108,6 +1150,13 @@ const EVP_CIPHER * EVP_rc4_40(void) { hcrypto_validate(); +#if defined(HCRYPTO_DEF_PROVIDER_IS_OPENSSL) && defined(HAVE_OPENSSL_30) +#if defined(HAVE_OPENSSL_FIPS_H) || defined(HAVE_OPENSSL_FIPS_MODE_SET_API) + if (_heim_openssl_fips_enabled()) + return NULL; +#endif + return EVP_DEF_OP(hcrypto, rc4_40); +#endif return EVP_DEF_OP(HCRYPTO_DEF_PROVIDER, rc4_40); } @@ -1123,6 +1172,13 @@ const EVP_CIPHER * EVP_des_cbc(void) { hcrypto_validate(); +#if defined(HCRYPTO_DEF_PROVIDER_IS_OPENSSL) && defined(HAVE_OPENSSL_30) +#if defined(HAVE_OPENSSL_FIPS_H) || defined(HAVE_OPENSSL_FIPS_MODE_SET_API) + if (_heim_openssl_fips_enabled()) + return NULL; +#endif + return EVP_DEF_OP(hcrypto, des_cbc); +#endif return EVP_DEF_OP(HCRYPTO_DEF_PROVIDER, des_cbc); } diff --git a/lib/hcrypto/evp.h b/lib/hcrypto/evp.h index 820c500f4275..7019abafd6d8 100644 --- a/lib/hcrypto/evp.h +++ b/lib/hcrypto/evp.h @@ -193,7 +193,7 @@ struct hc_CIPHER_CTX { unsigned long flags; void *cipher_data; int final_used; - int block_mask; + unsigned block_mask; unsigned char final[EVP_MAX_BLOCK_LENGTH]; }; diff --git a/lib/hcrypto/hmac.c b/lib/hcrypto/hmac.c index 29e6af479d6b..b646d5612217 100644 --- a/lib/hcrypto/hmac.c +++ b/lib/hcrypto/hmac.c @@ -46,17 +46,17 @@ void HMAC_CTX_cleanup(HMAC_CTX *ctx) { if (ctx->buf) { - memset(ctx->buf, 0, ctx->key_length); + memset_s(ctx->buf, ctx->key_length, 0, ctx->key_length); free(ctx->buf); ctx->buf = NULL; } if (ctx->opad) { - memset(ctx->opad, 0, EVP_MD_block_size(ctx->md)); + memset_s(ctx->opad, EVP_MD_block_size(ctx->md), 0, EVP_MD_block_size(ctx->md)); free(ctx->opad); ctx->opad = NULL; } if (ctx->ipad) { - memset(ctx->ipad, 0, EVP_MD_block_size(ctx->md)); + memset_s(ctx->ipad, EVP_MD_block_size(ctx->md), 0, EVP_MD_block_size(ctx->md)); free(ctx->ipad); ctx->ipad = NULL; } @@ -66,13 +66,26 @@ HMAC_CTX_cleanup(HMAC_CTX *ctx) } } +HMAC_CTX * +HMAC_CTX_new(void) +{ + return calloc(1, sizeof(HMAC_CTX)); +} + +void +HMAC_CTX_free(HMAC_CTX *ctx) +{ + HMAC_CTX_cleanup(ctx); + free(ctx); +} + size_t HMAC_size(const HMAC_CTX *ctx) { return EVP_MD_size(ctx->md); } -void +int HMAC_Init_ex(HMAC_CTX *ctx, const void *key, size_t keylen, @@ -80,51 +93,53 @@ HMAC_Init_ex(HMAC_CTX *ctx, ENGINE *engine) { unsigned char *p; - size_t i; + size_t i, blockSize; + + blockSize = EVP_MD_block_size(md); if (ctx->md != md) { + if (ctx->md != NULL) + HMAC_CTX_cleanup(ctx); + ctx->md = md; - if (ctx->buf) { - memset(ctx->buf, 0, ctx->key_length); - free (ctx->buf); - } ctx->key_length = EVP_MD_size(ctx->md); + ctx->opad = NULL; + ctx->ipad = NULL; + ctx->ctx = NULL; ctx->buf = malloc(ctx->key_length); + if (ctx->buf) + ctx->opad = malloc(blockSize); + if (ctx->opad) + ctx->ipad = malloc(blockSize); + if (ctx->ipad) + ctx->ctx = EVP_MD_CTX_create(); } + /* We do this check here to quiet scan-build */ + if (!ctx->buf || !ctx->opad || !ctx->ipad || !ctx->ctx) + return 0; #if 0 ctx->engine = engine; #endif - if (keylen > EVP_MD_block_size(ctx->md)) { - EVP_Digest(key, keylen, ctx->buf, NULL, ctx->md, engine); + if (keylen > blockSize) { + if (EVP_Digest(key, keylen, ctx->buf, NULL, ctx->md, engine) == 0) + return 0; key = ctx->buf; keylen = EVP_MD_size(ctx->md); } - if (ctx->opad) { - memset(ctx->opad, 0, ctx->key_length); - free(ctx->opad); - } - if (ctx->ipad) { - memset(ctx->ipad, 0, ctx->key_length); - free(ctx->ipad); - } - - ctx->opad = malloc(EVP_MD_block_size(ctx->md)); - ctx->ipad = malloc(EVP_MD_block_size(ctx->md)); - memset(ctx->ipad, 0x36, EVP_MD_block_size(ctx->md)); - memset(ctx->opad, 0x5c, EVP_MD_block_size(ctx->md)); + memset(ctx->ipad, 0x36, blockSize); + memset(ctx->opad, 0x5c, blockSize); for (i = 0, p = ctx->ipad; i < keylen; i++) p[i] ^= ((const unsigned char *)key)[i]; for (i = 0, p = ctx->opad; i < keylen; i++) p[i] ^= ((const unsigned char *)key)[i]; - if (ctx->ctx == NULL) - ctx->ctx = EVP_MD_CTX_create(); - - EVP_DigestInit_ex(ctx->ctx, ctx->md, ctx->engine); + if (EVP_DigestInit_ex(ctx->ctx, ctx->md, ctx->engine) == 0) + return 0; EVP_DigestUpdate(ctx->ctx, ctx->ipad, EVP_MD_block_size(ctx->md)); + return 1; } void @@ -153,7 +168,10 @@ HMAC(const EVP_MD *md, HMAC_CTX ctx; HMAC_CTX_init(&ctx); - HMAC_Init_ex(&ctx, key, key_size, md, NULL); + if (HMAC_Init_ex(&ctx, key, key_size, md, NULL) == 0) { + HMAC_CTX_cleanup(&ctx); + return NULL; + } HMAC_Update(&ctx, data, data_size); HMAC_Final(&ctx, hash, hash_len); HMAC_CTX_cleanup(&ctx); diff --git a/lib/hcrypto/hmac.h b/lib/hcrypto/hmac.h index 3ea17a93f020..cc99c879fb91 100644 --- a/lib/hcrypto/hmac.h +++ b/lib/hcrypto/hmac.h @@ -39,6 +39,8 @@ #include <hcrypto/evp.h> /* symbol renaming */ +#define HMAC_CTX_new hc_HMAC_CTX_new +#define HMAC_CTX_free hc_HMAC_CTX_free #define HMAC_CTX_init hc_HMAC_CTX_init #define HMAC_CTX_cleanup hc_HMAC_CTX_cleanup #define HMAC_size hc_HMAC_size @@ -68,10 +70,12 @@ struct hc_HMAC_CTX { void HMAC_CTX_init(HMAC_CTX *); void HMAC_CTX_cleanup(HMAC_CTX *ctx); +HMAC_CTX *HMAC_CTX_new(void); +void HMAC_CTX_free(HMAC_CTX *ctx); size_t HMAC_size(const HMAC_CTX *ctx); -void HMAC_Init_ex(HMAC_CTX *, const void *, size_t, +int HMAC_Init_ex(HMAC_CTX *, const void *, size_t, const EVP_MD *, ENGINE *); void HMAC_Update(HMAC_CTX *ctx, const void *data, size_t len); void HMAC_Final(HMAC_CTX *ctx, void *md, unsigned int *len); diff --git a/lib/hcrypto/libhcrypto-exports.def b/lib/hcrypto/libhcrypto-exports.def index 6a620148349b..b1e2d34b1165 100644 --- a/lib/hcrypto/libhcrypto-exports.def +++ b/lib/hcrypto/libhcrypto-exports.def @@ -253,6 +253,8 @@ EXPORTS hc_HMAC hc_HMAC_CTX_cleanup hc_HMAC_CTX_init + hc_HMAC_CTX_free + hc_HMAC_CTX_new hc_HMAC_Final hc_HMAC_Init_ex hc_HMAC_Update @@ -339,4 +341,5 @@ EXPORTS hc_EVP_CipherFinal_ex hc_hcrypto_validate - + hc_hcrypto_scalarmult_curve25519 + hc_hcrypto_scalarmult_curve25519_base diff --git a/lib/hcrypto/libtommath/LICENSE b/lib/hcrypto/libtommath/LICENSE new file mode 100644 index 000000000000..b23b3c8672b1 --- /dev/null +++ b/lib/hcrypto/libtommath/LICENSE @@ -0,0 +1,26 @@ + The LibTom license + +This is free and unencumbered software released into the public domain. + +Anyone is free to copy, modify, publish, use, compile, sell, or +distribute this software, either in source code form or as a compiled +binary, for any purpose, commercial or non-commercial, and by any +means. + +In jurisdictions that recognize copyright laws, the author or authors +of this software dedicate any and all copyright interest in the +software to the public domain. We make this dedication for the benefit +of the public at large and to the detriment of our heirs and +successors. We intend this dedication to be an overt act of +relinquishment in perpetuity of all present and future rights to this +software under copyright law. + +THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, +EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF +MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. +IN NO EVENT SHALL THE AUTHORS BE LIABLE FOR ANY CLAIM, DAMAGES OR +OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, +ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR +OTHER DEALINGS IN THE SOFTWARE. + +For more information, please refer to <http://unlicense.org/> diff --git a/lib/hcrypto/libtommath/NTMakefile b/lib/hcrypto/libtommath/NTMakefile new file mode 100644 index 000000000000..082054ac6e28 --- /dev/null +++ b/lib/hcrypto/libtommath/NTMakefile @@ -0,0 +1,203 @@ +######################################################################## +# +# Copyright (c) 2009, Secure Endpoints Inc. +# All rights reserved. +# +# Redistribution and use in source and binary forms, with or without +# modification, are permitted provided that the following conditions +# are met: +# +# - Redistributions of source code must retain the above copyright +# notice, this list of conditions and the following disclaimer. +# +# - Redistributions in binary form must reproduce the above copyright +# notice, this list of conditions and the following disclaimer in +# the documentation and/or other materials provided with the +# distribution. +# +# THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS +# "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT +# LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS +# FOR A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE +# COPYRIGHT HOLDER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, +# INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, +# BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; +# LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER +# CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT +# LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN +# ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE +# POSSIBILITY OF SUCH DAMAGE. +# + +RELDIR=lib\hcrypto\libtommath + +!include ../../../windows/NTMakefile.w32 + +INCFILES= \ + $(INCDIR)\tommath.h \ + $(INCDIR)\tommath_class.h \ + $(INCDIR)\tommath_superclass.h + +libltm_OBJs= \ + $(OBJ)\bn_cutoffs.obj \ + $(OBJ)\bn_deprecated.obj \ + $(OBJ)\bn_mp_2expt.obj \ + $(OBJ)\bn_mp_abs.obj \ + $(OBJ)\bn_mp_add.obj \ + $(OBJ)\bn_mp_add_d.obj \ + $(OBJ)\bn_mp_addmod.obj \ + $(OBJ)\bn_mp_and.obj \ + $(OBJ)\bn_mp_clamp.obj \ + 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$(OBJ)\bn_mp_sbin_size.obj \ + $(OBJ)\bn_mp_set.obj \ + $(OBJ)\bn_mp_set_double.obj \ + $(OBJ)\bn_mp_set_i32.obj \ + $(OBJ)\bn_mp_set_i64.obj \ + $(OBJ)\bn_mp_set_l.obj \ + $(OBJ)\bn_mp_set_ll.obj \ + $(OBJ)\bn_mp_set_u32.obj \ + $(OBJ)\bn_mp_set_u64.obj \ + $(OBJ)\bn_mp_set_ul.obj \ + $(OBJ)\bn_mp_set_ull.obj \ + $(OBJ)\bn_mp_shrink.obj \ + $(OBJ)\bn_mp_signed_rsh.obj \ + $(OBJ)\bn_mp_sqr.obj \ + $(OBJ)\bn_mp_sqrmod.obj \ + $(OBJ)\bn_mp_sqrt.obj \ + $(OBJ)\bn_mp_sqrtmod_prime.obj \ + $(OBJ)\bn_mp_sub.obj \ + $(OBJ)\bn_mp_sub_d.obj \ + $(OBJ)\bn_mp_submod.obj \ + $(OBJ)\bn_mp_to_radix.obj \ + $(OBJ)\bn_mp_to_sbin.obj \ + $(OBJ)\bn_mp_to_ubin.obj \ + $(OBJ)\bn_mp_ubin_size.obj \ + $(OBJ)\bn_mp_unpack.obj \ + $(OBJ)\bn_mp_xor.obj \ + $(OBJ)\bn_mp_zero.obj \ + $(OBJ)\bn_prime_tab.obj \ + $(OBJ)\bn_s_mp_add.obj \ + $(OBJ)\bn_s_mp_balance_mul.obj \ + $(OBJ)\bn_s_mp_exptmod.obj \ + $(OBJ)\bn_s_mp_exptmod_fast.obj \ + $(OBJ)\bn_s_mp_get_bit.obj \ + $(OBJ)\bn_s_mp_invmod_fast.obj \ + $(OBJ)\bn_s_mp_invmod_slow.obj \ + $(OBJ)\bn_s_mp_karatsuba_mul.obj\ + $(OBJ)\bn_s_mp_karatsuba_sqr.obj\ + $(OBJ)\bn_s_mp_montgomery_reduce_fast.obj \ + $(OBJ)\bn_s_mp_mul_digs.obj \ + $(OBJ)\bn_s_mp_mul_digs_fast.obj\ + $(OBJ)\bn_s_mp_mul_high_digs.obj\ + $(OBJ)\bn_s_mp_mul_high_digs_fast.obj \ + $(OBJ)\bn_s_mp_prime_is_divisible.obj \ + $(OBJ)\bn_s_mp_rand_jenkins.obj \ + $(OBJ)\bn_s_mp_rand_platform.obj\ + $(OBJ)\bn_s_mp_reverse.obj \ + $(OBJ)\bn_s_mp_sqr.obj \ + $(OBJ)\bn_s_mp_sqr_fast.obj \ + $(OBJ)\bn_s_mp_sub.obj \ + $(OBJ)\bn_s_mp_toom_mul.obj \ + $(OBJ)\bn_s_mp_toom_sqr.obj + +$(LIBLTM): $(libltm_OBJs) + $(LIBCON) + +all:: $(INCFILES) $(LIBLTM) diff --git a/lib/hcrypto/libtommath/README.md b/lib/hcrypto/libtommath/README.md new file mode 100644 index 000000000000..be5b20783e28 --- /dev/null +++ b/lib/hcrypto/libtommath/README.md @@ -0,0 +1,44 @@ +# libtommath + +This is the git repository for [LibTomMath](http://www.libtom.net/LibTomMath/), a free open source portable number theoretic multiple-precision integer (MPI) library written entirely in C. + +## Build Status + +### Travis CI + +master: [](https://travis-ci.org/libtom/libtommath) + +develop: [](https://travis-ci.org/libtom/libtommath) + +### AppVeyor + +master: [](https://ci.appveyor.com/project/libtom/libtommath/branch/master) + +develop: [](https://ci.appveyor.com/project/libtom/libtommath/branch/develop) + +### ABI Laboratory + +API/ABI changes: [check here](https://abi-laboratory.pro/tracker/timeline/libtommath/) + +## Summary + +The `develop` branch contains the in-development version. Stable releases are tagged. + +Documentation is built from the LaTeX file `bn.tex`. There is also limited documentation in `tommath.h`. +There is also a document, `tommath.pdf`, which describes the goals of the project and many of the algorithms used. + +The project can be build by using `make`. Along with the usual `make`, `make clean` and `make install`, +there are several other build targets, see the makefile for details. +There are also makefiles for certain specific platforms. + +## Testing + +Tests are located in `demo/` and can be built in two flavors. +* `make test` creates a stand-alone test binary that executes several test routines. +* `make mtest_opponent` creates a test binary that is intended to be run against `mtest`. + `mtest` can be built with `make mtest` and test execution is done like `./mtest/mtest | ./mtest_opponent`. + `mtest` is creating test vectors using an alternative MPI library and `test` is consuming these vectors to verify correct behavior of ltm + +## Building and Installing + +Building is straightforward for GNU Linux only, the section "Building LibTomMath" in the documentation in `doc/bn.pdf` has the details. diff --git a/lib/hcrypto/libtommath/appveyor.yml b/lib/hcrypto/libtommath/appveyor.yml new file mode 100644 index 000000000000..efe45688c075 --- /dev/null +++ b/lib/hcrypto/libtommath/appveyor.yml @@ -0,0 +1,20 @@ +version: 1.2.0-{build}
+branches:
+ only:
+ - master
+ - develop
+ - /^release/
+ - /^travis/
+image:
+- Visual Studio 2019
+- Visual Studio 2017
+- Visual Studio 2015
+build_script:
+- cmd: >-
+ if "Visual Studio 2019"=="%APPVEYOR_BUILD_WORKER_IMAGE%" call "C:\Program Files (x86)\Microsoft Visual Studio\2019\Community\VC\Auxiliary\Build\vcvars64.bat"
+ if "Visual Studio 2017"=="%APPVEYOR_BUILD_WORKER_IMAGE%" call "C:\Program Files (x86)\Microsoft Visual Studio\2017\Community\VC\Auxiliary\Build\vcvars64.bat"
+ if "Visual Studio 2015"=="%APPVEYOR_BUILD_WORKER_IMAGE%" call "C:\Program Files\Microsoft SDKs\Windows\v7.1\Bin\SetEnv.cmd" /x64
+ if "Visual Studio 2015"=="%APPVEYOR_BUILD_WORKER_IMAGE%" call "C:\Program Files (x86)\Microsoft Visual Studio 14.0\VC\vcvarsall.bat" x86_amd64
+ nmake -f makefile.msvc all
+test_script:
+- cmd: test.exe
diff --git a/lib/hcrypto/libtommath/astylerc b/lib/hcrypto/libtommath/astylerc new file mode 100644 index 000000000000..c5ff779403cd --- /dev/null +++ b/lib/hcrypto/libtommath/astylerc @@ -0,0 +1,30 @@ +# Artistic Style, see http://astyle.sourceforge.net/ +# full documentation, see: http://astyle.sourceforge.net/astyle.html +# +# usage: +# astyle --options=astylerc *.[ch] + +# Do not create backup, annonying in the times of git +suffix=none + +## Bracket Style Options +style=kr + +## Tab Options +indent=spaces=3 + +## Bracket Modify Options + +## Indentation Options +min-conditional-indent=0 + +## Padding Options +pad-header +unpad-paren +align-pointer=name + +## Formatting Options +break-after-logical +max-code-length=120 +convert-tabs +mode=c diff --git a/lib/hcrypto/libtommath/bn_cutoffs.c b/lib/hcrypto/libtommath/bn_cutoffs.c new file mode 100644 index 000000000000..b02ab716116c --- /dev/null +++ b/lib/hcrypto/libtommath/bn_cutoffs.c @@ -0,0 +1,14 @@ +#include "tommath_private.h" +#ifdef BN_CUTOFFS_C +/* LibTomMath, multiple-precision integer library -- Tom St Denis */ +/* SPDX-License-Identifier: Unlicense */ + +#ifndef MP_FIXED_CUTOFFS +#include "tommath_cutoffs.h" +int KARATSUBA_MUL_CUTOFF = MP_DEFAULT_KARATSUBA_MUL_CUTOFF, + KARATSUBA_SQR_CUTOFF = MP_DEFAULT_KARATSUBA_SQR_CUTOFF, + TOOM_MUL_CUTOFF = MP_DEFAULT_TOOM_MUL_CUTOFF, + TOOM_SQR_CUTOFF = MP_DEFAULT_TOOM_SQR_CUTOFF; +#endif + +#endif diff --git a/lib/hcrypto/libtommath/bn_deprecated.c b/lib/hcrypto/libtommath/bn_deprecated.c new file mode 100644 index 000000000000..2056b20e68ef --- /dev/null +++ b/lib/hcrypto/libtommath/bn_deprecated.c @@ -0,0 +1,321 @@ +#include "tommath_private.h" +#ifdef BN_DEPRECATED_C +/* LibTomMath, multiple-precision integer library -- Tom St Denis */ +/* SPDX-License-Identifier: Unlicense */ + +#ifdef BN_MP_GET_BIT_C +int mp_get_bit(const mp_int *a, int b) +{ + if (b < 0) { + return MP_VAL; + } + return (s_mp_get_bit(a, (unsigned int)b) == MP_YES) ? MP_YES : MP_NO; +} +#endif +#ifdef BN_MP_JACOBI_C +mp_err mp_jacobi(const mp_int *a, const mp_int *n, int *c) +{ + if (a->sign == MP_NEG) { + return MP_VAL; + } + if (mp_cmp_d(n, 0uL) != MP_GT) { + return MP_VAL; + } + return mp_kronecker(a, n, c); +} +#endif +#ifdef BN_MP_PRIME_RANDOM_EX_C +mp_err mp_prime_random_ex(mp_int *a, int t, int size, int flags, private_mp_prime_callback cb, void *dat) +{ + return s_mp_prime_random_ex(a, t, size, flags, cb, dat); +} +#endif +#ifdef BN_MP_RAND_DIGIT_C +mp_err mp_rand_digit(mp_digit *r) +{ + mp_err err = s_mp_rand_source(r, sizeof(mp_digit)); + *r &= MP_MASK; + return err; +} +#endif +#ifdef BN_FAST_MP_INVMOD_C +mp_err fast_mp_invmod(const mp_int *a, const mp_int *b, mp_int *c) +{ + return s_mp_invmod_fast(a, b, c); +} +#endif +#ifdef BN_FAST_MP_MONTGOMERY_REDUCE_C +mp_err fast_mp_montgomery_reduce(mp_int *x, const mp_int *n, mp_digit rho) +{ + return s_mp_montgomery_reduce_fast(x, n, rho); +} +#endif +#ifdef BN_FAST_S_MP_MUL_DIGS_C +mp_err fast_s_mp_mul_digs(const mp_int *a, const mp_int *b, mp_int *c, int digs) +{ + return s_mp_mul_digs_fast(a, b, c, digs); +} +#endif +#ifdef BN_FAST_S_MP_MUL_HIGH_DIGS_C +mp_err fast_s_mp_mul_high_digs(const mp_int *a, const mp_int *b, mp_int *c, int digs) +{ + return s_mp_mul_high_digs_fast(a, b, c, digs); +} +#endif +#ifdef BN_FAST_S_MP_SQR_C +mp_err fast_s_mp_sqr(const mp_int *a, mp_int *b) +{ + return s_mp_sqr_fast(a, b); +} +#endif +#ifdef BN_MP_BALANCE_MUL_C +mp_err mp_balance_mul(const mp_int *a, const mp_int *b, mp_int *c) +{ + return s_mp_balance_mul(a, b, c); +} +#endif +#ifdef BN_MP_EXPTMOD_FAST_C +mp_err mp_exptmod_fast(const mp_int *G, const mp_int *X, const mp_int *P, mp_int *Y, int redmode) +{ + return s_mp_exptmod_fast(G, X, P, Y, redmode); +} +#endif +#ifdef BN_MP_INVMOD_SLOW_C +mp_err mp_invmod_slow(const mp_int *a, const mp_int *b, mp_int *c) +{ + return s_mp_invmod_slow(a, b, c); +} +#endif +#ifdef BN_MP_KARATSUBA_MUL_C +mp_err mp_karatsuba_mul(const mp_int *a, const mp_int *b, mp_int *c) +{ + return s_mp_karatsuba_mul(a, b, c); +} +#endif +#ifdef BN_MP_KARATSUBA_SQR_C +mp_err mp_karatsuba_sqr(const mp_int *a, mp_int *b) +{ + return s_mp_karatsuba_sqr(a, b); +} +#endif +#ifdef BN_MP_TOOM_MUL_C +mp_err mp_toom_mul(const mp_int *a, const mp_int *b, mp_int *c) +{ + return s_mp_toom_mul(a, b, c); +} +#endif +#ifdef BN_MP_TOOM_SQR_C +mp_err mp_toom_sqr(const mp_int *a, mp_int *b) +{ + return s_mp_toom_sqr(a, b); +} +#endif +#ifdef S_MP_REVERSE_C +void bn_reverse(unsigned char *s, int len) +{ + if (len > 0) { + s_mp_reverse(s, (size_t)len); + } +} +#endif +#ifdef BN_MP_TC_AND_C +mp_err mp_tc_and(const mp_int *a, const mp_int *b, mp_int *c) +{ + return mp_and(a, b, c); +} +#endif +#ifdef BN_MP_TC_OR_C +mp_err mp_tc_or(const mp_int *a, const mp_int *b, mp_int *c) +{ + return mp_or(a, b, c); +} +#endif +#ifdef BN_MP_TC_XOR_C +mp_err mp_tc_xor(const mp_int *a, const mp_int *b, mp_int *c) +{ + return mp_xor(a, b, c); +} +#endif +#ifdef BN_MP_TC_DIV_2D_C +mp_err mp_tc_div_2d(const mp_int *a, int b, mp_int *c) +{ + return mp_signed_rsh(a, b, c); +} +#endif +#ifdef BN_MP_INIT_SET_INT_C +mp_err mp_init_set_int(mp_int *a, unsigned long b) +{ + return mp_init_u32(a, (uint32_t)b); +} +#endif +#ifdef BN_MP_SET_INT_C +mp_err mp_set_int(mp_int *a, unsigned long b) +{ + mp_set_u32(a, (uint32_t)b); + return MP_OKAY; +} +#endif +#ifdef BN_MP_SET_LONG_C +mp_err mp_set_long(mp_int *a, unsigned long b) +{ + mp_set_u64(a, b); + return MP_OKAY; +} +#endif +#ifdef BN_MP_SET_LONG_LONG_C +mp_err mp_set_long_long(mp_int *a, unsigned long long b) +{ + mp_set_u64(a, b); + return MP_OKAY; +} +#endif +#ifdef BN_MP_GET_INT_C +unsigned long mp_get_int(const mp_int *a) +{ + return (unsigned long)mp_get_mag_u32(a); +} +#endif +#ifdef BN_MP_GET_LONG_C +unsigned long mp_get_long(const mp_int *a) +{ + return (unsigned long)mp_get_mag_ul(a); +} +#endif +#ifdef BN_MP_GET_LONG_LONG_C +unsigned long long mp_get_long_long(const mp_int *a) +{ + return mp_get_mag_ull(a); +} +#endif +#ifdef BN_MP_PRIME_IS_DIVISIBLE_C +mp_err mp_prime_is_divisible(const mp_int *a, mp_bool *result) +{ + return s_mp_prime_is_divisible(a, result); +} +#endif +#ifdef BN_MP_EXPT_D_EX_C +mp_err mp_expt_d_ex(const mp_int *a, mp_digit b, mp_int *c, int fast) +{ + (void)fast; + if (b > MP_MIN(MP_DIGIT_MAX, UINT32_MAX)) { + return MP_VAL; + } + return mp_expt_u32(a, (uint32_t)b, c); +} +#endif +#ifdef BN_MP_EXPT_D_C +mp_err mp_expt_d(const mp_int *a, mp_digit b, mp_int *c) +{ + if (b > MP_MIN(MP_DIGIT_MAX, UINT32_MAX)) { + return MP_VAL; + } + return mp_expt_u32(a, (uint32_t)b, c); +} +#endif +#ifdef BN_MP_N_ROOT_EX_C +mp_err mp_n_root_ex(const mp_int *a, mp_digit b, mp_int *c, int fast) +{ + (void)fast; + if (b > MP_MIN(MP_DIGIT_MAX, UINT32_MAX)) { + return MP_VAL; + } + return mp_root_u32(a, (uint32_t)b, c); +} +#endif +#ifdef BN_MP_N_ROOT_C +mp_err mp_n_root(const mp_int *a, mp_digit b, mp_int *c) +{ + if (b > MP_MIN(MP_DIGIT_MAX, UINT32_MAX)) { + return MP_VAL; + } + return mp_root_u32(a, (uint32_t)b, c); +} +#endif +#ifdef BN_MP_UNSIGNED_BIN_SIZE_C +int mp_unsigned_bin_size(const mp_int *a) +{ + return (int)mp_ubin_size(a); +} +#endif +#ifdef BN_MP_READ_UNSIGNED_BIN_C +mp_err mp_read_unsigned_bin(mp_int *a, const unsigned char *b, int c) +{ + return mp_from_ubin(a, b, (size_t) c); +} +#endif +#ifdef BN_MP_TO_UNSIGNED_BIN_C +mp_err mp_to_unsigned_bin(const mp_int *a, unsigned char *b) +{ + return mp_to_ubin(a, b, SIZE_MAX, NULL); +} +#endif +#ifdef BN_MP_TO_UNSIGNED_BIN_N_C +mp_err mp_to_unsigned_bin_n(const mp_int *a, unsigned char *b, unsigned long *outlen) +{ + size_t n = mp_ubin_size(a); + if (*outlen < (unsigned long)n) { + return MP_VAL; + } + *outlen = (unsigned long)n; + return mp_to_ubin(a, b, n, NULL); +} +#endif +#ifdef BN_MP_SIGNED_BIN_SIZE_C +int mp_signed_bin_size(const mp_int *a) +{ + return (int)mp_sbin_size(a); +} +#endif +#ifdef BN_MP_READ_SIGNED_BIN_C +mp_err mp_read_signed_bin(mp_int *a, const unsigned char *b, int c) +{ + return mp_from_sbin(a, b, (size_t) c); +} +#endif +#ifdef BN_MP_TO_SIGNED_BIN_C +mp_err mp_to_signed_bin(const mp_int *a, unsigned char *b) +{ + return mp_to_sbin(a, b, SIZE_MAX, NULL); +} +#endif +#ifdef BN_MP_TO_SIGNED_BIN_N_C +mp_err mp_to_signed_bin_n(const mp_int *a, unsigned char *b, unsigned long *outlen) +{ + size_t n = mp_sbin_size(a); + if (*outlen < (unsigned long)n) { + return MP_VAL; + } + *outlen = (unsigned long)n; + return mp_to_sbin(a, b, n, NULL); +} +#endif +#ifdef BN_MP_TORADIX_N_C +mp_err mp_toradix_n(const mp_int *a, char *str, int radix, int maxlen) +{ + if (maxlen < 0) { + return MP_VAL; + } + return mp_to_radix(a, str, (size_t)maxlen, NULL, radix); +} +#endif +#ifdef BN_MP_TORADIX_C +mp_err mp_toradix(const mp_int *a, char *str, int radix) +{ + return mp_to_radix(a, str, SIZE_MAX, NULL, radix); +} +#endif +#ifdef BN_MP_IMPORT_C +mp_err mp_import(mp_int *rop, size_t count, int order, size_t size, int endian, size_t nails, + const void *op) +{ + return mp_unpack(rop, count, order, size, endian, nails, op); +} +#endif +#ifdef BN_MP_EXPORT_C +mp_err mp_export(void *rop, size_t *countp, int order, size_t size, + int endian, size_t nails, const mp_int *op) +{ + return mp_pack(rop, SIZE_MAX, countp, order, size, endian, nails, op); +} +#endif +#endif diff --git a/lib/hcrypto/libtommath/bn_error.c b/lib/hcrypto/libtommath/bn_error.c deleted file mode 100644 index fbba7aa1fb14..000000000000 --- a/lib/hcrypto/libtommath/bn_error.c +++ /dev/null @@ -1,47 +0,0 @@ -#include <tommath.h> -#ifdef BN_ERROR_C -/* LibTomMath, multiple-precision integer library -- Tom St Denis - * - * LibTomMath is a library that provides multiple-precision - * integer arithmetic as well as number theoretic functionality. - * - * The library was designed directly after the MPI library by - * Michael Fromberger but has been written from scratch with - * additional optimizations in place. - * - * The library is free for all purposes without any express - * guarantee it works. - * - * Tom St Denis, tomstdenis@gmail.com, http://libtom.org - */ - -static const struct { - int code; - const char *msg; -} msgs[] = { - { MP_OKAY, "Successful" }, - { MP_MEM, "Out of heap" }, - { MP_VAL, "Value out of range" } -}; - -/* return a char * string for a given code */ -const char *mp_error_to_string(int code) -{ - int x; - - /* scan the lookup table for the given message */ - for (x = 0; x < (int)(sizeof(msgs) / sizeof(msgs[0])); x++) { - if (msgs[x].code == code) { - return msgs[x].msg; - } - } - - /* generic reply for invalid code */ - return "Invalid error code"; -} - -#endif - -/* $Source: /cvs/libtom/libtommath/bn_error.c,v $ */ -/* $Revision: 1.4 $ */ -/* $Date: 2006/12/28 01:25:13 $ */ diff --git a/lib/hcrypto/libtommath/bn_fast_mp_invmod.c b/lib/hcrypto/libtommath/bn_fast_mp_invmod.c deleted file mode 100644 index f4780d8e8ccd..000000000000 --- a/lib/hcrypto/libtommath/bn_fast_mp_invmod.c +++ /dev/null @@ -1,148 +0,0 @@ -#include <tommath.h> -#ifdef BN_FAST_MP_INVMOD_C -/* LibTomMath, multiple-precision integer library -- Tom St Denis - * - * LibTomMath is a library that provides multiple-precision - * integer arithmetic as well as number theoretic functionality. - * - * The library was designed directly after the MPI library by - * Michael Fromberger but has been written from scratch with - * additional optimizations in place. - * - * The library is free for all purposes without any express - * guarantee it works. - * - * Tom St Denis, tomstdenis@gmail.com, http://libtom.org - */ - -/* computes the modular inverse via binary extended euclidean algorithm, - * that is c = 1/a mod b - * - * Based on slow invmod except this is optimized for the case where b is - * odd as per HAC Note 14.64 on pp. 610 - */ -int fast_mp_invmod (mp_int * a, mp_int * b, mp_int * c) -{ - mp_int x, y, u, v, B, D; - int res, neg; - - /* 2. [modified] b must be odd */ - if (mp_iseven (b) == 1) { - return MP_VAL; - } - - /* init all our temps */ - if ((res = mp_init_multi(&x, &y, &u, &v, &B, &D, NULL)) != MP_OKAY) { - return res; - } - - /* x == modulus, y == value to invert */ - if ((res = mp_copy (b, &x)) != MP_OKAY) { - goto LBL_ERR; - } - - /* we need y = |a| */ - if ((res = mp_mod (a, b, &y)) != MP_OKAY) { - goto LBL_ERR; - } - - /* 3. u=x, v=y, A=1, B=0, C=0,D=1 */ - if ((res = mp_copy (&x, &u)) != MP_OKAY) { - goto LBL_ERR; - } - if ((res = mp_copy (&y, &v)) != MP_OKAY) { - goto LBL_ERR; - } - mp_set (&D, 1); - -top: - /* 4. while u is even do */ - while (mp_iseven (&u) == 1) { - /* 4.1 u = u/2 */ - if ((res = mp_div_2 (&u, &u)) != MP_OKAY) { - goto LBL_ERR; - } - /* 4.2 if B is odd then */ - if (mp_isodd (&B) == 1) { - if ((res = mp_sub (&B, &x, &B)) != MP_OKAY) { - goto LBL_ERR; - } - } - /* B = B/2 */ - if ((res = mp_div_2 (&B, &B)) != MP_OKAY) { - goto LBL_ERR; - } - } - - /* 5. while v is even do */ - while (mp_iseven (&v) == 1) { - /* 5.1 v = v/2 */ - if ((res = mp_div_2 (&v, &v)) != MP_OKAY) { - goto LBL_ERR; - } - /* 5.2 if D is odd then */ - if (mp_isodd (&D) == 1) { - /* D = (D-x)/2 */ - if ((res = mp_sub (&D, &x, &D)) != MP_OKAY) { - goto LBL_ERR; - } - } - /* D = D/2 */ - if ((res = mp_div_2 (&D, &D)) != MP_OKAY) { - goto LBL_ERR; - } - } - - /* 6. if u >= v then */ - if (mp_cmp (&u, &v) != MP_LT) { - /* u = u - v, B = B - D */ - if ((res = mp_sub (&u, &v, &u)) != MP_OKAY) { - goto LBL_ERR; - } - - if ((res = mp_sub (&B, &D, &B)) != MP_OKAY) { - goto LBL_ERR; - } - } else { - /* v - v - u, D = D - B */ - if ((res = mp_sub (&v, &u, &v)) != MP_OKAY) { - goto LBL_ERR; - } - - if ((res = mp_sub (&D, &B, &D)) != MP_OKAY) { - goto LBL_ERR; - } - } - - /* if not zero goto step 4 */ - if (mp_iszero (&u) == 0) { - goto top; - } - - /* now a = C, b = D, gcd == g*v */ - - /* if v != 1 then there is no inverse */ - if (mp_cmp_d (&v, 1) != MP_EQ) { - res = MP_VAL; - goto LBL_ERR; - } - - /* b is now the inverse */ - neg = a->sign; - while (D.sign == MP_NEG) { - if ((res = mp_add (&D, b, &D)) != MP_OKAY) { - goto LBL_ERR; - } - } - mp_exch (&D, c); - c->sign = neg; - res = MP_OKAY; - -LBL_ERR:mp_clear_multi (&x, &y, &u, &v, &B, &D, NULL); - return res; -} -#endif - -/* $Source: /cvs/libtom/libtommath/bn_fast_mp_invmod.c,v $ */ -/* $Revision: 1.4 $ */ -/* $Date: 2006/12/28 01:25:13 $ */ diff --git a/lib/hcrypto/libtommath/bn_fast_mp_montgomery_reduce.c b/lib/hcrypto/libtommath/bn_fast_mp_montgomery_reduce.c deleted file mode 100644 index b6c0694bd2f5..000000000000 --- a/lib/hcrypto/libtommath/bn_fast_mp_montgomery_reduce.c +++ /dev/null @@ -1,172 +0,0 @@ -#include <tommath.h> -#ifdef BN_FAST_MP_MONTGOMERY_REDUCE_C -/* LibTomMath, multiple-precision integer library -- Tom St Denis - * - * LibTomMath is a library that provides multiple-precision - * integer arithmetic as well as number theoretic functionality. - * - * The library was designed directly after the MPI library by - * Michael Fromberger but has been written from scratch with - * additional optimizations in place. - * - * The library is free for all purposes without any express - * guarantee it works. - * - * Tom St Denis, tomstdenis@gmail.com, http://libtom.org - */ - -/* computes xR**-1 == x (mod N) via Montgomery Reduction - * - * This is an optimized implementation of montgomery_reduce - * which uses the comba method to quickly calculate the columns of the - * reduction. - * - * Based on Algorithm 14.32 on pp.601 of HAC. -*/ -int fast_mp_montgomery_reduce (mp_int * x, mp_int * n, mp_digit rho) -{ - int ix, res, olduse; - mp_word W[MP_WARRAY]; - - /* get old used count */ - olduse = x->used; - - /* grow a as required */ - if (x->alloc < n->used + 1) { - if ((res = mp_grow (x, n->used + 1)) != MP_OKAY) { - return res; - } - } - - /* first we have to get the digits of the input into - * an array of double precision words W[...] - */ - { - register mp_word *_W; - register mp_digit *tmpx; - - /* alias for the W[] array */ - _W = W; - - /* alias for the digits of x*/ - tmpx = x->dp; - - /* copy the digits of a into W[0..a->used-1] */ - for (ix = 0; ix < x->used; ix++) { - *_W++ = *tmpx++; - } - - /* zero the high words of W[a->used..m->used*2] */ - for (; ix < n->used * 2 + 1; ix++) { - *_W++ = 0; - } - } - - /* now we proceed to zero successive digits - * from the least significant upwards - */ - for (ix = 0; ix < n->used; ix++) { - /* mu = ai * m' mod b - * - * We avoid a double precision multiplication (which isn't required) - * by casting the value down to a mp_digit. Note this requires - * that W[ix-1] have the carry cleared (see after the inner loop) - */ - register mp_digit mu; - mu = (mp_digit) (((W[ix] & MP_MASK) * rho) & MP_MASK); - - /* a = a + mu * m * b**i - * - * This is computed in place and on the fly. The multiplication - * by b**i is handled by offseting which columns the results - * are added to. - * - * Note the comba method normally doesn't handle carries in the - * inner loop In this case we fix the carry from the previous - * column since the Montgomery reduction requires digits of the - * result (so far) [see above] to work. This is - * handled by fixing up one carry after the inner loop. The - * carry fixups are done in order so after these loops the - * first m->used words of W[] have the carries fixed - */ - { - register int iy; - register mp_digit *tmpn; - register mp_word *_W; - - /* alias for the digits of the modulus */ - tmpn = n->dp; - - /* Alias for the columns set by an offset of ix */ - _W = W + ix; - - /* inner loop */ - for (iy = 0; iy < n->used; iy++) { - *_W++ += ((mp_word)mu) * ((mp_word)*tmpn++); - } - } - - /* now fix carry for next digit, W[ix+1] */ - W[ix + 1] += W[ix] >> ((mp_word) DIGIT_BIT); - } - - /* now we have to propagate the carries and - * shift the words downward [all those least - * significant digits we zeroed]. - */ - { - register mp_digit *tmpx; - register mp_word *_W, *_W1; - - /* nox fix rest of carries */ - - /* alias for current word */ - _W1 = W + ix; - - /* alias for next word, where the carry goes */ - _W = W + ++ix; - - for (; ix <= n->used * 2 + 1; ix++) { - *_W++ += *_W1++ >> ((mp_word) DIGIT_BIT); - } - - /* copy out, A = A/b**n - * - * The result is A/b**n but instead of converting from an - * array of mp_word to mp_digit than calling mp_rshd - * we just copy them in the right order - */ - - /* alias for destination word */ - tmpx = x->dp; - - /* alias for shifted double precision result */ - _W = W + n->used; - - for (ix = 0; ix < n->used + 1; ix++) { - *tmpx++ = (mp_digit)(*_W++ & ((mp_word) MP_MASK)); - } - - /* zero oldused digits, if the input a was larger than - * m->used+1 we'll have to clear the digits - */ - for (; ix < olduse; ix++) { - *tmpx++ = 0; - } - } - - /* set the max used and clamp */ - x->used = n->used + 1; - mp_clamp (x); - - /* if A >= m then A = A - m */ - if (mp_cmp_mag (x, n) != MP_LT) { - return s_mp_sub (x, n, x); - } - return MP_OKAY; -} -#endif - -/* $Source: /cvs/libtom/libtommath/bn_fast_mp_montgomery_reduce.c,v $ */ -/* $Revision: 1.4 $ */ -/* $Date: 2006/12/28 01:25:13 $ */ diff --git a/lib/hcrypto/libtommath/bn_fast_s_mp_mul_digs.c b/lib/hcrypto/libtommath/bn_fast_s_mp_mul_digs.c deleted file mode 100644 index 90f161b10231..000000000000 --- a/lib/hcrypto/libtommath/bn_fast_s_mp_mul_digs.c +++ /dev/null @@ -1,107 +0,0 @@ -#include <tommath.h> -#ifdef BN_FAST_S_MP_MUL_DIGS_C -/* LibTomMath, multiple-precision integer library -- Tom St Denis - * - * LibTomMath is a library that provides multiple-precision - * integer arithmetic as well as number theoretic functionality. - * - * The library was designed directly after the MPI library by - * Michael Fromberger but has been written from scratch with - * additional optimizations in place. - * - * The library is free for all purposes without any express - * guarantee it works. - * - * Tom St Denis, tomstdenis@gmail.com, http://libtom.org - */ - -/* Fast (comba) multiplier - * - * This is the fast column-array [comba] multiplier. It is - * designed to compute the columns of the product first - * then handle the carries afterwards. This has the effect - * of making the nested loops that compute the columns very - * simple and schedulable on super-scalar processors. - * - * This has been modified to produce a variable number of - * digits of output so if say only a half-product is required - * you don't have to compute the upper half (a feature - * required for fast Barrett reduction). - * - * Based on Algorithm 14.12 on pp.595 of HAC. - * - */ -int fast_s_mp_mul_digs (mp_int * a, mp_int * b, mp_int * c, int digs) -{ - int olduse, res, pa, ix, iz; - mp_digit W[MP_WARRAY]; - register mp_word _W; - - /* grow the destination as required */ - if (c->alloc < digs) { - if ((res = mp_grow (c, digs)) != MP_OKAY) { - return res; - } - } - - /* number of output digits to produce */ - pa = MIN(digs, a->used + b->used); - - /* clear the carry */ - _W = 0; - for (ix = 0; ix < pa; ix++) { - int tx, ty; - int iy; - mp_digit *tmpx, *tmpy; - - /* get offsets into the two bignums */ - ty = MIN(b->used-1, ix); - tx = ix - ty; - - /* setup temp aliases */ - tmpx = a->dp + tx; - tmpy = b->dp + ty; - - /* this is the number of times the loop will iterrate, essentially - while (tx++ < a->used && ty-- >= 0) { ... } - */ - iy = MIN(a->used-tx, ty+1); - - /* execute loop */ - for (iz = 0; iz < iy; ++iz) { - _W += ((mp_word)*tmpx++)*((mp_word)*tmpy--); - - } - - /* store term */ - W[ix] = ((mp_digit)_W) & MP_MASK; - - /* make next carry */ - _W = _W >> ((mp_word)DIGIT_BIT); - } - - /* setup dest */ - olduse = c->used; - c->used = pa; - - { - register mp_digit *tmpc; - tmpc = c->dp; - for (ix = 0; ix < pa+1; ix++) { - /* now extract the previous digit [below the carry] */ - *tmpc++ = W[ix]; - } - - /* clear unused digits [that existed in the old copy of c] */ - for (; ix < olduse; ix++) { - *tmpc++ = 0; - } - } - mp_clamp (c); - return MP_OKAY; -} -#endif - -/* $Source: /cvs/libtom/libtommath/bn_fast_s_mp_mul_digs.c,v $ */ -/* $Revision: 1.8 $ */ -/* $Date: 2006/12/28 01:25:13 $ */ diff --git a/lib/hcrypto/libtommath/bn_fast_s_mp_mul_high_digs.c b/lib/hcrypto/libtommath/bn_fast_s_mp_mul_high_digs.c deleted file mode 100644 index a03b9f1324f8..000000000000 --- a/lib/hcrypto/libtommath/bn_fast_s_mp_mul_high_digs.c +++ /dev/null @@ -1,98 +0,0 @@ -#include <tommath.h> -#ifdef BN_FAST_S_MP_MUL_HIGH_DIGS_C -/* LibTomMath, multiple-precision integer library -- Tom St Denis - * - * LibTomMath is a library that provides multiple-precision - * integer arithmetic as well as number theoretic functionality. - * - * The library was designed directly after the MPI library by - * Michael Fromberger but has been written from scratch with - * additional optimizations in place. - * - * The library is free for all purposes without any express - * guarantee it works. - * - * Tom St Denis, tomstdenis@gmail.com, http://libtom.org - */ - -/* this is a modified version of fast_s_mul_digs that only produces - * output digits *above* digs. See the comments for fast_s_mul_digs - * to see how it works. - * - * This is used in the Barrett reduction since for one of the multiplications - * only the higher digits were needed. This essentially halves the work. - * - * Based on Algorithm 14.12 on pp.595 of HAC. - */ -int fast_s_mp_mul_high_digs (mp_int * a, mp_int * b, mp_int * c, int digs) -{ - int olduse, res, pa, ix, iz; - mp_digit W[MP_WARRAY]; - mp_word _W; - - /* grow the destination as required */ - pa = a->used + b->used; - if (c->alloc < pa) { - if ((res = mp_grow (c, pa)) != MP_OKAY) { - return res; - } - } - - /* number of output digits to produce */ - pa = a->used + b->used; - _W = 0; - for (ix = digs; ix < pa; ix++) { - int tx, ty, iy; - mp_digit *tmpx, *tmpy; - - /* get offsets into the two bignums */ - ty = MIN(b->used-1, ix); - tx = ix - ty; - - /* setup temp aliases */ - tmpx = a->dp + tx; - tmpy = b->dp + ty; - - /* this is the number of times the loop will iterrate, essentially its - while (tx++ < a->used && ty-- >= 0) { ... } - */ - iy = MIN(a->used-tx, ty+1); - - /* execute loop */ - for (iz = 0; iz < iy; iz++) { - _W += ((mp_word)*tmpx++)*((mp_word)*tmpy--); - } - - /* store term */ - W[ix] = ((mp_digit)_W) & MP_MASK; - - /* make next carry */ - _W = _W >> ((mp_word)DIGIT_BIT); - } - - /* setup dest */ - olduse = c->used; - c->used = pa; - - { - register mp_digit *tmpc; - - tmpc = c->dp + digs; - for (ix = digs; ix < pa; ix++) { - /* now extract the previous digit [below the carry] */ - *tmpc++ = W[ix]; - } - - /* clear unused digits [that existed in the old copy of c] */ - for (; ix < olduse; ix++) { - *tmpc++ = 0; - } - } - mp_clamp (c); - return MP_OKAY; -} -#endif - -/* $Source: /cvs/libtom/libtommath/bn_fast_s_mp_mul_high_digs.c,v $ */ -/* $Revision: 1.6 $ */ -/* $Date: 2006/12/28 01:25:13 $ */ diff --git a/lib/hcrypto/libtommath/bn_fast_s_mp_sqr.c b/lib/hcrypto/libtommath/bn_fast_s_mp_sqr.c deleted file mode 100644 index 848eaf04630f..000000000000 --- a/lib/hcrypto/libtommath/bn_fast_s_mp_sqr.c +++ /dev/null @@ -1,114 +0,0 @@ -#include <tommath.h> -#ifdef BN_FAST_S_MP_SQR_C -/* LibTomMath, multiple-precision integer library -- Tom St Denis - * - * LibTomMath is a library that provides multiple-precision - * integer arithmetic as well as number theoretic functionality. - * - * The library was designed directly after the MPI library by - * Michael Fromberger but has been written from scratch with - * additional optimizations in place. - * - * The library is free for all purposes without any express - * guarantee it works. - * - * Tom St Denis, tomstdenis@gmail.com, http://libtom.org - */ - -/* the jist of squaring... - * you do like mult except the offset of the tmpx [one that - * starts closer to zero] can't equal the offset of tmpy. - * So basically you set up iy like before then you min it with - * (ty-tx) so that it never happens. You double all those - * you add in the inner loop - -After that loop you do the squares and add them in. -*/ - -int fast_s_mp_sqr (mp_int * a, mp_int * b) -{ - int olduse, res, pa, ix, iz; - mp_digit W[MP_WARRAY], *tmpx; - mp_word W1; - - /* grow the destination as required */ - pa = a->used + a->used; - if (b->alloc < pa) { - if ((res = mp_grow (b, pa)) != MP_OKAY) { - return res; - } - } - - /* number of output digits to produce */ - W1 = 0; - for (ix = 0; ix < pa; ix++) { - int tx, ty, iy; - mp_word _W; - mp_digit *tmpy; - - /* clear counter */ - _W = 0; - - /* get offsets into the two bignums */ - ty = MIN(a->used-1, ix); - tx = ix - ty; - - /* setup temp aliases */ - tmpx = a->dp + tx; - tmpy = a->dp + ty; - - /* this is the number of times the loop will iterrate, essentially - while (tx++ < a->used && ty-- >= 0) { ... } - */ - iy = MIN(a->used-tx, ty+1); - - /* now for squaring tx can never equal ty - * we halve the distance since they approach at a rate of 2x - * and we have to round because odd cases need to be executed - */ - iy = MIN(iy, (ty-tx+1)>>1); - - /* execute loop */ - for (iz = 0; iz < iy; iz++) { - _W += ((mp_word)*tmpx++)*((mp_word)*tmpy--); - } - - /* double the inner product and add carry */ - _W = _W + _W + W1; - - /* even columns have the square term in them */ - if ((ix&1) == 0) { - _W += ((mp_word)a->dp[ix>>1])*((mp_word)a->dp[ix>>1]); - } - - /* store it */ - W[ix] = (mp_digit)(_W & MP_MASK); - - /* make next carry */ - W1 = _W >> ((mp_word)DIGIT_BIT); - } - - /* setup dest */ - olduse = b->used; - b->used = a->used+a->used; - - { - mp_digit *tmpb; - tmpb = b->dp; - for (ix = 0; ix < pa; ix++) { - *tmpb++ = W[ix] & MP_MASK; - } - - /* clear unused digits [that existed in the old copy of c] */ - for (; ix < olduse; ix++) { - *tmpb++ = 0; - } - } - mp_clamp (b); - return MP_OKAY; -} -#endif - -/* $Source: /cvs/libtom/libtommath/bn_fast_s_mp_sqr.c,v $ */ -/* $Revision: 1.4 $ */ -/* $Date: 2006/12/28 01:25:13 $ */ diff --git a/lib/hcrypto/libtommath/bn_mp_2expt.c b/lib/hcrypto/libtommath/bn_mp_2expt.c index 11a508c7fb73..0ae3df1bf953 100644 --- a/lib/hcrypto/libtommath/bn_mp_2expt.c +++ b/lib/hcrypto/libtommath/bn_mp_2expt.c @@ -1,48 +1,31 @@ -#include <tommath.h> +#include "tommath_private.h" #ifdef BN_MP_2EXPT_C -/* LibTomMath, multiple-precision integer library -- Tom St Denis - * - * LibTomMath is a library that provides multiple-precision - * integer arithmetic as well as number theoretic functionality. - * - * The library was designed directly after the MPI library by - * Michael Fromberger but has been written from scratch with - * additional optimizations in place. - * - * The library is free for all purposes without any express - * guarantee it works. - * - * Tom St Denis, tomstdenis@gmail.com, http://libtom.org - */ +/* LibTomMath, multiple-precision integer library -- Tom St Denis */ +/* SPDX-License-Identifier: Unlicense */ /* computes a = 2**b * * Simple algorithm which zeroes the int, grows it then just sets one bit * as required. */ -int -mp_2expt (mp_int * a, int b) +mp_err mp_2expt(mp_int *a, int b) { - int res; + mp_err err; - /* zero a as per default */ - mp_zero (a); + /* zero a as per default */ + mp_zero(a); - /* grow a to accomodate the single bit */ - if ((res = mp_grow (a, b / DIGIT_BIT + 1)) != MP_OKAY) { - return res; - } + /* grow a to accomodate the single bit */ + if ((err = mp_grow(a, (b / MP_DIGIT_BIT) + 1)) != MP_OKAY) { + return err; + } - /* set the used count of where the bit will go */ - a->used = b / DIGIT_BIT + 1; + /* set the used count of where the bit will go */ + a->used = (b / MP_DIGIT_BIT) + 1; - /* put the single bit in its place */ - a->dp[b / DIGIT_BIT] = ((mp_digit)1) << (b % DIGIT_BIT); + /* put the single bit in its place */ + a->dp[b / MP_DIGIT_BIT] = (mp_digit)1 << (mp_digit)(b % MP_DIGIT_BIT); - return MP_OKAY; + return MP_OKAY; } #endif - -/* $Source: /cvs/libtom/libtommath/bn_mp_2expt.c,v $ */ -/* $Revision: 1.4 $ */ -/* $Date: 2006/12/28 01:25:13 $ */ diff --git a/lib/hcrypto/libtommath/bn_mp_abs.c b/lib/hcrypto/libtommath/bn_mp_abs.c index d97e8db05f13..00900bbdd050 100644 --- a/lib/hcrypto/libtommath/bn_mp_abs.c +++ b/lib/hcrypto/libtommath/bn_mp_abs.c @@ -1,43 +1,26 @@ -#include <tommath.h> +#include "tommath_private.h" #ifdef BN_MP_ABS_C -/* LibTomMath, multiple-precision integer library -- Tom St Denis - * - * LibTomMath is a library that provides multiple-precision - * integer arithmetic as well as number theoretic functionality. - * - * The library was designed directly after the MPI library by - * Michael Fromberger but has been written from scratch with - * additional optimizations in place. - * - * The library is free for all purposes without any express - * guarantee it works. - * - * Tom St Denis, tomstdenis@gmail.com, http://libtom.org - */ +/* LibTomMath, multiple-precision integer library -- Tom St Denis */ +/* SPDX-License-Identifier: Unlicense */ /* b = |a| * * Simple function copies the input and fixes the sign to positive */ -int -mp_abs (mp_int * a, mp_int * b) +mp_err mp_abs(const mp_int *a, mp_int *b) { - int res; + mp_err err; - /* copy a to b */ - if (a != b) { - if ((res = mp_copy (a, b)) != MP_OKAY) { - return res; - } - } + /* copy a to b */ + if (a != b) { + if ((err = mp_copy(a, b)) != MP_OKAY) { + return err; + } + } - /* force the sign of b to positive */ - b->sign = MP_ZPOS; + /* force the sign of b to positive */ + b->sign = MP_ZPOS; - return MP_OKAY; + return MP_OKAY; } #endif - -/* $Source: /cvs/libtom/libtommath/bn_mp_abs.c,v $ */ -/* $Revision: 1.4 $ */ -/* $Date: 2006/12/28 01:25:13 $ */ diff --git a/lib/hcrypto/libtommath/bn_mp_add.c b/lib/hcrypto/libtommath/bn_mp_add.c index be20644770d3..dfa78de50e93 100644 --- a/lib/hcrypto/libtommath/bn_mp_add.c +++ b/lib/hcrypto/libtommath/bn_mp_add.c @@ -1,53 +1,38 @@ -#include <tommath.h> +#include "tommath_private.h" #ifdef BN_MP_ADD_C -/* LibTomMath, multiple-precision integer library -- Tom St Denis - * - * LibTomMath is a library that provides multiple-precision - * integer arithmetic as well as number theoretic functionality. - * - * The library was designed directly after the MPI library by - * Michael Fromberger but has been written from scratch with - * additional optimizations in place. - * - * The library is free for all purposes without any express - * guarantee it works. - * - * Tom St Denis, tomstdenis@gmail.com, http://libtom.org - */ +/* LibTomMath, multiple-precision integer library -- Tom St Denis */ +/* SPDX-License-Identifier: Unlicense */ /* high level addition (handles signs) */ -int mp_add (mp_int * a, mp_int * b, mp_int * c) +mp_err mp_add(const mp_int *a, const mp_int *b, mp_int *c) { - int sa, sb, res; + mp_sign sa, sb; + mp_err err; - /* get sign of both inputs */ - sa = a->sign; - sb = b->sign; + /* get sign of both inputs */ + sa = a->sign; + sb = b->sign; - /* handle two cases, not four */ - if (sa == sb) { - /* both positive or both negative */ - /* add their magnitudes, copy the sign */ - c->sign = sa; - res = s_mp_add (a, b, c); - } else { - /* one positive, the other negative */ - /* subtract the one with the greater magnitude from */ - /* the one of the lesser magnitude. The result gets */ - /* the sign of the one with the greater magnitude. */ - if (mp_cmp_mag (a, b) == MP_LT) { - c->sign = sb; - res = s_mp_sub (b, a, c); - } else { + /* handle two cases, not four */ + if (sa == sb) { + /* both positive or both negative */ + /* add their magnitudes, copy the sign */ c->sign = sa; - res = s_mp_sub (a, b, c); - } - } - return res; + err = s_mp_add(a, b, c); + } else { + /* one positive, the other negative */ + /* subtract the one with the greater magnitude from */ + /* the one of the lesser magnitude. The result gets */ + /* the sign of the one with the greater magnitude. */ + if (mp_cmp_mag(a, b) == MP_LT) { + c->sign = sb; + err = s_mp_sub(b, a, c); + } else { + c->sign = sa; + err = s_mp_sub(a, b, c); + } + } + return err; } #endif - -/* $Source: /cvs/libtom/libtommath/bn_mp_add.c,v $ */ -/* $Revision: 1.4 $ */ -/* $Date: 2006/12/28 01:25:13 $ */ diff --git a/lib/hcrypto/libtommath/bn_mp_add_d.c b/lib/hcrypto/libtommath/bn_mp_add_d.c index 8ca36c1124fa..f301575616d8 100644 --- a/lib/hcrypto/libtommath/bn_mp_add_d.c +++ b/lib/hcrypto/libtommath/bn_mp_add_d.c @@ -1,112 +1,89 @@ -#include <tommath.h> +#include "tommath_private.h" #ifdef BN_MP_ADD_D_C -/* LibTomMath, multiple-precision integer library -- Tom St Denis - * - * LibTomMath is a library that provides multiple-precision - * integer arithmetic as well as number theoretic functionality. - * - * The library was designed directly after the MPI library by - * Michael Fromberger but has been written from scratch with - * additional optimizations in place. - * - * The library is free for all purposes without any express - * guarantee it works. - * - * Tom St Denis, tomstdenis@gmail.com, http://libtom.org - */ +/* LibTomMath, multiple-precision integer library -- Tom St Denis */ +/* SPDX-License-Identifier: Unlicense */ /* single digit addition */ -int -mp_add_d (mp_int * a, mp_digit b, mp_int * c) +mp_err mp_add_d(const mp_int *a, mp_digit b, mp_int *c) { - int res, ix, oldused; - mp_digit *tmpa, *tmpc, mu; - - /* grow c as required */ - if (c->alloc < a->used + 1) { - if ((res = mp_grow(c, a->used + 1)) != MP_OKAY) { - return res; - } - } - - /* if a is negative and |a| >= b, call c = |a| - b */ - if (a->sign == MP_NEG && (a->used > 1 || a->dp[0] >= b)) { - /* temporarily fix sign of a */ - a->sign = MP_ZPOS; - - /* c = |a| - b */ - res = mp_sub_d(a, b, c); - - /* fix sign */ - a->sign = c->sign = MP_NEG; - - /* clamp */ - mp_clamp(c); - - return res; - } - - /* old number of used digits in c */ - oldused = c->used; - - /* sign always positive */ - c->sign = MP_ZPOS; - - /* source alias */ - tmpa = a->dp; - - /* destination alias */ - tmpc = c->dp; - - /* if a is positive */ - if (a->sign == MP_ZPOS) { - /* add digit, after this we're propagating - * the carry. - */ - *tmpc = *tmpa++ + b; - mu = *tmpc >> DIGIT_BIT; - *tmpc++ &= MP_MASK; - - /* now handle rest of the digits */ - for (ix = 1; ix < a->used; ix++) { - *tmpc = *tmpa++ + mu; - mu = *tmpc >> DIGIT_BIT; - *tmpc++ &= MP_MASK; - } - /* set final carry */ - ix++; - *tmpc++ = mu; - - /* setup size */ - c->used = a->used + 1; - } else { - /* a was negative and |a| < b */ - c->used = 1; - - /* the result is a single digit */ - if (a->used == 1) { - *tmpc++ = b - a->dp[0]; - } else { - *tmpc++ = b; - } - - /* setup count so the clearing of oldused - * can fall through correctly - */ - ix = 1; - } - - /* now zero to oldused */ - while (ix++ < oldused) { - *tmpc++ = 0; - } - mp_clamp(c); - - return MP_OKAY; + mp_err err; + int ix, oldused; + mp_digit *tmpa, *tmpc; + + /* grow c as required */ + if (c->alloc < (a->used + 1)) { + if ((err = mp_grow(c, a->used + 1)) != MP_OKAY) { + return err; + } + } + + /* if a is negative and |a| >= b, call c = |a| - b */ + if ((a->sign == MP_NEG) && ((a->used > 1) || (a->dp[0] >= b))) { + mp_int a_ = *a; + /* temporarily fix sign of a */ + a_.sign = MP_ZPOS; + + /* c = |a| - b */ + err = mp_sub_d(&a_, b, c); + + /* fix sign */ + c->sign = MP_NEG; + + /* clamp */ + mp_clamp(c); + + return err; + } + + /* old number of used digits in c */ + oldused = c->used; + + /* source alias */ + tmpa = a->dp; + + /* destination alias */ + tmpc = c->dp; + + /* if a is positive */ + if (a->sign == MP_ZPOS) { + /* add digits, mu is carry */ + mp_digit mu = b; + for (ix = 0; ix < a->used; ix++) { + *tmpc = *tmpa++ + mu; + mu = *tmpc >> MP_DIGIT_BIT; + *tmpc++ &= MP_MASK; + } + /* set final carry */ + ix++; + *tmpc++ = mu; + + /* setup size */ + c->used = a->used + 1; + } else { + /* a was negative and |a| < b */ + c->used = 1; + + /* the result is a single digit */ + if (a->used == 1) { + *tmpc++ = b - a->dp[0]; + } else { + *tmpc++ = b; + } + + /* setup count so the clearing of oldused + * can fall through correctly + */ + ix = 1; + } + + /* sign always positive */ + c->sign = MP_ZPOS; + + /* now zero to oldused */ + MP_ZERO_DIGITS(tmpc, oldused - ix); + mp_clamp(c); + + return MP_OKAY; } #endif - -/* $Source: /cvs/libtom/libtommath/bn_mp_add_d.c,v $ */ -/* $Revision: 1.5 $ */ -/* $Date: 2006/12/28 01:25:13 $ */ diff --git a/lib/hcrypto/libtommath/bn_mp_addmod.c b/lib/hcrypto/libtommath/bn_mp_addmod.c index 6d8afe18c93e..1dcfb678c9c8 100644 --- a/lib/hcrypto/libtommath/bn_mp_addmod.c +++ b/lib/hcrypto/libtommath/bn_mp_addmod.c @@ -1,41 +1,25 @@ -#include <tommath.h> +#include "tommath_private.h" #ifdef BN_MP_ADDMOD_C -/* LibTomMath, multiple-precision integer library -- Tom St Denis - * - * LibTomMath is a library that provides multiple-precision - * integer arithmetic as well as number theoretic functionality. - * - * The library was designed directly after the MPI library by - * Michael Fromberger but has been written from scratch with - * additional optimizations in place. - * - * The library is free for all purposes without any express - * guarantee it works. - * - * Tom St Denis, tomstdenis@gmail.com, http://libtom.org - */ +/* LibTomMath, multiple-precision integer library -- Tom St Denis */ +/* SPDX-License-Identifier: Unlicense */ /* d = a + b (mod c) */ -int -mp_addmod (mp_int * a, mp_int * b, mp_int * c, mp_int * d) +mp_err mp_addmod(const mp_int *a, const mp_int *b, const mp_int *c, mp_int *d) { - int res; - mp_int t; + mp_err err; + mp_int t; - if ((res = mp_init (&t)) != MP_OKAY) { - return res; - } + if ((err = mp_init(&t)) != MP_OKAY) { + return err; + } - if ((res = mp_add (a, b, &t)) != MP_OKAY) { - mp_clear (&t); - return res; - } - res = mp_mod (&t, c, d); - mp_clear (&t); - return res; + if ((err = mp_add(a, b, &t)) != MP_OKAY) { + goto LBL_ERR; + } + err = mp_mod(&t, c, d); + +LBL_ERR: + mp_clear(&t); + return err; } #endif - -/* $Source: /cvs/libtom/libtommath/bn_mp_addmod.c,v $ */ -/* $Revision: 1.4 $ */ -/* $Date: 2006/12/28 01:25:13 $ */ diff --git a/lib/hcrypto/libtommath/bn_mp_and.c b/lib/hcrypto/libtommath/bn_mp_and.c index 8ea22878f91a..c259f8dec18b 100644 --- a/lib/hcrypto/libtommath/bn_mp_and.c +++ b/lib/hcrypto/libtommath/bn_mp_and.c @@ -1,57 +1,56 @@ -#include <tommath.h> +#include "tommath_private.h" #ifdef BN_MP_AND_C -/* LibTomMath, multiple-precision integer library -- Tom St Denis - * - * LibTomMath is a library that provides multiple-precision - * integer arithmetic as well as number theoretic functionality. - * - * The library was designed directly after the MPI library by - * Michael Fromberger but has been written from scratch with - * additional optimizations in place. - * - * The library is free for all purposes without any express - * guarantee it works. - * - * Tom St Denis, tomstdenis@gmail.com, http://libtom.org - */ - -/* AND two ints together */ -int -mp_and (mp_int * a, mp_int * b, mp_int * c) +/* LibTomMath, multiple-precision integer library -- Tom St Denis */ +/* SPDX-License-Identifier: Unlicense */ + +/* two complement and */ +mp_err mp_and(const mp_int *a, const mp_int *b, mp_int *c) { - int res, ix, px; - mp_int t, *x; - - if (a->used > b->used) { - if ((res = mp_init_copy (&t, a)) != MP_OKAY) { - return res; - } - px = b->used; - x = b; - } else { - if ((res = mp_init_copy (&t, b)) != MP_OKAY) { - return res; - } - px = a->used; - x = a; - } - - for (ix = 0; ix < px; ix++) { - t.dp[ix] &= x->dp[ix]; - } - - /* zero digits above the last from the smallest mp_int */ - for (; ix < t.used; ix++) { - t.dp[ix] = 0; - } - - mp_clamp (&t); - mp_exch (c, &t); - mp_clear (&t); - return MP_OKAY; + int used = MP_MAX(a->used, b->used) + 1, i; + mp_err err; + mp_digit ac = 1, bc = 1, cc = 1; + mp_sign csign = ((a->sign == MP_NEG) && (b->sign == MP_NEG)) ? MP_NEG : MP_ZPOS; + + if (c->alloc < used) { + if ((err = mp_grow(c, used)) != MP_OKAY) { + return err; + } + } + + for (i = 0; i < used; i++) { + mp_digit x, y; + + /* convert to two complement if negative */ + if (a->sign == MP_NEG) { + ac += (i >= a->used) ? MP_MASK : (~a->dp[i] & MP_MASK); + x = ac & MP_MASK; + ac >>= MP_DIGIT_BIT; + } else { + x = (i >= a->used) ? 0uL : a->dp[i]; + } + + /* convert to two complement if negative */ + if (b->sign == MP_NEG) { + bc += (i >= b->used) ? MP_MASK : (~b->dp[i] & MP_MASK); + y = bc & MP_MASK; + bc >>= MP_DIGIT_BIT; + } else { + y = (i >= b->used) ? 0uL : b->dp[i]; + } + + c->dp[i] = x & y; + + /* convert to to sign-magnitude if negative */ + if (csign == MP_NEG) { + cc += ~c->dp[i] & MP_MASK; + c->dp[i] = cc & MP_MASK; + cc >>= MP_DIGIT_BIT; + } + } + + c->used = used; + c->sign = csign; + mp_clamp(c); + return MP_OKAY; } #endif - -/* $Source: /cvs/libtom/libtommath/bn_mp_and.c,v $ */ -/* $Revision: 1.4 $ */ -/* $Date: 2006/12/28 01:25:13 $ */ diff --git a/lib/hcrypto/libtommath/bn_mp_clamp.c b/lib/hcrypto/libtommath/bn_mp_clamp.c index 2a565e8dbd28..ac23bfd3fc20 100644 --- a/lib/hcrypto/libtommath/bn_mp_clamp.c +++ b/lib/hcrypto/libtommath/bn_mp_clamp.c @@ -1,19 +1,7 @@ -#include <tommath.h> +#include "tommath_private.h" #ifdef BN_MP_CLAMP_C -/* LibTomMath, multiple-precision integer library -- Tom St Denis - * - * LibTomMath is a library that provides multiple-precision - * integer arithmetic as well as number theoretic functionality. - * - * The library was designed directly after the MPI library by - * Michael Fromberger but has been written from scratch with - * additional optimizations in place. - * - * The library is free for all purposes without any express - * guarantee it works. - * - * Tom St Denis, tomstdenis@gmail.com, http://libtom.org - */ +/* LibTomMath, multiple-precision integer library -- Tom St Denis */ +/* SPDX-License-Identifier: Unlicense */ /* trim unused digits * @@ -22,23 +10,18 @@ * Typically very fast. Also fixes the sign if there * are no more leading digits */ -void -mp_clamp (mp_int * a) +void mp_clamp(mp_int *a) { - /* decrease used while the most significant digit is - * zero. - */ - while (a->used > 0 && a->dp[a->used - 1] == 0) { - --(a->used); - } + /* decrease used while the most significant digit is + * zero. + */ + while ((a->used > 0) && (a->dp[a->used - 1] == 0u)) { + --(a->used); + } - /* reset the sign flag if used == 0 */ - if (a->used == 0) { - a->sign = MP_ZPOS; - } + /* reset the sign flag if used == 0 */ + if (a->used == 0) { + a->sign = MP_ZPOS; + } } #endif - -/* $Source: /cvs/libtom/libtommath/bn_mp_clamp.c,v $ */ -/* $Revision: 1.4 $ */ -/* $Date: 2006/12/28 01:25:13 $ */ diff --git a/lib/hcrypto/libtommath/bn_mp_clear.c b/lib/hcrypto/libtommath/bn_mp_clear.c index a65f0a36c49f..ff78324d99d9 100644 --- a/lib/hcrypto/libtommath/bn_mp_clear.c +++ b/lib/hcrypto/libtommath/bn_mp_clear.c @@ -1,44 +1,20 @@ -#include <tommath.h> +#include "tommath_private.h" #ifdef BN_MP_CLEAR_C -/* LibTomMath, multiple-precision integer library -- Tom St Denis - * - * LibTomMath is a library that provides multiple-precision - * integer arithmetic as well as number theoretic functionality. - * - * The library was designed directly after the MPI library by - * Michael Fromberger but has been written from scratch with - * additional optimizations in place. - * - * The library is free for all purposes without any express - * guarantee it works. - * - * Tom St Denis, tomstdenis@gmail.com, http://libtom.org - */ +/* LibTomMath, multiple-precision integer library -- Tom St Denis */ +/* SPDX-License-Identifier: Unlicense */ /* clear one (frees) */ -void -mp_clear (mp_int * a) +void mp_clear(mp_int *a) { - int i; + /* only do anything if a hasn't been freed previously */ + if (a->dp != NULL) { + /* free ram */ + MP_FREE_DIGITS(a->dp, a->alloc); - /* only do anything if a hasn't been freed previously */ - if (a->dp != NULL) { - /* first zero the digits */ - for (i = 0; i < a->used; i++) { - a->dp[i] = 0; - } - - /* free ram */ - XFREE(a->dp); - - /* reset members to make debugging easier */ - a->dp = NULL; - a->alloc = a->used = 0; - a->sign = MP_ZPOS; - } + /* reset members to make debugging easier */ + a->dp = NULL; + a->alloc = a->used = 0; + a->sign = MP_ZPOS; + } } #endif - -/* $Source: /cvs/libtom/libtommath/bn_mp_clear.c,v $ */ -/* $Revision: 1.4 $ */ -/* $Date: 2006/12/28 01:25:13 $ */ diff --git a/lib/hcrypto/libtommath/bn_mp_clear_multi.c b/lib/hcrypto/libtommath/bn_mp_clear_multi.c index e5e3da340aea..794e45fa5c0f 100644 --- a/lib/hcrypto/libtommath/bn_mp_clear_multi.c +++ b/lib/hcrypto/libtommath/bn_mp_clear_multi.c @@ -1,34 +1,19 @@ -#include <tommath.h> +#include "tommath_private.h" #ifdef BN_MP_CLEAR_MULTI_C -/* LibTomMath, multiple-precision integer library -- Tom St Denis - * - * LibTomMath is a library that provides multiple-precision - * integer arithmetic as well as number theoretic functionality. - * - * The library was designed directly after the MPI library by - * Michael Fromberger but has been written from scratch with - * additional optimizations in place. - * - * The library is free for all purposes without any express - * guarantee it works. - * - * Tom St Denis, tomstdenis@gmail.com, http://libtom.org - */ +/* LibTomMath, multiple-precision integer library -- Tom St Denis */ +/* SPDX-License-Identifier: Unlicense */ + #include <stdarg.h> void mp_clear_multi(mp_int *mp, ...) { - mp_int* next_mp = mp; - va_list args; - va_start(args, mp); - while (next_mp != NULL) { - mp_clear(next_mp); - next_mp = va_arg(args, mp_int*); - } - va_end(args); + mp_int *next_mp = mp; + va_list args; + va_start(args, mp); + while (next_mp != NULL) { + mp_clear(next_mp); + next_mp = va_arg(args, mp_int *); + } + va_end(args); } #endif - -/* $Source: /cvs/libtom/libtommath/bn_mp_clear_multi.c,v $ */ -/* $Revision: 1.4 $ */ -/* $Date: 2006/12/28 01:25:13 $ */ diff --git a/lib/hcrypto/libtommath/bn_mp_cmp.c b/lib/hcrypto/libtommath/bn_mp_cmp.c index ccd2c8eb9b9b..ced484096803 100644 --- a/lib/hcrypto/libtommath/bn_mp_cmp.c +++ b/lib/hcrypto/libtommath/bn_mp_cmp.c @@ -1,43 +1,26 @@ -#include <tommath.h> +#include "tommath_private.h" #ifdef BN_MP_CMP_C -/* LibTomMath, multiple-precision integer library -- Tom St Denis - * - * LibTomMath is a library that provides multiple-precision - * integer arithmetic as well as number theoretic functionality. - * - * The library was designed directly after the MPI library by - * Michael Fromberger but has been written from scratch with - * additional optimizations in place. - * - * The library is free for all purposes without any express - * guarantee it works. - * - * Tom St Denis, tomstdenis@gmail.com, http://libtom.org - */ +/* LibTomMath, multiple-precision integer library -- Tom St Denis */ +/* SPDX-License-Identifier: Unlicense */ /* compare two ints (signed)*/ -int -mp_cmp (mp_int * a, mp_int * b) +mp_ord mp_cmp(const mp_int *a, const mp_int *b) { - /* compare based on sign */ - if (a->sign != b->sign) { - if (a->sign == MP_NEG) { - return MP_LT; - } else { - return MP_GT; - } - } + /* compare based on sign */ + if (a->sign != b->sign) { + if (a->sign == MP_NEG) { + return MP_LT; + } else { + return MP_GT; + } + } - /* compare digits */ - if (a->sign == MP_NEG) { - /* if negative compare opposite direction */ - return mp_cmp_mag(b, a); - } else { - return mp_cmp_mag(a, b); - } + /* compare digits */ + if (a->sign == MP_NEG) { + /* if negative compare opposite direction */ + return mp_cmp_mag(b, a); + } else { + return mp_cmp_mag(a, b); + } } #endif - -/* $Source: /cvs/libtom/libtommath/bn_mp_cmp.c,v $ */ -/* $Revision: 1.4 $ */ -/* $Date: 2006/12/28 01:25:13 $ */ diff --git a/lib/hcrypto/libtommath/bn_mp_cmp_d.c b/lib/hcrypto/libtommath/bn_mp_cmp_d.c index 724c1c36344d..5a8337b5b8c5 100644 --- a/lib/hcrypto/libtommath/bn_mp_cmp_d.c +++ b/lib/hcrypto/libtommath/bn_mp_cmp_d.c @@ -1,44 +1,28 @@ -#include <tommath.h> +#include "tommath_private.h" #ifdef BN_MP_CMP_D_C -/* LibTomMath, multiple-precision integer library -- Tom St Denis - * - * LibTomMath is a library that provides multiple-precision - * integer arithmetic as well as number theoretic functionality. - * - * The library was designed directly after the MPI library by - * Michael Fromberger but has been written from scratch with - * additional optimizations in place. - * - * The library is free for all purposes without any express - * guarantee it works. - * - * Tom St Denis, tomstdenis@gmail.com, http://libtom.org - */ +/* LibTomMath, multiple-precision integer library -- Tom St Denis */ +/* SPDX-License-Identifier: Unlicense */ /* compare a digit */ -int mp_cmp_d(mp_int * a, mp_digit b) +mp_ord mp_cmp_d(const mp_int *a, mp_digit b) { - /* compare based on sign */ - if (a->sign == MP_NEG) { - return MP_LT; - } + /* compare based on sign */ + if (a->sign == MP_NEG) { + return MP_LT; + } - /* compare based on magnitude */ - if (a->used > 1) { - return MP_GT; - } + /* compare based on magnitude */ + if (a->used > 1) { + return MP_GT; + } - /* compare the only digit of a to b */ - if (a->dp[0] > b) { - return MP_GT; - } else if (a->dp[0] < b) { - return MP_LT; - } else { - return MP_EQ; - } + /* compare the only digit of a to b */ + if (a->dp[0] > b) { + return MP_GT; + } else if (a->dp[0] < b) { + return MP_LT; + } else { + return MP_EQ; + } } #endif - -/* $Source: /cvs/libtom/libtommath/bn_mp_cmp_d.c,v $ */ -/* $Revision: 1.4 $ */ -/* $Date: 2006/12/28 01:25:13 $ */ diff --git a/lib/hcrypto/libtommath/bn_mp_cmp_mag.c b/lib/hcrypto/libtommath/bn_mp_cmp_mag.c index 4a505238a031..f144ea9e6bbc 100644 --- a/lib/hcrypto/libtommath/bn_mp_cmp_mag.c +++ b/lib/hcrypto/libtommath/bn_mp_cmp_mag.c @@ -1,55 +1,39 @@ -#include <tommath.h> +#include "tommath_private.h" #ifdef BN_MP_CMP_MAG_C -/* LibTomMath, multiple-precision integer library -- Tom St Denis - * - * LibTomMath is a library that provides multiple-precision - * integer arithmetic as well as number theoretic functionality. - * - * The library was designed directly after the MPI library by - * Michael Fromberger but has been written from scratch with - * additional optimizations in place. - * - * The library is free for all purposes without any express - * guarantee it works. - * - * Tom St Denis, tomstdenis@gmail.com, http://libtom.org - */ +/* LibTomMath, multiple-precision integer library -- Tom St Denis */ +/* SPDX-License-Identifier: Unlicense */ /* compare maginitude of two ints (unsigned) */ -int mp_cmp_mag (mp_int * a, mp_int * b) +mp_ord mp_cmp_mag(const mp_int *a, const mp_int *b) { - int n; - mp_digit *tmpa, *tmpb; + int n; + const mp_digit *tmpa, *tmpb; - /* compare based on # of non-zero digits */ - if (a->used > b->used) { - return MP_GT; - } + /* compare based on # of non-zero digits */ + if (a->used > b->used) { + return MP_GT; + } - if (a->used < b->used) { - return MP_LT; - } + if (a->used < b->used) { + return MP_LT; + } - /* alias for a */ - tmpa = a->dp + (a->used - 1); + /* alias for a */ + tmpa = a->dp + (a->used - 1); - /* alias for b */ - tmpb = b->dp + (a->used - 1); + /* alias for b */ + tmpb = b->dp + (a->used - 1); - /* compare based on digits */ - for (n = 0; n < a->used; ++n, --tmpa, --tmpb) { - if (*tmpa > *tmpb) { - return MP_GT; - } + /* compare based on digits */ + for (n = 0; n < a->used; ++n, --tmpa, --tmpb) { + if (*tmpa > *tmpb) { + return MP_GT; + } - if (*tmpa < *tmpb) { - return MP_LT; - } - } - return MP_EQ; + if (*tmpa < *tmpb) { + return MP_LT; + } + } + return MP_EQ; } #endif - -/* $Source: /cvs/libtom/libtommath/bn_mp_cmp_mag.c,v $ */ -/* $Revision: 1.4 $ */ -/* $Date: 2006/12/28 01:25:13 $ */ diff --git a/lib/hcrypto/libtommath/bn_mp_cnt_lsb.c b/lib/hcrypto/libtommath/bn_mp_cnt_lsb.c index 2d4a8d4f0f20..4b2d206ebe06 100644 --- a/lib/hcrypto/libtommath/bn_mp_cnt_lsb.c +++ b/lib/hcrypto/libtommath/bn_mp_cnt_lsb.c @@ -1,53 +1,37 @@ -#include <tommath.h> +#include "tommath_private.h" #ifdef BN_MP_CNT_LSB_C -/* LibTomMath, multiple-precision integer library -- Tom St Denis - * - * LibTomMath is a library that provides multiple-precision - * integer arithmetic as well as number theoretic functionality. - * - * The library was designed directly after the MPI library by - * Michael Fromberger but has been written from scratch with - * additional optimizations in place. - * - * The library is free for all purposes without any express - * guarantee it works. - * - * Tom St Denis, tomstdenis@gmail.com, http://libtom.org - */ +/* LibTomMath, multiple-precision integer library -- Tom St Denis */ +/* SPDX-License-Identifier: Unlicense */ static const int lnz[16] = { 4, 0, 1, 0, 2, 0, 1, 0, 3, 0, 1, 0, 2, 0, 1, 0 }; /* Counts the number of lsbs which are zero before the first zero bit */ -int mp_cnt_lsb(mp_int *a) +int mp_cnt_lsb(const mp_int *a) { int x; mp_digit q, qq; /* easy out */ - if (mp_iszero(a) == 1) { + if (MP_IS_ZERO(a)) { return 0; } /* scan lower digits until non-zero */ - for (x = 0; x < a->used && a->dp[x] == 0; x++); + for (x = 0; (x < a->used) && (a->dp[x] == 0u); x++) {} q = a->dp[x]; - x *= DIGIT_BIT; + x *= MP_DIGIT_BIT; /* now scan this digit until a 1 is found */ - if ((q & 1) == 0) { + if ((q & 1u) == 0u) { do { - qq = q & 15; + qq = q & 15u; x += lnz[qq]; q >>= 4; - } while (qq == 0); + } while (qq == 0u); } return x; } #endif - -/* $Source: /cvs/libtom/libtommath/bn_mp_cnt_lsb.c,v $ */ -/* $Revision: 1.4 $ */ -/* $Date: 2006/12/28 01:25:13 $ */ diff --git a/lib/hcrypto/libtommath/bn_mp_complement.c b/lib/hcrypto/libtommath/bn_mp_complement.c new file mode 100644 index 000000000000..fef1423c54c6 --- /dev/null +++ b/lib/hcrypto/libtommath/bn_mp_complement.c @@ -0,0 +1,12 @@ +#include "tommath_private.h" +#ifdef BN_MP_COMPLEMENT_C +/* LibTomMath, multiple-precision integer library -- Tom St Denis */ +/* SPDX-License-Identifier: Unlicense */ + +/* b = ~a */ +mp_err mp_complement(const mp_int *a, mp_int *b) +{ + mp_err err = mp_neg(a, b); + return (err == MP_OKAY) ? mp_sub_d(b, 1uL, b) : err; +} +#endif diff --git a/lib/hcrypto/libtommath/bn_mp_copy.c b/lib/hcrypto/libtommath/bn_mp_copy.c index b0de16d8abff..e72fcf6d53f1 100644 --- a/lib/hcrypto/libtommath/bn_mp_copy.c +++ b/lib/hcrypto/libtommath/bn_mp_copy.c @@ -1,68 +1,47 @@ -#include <tommath.h> +#include "tommath_private.h" #ifdef BN_MP_COPY_C -/* LibTomMath, multiple-precision integer library -- Tom St Denis - * - * LibTomMath is a library that provides multiple-precision - * integer arithmetic as well as number theoretic functionality. - * - * The library was designed directly after the MPI library by - * Michael Fromberger but has been written from scratch with - * additional optimizations in place. - * - * The library is free for all purposes without any express - * guarantee it works. - * - * Tom St Denis, tomstdenis@gmail.com, http://libtom.org - */ +/* LibTomMath, multiple-precision integer library -- Tom St Denis */ +/* SPDX-License-Identifier: Unlicense */ /* copy, b = a */ -int -mp_copy (mp_int * a, mp_int * b) +mp_err mp_copy(const mp_int *a, mp_int *b) { - int res, n; + int n; + mp_digit *tmpa, *tmpb; + mp_err err; - /* if dst == src do nothing */ - if (a == b) { - return MP_OKAY; - } + /* if dst == src do nothing */ + if (a == b) { + return MP_OKAY; + } - /* grow dest */ - if (b->alloc < a->used) { - if ((res = mp_grow (b, a->used)) != MP_OKAY) { - return res; - } - } + /* grow dest */ + if (b->alloc < a->used) { + if ((err = mp_grow(b, a->used)) != MP_OKAY) { + return err; + } + } - /* zero b and copy the parameters over */ - { - register mp_digit *tmpa, *tmpb; + /* zero b and copy the parameters over */ + /* pointer aliases */ - /* pointer aliases */ + /* source */ + tmpa = a->dp; - /* source */ - tmpa = a->dp; + /* destination */ + tmpb = b->dp; - /* destination */ - tmpb = b->dp; - - /* copy all the digits */ - for (n = 0; n < a->used; n++) { + /* copy all the digits */ + for (n = 0; n < a->used; n++) { *tmpb++ = *tmpa++; - } + } - /* clear high digits */ - for (; n < b->used; n++) { - *tmpb++ = 0; - } - } + /* clear high digits */ + MP_ZERO_DIGITS(tmpb, b->used - n); - /* copy used count and sign */ - b->used = a->used; - b->sign = a->sign; - return MP_OKAY; + /* copy used count and sign */ + b->used = a->used; + b->sign = a->sign; + return MP_OKAY; } #endif - -/* $Source: /cvs/libtom/libtommath/bn_mp_copy.c,v $ */ -/* $Revision: 1.4 $ */ -/* $Date: 2006/12/28 01:25:13 $ */ diff --git a/lib/hcrypto/libtommath/bn_mp_count_bits.c b/lib/hcrypto/libtommath/bn_mp_count_bits.c index 5dfd5f375cb6..b7c2cad101da 100644 --- a/lib/hcrypto/libtommath/bn_mp_count_bits.c +++ b/lib/hcrypto/libtommath/bn_mp_count_bits.c @@ -1,45 +1,28 @@ -#include <tommath.h> +#include "tommath_private.h" #ifdef BN_MP_COUNT_BITS_C -/* LibTomMath, multiple-precision integer library -- Tom St Denis - * - * LibTomMath is a library that provides multiple-precision - * integer arithmetic as well as number theoretic functionality. - * - * The library was designed directly after the MPI library by - * Michael Fromberger but has been written from scratch with - * additional optimizations in place. - * - * The library is free for all purposes without any express - * guarantee it works. - * - * Tom St Denis, tomstdenis@gmail.com, http://libtom.org - */ +/* LibTomMath, multiple-precision integer library -- Tom St Denis */ +/* SPDX-License-Identifier: Unlicense */ /* returns the number of bits in an int */ -int -mp_count_bits (mp_int * a) +int mp_count_bits(const mp_int *a) { - int r; - mp_digit q; + int r; + mp_digit q; - /* shortcut */ - if (a->used == 0) { - return 0; - } + /* shortcut */ + if (MP_IS_ZERO(a)) { + return 0; + } - /* get number of digits and add that */ - r = (a->used - 1) * DIGIT_BIT; + /* get number of digits and add that */ + r = (a->used - 1) * MP_DIGIT_BIT; - /* take the last digit and count the bits in it */ - q = a->dp[a->used - 1]; - while (q > ((mp_digit) 0)) { - ++r; - q >>= ((mp_digit) 1); - } - return r; + /* take the last digit and count the bits in it */ + q = a->dp[a->used - 1]; + while (q > 0u) { + ++r; + q >>= 1u; + } + return r; } #endif - -/* $Source: /cvs/libtom/libtommath/bn_mp_count_bits.c,v $ */ -/* $Revision: 1.4 $ */ -/* $Date: 2006/12/28 01:25:13 $ */ diff --git a/lib/hcrypto/libtommath/bn_mp_decr.c b/lib/hcrypto/libtommath/bn_mp_decr.c new file mode 100644 index 000000000000..c6a1572c6e3f --- /dev/null +++ b/lib/hcrypto/libtommath/bn_mp_decr.c @@ -0,0 +1,34 @@ +#include "tommath_private.h" +#ifdef BN_MP_DECR_C +/* LibTomMath, multiple-precision integer library -- Tom St Denis */ +/* SPDX-License-Identifier: Unlicense */ + +/* Decrement "a" by one like "a--". Changes input! */ +mp_err mp_decr(mp_int *a) +{ + if (MP_IS_ZERO(a)) { + mp_set(a,1uL); + a->sign = MP_NEG; + return MP_OKAY; + } else if (a->sign == MP_NEG) { + mp_err err; + a->sign = MP_ZPOS; + if ((err = mp_incr(a)) != MP_OKAY) { + return err; + } + /* There is no -0 in LTM */ + if (!MP_IS_ZERO(a)) { + a->sign = MP_NEG; + } + return MP_OKAY; + } else if (a->dp[0] > 1uL) { + a->dp[0]--; + if (a->dp[0] == 0u) { + mp_zero(a); + } + return MP_OKAY; + } else { + return mp_sub_d(a, 1uL,a); + } +} +#endif diff --git a/lib/hcrypto/libtommath/bn_mp_div.c b/lib/hcrypto/libtommath/bn_mp_div.c index 2c364b396fc0..71de55beaeb9 100644 --- a/lib/hcrypto/libtommath/bn_mp_div.c +++ b/lib/hcrypto/libtommath/bn_mp_div.c @@ -1,88 +1,71 @@ -#include <tommath.h> +#include "tommath_private.h" #ifdef BN_MP_DIV_C -/* LibTomMath, multiple-precision integer library -- Tom St Denis - * - * LibTomMath is a library that provides multiple-precision - * integer arithmetic as well as number theoretic functionality. - * - * The library was designed directly after the MPI library by - * Michael Fromberger but has been written from scratch with - * additional optimizations in place. - * - * The library is free for all purposes without any express - * guarantee it works. - * - * Tom St Denis, tomstdenis@gmail.com, http://libtom.org - */ +/* LibTomMath, multiple-precision integer library -- Tom St Denis */ +/* SPDX-License-Identifier: Unlicense */ #ifdef BN_MP_DIV_SMALL /* slower bit-bang division... also smaller */ -int mp_div(mp_int * a, mp_int * b, mp_int * c, mp_int * d) +mp_err mp_div(const mp_int *a, const mp_int *b, mp_int *c, mp_int *d) { mp_int ta, tb, tq, q; - int res, n, n2; - - /* is divisor zero ? */ - if (mp_iszero (b) == 1) { - return MP_VAL; - } - - /* if a < b then q=0, r = a */ - if (mp_cmp_mag (a, b) == MP_LT) { - if (d != NULL) { - res = mp_copy (a, d); - } else { - res = MP_OKAY; - } - if (c != NULL) { - mp_zero (c); - } - return res; - } - - /* init our temps */ - if ((res = mp_init_multi(&ta, &tb, &tq, &q, NULL) != MP_OKAY)) { - return res; - } - - - mp_set(&tq, 1); - n = mp_count_bits(a) - mp_count_bits(b); - if (((res = mp_abs(a, &ta)) != MP_OKAY) || - ((res = mp_abs(b, &tb)) != MP_OKAY) || - ((res = mp_mul_2d(&tb, n, &tb)) != MP_OKAY) || - ((res = mp_mul_2d(&tq, n, &tq)) != MP_OKAY)) { - goto LBL_ERR; - } - - while (n-- >= 0) { - if (mp_cmp(&tb, &ta) != MP_GT) { - if (((res = mp_sub(&ta, &tb, &ta)) != MP_OKAY) || - ((res = mp_add(&q, &tq, &q)) != MP_OKAY)) { - goto LBL_ERR; - } - } - if (((res = mp_div_2d(&tb, 1, &tb, NULL)) != MP_OKAY) || - ((res = mp_div_2d(&tq, 1, &tq, NULL)) != MP_OKAY)) { - goto LBL_ERR; - } - } - - /* now q == quotient and ta == remainder */ - n = a->sign; - n2 = (a->sign == b->sign ? MP_ZPOS : MP_NEG); - if (c != NULL) { - mp_exch(c, &q); - c->sign = (mp_iszero(c) == MP_YES) ? MP_ZPOS : n2; - } - if (d != NULL) { - mp_exch(d, &ta); - d->sign = (mp_iszero(d) == MP_YES) ? MP_ZPOS : n; - } + int n, n2; + mp_err err; + + /* is divisor zero ? */ + if (MP_IS_ZERO(b)) { + return MP_VAL; + } + + /* if a < b then q=0, r = a */ + if (mp_cmp_mag(a, b) == MP_LT) { + if (d != NULL) { + err = mp_copy(a, d); + } else { + err = MP_OKAY; + } + if (c != NULL) { + mp_zero(c); + } + return err; + } + + /* init our temps */ + if ((err = mp_init_multi(&ta, &tb, &tq, &q, NULL)) != MP_OKAY) { + return err; + } + + + mp_set(&tq, 1uL); + n = mp_count_bits(a) - mp_count_bits(b); + if ((err = mp_abs(a, &ta)) != MP_OKAY) goto LBL_ERR; + if ((err = mp_abs(b, &tb)) != MP_OKAY) goto LBL_ERR; + if ((err = mp_mul_2d(&tb, n, &tb)) != MP_OKAY) goto LBL_ERR; + if ((err = mp_mul_2d(&tq, n, &tq)) != MP_OKAY) goto LBL_ERR; + + while (n-- >= 0) { + if (mp_cmp(&tb, &ta) != MP_GT) { + if ((err = mp_sub(&ta, &tb, &ta)) != MP_OKAY) goto LBL_ERR; + if ((err = mp_add(&q, &tq, &q)) != MP_OKAY) goto LBL_ERR; + } + if ((err = mp_div_2d(&tb, 1, &tb, NULL)) != MP_OKAY) goto LBL_ERR; + if ((err = mp_div_2d(&tq, 1, &tq, NULL)) != MP_OKAY) goto LBL_ERR; + } + + /* now q == quotient and ta == remainder */ + n = a->sign; + n2 = (a->sign == b->sign) ? MP_ZPOS : MP_NEG; + if (c != NULL) { + mp_exch(c, &q); + c->sign = MP_IS_ZERO(c) ? MP_ZPOS : n2; + } + if (d != NULL) { + mp_exch(d, &ta); + d->sign = MP_IS_ZERO(d) ? MP_ZPOS : n; + } LBL_ERR: mp_clear_multi(&ta, &tb, &tq, &q, NULL); - return res; + return err; } #else @@ -100,193 +83,168 @@ LBL_ERR: * The overall algorithm is as described as * 14.20 from HAC but fixed to treat these cases. */ -int mp_div (mp_int * a, mp_int * b, mp_int * c, mp_int * d) +mp_err mp_div(const mp_int *a, const mp_int *b, mp_int *c, mp_int *d) { - mp_int q, x, y, t1, t2; - int res, n, t, i, norm, neg; - - /* is divisor zero ? */ - if (mp_iszero (b) == 1) { - return MP_VAL; - } - - /* if a < b then q=0, r = a */ - if (mp_cmp_mag (a, b) == MP_LT) { - if (d != NULL) { - res = mp_copy (a, d); - } else { - res = MP_OKAY; - } - if (c != NULL) { - mp_zero (c); - } - return res; - } - - if ((res = mp_init_size (&q, a->used + 2)) != MP_OKAY) { - return res; - } - q.used = a->used + 2; - - if ((res = mp_init (&t1)) != MP_OKAY) { - goto LBL_Q; - } - - if ((res = mp_init (&t2)) != MP_OKAY) { - goto LBL_T1; - } - - if ((res = mp_init_copy (&x, a)) != MP_OKAY) { - goto LBL_T2; - } - - if ((res = mp_init_copy (&y, b)) != MP_OKAY) { - goto LBL_X; - } - - /* fix the sign */ - neg = (a->sign == b->sign) ? MP_ZPOS : MP_NEG; - x.sign = y.sign = MP_ZPOS; - - /* normalize both x and y, ensure that y >= b/2, [b == 2**DIGIT_BIT] */ - norm = mp_count_bits(&y) % DIGIT_BIT; - if (norm < (int)(DIGIT_BIT-1)) { - norm = (DIGIT_BIT-1) - norm; - if ((res = mp_mul_2d (&x, norm, &x)) != MP_OKAY) { - goto LBL_Y; - } - if ((res = mp_mul_2d (&y, norm, &y)) != MP_OKAY) { - goto LBL_Y; - } - } else { - norm = 0; - } - - /* note hac does 0 based, so if used==5 then its 0,1,2,3,4, e.g. use 4 */ - n = x.used - 1; - t = y.used - 1; - - /* while (x >= y*b**n-t) do { q[n-t] += 1; x -= y*b**{n-t} } */ - if ((res = mp_lshd (&y, n - t)) != MP_OKAY) { /* y = y*b**{n-t} */ - goto LBL_Y; - } - - while (mp_cmp (&x, &y) != MP_LT) { - ++(q.dp[n - t]); - if ((res = mp_sub (&x, &y, &x)) != MP_OKAY) { - goto LBL_Y; - } - } - - /* reset y by shifting it back down */ - mp_rshd (&y, n - t); - - /* step 3. for i from n down to (t + 1) */ - for (i = n; i >= (t + 1); i--) { - if (i > x.used) { - continue; - } - - /* step 3.1 if xi == yt then set q{i-t-1} to b-1, - * otherwise set q{i-t-1} to (xi*b + x{i-1})/yt */ - if (x.dp[i] == y.dp[t]) { - q.dp[i - t - 1] = ((((mp_digit)1) << DIGIT_BIT) - 1); - } else { - mp_word tmp; - tmp = ((mp_word) x.dp[i]) << ((mp_word) DIGIT_BIT); - tmp |= ((mp_word) x.dp[i - 1]); - tmp /= ((mp_word) y.dp[t]); - if (tmp > (mp_word) MP_MASK) - tmp = MP_MASK; - q.dp[i - t - 1] = (mp_digit) (tmp & (mp_word) (MP_MASK)); - } - - /* while (q{i-t-1} * (yt * b + y{t-1})) > - xi * b**2 + xi-1 * b + xi-2 - - do q{i-t-1} -= 1; - */ - q.dp[i - t - 1] = (q.dp[i - t - 1] + 1) & MP_MASK; - do { - q.dp[i - t - 1] = (q.dp[i - t - 1] - 1) & MP_MASK; - - /* find left hand */ - mp_zero (&t1); - t1.dp[0] = (t - 1 < 0) ? 0 : y.dp[t - 1]; - t1.dp[1] = y.dp[t]; - t1.used = 2; - if ((res = mp_mul_d (&t1, q.dp[i - t - 1], &t1)) != MP_OKAY) { - goto LBL_Y; + mp_int q, x, y, t1, t2; + int n, t, i, norm; + mp_sign neg; + mp_err err; + + /* is divisor zero ? */ + if (MP_IS_ZERO(b)) { + return MP_VAL; + } + + /* if a < b then q=0, r = a */ + if (mp_cmp_mag(a, b) == MP_LT) { + if (d != NULL) { + err = mp_copy(a, d); + } else { + err = MP_OKAY; } - - /* find right hand */ - t2.dp[0] = (i - 2 < 0) ? 0 : x.dp[i - 2]; - t2.dp[1] = (i - 1 < 0) ? 0 : x.dp[i - 1]; - t2.dp[2] = x.dp[i]; - t2.used = 3; - } while (mp_cmp_mag(&t1, &t2) == MP_GT); - - /* step 3.3 x = x - q{i-t-1} * y * b**{i-t-1} */ - if ((res = mp_mul_d (&y, q.dp[i - t - 1], &t1)) != MP_OKAY) { - goto LBL_Y; - } - - if ((res = mp_lshd (&t1, i - t - 1)) != MP_OKAY) { - goto LBL_Y; - } - - if ((res = mp_sub (&x, &t1, &x)) != MP_OKAY) { - goto LBL_Y; - } - - /* if x < 0 then { x = x + y*b**{i-t-1}; q{i-t-1} -= 1; } */ - if (x.sign == MP_NEG) { - if ((res = mp_copy (&y, &t1)) != MP_OKAY) { - goto LBL_Y; + if (c != NULL) { + mp_zero(c); } - if ((res = mp_lshd (&t1, i - t - 1)) != MP_OKAY) { - goto LBL_Y; + return err; + } + + if ((err = mp_init_size(&q, a->used + 2)) != MP_OKAY) { + return err; + } + q.used = a->used + 2; + + if ((err = mp_init(&t1)) != MP_OKAY) goto LBL_Q; + + if ((err = mp_init(&t2)) != MP_OKAY) goto LBL_T1; + + if ((err = mp_init_copy(&x, a)) != MP_OKAY) goto LBL_T2; + + if ((err = mp_init_copy(&y, b)) != MP_OKAY) goto LBL_X; + + /* fix the sign */ + neg = (a->sign == b->sign) ? MP_ZPOS : MP_NEG; + x.sign = y.sign = MP_ZPOS; + + /* normalize both x and y, ensure that y >= b/2, [b == 2**MP_DIGIT_BIT] */ + norm = mp_count_bits(&y) % MP_DIGIT_BIT; + if (norm < (MP_DIGIT_BIT - 1)) { + norm = (MP_DIGIT_BIT - 1) - norm; + if ((err = mp_mul_2d(&x, norm, &x)) != MP_OKAY) goto LBL_Y; + if ((err = mp_mul_2d(&y, norm, &y)) != MP_OKAY) goto LBL_Y; + } else { + norm = 0; + } + + /* note hac does 0 based, so if used==5 then its 0,1,2,3,4, e.g. use 4 */ + n = x.used - 1; + t = y.used - 1; + + /* while (x >= y*b**n-t) do { q[n-t] += 1; x -= y*b**{n-t} } */ + /* y = y*b**{n-t} */ + if ((err = mp_lshd(&y, n - t)) != MP_OKAY) goto LBL_Y; + + while (mp_cmp(&x, &y) != MP_LT) { + ++(q.dp[n - t]); + if ((err = mp_sub(&x, &y, &x)) != MP_OKAY) goto LBL_Y; + } + + /* reset y by shifting it back down */ + mp_rshd(&y, n - t); + + /* step 3. for i from n down to (t + 1) */ + for (i = n; i >= (t + 1); i--) { + if (i > x.used) { + continue; } - if ((res = mp_add (&x, &t1, &x)) != MP_OKAY) { - goto LBL_Y; + + /* step 3.1 if xi == yt then set q{i-t-1} to b-1, + * otherwise set q{i-t-1} to (xi*b + x{i-1})/yt */ + if (x.dp[i] == y.dp[t]) { + q.dp[(i - t) - 1] = ((mp_digit)1 << (mp_digit)MP_DIGIT_BIT) - (mp_digit)1; + } else { + mp_word tmp; + tmp = (mp_word)x.dp[i] << (mp_word)MP_DIGIT_BIT; + tmp |= (mp_word)x.dp[i - 1]; + tmp /= (mp_word)y.dp[t]; + if (tmp > (mp_word)MP_MASK) { + tmp = MP_MASK; + } + q.dp[(i - t) - 1] = (mp_digit)(tmp & (mp_word)MP_MASK); } - q.dp[i - t - 1] = (q.dp[i - t - 1] - 1UL) & MP_MASK; - } - } + /* while (q{i-t-1} * (yt * b + y{t-1})) > + xi * b**2 + xi-1 * b + xi-2 - /* now q is the quotient and x is the remainder - * [which we have to normalize] - */ + do q{i-t-1} -= 1; + */ + q.dp[(i - t) - 1] = (q.dp[(i - t) - 1] + 1uL) & (mp_digit)MP_MASK; + do { + q.dp[(i - t) - 1] = (q.dp[(i - t) - 1] - 1uL) & (mp_digit)MP_MASK; - /* get sign before writing to c */ - x.sign = x.used == 0 ? MP_ZPOS : a->sign; + /* find left hand */ + mp_zero(&t1); + t1.dp[0] = ((t - 1) < 0) ? 0u : y.dp[t - 1]; + t1.dp[1] = y.dp[t]; + t1.used = 2; + if ((err = mp_mul_d(&t1, q.dp[(i - t) - 1], &t1)) != MP_OKAY) goto LBL_Y; - if (c != NULL) { - mp_clamp (&q); - mp_exch (&q, c); - c->sign = neg; - } + /* find right hand */ + t2.dp[0] = ((i - 2) < 0) ? 0u : x.dp[i - 2]; + t2.dp[1] = x.dp[i - 1]; /* i >= 1 always holds */ + t2.dp[2] = x.dp[i]; + t2.used = 3; + } while (mp_cmp_mag(&t1, &t2) == MP_GT); - if (d != NULL) { - mp_div_2d (&x, norm, &x, NULL); - mp_exch (&x, d); - } + /* step 3.3 x = x - q{i-t-1} * y * b**{i-t-1} */ + if ((err = mp_mul_d(&y, q.dp[(i - t) - 1], &t1)) != MP_OKAY) goto LBL_Y; - res = MP_OKAY; + if ((err = mp_lshd(&t1, (i - t) - 1)) != MP_OKAY) goto LBL_Y; -LBL_Y:mp_clear (&y); -LBL_X:mp_clear (&x); -LBL_T2:mp_clear (&t2); -LBL_T1:mp_clear (&t1); -LBL_Q:mp_clear (&q); - return res; + if ((err = mp_sub(&x, &t1, &x)) != MP_OKAY) goto LBL_Y; + + /* if x < 0 then { x = x + y*b**{i-t-1}; q{i-t-1} -= 1; } */ + if (x.sign == MP_NEG) { + if ((err = mp_copy(&y, &t1)) != MP_OKAY) goto LBL_Y; + if ((err = mp_lshd(&t1, (i - t) - 1)) != MP_OKAY) goto LBL_Y; + if ((err = mp_add(&x, &t1, &x)) != MP_OKAY) goto LBL_Y; + + q.dp[(i - t) - 1] = (q.dp[(i - t) - 1] - 1uL) & MP_MASK; + } + } + + /* now q is the quotient and x is the remainder + * [which we have to normalize] + */ + + /* get sign before writing to c */ + x.sign = (x.used == 0) ? MP_ZPOS : a->sign; + + if (c != NULL) { + mp_clamp(&q); + mp_exch(&q, c); + c->sign = neg; + } + + if (d != NULL) { + if ((err = mp_div_2d(&x, norm, &x, NULL)) != MP_OKAY) goto LBL_Y; + mp_exch(&x, d); + } + + err = MP_OKAY; + +LBL_Y: + mp_clear(&y); +LBL_X: + mp_clear(&x); +LBL_T2: + mp_clear(&t2); +LBL_T1: + mp_clear(&t1); +LBL_Q: + mp_clear(&q); + return err; } #endif #endif - -/* $Source: /cvs/libtom/libtommath/bn_mp_div.c,v $ */ -/* $Revision: 1.4 $ */ -/* $Date: 2006/12/28 01:25:13 $ */ diff --git a/lib/hcrypto/libtommath/bn_mp_div_2.c b/lib/hcrypto/libtommath/bn_mp_div_2.c index 7ee3e5b70fd7..f56ea8199928 100644 --- a/lib/hcrypto/libtommath/bn_mp_div_2.c +++ b/lib/hcrypto/libtommath/bn_mp_div_2.c @@ -1,68 +1,49 @@ -#include <tommath.h> +#include "tommath_private.h" #ifdef BN_MP_DIV_2_C -/* LibTomMath, multiple-precision integer library -- Tom St Denis - * - * LibTomMath is a library that provides multiple-precision - * integer arithmetic as well as number theoretic functionality. - * - * The library was designed directly after the MPI library by - * Michael Fromberger but has been written from scratch with - * additional optimizations in place. - * - * The library is free for all purposes without any express - * guarantee it works. - * - * Tom St Denis, tomstdenis@gmail.com, http://libtom.org - */ +/* LibTomMath, multiple-precision integer library -- Tom St Denis */ +/* SPDX-License-Identifier: Unlicense */ /* b = a/2 */ -int mp_div_2(mp_int * a, mp_int * b) +mp_err mp_div_2(const mp_int *a, mp_int *b) { - int x, res, oldused; + int x, oldused; + mp_digit r, rr, *tmpa, *tmpb; + mp_err err; - /* copy */ - if (b->alloc < a->used) { - if ((res = mp_grow (b, a->used)) != MP_OKAY) { - return res; - } - } + /* copy */ + if (b->alloc < a->used) { + if ((err = mp_grow(b, a->used)) != MP_OKAY) { + return err; + } + } - oldused = b->used; - b->used = a->used; - { - register mp_digit r, rr, *tmpa, *tmpb; + oldused = b->used; + b->used = a->used; - /* source alias */ - tmpa = a->dp + b->used - 1; + /* source alias */ + tmpa = a->dp + b->used - 1; - /* dest alias */ - tmpb = b->dp + b->used - 1; + /* dest alias */ + tmpb = b->dp + b->used - 1; - /* carry */ - r = 0; - for (x = b->used - 1; x >= 0; x--) { + /* carry */ + r = 0; + for (x = b->used - 1; x >= 0; x--) { /* get the carry for the next iteration */ - rr = *tmpa & 1; + rr = *tmpa & 1u; /* shift the current digit, add in carry and store */ - *tmpb-- = (*tmpa-- >> 1) | (r << (DIGIT_BIT - 1)); + *tmpb-- = (*tmpa-- >> 1) | (r << (MP_DIGIT_BIT - 1)); /* forward carry to next iteration */ r = rr; - } + } - /* zero excess digits */ - tmpb = b->dp + b->used; - for (x = b->used; x < oldused; x++) { - *tmpb++ = 0; - } - } - b->sign = a->sign; - mp_clamp (b); - return MP_OKAY; + /* zero excess digits */ + MP_ZERO_DIGITS(b->dp + b->used, oldused - b->used); + + b->sign = a->sign; + mp_clamp(b); + return MP_OKAY; } #endif - -/* $Source: /cvs/libtom/libtommath/bn_mp_div_2.c,v $ */ -/* $Revision: 1.4 $ */ -/* $Date: 2006/12/28 01:25:13 $ */ diff --git a/lib/hcrypto/libtommath/bn_mp_div_2d.c b/lib/hcrypto/libtommath/bn_mp_div_2d.c index 4f7fa59e3f32..c47d5ce35d63 100644 --- a/lib/hcrypto/libtommath/bn_mp_div_2d.c +++ b/lib/hcrypto/libtommath/bn_mp_div_2d.c @@ -1,97 +1,71 @@ -#include <tommath.h> +#include "tommath_private.h" #ifdef BN_MP_DIV_2D_C -/* LibTomMath, multiple-precision integer library -- Tom St Denis - * - * LibTomMath is a library that provides multiple-precision - * integer arithmetic as well as number theoretic functionality. - * - * The library was designed directly after the MPI library by - * Michael Fromberger but has been written from scratch with - * additional optimizations in place. - * - * The library is free for all purposes without any express - * guarantee it works. - * - * Tom St Denis, tomstdenis@gmail.com, http://libtom.org - */ +/* LibTomMath, multiple-precision integer library -- Tom St Denis */ +/* SPDX-License-Identifier: Unlicense */ /* shift right by a certain bit count (store quotient in c, optional remainder in d) */ -int mp_div_2d (mp_int * a, int b, mp_int * c, mp_int * d) +mp_err mp_div_2d(const mp_int *a, int b, mp_int *c, mp_int *d) { - mp_digit D, r, rr; - int x, res; - mp_int t; + mp_digit D, r, rr; + int x; + mp_err err; + /* if the shift count is <= 0 then we do no work */ + if (b <= 0) { + err = mp_copy(a, c); + if (d != NULL) { + mp_zero(d); + } + return err; + } - /* if the shift count is <= 0 then we do no work */ - if (b <= 0) { - res = mp_copy (a, c); - if (d != NULL) { - mp_zero (d); - } - return res; - } + /* copy */ + if ((err = mp_copy(a, c)) != MP_OKAY) { + return err; + } + /* 'a' should not be used after here - it might be the same as d */ - if ((res = mp_init (&t)) != MP_OKAY) { - return res; - } + /* get the remainder */ + if (d != NULL) { + if ((err = mp_mod_2d(a, b, d)) != MP_OKAY) { + return err; + } + } - /* get the remainder */ - if (d != NULL) { - if ((res = mp_mod_2d (a, b, &t)) != MP_OKAY) { - mp_clear (&t); - return res; - } - } + /* shift by as many digits in the bit count */ + if (b >= MP_DIGIT_BIT) { + mp_rshd(c, b / MP_DIGIT_BIT); + } - /* copy */ - if ((res = mp_copy (a, c)) != MP_OKAY) { - mp_clear (&t); - return res; - } + /* shift any bit count < MP_DIGIT_BIT */ + D = (mp_digit)(b % MP_DIGIT_BIT); + if (D != 0u) { + mp_digit *tmpc, mask, shift; - /* shift by as many digits in the bit count */ - if (b >= (int)DIGIT_BIT) { - mp_rshd (c, b / DIGIT_BIT); - } + /* mask */ + mask = ((mp_digit)1 << D) - 1uL; - /* shift any bit count < DIGIT_BIT */ - D = (mp_digit) (b % DIGIT_BIT); - if (D != 0) { - register mp_digit *tmpc, mask, shift; + /* shift for lsb */ + shift = (mp_digit)MP_DIGIT_BIT - D; - /* mask */ - mask = (((mp_digit)1) << D) - 1; + /* alias */ + tmpc = c->dp + (c->used - 1); - /* shift for lsb */ - shift = DIGIT_BIT - D; + /* carry */ + r = 0; + for (x = c->used - 1; x >= 0; x--) { + /* get the lower bits of this word in a temp */ + rr = *tmpc & mask; - /* alias */ - tmpc = c->dp + (c->used - 1); + /* shift the current word and mix in the carry bits from the previous word */ + *tmpc = (*tmpc >> D) | (r << shift); + --tmpc; - /* carry */ - r = 0; - for (x = c->used - 1; x >= 0; x--) { - /* get the lower bits of this word in a temp */ - rr = *tmpc & mask; - - /* shift the current word and mix in the carry bits from the previous word */ - *tmpc = (*tmpc >> D) | (r << shift); - --tmpc; - - /* set the carry to the carry bits of the current word found above */ - r = rr; - } - } - mp_clamp (c); - if (d != NULL) { - mp_exch (&t, d); - } - mp_clear (&t); - return MP_OKAY; + /* set the carry to the carry bits of the current word found above */ + r = rr; + } + } + mp_clamp(c); + return MP_OKAY; } #endif - -/* $Source: /cvs/libtom/libtommath/bn_mp_div_2d.c,v $ */ -/* $Revision: 1.4 $ */ -/* $Date: 2006/12/28 01:25:13 $ */ diff --git a/lib/hcrypto/libtommath/bn_mp_div_3.c b/lib/hcrypto/libtommath/bn_mp_div_3.c index 78e2381b6e73..3a23fdff2fbb 100644 --- a/lib/hcrypto/libtommath/bn_mp_div_3.c +++ b/lib/hcrypto/libtommath/bn_mp_div_3.c @@ -1,79 +1,63 @@ -#include <tommath.h> +#include "tommath_private.h" #ifdef BN_MP_DIV_3_C -/* LibTomMath, multiple-precision integer library -- Tom St Denis - * - * LibTomMath is a library that provides multiple-precision - * integer arithmetic as well as number theoretic functionality. - * - * The library was designed directly after the MPI library by - * Michael Fromberger but has been written from scratch with - * additional optimizations in place. - * - * The library is free for all purposes without any express - * guarantee it works. - * - * Tom St Denis, tomstdenis@gmail.com, http://libtom.org - */ +/* LibTomMath, multiple-precision integer library -- Tom St Denis */ +/* SPDX-License-Identifier: Unlicense */ /* divide by three (based on routine from MPI and the GMP manual) */ -int -mp_div_3 (mp_int * a, mp_int *c, mp_digit * d) +mp_err mp_div_3(const mp_int *a, mp_int *c, mp_digit *d) { - mp_int q; - mp_word w, t; - mp_digit b; - int res, ix; - - /* b = 2**DIGIT_BIT / 3 */ - b = (((mp_word)1) << ((mp_word)DIGIT_BIT)) / ((mp_word)3); - - if ((res = mp_init_size(&q, a->used)) != MP_OKAY) { - return res; - } - - q.used = a->used; - q.sign = a->sign; - w = 0; - for (ix = a->used - 1; ix >= 0; ix--) { - w = (w << ((mp_word)DIGIT_BIT)) | ((mp_word)a->dp[ix]); - - if (w >= 3) { - /* multiply w by [1/3] */ - t = (w * ((mp_word)b)) >> ((mp_word)DIGIT_BIT); - - /* now subtract 3 * [w/3] from w, to get the remainder */ - w -= t+t+t; - - /* fixup the remainder as required since - * the optimization is not exact. - */ - while (w >= 3) { - t += 1; - w -= 3; - } + mp_int q; + mp_word w, t; + mp_digit b; + mp_err err; + int ix; + + /* b = 2**MP_DIGIT_BIT / 3 */ + b = ((mp_word)1 << (mp_word)MP_DIGIT_BIT) / (mp_word)3; + + if ((err = mp_init_size(&q, a->used)) != MP_OKAY) { + return err; + } + + q.used = a->used; + q.sign = a->sign; + w = 0; + for (ix = a->used - 1; ix >= 0; ix--) { + w = (w << (mp_word)MP_DIGIT_BIT) | (mp_word)a->dp[ix]; + + if (w >= 3u) { + /* multiply w by [1/3] */ + t = (w * (mp_word)b) >> (mp_word)MP_DIGIT_BIT; + + /* now subtract 3 * [w/3] from w, to get the remainder */ + w -= t+t+t; + + /* fixup the remainder as required since + * the optimization is not exact. + */ + while (w >= 3u) { + t += 1u; + w -= 3u; + } } else { - t = 0; + t = 0; } q.dp[ix] = (mp_digit)t; - } + } - /* [optional] store the remainder */ - if (d != NULL) { - *d = (mp_digit)w; - } + /* [optional] store the remainder */ + if (d != NULL) { + *d = (mp_digit)w; + } - /* [optional] store the quotient */ - if (c != NULL) { - mp_clamp(&q); - mp_exch(&q, c); - } - mp_clear(&q); + /* [optional] store the quotient */ + if (c != NULL) { + mp_clamp(&q); + mp_exch(&q, c); + } + mp_clear(&q); - return res; + return err; } #endif - -/* $Source: /cvs/libtom/libtommath/bn_mp_div_3.c,v $ */ -/* $Revision: 1.4 $ */ -/* $Date: 2006/12/28 01:25:13 $ */ diff --git a/lib/hcrypto/libtommath/bn_mp_div_d.c b/lib/hcrypto/libtommath/bn_mp_div_d.c index 7bd372c20d37..b9d718bb062a 100644 --- a/lib/hcrypto/libtommath/bn_mp_div_d.c +++ b/lib/hcrypto/libtommath/bn_mp_div_d.c @@ -1,115 +1,84 @@ -#include <tommath.h> +#include "tommath_private.h" #ifdef BN_MP_DIV_D_C -/* LibTomMath, multiple-precision integer library -- Tom St Denis - * - * LibTomMath is a library that provides multiple-precision - * integer arithmetic as well as number theoretic functionality. - * - * The library was designed directly after the MPI library by - * Michael Fromberger but has been written from scratch with - * additional optimizations in place. - * - * The library is free for all purposes without any express - * guarantee it works. - * - * Tom St Denis, tomstdenis@gmail.com, http://libtom.org - */ +/* LibTomMath, multiple-precision integer library -- Tom St Denis */ +/* SPDX-License-Identifier: Unlicense */ -static int s_is_power_of_two(mp_digit b, int *p) +/* single digit division (based on routine from MPI) */ +mp_err mp_div_d(const mp_int *a, mp_digit b, mp_int *c, mp_digit *d) { - int x; - - /* fast return if no power of two */ - if ((b==0) || (b & (b-1))) { - return 0; + mp_int q; + mp_word w; + mp_digit t; + mp_err err; + int ix; + + /* cannot divide by zero */ + if (b == 0u) { + return MP_VAL; } - for (x = 0; x < DIGIT_BIT; x++) { - if (b == (((mp_digit)1)<<x)) { - *p = x; - return 1; + /* quick outs */ + if ((b == 1u) || MP_IS_ZERO(a)) { + if (d != NULL) { + *d = 0; + } + if (c != NULL) { + return mp_copy(a, c); } + return MP_OKAY; } - return 0; -} - -/* single digit division (based on routine from MPI) */ -int mp_div_d (mp_int * a, mp_digit b, mp_int * c, mp_digit * d) -{ - mp_int q; - mp_word w; - mp_digit t; - int res, ix; - - /* cannot divide by zero */ - if (b == 0) { - return MP_VAL; - } - /* quick outs */ - if (b == 1 || mp_iszero(a) == 1) { - if (d != NULL) { - *d = 0; - } - if (c != NULL) { - return mp_copy(a, c); - } - return MP_OKAY; - } - - /* power of two ? */ - if (s_is_power_of_two(b, &ix) == 1) { - if (d != NULL) { - *d = a->dp[0] & ((((mp_digit)1)<<ix) - 1); - } - if (c != NULL) { - return mp_div_2d(a, ix, c, NULL); - } - return MP_OKAY; - } + /* power of two ? */ + if ((b & (b - 1u)) == 0u) { + ix = 1; + while ((ix < MP_DIGIT_BIT) && (b != (((mp_digit)1)<<ix))) { + ix++; + } + if (d != NULL) { + *d = a->dp[0] & (((mp_digit)1<<(mp_digit)ix) - 1uL); + } + if (c != NULL) { + return mp_div_2d(a, ix, c, NULL); + } + return MP_OKAY; + } -#ifdef BN_MP_DIV_3_C - /* three? */ - if (b == 3) { - return mp_div_3(a, c, d); - } -#endif + /* three? */ + if (MP_HAS(MP_DIV_3) && (b == 3u)) { + return mp_div_3(a, c, d); + } - /* no easy answer [c'est la vie]. Just division */ - if ((res = mp_init_size(&q, a->used)) != MP_OKAY) { - return res; - } + /* no easy answer [c'est la vie]. Just division */ + if ((err = mp_init_size(&q, a->used)) != MP_OKAY) { + return err; + } - q.used = a->used; - q.sign = a->sign; - w = 0; - for (ix = a->used - 1; ix >= 0; ix--) { - w = (w << ((mp_word)DIGIT_BIT)) | ((mp_word)a->dp[ix]); + q.used = a->used; + q.sign = a->sign; + w = 0; + for (ix = a->used - 1; ix >= 0; ix--) { + w = (w << (mp_word)MP_DIGIT_BIT) | (mp_word)a->dp[ix]; - if (w >= b) { - t = (mp_digit)(w / b); - w -= ((mp_word)t) * ((mp_word)b); + if (w >= b) { + t = (mp_digit)(w / b); + w -= (mp_word)t * (mp_word)b; } else { - t = 0; + t = 0; } - q.dp[ix] = (mp_digit)t; - } + q.dp[ix] = t; + } - if (d != NULL) { - *d = (mp_digit)w; - } + if (d != NULL) { + *d = (mp_digit)w; + } - if (c != NULL) { - mp_clamp(&q); - mp_exch(&q, c); - } - mp_clear(&q); + if (c != NULL) { + mp_clamp(&q); + mp_exch(&q, c); + } + mp_clear(&q); - return res; + return err; } #endif - -/* $Source: /cvs/libtom/libtommath/bn_mp_div_d.c,v $ */ -/* $Revision: 1.5 $ */ -/* $Date: 2007/01/09 04:44:32 $ */ diff --git a/lib/hcrypto/libtommath/bn_mp_dr_is_modulus.c b/lib/hcrypto/libtommath/bn_mp_dr_is_modulus.c index 52373440d836..83760eacca08 100644 --- a/lib/hcrypto/libtommath/bn_mp_dr_is_modulus.c +++ b/lib/hcrypto/libtommath/bn_mp_dr_is_modulus.c @@ -1,43 +1,27 @@ -#include <tommath.h> +#include "tommath_private.h" #ifdef BN_MP_DR_IS_MODULUS_C -/* LibTomMath, multiple-precision integer library -- Tom St Denis - * - * LibTomMath is a library that provides multiple-precision - * integer arithmetic as well as number theoretic functionality. - * - * The library was designed directly after the MPI library by - * Michael Fromberger but has been written from scratch with - * additional optimizations in place. - * - * The library is free for all purposes without any express - * guarantee it works. - * - * Tom St Denis, tomstdenis@gmail.com, http://libtom.org - */ +/* LibTomMath, multiple-precision integer library -- Tom St Denis */ +/* SPDX-License-Identifier: Unlicense */ /* determines if a number is a valid DR modulus */ -int mp_dr_is_modulus(mp_int *a) +mp_bool mp_dr_is_modulus(const mp_int *a) { int ix; /* must be at least two digits */ if (a->used < 2) { - return 0; + return MP_NO; } /* must be of the form b**k - a [a <= b] so all * but the first digit must be equal to -1 (mod b). */ for (ix = 1; ix < a->used; ix++) { - if (a->dp[ix] != MP_MASK) { - return 0; - } + if (a->dp[ix] != MP_MASK) { + return MP_NO; + } } - return 1; + return MP_YES; } #endif - -/* $Source: /cvs/libtom/libtommath/bn_mp_dr_is_modulus.c,v $ */ -/* $Revision: 1.4 $ */ -/* $Date: 2006/12/28 01:25:13 $ */ diff --git a/lib/hcrypto/libtommath/bn_mp_dr_reduce.c b/lib/hcrypto/libtommath/bn_mp_dr_reduce.c index e60b5784f162..ffc33a6b50e0 100644 --- a/lib/hcrypto/libtommath/bn_mp_dr_reduce.c +++ b/lib/hcrypto/libtommath/bn_mp_dr_reduce.c @@ -1,19 +1,7 @@ -#include <tommath.h> +#include "tommath_private.h" #ifdef BN_MP_DR_REDUCE_C -/* LibTomMath, multiple-precision integer library -- Tom St Denis - * - * LibTomMath is a library that provides multiple-precision - * integer arithmetic as well as number theoretic functionality. - * - * The library was designed directly after the MPI library by - * Michael Fromberger but has been written from scratch with - * additional optimizations in place. - * - * The library is free for all purposes without any express - * guarantee it works. - * - * Tom St Denis, tomstdenis@gmail.com, http://libtom.org - */ +/* LibTomMath, multiple-precision integer library -- Tom St Denis */ +/* SPDX-License-Identifier: Unlicense */ /* reduce "x" in place modulo "n" using the Diminished Radix algorithm. * @@ -29,66 +17,62 @@ * * Input x must be in the range 0 <= x <= (n-1)**2 */ -int -mp_dr_reduce (mp_int * x, mp_int * n, mp_digit k) +mp_err mp_dr_reduce(mp_int *x, const mp_int *n, mp_digit k) { - int err, i, m; - mp_word r; - mp_digit mu, *tmpx1, *tmpx2; + mp_err err; + int i, m; + mp_word r; + mp_digit mu, *tmpx1, *tmpx2; - /* m = digits in modulus */ - m = n->used; + /* m = digits in modulus */ + m = n->used; - /* ensure that "x" has at least 2m digits */ - if (x->alloc < m + m) { - if ((err = mp_grow (x, m + m)) != MP_OKAY) { - return err; - } - } + /* ensure that "x" has at least 2m digits */ + if (x->alloc < (m + m)) { + if ((err = mp_grow(x, m + m)) != MP_OKAY) { + return err; + } + } -/* top of loop, this is where the code resumes if - * another reduction pass is required. - */ + /* top of loop, this is where the code resumes if + * another reduction pass is required. + */ top: - /* aliases for digits */ - /* alias for lower half of x */ - tmpx1 = x->dp; + /* aliases for digits */ + /* alias for lower half of x */ + tmpx1 = x->dp; - /* alias for upper half of x, or x/B**m */ - tmpx2 = x->dp + m; + /* alias for upper half of x, or x/B**m */ + tmpx2 = x->dp + m; - /* set carry to zero */ - mu = 0; + /* set carry to zero */ + mu = 0; - /* compute (x mod B**m) + k * [x/B**m] inline and inplace */ - for (i = 0; i < m; i++) { - r = ((mp_word)*tmpx2++) * ((mp_word)k) + *tmpx1 + mu; + /* compute (x mod B**m) + k * [x/B**m] inline and inplace */ + for (i = 0; i < m; i++) { + r = ((mp_word)*tmpx2++ * (mp_word)k) + *tmpx1 + mu; *tmpx1++ = (mp_digit)(r & MP_MASK); - mu = (mp_digit)(r >> ((mp_word)DIGIT_BIT)); - } + mu = (mp_digit)(r >> ((mp_word)MP_DIGIT_BIT)); + } - /* set final carry */ - *tmpx1++ = mu; + /* set final carry */ + *tmpx1++ = mu; - /* zero words above m */ - for (i = m + 1; i < x->used; i++) { - *tmpx1++ = 0; - } + /* zero words above m */ + MP_ZERO_DIGITS(tmpx1, (x->used - m) - 1); - /* clamp, sub and return */ - mp_clamp (x); + /* clamp, sub and return */ + mp_clamp(x); - /* if x >= n then subtract and reduce again - * Each successive "recursion" makes the input smaller and smaller. - */ - if (mp_cmp_mag (x, n) != MP_LT) { - s_mp_sub(x, n, x); - goto top; - } - return MP_OKAY; + /* if x >= n then subtract and reduce again + * Each successive "recursion" makes the input smaller and smaller. + */ + if (mp_cmp_mag(x, n) != MP_LT) { + if ((err = s_mp_sub(x, n, x)) != MP_OKAY) { + return err; + } + goto top; + } + return MP_OKAY; } #endif - -/* $Source: /cvs/libtom/libtommath/bn_mp_dr_reduce.c,v $ */ -/* $Revision: 1.4 $ */ -/* $Date: 2006/12/28 01:25:13 $ */ diff --git a/lib/hcrypto/libtommath/bn_mp_dr_setup.c b/lib/hcrypto/libtommath/bn_mp_dr_setup.c index b7d5ed7c03e1..32d5f389074b 100644 --- a/lib/hcrypto/libtommath/bn_mp_dr_setup.c +++ b/lib/hcrypto/libtommath/bn_mp_dr_setup.c @@ -1,32 +1,15 @@ -#include <tommath.h> +#include "tommath_private.h" #ifdef BN_MP_DR_SETUP_C -/* LibTomMath, multiple-precision integer library -- Tom St Denis - * - * LibTomMath is a library that provides multiple-precision - * integer arithmetic as well as number theoretic functionality. - * - * The library was designed directly after the MPI library by - * Michael Fromberger but has been written from scratch with - * additional optimizations in place. - * - * The library is free for all purposes without any express - * guarantee it works. - * - * Tom St Denis, tomstdenis@gmail.com, http://libtom.org - */ +/* LibTomMath, multiple-precision integer library -- Tom St Denis */ +/* SPDX-License-Identifier: Unlicense */ /* determines the setup value */ -void mp_dr_setup(mp_int *a, mp_digit *d) +void mp_dr_setup(const mp_int *a, mp_digit *d) { - /* the casts are required if DIGIT_BIT is one less than - * the number of bits in a mp_digit [e.g. DIGIT_BIT==31] + /* the casts are required if MP_DIGIT_BIT is one less than + * the number of bits in a mp_digit [e.g. MP_DIGIT_BIT==31] */ - *d = (mp_digit)((((mp_word)1) << ((mp_word)DIGIT_BIT)) - - ((mp_word)a->dp[0])); + *d = (mp_digit)(((mp_word)1 << (mp_word)MP_DIGIT_BIT) - (mp_word)a->dp[0]); } #endif - -/* $Source: /cvs/libtom/libtommath/bn_mp_dr_setup.c,v $ */ -/* $Revision: 1.4 $ */ -/* $Date: 2006/12/28 01:25:13 $ */ diff --git a/lib/hcrypto/libtommath/bn_mp_error_to_string.c b/lib/hcrypto/libtommath/bn_mp_error_to_string.c new file mode 100644 index 000000000000..2e2adb0f2a37 --- /dev/null +++ b/lib/hcrypto/libtommath/bn_mp_error_to_string.c @@ -0,0 +1,27 @@ +#include "tommath_private.h" +#ifdef BN_MP_ERROR_TO_STRING_C +/* LibTomMath, multiple-precision integer library -- Tom St Denis */ +/* SPDX-License-Identifier: Unlicense */ + +/* return a char * string for a given code */ +const char *mp_error_to_string(mp_err code) +{ + switch (code) { + case MP_OKAY: + return "Successful"; + case MP_ERR: + return "Unknown error"; + case MP_MEM: + return "Out of heap"; + case MP_VAL: + return "Value out of range"; + case MP_ITER: + return "Max. iterations reached"; + case MP_BUF: + return "Buffer overflow"; + default: + return "Invalid error code"; + } +} + +#endif diff --git a/lib/hcrypto/libtommath/bn_mp_exch.c b/lib/hcrypto/libtommath/bn_mp_exch.c index ee551bc3e196..552094c6b523 100644 --- a/lib/hcrypto/libtommath/bn_mp_exch.c +++ b/lib/hcrypto/libtommath/bn_mp_exch.c @@ -1,34 +1,17 @@ -#include <tommath.h> +#include "tommath_private.h" #ifdef BN_MP_EXCH_C -/* LibTomMath, multiple-precision integer library -- Tom St Denis - * - * LibTomMath is a library that provides multiple-precision - * integer arithmetic as well as number theoretic functionality. - * - * The library was designed directly after the MPI library by - * Michael Fromberger but has been written from scratch with - * additional optimizations in place. - * - * The library is free for all purposes without any express - * guarantee it works. - * - * Tom St Denis, tomstdenis@gmail.com, http://libtom.org - */ +/* LibTomMath, multiple-precision integer library -- Tom St Denis */ +/* SPDX-License-Identifier: Unlicense */ /* swap the elements of two integers, for cases where you can't simply swap the * mp_int pointers around */ -void -mp_exch (mp_int * a, mp_int * b) +void mp_exch(mp_int *a, mp_int *b) { - mp_int t; + mp_int t; - t = *a; - *a = *b; - *b = t; + t = *a; + *a = *b; + *b = t; } #endif - -/* $Source: /cvs/libtom/libtommath/bn_mp_exch.c,v $ */ -/* $Revision: 1.4 $ */ -/* $Date: 2006/12/28 01:25:13 $ */ diff --git a/lib/hcrypto/libtommath/bn_mp_expt_d.c b/lib/hcrypto/libtommath/bn_mp_expt_d.c deleted file mode 100644 index 4bdc2d13a695..000000000000 --- a/lib/hcrypto/libtommath/bn_mp_expt_d.c +++ /dev/null @@ -1,57 +0,0 @@ -#include <tommath.h> -#ifdef BN_MP_EXPT_D_C -/* LibTomMath, multiple-precision integer library -- Tom St Denis - * - * LibTomMath is a library that provides multiple-precision - * integer arithmetic as well as number theoretic functionality. - * - * The library was designed directly after the MPI library by - * Michael Fromberger but has been written from scratch with - * additional optimizations in place. - * - * The library is free for all purposes without any express - * guarantee it works. - * - * Tom St Denis, tomstdenis@gmail.com, http://libtom.org - */ - -/* calculate c = a**b using a square-multiply algorithm */ -int mp_expt_d (mp_int * a, mp_digit b, mp_int * c) -{ - int res, x; - mp_int g; - - if ((res = mp_init_copy (&g, a)) != MP_OKAY) { - return res; - } - - /* set initial result */ - mp_set (c, 1); - - for (x = 0; x < (int) DIGIT_BIT; x++) { - /* square */ - if ((res = mp_sqr (c, c)) != MP_OKAY) { - mp_clear (&g); - return res; - } - - /* if the bit is set multiply */ - if ((b & (mp_digit) (((mp_digit)1) << (DIGIT_BIT - 1))) != 0) { - if ((res = mp_mul (c, &g, c)) != MP_OKAY) { - mp_clear (&g); - return res; - } - } - - /* shift to next bit */ - b <<= 1; - } - - mp_clear (&g); - return MP_OKAY; -} -#endif - -/* $Source: /cvs/libtom/libtommath/bn_mp_expt_d.c,v $ */ -/* $Revision: 1.4 $ */ -/* $Date: 2006/12/28 01:25:13 $ */ diff --git a/lib/hcrypto/libtommath/bn_mp_expt_u32.c b/lib/hcrypto/libtommath/bn_mp_expt_u32.c new file mode 100644 index 000000000000..2ab67ba5320b --- /dev/null +++ b/lib/hcrypto/libtommath/bn_mp_expt_u32.c @@ -0,0 +1,46 @@ +#include "tommath_private.h" +#ifdef BN_MP_EXPT_U32_C +/* LibTomMath, multiple-precision integer library -- Tom St Denis */ +/* SPDX-License-Identifier: Unlicense */ + +/* calculate c = a**b using a square-multiply algorithm */ +mp_err mp_expt_u32(const mp_int *a, uint32_t b, mp_int *c) +{ + mp_err err; + + mp_int g; + + if ((err = mp_init_copy(&g, a)) != MP_OKAY) { + return err; + } + + /* set initial result */ + mp_set(c, 1uL); + + while (b > 0u) { + /* if the bit is set multiply */ + if ((b & 1u) != 0u) { + if ((err = mp_mul(c, &g, c)) != MP_OKAY) { + goto LBL_ERR; + } + } + + /* square */ + if (b > 1u) { + if ((err = mp_sqr(&g, &g)) != MP_OKAY) { + goto LBL_ERR; + } + } + + /* shift to next bit */ + b >>= 1; + } + + err = MP_OKAY; + +LBL_ERR: + mp_clear(&g); + return err; +} + +#endif diff --git a/lib/hcrypto/libtommath/bn_mp_exptmod.c b/lib/hcrypto/libtommath/bn_mp_exptmod.c index 56d7c11d26e4..5f811ebd87a4 100644 --- a/lib/hcrypto/libtommath/bn_mp_exptmod.c +++ b/lib/hcrypto/libtommath/bn_mp_exptmod.c @@ -1,112 +1,76 @@ -#include <tommath.h> +#include "tommath_private.h" #ifdef BN_MP_EXPTMOD_C -/* LibTomMath, multiple-precision integer library -- Tom St Denis - * - * LibTomMath is a library that provides multiple-precision - * integer arithmetic as well as number theoretic functionality. - * - * The library was designed directly after the MPI library by - * Michael Fromberger but has been written from scratch with - * additional optimizations in place. - * - * The library is free for all purposes without any express - * guarantee it works. - * - * Tom St Denis, tomstdenis@gmail.com, http://libtom.org - */ - +/* LibTomMath, multiple-precision integer library -- Tom St Denis */ +/* SPDX-License-Identifier: Unlicense */ /* this is a shell function that calls either the normal or Montgomery * exptmod functions. Originally the call to the montgomery code was * embedded in the normal function but that wasted alot of stack space * for nothing (since 99% of the time the Montgomery code would be called) */ -int mp_exptmod (mp_int * G, mp_int * X, mp_int * P, mp_int * Y) +mp_err mp_exptmod(const mp_int *G, const mp_int *X, const mp_int *P, mp_int *Y) { - int dr; + int dr; - /* modulus P must be positive */ - if (P->sign == MP_NEG) { - return MP_VAL; - } + /* modulus P must be positive */ + if (P->sign == MP_NEG) { + return MP_VAL; + } - /* if exponent X is negative we have to recurse */ - if (X->sign == MP_NEG) { -#ifdef BN_MP_INVMOD_C - mp_int tmpG, tmpX; - int err; + /* if exponent X is negative we have to recurse */ + if (X->sign == MP_NEG) { + mp_int tmpG, tmpX; + mp_err err; - /* first compute 1/G mod P */ - if ((err = mp_init(&tmpG)) != MP_OKAY) { - return err; - } - if ((err = mp_invmod(G, P, &tmpG)) != MP_OKAY) { - mp_clear(&tmpG); - return err; - } + if (!MP_HAS(MP_INVMOD)) { + return MP_VAL; + } - /* now get |X| */ - if ((err = mp_init(&tmpX)) != MP_OKAY) { - mp_clear(&tmpG); - return err; - } - if ((err = mp_abs(X, &tmpX)) != MP_OKAY) { - mp_clear_multi(&tmpG, &tmpX, NULL); - return err; - } + if ((err = mp_init_multi(&tmpG, &tmpX, NULL)) != MP_OKAY) { + return err; + } - /* and now compute (1/G)**|X| instead of G**X [X < 0] */ - err = mp_exptmod(&tmpG, &tmpX, P, Y); - mp_clear_multi(&tmpG, &tmpX, NULL); - return err; -#else - /* no invmod */ - return MP_VAL; -#endif - } + /* first compute 1/G mod P */ + if ((err = mp_invmod(G, P, &tmpG)) != MP_OKAY) { + goto LBL_ERR; + } -/* modified diminished radix reduction */ -#if defined(BN_MP_REDUCE_IS_2K_L_C) && defined(BN_MP_REDUCE_2K_L_C) && defined(BN_S_MP_EXPTMOD_C) - if (mp_reduce_is_2k_l(P) == MP_YES) { - return s_mp_exptmod(G, X, P, Y, 1); - } -#endif + /* now get |X| */ + if ((err = mp_abs(X, &tmpX)) != MP_OKAY) { + goto LBL_ERR; + } -#ifdef BN_MP_DR_IS_MODULUS_C - /* is it a DR modulus? */ - dr = mp_dr_is_modulus(P); -#else - /* default to no */ - dr = 0; -#endif + /* and now compute (1/G)**|X| instead of G**X [X < 0] */ + err = mp_exptmod(&tmpG, &tmpX, P, Y); +LBL_ERR: + mp_clear_multi(&tmpG, &tmpX, NULL); + return err; + } -#ifdef BN_MP_REDUCE_IS_2K_C - /* if not, is it a unrestricted DR modulus? */ - if (dr == 0) { - dr = mp_reduce_is_2k(P) << 1; - } -#endif + /* modified diminished radix reduction */ + if (MP_HAS(MP_REDUCE_IS_2K_L) && MP_HAS(MP_REDUCE_2K_L) && MP_HAS(S_MP_EXPTMOD) && + (mp_reduce_is_2k_l(P) == MP_YES)) { + return s_mp_exptmod(G, X, P, Y, 1); + } - /* if the modulus is odd or dr != 0 use the montgomery method */ -#ifdef BN_MP_EXPTMOD_FAST_C - if (mp_isodd (P) == 1 || dr != 0) { - return mp_exptmod_fast (G, X, P, Y, dr); - } else { -#endif -#ifdef BN_S_MP_EXPTMOD_C - /* otherwise use the generic Barrett reduction technique */ - return s_mp_exptmod (G, X, P, Y, 0); -#else - /* no exptmod for evens */ - return MP_VAL; -#endif -#ifdef BN_MP_EXPTMOD_FAST_C - } -#endif + /* is it a DR modulus? default to no */ + dr = (MP_HAS(MP_DR_IS_MODULUS) && (mp_dr_is_modulus(P) == MP_YES)) ? 1 : 0; + + /* if not, is it a unrestricted DR modulus? */ + if (MP_HAS(MP_REDUCE_IS_2K) && (dr == 0)) { + dr = (mp_reduce_is_2k(P) == MP_YES) ? 2 : 0; + } + + /* if the modulus is odd or dr != 0 use the montgomery method */ + if (MP_HAS(S_MP_EXPTMOD_FAST) && (MP_IS_ODD(P) || (dr != 0))) { + return s_mp_exptmod_fast(G, X, P, Y, dr); + } else if (MP_HAS(S_MP_EXPTMOD)) { + /* otherwise use the generic Barrett reduction technique */ + return s_mp_exptmod(G, X, P, Y, 0); + } else { + /* no exptmod for evens */ + return MP_VAL; + } } #endif - -/* $Source: /cvs/libtom/libtommath/bn_mp_exptmod.c,v $ */ -/* $Revision: 1.5 $ */ -/* $Date: 2006/12/28 01:25:13 $ */ diff --git a/lib/hcrypto/libtommath/bn_mp_exptmod_fast.c b/lib/hcrypto/libtommath/bn_mp_exptmod_fast.c deleted file mode 100644 index 64fbe7fe2107..000000000000 --- a/lib/hcrypto/libtommath/bn_mp_exptmod_fast.c +++ /dev/null @@ -1,321 +0,0 @@ -#include <tommath.h> -#ifdef BN_MP_EXPTMOD_FAST_C -/* LibTomMath, multiple-precision integer library -- Tom St Denis - * - * LibTomMath is a library that provides multiple-precision - * integer arithmetic as well as number theoretic functionality. - * - * The library was designed directly after the MPI library by - * Michael Fromberger but has been written from scratch with - * additional optimizations in place. - * - * The library is free for all purposes without any express - * guarantee it works. - * - * Tom St Denis, tomstdenis@gmail.com, http://libtom.org - */ - -/* computes Y == G**X mod P, HAC pp.616, Algorithm 14.85 - * - * Uses a left-to-right k-ary sliding window to compute the modular exponentiation. - * The value of k changes based on the size of the exponent. - * - * Uses Montgomery or Diminished Radix reduction [whichever appropriate] - */ - -#ifdef MP_LOW_MEM - #define TAB_SIZE 32 -#else - #define TAB_SIZE 256 -#endif - -int mp_exptmod_fast (mp_int * G, mp_int * X, mp_int * P, mp_int * Y, int redmode) -{ - mp_int M[TAB_SIZE], res; - mp_digit buf, mp; - int err, bitbuf, bitcpy, bitcnt, mode, digidx, x, y, winsize; - - /* use a pointer to the reduction algorithm. This allows us to use - * one of many reduction algorithms without modding the guts of - * the code with if statements everywhere. - */ - int (*redux)(mp_int*,mp_int*,mp_digit); - - /* find window size */ - x = mp_count_bits (X); - if (x <= 7) { - winsize = 2; - } else if (x <= 36) { - winsize = 3; - } else if (x <= 140) { - winsize = 4; - } else if (x <= 450) { - winsize = 5; - } else if (x <= 1303) { - winsize = 6; - } else if (x <= 3529) { - winsize = 7; - } else { - winsize = 8; - } - -#ifdef MP_LOW_MEM - if (winsize > 5) { - winsize = 5; - } -#endif - - /* init M array */ - /* init first cell */ - if ((err = mp_init(&M[1])) != MP_OKAY) { - return err; - } - - /* now init the second half of the array */ - for (x = 1<<(winsize-1); x < (1 << winsize); x++) { - if ((err = mp_init(&M[x])) != MP_OKAY) { - for (y = 1<<(winsize-1); y < x; y++) { - mp_clear (&M[y]); - } - mp_clear(&M[1]); - return err; - } - } - - /* determine and setup reduction code */ - if (redmode == 0) { -#ifdef BN_MP_MONTGOMERY_SETUP_C - /* now setup montgomery */ - if ((err = mp_montgomery_setup (P, &mp)) != MP_OKAY) { - goto LBL_M; - } -#else - err = MP_VAL; - goto LBL_M; -#endif - - /* automatically pick the comba one if available (saves quite a few calls/ifs) */ -#ifdef BN_FAST_MP_MONTGOMERY_REDUCE_C - if (((P->used * 2 + 1) < MP_WARRAY) && - P->used < (1 << ((CHAR_BIT * sizeof (mp_word)) - (2 * DIGIT_BIT)))) { - redux = fast_mp_montgomery_reduce; - } else -#endif - { -#ifdef BN_MP_MONTGOMERY_REDUCE_C - /* use slower baseline Montgomery method */ - redux = mp_montgomery_reduce; -#else - err = MP_VAL; - goto LBL_M; -#endif - } - } else if (redmode == 1) { -#if defined(BN_MP_DR_SETUP_C) && defined(BN_MP_DR_REDUCE_C) - /* setup DR reduction for moduli of the form B**k - b */ - mp_dr_setup(P, &mp); - redux = mp_dr_reduce; -#else - err = MP_VAL; - goto LBL_M; -#endif - } else { -#if defined(BN_MP_REDUCE_2K_SETUP_C) && defined(BN_MP_REDUCE_2K_C) - /* setup DR reduction for moduli of the form 2**k - b */ - if ((err = mp_reduce_2k_setup(P, &mp)) != MP_OKAY) { - goto LBL_M; - } - redux = mp_reduce_2k; -#else - err = MP_VAL; - goto LBL_M; -#endif - } - - /* setup result */ - if ((err = mp_init (&res)) != MP_OKAY) { - goto LBL_M; - } - - /* create M table - * - - * - * The first half of the table is not computed though accept for M[0] and M[1] - */ - - if (redmode == 0) { -#ifdef BN_MP_MONTGOMERY_CALC_NORMALIZATION_C - /* now we need R mod m */ - if ((err = mp_montgomery_calc_normalization (&res, P)) != MP_OKAY) { - goto LBL_RES; - } -#else - err = MP_VAL; - goto LBL_RES; -#endif - - /* now set M[1] to G * R mod m */ - if ((err = mp_mulmod (G, &res, P, &M[1])) != MP_OKAY) { - goto LBL_RES; - } - } else { - mp_set(&res, 1); - if ((err = mp_mod(G, P, &M[1])) != MP_OKAY) { - goto LBL_RES; - } - } - - /* compute the value at M[1<<(winsize-1)] by squaring M[1] (winsize-1) times */ - if ((err = mp_copy (&M[1], &M[1 << (winsize - 1)])) != MP_OKAY) { - goto LBL_RES; - } - - for (x = 0; x < (winsize - 1); x++) { - if ((err = mp_sqr (&M[1 << (winsize - 1)], &M[1 << (winsize - 1)])) != MP_OKAY) { - goto LBL_RES; - } - if ((err = redux (&M[1 << (winsize - 1)], P, mp)) != MP_OKAY) { - goto LBL_RES; - } - } - - /* create upper table */ - for (x = (1 << (winsize - 1)) + 1; x < (1 << winsize); x++) { - if ((err = mp_mul (&M[x - 1], &M[1], &M[x])) != MP_OKAY) { - goto LBL_RES; - } - if ((err = redux (&M[x], P, mp)) != MP_OKAY) { - goto LBL_RES; - } - } - - /* set initial mode and bit cnt */ - mode = 0; - bitcnt = 1; - buf = 0; - digidx = X->used - 1; - bitcpy = 0; - bitbuf = 0; - - for (;;) { - /* grab next digit as required */ - if (--bitcnt == 0) { - /* if digidx == -1 we are out of digits so break */ - if (digidx == -1) { - break; - } - /* read next digit and reset bitcnt */ - buf = X->dp[digidx--]; - bitcnt = (int)DIGIT_BIT; - } - - /* grab the next msb from the exponent */ - y = (mp_digit)(buf >> (DIGIT_BIT - 1)) & 1; - buf <<= (mp_digit)1; - - /* if the bit is zero and mode == 0 then we ignore it - * These represent the leading zero bits before the first 1 bit - * in the exponent. Technically this opt is not required but it - * does lower the # of trivial squaring/reductions used - */ - if (mode == 0 && y == 0) { - continue; - } - - /* if the bit is zero and mode == 1 then we square */ - if (mode == 1 && y == 0) { - if ((err = mp_sqr (&res, &res)) != MP_OKAY) { - goto LBL_RES; - } - if ((err = redux (&res, P, mp)) != MP_OKAY) { - goto LBL_RES; - } - continue; - } - - /* else we add it to the window */ - bitbuf |= (y << (winsize - ++bitcpy)); - mode = 2; - - if (bitcpy == winsize) { - /* ok window is filled so square as required and multiply */ - /* square first */ - for (x = 0; x < winsize; x++) { - if ((err = mp_sqr (&res, &res)) != MP_OKAY) { - goto LBL_RES; - } - if ((err = redux (&res, P, mp)) != MP_OKAY) { - goto LBL_RES; - } - } - - /* then multiply */ - if ((err = mp_mul (&res, &M[bitbuf], &res)) != MP_OKAY) { - goto LBL_RES; - } - if ((err = redux (&res, P, mp)) != MP_OKAY) { - goto LBL_RES; - } - - /* empty window and reset */ - bitcpy = 0; - bitbuf = 0; - mode = 1; - } - } - - /* if bits remain then square/multiply */ - if (mode == 2 && bitcpy > 0) { - /* square then multiply if the bit is set */ - for (x = 0; x < bitcpy; x++) { - if ((err = mp_sqr (&res, &res)) != MP_OKAY) { - goto LBL_RES; - } - if ((err = redux (&res, P, mp)) != MP_OKAY) { - goto LBL_RES; - } - - /* get next bit of the window */ - bitbuf <<= 1; - if ((bitbuf & (1 << winsize)) != 0) { - /* then multiply */ - if ((err = mp_mul (&res, &M[1], &res)) != MP_OKAY) { - goto LBL_RES; - } - if ((err = redux (&res, P, mp)) != MP_OKAY) { - goto LBL_RES; - } - } - } - } - - if (redmode == 0) { - /* fixup result if Montgomery reduction is used - * recall that any value in a Montgomery system is - * actually multiplied by R mod n. So we have - * to reduce one more time to cancel out the factor - * of R. - */ - if ((err = redux(&res, P, mp)) != MP_OKAY) { - goto LBL_RES; - } - } - - /* swap res with Y */ - mp_exch (&res, Y); - err = MP_OKAY; -LBL_RES:mp_clear (&res); -LBL_M: - mp_clear(&M[1]); - for (x = 1<<(winsize-1); x < (1 << winsize); x++) { - mp_clear (&M[x]); - } - return err; -} -#endif - - -/* $Source: /cvs/libtom/libtommath/bn_mp_exptmod_fast.c,v $ */ -/* $Revision: 1.4 $ */ -/* $Date: 2006/12/28 01:25:13 $ */ diff --git a/lib/hcrypto/libtommath/bn_mp_exteuclid.c b/lib/hcrypto/libtommath/bn_mp_exteuclid.c index daf0c95ea6ff..faf47ba6af19 100644 --- a/lib/hcrypto/libtommath/bn_mp_exteuclid.c +++ b/lib/hcrypto/libtommath/bn_mp_exteuclid.c @@ -1,82 +1,73 @@ -#include <tommath.h> +#include "tommath_private.h" #ifdef BN_MP_EXTEUCLID_C -/* LibTomMath, multiple-precision integer library -- Tom St Denis - * - * LibTomMath is a library that provides multiple-precision - * integer arithmetic as well as number theoretic functionality. - * - * The library was designed directly after the MPI library by - * Michael Fromberger but has been written from scratch with - * additional optimizations in place. - * - * The library is free for all purposes without any express - * guarantee it works. - * - * Tom St Denis, tomstdenis@gmail.com, http://libtom.org - */ +/* LibTomMath, multiple-precision integer library -- Tom St Denis */ +/* SPDX-License-Identifier: Unlicense */ /* Extended euclidean algorithm of (a, b) produces a*u1 + b*u2 = u3 */ -int mp_exteuclid(mp_int *a, mp_int *b, mp_int *U1, mp_int *U2, mp_int *U3) +mp_err mp_exteuclid(const mp_int *a, const mp_int *b, mp_int *U1, mp_int *U2, mp_int *U3) { - mp_int u1,u2,u3,v1,v2,v3,t1,t2,t3,q,tmp; - int err; + mp_int u1, u2, u3, v1, v2, v3, t1, t2, t3, q, tmp; + mp_err err; if ((err = mp_init_multi(&u1, &u2, &u3, &v1, &v2, &v3, &t1, &t2, &t3, &q, &tmp, NULL)) != MP_OKAY) { return err; } /* initialize, (u1,u2,u3) = (1,0,a) */ - mp_set(&u1, 1); - if ((err = mp_copy(a, &u3)) != MP_OKAY) { goto _ERR; } + mp_set(&u1, 1uL); + if ((err = mp_copy(a, &u3)) != MP_OKAY) goto LBL_ERR; /* initialize, (v1,v2,v3) = (0,1,b) */ - mp_set(&v2, 1); - if ((err = mp_copy(b, &v3)) != MP_OKAY) { goto _ERR; } + mp_set(&v2, 1uL); + if ((err = mp_copy(b, &v3)) != MP_OKAY) goto LBL_ERR; /* loop while v3 != 0 */ - while (mp_iszero(&v3) == MP_NO) { - /* q = u3/v3 */ - if ((err = mp_div(&u3, &v3, &q, NULL)) != MP_OKAY) { goto _ERR; } + while (!MP_IS_ZERO(&v3)) { + /* q = u3/v3 */ + if ((err = mp_div(&u3, &v3, &q, NULL)) != MP_OKAY) goto LBL_ERR; - /* (t1,t2,t3) = (u1,u2,u3) - (v1,v2,v3)q */ - if ((err = mp_mul(&v1, &q, &tmp)) != MP_OKAY) { goto _ERR; } - if ((err = mp_sub(&u1, &tmp, &t1)) != MP_OKAY) { goto _ERR; } - if ((err = mp_mul(&v2, &q, &tmp)) != MP_OKAY) { goto _ERR; } - if ((err = mp_sub(&u2, &tmp, &t2)) != MP_OKAY) { goto _ERR; } - if ((err = mp_mul(&v3, &q, &tmp)) != MP_OKAY) { goto _ERR; } - if ((err = mp_sub(&u3, &tmp, &t3)) != MP_OKAY) { goto _ERR; } + /* (t1,t2,t3) = (u1,u2,u3) - (v1,v2,v3)q */ + if ((err = mp_mul(&v1, &q, &tmp)) != MP_OKAY) goto LBL_ERR; + if ((err = mp_sub(&u1, &tmp, &t1)) != MP_OKAY) goto LBL_ERR; + if ((err = mp_mul(&v2, &q, &tmp)) != MP_OKAY) goto LBL_ERR; + if ((err = mp_sub(&u2, &tmp, &t2)) != MP_OKAY) goto LBL_ERR; + if ((err = mp_mul(&v3, &q, &tmp)) != MP_OKAY) goto LBL_ERR; + if ((err = mp_sub(&u3, &tmp, &t3)) != MP_OKAY) goto LBL_ERR; - /* (u1,u2,u3) = (v1,v2,v3) */ - if ((err = mp_copy(&v1, &u1)) != MP_OKAY) { goto _ERR; } - if ((err = mp_copy(&v2, &u2)) != MP_OKAY) { goto _ERR; } - if ((err = mp_copy(&v3, &u3)) != MP_OKAY) { goto _ERR; } + /* (u1,u2,u3) = (v1,v2,v3) */ + if ((err = mp_copy(&v1, &u1)) != MP_OKAY) goto LBL_ERR; + if ((err = mp_copy(&v2, &u2)) != MP_OKAY) goto LBL_ERR; + if ((err = mp_copy(&v3, &u3)) != MP_OKAY) goto LBL_ERR; - /* (v1,v2,v3) = (t1,t2,t3) */ - if ((err = mp_copy(&t1, &v1)) != MP_OKAY) { goto _ERR; } - if ((err = mp_copy(&t2, &v2)) != MP_OKAY) { goto _ERR; } - if ((err = mp_copy(&t3, &v3)) != MP_OKAY) { goto _ERR; } + /* (v1,v2,v3) = (t1,t2,t3) */ + if ((err = mp_copy(&t1, &v1)) != MP_OKAY) goto LBL_ERR; + if ((err = mp_copy(&t2, &v2)) != MP_OKAY) goto LBL_ERR; + if ((err = mp_copy(&t3, &v3)) != MP_OKAY) goto LBL_ERR; } /* make sure U3 >= 0 */ if (u3.sign == MP_NEG) { - mp_neg(&u1, &u1); - mp_neg(&u2, &u2); - mp_neg(&u3, &u3); + if ((err = mp_neg(&u1, &u1)) != MP_OKAY) goto LBL_ERR; + if ((err = mp_neg(&u2, &u2)) != MP_OKAY) goto LBL_ERR; + if ((err = mp_neg(&u3, &u3)) != MP_OKAY) goto LBL_ERR; } /* copy result out */ - if (U1 != NULL) { mp_exch(U1, &u1); } - if (U2 != NULL) { mp_exch(U2, &u2); } - if (U3 != NULL) { mp_exch(U3, &u3); } + if (U1 != NULL) { + mp_exch(U1, &u1); + } + if (U2 != NULL) { + mp_exch(U2, &u2); + } + if (U3 != NULL) { + mp_exch(U3, &u3); + } err = MP_OKAY; -_ERR: mp_clear_multi(&u1, &u2, &u3, &v1, &v2, &v3, &t1, &t2, &t3, &q, &tmp, NULL); +LBL_ERR: + mp_clear_multi(&u1, &u2, &u3, &v1, &v2, &v3, &t1, &t2, &t3, &q, &tmp, NULL); return err; } #endif - -/* $Source: /cvs/libtom/libtommath/bn_mp_exteuclid.c,v $ */ -/* $Revision: 1.4 $ */ -/* $Date: 2006/12/28 01:25:13 $ */ diff --git a/lib/hcrypto/libtommath/bn_mp_find_prime.c b/lib/hcrypto/libtommath/bn_mp_find_prime.c deleted file mode 100644 index 29ef8747d623..000000000000 --- a/lib/hcrypto/libtommath/bn_mp_find_prime.c +++ /dev/null @@ -1,36 +0,0 @@ -/* TomsFastMath, a fast ISO C bignum library. - * - * This project is public domain and free for all purposes. - * - * Love Hornquist Astrand <lha@h5l.org> - */ -#include <tommath.h> -#ifdef BN_MP_FIND_PRIME_C -int mp_find_prime(mp_int *a, int t) -{ - int res = MP_NO; - - /* valid value of t? */ - if (t <= 0 || t > PRIME_SIZE) { - return MP_VAL; - } - - if (mp_iseven(a)) - mp_add_d(a, 1, a); - - do { - if (mp_prime_is_prime(a, t, &res) != 0) { - res = MP_VAL; - break; - } - - if (res == MP_NO) { - mp_add_d(a, 2, a); - continue; - } - - } while (res != MP_YES); - - return res; -} -#endif diff --git a/lib/hcrypto/libtommath/bn_mp_fread.c b/lib/hcrypto/libtommath/bn_mp_fread.c index 52f7f32f0d10..52ea773e4909 100644 --- a/lib/hcrypto/libtommath/bn_mp_fread.c +++ b/lib/hcrypto/libtommath/bn_mp_fread.c @@ -1,67 +1,60 @@ -#include <tommath.h> +#include "tommath_private.h" #ifdef BN_MP_FREAD_C -/* LibTomMath, multiple-precision integer library -- Tom St Denis - * - * LibTomMath is a library that provides multiple-precision - * integer arithmetic as well as number theoretic functionality. - * - * The library was designed directly after the MPI library by - * Michael Fromberger but has been written from scratch with - * additional optimizations in place. - * - * The library is free for all purposes without any express - * guarantee it works. - * - * Tom St Denis, tomstdenis@gmail.com, http://libtom.org - */ +/* LibTomMath, multiple-precision integer library -- Tom St Denis */ +/* SPDX-License-Identifier: Unlicense */ +#ifndef MP_NO_FILE /* read a bigint from a file stream in ASCII */ -int mp_fread(mp_int *a, int radix, FILE *stream) +mp_err mp_fread(mp_int *a, int radix, FILE *stream) { - int err, ch, neg, y; - - /* clear a */ - mp_zero(a); + mp_err err; + mp_sign neg; /* if first digit is - then set negative */ - ch = fgetc(stream); - if (ch == '-') { + int ch = fgetc(stream); + if (ch == (int)'-') { neg = MP_NEG; ch = fgetc(stream); } else { neg = MP_ZPOS; } - for (;;) { - /* find y in the radix map */ - for (y = 0; y < radix; y++) { - if (mp_s_rmap[y] == ch) { - break; - } + /* no digits, return error */ + if (ch == EOF) { + return MP_ERR; + } + + /* clear a */ + mp_zero(a); + + do { + int y; + unsigned pos = (unsigned)(ch - (int)'('); + if (mp_s_rmap_reverse_sz < pos) { + break; } - if (y == radix) { + + y = (int)mp_s_rmap_reverse[pos]; + + if ((y == 0xff) || (y >= radix)) { break; } /* shift up and add */ - if ((err = mp_mul_d(a, radix, a)) != MP_OKAY) { + if ((err = mp_mul_d(a, (mp_digit)radix, a)) != MP_OKAY) { return err; } - if ((err = mp_add_d(a, y, a)) != MP_OKAY) { + if ((err = mp_add_d(a, (mp_digit)y, a)) != MP_OKAY) { return err; } + } while ((ch = fgetc(stream)) != EOF); - ch = fgetc(stream); - } - if (mp_cmp_d(a, 0) != MP_EQ) { + if (a->used != 0) { a->sign = neg; } return MP_OKAY; } - #endif -/* $Source: /cvs/libtom/libtommath/bn_mp_fread.c,v $ */ -/* $Revision: 1.4 $ */ -/* $Date: 2006/12/28 01:25:13 $ */ +#endif diff --git a/lib/hcrypto/libtommath/bn_mp_from_sbin.c b/lib/hcrypto/libtommath/bn_mp_from_sbin.c new file mode 100644 index 000000000000..20e45971ecb1 --- /dev/null +++ b/lib/hcrypto/libtommath/bn_mp_from_sbin.c @@ -0,0 +1,25 @@ +#include "tommath_private.h" +#ifdef BN_MP_FROM_SBIN_C +/* LibTomMath, multiple-precision integer library -- Tom St Denis */ +/* SPDX-License-Identifier: Unlicense */ + +/* read signed bin, big endian, first byte is 0==positive or 1==negative */ +mp_err mp_from_sbin(mp_int *a, const unsigned char *buf, size_t size) +{ + mp_err err; + + /* read magnitude */ + if ((err = mp_from_ubin(a, buf + 1, size - 1u)) != MP_OKAY) { + return err; + } + + /* first byte is 0 for positive, non-zero for negative */ + if (buf[0] == (unsigned char)0) { + a->sign = MP_ZPOS; + } else { + a->sign = MP_NEG; + } + + return MP_OKAY; +} +#endif diff --git a/lib/hcrypto/libtommath/bn_mp_from_ubin.c b/lib/hcrypto/libtommath/bn_mp_from_ubin.c new file mode 100644 index 000000000000..7f73cbccd507 --- /dev/null +++ b/lib/hcrypto/libtommath/bn_mp_from_ubin.c @@ -0,0 +1,39 @@ +#include "tommath_private.h" +#ifdef BN_MP_FROM_UBIN_C +/* LibTomMath, multiple-precision integer library -- Tom St Denis */ +/* SPDX-License-Identifier: Unlicense */ + +/* reads a unsigned char array, assumes the msb is stored first [big endian] */ +mp_err mp_from_ubin(mp_int *a, const unsigned char *buf, size_t size) +{ + mp_err err; + + /* make sure there are at least two digits */ + if (a->alloc < 2) { + if ((err = mp_grow(a, 2)) != MP_OKAY) { + return err; + } + } + + /* zero the int */ + mp_zero(a); + + /* read the bytes in */ + while (size-- > 0u) { + if ((err = mp_mul_2d(a, 8, a)) != MP_OKAY) { + return err; + } + +#ifndef MP_8BIT + a->dp[0] |= *buf++; + a->used += 1; +#else + a->dp[0] = (*buf & MP_MASK); + a->dp[1] |= ((*buf++ >> 7) & 1u); + a->used += 2; +#endif + } + mp_clamp(a); + return MP_OKAY; +} +#endif diff --git a/lib/hcrypto/libtommath/bn_mp_fwrite.c b/lib/hcrypto/libtommath/bn_mp_fwrite.c index dc4529ba2291..abe2e67176e2 100644 --- a/lib/hcrypto/libtommath/bn_mp_fwrite.c +++ b/lib/hcrypto/libtommath/bn_mp_fwrite.c @@ -1,52 +1,45 @@ -#include <tommath.h> +#include "tommath_private.h" #ifdef BN_MP_FWRITE_C -/* LibTomMath, multiple-precision integer library -- Tom St Denis - * - * LibTomMath is a library that provides multiple-precision - * integer arithmetic as well as number theoretic functionality. - * - * The library was designed directly after the MPI library by - * Michael Fromberger but has been written from scratch with - * additional optimizations in place. - * - * The library is free for all purposes without any express - * guarantee it works. - * - * Tom St Denis, tomstdenis@gmail.com, http://libtom.org - */ - -int mp_fwrite(mp_int *a, int radix, FILE *stream) +/* LibTomMath, multiple-precision integer library -- Tom St Denis */ +/* SPDX-License-Identifier: Unlicense */ + +#ifndef MP_NO_FILE +mp_err mp_fwrite(const mp_int *a, int radix, FILE *stream) { char *buf; - int err, len, x; - - if ((err = mp_radix_size(a, radix, &len)) != MP_OKAY) { - return err; + mp_err err; + int len; + size_t written; + + /* TODO: this function is not in this PR */ + if (MP_HAS(MP_RADIX_SIZE_OVERESTIMATE)) { + /* if ((err = mp_radix_size_overestimate(&t, base, &len)) != MP_OKAY) goto LBL_ERR; */ + } else { + if ((err = mp_radix_size(a, radix, &len)) != MP_OKAY) { + return err; + } } - buf = OPT_CAST(char) XMALLOC (len); + buf = (char *) MP_MALLOC((size_t)len); if (buf == NULL) { return MP_MEM; } - if ((err = mp_toradix(a, buf, radix)) != MP_OKAY) { - XFREE (buf); - return err; + if ((err = mp_to_radix(a, buf, (size_t)len, &written, radix)) != MP_OKAY) { + goto LBL_ERR; } - for (x = 0; x < len; x++) { - if (fputc(buf[x], stream) == EOF) { - XFREE (buf); - return MP_VAL; - } + if (fwrite(buf, written, 1uL, stream) != 1uL) { + err = MP_ERR; + goto LBL_ERR; } + err = MP_OKAY; - XFREE (buf); - return MP_OKAY; -} +LBL_ERR: + MP_FREE_BUFFER(buf, (size_t)len); + return err; +} #endif -/* $Source: /cvs/libtom/libtommath/bn_mp_fwrite.c,v $ */ -/* $Revision: 1.4 $ */ -/* $Date: 2006/12/28 01:25:13 $ */ +#endif diff --git a/lib/hcrypto/libtommath/bn_mp_gcd.c b/lib/hcrypto/libtommath/bn_mp_gcd.c index 89795d564ed9..53029baf3043 100644 --- a/lib/hcrypto/libtommath/bn_mp_gcd.c +++ b/lib/hcrypto/libtommath/bn_mp_gcd.c @@ -1,105 +1,92 @@ -#include <tommath.h> +#include "tommath_private.h" #ifdef BN_MP_GCD_C -/* LibTomMath, multiple-precision integer library -- Tom St Denis - * - * LibTomMath is a library that provides multiple-precision - * integer arithmetic as well as number theoretic functionality. - * - * The library was designed directly after the MPI library by - * Michael Fromberger but has been written from scratch with - * additional optimizations in place. - * - * The library is free for all purposes without any express - * guarantee it works. - * - * Tom St Denis, tomstdenis@gmail.com, http://libtom.org - */ +/* LibTomMath, multiple-precision integer library -- Tom St Denis */ +/* SPDX-License-Identifier: Unlicense */ /* Greatest Common Divisor using the binary method */ -int mp_gcd (mp_int * a, mp_int * b, mp_int * c) +mp_err mp_gcd(const mp_int *a, const mp_int *b, mp_int *c) { - mp_int u, v; - int k, u_lsb, v_lsb, res; + mp_int u, v; + int k, u_lsb, v_lsb; + mp_err err; - /* either zero than gcd is the largest */ - if (mp_iszero (a) == MP_YES) { - return mp_abs (b, c); - } - if (mp_iszero (b) == MP_YES) { - return mp_abs (a, c); - } + /* either zero than gcd is the largest */ + if (MP_IS_ZERO(a)) { + return mp_abs(b, c); + } + if (MP_IS_ZERO(b)) { + return mp_abs(a, c); + } - /* get copies of a and b we can modify */ - if ((res = mp_init_copy (&u, a)) != MP_OKAY) { - return res; - } + /* get copies of a and b we can modify */ + if ((err = mp_init_copy(&u, a)) != MP_OKAY) { + return err; + } - if ((res = mp_init_copy (&v, b)) != MP_OKAY) { - goto LBL_U; - } + if ((err = mp_init_copy(&v, b)) != MP_OKAY) { + goto LBL_U; + } - /* must be positive for the remainder of the algorithm */ - u.sign = v.sign = MP_ZPOS; + /* must be positive for the remainder of the algorithm */ + u.sign = v.sign = MP_ZPOS; - /* B1. Find the common power of two for u and v */ - u_lsb = mp_cnt_lsb(&u); - v_lsb = mp_cnt_lsb(&v); - k = MIN(u_lsb, v_lsb); + /* B1. Find the common power of two for u and v */ + u_lsb = mp_cnt_lsb(&u); + v_lsb = mp_cnt_lsb(&v); + k = MP_MIN(u_lsb, v_lsb); - if (k > 0) { - /* divide the power of two out */ - if ((res = mp_div_2d(&u, k, &u, NULL)) != MP_OKAY) { - goto LBL_V; - } + if (k > 0) { + /* divide the power of two out */ + if ((err = mp_div_2d(&u, k, &u, NULL)) != MP_OKAY) { + goto LBL_V; + } - if ((res = mp_div_2d(&v, k, &v, NULL)) != MP_OKAY) { - goto LBL_V; - } - } + if ((err = mp_div_2d(&v, k, &v, NULL)) != MP_OKAY) { + goto LBL_V; + } + } - /* divide any remaining factors of two out */ - if (u_lsb != k) { - if ((res = mp_div_2d(&u, u_lsb - k, &u, NULL)) != MP_OKAY) { - goto LBL_V; - } - } + /* divide any remaining factors of two out */ + if (u_lsb != k) { + if ((err = mp_div_2d(&u, u_lsb - k, &u, NULL)) != MP_OKAY) { + goto LBL_V; + } + } - if (v_lsb != k) { - if ((res = mp_div_2d(&v, v_lsb - k, &v, NULL)) != MP_OKAY) { - goto LBL_V; - } - } + if (v_lsb != k) { + if ((err = mp_div_2d(&v, v_lsb - k, &v, NULL)) != MP_OKAY) { + goto LBL_V; + } + } - while (mp_iszero(&v) == 0) { - /* make sure v is the largest */ - if (mp_cmp_mag(&u, &v) == MP_GT) { - /* swap u and v to make sure v is >= u */ - mp_exch(&u, &v); - } + while (!MP_IS_ZERO(&v)) { + /* make sure v is the largest */ + if (mp_cmp_mag(&u, &v) == MP_GT) { + /* swap u and v to make sure v is >= u */ + mp_exch(&u, &v); + } - /* subtract smallest from largest */ - if ((res = s_mp_sub(&v, &u, &v)) != MP_OKAY) { - goto LBL_V; - } + /* subtract smallest from largest */ + if ((err = s_mp_sub(&v, &u, &v)) != MP_OKAY) { + goto LBL_V; + } - /* Divide out all factors of two */ - if ((res = mp_div_2d(&v, mp_cnt_lsb(&v), &v, NULL)) != MP_OKAY) { - goto LBL_V; - } - } + /* Divide out all factors of two */ + if ((err = mp_div_2d(&v, mp_cnt_lsb(&v), &v, NULL)) != MP_OKAY) { + goto LBL_V; + } + } - /* multiply by 2**k which we divided out at the beginning */ - if ((res = mp_mul_2d (&u, k, c)) != MP_OKAY) { - goto LBL_V; - } - c->sign = MP_ZPOS; - res = MP_OKAY; -LBL_V:mp_clear (&u); -LBL_U:mp_clear (&v); - return res; + /* multiply by 2**k which we divided out at the beginning */ + if ((err = mp_mul_2d(&u, k, c)) != MP_OKAY) { + goto LBL_V; + } + c->sign = MP_ZPOS; + err = MP_OKAY; +LBL_V: + mp_clear(&u); +LBL_U: + mp_clear(&v); + return err; } #endif - -/* $Source: /cvs/libtom/libtommath/bn_mp_gcd.c,v $ */ -/* $Revision: 1.5 $ */ -/* $Date: 2006/12/28 01:25:13 $ */ diff --git a/lib/hcrypto/libtommath/bn_mp_get_double.c b/lib/hcrypto/libtommath/bn_mp_get_double.c new file mode 100644 index 000000000000..c9b1b19f4fdd --- /dev/null +++ b/lib/hcrypto/libtommath/bn_mp_get_double.c @@ -0,0 +1,18 @@ +#include "tommath_private.h" +#ifdef BN_MP_GET_DOUBLE_C +/* LibTomMath, multiple-precision integer library -- Tom St Denis */ +/* SPDX-License-Identifier: Unlicense */ + +double mp_get_double(const mp_int *a) +{ + int i; + double d = 0.0, fac = 1.0; + for (i = 0; i < MP_DIGIT_BIT; ++i) { + fac *= 2.0; + } + for (i = a->used; i --> 0;) { + d = (d * fac) + (double)a->dp[i]; + } + return (a->sign == MP_NEG) ? -d : d; +} +#endif diff --git a/lib/hcrypto/libtommath/bn_mp_get_i32.c b/lib/hcrypto/libtommath/bn_mp_get_i32.c new file mode 100644 index 000000000000..030b657a326e --- /dev/null +++ b/lib/hcrypto/libtommath/bn_mp_get_i32.c @@ -0,0 +1,7 @@ +#include "tommath_private.h" +#ifdef BN_MP_GET_I32_C +/* LibTomMath, multiple-precision integer library -- Tom St Denis */ +/* SPDX-License-Identifier: Unlicense */ + +MP_GET_SIGNED(mp_get_i32, mp_get_mag_u32, int32_t, uint32_t) +#endif diff --git a/lib/hcrypto/libtommath/bn_mp_get_i64.c b/lib/hcrypto/libtommath/bn_mp_get_i64.c new file mode 100644 index 000000000000..969c8d23ca4f --- /dev/null +++ b/lib/hcrypto/libtommath/bn_mp_get_i64.c @@ -0,0 +1,7 @@ +#include "tommath_private.h" +#ifdef BN_MP_GET_I64_C +/* LibTomMath, multiple-precision integer library -- Tom St Denis */ +/* SPDX-License-Identifier: Unlicense */ + +MP_GET_SIGNED(mp_get_i64, mp_get_mag_u64, int64_t, uint64_t) +#endif diff --git a/lib/hcrypto/libtommath/bn_mp_get_int.c b/lib/hcrypto/libtommath/bn_mp_get_int.c deleted file mode 100644 index e8e9b1d44073..000000000000 --- a/lib/hcrypto/libtommath/bn_mp_get_int.c +++ /dev/null @@ -1,45 +0,0 @@ -#include <tommath.h> -#ifdef BN_MP_GET_INT_C -/* LibTomMath, multiple-precision integer library -- Tom St Denis - * - * LibTomMath is a library that provides multiple-precision - * integer arithmetic as well as number theoretic functionality. - * - * The library was designed directly after the MPI library by - * Michael Fromberger but has been written from scratch with - * additional optimizations in place. - * - * The library is free for all purposes without any express - * guarantee it works. - * - * Tom St Denis, tomstdenis@gmail.com, http://libtom.org - */ - -/* get the lower 32-bits of an mp_int */ -unsigned long mp_get_int(mp_int * a) -{ - int i; - unsigned long res; - - if (a->used == 0) { - return 0; - } - - /* get number of digits of the lsb we have to read */ - i = MIN(a->used,(int)((sizeof(unsigned long)*CHAR_BIT+DIGIT_BIT-1)/DIGIT_BIT))-1; - - /* get most significant digit of result */ - res = DIGIT(a,i); - - while (--i >= 0) { - res = (res << DIGIT_BIT) | DIGIT(a,i); - } - - /* force result to 32-bits always so it is consistent on non 32-bit platforms */ - return res & 0xFFFFFFFFUL; -} -#endif - -/* $Source: /cvs/libtom/libtommath/bn_mp_get_int.c,v $ */ -/* $Revision: 1.4 $ */ -/* $Date: 2006/12/28 01:25:13 $ */ diff --git a/lib/hcrypto/libtommath/bn_mp_get_l.c b/lib/hcrypto/libtommath/bn_mp_get_l.c new file mode 100644 index 000000000000..55d78ec034e3 --- /dev/null +++ b/lib/hcrypto/libtommath/bn_mp_get_l.c @@ -0,0 +1,7 @@ +#include "tommath_private.h" +#ifdef BN_MP_GET_L_C +/* LibTomMath, multiple-precision integer library -- Tom St Denis */ +/* SPDX-License-Identifier: Unlicense */ + +MP_GET_SIGNED(mp_get_l, mp_get_mag_ul, long, unsigned long) +#endif diff --git a/lib/hcrypto/libtommath/bn_mp_get_ll.c b/lib/hcrypto/libtommath/bn_mp_get_ll.c new file mode 100644 index 000000000000..268753490fdc --- /dev/null +++ b/lib/hcrypto/libtommath/bn_mp_get_ll.c @@ -0,0 +1,7 @@ +#include "tommath_private.h" +#ifdef BN_MP_GET_LL_C +/* LibTomMath, multiple-precision integer library -- Tom St Denis */ +/* SPDX-License-Identifier: Unlicense */ + +MP_GET_SIGNED(mp_get_ll, mp_get_mag_ull, long long, unsigned long long) +#endif diff --git a/lib/hcrypto/libtommath/bn_mp_get_mag_u32.c b/lib/hcrypto/libtommath/bn_mp_get_mag_u32.c new file mode 100644 index 000000000000..d77189be6d6b --- /dev/null +++ b/lib/hcrypto/libtommath/bn_mp_get_mag_u32.c @@ -0,0 +1,7 @@ +#include "tommath_private.h" +#ifdef BN_MP_GET_MAG_U32_C +/* LibTomMath, multiple-precision integer library -- Tom St Denis */ +/* SPDX-License-Identifier: Unlicense */ + +MP_GET_MAG(mp_get_mag_u32, uint32_t) +#endif diff --git a/lib/hcrypto/libtommath/bn_mp_get_mag_u64.c b/lib/hcrypto/libtommath/bn_mp_get_mag_u64.c new file mode 100644 index 000000000000..36dd73f6279b --- /dev/null +++ b/lib/hcrypto/libtommath/bn_mp_get_mag_u64.c @@ -0,0 +1,7 @@ +#include "tommath_private.h" +#ifdef BN_MP_GET_MAG_U64_C +/* LibTomMath, multiple-precision integer library -- Tom St Denis */ +/* SPDX-License-Identifier: Unlicense */ + +MP_GET_MAG(mp_get_mag_u64, uint64_t) +#endif diff --git a/lib/hcrypto/libtommath/bn_mp_get_mag_ul.c b/lib/hcrypto/libtommath/bn_mp_get_mag_ul.c new file mode 100644 index 000000000000..e8819aef64c4 --- /dev/null +++ b/lib/hcrypto/libtommath/bn_mp_get_mag_ul.c @@ -0,0 +1,7 @@ +#include "tommath_private.h" +#ifdef BN_MP_GET_MAG_UL_C +/* LibTomMath, multiple-precision integer library -- Tom St Denis */ +/* SPDX-License-Identifier: Unlicense */ + +MP_GET_MAG(mp_get_mag_ul, unsigned long) +#endif diff --git a/lib/hcrypto/libtommath/bn_mp_get_mag_ull.c b/lib/hcrypto/libtommath/bn_mp_get_mag_ull.c new file mode 100644 index 000000000000..63a27412c1d6 --- /dev/null +++ b/lib/hcrypto/libtommath/bn_mp_get_mag_ull.c @@ -0,0 +1,7 @@ +#include "tommath_private.h" +#ifdef BN_MP_GET_MAG_ULL_C +/* LibTomMath, multiple-precision integer library -- Tom St Denis */ +/* SPDX-License-Identifier: Unlicense */ + +MP_GET_MAG(mp_get_mag_ull, unsigned long long) +#endif diff --git a/lib/hcrypto/libtommath/bn_mp_grow.c b/lib/hcrypto/libtommath/bn_mp_grow.c index cf2b949b2483..9e904c547e11 100644 --- a/lib/hcrypto/libtommath/bn_mp_grow.c +++ b/lib/hcrypto/libtommath/bn_mp_grow.c @@ -1,57 +1,38 @@ -#include <tommath.h> +#include "tommath_private.h" #ifdef BN_MP_GROW_C -/* LibTomMath, multiple-precision integer library -- Tom St Denis - * - * LibTomMath is a library that provides multiple-precision - * integer arithmetic as well as number theoretic functionality. - * - * The library was designed directly after the MPI library by - * Michael Fromberger but has been written from scratch with - * additional optimizations in place. - * - * The library is free for all purposes without any express - * guarantee it works. - * - * Tom St Denis, tomstdenis@gmail.com, http://libtom.org - */ +/* LibTomMath, multiple-precision integer library -- Tom St Denis */ +/* SPDX-License-Identifier: Unlicense */ /* grow as required */ -int mp_grow (mp_int * a, int size) +mp_err mp_grow(mp_int *a, int size) { - int i; - mp_digit *tmp; + int i; + mp_digit *tmp; - /* if the alloc size is smaller alloc more ram */ - if (a->alloc < size) { - /* ensure there are always at least MP_PREC digits extra on top */ - size += (MP_PREC * 2) - (size % MP_PREC); + /* if the alloc size is smaller alloc more ram */ + if (a->alloc < size) { + /* reallocate the array a->dp + * + * We store the return in a temporary variable + * in case the operation failed we don't want + * to overwrite the dp member of a. + */ + tmp = (mp_digit *) MP_REALLOC(a->dp, + (size_t)a->alloc * sizeof(mp_digit), + (size_t)size * sizeof(mp_digit)); + if (tmp == NULL) { + /* reallocation failed but "a" is still valid [can be freed] */ + return MP_MEM; + } - /* reallocate the array a->dp - * - * We store the return in a temporary variable - * in case the operation failed we don't want - * to overwrite the dp member of a. - */ - tmp = OPT_CAST(mp_digit) XREALLOC (a->dp, sizeof (mp_digit) * size); - if (tmp == NULL) { - /* reallocation failed but "a" is still valid [can be freed] */ - return MP_MEM; - } + /* reallocation succeeded so set a->dp */ + a->dp = tmp; - /* reallocation succeeded so set a->dp */ - a->dp = tmp; - - /* zero excess digits */ - i = a->alloc; - a->alloc = size; - for (; i < a->alloc; i++) { - a->dp[i] = 0; - } - } - return MP_OKAY; + /* zero excess digits */ + i = a->alloc; + a->alloc = size; + MP_ZERO_DIGITS(a->dp + i, a->alloc - i); + } + return MP_OKAY; } #endif - -/* $Source: /cvs/libtom/libtommath/bn_mp_grow.c,v $ */ -/* $Revision: 1.4 $ */ -/* $Date: 2006/12/28 01:25:13 $ */ diff --git a/lib/hcrypto/libtommath/bn_mp_incr.c b/lib/hcrypto/libtommath/bn_mp_incr.c new file mode 100644 index 000000000000..7695ac73c15f --- /dev/null +++ b/lib/hcrypto/libtommath/bn_mp_incr.c @@ -0,0 +1,30 @@ +#include "tommath_private.h" +#ifdef BN_MP_INCR_C +/* LibTomMath, multiple-precision integer library -- Tom St Denis */ +/* SPDX-License-Identifier: Unlicense */ + +/* Increment "a" by one like "a++". Changes input! */ +mp_err mp_incr(mp_int *a) +{ + if (MP_IS_ZERO(a)) { + mp_set(a,1uL); + return MP_OKAY; + } else if (a->sign == MP_NEG) { + mp_err err; + a->sign = MP_ZPOS; + if ((err = mp_decr(a)) != MP_OKAY) { + return err; + } + /* There is no -0 in LTM */ + if (!MP_IS_ZERO(a)) { + a->sign = MP_NEG; + } + return MP_OKAY; + } else if (a->dp[0] < MP_DIGIT_MAX) { + a->dp[0]++; + return MP_OKAY; + } else { + return mp_add_d(a, 1uL,a); + } +} +#endif diff --git a/lib/hcrypto/libtommath/bn_mp_init.c b/lib/hcrypto/libtommath/bn_mp_init.c index 8be27f5696a7..2eb792409b5b 100644 --- a/lib/hcrypto/libtommath/bn_mp_init.c +++ b/lib/hcrypto/libtommath/bn_mp_init.c @@ -1,46 +1,23 @@ -#include <tommath.h> +#include "tommath_private.h" #ifdef BN_MP_INIT_C -/* LibTomMath, multiple-precision integer library -- Tom St Denis - * - * LibTomMath is a library that provides multiple-precision - * integer arithmetic as well as number theoretic functionality. - * - * The library was designed directly after the MPI library by - * Michael Fromberger but has been written from scratch with - * additional optimizations in place. - * - * The library is free for all purposes without any express - * guarantee it works. - * - * Tom St Denis, tomstdenis@gmail.com, http://libtom.org - */ +/* LibTomMath, multiple-precision integer library -- Tom St Denis */ +/* SPDX-License-Identifier: Unlicense */ /* init a new mp_int */ -int mp_init (mp_int * a) +mp_err mp_init(mp_int *a) { - int i; + /* allocate memory required and clear it */ + a->dp = (mp_digit *) MP_CALLOC((size_t)MP_PREC, sizeof(mp_digit)); + if (a->dp == NULL) { + return MP_MEM; + } - /* allocate memory required and clear it */ - a->dp = OPT_CAST(mp_digit) XMALLOC (sizeof (mp_digit) * MP_PREC); - if (a->dp == NULL) { - return MP_MEM; - } + /* set the used to zero, allocated digits to the default precision + * and sign to positive */ + a->used = 0; + a->alloc = MP_PREC; + a->sign = MP_ZPOS; - /* set the digits to zero */ - for (i = 0; i < MP_PREC; i++) { - a->dp[i] = 0; - } - - /* set the used to zero, allocated digits to the default precision - * and sign to positive */ - a->used = 0; - a->alloc = MP_PREC; - a->sign = MP_ZPOS; - - return MP_OKAY; + return MP_OKAY; } #endif - -/* $Source: /cvs/libtom/libtommath/bn_mp_init.c,v $ */ -/* $Revision: 1.4 $ */ -/* $Date: 2006/12/28 01:25:13 $ */ diff --git a/lib/hcrypto/libtommath/bn_mp_init_copy.c b/lib/hcrypto/libtommath/bn_mp_init_copy.c index 0160811affb2..1888203d2289 100644 --- a/lib/hcrypto/libtommath/bn_mp_init_copy.c +++ b/lib/hcrypto/libtommath/bn_mp_init_copy.c @@ -1,32 +1,21 @@ -#include <tommath.h> +#include "tommath_private.h" #ifdef BN_MP_INIT_COPY_C -/* LibTomMath, multiple-precision integer library -- Tom St Denis - * - * LibTomMath is a library that provides multiple-precision - * integer arithmetic as well as number theoretic functionality. - * - * The library was designed directly after the MPI library by - * Michael Fromberger but has been written from scratch with - * additional optimizations in place. - * - * The library is free for all purposes without any express - * guarantee it works. - * - * Tom St Denis, tomstdenis@gmail.com, http://libtom.org - */ +/* LibTomMath, multiple-precision integer library -- Tom St Denis */ +/* SPDX-License-Identifier: Unlicense */ /* creates "a" then copies b into it */ -int mp_init_copy (mp_int * a, mp_int * b) +mp_err mp_init_copy(mp_int *a, const mp_int *b) { - int res; + mp_err err; - if ((res = mp_init (a)) != MP_OKAY) { - return res; - } - return mp_copy (b, a); + if ((err = mp_init_size(a, b->used)) != MP_OKAY) { + return err; + } + + if ((err = mp_copy(b, a)) != MP_OKAY) { + mp_clear(a); + } + + return err; } #endif - -/* $Source: /cvs/libtom/libtommath/bn_mp_init_copy.c,v $ */ -/* $Revision: 1.4 $ */ -/* $Date: 2006/12/28 01:25:13 $ */ diff --git a/lib/hcrypto/libtommath/bn_mp_init_i32.c b/lib/hcrypto/libtommath/bn_mp_init_i32.c new file mode 100644 index 000000000000..bc4de8d5040b --- /dev/null +++ b/lib/hcrypto/libtommath/bn_mp_init_i32.c @@ -0,0 +1,7 @@ +#include "tommath_private.h" +#ifdef BN_MP_INIT_I32_C +/* LibTomMath, multiple-precision integer library -- Tom St Denis */ +/* SPDX-License-Identifier: Unlicense */ + +MP_INIT_INT(mp_init_i32, mp_set_i32, int32_t) +#endif diff --git a/lib/hcrypto/libtommath/bn_mp_init_i64.c b/lib/hcrypto/libtommath/bn_mp_init_i64.c new file mode 100644 index 000000000000..2fa1516eb854 --- /dev/null +++ b/lib/hcrypto/libtommath/bn_mp_init_i64.c @@ -0,0 +1,7 @@ +#include "tommath_private.h" +#ifdef BN_MP_INIT_I64_C +/* LibTomMath, multiple-precision integer library -- Tom St Denis */ +/* SPDX-License-Identifier: Unlicense */ + +MP_INIT_INT(mp_init_i64, mp_set_i64, int64_t) +#endif diff --git a/lib/hcrypto/libtommath/bn_mp_init_l.c b/lib/hcrypto/libtommath/bn_mp_init_l.c new file mode 100644 index 000000000000..bc380b539fc5 --- /dev/null +++ b/lib/hcrypto/libtommath/bn_mp_init_l.c @@ -0,0 +1,7 @@ +#include "tommath_private.h" +#ifdef BN_MP_INIT_L_C +/* LibTomMath, multiple-precision integer library -- Tom St Denis */ +/* SPDX-License-Identifier: Unlicense */ + +MP_INIT_INT(mp_init_l, mp_set_l, long) +#endif diff --git a/lib/hcrypto/libtommath/bn_mp_init_ll.c b/lib/hcrypto/libtommath/bn_mp_init_ll.c new file mode 100644 index 000000000000..dc7c4a44e2a6 --- /dev/null +++ b/lib/hcrypto/libtommath/bn_mp_init_ll.c @@ -0,0 +1,7 @@ +#include "tommath_private.h" +#ifdef BN_MP_INIT_LL_C +/* LibTomMath, multiple-precision integer library -- Tom St Denis */ +/* SPDX-License-Identifier: Unlicense */ + +MP_INIT_INT(mp_init_ll, mp_set_ll, long long) +#endif diff --git a/lib/hcrypto/libtommath/bn_mp_init_multi.c b/lib/hcrypto/libtommath/bn_mp_init_multi.c index 56e860276752..d8390b5a0335 100644 --- a/lib/hcrypto/libtommath/bn_mp_init_multi.c +++ b/lib/hcrypto/libtommath/bn_mp_init_multi.c @@ -1,59 +1,41 @@ -#include <tommath.h> +#include "tommath_private.h" #ifdef BN_MP_INIT_MULTI_C -/* LibTomMath, multiple-precision integer library -- Tom St Denis - * - * LibTomMath is a library that provides multiple-precision - * integer arithmetic as well as number theoretic functionality. - * - * The library was designed directly after the MPI library by - * Michael Fromberger but has been written from scratch with - * additional optimizations in place. - * - * The library is free for all purposes without any express - * guarantee it works. - * - * Tom St Denis, tomstdenis@gmail.com, http://libtom.org - */ +/* LibTomMath, multiple-precision integer library -- Tom St Denis */ +/* SPDX-License-Identifier: Unlicense */ + #include <stdarg.h> -int mp_init_multi(mp_int *mp, ...) +mp_err mp_init_multi(mp_int *mp, ...) { - mp_err res = MP_OKAY; /* Assume ok until proven otherwise */ - int n = 0; /* Number of ok inits */ - mp_int* cur_arg = mp; - va_list args; - - va_start(args, mp); /* init args to next argument from caller */ - while (cur_arg != NULL) { - if (mp_init(cur_arg) != MP_OKAY) { - /* Oops - error! Back-track and mp_clear what we already - succeeded in init-ing, then return error. - */ - va_list clean_args; + mp_err err = MP_OKAY; /* Assume ok until proven otherwise */ + int n = 0; /* Number of ok inits */ + mp_int *cur_arg = mp; + va_list args; - /* end the current list */ - va_end(args); + va_start(args, mp); /* init args to next argument from caller */ + while (cur_arg != NULL) { + if (mp_init(cur_arg) != MP_OKAY) { + /* Oops - error! Back-track and mp_clear what we already + succeeded in init-ing, then return error. + */ + va_list clean_args; - /* now start cleaning up */ - cur_arg = mp; - va_start(clean_args, mp); - while (n--) { - mp_clear(cur_arg); - cur_arg = va_arg(clean_args, mp_int*); - } - va_end(clean_args); - res = MP_MEM; - break; - } - n++; - cur_arg = va_arg(args, mp_int*); - } - va_end(args); - return res; /* Assumed ok, if error flagged above. */ + /* now start cleaning up */ + cur_arg = mp; + va_start(clean_args, mp); + while (n-- != 0) { + mp_clear(cur_arg); + cur_arg = va_arg(clean_args, mp_int *); + } + va_end(clean_args); + err = MP_MEM; + break; + } + n++; + cur_arg = va_arg(args, mp_int *); + } + va_end(args); + return err; /* Assumed ok, if error flagged above. */ } #endif - -/* $Source: /cvs/libtom/libtommath/bn_mp_init_multi.c,v $ */ -/* $Revision: 1.4 $ */ -/* $Date: 2006/12/28 01:25:13 $ */ diff --git a/lib/hcrypto/libtommath/bn_mp_init_set.c b/lib/hcrypto/libtommath/bn_mp_init_set.c index 34edad92ff06..5068f2bf6be4 100644 --- a/lib/hcrypto/libtommath/bn_mp_init_set.c +++ b/lib/hcrypto/libtommath/bn_mp_init_set.c @@ -1,32 +1,16 @@ -#include <tommath.h> +#include "tommath_private.h" #ifdef BN_MP_INIT_SET_C -/* LibTomMath, multiple-precision integer library -- Tom St Denis - * - * LibTomMath is a library that provides multiple-precision - * integer arithmetic as well as number theoretic functionality. - * - * The library was designed directly after the MPI library by - * Michael Fromberger but has been written from scratch with - * additional optimizations in place. - * - * The library is free for all purposes without any express - * guarantee it works. - * - * Tom St Denis, tomstdenis@gmail.com, http://libtom.org - */ +/* LibTomMath, multiple-precision integer library -- Tom St Denis */ +/* SPDX-License-Identifier: Unlicense */ /* initialize and set a digit */ -int mp_init_set (mp_int * a, mp_digit b) +mp_err mp_init_set(mp_int *a, mp_digit b) { - int err; - if ((err = mp_init(a)) != MP_OKAY) { - return err; - } - mp_set(a, b); - return err; + mp_err err; + if ((err = mp_init(a)) != MP_OKAY) { + return err; + } + mp_set(a, b); + return err; } #endif - -/* $Source: /cvs/libtom/libtommath/bn_mp_init_set.c,v $ */ -/* $Revision: 1.4 $ */ -/* $Date: 2006/12/28 01:25:13 $ */ diff --git a/lib/hcrypto/libtommath/bn_mp_init_set_int.c b/lib/hcrypto/libtommath/bn_mp_init_set_int.c deleted file mode 100644 index 5c559931520d..000000000000 --- a/lib/hcrypto/libtommath/bn_mp_init_set_int.c +++ /dev/null @@ -1,31 +0,0 @@ -#include <tommath.h> -#ifdef BN_MP_INIT_SET_INT_C -/* LibTomMath, multiple-precision integer library -- Tom St Denis - * - * LibTomMath is a library that provides multiple-precision - * integer arithmetic as well as number theoretic functionality. - * - * The library was designed directly after the MPI library by - * Michael Fromberger but has been written from scratch with - * additional optimizations in place. - * - * The library is free for all purposes without any express - * guarantee it works. - * - * Tom St Denis, tomstdenis@gmail.com, http://libtom.org - */ - -/* initialize and set a digit */ -int mp_init_set_int (mp_int * a, unsigned long b) -{ - int err; - if ((err = mp_init(a)) != MP_OKAY) { - return err; - } - return mp_set_int(a, b); -} -#endif - -/* $Source: /cvs/libtom/libtommath/bn_mp_init_set_int.c,v $ */ -/* $Revision: 1.4 $ */ -/* $Date: 2006/12/28 01:25:13 $ */ diff --git a/lib/hcrypto/libtommath/bn_mp_init_size.c b/lib/hcrypto/libtommath/bn_mp_init_size.c index 9578ac754c6c..d62268721a82 100644 --- a/lib/hcrypto/libtommath/bn_mp_init_size.c +++ b/lib/hcrypto/libtommath/bn_mp_init_size.c @@ -1,48 +1,24 @@ -#include <tommath.h> +#include "tommath_private.h" #ifdef BN_MP_INIT_SIZE_C -/* LibTomMath, multiple-precision integer library -- Tom St Denis - * - * LibTomMath is a library that provides multiple-precision - * integer arithmetic as well as number theoretic functionality. - * - * The library was designed directly after the MPI library by - * Michael Fromberger but has been written from scratch with - * additional optimizations in place. - * - * The library is free for all purposes without any express - * guarantee it works. - * - * Tom St Denis, tomstdenis@gmail.com, http://libtom.org - */ +/* LibTomMath, multiple-precision integer library -- Tom St Denis */ +/* SPDX-License-Identifier: Unlicense */ /* init an mp_init for a given size */ -int mp_init_size (mp_int * a, int size) +mp_err mp_init_size(mp_int *a, int size) { - int x; + size = MP_MAX(MP_MIN_PREC, size); - /* pad size so there are always extra digits */ - size += (MP_PREC * 2) - (size % MP_PREC); + /* alloc mem */ + a->dp = (mp_digit *) MP_CALLOC((size_t)size, sizeof(mp_digit)); + if (a->dp == NULL) { + return MP_MEM; + } - /* alloc mem */ - a->dp = OPT_CAST(mp_digit) XMALLOC (sizeof (mp_digit) * size); - if (a->dp == NULL) { - return MP_MEM; - } + /* set the members */ + a->used = 0; + a->alloc = size; + a->sign = MP_ZPOS; - /* set the members */ - a->used = 0; - a->alloc = size; - a->sign = MP_ZPOS; - - /* zero the digits */ - for (x = 0; x < size; x++) { - a->dp[x] = 0; - } - - return MP_OKAY; + return MP_OKAY; } #endif - -/* $Source: /cvs/libtom/libtommath/bn_mp_init_size.c,v $ */ -/* $Revision: 1.4 $ */ -/* $Date: 2006/12/28 01:25:13 $ */ diff --git a/lib/hcrypto/libtommath/bn_mp_init_u32.c b/lib/hcrypto/libtommath/bn_mp_init_u32.c new file mode 100644 index 000000000000..015d89b904d1 --- /dev/null +++ b/lib/hcrypto/libtommath/bn_mp_init_u32.c @@ -0,0 +1,7 @@ +#include "tommath_private.h" +#ifdef BN_MP_INIT_U32_C +/* LibTomMath, multiple-precision integer library -- Tom St Denis */ +/* SPDX-License-Identifier: Unlicense */ + +MP_INIT_INT(mp_init_u32, mp_set_u32, uint32_t) +#endif diff --git a/lib/hcrypto/libtommath/bn_mp_init_u64.c b/lib/hcrypto/libtommath/bn_mp_init_u64.c new file mode 100644 index 000000000000..2b35f7ef82ac --- /dev/null +++ b/lib/hcrypto/libtommath/bn_mp_init_u64.c @@ -0,0 +1,7 @@ +#include "tommath_private.h" +#ifdef BN_MP_INIT_U64_C +/* LibTomMath, multiple-precision integer library -- Tom St Denis */ +/* SPDX-License-Identifier: Unlicense */ + +MP_INIT_INT(mp_init_u64, mp_set_u64, uint64_t) +#endif diff --git a/lib/hcrypto/libtommath/bn_mp_init_ul.c b/lib/hcrypto/libtommath/bn_mp_init_ul.c new file mode 100644 index 000000000000..5164f728719f --- /dev/null +++ b/lib/hcrypto/libtommath/bn_mp_init_ul.c @@ -0,0 +1,7 @@ +#include "tommath_private.h" +#ifdef BN_MP_INIT_UL_C +/* LibTomMath, multiple-precision integer library -- Tom St Denis */ +/* SPDX-License-Identifier: Unlicense */ + +MP_INIT_INT(mp_init_ul, mp_set_ul, unsigned long) +#endif diff --git a/lib/hcrypto/libtommath/bn_mp_init_ull.c b/lib/hcrypto/libtommath/bn_mp_init_ull.c new file mode 100644 index 000000000000..84110c002d28 --- /dev/null +++ b/lib/hcrypto/libtommath/bn_mp_init_ull.c @@ -0,0 +1,7 @@ +#include "tommath_private.h" +#ifdef BN_MP_INIT_ULL_C +/* LibTomMath, multiple-precision integer library -- Tom St Denis */ +/* SPDX-License-Identifier: Unlicense */ + +MP_INIT_INT(mp_init_ull, mp_set_ull, unsigned long long) +#endif diff --git a/lib/hcrypto/libtommath/bn_mp_invmod.c b/lib/hcrypto/libtommath/bn_mp_invmod.c index ac1a9523191c..7b35a2431905 100644 --- a/lib/hcrypto/libtommath/bn_mp_invmod.c +++ b/lib/hcrypto/libtommath/bn_mp_invmod.c @@ -1,43 +1,23 @@ -#include <tommath.h> +#include "tommath_private.h" #ifdef BN_MP_INVMOD_C -/* LibTomMath, multiple-precision integer library -- Tom St Denis - * - * LibTomMath is a library that provides multiple-precision - * integer arithmetic as well as number theoretic functionality. - * - * The library was designed directly after the MPI library by - * Michael Fromberger but has been written from scratch with - * additional optimizations in place. - * - * The library is free for all purposes without any express - * guarantee it works. - * - * Tom St Denis, tomstdenis@gmail.com, http://libtom.org - */ +/* LibTomMath, multiple-precision integer library -- Tom St Denis */ +/* SPDX-License-Identifier: Unlicense */ /* hac 14.61, pp608 */ -int mp_invmod (mp_int * a, mp_int * b, mp_int * c) +mp_err mp_invmod(const mp_int *a, const mp_int *b, mp_int *c) { - /* b cannot be negative */ - if (b->sign == MP_NEG || mp_iszero(b) == 1) { - return MP_VAL; - } + /* b cannot be negative and has to be >1 */ + if ((b->sign == MP_NEG) || (mp_cmp_d(b, 1uL) != MP_GT)) { + return MP_VAL; + } -#ifdef BN_FAST_MP_INVMOD_C - /* if the modulus is odd we can use a faster routine instead */ - if (mp_isodd (b) == 1) { - return fast_mp_invmod (a, b, c); - } -#endif + /* if the modulus is odd we can use a faster routine instead */ + if (MP_HAS(S_MP_INVMOD_FAST) && MP_IS_ODD(b)) { + return s_mp_invmod_fast(a, b, c); + } -#ifdef BN_MP_INVMOD_SLOW_C - return mp_invmod_slow(a, b, c); -#else - return MP_VAL; -#endif + return MP_HAS(S_MP_INVMOD_SLOW) + ? s_mp_invmod_slow(a, b, c) + : MP_VAL; } #endif - -/* $Source: /cvs/libtom/libtommath/bn_mp_invmod.c,v $ */ -/* $Revision: 1.4 $ */ -/* $Date: 2006/12/28 01:25:13 $ */ diff --git a/lib/hcrypto/libtommath/bn_mp_invmod_slow.c b/lib/hcrypto/libtommath/bn_mp_invmod_slow.c deleted file mode 100644 index 4ec487efae2e..000000000000 --- a/lib/hcrypto/libtommath/bn_mp_invmod_slow.c +++ /dev/null @@ -1,175 +0,0 @@ -#include <tommath.h> -#ifdef BN_MP_INVMOD_SLOW_C -/* LibTomMath, multiple-precision integer library -- Tom St Denis - * - * LibTomMath is a library that provides multiple-precision - * integer arithmetic as well as number theoretic functionality. - * - * The library was designed directly after the MPI library by - * Michael Fromberger but has been written from scratch with - * additional optimizations in place. - * - * The library is free for all purposes without any express - * guarantee it works. - * - * Tom St Denis, tomstdenis@gmail.com, http://libtom.org - */ - -/* hac 14.61, pp608 */ -int mp_invmod_slow (mp_int * a, mp_int * b, mp_int * c) -{ - mp_int x, y, u, v, A, B, C, D; - int res; - - /* b cannot be negative */ - if (b->sign == MP_NEG || mp_iszero(b) == 1) { - return MP_VAL; - } - - /* init temps */ - if ((res = mp_init_multi(&x, &y, &u, &v, - &A, &B, &C, &D, NULL)) != MP_OKAY) { - return res; - } - - /* x = a, y = b */ - if ((res = mp_mod(a, b, &x)) != MP_OKAY) { - goto LBL_ERR; - } - if ((res = mp_copy (b, &y)) != MP_OKAY) { - goto LBL_ERR; - } - - /* 2. [modified] if x,y are both even then return an error! */ - if (mp_iseven (&x) == 1 && mp_iseven (&y) == 1) { - res = MP_VAL; - goto LBL_ERR; - } - - /* 3. u=x, v=y, A=1, B=0, C=0,D=1 */ - if ((res = mp_copy (&x, &u)) != MP_OKAY) { - goto LBL_ERR; - } - if ((res = mp_copy (&y, &v)) != MP_OKAY) { - goto LBL_ERR; - } - mp_set (&A, 1); - mp_set (&D, 1); - -top: - /* 4. while u is even do */ - while (mp_iseven (&u) == 1) { - /* 4.1 u = u/2 */ - if ((res = mp_div_2 (&u, &u)) != MP_OKAY) { - goto LBL_ERR; - } - /* 4.2 if A or B is odd then */ - if (mp_isodd (&A) == 1 || mp_isodd (&B) == 1) { - /* A = (A+y)/2, B = (B-x)/2 */ - if ((res = mp_add (&A, &y, &A)) != MP_OKAY) { - goto LBL_ERR; - } - if ((res = mp_sub (&B, &x, &B)) != MP_OKAY) { - goto LBL_ERR; - } - } - /* A = A/2, B = B/2 */ - if ((res = mp_div_2 (&A, &A)) != MP_OKAY) { - goto LBL_ERR; - } - if ((res = mp_div_2 (&B, &B)) != MP_OKAY) { - goto LBL_ERR; - } - } - - /* 5. while v is even do */ - while (mp_iseven (&v) == 1) { - /* 5.1 v = v/2 */ - if ((res = mp_div_2 (&v, &v)) != MP_OKAY) { - goto LBL_ERR; - } - /* 5.2 if C or D is odd then */ - if (mp_isodd (&C) == 1 || mp_isodd (&D) == 1) { - /* C = (C+y)/2, D = (D-x)/2 */ - if ((res = mp_add (&C, &y, &C)) != MP_OKAY) { - goto LBL_ERR; - } - if ((res = mp_sub (&D, &x, &D)) != MP_OKAY) { - goto LBL_ERR; - } - } - /* C = C/2, D = D/2 */ - if ((res = mp_div_2 (&C, &C)) != MP_OKAY) { - goto LBL_ERR; - } - if ((res = mp_div_2 (&D, &D)) != MP_OKAY) { - goto LBL_ERR; - } - } - - /* 6. if u >= v then */ - if (mp_cmp (&u, &v) != MP_LT) { - /* u = u - v, A = A - C, B = B - D */ - if ((res = mp_sub (&u, &v, &u)) != MP_OKAY) { - goto LBL_ERR; - } - - if ((res = mp_sub (&A, &C, &A)) != MP_OKAY) { - goto LBL_ERR; - } - - if ((res = mp_sub (&B, &D, &B)) != MP_OKAY) { - goto LBL_ERR; - } - } else { - /* v - v - u, C = C - A, D = D - B */ - if ((res = mp_sub (&v, &u, &v)) != MP_OKAY) { - goto LBL_ERR; - } - - if ((res = mp_sub (&C, &A, &C)) != MP_OKAY) { - goto LBL_ERR; - } - - if ((res = mp_sub (&D, &B, &D)) != MP_OKAY) { - goto LBL_ERR; - } - } - - /* if not zero goto step 4 */ - if (mp_iszero (&u) == 0) - goto top; - - /* now a = C, b = D, gcd == g*v */ - - /* if v != 1 then there is no inverse */ - if (mp_cmp_d (&v, 1) != MP_EQ) { - res = MP_VAL; - goto LBL_ERR; - } - - /* if its too low */ - while (mp_cmp_d(&C, 0) == MP_LT) { - if ((res = mp_add(&C, b, &C)) != MP_OKAY) { - goto LBL_ERR; - } - } - - /* too big */ - while (mp_cmp_mag(&C, b) != MP_LT) { - if ((res = mp_sub(&C, b, &C)) != MP_OKAY) { - goto LBL_ERR; - } - } - - /* C is now the inverse */ - mp_exch (&C, c); - res = MP_OKAY; -LBL_ERR:mp_clear_multi (&x, &y, &u, &v, &A, &B, &C, &D, NULL); - return res; -} -#endif - -/* $Source: /cvs/libtom/libtommath/bn_mp_invmod_slow.c,v $ */ -/* $Revision: 1.4 $ */ -/* $Date: 2006/12/28 01:25:13 $ */ diff --git a/lib/hcrypto/libtommath/bn_mp_is_square.c b/lib/hcrypto/libtommath/bn_mp_is_square.c index 027fcd2f5add..69e77a21a74d 100644 --- a/lib/hcrypto/libtommath/bn_mp_is_square.c +++ b/lib/hcrypto/libtommath/bn_mp_is_square.c @@ -1,109 +1,93 @@ -#include <tommath.h> +#include "tommath_private.h" #ifdef BN_MP_IS_SQUARE_C -/* LibTomMath, multiple-precision integer library -- Tom St Denis - * - * LibTomMath is a library that provides multiple-precision - * integer arithmetic as well as number theoretic functionality. - * - * The library was designed directly after the MPI library by - * Michael Fromberger but has been written from scratch with - * additional optimizations in place. - * - * The library is free for all purposes without any express - * guarantee it works. - * - * Tom St Denis, tomstdenis@gmail.com, http://libtom.org - */ +/* LibTomMath, multiple-precision integer library -- Tom St Denis */ +/* SPDX-License-Identifier: Unlicense */ /* Check if remainders are possible squares - fast exclude non-squares */ static const char rem_128[128] = { - 0, 0, 1, 1, 0, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, - 0, 0, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, - 1, 0, 1, 1, 0, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, - 1, 0, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, - 0, 0, 1, 1, 0, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, - 1, 0, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, - 1, 0, 1, 1, 0, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, - 1, 0, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1 + 0, 0, 1, 1, 0, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, + 0, 0, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, + 1, 0, 1, 1, 0, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, + 1, 0, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, + 0, 0, 1, 1, 0, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, + 1, 0, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, + 1, 0, 1, 1, 0, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, + 1, 0, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1 }; static const char rem_105[105] = { - 0, 0, 1, 1, 0, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, - 0, 0, 1, 1, 1, 1, 0, 1, 1, 1, 0, 1, 1, 1, 1, - 0, 1, 1, 1, 1, 1, 0, 1, 1, 0, 1, 1, 1, 1, 1, - 1, 0, 1, 1, 0, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, - 0, 1, 1, 1, 0, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, - 1, 1, 1, 1, 0, 1, 0, 1, 1, 0, 0, 1, 1, 1, 1, - 1, 0, 1, 1, 1, 1, 1, 1, 1, 0, 0, 1, 1, 1, 1 + 0, 0, 1, 1, 0, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, + 0, 0, 1, 1, 1, 1, 0, 1, 1, 1, 0, 1, 1, 1, 1, + 0, 1, 1, 1, 1, 1, 0, 1, 1, 0, 1, 1, 1, 1, 1, + 1, 0, 1, 1, 0, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, + 0, 1, 1, 1, 0, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, + 1, 1, 1, 1, 0, 1, 0, 1, 1, 0, 0, 1, 1, 1, 1, + 1, 0, 1, 1, 1, 1, 1, 1, 1, 0, 0, 1, 1, 1, 1 }; /* Store non-zero to ret if arg is square, and zero if not */ -int mp_is_square(mp_int *arg,int *ret) +mp_err mp_is_square(const mp_int *arg, mp_bool *ret) { - int res; - mp_digit c; - mp_int t; - unsigned long r; + mp_err err; + mp_digit c; + mp_int t; + unsigned long r; - /* Default to Non-square :) */ - *ret = MP_NO; + /* Default to Non-square :) */ + *ret = MP_NO; - if (arg->sign == MP_NEG) { - return MP_VAL; - } + if (arg->sign == MP_NEG) { + return MP_VAL; + } - /* digits used? (TSD) */ - if (arg->used == 0) { - return MP_OKAY; - } + if (MP_IS_ZERO(arg)) { + return MP_OKAY; + } - /* First check mod 128 (suppose that DIGIT_BIT is at least 7) */ - if (rem_128[127 & DIGIT(arg,0)] == 1) { - return MP_OKAY; - } + /* First check mod 128 (suppose that MP_DIGIT_BIT is at least 7) */ + if (rem_128[127u & arg->dp[0]] == (char)1) { + return MP_OKAY; + } - /* Next check mod 105 (3*5*7) */ - if ((res = mp_mod_d(arg,105,&c)) != MP_OKAY) { - return res; - } - if (rem_105[c] == 1) { - return MP_OKAY; - } + /* Next check mod 105 (3*5*7) */ + if ((err = mp_mod_d(arg, 105uL, &c)) != MP_OKAY) { + return err; + } + if (rem_105[c] == (char)1) { + return MP_OKAY; + } - if ((res = mp_init_set_int(&t,11L*13L*17L*19L*23L*29L*31L)) != MP_OKAY) { - return res; - } - if ((res = mp_mod(arg,&t,&t)) != MP_OKAY) { - goto ERR; - } - r = mp_get_int(&t); - /* Check for other prime modules, note it's not an ERROR but we must - * free "t" so the easiest way is to goto ERR. We know that res - * is already equal to MP_OKAY from the mp_mod call - */ - if ( (1L<<(r%11)) & 0x5C4L ) goto ERR; - if ( (1L<<(r%13)) & 0x9E4L ) goto ERR; - if ( (1L<<(r%17)) & 0x5CE8L ) goto ERR; - if ( (1L<<(r%19)) & 0x4F50CL ) goto ERR; - if ( (1L<<(r%23)) & 0x7ACCA0L ) goto ERR; - if ( (1L<<(r%29)) & 0xC2EDD0CL ) goto ERR; - if ( (1L<<(r%31)) & 0x6DE2B848L ) goto ERR; + if ((err = mp_init_u32(&t, 11u*13u*17u*19u*23u*29u*31u)) != MP_OKAY) { + return err; + } + if ((err = mp_mod(arg, &t, &t)) != MP_OKAY) { + goto LBL_ERR; + } + r = mp_get_u32(&t); + /* Check for other prime modules, note it's not an ERROR but we must + * free "t" so the easiest way is to goto LBL_ERR. We know that err + * is already equal to MP_OKAY from the mp_mod call + */ + if (((1uL<<(r%11uL)) & 0x5C4uL) != 0uL) goto LBL_ERR; + if (((1uL<<(r%13uL)) & 0x9E4uL) != 0uL) goto LBL_ERR; + if (((1uL<<(r%17uL)) & 0x5CE8uL) != 0uL) goto LBL_ERR; + if (((1uL<<(r%19uL)) & 0x4F50CuL) != 0uL) goto LBL_ERR; + if (((1uL<<(r%23uL)) & 0x7ACCA0uL) != 0uL) goto LBL_ERR; + if (((1uL<<(r%29uL)) & 0xC2EDD0CuL) != 0uL) goto LBL_ERR; + if (((1uL<<(r%31uL)) & 0x6DE2B848uL) != 0uL) goto LBL_ERR; - /* Final check - is sqr(sqrt(arg)) == arg ? */ - if ((res = mp_sqrt(arg,&t)) != MP_OKAY) { - goto ERR; - } - if ((res = mp_sqr(&t,&t)) != MP_OKAY) { - goto ERR; - } + /* Final check - is sqr(sqrt(arg)) == arg ? */ + if ((err = mp_sqrt(arg, &t)) != MP_OKAY) { + goto LBL_ERR; + } + if ((err = mp_sqr(&t, &t)) != MP_OKAY) { + goto LBL_ERR; + } - *ret = (mp_cmp_mag(&t,arg) == MP_EQ) ? MP_YES : MP_NO; -ERR:mp_clear(&t); - return res; + *ret = (mp_cmp_mag(&t, arg) == MP_EQ) ? MP_YES : MP_NO; +LBL_ERR: + mp_clear(&t); + return err; } #endif - -/* $Source: /cvs/libtom/libtommath/bn_mp_is_square.c,v $ */ -/* $Revision: 1.4 $ */ -/* $Date: 2006/12/28 01:25:13 $ */ diff --git a/lib/hcrypto/libtommath/bn_mp_iseven.c b/lib/hcrypto/libtommath/bn_mp_iseven.c new file mode 100644 index 000000000000..5cb9622844d1 --- /dev/null +++ b/lib/hcrypto/libtommath/bn_mp_iseven.c @@ -0,0 +1,10 @@ +#include "tommath_private.h" +#ifdef BN_MP_ISEVEN_C +/* LibTomMath, multiple-precision integer library -- Tom St Denis */ +/* SPDX-License-Identifier: Unlicense */ + +mp_bool mp_iseven(const mp_int *a) +{ + return MP_IS_EVEN(a) ? MP_YES : MP_NO; +} +#endif diff --git a/lib/hcrypto/libtommath/bn_mp_isodd.c b/lib/hcrypto/libtommath/bn_mp_isodd.c new file mode 100644 index 000000000000..bf17646d7036 --- /dev/null +++ b/lib/hcrypto/libtommath/bn_mp_isodd.c @@ -0,0 +1,10 @@ +#include "tommath_private.h" +#ifdef BN_MP_ISODD_C +/* LibTomMath, multiple-precision integer library -- Tom St Denis */ +/* SPDX-License-Identifier: Unlicense */ + +mp_bool mp_isodd(const mp_int *a) +{ + return MP_IS_ODD(a) ? MP_YES : MP_NO; +} +#endif diff --git a/lib/hcrypto/libtommath/bn_mp_jacobi.c b/lib/hcrypto/libtommath/bn_mp_jacobi.c deleted file mode 100644 index 91cfeeade4c3..000000000000 --- a/lib/hcrypto/libtommath/bn_mp_jacobi.c +++ /dev/null @@ -1,105 +0,0 @@ -#include <tommath.h> -#ifdef BN_MP_JACOBI_C -/* LibTomMath, multiple-precision integer library -- Tom St Denis - * - * LibTomMath is a library that provides multiple-precision - * integer arithmetic as well as number theoretic functionality. - * - * The library was designed directly after the MPI library by - * Michael Fromberger but has been written from scratch with - * additional optimizations in place. - * - * The library is free for all purposes without any express - * guarantee it works. - * - * Tom St Denis, tomstdenis@gmail.com, http://libtom.org - */ - -/* computes the jacobi c = (a | n) (or Legendre if n is prime) - * HAC pp. 73 Algorithm 2.149 - */ -int mp_jacobi (mp_int * a, mp_int * p, int *c) -{ - mp_int a1, p1; - int k, s, r, res; - mp_digit residue; - - /* if p <= 0 return MP_VAL */ - if (mp_cmp_d(p, 0) != MP_GT) { - return MP_VAL; - } - - /* step 1. if a == 0, return 0 */ - if (mp_iszero (a) == 1) { - *c = 0; - return MP_OKAY; - } - - /* step 2. if a == 1, return 1 */ - if (mp_cmp_d (a, 1) == MP_EQ) { - *c = 1; - return MP_OKAY; - } - - /* default */ - s = 0; - - /* step 3. write a = a1 * 2**k */ - if ((res = mp_init_copy (&a1, a)) != MP_OKAY) { - return res; - } - - if ((res = mp_init (&p1)) != MP_OKAY) { - goto LBL_A1; - } - - /* divide out larger power of two */ - k = mp_cnt_lsb(&a1); - if ((res = mp_div_2d(&a1, k, &a1, NULL)) != MP_OKAY) { - goto LBL_P1; - } - - /* step 4. if e is even set s=1 */ - if ((k & 1) == 0) { - s = 1; - } else { - /* else set s=1 if p = 1/7 (mod 8) or s=-1 if p = 3/5 (mod 8) */ - residue = p->dp[0] & 7; - - if (residue == 1 || residue == 7) { - s = 1; - } else if (residue == 3 || residue == 5) { - s = -1; - } - } - - /* step 5. if p == 3 (mod 4) *and* a1 == 3 (mod 4) then s = -s */ - if ( ((p->dp[0] & 3) == 3) && ((a1.dp[0] & 3) == 3)) { - s = -s; - } - - /* if a1 == 1 we're done */ - if (mp_cmp_d (&a1, 1) == MP_EQ) { - *c = s; - } else { - /* n1 = n mod a1 */ - if ((res = mp_mod (p, &a1, &p1)) != MP_OKAY) { - goto LBL_P1; - } - if ((res = mp_jacobi (&p1, &a1, &r)) != MP_OKAY) { - goto LBL_P1; - } - *c = s * r; - } - - /* done */ - res = MP_OKAY; -LBL_P1:mp_clear (&p1); -LBL_A1:mp_clear (&a1); - return res; -} -#endif - -/* $Source: /cvs/libtom/libtommath/bn_mp_jacobi.c,v $ */ -/* $Revision: 1.4 $ */ -/* $Date: 2006/12/28 01:25:13 $ */ diff --git a/lib/hcrypto/libtommath/bn_mp_karatsuba_mul.c b/lib/hcrypto/libtommath/bn_mp_karatsuba_mul.c deleted file mode 100644 index 72a2319c0672..000000000000 --- a/lib/hcrypto/libtommath/bn_mp_karatsuba_mul.c +++ /dev/null @@ -1,167 +0,0 @@ -#include <tommath.h> -#ifdef BN_MP_KARATSUBA_MUL_C -/* LibTomMath, multiple-precision integer library -- Tom St Denis - * - * LibTomMath is a library that provides multiple-precision - * integer arithmetic as well as number theoretic functionality. - * - * The library was designed directly after the MPI library by - * Michael Fromberger but has been written from scratch with - * additional optimizations in place. - * - * The library is free for all purposes without any express - * guarantee it works. - * - * Tom St Denis, tomstdenis@gmail.com, http://libtom.org - */ - -/* c = |a| * |b| using Karatsuba Multiplication using - * three half size multiplications - * - * Let B represent the radix [e.g. 2**DIGIT_BIT] and - * let n represent half of the number of digits in - * the min(a,b) - * - * a = a1 * B**n + a0 - * b = b1 * B**n + b0 - * - * Then, a * b => - a1b1 * B**2n + ((a1 + a0)(b1 + b0) - (a0b0 + a1b1)) * B + a0b0 - * - * Note that a1b1 and a0b0 are used twice and only need to be - * computed once. So in total three half size (half # of - * digit) multiplications are performed, a0b0, a1b1 and - * (a1+b1)(a0+b0) - * - * Note that a multiplication of half the digits requires - * 1/4th the number of single precision multiplications so in - * total after one call 25% of the single precision multiplications - * are saved. Note also that the call to mp_mul can end up back - * in this function if the a0, a1, b0, or b1 are above the threshold. - * This is known as divide-and-conquer and leads to the famous - * O(N**lg(3)) or O(N**1.584) work which is asymptopically lower than - * the standard O(N**2) that the baseline/comba methods use. - * Generally though the overhead of this method doesn't pay off - * until a certain size (N ~ 80) is reached. - */ -int mp_karatsuba_mul (mp_int * a, mp_int * b, mp_int * c) -{ - mp_int x0, x1, y0, y1, t1, x0y0, x1y1; - int B, err; - - /* default the return code to an error */ - err = MP_MEM; - - /* min # of digits */ - B = MIN (a->used, b->used); - - /* now divide in two */ - B = B >> 1; - - /* init copy all the temps */ - if (mp_init_size (&x0, B) != MP_OKAY) - goto ERR; - if (mp_init_size (&x1, a->used - B) != MP_OKAY) - goto X0; - if (mp_init_size (&y0, B) != MP_OKAY) - goto X1; - if (mp_init_size (&y1, b->used - B) != MP_OKAY) - goto Y0; - - /* init temps */ - if (mp_init_size (&t1, B * 2) != MP_OKAY) - goto Y1; - if (mp_init_size (&x0y0, B * 2) != MP_OKAY) - goto T1; - if (mp_init_size (&x1y1, B * 2) != MP_OKAY) - goto X0Y0; - - /* now shift the digits */ - x0.used = y0.used = B; - x1.used = a->used - B; - y1.used = b->used - B; - - { - register int x; - register mp_digit *tmpa, *tmpb, *tmpx, *tmpy; - - /* we copy the digits directly instead of using higher level functions - * since we also need to shift the digits - */ - tmpa = a->dp; - tmpb = b->dp; - - tmpx = x0.dp; - tmpy = y0.dp; - for (x = 0; x < B; x++) { - *tmpx++ = *tmpa++; - *tmpy++ = *tmpb++; - } - - tmpx = x1.dp; - for (x = B; x < a->used; x++) { - *tmpx++ = *tmpa++; - } - - tmpy = y1.dp; - for (x = B; x < b->used; x++) { - *tmpy++ = *tmpb++; - } - } - - /* only need to clamp the lower words since by definition the - * upper words x1/y1 must have a known number of digits - */ - mp_clamp (&x0); - mp_clamp (&y0); - - /* now calc the products x0y0 and x1y1 */ - /* after this x0 is no longer required, free temp [x0==t2]! */ - if (mp_mul (&x0, &y0, &x0y0) != MP_OKAY) - goto X1Y1; /* x0y0 = x0*y0 */ - if (mp_mul (&x1, &y1, &x1y1) != MP_OKAY) - goto X1Y1; /* x1y1 = x1*y1 */ - - /* now calc x1+x0 and y1+y0 */ - if (s_mp_add (&x1, &x0, &t1) != MP_OKAY) - goto X1Y1; /* t1 = x1 - x0 */ - if (s_mp_add (&y1, &y0, &x0) != MP_OKAY) - goto X1Y1; /* t2 = y1 - y0 */ - if (mp_mul (&t1, &x0, &t1) != MP_OKAY) - goto X1Y1; /* t1 = (x1 + x0) * (y1 + y0) */ - - /* add x0y0 */ - if (mp_add (&x0y0, &x1y1, &x0) != MP_OKAY) - goto X1Y1; /* t2 = x0y0 + x1y1 */ - if (s_mp_sub (&t1, &x0, &t1) != MP_OKAY) - goto X1Y1; /* t1 = (x1+x0)*(y1+y0) - (x1y1 + x0y0) */ - - /* shift by B */ - if (mp_lshd (&t1, B) != MP_OKAY) - goto X1Y1; /* t1 = (x0y0 + x1y1 - (x1-x0)*(y1-y0))<<B */ - if (mp_lshd (&x1y1, B * 2) != MP_OKAY) - goto X1Y1; /* x1y1 = x1y1 << 2*B */ - - if (mp_add (&x0y0, &t1, &t1) != MP_OKAY) - goto X1Y1; /* t1 = x0y0 + t1 */ - if (mp_add (&t1, &x1y1, c) != MP_OKAY) - goto X1Y1; /* t1 = x0y0 + t1 + x1y1 */ - - /* Algorithm succeeded set the return code to MP_OKAY */ - err = MP_OKAY; - -X1Y1:mp_clear (&x1y1); -X0Y0:mp_clear (&x0y0); -T1:mp_clear (&t1); -Y1:mp_clear (&y1); -Y0:mp_clear (&y0); -X1:mp_clear (&x1); -X0:mp_clear (&x0); -ERR: - return err; -} -#endif - -/* $Source: /cvs/libtom/libtommath/bn_mp_karatsuba_mul.c,v $ */ -/* $Revision: 1.6 $ */ -/* $Date: 2006/12/28 01:25:13 $ */ diff --git a/lib/hcrypto/libtommath/bn_mp_karatsuba_sqr.c b/lib/hcrypto/libtommath/bn_mp_karatsuba_sqr.c deleted file mode 100644 index 56692c5ae700..000000000000 --- a/lib/hcrypto/libtommath/bn_mp_karatsuba_sqr.c +++ /dev/null @@ -1,121 +0,0 @@ -#include <tommath.h> -#ifdef BN_MP_KARATSUBA_SQR_C -/* LibTomMath, multiple-precision integer library -- Tom St Denis - * - * LibTomMath is a library that provides multiple-precision - * integer arithmetic as well as number theoretic functionality. - * - * The library was designed directly after the MPI library by - * Michael Fromberger but has been written from scratch with - * additional optimizations in place. - * - * The library is free for all purposes without any express - * guarantee it works. - * - * Tom St Denis, tomstdenis@gmail.com, http://libtom.org - */ - -/* Karatsuba squaring, computes b = a*a using three - * half size squarings - * - * See comments of karatsuba_mul for details. It - * is essentially the same algorithm but merely - * tuned to perform recursive squarings. - */ -int mp_karatsuba_sqr (mp_int * a, mp_int * b) -{ - mp_int x0, x1, t1, t2, x0x0, x1x1; - int B, err; - - err = MP_MEM; - - /* min # of digits */ - B = a->used; - - /* now divide in two */ - B = B >> 1; - - /* init copy all the temps */ - if (mp_init_size (&x0, B) != MP_OKAY) - goto ERR; - if (mp_init_size (&x1, a->used - B) != MP_OKAY) - goto X0; - - /* init temps */ - if (mp_init_size (&t1, a->used * 2) != MP_OKAY) - goto X1; - if (mp_init_size (&t2, a->used * 2) != MP_OKAY) - goto T1; - if (mp_init_size (&x0x0, B * 2) != MP_OKAY) - goto T2; - if (mp_init_size (&x1x1, (a->used - B) * 2) != MP_OKAY) - goto X0X0; - - { - register int x; - register mp_digit *dst, *src; - - src = a->dp; - - /* now shift the digits */ - dst = x0.dp; - for (x = 0; x < B; x++) { - *dst++ = *src++; - } - - dst = x1.dp; - for (x = B; x < a->used; x++) { - *dst++ = *src++; - } - } - - x0.used = B; - x1.used = a->used - B; - - mp_clamp (&x0); - - /* now calc the products x0*x0 and x1*x1 */ - if (mp_sqr (&x0, &x0x0) != MP_OKAY) - goto X1X1; /* x0x0 = x0*x0 */ - if (mp_sqr (&x1, &x1x1) != MP_OKAY) - goto X1X1; /* x1x1 = x1*x1 */ - - /* now calc (x1+x0)**2 */ - if (s_mp_add (&x1, &x0, &t1) != MP_OKAY) - goto X1X1; /* t1 = x1 - x0 */ - if (mp_sqr (&t1, &t1) != MP_OKAY) - goto X1X1; /* t1 = (x1 - x0) * (x1 - x0) */ - - /* add x0y0 */ - if (s_mp_add (&x0x0, &x1x1, &t2) != MP_OKAY) - goto X1X1; /* t2 = x0x0 + x1x1 */ - if (s_mp_sub (&t1, &t2, &t1) != MP_OKAY) - goto X1X1; /* t1 = (x1+x0)**2 - (x0x0 + x1x1) */ - - /* shift by B */ - if (mp_lshd (&t1, B) != MP_OKAY) - goto X1X1; /* t1 = (x0x0 + x1x1 - (x1-x0)*(x1-x0))<<B */ - if (mp_lshd (&x1x1, B * 2) != MP_OKAY) - goto X1X1; /* x1x1 = x1x1 << 2*B */ - - if (mp_add (&x0x0, &t1, &t1) != MP_OKAY) - goto X1X1; /* t1 = x0x0 + t1 */ - if (mp_add (&t1, &x1x1, b) != MP_OKAY) - goto X1X1; /* t1 = x0x0 + t1 + x1x1 */ - - err = MP_OKAY; - -X1X1:mp_clear (&x1x1); -X0X0:mp_clear (&x0x0); -T2:mp_clear (&t2); -T1:mp_clear (&t1); -X1:mp_clear (&x1); -X0:mp_clear (&x0); -ERR: - return err; -} -#endif - -/* $Source: /cvs/libtom/libtommath/bn_mp_karatsuba_sqr.c,v $ */ -/* $Revision: 1.6 $ */ -/* $Date: 2006/12/28 01:25:13 $ */ diff --git a/lib/hcrypto/libtommath/bn_mp_kronecker.c b/lib/hcrypto/libtommath/bn_mp_kronecker.c new file mode 100644 index 000000000000..525a82034593 --- /dev/null +++ b/lib/hcrypto/libtommath/bn_mp_kronecker.c @@ -0,0 +1,129 @@ +#include "tommath_private.h" +#ifdef BN_MP_KRONECKER_C + +/* LibTomMath, multiple-precision integer library -- Tom St Denis */ +/* SPDX-License-Identifier: Unlicense */ + +/* + Kronecker symbol (a|p) + Straightforward implementation of algorithm 1.4.10 in + Henri Cohen: "A Course in Computational Algebraic Number Theory" + + @book{cohen2013course, + title={A course in computational algebraic number theory}, + author={Cohen, Henri}, + volume={138}, + year={2013}, + publisher={Springer Science \& Business Media} + } + */ +mp_err mp_kronecker(const mp_int *a, const mp_int *p, int *c) +{ + mp_int a1, p1, r; + mp_err err; + int v, k; + + static const int table[8] = {0, 1, 0, -1, 0, -1, 0, 1}; + + if (MP_IS_ZERO(p)) { + if ((a->used == 1) && (a->dp[0] == 1u)) { + *c = 1; + } else { + *c = 0; + } + return MP_OKAY; + } + + if (MP_IS_EVEN(a) && MP_IS_EVEN(p)) { + *c = 0; + return MP_OKAY; + } + + if ((err = mp_init_copy(&a1, a)) != MP_OKAY) { + return err; + } + if ((err = mp_init_copy(&p1, p)) != MP_OKAY) { + goto LBL_KRON_0; + } + + v = mp_cnt_lsb(&p1); + if ((err = mp_div_2d(&p1, v, &p1, NULL)) != MP_OKAY) { + goto LBL_KRON_1; + } + + if ((v & 1) == 0) { + k = 1; + } else { + k = table[a->dp[0] & 7u]; + } + + if (p1.sign == MP_NEG) { + p1.sign = MP_ZPOS; + if (a1.sign == MP_NEG) { + k = -k; + } + } + + if ((err = mp_init(&r)) != MP_OKAY) { + goto LBL_KRON_1; + } + + for (;;) { + if (MP_IS_ZERO(&a1)) { + if (mp_cmp_d(&p1, 1uL) == MP_EQ) { + *c = k; + goto LBL_KRON; + } else { + *c = 0; + goto LBL_KRON; + } + } + + v = mp_cnt_lsb(&a1); + if ((err = mp_div_2d(&a1, v, &a1, NULL)) != MP_OKAY) { + goto LBL_KRON; + } + + if ((v & 1) == 1) { + k = k * table[p1.dp[0] & 7u]; + } + + if (a1.sign == MP_NEG) { + /* + * Compute k = (-1)^((a1)*(p1-1)/4) * k + * a1.dp[0] + 1 cannot overflow because the MSB + * of the type mp_digit is not set by definition + */ + if (((a1.dp[0] + 1u) & p1.dp[0] & 2u) != 0u) { + k = -k; + } + } else { + /* compute k = (-1)^((a1-1)*(p1-1)/4) * k */ + if ((a1.dp[0] & p1.dp[0] & 2u) != 0u) { + k = -k; + } + } + + if ((err = mp_copy(&a1, &r)) != MP_OKAY) { + goto LBL_KRON; + } + r.sign = MP_ZPOS; + if ((err = mp_mod(&p1, &r, &a1)) != MP_OKAY) { + goto LBL_KRON; + } + if ((err = mp_copy(&r, &p1)) != MP_OKAY) { + goto LBL_KRON; + } + } + +LBL_KRON: + mp_clear(&r); +LBL_KRON_1: + mp_clear(&p1); +LBL_KRON_0: + mp_clear(&a1); + + return err; +} + +#endif diff --git a/lib/hcrypto/libtommath/bn_mp_lcm.c b/lib/hcrypto/libtommath/bn_mp_lcm.c index 781eef5659ee..c32b269e67de 100644 --- a/lib/hcrypto/libtommath/bn_mp_lcm.c +++ b/lib/hcrypto/libtommath/bn_mp_lcm.c @@ -1,60 +1,44 @@ -#include <tommath.h> +#include "tommath_private.h" #ifdef BN_MP_LCM_C -/* LibTomMath, multiple-precision integer library -- Tom St Denis - * - * LibTomMath is a library that provides multiple-precision - * integer arithmetic as well as number theoretic functionality. - * - * The library was designed directly after the MPI library by - * Michael Fromberger but has been written from scratch with - * additional optimizations in place. - * - * The library is free for all purposes without any express - * guarantee it works. - * - * Tom St Denis, tomstdenis@gmail.com, http://libtom.org - */ +/* LibTomMath, multiple-precision integer library -- Tom St Denis */ +/* SPDX-License-Identifier: Unlicense */ /* computes least common multiple as |a*b|/(a, b) */ -int mp_lcm (mp_int * a, mp_int * b, mp_int * c) +mp_err mp_lcm(const mp_int *a, const mp_int *b, mp_int *c) { - int res; - mp_int t1, t2; - - - if ((res = mp_init_multi (&t1, &t2, NULL)) != MP_OKAY) { - return res; - } - - /* t1 = get the GCD of the two inputs */ - if ((res = mp_gcd (a, b, &t1)) != MP_OKAY) { - goto LBL_T; - } - - /* divide the smallest by the GCD */ - if (mp_cmp_mag(a, b) == MP_LT) { - /* store quotient in t2 such that t2 * b is the LCM */ - if ((res = mp_div(a, &t1, &t2, NULL)) != MP_OKAY) { - goto LBL_T; - } - res = mp_mul(b, &t2, c); - } else { - /* store quotient in t2 such that t2 * a is the LCM */ - if ((res = mp_div(b, &t1, &t2, NULL)) != MP_OKAY) { - goto LBL_T; - } - res = mp_mul(a, &t2, c); - } - - /* fix the sign to positive */ - c->sign = MP_ZPOS; + mp_err err; + mp_int t1, t2; + + + if ((err = mp_init_multi(&t1, &t2, NULL)) != MP_OKAY) { + return err; + } + + /* t1 = get the GCD of the two inputs */ + if ((err = mp_gcd(a, b, &t1)) != MP_OKAY) { + goto LBL_T; + } + + /* divide the smallest by the GCD */ + if (mp_cmp_mag(a, b) == MP_LT) { + /* store quotient in t2 such that t2 * b is the LCM */ + if ((err = mp_div(a, &t1, &t2, NULL)) != MP_OKAY) { + goto LBL_T; + } + err = mp_mul(b, &t2, c); + } else { + /* store quotient in t2 such that t2 * a is the LCM */ + if ((err = mp_div(b, &t1, &t2, NULL)) != MP_OKAY) { + goto LBL_T; + } + err = mp_mul(a, &t2, c); + } + + /* fix the sign to positive */ + c->sign = MP_ZPOS; LBL_T: - mp_clear_multi (&t1, &t2, NULL); - return res; + mp_clear_multi(&t1, &t2, NULL); + return err; } #endif - -/* $Source: /cvs/libtom/libtommath/bn_mp_lcm.c,v $ */ -/* $Revision: 1.4 $ */ -/* $Date: 2006/12/28 01:25:13 $ */ diff --git a/lib/hcrypto/libtommath/bn_mp_log_u32.c b/lib/hcrypto/libtommath/bn_mp_log_u32.c new file mode 100644 index 000000000000..c9cc157911e2 --- /dev/null +++ b/lib/hcrypto/libtommath/bn_mp_log_u32.c @@ -0,0 +1,191 @@ +#include "tommath_private.h" +#ifdef BN_MP_LOG_U32_C +/* LibTomMath, multiple-precision integer library -- Tom St Denis */ +/* SPDX-License-Identifier: Unlicense */ + +/* Compute log_{base}(a) */ +static mp_word s_pow(mp_word base, mp_word exponent) +{ + mp_word result = 1uLL; + while (exponent != 0u) { + if ((exponent & 1u) == 1u) { + result *= base; + } + exponent >>= 1; + base *= base; + } + + return result; +} + +static mp_digit s_digit_ilogb(mp_digit base, mp_digit n) +{ + mp_word bracket_low = 1uLL, bracket_mid, bracket_high, N; + mp_digit ret, high = 1uL, low = 0uL, mid; + + if (n < base) { + return 0uL; + } + if (n == base) { + return 1uL; + } + + bracket_high = (mp_word) base ; + N = (mp_word) n; + + while (bracket_high < N) { + low = high; + bracket_low = bracket_high; + high <<= 1; + bracket_high *= bracket_high; + } + + while (((mp_digit)(high - low)) > 1uL) { + mid = (low + high) >> 1; + bracket_mid = bracket_low * s_pow(base, (mp_word)(mid - low)); + + if (N < bracket_mid) { + high = mid ; + bracket_high = bracket_mid ; + } + if (N > bracket_mid) { + low = mid ; + bracket_low = bracket_mid ; + } + if (N == bracket_mid) { + return (mp_digit) mid; + } + } + + if (bracket_high == N) { + ret = high; + } else { + ret = low; + } + + return ret; +} + +/* TODO: output could be "int" because the output of mp_radix_size is int, too, + as is the output of mp_bitcount. + With the same problem: max size is INT_MAX * MP_DIGIT not INT_MAX only! +*/ +mp_err mp_log_u32(const mp_int *a, uint32_t base, uint32_t *c) +{ + mp_err err; + mp_ord cmp; + uint32_t high, low, mid; + mp_int bracket_low, bracket_high, bracket_mid, t, bi_base; + + err = MP_OKAY; + + if (a->sign == MP_NEG) { + return MP_VAL; + } + + if (MP_IS_ZERO(a)) { + return MP_VAL; + } + + if (base < 2u) { + return MP_VAL; + } + + /* `base' is at least 2 */ + + /* A small shortcut for bases that are powers of two. */ + if ((base & (base - 1u)) == 0u) { + int y, bit_count; + + for (y=0; (y < 7) && ((base & 1u) == 0u); y++) { + /* We must go through this loop at least once */ + base >>= 1; + } + bit_count = mp_count_bits(a) - 1; + /* + * `y' is necessarily at least 1 because `base' is a power of two and + * larger than 1, so we must have gone through the loop at least once, so + * we can't be dividing by zero. + * + * scan-build thinks we can be dividing by zero... WAT. + */ + *c = (uint32_t)(bit_count/y); + return MP_OKAY; + } + + if (a->used == 1) { + *c = (uint32_t)s_digit_ilogb(base, a->dp[0]); + return err; + } + + cmp = mp_cmp_d(a, base); + if ((cmp == MP_LT) || (cmp == MP_EQ)) { + *c = cmp == MP_EQ; + return err; + } + + if ((err = + mp_init_multi(&bracket_low, &bracket_high, + &bracket_mid, &t, &bi_base, NULL)) != MP_OKAY) { + return err; + } + + low = 0u; + mp_set(&bracket_low, 1uL); + high = 1u; + + mp_set(&bracket_high, base); + + /* + A kind of Giant-step/baby-step algorithm. + Idea shamelessly stolen from https://programmingpraxis.com/2010/05/07/integer-logarithms/2/ + The effect is asymptotic, hence needs benchmarks to test if the Giant-step should be skipped + for small n. + */ + while (mp_cmp(&bracket_high, a) == MP_LT) { + low = high; + if ((err = mp_copy(&bracket_high, &bracket_low)) != MP_OKAY) { + goto LBL_ERR; + } + high <<= 1; + if ((err = mp_sqr(&bracket_high, &bracket_high)) != MP_OKAY) { + goto LBL_ERR; + } + } + mp_set(&bi_base, base); + + while ((high - low) > 1u) { + mid = (high + low) >> 1; + + if ((err = mp_expt_u32(&bi_base, (uint32_t)(mid - low), &t)) != MP_OKAY) { + goto LBL_ERR; + } + if ((err = mp_mul(&bracket_low, &t, &bracket_mid)) != MP_OKAY) { + goto LBL_ERR; + } + cmp = mp_cmp(a, &bracket_mid); + if (cmp == MP_LT) { + high = mid; + mp_exch(&bracket_mid, &bracket_high); + } + if (cmp == MP_GT) { + low = mid; + mp_exch(&bracket_mid, &bracket_low); + } + if (cmp == MP_EQ) { + *c = mid; + goto LBL_END; + } + } + + *c = (mp_cmp(&bracket_high, a) == MP_EQ) ? high : low; + +LBL_END: +LBL_ERR: + mp_clear_multi(&bracket_low, &bracket_high, &bracket_mid, + &t, &bi_base, NULL); + return err; +} + + +#endif diff --git a/lib/hcrypto/libtommath/bn_mp_lshd.c b/lib/hcrypto/libtommath/bn_mp_lshd.c index f118cf1ae566..82345809cc09 100644 --- a/lib/hcrypto/libtommath/bn_mp_lshd.c +++ b/lib/hcrypto/libtommath/bn_mp_lshd.c @@ -1,67 +1,51 @@ -#include <tommath.h> +#include "tommath_private.h" #ifdef BN_MP_LSHD_C -/* LibTomMath, multiple-precision integer library -- Tom St Denis - * - * LibTomMath is a library that provides multiple-precision - * integer arithmetic as well as number theoretic functionality. - * - * The library was designed directly after the MPI library by - * Michael Fromberger but has been written from scratch with - * additional optimizations in place. - * - * The library is free for all purposes without any express - * guarantee it works. - * - * Tom St Denis, tomstdenis@gmail.com, http://libtom.org - */ +/* LibTomMath, multiple-precision integer library -- Tom St Denis */ +/* SPDX-License-Identifier: Unlicense */ /* shift left a certain amount of digits */ -int mp_lshd (mp_int * a, int b) +mp_err mp_lshd(mp_int *a, int b) { - int x, res; - - /* if its less than zero return */ - if (b <= 0) { - return MP_OKAY; - } - - /* grow to fit the new digits */ - if (a->alloc < a->used + b) { - if ((res = mp_grow (a, a->used + b)) != MP_OKAY) { - return res; - } - } - - { - register mp_digit *top, *bottom; - - /* increment the used by the shift amount then copy upwards */ - a->used += b; - - /* top */ - top = a->dp + a->used - 1; - - /* base */ - bottom = a->dp + a->used - 1 - b; - - /* much like mp_rshd this is implemented using a sliding window - * except the window goes the otherway around. Copying from - * the bottom to the top. see bn_mp_rshd.c for more info. - */ - for (x = a->used - 1; x >= b; x--) { + int x; + mp_err err; + mp_digit *top, *bottom; + + /* if its less than zero return */ + if (b <= 0) { + return MP_OKAY; + } + /* no need to shift 0 around */ + if (MP_IS_ZERO(a)) { + return MP_OKAY; + } + + /* grow to fit the new digits */ + if (a->alloc < (a->used + b)) { + if ((err = mp_grow(a, a->used + b)) != MP_OKAY) { + return err; + } + } + + /* increment the used by the shift amount then copy upwards */ + a->used += b; + + /* top */ + top = a->dp + a->used - 1; + + /* base */ + bottom = (a->dp + a->used - 1) - b; + + /* much like mp_rshd this is implemented using a sliding window + * except the window goes the otherway around. Copying from + * the bottom to the top. see bn_mp_rshd.c for more info. + */ + for (x = a->used - 1; x >= b; x--) { *top-- = *bottom--; - } + } - /* zero the lower digits */ - top = a->dp; - for (x = 0; x < b; x++) { - *top++ = 0; - } - } - return MP_OKAY; + /* zero the lower digits */ + MP_ZERO_DIGITS(a->dp, b); + + return MP_OKAY; } #endif - -/* $Source: /cvs/libtom/libtommath/bn_mp_lshd.c,v $ */ -/* $Revision: 1.4 $ */ -/* $Date: 2006/12/28 01:25:13 $ */ diff --git a/lib/hcrypto/libtommath/bn_mp_mod.c b/lib/hcrypto/libtommath/bn_mp_mod.c index 757335aebc5b..8fbfe08dcde0 100644 --- a/lib/hcrypto/libtommath/bn_mp_mod.c +++ b/lib/hcrypto/libtommath/bn_mp_mod.c @@ -1,48 +1,31 @@ -#include <tommath.h> +#include "tommath_private.h" #ifdef BN_MP_MOD_C -/* LibTomMath, multiple-precision integer library -- Tom St Denis - * - * LibTomMath is a library that provides multiple-precision - * integer arithmetic as well as number theoretic functionality. - * - * The library was designed directly after the MPI library by - * Michael Fromberger but has been written from scratch with - * additional optimizations in place. - * - * The library is free for all purposes without any express - * guarantee it works. - * - * Tom St Denis, tomstdenis@gmail.com, http://libtom.org - */ +/* LibTomMath, multiple-precision integer library -- Tom St Denis */ +/* SPDX-License-Identifier: Unlicense */ /* c = a mod b, 0 <= c < b if b > 0, b < c <= 0 if b < 0 */ -int -mp_mod (mp_int * a, mp_int * b, mp_int * c) +mp_err mp_mod(const mp_int *a, const mp_int *b, mp_int *c) { - mp_int t; - int res; + mp_int t; + mp_err err; - if ((res = mp_init (&t)) != MP_OKAY) { - return res; - } + if ((err = mp_init_size(&t, b->used)) != MP_OKAY) { + return err; + } - if ((res = mp_div (a, b, NULL, &t)) != MP_OKAY) { - mp_clear (&t); - return res; - } + if ((err = mp_div(a, b, NULL, &t)) != MP_OKAY) { + goto LBL_ERR; + } - if (mp_iszero(&t) || t.sign == b->sign) { - res = MP_OKAY; - mp_exch (&t, c); - } else { - res = mp_add (b, &t, c); - } + if (MP_IS_ZERO(&t) || (t.sign == b->sign)) { + err = MP_OKAY; + mp_exch(&t, c); + } else { + err = mp_add(b, &t, c); + } - mp_clear (&t); - return res; +LBL_ERR: + mp_clear(&t); + return err; } #endif - -/* $Source: /cvs/libtom/libtommath/bn_mp_mod.c,v $ */ -/* $Revision: 1.4 $ */ -/* $Date: 2006/12/28 01:25:13 $ */ diff --git a/lib/hcrypto/libtommath/bn_mp_mod_2d.c b/lib/hcrypto/libtommath/bn_mp_mod_2d.c index e194a068702d..5bf57a1a3bef 100644 --- a/lib/hcrypto/libtommath/bn_mp_mod_2d.c +++ b/lib/hcrypto/libtommath/bn_mp_mod_2d.c @@ -1,55 +1,38 @@ -#include <tommath.h> +#include "tommath_private.h" #ifdef BN_MP_MOD_2D_C -/* LibTomMath, multiple-precision integer library -- Tom St Denis - * - * LibTomMath is a library that provides multiple-precision - * integer arithmetic as well as number theoretic functionality. - * - * The library was designed directly after the MPI library by - * Michael Fromberger but has been written from scratch with - * additional optimizations in place. - * - * The library is free for all purposes without any express - * guarantee it works. - * - * Tom St Denis, tomstdenis@gmail.com, http://libtom.org - */ +/* LibTomMath, multiple-precision integer library -- Tom St Denis */ +/* SPDX-License-Identifier: Unlicense */ /* calc a value mod 2**b */ -int -mp_mod_2d (mp_int * a, int b, mp_int * c) +mp_err mp_mod_2d(const mp_int *a, int b, mp_int *c) { - int x, res; + int x; + mp_err err; - /* if b is <= 0 then zero the int */ - if (b <= 0) { - mp_zero (c); - return MP_OKAY; - } + /* if b is <= 0 then zero the int */ + if (b <= 0) { + mp_zero(c); + return MP_OKAY; + } - /* if the modulus is larger than the value than return */ - if (b >= (int) (a->used * DIGIT_BIT)) { - res = mp_copy (a, c); - return res; - } + /* if the modulus is larger than the value than return */ + if (b >= (a->used * MP_DIGIT_BIT)) { + return mp_copy(a, c); + } - /* copy */ - if ((res = mp_copy (a, c)) != MP_OKAY) { - return res; - } + /* copy */ + if ((err = mp_copy(a, c)) != MP_OKAY) { + return err; + } - /* zero digits above the last digit of the modulus */ - for (x = (b / DIGIT_BIT) + ((b % DIGIT_BIT) == 0 ? 0 : 1); x < c->used; x++) { - c->dp[x] = 0; - } - /* clear the digit that is not completely outside/inside the modulus */ - c->dp[b / DIGIT_BIT] &= - (mp_digit) ((((mp_digit) 1) << (((mp_digit) b) % DIGIT_BIT)) - ((mp_digit) 1)); - mp_clamp (c); - return MP_OKAY; + /* zero digits above the last digit of the modulus */ + x = (b / MP_DIGIT_BIT) + (((b % MP_DIGIT_BIT) == 0) ? 0 : 1); + MP_ZERO_DIGITS(c->dp + x, c->used - x); + + /* clear the digit that is not completely outside/inside the modulus */ + c->dp[b / MP_DIGIT_BIT] &= + ((mp_digit)1 << (mp_digit)(b % MP_DIGIT_BIT)) - (mp_digit)1; + mp_clamp(c); + return MP_OKAY; } #endif - -/* $Source: /cvs/libtom/libtommath/bn_mp_mod_2d.c,v $ */ -/* $Revision: 1.4 $ */ -/* $Date: 2006/12/28 01:25:13 $ */ diff --git a/lib/hcrypto/libtommath/bn_mp_mod_d.c b/lib/hcrypto/libtommath/bn_mp_mod_d.c index 9ca37e673278..0b6c12a9ef4b 100644 --- a/lib/hcrypto/libtommath/bn_mp_mod_d.c +++ b/lib/hcrypto/libtommath/bn_mp_mod_d.c @@ -1,27 +1,10 @@ -#include <tommath.h> +#include "tommath_private.h" #ifdef BN_MP_MOD_D_C -/* LibTomMath, multiple-precision integer library -- Tom St Denis - * - * LibTomMath is a library that provides multiple-precision - * integer arithmetic as well as number theoretic functionality. - * - * The library was designed directly after the MPI library by - * Michael Fromberger but has been written from scratch with - * additional optimizations in place. - * - * The library is free for all purposes without any express - * guarantee it works. - * - * Tom St Denis, tomstdenis@gmail.com, http://libtom.org - */ +/* LibTomMath, multiple-precision integer library -- Tom St Denis */ +/* SPDX-License-Identifier: Unlicense */ -int -mp_mod_d (mp_int * a, mp_digit b, mp_digit * c) +mp_err mp_mod_d(const mp_int *a, mp_digit b, mp_digit *c) { - return mp_div_d(a, b, NULL, c); + return mp_div_d(a, b, NULL, c); } #endif - -/* $Source: /cvs/libtom/libtommath/bn_mp_mod_d.c,v $ */ -/* $Revision: 1.4 $ */ -/* $Date: 2006/12/28 01:25:13 $ */ diff --git a/lib/hcrypto/libtommath/bn_mp_montgomery_calc_normalization.c b/lib/hcrypto/libtommath/bn_mp_montgomery_calc_normalization.c index c669fe0ec3a0..8379789251ac 100644 --- a/lib/hcrypto/libtommath/bn_mp_montgomery_calc_normalization.c +++ b/lib/hcrypto/libtommath/bn_mp_montgomery_calc_normalization.c @@ -1,19 +1,7 @@ -#include <tommath.h> +#include "tommath_private.h" #ifdef BN_MP_MONTGOMERY_CALC_NORMALIZATION_C -/* LibTomMath, multiple-precision integer library -- Tom St Denis - * - * LibTomMath is a library that provides multiple-precision - * integer arithmetic as well as number theoretic functionality. - * - * The library was designed directly after the MPI library by - * Michael Fromberger but has been written from scratch with - * additional optimizations in place. - * - * The library is free for all purposes without any express - * guarantee it works. - * - * Tom St Denis, tomstdenis@gmail.com, http://libtom.org - */ +/* LibTomMath, multiple-precision integer library -- Tom St Denis */ +/* SPDX-License-Identifier: Unlicense */ /* * shifts with subtractions when the result is greater than b. @@ -21,39 +9,36 @@ * The method is slightly modified to shift B unconditionally upto just under * the leading bit of b. This saves alot of multiple precision shifting. */ -int mp_montgomery_calc_normalization (mp_int * a, mp_int * b) +mp_err mp_montgomery_calc_normalization(mp_int *a, const mp_int *b) { - int x, bits, res; + int x, bits; + mp_err err; - /* how many bits of last digit does b use */ - bits = mp_count_bits (b) % DIGIT_BIT; + /* how many bits of last digit does b use */ + bits = mp_count_bits(b) % MP_DIGIT_BIT; - if (b->used > 1) { - if ((res = mp_2expt (a, (b->used - 1) * DIGIT_BIT + bits - 1)) != MP_OKAY) { - return res; - } - } else { - mp_set(a, 1); - bits = 1; - } + if (b->used > 1) { + if ((err = mp_2expt(a, ((b->used - 1) * MP_DIGIT_BIT) + bits - 1)) != MP_OKAY) { + return err; + } + } else { + mp_set(a, 1uL); + bits = 1; + } - /* now compute C = A * B mod b */ - for (x = bits - 1; x < (int)DIGIT_BIT; x++) { - if ((res = mp_mul_2 (a, a)) != MP_OKAY) { - return res; - } - if (mp_cmp_mag (a, b) != MP_LT) { - if ((res = s_mp_sub (a, b, a)) != MP_OKAY) { - return res; + /* now compute C = A * B mod b */ + for (x = bits - 1; x < (int)MP_DIGIT_BIT; x++) { + if ((err = mp_mul_2(a, a)) != MP_OKAY) { + return err; } - } - } + if (mp_cmp_mag(a, b) != MP_LT) { + if ((err = s_mp_sub(a, b, a)) != MP_OKAY) { + return err; + } + } + } - return MP_OKAY; + return MP_OKAY; } #endif - -/* $Source: /cvs/libtom/libtommath/bn_mp_montgomery_calc_normalization.c,v $ */ -/* $Revision: 1.4 $ */ -/* $Date: 2006/12/28 01:25:13 $ */ diff --git a/lib/hcrypto/libtommath/bn_mp_montgomery_reduce.c b/lib/hcrypto/libtommath/bn_mp_montgomery_reduce.c index b76509051be7..ffe8341eef50 100644 --- a/lib/hcrypto/libtommath/bn_mp_montgomery_reduce.c +++ b/lib/hcrypto/libtommath/bn_mp_montgomery_reduce.c @@ -1,118 +1,102 @@ -#include <tommath.h> +#include "tommath_private.h" #ifdef BN_MP_MONTGOMERY_REDUCE_C -/* LibTomMath, multiple-precision integer library -- Tom St Denis - * - * LibTomMath is a library that provides multiple-precision - * integer arithmetic as well as number theoretic functionality. - * - * The library was designed directly after the MPI library by - * Michael Fromberger but has been written from scratch with - * additional optimizations in place. - * - * The library is free for all purposes without any express - * guarantee it works. - * - * Tom St Denis, tomstdenis@gmail.com, http://libtom.org - */ +/* LibTomMath, multiple-precision integer library -- Tom St Denis */ +/* SPDX-License-Identifier: Unlicense */ /* computes xR**-1 == x (mod N) via Montgomery Reduction */ -int -mp_montgomery_reduce (mp_int * x, mp_int * n, mp_digit rho) +mp_err mp_montgomery_reduce(mp_int *x, const mp_int *n, mp_digit rho) { - int ix, res, digs; - mp_digit mu; - - /* can the fast reduction [comba] method be used? - * - * Note that unlike in mul you're safely allowed *less* - * than the available columns [255 per default] since carries - * are fixed up in the inner loop. - */ - digs = n->used * 2 + 1; - if ((digs < MP_WARRAY) && - n->used < - (1 << ((CHAR_BIT * sizeof (mp_word)) - (2 * DIGIT_BIT)))) { - return fast_mp_montgomery_reduce (x, n, rho); - } - - /* grow the input as required */ - if (x->alloc < digs) { - if ((res = mp_grow (x, digs)) != MP_OKAY) { - return res; - } - } - x->used = digs; - - for (ix = 0; ix < n->used; ix++) { - /* mu = ai * rho mod b - * - * The value of rho must be precalculated via - * montgomery_setup() such that - * it equals -1/n0 mod b this allows the - * following inner loop to reduce the - * input one digit at a time - */ - mu = (mp_digit) (((mp_word)x->dp[ix]) * ((mp_word)rho) & MP_MASK); - - /* a = a + mu * m * b**i */ - { - register int iy; - register mp_digit *tmpn, *tmpx, u; - register mp_word r; - - /* alias for digits of the modulus */ - tmpn = n->dp; - - /* alias for the digits of x [the input] */ - tmpx = x->dp + ix; - - /* set the carry to zero */ - u = 0; - - /* Multiply and add in place */ - for (iy = 0; iy < n->used; iy++) { - /* compute product and sum */ - r = ((mp_word)mu) * ((mp_word)*tmpn++) + - ((mp_word) u) + ((mp_word) * tmpx); - - /* get carry */ - u = (mp_digit)(r >> ((mp_word) DIGIT_BIT)); - - /* fix digit */ - *tmpx++ = (mp_digit)(r & ((mp_word) MP_MASK)); + int ix, digs; + mp_err err; + mp_digit mu; + + /* can the fast reduction [comba] method be used? + * + * Note that unlike in mul you're safely allowed *less* + * than the available columns [255 per default] since carries + * are fixed up in the inner loop. + */ + digs = (n->used * 2) + 1; + if ((digs < MP_WARRAY) && + (x->used <= MP_WARRAY) && + (n->used < MP_MAXFAST)) { + return s_mp_montgomery_reduce_fast(x, n, rho); + } + + /* grow the input as required */ + if (x->alloc < digs) { + if ((err = mp_grow(x, digs)) != MP_OKAY) { + return err; } - /* At this point the ix'th digit of x should be zero */ + } + x->used = digs; + + for (ix = 0; ix < n->used; ix++) { + /* mu = ai * rho mod b + * + * The value of rho must be precalculated via + * montgomery_setup() such that + * it equals -1/n0 mod b this allows the + * following inner loop to reduce the + * input one digit at a time + */ + mu = (mp_digit)(((mp_word)x->dp[ix] * (mp_word)rho) & MP_MASK); + + /* a = a + mu * m * b**i */ + { + int iy; + mp_digit *tmpn, *tmpx, u; + mp_word r; + + /* alias for digits of the modulus */ + tmpn = n->dp; + + /* alias for the digits of x [the input] */ + tmpx = x->dp + ix; + + /* set the carry to zero */ + u = 0; + + /* Multiply and add in place */ + for (iy = 0; iy < n->used; iy++) { + /* compute product and sum */ + r = ((mp_word)mu * (mp_word)*tmpn++) + + (mp_word)u + (mp_word)*tmpx; + + /* get carry */ + u = (mp_digit)(r >> (mp_word)MP_DIGIT_BIT); + + /* fix digit */ + *tmpx++ = (mp_digit)(r & (mp_word)MP_MASK); + } + /* At this point the ix'th digit of x should be zero */ + + + /* propagate carries upwards as required*/ + while (u != 0u) { + *tmpx += u; + u = *tmpx >> MP_DIGIT_BIT; + *tmpx++ &= MP_MASK; + } + } + } + /* at this point the n.used'th least + * significant digits of x are all zero + * which means we can shift x to the + * right by n.used digits and the + * residue is unchanged. + */ - /* propagate carries upwards as required*/ - while (u) { - *tmpx += u; - u = *tmpx >> DIGIT_BIT; - *tmpx++ &= MP_MASK; - } - } - } - - /* at this point the n.used'th least - * significant digits of x are all zero - * which means we can shift x to the - * right by n.used digits and the - * residue is unchanged. - */ - - /* x = x/b**n.used */ - mp_clamp(x); - mp_rshd (x, n->used); - - /* if x >= n then x = x - n */ - if (mp_cmp_mag (x, n) != MP_LT) { - return s_mp_sub (x, n, x); - } - - return MP_OKAY; + /* x = x/b**n.used */ + mp_clamp(x); + mp_rshd(x, n->used); + + /* if x >= n then x = x - n */ + if (mp_cmp_mag(x, n) != MP_LT) { + return s_mp_sub(x, n, x); + } + + return MP_OKAY; } #endif - -/* $Source: /cvs/libtom/libtommath/bn_mp_montgomery_reduce.c,v $ */ -/* $Revision: 1.4 $ */ -/* $Date: 2006/12/28 01:25:13 $ */ diff --git a/lib/hcrypto/libtommath/bn_mp_montgomery_setup.c b/lib/hcrypto/libtommath/bn_mp_montgomery_setup.c index f08274936ed7..39f6e9d24a8f 100644 --- a/lib/hcrypto/libtommath/bn_mp_montgomery_setup.c +++ b/lib/hcrypto/libtommath/bn_mp_montgomery_setup.c @@ -1,59 +1,42 @@ -#include <tommath.h> +#include "tommath_private.h" #ifdef BN_MP_MONTGOMERY_SETUP_C -/* LibTomMath, multiple-precision integer library -- Tom St Denis - * - * LibTomMath is a library that provides multiple-precision - * integer arithmetic as well as number theoretic functionality. - * - * The library was designed directly after the MPI library by - * Michael Fromberger but has been written from scratch with - * additional optimizations in place. - * - * The library is free for all purposes without any express - * guarantee it works. - * - * Tom St Denis, tomstdenis@gmail.com, http://libtom.org - */ +/* LibTomMath, multiple-precision integer library -- Tom St Denis */ +/* SPDX-License-Identifier: Unlicense */ /* setups the montgomery reduction stuff */ -int -mp_montgomery_setup (mp_int * n, mp_digit * rho) +mp_err mp_montgomery_setup(const mp_int *n, mp_digit *rho) { - mp_digit x, b; + mp_digit x, b; -/* fast inversion mod 2**k - * - * Based on the fact that - * - * XA = 1 (mod 2**n) => (X(2-XA)) A = 1 (mod 2**2n) - * => 2*X*A - X*X*A*A = 1 - * => 2*(1) - (1) = 1 - */ - b = n->dp[0]; + /* fast inversion mod 2**k + * + * Based on the fact that + * + * XA = 1 (mod 2**n) => (X(2-XA)) A = 1 (mod 2**2n) + * => 2*X*A - X*X*A*A = 1 + * => 2*(1) - (1) = 1 + */ + b = n->dp[0]; - if ((b & 1) == 0) { - return MP_VAL; - } + if ((b & 1u) == 0u) { + return MP_VAL; + } - x = (((b + 2) & 4) << 1) + b; /* here x*a==1 mod 2**4 */ - x *= 2 - b * x; /* here x*a==1 mod 2**8 */ + x = (((b + 2u) & 4u) << 1) + b; /* here x*a==1 mod 2**4 */ + x *= 2u - (b * x); /* here x*a==1 mod 2**8 */ #if !defined(MP_8BIT) - x *= 2 - b * x; /* here x*a==1 mod 2**16 */ + x *= 2u - (b * x); /* here x*a==1 mod 2**16 */ #endif #if defined(MP_64BIT) || !(defined(MP_8BIT) || defined(MP_16BIT)) - x *= 2 - b * x; /* here x*a==1 mod 2**32 */ + x *= 2u - (b * x); /* here x*a==1 mod 2**32 */ #endif #ifdef MP_64BIT - x *= 2 - b * x; /* here x*a==1 mod 2**64 */ + x *= 2u - (b * x); /* here x*a==1 mod 2**64 */ #endif - /* rho = -1/m mod b */ - *rho = (unsigned long)(((mp_word)1 << ((mp_word) DIGIT_BIT)) - x) & MP_MASK; + /* rho = -1/m mod b */ + *rho = (mp_digit)(((mp_word)1 << (mp_word)MP_DIGIT_BIT) - x) & MP_MASK; - return MP_OKAY; + return MP_OKAY; } #endif - -/* $Source: /cvs/libtom/libtommath/bn_mp_montgomery_setup.c,v $ */ -/* $Revision: 1.5 $ */ -/* $Date: 2006/12/28 01:25:13 $ */ diff --git a/lib/hcrypto/libtommath/bn_mp_mul.c b/lib/hcrypto/libtommath/bn_mp_mul.c index 816e7b2f0bd7..561913a5e6ed 100644 --- a/lib/hcrypto/libtommath/bn_mp_mul.c +++ b/lib/hcrypto/libtommath/bn_mp_mul.c @@ -1,66 +1,52 @@ -#include <tommath.h> +#include "tommath_private.h" #ifdef BN_MP_MUL_C -/* LibTomMath, multiple-precision integer library -- Tom St Denis - * - * LibTomMath is a library that provides multiple-precision - * integer arithmetic as well as number theoretic functionality. - * - * The library was designed directly after the MPI library by - * Michael Fromberger but has been written from scratch with - * additional optimizations in place. - * - * The library is free for all purposes without any express - * guarantee it works. - * - * Tom St Denis, tomstdenis@gmail.com, http://libtom.org - */ +/* LibTomMath, multiple-precision integer library -- Tom St Denis */ +/* SPDX-License-Identifier: Unlicense */ /* high level multiplication (handles sign) */ -int mp_mul (mp_int * a, mp_int * b, mp_int * c) +mp_err mp_mul(const mp_int *a, const mp_int *b, mp_int *c) { - int res, neg; - neg = (a->sign == b->sign) ? MP_ZPOS : MP_NEG; + mp_err err; + int min_len = MP_MIN(a->used, b->used), + max_len = MP_MAX(a->used, b->used), + digs = a->used + b->used + 1; + mp_sign neg = (a->sign == b->sign) ? MP_ZPOS : MP_NEG; - /* use Toom-Cook? */ -#ifdef BN_MP_TOOM_MUL_C - if (MIN (a->used, b->used) >= TOOM_MUL_CUTOFF) { - res = mp_toom_mul(a, b, c); - } else -#endif -#ifdef BN_MP_KARATSUBA_MUL_C - /* use Karatsuba? */ - if (MIN (a->used, b->used) >= KARATSUBA_MUL_CUTOFF) { - res = mp_karatsuba_mul (a, b, c); - } else -#endif - { - /* can we use the fast multiplier? - * - * The fast multiplier can be used if the output will - * have less than MP_WARRAY digits and the number of - * digits won't affect carry propagation - */ - int digs = a->used + b->used + 1; - -#ifdef BN_FAST_S_MP_MUL_DIGS_C - if ((digs < MP_WARRAY) && - MIN(a->used, b->used) <= - (1 << ((CHAR_BIT * sizeof (mp_word)) - (2 * DIGIT_BIT)))) { - res = fast_s_mp_mul_digs (a, b, c, digs); - } else -#endif -#ifdef BN_S_MP_MUL_DIGS_C - res = s_mp_mul (a, b, c); /* uses s_mp_mul_digs */ -#else - res = MP_VAL; -#endif - - } - c->sign = (c->used > 0) ? neg : MP_ZPOS; - return res; + if (MP_HAS(S_MP_BALANCE_MUL) && + /* Check sizes. The smaller one needs to be larger than the Karatsuba cut-off. + * The bigger one needs to be at least about one MP_KARATSUBA_MUL_CUTOFF bigger + * to make some sense, but it depends on architecture, OS, position of the + * stars... so YMMV. + * Using it to cut the input into slices small enough for fast_s_mp_mul_digs + * was actually slower on the author's machine, but YMMV. + */ + (min_len >= MP_KARATSUBA_MUL_CUTOFF) && + ((max_len / 2) >= MP_KARATSUBA_MUL_CUTOFF) && + /* Not much effect was observed below a ratio of 1:2, but again: YMMV. */ + (max_len >= (2 * min_len))) { + err = s_mp_balance_mul(a,b,c); + } else if (MP_HAS(S_MP_TOOM_MUL) && + (min_len >= MP_TOOM_MUL_CUTOFF)) { + err = s_mp_toom_mul(a, b, c); + } else if (MP_HAS(S_MP_KARATSUBA_MUL) && + (min_len >= MP_KARATSUBA_MUL_CUTOFF)) { + err = s_mp_karatsuba_mul(a, b, c); + } else if (MP_HAS(S_MP_MUL_DIGS_FAST) && + /* can we use the fast multiplier? + * + * The fast multiplier can be used if the output will + * have less than MP_WARRAY digits and the number of + * digits won't affect carry propagation + */ + (digs < MP_WARRAY) && + (min_len <= MP_MAXFAST)) { + err = s_mp_mul_digs_fast(a, b, c, digs); + } else if (MP_HAS(S_MP_MUL_DIGS)) { + err = s_mp_mul_digs(a, b, c, digs); + } else { + err = MP_VAL; + } + c->sign = (c->used > 0) ? neg : MP_ZPOS; + return err; } #endif - -/* $Source: /cvs/libtom/libtommath/bn_mp_mul.c,v $ */ -/* $Revision: 1.4 $ */ -/* $Date: 2006/12/28 01:25:13 $ */ diff --git a/lib/hcrypto/libtommath/bn_mp_mul_2.c b/lib/hcrypto/libtommath/bn_mp_mul_2.c index f90654832bec..bc0691a0d14f 100644 --- a/lib/hcrypto/libtommath/bn_mp_mul_2.c +++ b/lib/hcrypto/libtommath/bn_mp_mul_2.c @@ -1,82 +1,64 @@ -#include <tommath.h> +#include "tommath_private.h" #ifdef BN_MP_MUL_2_C -/* LibTomMath, multiple-precision integer library -- Tom St Denis - * - * LibTomMath is a library that provides multiple-precision - * integer arithmetic as well as number theoretic functionality. - * - * The library was designed directly after the MPI library by - * Michael Fromberger but has been written from scratch with - * additional optimizations in place. - * - * The library is free for all purposes without any express - * guarantee it works. - * - * Tom St Denis, tomstdenis@gmail.com, http://libtom.org - */ +/* LibTomMath, multiple-precision integer library -- Tom St Denis */ +/* SPDX-License-Identifier: Unlicense */ /* b = a*2 */ -int mp_mul_2(mp_int * a, mp_int * b) +mp_err mp_mul_2(const mp_int *a, mp_int *b) { - int x, res, oldused; + int x, oldused; + mp_err err; - /* grow to accomodate result */ - if (b->alloc < a->used + 1) { - if ((res = mp_grow (b, a->used + 1)) != MP_OKAY) { - return res; - } - } + /* grow to accomodate result */ + if (b->alloc < (a->used + 1)) { + if ((err = mp_grow(b, a->used + 1)) != MP_OKAY) { + return err; + } + } - oldused = b->used; - b->used = a->used; + oldused = b->used; + b->used = a->used; - { - register mp_digit r, rr, *tmpa, *tmpb; + { + mp_digit r, rr, *tmpa, *tmpb; - /* alias for source */ - tmpa = a->dp; + /* alias for source */ + tmpa = a->dp; - /* alias for dest */ - tmpb = b->dp; + /* alias for dest */ + tmpb = b->dp; - /* carry */ - r = 0; - for (x = 0; x < a->used; x++) { + /* carry */ + r = 0; + for (x = 0; x < a->used; x++) { - /* get what will be the *next* carry bit from the - * MSB of the current digit - */ - rr = *tmpa >> ((mp_digit)(DIGIT_BIT - 1)); + /* get what will be the *next* carry bit from the + * MSB of the current digit + */ + rr = *tmpa >> (mp_digit)(MP_DIGIT_BIT - 1); - /* now shift up this digit, add in the carry [from the previous] */ - *tmpb++ = ((*tmpa++ << ((mp_digit)1)) | r) & MP_MASK; + /* now shift up this digit, add in the carry [from the previous] */ + *tmpb++ = ((*tmpa++ << 1uL) | r) & MP_MASK; - /* copy the carry that would be from the source - * digit into the next iteration - */ - r = rr; - } + /* copy the carry that would be from the source + * digit into the next iteration + */ + r = rr; + } - /* new leading digit? */ - if (r != 0) { - /* add a MSB which is always 1 at this point */ - *tmpb = 1; - ++(b->used); - } + /* new leading digit? */ + if (r != 0u) { + /* add a MSB which is always 1 at this point */ + *tmpb = 1; + ++(b->used); + } - /* now zero any excess digits on the destination - * that we didn't write to - */ - tmpb = b->dp + b->used; - for (x = b->used; x < oldused; x++) { - *tmpb++ = 0; - } - } - b->sign = a->sign; - return MP_OKAY; + /* now zero any excess digits on the destination + * that we didn't write to + */ + MP_ZERO_DIGITS(b->dp + b->used, oldused - b->used); + } + b->sign = a->sign; + return MP_OKAY; } #endif - -/* $Source: /cvs/libtom/libtommath/bn_mp_mul_2.c,v $ */ -/* $Revision: 1.4 $ */ -/* $Date: 2006/12/28 01:25:13 $ */ diff --git a/lib/hcrypto/libtommath/bn_mp_mul_2d.c b/lib/hcrypto/libtommath/bn_mp_mul_2d.c index d023b382cc12..87354de20245 100644 --- a/lib/hcrypto/libtommath/bn_mp_mul_2d.c +++ b/lib/hcrypto/libtommath/bn_mp_mul_2d.c @@ -1,85 +1,69 @@ -#include <tommath.h> +#include "tommath_private.h" #ifdef BN_MP_MUL_2D_C -/* LibTomMath, multiple-precision integer library -- Tom St Denis - * - * LibTomMath is a library that provides multiple-precision - * integer arithmetic as well as number theoretic functionality. - * - * The library was designed directly after the MPI library by - * Michael Fromberger but has been written from scratch with - * additional optimizations in place. - * - * The library is free for all purposes without any express - * guarantee it works. - * - * Tom St Denis, tomstdenis@gmail.com, http://libtom.org - */ +/* LibTomMath, multiple-precision integer library -- Tom St Denis */ +/* SPDX-License-Identifier: Unlicense */ /* shift left by a certain bit count */ -int mp_mul_2d (mp_int * a, int b, mp_int * c) +mp_err mp_mul_2d(const mp_int *a, int b, mp_int *c) { - mp_digit d; - int res; + mp_digit d; + mp_err err; - /* copy */ - if (a != c) { - if ((res = mp_copy (a, c)) != MP_OKAY) { - return res; - } - } + /* copy */ + if (a != c) { + if ((err = mp_copy(a, c)) != MP_OKAY) { + return err; + } + } - if (c->alloc < (int)(c->used + b/DIGIT_BIT + 1)) { - if ((res = mp_grow (c, c->used + b / DIGIT_BIT + 1)) != MP_OKAY) { - return res; - } - } + if (c->alloc < (c->used + (b / MP_DIGIT_BIT) + 1)) { + if ((err = mp_grow(c, c->used + (b / MP_DIGIT_BIT) + 1)) != MP_OKAY) { + return err; + } + } - /* shift by as many digits in the bit count */ - if (b >= (int)DIGIT_BIT) { - if ((res = mp_lshd (c, b / DIGIT_BIT)) != MP_OKAY) { - return res; - } - } + /* shift by as many digits in the bit count */ + if (b >= MP_DIGIT_BIT) { + if ((err = mp_lshd(c, b / MP_DIGIT_BIT)) != MP_OKAY) { + return err; + } + } - /* shift any bit count < DIGIT_BIT */ - d = (mp_digit) (b % DIGIT_BIT); - if (d != 0) { - register mp_digit *tmpc, shift, mask, r, rr; - register int x; + /* shift any bit count < MP_DIGIT_BIT */ + d = (mp_digit)(b % MP_DIGIT_BIT); + if (d != 0u) { + mp_digit *tmpc, shift, mask, r, rr; + int x; - /* bitmask for carries */ - mask = (((mp_digit)1) << d) - 1; + /* bitmask for carries */ + mask = ((mp_digit)1 << d) - (mp_digit)1; - /* shift for msbs */ - shift = DIGIT_BIT - d; + /* shift for msbs */ + shift = (mp_digit)MP_DIGIT_BIT - d; - /* alias */ - tmpc = c->dp; + /* alias */ + tmpc = c->dp; - /* carry */ - r = 0; - for (x = 0; x < c->used; x++) { - /* get the higher bits of the current word */ - rr = (*tmpc >> shift) & mask; + /* carry */ + r = 0; + for (x = 0; x < c->used; x++) { + /* get the higher bits of the current word */ + rr = (*tmpc >> shift) & mask; - /* shift the current word and OR in the carry */ - *tmpc = ((*tmpc << d) | r) & MP_MASK; - ++tmpc; + /* shift the current word and OR in the carry */ + *tmpc = ((*tmpc << d) | r) & MP_MASK; + ++tmpc; - /* set the carry to the carry bits of the current word */ - r = rr; - } + /* set the carry to the carry bits of the current word */ + r = rr; + } - /* set final carry */ - if (r != 0) { - c->dp[(c->used)++] = r; - } - } - mp_clamp (c); - return MP_OKAY; + /* set final carry */ + if (r != 0u) { + c->dp[(c->used)++] = r; + } + } + mp_clamp(c); + return MP_OKAY; } #endif - -/* $Source: /cvs/libtom/libtommath/bn_mp_mul_2d.c,v $ */ -/* $Revision: 1.4 $ */ -/* $Date: 2006/12/28 01:25:13 $ */ diff --git a/lib/hcrypto/libtommath/bn_mp_mul_d.c b/lib/hcrypto/libtommath/bn_mp_mul_d.c index 00f9a899ef47..b56dfa3c9db0 100644 --- a/lib/hcrypto/libtommath/bn_mp_mul_d.c +++ b/lib/hcrypto/libtommath/bn_mp_mul_d.c @@ -1,79 +1,61 @@ -#include <tommath.h> +#include "tommath_private.h" #ifdef BN_MP_MUL_D_C -/* LibTomMath, multiple-precision integer library -- Tom St Denis - * - * LibTomMath is a library that provides multiple-precision - * integer arithmetic as well as number theoretic functionality. - * - * The library was designed directly after the MPI library by - * Michael Fromberger but has been written from scratch with - * additional optimizations in place. - * - * The library is free for all purposes without any express - * guarantee it works. - * - * Tom St Denis, tomstdenis@gmail.com, http://libtom.org - */ +/* LibTomMath, multiple-precision integer library -- Tom St Denis */ +/* SPDX-License-Identifier: Unlicense */ /* multiply by a digit */ -int -mp_mul_d (mp_int * a, mp_digit b, mp_int * c) +mp_err mp_mul_d(const mp_int *a, mp_digit b, mp_int *c) { - mp_digit u, *tmpa, *tmpc; - mp_word r; - int ix, res, olduse; + mp_digit u, *tmpa, *tmpc; + mp_word r; + mp_err err; + int ix, olduse; - /* make sure c is big enough to hold a*b */ - if (c->alloc < a->used + 1) { - if ((res = mp_grow (c, a->used + 1)) != MP_OKAY) { - return res; - } - } + /* make sure c is big enough to hold a*b */ + if (c->alloc < (a->used + 1)) { + if ((err = mp_grow(c, a->used + 1)) != MP_OKAY) { + return err; + } + } - /* get the original destinations used count */ - olduse = c->used; + /* get the original destinations used count */ + olduse = c->used; - /* set the sign */ - c->sign = a->sign; + /* set the sign */ + c->sign = a->sign; - /* alias for a->dp [source] */ - tmpa = a->dp; + /* alias for a->dp [source] */ + tmpa = a->dp; - /* alias for c->dp [dest] */ - tmpc = c->dp; + /* alias for c->dp [dest] */ + tmpc = c->dp; - /* zero carry */ - u = 0; + /* zero carry */ + u = 0; - /* compute columns */ - for (ix = 0; ix < a->used; ix++) { - /* compute product and carry sum for this term */ - r = ((mp_word) u) + ((mp_word)*tmpa++) * ((mp_word)b); + /* compute columns */ + for (ix = 0; ix < a->used; ix++) { + /* compute product and carry sum for this term */ + r = (mp_word)u + ((mp_word)*tmpa++ * (mp_word)b); - /* mask off higher bits to get a single digit */ - *tmpc++ = (mp_digit) (r & ((mp_word) MP_MASK)); + /* mask off higher bits to get a single digit */ + *tmpc++ = (mp_digit)(r & (mp_word)MP_MASK); - /* send carry into next iteration */ - u = (mp_digit) (r >> ((mp_word) DIGIT_BIT)); - } + /* send carry into next iteration */ + u = (mp_digit)(r >> (mp_word)MP_DIGIT_BIT); + } - /* store final carry [if any] and increment ix offset */ - *tmpc++ = u; - ++ix; + /* store final carry [if any] and increment ix offset */ + *tmpc++ = u; + ++ix; - /* now zero digits above the top */ - while (ix++ < olduse) { - *tmpc++ = 0; - } + /* now zero digits above the top */ + MP_ZERO_DIGITS(tmpc, olduse - ix); - /* set used count */ - c->used = a->used + 1; - mp_clamp(c); + /* set used count */ + c->used = a->used + 1; + mp_clamp(c); - return MP_OKAY; + return MP_OKAY; } #endif - -/* $Source: /cvs/libtom/libtommath/bn_mp_mul_d.c,v $ */ -/* $Revision: 1.4 $ */ -/* $Date: 2006/12/28 01:25:13 $ */ diff --git a/lib/hcrypto/libtommath/bn_mp_mulmod.c b/lib/hcrypto/libtommath/bn_mp_mulmod.c index 003ceb9b97e0..160d1626a142 100644 --- a/lib/hcrypto/libtommath/bn_mp_mulmod.c +++ b/lib/hcrypto/libtommath/bn_mp_mulmod.c @@ -1,40 +1,25 @@ -#include <tommath.h> +#include "tommath_private.h" #ifdef BN_MP_MULMOD_C -/* LibTomMath, multiple-precision integer library -- Tom St Denis - * - * LibTomMath is a library that provides multiple-precision - * integer arithmetic as well as number theoretic functionality. - * - * The library was designed directly after the MPI library by - * Michael Fromberger but has been written from scratch with - * additional optimizations in place. - * - * The library is free for all purposes without any express - * guarantee it works. - * - * Tom St Denis, tomstdenis@gmail.com, http://libtom.org - */ +/* LibTomMath, multiple-precision integer library -- Tom St Denis */ +/* SPDX-License-Identifier: Unlicense */ /* d = a * b (mod c) */ -int mp_mulmod (mp_int * a, mp_int * b, mp_int * c, mp_int * d) +mp_err mp_mulmod(const mp_int *a, const mp_int *b, const mp_int *c, mp_int *d) { - int res; - mp_int t; + mp_err err; + mp_int t; - if ((res = mp_init (&t)) != MP_OKAY) { - return res; - } + if ((err = mp_init_size(&t, c->used)) != MP_OKAY) { + return err; + } - if ((res = mp_mul (a, b, &t)) != MP_OKAY) { - mp_clear (&t); - return res; - } - res = mp_mod (&t, c, d); - mp_clear (&t); - return res; + if ((err = mp_mul(a, b, &t)) != MP_OKAY) { + goto LBL_ERR; + } + err = mp_mod(&t, c, d); + +LBL_ERR: + mp_clear(&t); + return err; } #endif - -/* $Source: /cvs/libtom/libtommath/bn_mp_mulmod.c,v $ */ -/* $Revision: 1.5 $ */ -/* $Date: 2006/12/28 01:25:13 $ */ diff --git a/lib/hcrypto/libtommath/bn_mp_n_root.c b/lib/hcrypto/libtommath/bn_mp_n_root.c deleted file mode 100644 index 85d335cb9ef1..000000000000 --- a/lib/hcrypto/libtommath/bn_mp_n_root.c +++ /dev/null @@ -1,132 +0,0 @@ -#include <tommath.h> -#ifdef BN_MP_N_ROOT_C -/* LibTomMath, multiple-precision integer library -- Tom St Denis - * - * LibTomMath is a library that provides multiple-precision - * integer arithmetic as well as number theoretic functionality. - * - * The library was designed directly after the MPI library by - * Michael Fromberger but has been written from scratch with - * additional optimizations in place. - * - * The library is free for all purposes without any express - * guarantee it works. - * - * Tom St Denis, tomstdenis@gmail.com, http://libtom.org - */ - -/* find the n'th root of an integer - * - * Result found such that (c)**b <= a and (c+1)**b > a - * - * This algorithm uses Newton's approximation - * x[i+1] = x[i] - f(x[i])/f'(x[i]) - * which will find the root in log(N) time where - * each step involves a fair bit. This is not meant to - * find huge roots [square and cube, etc]. - */ -int mp_n_root (mp_int * a, mp_digit b, mp_int * c) -{ - mp_int t1, t2, t3; - int res, neg; - - /* input must be positive if b is even */ - if ((b & 1) == 0 && a->sign == MP_NEG) { - return MP_VAL; - } - - if ((res = mp_init (&t1)) != MP_OKAY) { - return res; - } - - if ((res = mp_init (&t2)) != MP_OKAY) { - goto LBL_T1; - } - - if ((res = mp_init (&t3)) != MP_OKAY) { - goto LBL_T2; - } - - /* if a is negative fudge the sign but keep track */ - neg = a->sign; - a->sign = MP_ZPOS; - - /* t2 = 2 */ - mp_set (&t2, 2); - - do { - /* t1 = t2 */ - if ((res = mp_copy (&t2, &t1)) != MP_OKAY) { - goto LBL_T3; - } - - /* t2 = t1 - ((t1**b - a) / (b * t1**(b-1))) */ - - /* t3 = t1**(b-1) */ - if ((res = mp_expt_d (&t1, b - 1, &t3)) != MP_OKAY) { - goto LBL_T3; - } - - /* numerator */ - /* t2 = t1**b */ - if ((res = mp_mul (&t3, &t1, &t2)) != MP_OKAY) { - goto LBL_T3; - } - - /* t2 = t1**b - a */ - if ((res = mp_sub (&t2, a, &t2)) != MP_OKAY) { - goto LBL_T3; - } - - /* denominator */ - /* t3 = t1**(b-1) * b */ - if ((res = mp_mul_d (&t3, b, &t3)) != MP_OKAY) { - goto LBL_T3; - } - - /* t3 = (t1**b - a)/(b * t1**(b-1)) */ - if ((res = mp_div (&t2, &t3, &t3, NULL)) != MP_OKAY) { - goto LBL_T3; - } - - if ((res = mp_sub (&t1, &t3, &t2)) != MP_OKAY) { - goto LBL_T3; - } - } while (mp_cmp (&t1, &t2) != MP_EQ); - - /* result can be off by a few so check */ - for (;;) { - if ((res = mp_expt_d (&t1, b, &t2)) != MP_OKAY) { - goto LBL_T3; - } - - if (mp_cmp (&t2, a) == MP_GT) { - if ((res = mp_sub_d (&t1, 1, &t1)) != MP_OKAY) { - goto LBL_T3; - } - } else { - break; - } - } - - /* reset the sign of a first */ - a->sign = neg; - - /* set the result */ - mp_exch (&t1, c); - - /* set the sign of the result */ - c->sign = neg; - - res = MP_OKAY; - -LBL_T3:mp_clear (&t3); -LBL_T2:mp_clear (&t2); -LBL_T1:mp_clear (&t1); - return res; -} -#endif - -/* $Source: /cvs/libtom/libtommath/bn_mp_n_root.c,v $ */ -/* $Revision: 1.4 $ */ -/* $Date: 2006/12/28 01:25:13 $ */ diff --git a/lib/hcrypto/libtommath/bn_mp_neg.c b/lib/hcrypto/libtommath/bn_mp_neg.c index a7d035ab6dde..264d90097cf5 100644 --- a/lib/hcrypto/libtommath/bn_mp_neg.c +++ b/lib/hcrypto/libtommath/bn_mp_neg.c @@ -1,40 +1,24 @@ -#include <tommath.h> +#include "tommath_private.h" #ifdef BN_MP_NEG_C -/* LibTomMath, multiple-precision integer library -- Tom St Denis - * - * LibTomMath is a library that provides multiple-precision - * integer arithmetic as well as number theoretic functionality. - * - * The library was designed directly after the MPI library by - * Michael Fromberger but has been written from scratch with - * additional optimizations in place. - * - * The library is free for all purposes without any express - * guarantee it works. - * - * Tom St Denis, tomstdenis@gmail.com, http://libtom.org - */ +/* LibTomMath, multiple-precision integer library -- Tom St Denis */ +/* SPDX-License-Identifier: Unlicense */ /* b = -a */ -int mp_neg (mp_int * a, mp_int * b) +mp_err mp_neg(const mp_int *a, mp_int *b) { - int res; - if (a != b) { - if ((res = mp_copy (a, b)) != MP_OKAY) { - return res; - } - } + mp_err err; + if (a != b) { + if ((err = mp_copy(a, b)) != MP_OKAY) { + return err; + } + } - if (mp_iszero(b) != MP_YES) { - b->sign = (a->sign == MP_ZPOS) ? MP_NEG : MP_ZPOS; - } else { - b->sign = MP_ZPOS; - } + if (!MP_IS_ZERO(b)) { + b->sign = (a->sign == MP_ZPOS) ? MP_NEG : MP_ZPOS; + } else { + b->sign = MP_ZPOS; + } - return MP_OKAY; + return MP_OKAY; } #endif - -/* $Source: /cvs/libtom/libtommath/bn_mp_neg.c,v $ */ -/* $Revision: 1.4 $ */ -/* $Date: 2006/12/28 01:25:13 $ */ diff --git a/lib/hcrypto/libtommath/bn_mp_or.c b/lib/hcrypto/libtommath/bn_mp_or.c index bff49954896f..cdacbfbe581c 100644 --- a/lib/hcrypto/libtommath/bn_mp_or.c +++ b/lib/hcrypto/libtommath/bn_mp_or.c @@ -1,50 +1,56 @@ -#include <tommath.h> +#include "tommath_private.h" #ifdef BN_MP_OR_C -/* LibTomMath, multiple-precision integer library -- Tom St Denis - * - * LibTomMath is a library that provides multiple-precision - * integer arithmetic as well as number theoretic functionality. - * - * The library was designed directly after the MPI library by - * Michael Fromberger but has been written from scratch with - * additional optimizations in place. - * - * The library is free for all purposes without any express - * guarantee it works. - * - * Tom St Denis, tomstdenis@gmail.com, http://libtom.org - */ - -/* OR two ints together */ -int mp_or (mp_int * a, mp_int * b, mp_int * c) +/* LibTomMath, multiple-precision integer library -- Tom St Denis */ +/* SPDX-License-Identifier: Unlicense */ + +/* two complement or */ +mp_err mp_or(const mp_int *a, const mp_int *b, mp_int *c) { - int res, ix, px; - mp_int t, *x; - - if (a->used > b->used) { - if ((res = mp_init_copy (&t, a)) != MP_OKAY) { - return res; - } - px = b->used; - x = b; - } else { - if ((res = mp_init_copy (&t, b)) != MP_OKAY) { - return res; - } - px = a->used; - x = a; - } - - for (ix = 0; ix < px; ix++) { - t.dp[ix] |= x->dp[ix]; - } - mp_clamp (&t); - mp_exch (c, &t); - mp_clear (&t); - return MP_OKAY; + int used = MP_MAX(a->used, b->used) + 1, i; + mp_err err; + mp_digit ac = 1, bc = 1, cc = 1; + mp_sign csign = ((a->sign == MP_NEG) || (b->sign == MP_NEG)) ? MP_NEG : MP_ZPOS; + + if (c->alloc < used) { + if ((err = mp_grow(c, used)) != MP_OKAY) { + return err; + } + } + + for (i = 0; i < used; i++) { + mp_digit x, y; + + /* convert to two complement if negative */ + if (a->sign == MP_NEG) { + ac += (i >= a->used) ? MP_MASK : (~a->dp[i] & MP_MASK); + x = ac & MP_MASK; + ac >>= MP_DIGIT_BIT; + } else { + x = (i >= a->used) ? 0uL : a->dp[i]; + } + + /* convert to two complement if negative */ + if (b->sign == MP_NEG) { + bc += (i >= b->used) ? MP_MASK : (~b->dp[i] & MP_MASK); + y = bc & MP_MASK; + bc >>= MP_DIGIT_BIT; + } else { + y = (i >= b->used) ? 0uL : b->dp[i]; + } + + c->dp[i] = x | y; + + /* convert to to sign-magnitude if negative */ + if (csign == MP_NEG) { + cc += ~c->dp[i] & MP_MASK; + c->dp[i] = cc & MP_MASK; + cc >>= MP_DIGIT_BIT; + } + } + + c->used = used; + c->sign = csign; + mp_clamp(c); + return MP_OKAY; } #endif - -/* $Source: /cvs/libtom/libtommath/bn_mp_or.c,v $ */ -/* $Revision: 1.4 $ */ -/* $Date: 2006/12/28 01:25:13 $ */ diff --git a/lib/hcrypto/libtommath/bn_mp_pack.c b/lib/hcrypto/libtommath/bn_mp_pack.c new file mode 100644 index 000000000000..6e00b6fc6795 --- /dev/null +++ b/lib/hcrypto/libtommath/bn_mp_pack.c @@ -0,0 +1,69 @@ +#include "tommath_private.h" +#ifdef BN_MP_PACK_C +/* LibTomMath, multiple-precision integer library -- Tom St Denis */ +/* SPDX-License-Identifier: Unlicense */ + +/* based on gmp's mpz_export. + * see http://gmplib.org/manual/Integer-Import-and-Export.html + */ +mp_err mp_pack(void *rop, size_t maxcount, size_t *written, mp_order order, size_t size, + mp_endian endian, size_t nails, const mp_int *op) +{ + mp_err err; + size_t odd_nails, nail_bytes, i, j, count; + unsigned char odd_nail_mask; + + mp_int t; + + count = mp_pack_count(op, nails, size); + + if (count > maxcount) { + return MP_BUF; + } + + if ((err = mp_init_copy(&t, op)) != MP_OKAY) { + return err; + } + + if (endian == MP_NATIVE_ENDIAN) { + MP_GET_ENDIANNESS(endian); + } + + odd_nails = (nails % 8u); + odd_nail_mask = 0xff; + for (i = 0u; i < odd_nails; ++i) { + odd_nail_mask ^= (unsigned char)(1u << (7u - i)); + } + nail_bytes = nails / 8u; + + for (i = 0u; i < count; ++i) { + for (j = 0u; j < size; ++j) { + unsigned char *byte = (unsigned char *)rop + + (((order == MP_LSB_FIRST) ? i : ((count - 1u) - i)) * size) + + ((endian == MP_LITTLE_ENDIAN) ? j : ((size - 1u) - j)); + + if (j >= (size - nail_bytes)) { + *byte = 0; + continue; + } + + *byte = (unsigned char)((j == ((size - nail_bytes) - 1u)) ? (t.dp[0] & odd_nail_mask) : (t.dp[0] & 0xFFuL)); + + if ((err = mp_div_2d(&t, (j == ((size - nail_bytes) - 1u)) ? (int)(8u - odd_nails) : 8, &t, NULL)) != MP_OKAY) { + goto LBL_ERR; + } + + } + } + + if (written != NULL) { + *written = count; + } + err = MP_OKAY; + +LBL_ERR: + mp_clear(&t); + return err; +} + +#endif diff --git a/lib/hcrypto/libtommath/bn_mp_pack_count.c b/lib/hcrypto/libtommath/bn_mp_pack_count.c new file mode 100644 index 000000000000..dfecdf98fea8 --- /dev/null +++ b/lib/hcrypto/libtommath/bn_mp_pack_count.c @@ -0,0 +1,12 @@ +#include "tommath_private.h" +#ifdef BN_MP_PACK_COUNT_C +/* LibTomMath, multiple-precision integer library -- Tom St Denis */ +/* SPDX-License-Identifier: Unlicense */ + +size_t mp_pack_count(const mp_int *a, size_t nails, size_t size) +{ + size_t bits = (size_t)mp_count_bits(a); + return ((bits / ((size * 8u) - nails)) + (((bits % ((size * 8u) - nails)) != 0u) ? 1u : 0u)); +} + +#endif diff --git a/lib/hcrypto/libtommath/bn_mp_prime_fermat.c b/lib/hcrypto/libtommath/bn_mp_prime_fermat.c index 8e74a337c543..af3e884bbc99 100644 --- a/lib/hcrypto/libtommath/bn_mp_prime_fermat.c +++ b/lib/hcrypto/libtommath/bn_mp_prime_fermat.c @@ -1,19 +1,7 @@ -#include <tommath.h> +#include "tommath_private.h" #ifdef BN_MP_PRIME_FERMAT_C -/* LibTomMath, multiple-precision integer library -- Tom St Denis - * - * LibTomMath is a library that provides multiple-precision - * integer arithmetic as well as number theoretic functionality. - * - * The library was designed directly after the MPI library by - * Michael Fromberger but has been written from scratch with - * additional optimizations in place. - * - * The library is free for all purposes without any express - * guarantee it works. - * - * Tom St Denis, tomstdenis@gmail.com, http://libtom.org - */ +/* LibTomMath, multiple-precision integer library -- Tom St Denis */ +/* SPDX-License-Identifier: Unlicense */ /* performs one Fermat test. * @@ -23,40 +11,37 @@ * * Sets result to 1 if the congruence holds, or zero otherwise. */ -int mp_prime_fermat (mp_int * a, mp_int * b, int *result) +mp_err mp_prime_fermat(const mp_int *a, const mp_int *b, mp_bool *result) { - mp_int t; - int err; - - /* default to composite */ - *result = MP_NO; - - /* ensure b > 1 */ - if (mp_cmp_d(b, 1) != MP_GT) { - return MP_VAL; - } - - /* init t */ - if ((err = mp_init (&t)) != MP_OKAY) { - return err; - } - - /* compute t = b**a mod a */ - if ((err = mp_exptmod (b, a, a, &t)) != MP_OKAY) { - goto LBL_T; - } - - /* is it equal to b? */ - if (mp_cmp (&t, b) == MP_EQ) { - *result = MP_YES; - } - - err = MP_OKAY; -LBL_T:mp_clear (&t); - return err; + mp_int t; + mp_err err; + + /* default to composite */ + *result = MP_NO; + + /* ensure b > 1 */ + if (mp_cmp_d(b, 1uL) != MP_GT) { + return MP_VAL; + } + + /* init t */ + if ((err = mp_init(&t)) != MP_OKAY) { + return err; + } + + /* compute t = b**a mod a */ + if ((err = mp_exptmod(b, a, a, &t)) != MP_OKAY) { + goto LBL_T; + } + + /* is it equal to b? */ + if (mp_cmp(&t, b) == MP_EQ) { + *result = MP_YES; + } + + err = MP_OKAY; +LBL_T: + mp_clear(&t); + return err; } #endif - -/* $Source: /cvs/libtom/libtommath/bn_mp_prime_fermat.c,v $ */ -/* $Revision: 1.4 $ */ -/* $Date: 2006/12/28 01:25:13 $ */ diff --git a/lib/hcrypto/libtommath/bn_mp_prime_frobenius_underwood.c b/lib/hcrypto/libtommath/bn_mp_prime_frobenius_underwood.c new file mode 100644 index 000000000000..253e8d53bc27 --- /dev/null +++ b/lib/hcrypto/libtommath/bn_mp_prime_frobenius_underwood.c @@ -0,0 +1,132 @@ +#include "tommath_private.h" +#ifdef BN_MP_PRIME_FROBENIUS_UNDERWOOD_C + +/* LibTomMath, multiple-precision integer library -- Tom St Denis */ +/* SPDX-License-Identifier: Unlicense */ + +/* + * See file bn_mp_prime_is_prime.c or the documentation in doc/bn.tex for the details + */ +#ifndef LTM_USE_ONLY_MR + +#ifdef MP_8BIT +/* + * floor of positive solution of + * (2^16)-1 = (a+4)*(2*a+5) + * TODO: Both values are smaller than N^(1/4), would have to use a bigint + * for a instead but any a biger than about 120 are already so rare that + * it is possible to ignore them and still get enough pseudoprimes. + * But it is still a restriction of the set of available pseudoprimes + * which makes this implementation less secure if used stand-alone. + */ +#define LTM_FROBENIUS_UNDERWOOD_A 177 +#else +#define LTM_FROBENIUS_UNDERWOOD_A 32764 +#endif +mp_err mp_prime_frobenius_underwood(const mp_int *N, mp_bool *result) +{ + mp_int T1z, T2z, Np1z, sz, tz; + + int a, ap2, length, i, j; + mp_err err; + + *result = MP_NO; + + if ((err = mp_init_multi(&T1z, &T2z, &Np1z, &sz, &tz, NULL)) != MP_OKAY) { + return err; + } + + for (a = 0; a < LTM_FROBENIUS_UNDERWOOD_A; a++) { + /* TODO: That's ugly! No, really, it is! */ + if ((a==2) || (a==4) || (a==7) || (a==8) || (a==10) || + (a==14) || (a==18) || (a==23) || (a==26) || (a==28)) { + continue; + } + /* (32764^2 - 4) < 2^31, no bigint for >MP_8BIT needed) */ + mp_set_u32(&T1z, (uint32_t)a); + + if ((err = mp_sqr(&T1z, &T1z)) != MP_OKAY) goto LBL_FU_ERR; + + if ((err = mp_sub_d(&T1z, 4uL, &T1z)) != MP_OKAY) goto LBL_FU_ERR; + + if ((err = mp_kronecker(&T1z, N, &j)) != MP_OKAY) goto LBL_FU_ERR; + + if (j == -1) { + break; + } + + if (j == 0) { + /* composite */ + goto LBL_FU_ERR; + } + } + /* Tell it a composite and set return value accordingly */ + if (a >= LTM_FROBENIUS_UNDERWOOD_A) { + err = MP_ITER; + goto LBL_FU_ERR; + } + /* Composite if N and (a+4)*(2*a+5) are not coprime */ + mp_set_u32(&T1z, (uint32_t)((a+4)*((2*a)+5))); + + if ((err = mp_gcd(N, &T1z, &T1z)) != MP_OKAY) goto LBL_FU_ERR; + + if (!((T1z.used == 1) && (T1z.dp[0] == 1u))) goto LBL_FU_ERR; + + ap2 = a + 2; + if ((err = mp_add_d(N, 1uL, &Np1z)) != MP_OKAY) goto LBL_FU_ERR; + + mp_set(&sz, 1uL); + mp_set(&tz, 2uL); + length = mp_count_bits(&Np1z); + + for (i = length - 2; i >= 0; i--) { + /* + * temp = (sz*(a*sz+2*tz))%N; + * tz = ((tz-sz)*(tz+sz))%N; + * sz = temp; + */ + if ((err = mp_mul_2(&tz, &T2z)) != MP_OKAY) goto LBL_FU_ERR; + + /* a = 0 at about 50% of the cases (non-square and odd input) */ + if (a != 0) { + if ((err = mp_mul_d(&sz, (mp_digit)a, &T1z)) != MP_OKAY) goto LBL_FU_ERR; + if ((err = mp_add(&T1z, &T2z, &T2z)) != MP_OKAY) goto LBL_FU_ERR; + } + + if ((err = mp_mul(&T2z, &sz, &T1z)) != MP_OKAY) goto LBL_FU_ERR; + if ((err = mp_sub(&tz, &sz, &T2z)) != MP_OKAY) goto LBL_FU_ERR; + if ((err = mp_add(&sz, &tz, &sz)) != MP_OKAY) goto LBL_FU_ERR; + if ((err = mp_mul(&sz, &T2z, &tz)) != MP_OKAY) goto LBL_FU_ERR; + if ((err = mp_mod(&tz, N, &tz)) != MP_OKAY) goto LBL_FU_ERR; + if ((err = mp_mod(&T1z, N, &sz)) != MP_OKAY) goto LBL_FU_ERR; + if (s_mp_get_bit(&Np1z, (unsigned int)i) == MP_YES) { + /* + * temp = (a+2) * sz + tz + * tz = 2 * tz - sz + * sz = temp + */ + if (a == 0) { + if ((err = mp_mul_2(&sz, &T1z)) != MP_OKAY) goto LBL_FU_ERR; + } else { + if ((err = mp_mul_d(&sz, (mp_digit)ap2, &T1z)) != MP_OKAY) goto LBL_FU_ERR; + } + if ((err = mp_add(&T1z, &tz, &T1z)) != MP_OKAY) goto LBL_FU_ERR; + if ((err = mp_mul_2(&tz, &T2z)) != MP_OKAY) goto LBL_FU_ERR; + if ((err = mp_sub(&T2z, &sz, &tz)) != MP_OKAY) goto LBL_FU_ERR; + mp_exch(&sz, &T1z); + } + } + + mp_set_u32(&T1z, (uint32_t)((2 * a) + 5)); + if ((err = mp_mod(&T1z, N, &T1z)) != MP_OKAY) goto LBL_FU_ERR; + if (MP_IS_ZERO(&sz) && (mp_cmp(&tz, &T1z) == MP_EQ)) { + *result = MP_YES; + } + +LBL_FU_ERR: + mp_clear_multi(&tz, &sz, &Np1z, &T2z, &T1z, NULL); + return err; +} + +#endif +#endif diff --git a/lib/hcrypto/libtommath/bn_mp_prime_is_divisible.c b/lib/hcrypto/libtommath/bn_mp_prime_is_divisible.c deleted file mode 100644 index 766cde95a683..000000000000 --- a/lib/hcrypto/libtommath/bn_mp_prime_is_divisible.c +++ /dev/null @@ -1,50 +0,0 @@ -#include <tommath.h> -#ifdef BN_MP_PRIME_IS_DIVISIBLE_C -/* LibTomMath, multiple-precision integer library -- Tom St Denis - * - * LibTomMath is a library that provides multiple-precision - * integer arithmetic as well as number theoretic functionality. - * - * The library was designed directly after the MPI library by - * Michael Fromberger but has been written from scratch with - * additional optimizations in place. - * - * The library is free for all purposes without any express - * guarantee it works. - * - * Tom St Denis, tomstdenis@gmail.com, http://libtom.org - */ - -/* determines if an integers is divisible by one - * of the first PRIME_SIZE primes or not - * - * sets result to 0 if not, 1 if yes - */ -int mp_prime_is_divisible (mp_int * a, int *result) -{ - int err, ix; - mp_digit res; - - /* default to not */ - *result = MP_NO; - - for (ix = 0; ix < PRIME_SIZE; ix++) { - /* what is a mod LBL_prime_tab[ix] */ - if ((err = mp_mod_d (a, ltm_prime_tab[ix], &res)) != MP_OKAY) { - return err; - } - - /* is the residue zero? */ - if (res == 0) { - *result = MP_YES; - return MP_OKAY; - } - } - - return MP_OKAY; -} -#endif - -/* $Source: /cvs/libtom/libtommath/bn_mp_prime_is_divisible.c,v $ */ -/* $Revision: 1.4 $ */ -/* $Date: 2006/12/28 01:25:13 $ */ diff --git a/lib/hcrypto/libtommath/bn_mp_prime_is_prime.c b/lib/hcrypto/libtommath/bn_mp_prime_is_prime.c index c316d621090b..7f9fc0b4505c 100644 --- a/lib/hcrypto/libtommath/bn_mp_prime_is_prime.c +++ b/lib/hcrypto/libtommath/bn_mp_prime_is_prime.c @@ -1,83 +1,314 @@ -#include <tommath.h> +#include "tommath_private.h" #ifdef BN_MP_PRIME_IS_PRIME_C -/* LibTomMath, multiple-precision integer library -- Tom St Denis - * - * LibTomMath is a library that provides multiple-precision - * integer arithmetic as well as number theoretic functionality. - * - * The library was designed directly after the MPI library by - * Michael Fromberger but has been written from scratch with - * additional optimizations in place. - * - * The library is free for all purposes without any express - * guarantee it works. - * - * Tom St Denis, tomstdenis@gmail.com, http://libtom.org - */ - -/* performs a variable number of rounds of Miller-Rabin - * - * Probability of error after t rounds is no more than - - * - * Sets result to 1 if probably prime, 0 otherwise - */ -int mp_prime_is_prime (mp_int * a, int t, int *result) +/* LibTomMath, multiple-precision integer library -- Tom St Denis */ +/* SPDX-License-Identifier: Unlicense */ + +/* portable integer log of two with small footprint */ +static unsigned int s_floor_ilog2(int value) { - mp_int b; - int ix, err, res; + unsigned int r = 0; + while ((value >>= 1) != 0) { + r++; + } + return r; +} + - /* default to no */ - *result = MP_NO; +mp_err mp_prime_is_prime(const mp_int *a, int t, mp_bool *result) +{ + mp_int b; + int ix, p_max = 0, size_a, len; + mp_bool res; + mp_err err; + unsigned int fips_rand, mask; - /* valid value of t? */ - if (t <= 0 || t > PRIME_SIZE) { - return MP_VAL; - } + /* default to no */ + *result = MP_NO; - /* is the input equal to one of the primes in the table? */ - for (ix = 0; ix < PRIME_SIZE; ix++) { - if (mp_cmp_d(a, ltm_prime_tab[ix]) == MP_EQ) { - *result = 1; + /* Some shortcuts */ + /* N > 3 */ + if (a->used == 1) { + if ((a->dp[0] == 0u) || (a->dp[0] == 1u)) { + *result = MP_NO; + return MP_OKAY; + } + if (a->dp[0] == 2u) { + *result = MP_YES; return MP_OKAY; } - } + } - /* first perform trial division */ - if ((err = mp_prime_is_divisible (a, &res)) != MP_OKAY) { - return err; - } + /* N must be odd */ + if (MP_IS_EVEN(a)) { + return MP_OKAY; + } + /* N is not a perfect square: floor(sqrt(N))^2 != N */ + if ((err = mp_is_square(a, &res)) != MP_OKAY) { + return err; + } + if (res != MP_NO) { + return MP_OKAY; + } - /* return if it was trivially divisible */ - if (res == MP_YES) { - return MP_OKAY; - } + /* is the input equal to one of the primes in the table? */ + for (ix = 0; ix < PRIVATE_MP_PRIME_TAB_SIZE; ix++) { + if (mp_cmp_d(a, s_mp_prime_tab[ix]) == MP_EQ) { + *result = MP_YES; + return MP_OKAY; + } + } +#ifdef MP_8BIT + /* The search in the loop above was exhaustive in this case */ + if ((a->used == 1) && (PRIVATE_MP_PRIME_TAB_SIZE >= 31)) { + return MP_OKAY; + } +#endif - /* now perform the miller-rabin rounds */ - if ((err = mp_init (&b)) != MP_OKAY) { - return err; - } + /* first perform trial division */ + if ((err = s_mp_prime_is_divisible(a, &res)) != MP_OKAY) { + return err; + } - for (ix = 0; ix < t; ix++) { - /* set the prime */ - mp_set (&b, ltm_prime_tab[ix]); + /* return if it was trivially divisible */ + if (res == MP_YES) { + return MP_OKAY; + } - if ((err = mp_prime_miller_rabin (a, &b, &res)) != MP_OKAY) { - goto LBL_B; - } + /* + Run the Miller-Rabin test with base 2 for the BPSW test. + */ + if ((err = mp_init_set(&b, 2uL)) != MP_OKAY) { + return err; + } - if (res == MP_NO) { + if ((err = mp_prime_miller_rabin(a, &b, &res)) != MP_OKAY) { + goto LBL_B; + } + if (res == MP_NO) { goto LBL_B; - } - } + } + /* + Rumours have it that Mathematica does a second M-R test with base 3. + Other rumours have it that their strong L-S test is slightly different. + It does not hurt, though, beside a bit of extra runtime. + */ + b.dp[0]++; + if ((err = mp_prime_miller_rabin(a, &b, &res)) != MP_OKAY) { + goto LBL_B; + } + if (res == MP_NO) { + goto LBL_B; + } - /* passed the test */ - *result = MP_YES; -LBL_B:mp_clear (&b); - return err; -} + /* + * Both, the Frobenius-Underwood test and the the Lucas-Selfridge test are quite + * slow so if speed is an issue, define LTM_USE_ONLY_MR to use M-R tests with + * bases 2, 3 and t random bases. + */ +#ifndef LTM_USE_ONLY_MR + if (t >= 0) { + /* + * Use a Frobenius-Underwood test instead of the Lucas-Selfridge test for + * MP_8BIT (It is unknown if the Lucas-Selfridge test works with 16-bit + * integers but the necesssary analysis is on the todo-list). + */ +#if defined (MP_8BIT) || defined (LTM_USE_FROBENIUS_TEST) + err = mp_prime_frobenius_underwood(a, &res); + if ((err != MP_OKAY) && (err != MP_ITER)) { + goto LBL_B; + } + if (res == MP_NO) { + goto LBL_B; + } +#else + if ((err = mp_prime_strong_lucas_selfridge(a, &res)) != MP_OKAY) { + goto LBL_B; + } + if (res == MP_NO) { + goto LBL_B; + } +#endif + } #endif -/* $Source: /cvs/libtom/libtommath/bn_mp_prime_is_prime.c,v $ */ -/* $Revision: 1.4 $ */ -/* $Date: 2006/12/28 01:25:13 $ */ + /* run at least one Miller-Rabin test with a random base */ + if (t == 0) { + t = 1; + } + + /* + Only recommended if the input range is known to be < 3317044064679887385961981 + + It uses the bases necessary for a deterministic M-R test if the input is + smaller than 3317044064679887385961981 + The caller has to check the size. + TODO: can be made a bit finer grained but comparing is not free. + */ + if (t < 0) { + /* + Sorenson, Jonathan; Webster, Jonathan (2015). + "Strong Pseudoprimes to Twelve Prime Bases". + */ + /* 0x437ae92817f9fc85b7e5 = 318665857834031151167461 */ + if ((err = mp_read_radix(&b, "437ae92817f9fc85b7e5", 16)) != MP_OKAY) { + goto LBL_B; + } + + if (mp_cmp(a, &b) == MP_LT) { + p_max = 12; + } else { + /* 0x2be6951adc5b22410a5fd = 3317044064679887385961981 */ + if ((err = mp_read_radix(&b, "2be6951adc5b22410a5fd", 16)) != MP_OKAY) { + goto LBL_B; + } + + if (mp_cmp(a, &b) == MP_LT) { + p_max = 13; + } else { + err = MP_VAL; + goto LBL_B; + } + } + + /* we did bases 2 and 3 already, skip them */ + for (ix = 2; ix < p_max; ix++) { + mp_set(&b, s_mp_prime_tab[ix]); + if ((err = mp_prime_miller_rabin(a, &b, &res)) != MP_OKAY) { + goto LBL_B; + } + if (res == MP_NO) { + goto LBL_B; + } + } + } + /* + Do "t" M-R tests with random bases between 3 and "a". + See Fips 186.4 p. 126ff + */ + else if (t > 0) { + /* + * The mp_digit's have a defined bit-size but the size of the + * array a.dp is a simple 'int' and this library can not assume full + * compliance to the current C-standard (ISO/IEC 9899:2011) because + * it gets used for small embeded processors, too. Some of those MCUs + * have compilers that one cannot call standard compliant by any means. + * Hence the ugly type-fiddling in the following code. + */ + size_a = mp_count_bits(a); + mask = (1u << s_floor_ilog2(size_a)) - 1u; + /* + Assuming the General Rieman hypothesis (never thought to write that in a + comment) the upper bound can be lowered to 2*(log a)^2. + E. Bach, "Explicit bounds for primality testing and related problems," + Math. Comp. 55 (1990), 355-380. + + size_a = (size_a/10) * 7; + len = 2 * (size_a * size_a); + + E.g.: a number of size 2^2048 would be reduced to the upper limit + + floor(2048/10)*7 = 1428 + 2 * 1428^2 = 4078368 + + (would have been ~4030331.9962 with floats and natural log instead) + That number is smaller than 2^28, the default bit-size of mp_digit. + */ + + /* + How many tests, you might ask? Dana Jacobsen of Math::Prime::Util fame + does exactly 1. In words: one. Look at the end of _GMP_is_prime() in + Math-Prime-Util-GMP-0.50/primality.c if you do not believe it. + + The function mp_rand() goes to some length to use a cryptographically + good PRNG. That also means that the chance to always get the same base + in the loop is non-zero, although very low. + If the BPSW test and/or the addtional Frobenious test have been + performed instead of just the Miller-Rabin test with the bases 2 and 3, + a single extra test should suffice, so such a very unlikely event + will not do much harm. + + To preemptivly answer the dangling question: no, a witness does not + need to be prime. + */ + for (ix = 0; ix < t; ix++) { + /* mp_rand() guarantees the first digit to be non-zero */ + if ((err = mp_rand(&b, 1)) != MP_OKAY) { + goto LBL_B; + } + /* + * Reduce digit before casting because mp_digit might be bigger than + * an unsigned int and "mask" on the other side is most probably not. + */ + fips_rand = (unsigned int)(b.dp[0] & (mp_digit) mask); +#ifdef MP_8BIT + /* + * One 8-bit digit is too small, so concatenate two if the size of + * unsigned int allows for it. + */ + if ((MP_SIZEOF_BITS(unsigned int)/2) >= MP_SIZEOF_BITS(mp_digit)) { + if ((err = mp_rand(&b, 1)) != MP_OKAY) { + goto LBL_B; + } + fips_rand <<= MP_SIZEOF_BITS(mp_digit); + fips_rand |= (unsigned int) b.dp[0]; + fips_rand &= mask; + } +#endif + if (fips_rand > (unsigned int)(INT_MAX - MP_DIGIT_BIT)) { + len = INT_MAX / MP_DIGIT_BIT; + } else { + len = (((int)fips_rand + MP_DIGIT_BIT) / MP_DIGIT_BIT); + } + /* Unlikely. */ + if (len < 0) { + ix--; + continue; + } + /* + * As mentioned above, one 8-bit digit is too small and + * although it can only happen in the unlikely case that + * an "unsigned int" is smaller than 16 bit a simple test + * is cheap and the correction even cheaper. + */ +#ifdef MP_8BIT + /* All "a" < 2^8 have been caught before */ + if (len == 1) { + len++; + } +#endif + if ((err = mp_rand(&b, len)) != MP_OKAY) { + goto LBL_B; + } + /* + * That number might got too big and the witness has to be + * smaller than "a" + */ + len = mp_count_bits(&b); + if (len >= size_a) { + len = (len - size_a) + 1; + if ((err = mp_div_2d(&b, len, &b, NULL)) != MP_OKAY) { + goto LBL_B; + } + } + /* Although the chance for b <= 3 is miniscule, try again. */ + if (mp_cmp_d(&b, 3uL) != MP_GT) { + ix--; + continue; + } + if ((err = mp_prime_miller_rabin(a, &b, &res)) != MP_OKAY) { + goto LBL_B; + } + if (res == MP_NO) { + goto LBL_B; + } + } + } + + /* passed the test */ + *result = MP_YES; +LBL_B: + mp_clear(&b); + return err; +} + +#endif diff --git a/lib/hcrypto/libtommath/bn_mp_prime_miller_rabin.c b/lib/hcrypto/libtommath/bn_mp_prime_miller_rabin.c index 60a8c48eae95..96470dba71fd 100644 --- a/lib/hcrypto/libtommath/bn_mp_prime_miller_rabin.c +++ b/lib/hcrypto/libtommath/bn_mp_prime_miller_rabin.c @@ -1,19 +1,7 @@ -#include <tommath.h> +#include "tommath_private.h" #ifdef BN_MP_PRIME_MILLER_RABIN_C -/* LibTomMath, multiple-precision integer library -- Tom St Denis - * - * LibTomMath is a library that provides multiple-precision - * integer arithmetic as well as number theoretic functionality. - * - * The library was designed directly after the MPI library by - * Michael Fromberger but has been written from scratch with - * additional optimizations in place. - * - * The library is free for all purposes without any express - * guarantee it works. - * - * Tom St Denis, tomstdenis@gmail.com, http://libtom.org - */ +/* LibTomMath, multiple-precision integer library -- Tom St Denis */ +/* SPDX-License-Identifier: Unlicense */ /* Miller-Rabin test of "a" to the base of "b" as described in * HAC pp. 139 Algorithm 4.24 @@ -22,82 +10,82 @@ * Randomly the chance of error is no more than 1/4 and often * very much lower. */ -int mp_prime_miller_rabin (mp_int * a, mp_int * b, int *result) +mp_err mp_prime_miller_rabin(const mp_int *a, const mp_int *b, mp_bool *result) { - mp_int n1, y, r; - int s, j, err; + mp_int n1, y, r; + mp_err err; + int s, j; - /* default */ - *result = MP_NO; + /* default */ + *result = MP_NO; - /* ensure b > 1 */ - if (mp_cmp_d(b, 1) != MP_GT) { - return MP_VAL; - } + /* ensure b > 1 */ + if (mp_cmp_d(b, 1uL) != MP_GT) { + return MP_VAL; + } - /* get n1 = a - 1 */ - if ((err = mp_init_copy (&n1, a)) != MP_OKAY) { - return err; - } - if ((err = mp_sub_d (&n1, 1, &n1)) != MP_OKAY) { - goto LBL_N1; - } + /* get n1 = a - 1 */ + if ((err = mp_init_copy(&n1, a)) != MP_OKAY) { + return err; + } + if ((err = mp_sub_d(&n1, 1uL, &n1)) != MP_OKAY) { + goto LBL_N1; + } - /* set 2**s * r = n1 */ - if ((err = mp_init_copy (&r, &n1)) != MP_OKAY) { - goto LBL_N1; - } + /* set 2**s * r = n1 */ + if ((err = mp_init_copy(&r, &n1)) != MP_OKAY) { + goto LBL_N1; + } - /* count the number of least significant bits - * which are zero - */ - s = mp_cnt_lsb(&r); + /* count the number of least significant bits + * which are zero + */ + s = mp_cnt_lsb(&r); - /* now divide n - 1 by 2**s */ - if ((err = mp_div_2d (&r, s, &r, NULL)) != MP_OKAY) { - goto LBL_R; - } + /* now divide n - 1 by 2**s */ + if ((err = mp_div_2d(&r, s, &r, NULL)) != MP_OKAY) { + goto LBL_R; + } - /* compute y = b**r mod a */ - if ((err = mp_init (&y)) != MP_OKAY) { - goto LBL_R; - } - if ((err = mp_exptmod (b, &r, a, &y)) != MP_OKAY) { - goto LBL_Y; - } + /* compute y = b**r mod a */ + if ((err = mp_init(&y)) != MP_OKAY) { + goto LBL_R; + } + if ((err = mp_exptmod(b, &r, a, &y)) != MP_OKAY) { + goto LBL_Y; + } - /* if y != 1 and y != n1 do */ - if (mp_cmp_d (&y, 1) != MP_EQ && mp_cmp (&y, &n1) != MP_EQ) { - j = 1; - /* while j <= s-1 and y != n1 */ - while ((j <= (s - 1)) && mp_cmp (&y, &n1) != MP_EQ) { - if ((err = mp_sqrmod (&y, a, &y)) != MP_OKAY) { - goto LBL_Y; + /* if y != 1 and y != n1 do */ + if ((mp_cmp_d(&y, 1uL) != MP_EQ) && (mp_cmp(&y, &n1) != MP_EQ)) { + j = 1; + /* while j <= s-1 and y != n1 */ + while ((j <= (s - 1)) && (mp_cmp(&y, &n1) != MP_EQ)) { + if ((err = mp_sqrmod(&y, a, &y)) != MP_OKAY) { + goto LBL_Y; + } + + /* if y == 1 then composite */ + if (mp_cmp_d(&y, 1uL) == MP_EQ) { + goto LBL_Y; + } + + ++j; } - /* if y == 1 then composite */ - if (mp_cmp_d (&y, 1) == MP_EQ) { + /* if y != n1 then composite */ + if (mp_cmp(&y, &n1) != MP_EQ) { goto LBL_Y; } + } - ++j; - } - - /* if y != n1 then composite */ - if (mp_cmp (&y, &n1) != MP_EQ) { - goto LBL_Y; - } - } - - /* probably prime now */ - *result = MP_YES; -LBL_Y:mp_clear (&y); -LBL_R:mp_clear (&r); -LBL_N1:mp_clear (&n1); - return err; + /* probably prime now */ + *result = MP_YES; +LBL_Y: + mp_clear(&y); +LBL_R: + mp_clear(&r); +LBL_N1: + mp_clear(&n1); + return err; } #endif - -/* $Source: /cvs/libtom/libtommath/bn_mp_prime_miller_rabin.c,v $ */ -/* $Revision: 1.4 $ */ -/* $Date: 2006/12/28 01:25:13 $ */ diff --git a/lib/hcrypto/libtommath/bn_mp_prime_next_prime.c b/lib/hcrypto/libtommath/bn_mp_prime_next_prime.c index 8cd3ec2a5270..d65656578fa2 100644 --- a/lib/hcrypto/libtommath/bn_mp_prime_next_prime.c +++ b/lib/hcrypto/libtommath/bn_mp_prime_next_prime.c @@ -1,70 +1,42 @@ -#include <tommath.h> +#include "tommath_private.h" #ifdef BN_MP_PRIME_NEXT_PRIME_C -/* LibTomMath, multiple-precision integer library -- Tom St Denis - * - * LibTomMath is a library that provides multiple-precision - * integer arithmetic as well as number theoretic functionality. - * - * The library was designed directly after the MPI library by - * Michael Fromberger but has been written from scratch with - * additional optimizations in place. - * - * The library is free for all purposes without any express - * guarantee it works. - * - * Tom St Denis, tomstdenis@gmail.com, http://libtom.org - */ +/* LibTomMath, multiple-precision integer library -- Tom St Denis */ +/* SPDX-License-Identifier: Unlicense */ /* finds the next prime after the number "a" using "t" trials * of Miller-Rabin. * * bbs_style = 1 means the prime must be congruent to 3 mod 4 */ -int mp_prime_next_prime(mp_int *a, int t, int bbs_style) +mp_err mp_prime_next_prime(mp_int *a, int t, int bbs_style) { - int err, res = MP_NO, x, y; - mp_digit res_tab[PRIME_SIZE], step, kstep; + int x, y; + mp_ord cmp; + mp_err err; + mp_bool res = MP_NO; + mp_digit res_tab[PRIVATE_MP_PRIME_TAB_SIZE], step, kstep; mp_int b; - /* ensure t is valid */ - if (t <= 0 || t > PRIME_SIZE) { - return MP_VAL; - } - /* force positive */ a->sign = MP_ZPOS; /* simple algo if a is less than the largest prime in the table */ - if (mp_cmp_d(a, ltm_prime_tab[PRIME_SIZE-1]) == MP_LT) { - /* find which prime it is bigger than */ - for (x = PRIME_SIZE - 2; x >= 0; x--) { - if (mp_cmp_d(a, ltm_prime_tab[x]) != MP_LT) { - if (bbs_style == 1) { - /* ok we found a prime smaller or - * equal [so the next is larger] - * - * however, the prime must be - * congruent to 3 mod 4 - */ - if ((ltm_prime_tab[x + 1] & 3) != 3) { - /* scan upwards for a prime congruent to 3 mod 4 */ - for (y = x + 1; y < PRIME_SIZE; y++) { - if ((ltm_prime_tab[y] & 3) == 3) { - mp_set(a, ltm_prime_tab[y]); - return MP_OKAY; - } - } - } - } else { - mp_set(a, ltm_prime_tab[x + 1]); - return MP_OKAY; - } - } - } - /* at this point a maybe 1 */ - if (mp_cmp_d(a, 1) == MP_EQ) { - mp_set(a, 2); - return MP_OKAY; + if (mp_cmp_d(a, s_mp_prime_tab[PRIVATE_MP_PRIME_TAB_SIZE-1]) == MP_LT) { + /* find which prime it is bigger than "a" */ + for (x = 0; x < PRIVATE_MP_PRIME_TAB_SIZE; x++) { + cmp = mp_cmp_d(a, s_mp_prime_tab[x]); + if (cmp == MP_EQ) { + continue; + } + if (cmp != MP_GT) { + if ((bbs_style == 1) && ((s_mp_prime_tab[x] & 3u) != 3u)) { + /* try again until we get a prime congruent to 3 mod 4 */ + continue; + } else { + mp_set(a, s_mp_prime_tab[x]); + return MP_OKAY; + } + } } /* fall through to the sieve */ } @@ -80,21 +52,23 @@ int mp_prime_next_prime(mp_int *a, int t, int bbs_style) if (bbs_style == 1) { /* if a mod 4 != 3 subtract the correct value to make it so */ - if ((a->dp[0] & 3) != 3) { - if ((err = mp_sub_d(a, (a->dp[0] & 3) + 1, a)) != MP_OKAY) { return err; }; + if ((a->dp[0] & 3u) != 3u) { + if ((err = mp_sub_d(a, (a->dp[0] & 3u) + 1u, a)) != MP_OKAY) { + return err; + } } } else { - if (mp_iseven(a) == 1) { + if (MP_IS_EVEN(a)) { /* force odd */ - if ((err = mp_sub_d(a, 1, a)) != MP_OKAY) { + if ((err = mp_sub_d(a, 1uL, a)) != MP_OKAY) { return err; } } } /* generate the restable */ - for (x = 1; x < PRIME_SIZE; x++) { - if ((err = mp_mod_d(a, ltm_prime_tab[x], res_tab + x)) != MP_OKAY) { + for (x = 1; x < PRIVATE_MP_PRIME_TAB_SIZE; x++) { + if ((err = mp_mod_d(a, s_mp_prime_tab[x], res_tab + x)) != MP_OKAY) { return err; } } @@ -115,43 +89,35 @@ int mp_prime_next_prime(mp_int *a, int t, int bbs_style) step += kstep; /* compute the new residue without using division */ - for (x = 1; x < PRIME_SIZE; x++) { - /* add the step to each residue */ - res_tab[x] += kstep; - - /* subtract the modulus [instead of using division] */ - if (res_tab[x] >= ltm_prime_tab[x]) { - res_tab[x] -= ltm_prime_tab[x]; - } - - /* set flag if zero */ - if (res_tab[x] == 0) { - y = 1; - } + for (x = 1; x < PRIVATE_MP_PRIME_TAB_SIZE; x++) { + /* add the step to each residue */ + res_tab[x] += kstep; + + /* subtract the modulus [instead of using division] */ + if (res_tab[x] >= s_mp_prime_tab[x]) { + res_tab[x] -= s_mp_prime_tab[x]; + } + + /* set flag if zero */ + if (res_tab[x] == 0u) { + y = 1; + } } - } while (y == 1 && step < ((((mp_digit)1)<<DIGIT_BIT) - kstep)); + } while ((y == 1) && (step < (((mp_digit)1 << MP_DIGIT_BIT) - kstep))); /* add the step */ if ((err = mp_add_d(a, step, a)) != MP_OKAY) { goto LBL_ERR; } - /* if didn't pass sieve and step == MAX then skip test */ - if (y == 1 && step >= ((((mp_digit)1)<<DIGIT_BIT) - kstep)) { + /* if didn't pass sieve and step == MP_MAX then skip test */ + if ((y == 1) && (step >= (((mp_digit)1 << MP_DIGIT_BIT) - kstep))) { continue; } - /* is this prime? */ - for (x = 0; x < t; x++) { - mp_set(&b, ltm_prime_tab[x]); - if ((err = mp_prime_miller_rabin(a, &b, &res)) != MP_OKAY) { - goto LBL_ERR; - } - if (res == MP_NO) { - break; - } + if ((err = mp_prime_is_prime(a, t, &res)) != MP_OKAY) { + goto LBL_ERR; } - if (res == MP_YES) { break; } @@ -164,7 +130,3 @@ LBL_ERR: } #endif - -/* $Source: /cvs/libtom/libtommath/bn_mp_prime_next_prime.c,v $ */ -/* $Revision: 1.4 $ */ -/* $Date: 2006/12/28 01:25:13 $ */ diff --git a/lib/hcrypto/libtommath/bn_mp_prime_rabin_miller_trials.c b/lib/hcrypto/libtommath/bn_mp_prime_rabin_miller_trials.c index 248c2fd2e6e7..8bbaf6cf929d 100644 --- a/lib/hcrypto/libtommath/bn_mp_prime_rabin_miller_trials.c +++ b/lib/hcrypto/libtommath/bn_mp_prime_rabin_miller_trials.c @@ -1,32 +1,31 @@ -#include <tommath.h> +#include "tommath_private.h" #ifdef BN_MP_PRIME_RABIN_MILLER_TRIALS_C -/* LibTomMath, multiple-precision integer library -- Tom St Denis - * - * LibTomMath is a library that provides multiple-precision - * integer arithmetic as well as number theoretic functionality. - * - * The library was designed directly after the MPI library by - * Michael Fromberger but has been written from scratch with - * additional optimizations in place. - * - * The library is free for all purposes without any express - * guarantee it works. - * - * Tom St Denis, tomstdenis@gmail.com, http://libtom.org - */ - +/* LibTomMath, multiple-precision integer library -- Tom St Denis */ +/* SPDX-License-Identifier: Unlicense */ static const struct { int k, t; } sizes[] = { -{ 128, 28 }, -{ 256, 16 }, -{ 384, 10 }, -{ 512, 7 }, -{ 640, 6 }, -{ 768, 5 }, -{ 896, 4 }, -{ 1024, 4 } + { 80, -1 }, /* Use deterministic algorithm for size <= 80 bits */ + { 81, 37 }, /* max. error = 2^(-96)*/ + { 96, 32 }, /* max. error = 2^(-96)*/ + { 128, 40 }, /* max. error = 2^(-112)*/ + { 160, 35 }, /* max. error = 2^(-112)*/ + { 256, 27 }, /* max. error = 2^(-128)*/ + { 384, 16 }, /* max. error = 2^(-128)*/ + { 512, 18 }, /* max. error = 2^(-160)*/ + { 768, 11 }, /* max. error = 2^(-160)*/ + { 896, 10 }, /* max. error = 2^(-160)*/ + { 1024, 12 }, /* max. error = 2^(-192)*/ + { 1536, 8 }, /* max. error = 2^(-192)*/ + { 2048, 6 }, /* max. error = 2^(-192)*/ + { 3072, 4 }, /* max. error = 2^(-192)*/ + { 4096, 5 }, /* max. error = 2^(-256)*/ + { 5120, 4 }, /* max. error = 2^(-256)*/ + { 6144, 4 }, /* max. error = 2^(-256)*/ + { 8192, 3 }, /* max. error = 2^(-256)*/ + { 9216, 3 }, /* max. error = 2^(-256)*/ + { 10240, 2 } /* For bigger keysizes use always at least 2 Rounds */ }; /* returns # of RM trials required for a given bit size */ @@ -35,18 +34,14 @@ int mp_prime_rabin_miller_trials(int size) int x; for (x = 0; x < (int)(sizeof(sizes)/(sizeof(sizes[0]))); x++) { - if (sizes[x].k == size) { - return sizes[x].t; - } else if (sizes[x].k > size) { - return (x == 0) ? sizes[0].t : sizes[x - 1].t; - } + if (sizes[x].k == size) { + return sizes[x].t; + } else if (sizes[x].k > size) { + return (x == 0) ? sizes[0].t : sizes[x - 1].t; + } } - return sizes[x-1].t + 1; + return sizes[x-1].t; } #endif - -/* $Source: /cvs/libtom/libtommath/bn_mp_prime_rabin_miller_trials.c,v $ */ -/* $Revision: 1.4 $ */ -/* $Date: 2006/12/28 01:25:13 $ */ diff --git a/lib/hcrypto/libtommath/bn_mp_prime_rand.c b/lib/hcrypto/libtommath/bn_mp_prime_rand.c new file mode 100644 index 000000000000..23a1c4f78dc8 --- /dev/null +++ b/lib/hcrypto/libtommath/bn_mp_prime_rand.c @@ -0,0 +1,141 @@ +#include "tommath_private.h" +#ifdef BN_MP_PRIME_RAND_C +/* LibTomMath, multiple-precision integer library -- Tom St Denis */ +/* SPDX-License-Identifier: Unlicense */ + +/* makes a truly random prime of a given size (bits), + * + * Flags are as follows: + * + * MP_PRIME_BBS - make prime congruent to 3 mod 4 + * MP_PRIME_SAFE - make sure (p-1)/2 is prime as well (implies MP_PRIME_BBS) + * MP_PRIME_2MSB_ON - make the 2nd highest bit one + * + * You have to supply a callback which fills in a buffer with random bytes. "dat" is a parameter you can + * have passed to the callback (e.g. a state or something). This function doesn't use "dat" itself + * so it can be NULL + * + */ + +/* This is possibly the mother of all prime generation functions, muahahahahaha! */ +mp_err s_mp_prime_random_ex(mp_int *a, int t, int size, int flags, private_mp_prime_callback cb, void *dat) +{ + unsigned char *tmp, maskAND, maskOR_msb, maskOR_lsb; + int bsize, maskOR_msb_offset; + mp_bool res; + mp_err err; + + /* sanity check the input */ + if ((size <= 1) || (t <= 0)) { + return MP_VAL; + } + + /* MP_PRIME_SAFE implies MP_PRIME_BBS */ + if ((flags & MP_PRIME_SAFE) != 0) { + flags |= MP_PRIME_BBS; + } + + /* calc the byte size */ + bsize = (size>>3) + ((size&7)?1:0); + + /* we need a buffer of bsize bytes */ + tmp = (unsigned char *) MP_CALLOC(1, (size_t)bsize); + if (tmp == NULL) { + return MP_MEM; + } + + /* calc the maskAND value for the MSbyte*/ + maskAND = ((size&7) == 0) ? 0xFFu : (unsigned char)(0xFFu >> (8 - (size & 7))); + + /* calc the maskOR_msb */ + maskOR_msb = 0; + maskOR_msb_offset = ((size & 7) == 1) ? 1 : 0; + if ((flags & MP_PRIME_2MSB_ON) != 0) { + maskOR_msb |= (unsigned char)(0x80 >> ((9 - size) & 7)); + } + + /* get the maskOR_lsb */ + maskOR_lsb = 1u; + if ((flags & MP_PRIME_BBS) != 0) { + maskOR_lsb |= 3u; + } + + do { + /* read the bytes */ + if (cb(tmp, bsize, dat) != bsize) { + err = MP_VAL; + goto error; + } + + /* work over the MSbyte */ + tmp[0] &= maskAND; + tmp[0] |= (unsigned char)(1 << ((size - 1) & 7)); + + /* mix in the maskORs */ + tmp[maskOR_msb_offset] |= maskOR_msb; + tmp[bsize-1] |= maskOR_lsb; + + /* read it in */ + /* TODO: casting only for now until all lengths have been changed to the type "size_t"*/ + if ((err = mp_from_ubin(a, tmp, (size_t)bsize)) != MP_OKAY) { + goto error; + } + + /* is it prime? */ + if ((err = mp_prime_is_prime(a, t, &res)) != MP_OKAY) { + goto error; + } + if (res == MP_NO) { + continue; + } + + if ((flags & MP_PRIME_SAFE) != 0) { + /* see if (a-1)/2 is prime */ + if ((err = mp_sub_d(a, 1uL, a)) != MP_OKAY) { + goto error; + } + if ((err = mp_div_2(a, a)) != MP_OKAY) { + goto error; + } + + /* is it prime? */ + if ((err = mp_prime_is_prime(a, t, &res)) != MP_OKAY) { + goto error; + } + } + } while (res == MP_NO); + + if ((flags & MP_PRIME_SAFE) != 0) { + /* restore a to the original value */ + if ((err = mp_mul_2(a, a)) != MP_OKAY) { + goto error; + } + if ((err = mp_add_d(a, 1uL, a)) != MP_OKAY) { + goto error; + } + } + + err = MP_OKAY; +error: + MP_FREE_BUFFER(tmp, (size_t)bsize); + return err; +} + +static int s_mp_rand_cb(unsigned char *dst, int len, void *dat) +{ + (void)dat; + if (len <= 0) { + return len; + } + if (s_mp_rand_source(dst, (size_t)len) != MP_OKAY) { + return 0; + } + return len; +} + +mp_err mp_prime_rand(mp_int *a, int t, int size, int flags) +{ + return s_mp_prime_random_ex(a, t, size, flags, s_mp_rand_cb, NULL); +} + +#endif diff --git a/lib/hcrypto/libtommath/bn_mp_prime_random_ex.c b/lib/hcrypto/libtommath/bn_mp_prime_random_ex.c deleted file mode 100644 index 7b0d15c94d7f..000000000000 --- a/lib/hcrypto/libtommath/bn_mp_prime_random_ex.c +++ /dev/null @@ -1,125 +0,0 @@ -#include <tommath.h> -#ifdef BN_MP_PRIME_RANDOM_EX_C -/* LibTomMath, multiple-precision integer library -- Tom St Denis - * - * LibTomMath is a library that provides multiple-precision - * integer arithmetic as well as number theoretic functionality. - * - * The library was designed directly after the MPI library by - * Michael Fromberger but has been written from scratch with - * additional optimizations in place. - * - * The library is free for all purposes without any express - * guarantee it works. - * - * Tom St Denis, tomstdenis@gmail.com, http://libtom.org - */ - -/* makes a truly random prime of a given size (bits), - * - * Flags are as follows: - * - * LTM_PRIME_BBS - make prime congruent to 3 mod 4 - * LTM_PRIME_SAFE - make sure (p-1)/2 is prime as well (implies LTM_PRIME_BBS) - * LTM_PRIME_2MSB_OFF - make the 2nd highest bit zero - * LTM_PRIME_2MSB_ON - make the 2nd highest bit one - * - * You have to supply a callback which fills in a buffer with random bytes. "dat" is a parameter you can - * have passed to the callback (e.g. a state or something). This function doesn't use "dat" itself - * so it can be NULL - * - */ - -/* This is possibly the mother of all prime generation functions, muahahahahaha! */ -int mp_prime_random_ex(mp_int *a, int t, int size, int flags, ltm_prime_callback cb, void *dat) -{ - unsigned char *tmp, maskAND, maskOR_msb, maskOR_lsb; - int res, err, bsize, maskOR_msb_offset; - - /* sanity check the input */ - if (size <= 1 || t <= 0) { - return MP_VAL; - } - - /* LTM_PRIME_SAFE implies LTM_PRIME_BBS */ - if (flags & LTM_PRIME_SAFE) { - flags |= LTM_PRIME_BBS; - } - - /* calc the byte size */ - bsize = (size>>3) + ((size&7)?1:0); - - /* we need a buffer of bsize bytes */ - tmp = OPT_CAST(unsigned char) XMALLOC(bsize); - if (tmp == NULL) { - return MP_MEM; - } - - /* calc the maskAND value for the MSbyte*/ - maskAND = ((size&7) == 0) ? 0xFF : (0xFF >> (8 - (size & 7))); - - /* calc the maskOR_msb */ - maskOR_msb = 0; - maskOR_msb_offset = ((size & 7) == 1) ? 1 : 0; - if (flags & LTM_PRIME_2MSB_ON) { - maskOR_msb |= 0x80 >> ((9 - size) & 7); - } - - /* get the maskOR_lsb */ - maskOR_lsb = 1; - if (flags & LTM_PRIME_BBS) { - maskOR_lsb |= 3; - } - - do { - /* read the bytes */ - if (cb(tmp, bsize, dat) != bsize) { - err = MP_VAL; - goto error; - } - - /* work over the MSbyte */ - tmp[0] &= maskAND; - tmp[0] |= 1 << ((size - 1) & 7); - - /* mix in the maskORs */ - tmp[maskOR_msb_offset] |= maskOR_msb; - tmp[bsize-1] |= maskOR_lsb; - - /* read it in */ - if ((err = mp_read_unsigned_bin(a, tmp, bsize)) != MP_OKAY) { goto error; } - - /* is it prime? */ - if ((err = mp_prime_is_prime(a, t, &res)) != MP_OKAY) { goto error; } - if (res == MP_NO) { - continue; - } - - if (flags & LTM_PRIME_SAFE) { - /* see if (a-1)/2 is prime */ - if ((err = mp_sub_d(a, 1, a)) != MP_OKAY) { goto error; } - if ((err = mp_div_2(a, a)) != MP_OKAY) { goto error; } - - /* is it prime? */ - if ((err = mp_prime_is_prime(a, t, &res)) != MP_OKAY) { goto error; } - } - } while (res == MP_NO); - - if (flags & LTM_PRIME_SAFE) { - /* restore a to the original value */ - if ((err = mp_mul_2(a, a)) != MP_OKAY) { goto error; } - if ((err = mp_add_d(a, 1, a)) != MP_OKAY) { goto error; } - } - - err = MP_OKAY; -error: - XFREE(tmp); - return err; -} - - -#endif - -/* $Source: /cvs/libtom/libtommath/bn_mp_prime_random_ex.c,v $ */ -/* $Revision: 1.5 $ */ -/* $Date: 2006/12/28 01:25:13 $ */ diff --git a/lib/hcrypto/libtommath/bn_mp_prime_strong_lucas_selfridge.c b/lib/hcrypto/libtommath/bn_mp_prime_strong_lucas_selfridge.c new file mode 100644 index 000000000000..b50bbcd2f312 --- /dev/null +++ b/lib/hcrypto/libtommath/bn_mp_prime_strong_lucas_selfridge.c @@ -0,0 +1,289 @@ +#include "tommath_private.h" +#ifdef BN_MP_PRIME_STRONG_LUCAS_SELFRIDGE_C + +/* LibTomMath, multiple-precision integer library -- Tom St Denis */ +/* SPDX-License-Identifier: Unlicense */ + +/* + * See file bn_mp_prime_is_prime.c or the documentation in doc/bn.tex for the details + */ +#ifndef LTM_USE_ONLY_MR + +/* + * 8-bit is just too small. You can try the Frobenius test + * but that frobenius test can fail, too, for the same reason. + */ +#ifndef MP_8BIT + +/* + * multiply bigint a with int d and put the result in c + * Like mp_mul_d() but with a signed long as the small input + */ +static mp_err s_mp_mul_si(const mp_int *a, int32_t d, mp_int *c) +{ + mp_int t; + mp_err err; + + if ((err = mp_init(&t)) != MP_OKAY) { + return err; + } + + /* + * mp_digit might be smaller than a long, which excludes + * the use of mp_mul_d() here. + */ + mp_set_i32(&t, d); + err = mp_mul(a, &t, c); + mp_clear(&t); + return err; +} +/* + Strong Lucas-Selfridge test. + returns MP_YES if it is a strong L-S prime, MP_NO if it is composite + + Code ported from Thomas Ray Nicely's implementation of the BPSW test + at http://www.trnicely.net/misc/bpsw.html + + Freeware copyright (C) 2016 Thomas R. Nicely <http://www.trnicely.net>. + Released into the public domain by the author, who disclaims any legal + liability arising from its use + + The multi-line comments are made by Thomas R. Nicely and are copied verbatim. + Additional comments marked "CZ" (without the quotes) are by the code-portist. + + (If that name sounds familiar, he is the guy who found the fdiv bug in the + Pentium (P5x, I think) Intel processor) +*/ +mp_err mp_prime_strong_lucas_selfridge(const mp_int *a, mp_bool *result) +{ + /* CZ TODO: choose better variable names! */ + mp_int Dz, gcd, Np1, Uz, Vz, U2mz, V2mz, Qmz, Q2mz, Qkdz, T1z, T2z, T3z, T4z, Q2kdz; + /* CZ TODO: Some of them need the full 32 bit, hence the (temporary) exclusion of MP_8BIT */ + int32_t D, Ds, J, sign, P, Q, r, s, u, Nbits; + mp_err err; + mp_bool oddness; + + *result = MP_NO; + /* + Find the first element D in the sequence {5, -7, 9, -11, 13, ...} + such that Jacobi(D,N) = -1 (Selfridge's algorithm). Theory + indicates that, if N is not a perfect square, D will "nearly + always" be "small." Just in case, an overflow trap for D is + included. + */ + + if ((err = mp_init_multi(&Dz, &gcd, &Np1, &Uz, &Vz, &U2mz, &V2mz, &Qmz, &Q2mz, &Qkdz, &T1z, &T2z, &T3z, &T4z, &Q2kdz, + NULL)) != MP_OKAY) { + return err; + } + + D = 5; + sign = 1; + + for (;;) { + Ds = sign * D; + sign = -sign; + mp_set_u32(&Dz, (uint32_t)D); + if ((err = mp_gcd(a, &Dz, &gcd)) != MP_OKAY) goto LBL_LS_ERR; + + /* if 1 < GCD < N then N is composite with factor "D", and + Jacobi(D,N) is technically undefined (but often returned + as zero). */ + if ((mp_cmp_d(&gcd, 1uL) == MP_GT) && (mp_cmp(&gcd, a) == MP_LT)) { + goto LBL_LS_ERR; + } + if (Ds < 0) { + Dz.sign = MP_NEG; + } + if ((err = mp_kronecker(&Dz, a, &J)) != MP_OKAY) goto LBL_LS_ERR; + + if (J == -1) { + break; + } + D += 2; + + if (D > (INT_MAX - 2)) { + err = MP_VAL; + goto LBL_LS_ERR; + } + } + + + + P = 1; /* Selfridge's choice */ + Q = (1 - Ds) / 4; /* Required so D = P*P - 4*Q */ + + /* NOTE: The conditions (a) N does not divide Q, and + (b) D is square-free or not a perfect square, are included by + some authors; e.g., "Prime numbers and computer methods for + factorization," Hans Riesel (2nd ed., 1994, Birkhauser, Boston), + p. 130. For this particular application of Lucas sequences, + these conditions were found to be immaterial. */ + + /* Now calculate N - Jacobi(D,N) = N + 1 (even), and calculate the + odd positive integer d and positive integer s for which + N + 1 = 2^s*d (similar to the step for N - 1 in Miller's test). + The strong Lucas-Selfridge test then returns N as a strong + Lucas probable prime (slprp) if any of the following + conditions is met: U_d=0, V_d=0, V_2d=0, V_4d=0, V_8d=0, + V_16d=0, ..., etc., ending with V_{2^(s-1)*d}=V_{(N+1)/2}=0 + (all equalities mod N). Thus d is the highest index of U that + must be computed (since V_2m is independent of U), compared + to U_{N+1} for the standard Lucas-Selfridge test; and no + index of V beyond (N+1)/2 is required, just as in the + standard Lucas-Selfridge test. However, the quantity Q^d must + be computed for use (if necessary) in the latter stages of + the test. The result is that the strong Lucas-Selfridge test + has a running time only slightly greater (order of 10 %) than + that of the standard Lucas-Selfridge test, while producing + only (roughly) 30 % as many pseudoprimes (and every strong + Lucas pseudoprime is also a standard Lucas pseudoprime). Thus + the evidence indicates that the strong Lucas-Selfridge test is + more effective than the standard Lucas-Selfridge test, and a + Baillie-PSW test based on the strong Lucas-Selfridge test + should be more reliable. */ + + if ((err = mp_add_d(a, 1uL, &Np1)) != MP_OKAY) goto LBL_LS_ERR; + s = mp_cnt_lsb(&Np1); + + /* CZ + * This should round towards zero because + * Thomas R. Nicely used GMP's mpz_tdiv_q_2exp() + * and mp_div_2d() is equivalent. Additionally: + * dividing an even number by two does not produce + * any leftovers. + */ + if ((err = mp_div_2d(&Np1, s, &Dz, NULL)) != MP_OKAY) goto LBL_LS_ERR; + /* We must now compute U_d and V_d. Since d is odd, the accumulated + values U and V are initialized to U_1 and V_1 (if the target + index were even, U and V would be initialized instead to U_0=0 + and V_0=2). The values of U_2m and V_2m are also initialized to + U_1 and V_1; the FOR loop calculates in succession U_2 and V_2, + U_4 and V_4, U_8 and V_8, etc. If the corresponding bits + (1, 2, 3, ...) of t are on (the zero bit having been accounted + for in the initialization of U and V), these values are then + combined with the previous totals for U and V, using the + composition formulas for addition of indices. */ + + mp_set(&Uz, 1uL); /* U=U_1 */ + mp_set(&Vz, (mp_digit)P); /* V=V_1 */ + mp_set(&U2mz, 1uL); /* U_1 */ + mp_set(&V2mz, (mp_digit)P); /* V_1 */ + + mp_set_i32(&Qmz, Q); + if ((err = mp_mul_2(&Qmz, &Q2mz)) != MP_OKAY) goto LBL_LS_ERR; + /* Initializes calculation of Q^d */ + mp_set_i32(&Qkdz, Q); + + Nbits = mp_count_bits(&Dz); + + for (u = 1; u < Nbits; u++) { /* zero bit off, already accounted for */ + /* Formulas for doubling of indices (carried out mod N). Note that + * the indices denoted as "2m" are actually powers of 2, specifically + * 2^(ul-1) beginning each loop and 2^ul ending each loop. + * + * U_2m = U_m*V_m + * V_2m = V_m*V_m - 2*Q^m + */ + + if ((err = mp_mul(&U2mz, &V2mz, &U2mz)) != MP_OKAY) goto LBL_LS_ERR; + if ((err = mp_mod(&U2mz, a, &U2mz)) != MP_OKAY) goto LBL_LS_ERR; + if ((err = mp_sqr(&V2mz, &V2mz)) != MP_OKAY) goto LBL_LS_ERR; + if ((err = mp_sub(&V2mz, &Q2mz, &V2mz)) != MP_OKAY) goto LBL_LS_ERR; + if ((err = mp_mod(&V2mz, a, &V2mz)) != MP_OKAY) goto LBL_LS_ERR; + + /* Must calculate powers of Q for use in V_2m, also for Q^d later */ + if ((err = mp_sqr(&Qmz, &Qmz)) != MP_OKAY) goto LBL_LS_ERR; + + /* prevents overflow */ /* CZ still necessary without a fixed prealloc'd mem.? */ + if ((err = mp_mod(&Qmz, a, &Qmz)) != MP_OKAY) goto LBL_LS_ERR; + if ((err = mp_mul_2(&Qmz, &Q2mz)) != MP_OKAY) goto LBL_LS_ERR; + + if (s_mp_get_bit(&Dz, (unsigned int)u) == MP_YES) { + /* Formulas for addition of indices (carried out mod N); + * + * U_(m+n) = (U_m*V_n + U_n*V_m)/2 + * V_(m+n) = (V_m*V_n + D*U_m*U_n)/2 + * + * Be careful with division by 2 (mod N)! + */ + if ((err = mp_mul(&U2mz, &Vz, &T1z)) != MP_OKAY) goto LBL_LS_ERR; + if ((err = mp_mul(&Uz, &V2mz, &T2z)) != MP_OKAY) goto LBL_LS_ERR; + if ((err = mp_mul(&V2mz, &Vz, &T3z)) != MP_OKAY) goto LBL_LS_ERR; + if ((err = mp_mul(&U2mz, &Uz, &T4z)) != MP_OKAY) goto LBL_LS_ERR; + if ((err = s_mp_mul_si(&T4z, Ds, &T4z)) != MP_OKAY) goto LBL_LS_ERR; + if ((err = mp_add(&T1z, &T2z, &Uz)) != MP_OKAY) goto LBL_LS_ERR; + if (MP_IS_ODD(&Uz)) { + if ((err = mp_add(&Uz, a, &Uz)) != MP_OKAY) goto LBL_LS_ERR; + } + /* CZ + * This should round towards negative infinity because + * Thomas R. Nicely used GMP's mpz_fdiv_q_2exp(). + * But mp_div_2() does not do so, it is truncating instead. + */ + oddness = MP_IS_ODD(&Uz) ? MP_YES : MP_NO; + if ((err = mp_div_2(&Uz, &Uz)) != MP_OKAY) goto LBL_LS_ERR; + if ((Uz.sign == MP_NEG) && (oddness != MP_NO)) { + if ((err = mp_sub_d(&Uz, 1uL, &Uz)) != MP_OKAY) goto LBL_LS_ERR; + } + if ((err = mp_add(&T3z, &T4z, &Vz)) != MP_OKAY) goto LBL_LS_ERR; + if (MP_IS_ODD(&Vz)) { + if ((err = mp_add(&Vz, a, &Vz)) != MP_OKAY) goto LBL_LS_ERR; + } + oddness = MP_IS_ODD(&Vz) ? MP_YES : MP_NO; + if ((err = mp_div_2(&Vz, &Vz)) != MP_OKAY) goto LBL_LS_ERR; + if ((Vz.sign == MP_NEG) && (oddness != MP_NO)) { + if ((err = mp_sub_d(&Vz, 1uL, &Vz)) != MP_OKAY) goto LBL_LS_ERR; + } + if ((err = mp_mod(&Uz, a, &Uz)) != MP_OKAY) goto LBL_LS_ERR; + if ((err = mp_mod(&Vz, a, &Vz)) != MP_OKAY) goto LBL_LS_ERR; + + /* Calculating Q^d for later use */ + if ((err = mp_mul(&Qkdz, &Qmz, &Qkdz)) != MP_OKAY) goto LBL_LS_ERR; + if ((err = mp_mod(&Qkdz, a, &Qkdz)) != MP_OKAY) goto LBL_LS_ERR; + } + } + + /* If U_d or V_d is congruent to 0 mod N, then N is a prime or a + strong Lucas pseudoprime. */ + if (MP_IS_ZERO(&Uz) || MP_IS_ZERO(&Vz)) { + *result = MP_YES; + goto LBL_LS_ERR; + } + + /* NOTE: Ribenboim ("The new book of prime number records," 3rd ed., + 1995/6) omits the condition V0 on p.142, but includes it on + p. 130. The condition is NECESSARY; otherwise the test will + return false negatives---e.g., the primes 29 and 2000029 will be + returned as composite. */ + + /* Otherwise, we must compute V_2d, V_4d, V_8d, ..., V_{2^(s-1)*d} + by repeated use of the formula V_2m = V_m*V_m - 2*Q^m. If any of + these are congruent to 0 mod N, then N is a prime or a strong + Lucas pseudoprime. */ + + /* Initialize 2*Q^(d*2^r) for V_2m */ + if ((err = mp_mul_2(&Qkdz, &Q2kdz)) != MP_OKAY) goto LBL_LS_ERR; + + for (r = 1; r < s; r++) { + if ((err = mp_sqr(&Vz, &Vz)) != MP_OKAY) goto LBL_LS_ERR; + if ((err = mp_sub(&Vz, &Q2kdz, &Vz)) != MP_OKAY) goto LBL_LS_ERR; + if ((err = mp_mod(&Vz, a, &Vz)) != MP_OKAY) goto LBL_LS_ERR; + if (MP_IS_ZERO(&Vz)) { + *result = MP_YES; + goto LBL_LS_ERR; + } + /* Calculate Q^{d*2^r} for next r (final iteration irrelevant). */ + if (r < (s - 1)) { + if ((err = mp_sqr(&Qkdz, &Qkdz)) != MP_OKAY) goto LBL_LS_ERR; + if ((err = mp_mod(&Qkdz, a, &Qkdz)) != MP_OKAY) goto LBL_LS_ERR; + if ((err = mp_mul_2(&Qkdz, &Q2kdz)) != MP_OKAY) goto LBL_LS_ERR; + } + } +LBL_LS_ERR: + mp_clear_multi(&Q2kdz, &T4z, &T3z, &T2z, &T1z, &Qkdz, &Q2mz, &Qmz, &V2mz, &U2mz, &Vz, &Uz, &Np1, &gcd, &Dz, NULL); + return err; +} +#endif +#endif +#endif diff --git a/lib/hcrypto/libtommath/bn_mp_radix_size.c b/lib/hcrypto/libtommath/bn_mp_radix_size.c index af94be8676ab..b96f4874c492 100644 --- a/lib/hcrypto/libtommath/bn_mp_radix_size.c +++ b/lib/hcrypto/libtommath/bn_mp_radix_size.c @@ -1,78 +1,65 @@ -#include <tommath.h> +#include "tommath_private.h" #ifdef BN_MP_RADIX_SIZE_C -/* LibTomMath, multiple-precision integer library -- Tom St Denis - * - * LibTomMath is a library that provides multiple-precision - * integer arithmetic as well as number theoretic functionality. - * - * The library was designed directly after the MPI library by - * Michael Fromberger but has been written from scratch with - * additional optimizations in place. - * - * The library is free for all purposes without any express - * guarantee it works. - * - * Tom St Denis, tomstdenis@gmail.com, http://libtom.org - */ +/* LibTomMath, multiple-precision integer library -- Tom St Denis */ +/* SPDX-License-Identifier: Unlicense */ -/* returns size of ASCII reprensentation */ -int mp_radix_size (mp_int * a, int radix, int *size) +/* returns size of ASCII representation */ +mp_err mp_radix_size(const mp_int *a, int radix, int *size) { - int res, digs; - mp_int t; - mp_digit d; + mp_err err; + int digs; + mp_int t; + mp_digit d; - *size = 0; + *size = 0; - /* special case for binary */ - if (radix == 2) { - *size = mp_count_bits (a) + (a->sign == MP_NEG ? 1 : 0) + 1; - return MP_OKAY; - } + /* make sure the radix is in range */ + if ((radix < 2) || (radix > 64)) { + return MP_VAL; + } - /* make sure the radix is in range */ - if (radix < 2 || radix > 64) { - return MP_VAL; - } + if (MP_IS_ZERO(a)) { + *size = 2; + return MP_OKAY; + } - if (mp_iszero(a) == MP_YES) { - *size = 2; - return MP_OKAY; - } + /* special case for binary */ + if (radix == 2) { + *size = (mp_count_bits(a) + ((a->sign == MP_NEG) ? 1 : 0) + 1); + return MP_OKAY; + } - /* digs is the digit count */ - digs = 0; + /* digs is the digit count */ + digs = 0; - /* if it's negative add one for the sign */ - if (a->sign == MP_NEG) { - ++digs; - } + /* if it's negative add one for the sign */ + if (a->sign == MP_NEG) { + ++digs; + } - /* init a copy of the input */ - if ((res = mp_init_copy (&t, a)) != MP_OKAY) { - return res; - } + /* init a copy of the input */ + if ((err = mp_init_copy(&t, a)) != MP_OKAY) { + return err; + } - /* force temp to positive */ - t.sign = MP_ZPOS; + /* force temp to positive */ + t.sign = MP_ZPOS; - /* fetch out all of the digits */ - while (mp_iszero (&t) == MP_NO) { - if ((res = mp_div_d (&t, (mp_digit) radix, &t, &d)) != MP_OKAY) { - mp_clear (&t); - return res; - } - ++digs; - } - mp_clear (&t); + /* fetch out all of the digits */ + while (!MP_IS_ZERO(&t)) { + if ((err = mp_div_d(&t, (mp_digit)radix, &t, &d)) != MP_OKAY) { + goto LBL_ERR; + } + ++digs; + } - /* return digs + 1, the 1 is for the NULL byte that would be required. */ - *size = digs + 1; - return MP_OKAY; + /* return digs + 1, the 1 is for the NULL byte that would be required. */ + *size = digs + 1; + err = MP_OKAY; + +LBL_ERR: + mp_clear(&t); + return err; } #endif - -/* $Source: /cvs/libtom/libtommath/bn_mp_radix_size.c,v $ */ -/* $Revision: 1.5 $ */ -/* $Date: 2006/12/28 01:25:13 $ */ diff --git a/lib/hcrypto/libtommath/bn_mp_radix_smap.c b/lib/hcrypto/libtommath/bn_mp_radix_smap.c index 7d72feb84e6a..a16128d79e63 100644 --- a/lib/hcrypto/libtommath/bn_mp_radix_smap.c +++ b/lib/hcrypto/libtommath/bn_mp_radix_smap.c @@ -1,24 +1,22 @@ -#include <tommath.h> +#include "tommath_private.h" #ifdef BN_MP_RADIX_SMAP_C -/* LibTomMath, multiple-precision integer library -- Tom St Denis - * - * LibTomMath is a library that provides multiple-precision - * integer arithmetic as well as number theoretic functionality. - * - * The library was designed directly after the MPI library by - * Michael Fromberger but has been written from scratch with - * additional optimizations in place. - * - * The library is free for all purposes without any express - * guarantee it works. - * - * Tom St Denis, tomstdenis@gmail.com, http://libtom.org - */ +/* LibTomMath, multiple-precision integer library -- Tom St Denis */ +/* SPDX-License-Identifier: Unlicense */ /* chars used in radix conversions */ -const char *mp_s_rmap = "0123456789ABCDEFGHIJKLMNOPQRSTUVWXYZabcdefghijklmnopqrstuvwxyz+/"; +const char *const mp_s_rmap = "0123456789ABCDEFGHIJKLMNOPQRSTUVWXYZabcdefghijklmnopqrstuvwxyz+/"; +const uint8_t mp_s_rmap_reverse[] = { + 0xff, 0xff, 0xff, 0x3e, 0xff, 0xff, 0xff, 0x3f, /* ()*+,-./ */ + 0x00, 0x01, 0x02, 0x03, 0x04, 0x05, 0x06, 0x07, /* 01234567 */ + 0x08, 0x09, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, /* 89:;<=>? */ + 0xff, 0x0a, 0x0b, 0x0c, 0x0d, 0x0e, 0x0f, 0x10, /* @ABCDEFG */ + 0x11, 0x12, 0x13, 0x14, 0x15, 0x16, 0x17, 0x18, /* HIJKLMNO */ + 0x19, 0x1a, 0x1b, 0x1c, 0x1d, 0x1e, 0x1f, 0x20, /* PQRSTUVW */ + 0x21, 0x22, 0x23, 0xff, 0xff, 0xff, 0xff, 0xff, /* XYZ[\]^_ */ + 0xff, 0x24, 0x25, 0x26, 0x27, 0x28, 0x29, 0x2a, /* `abcdefg */ + 0x2b, 0x2c, 0x2d, 0x2e, 0x2f, 0x30, 0x31, 0x32, /* hijklmno */ + 0x33, 0x34, 0x35, 0x36, 0x37, 0x38, 0x39, 0x3a, /* pqrstuvw */ + 0x3b, 0x3c, 0x3d, 0xff, 0xff, 0xff, 0xff, 0xff, /* xyz{|}~. */ +}; +const size_t mp_s_rmap_reverse_sz = sizeof(mp_s_rmap_reverse); #endif - -/* $Source: /cvs/libtom/libtommath/bn_mp_radix_smap.c,v $ */ -/* $Revision: 1.4 $ */ -/* $Date: 2006/12/28 01:25:13 $ */ diff --git a/lib/hcrypto/libtommath/bn_mp_rand.c b/lib/hcrypto/libtommath/bn_mp_rand.c index 14f5b7503bc7..7e9052c2ba05 100644 --- a/lib/hcrypto/libtommath/bn_mp_rand.c +++ b/lib/hcrypto/libtommath/bn_mp_rand.c @@ -1,55 +1,46 @@ -#include <tommath.h> +#include "tommath_private.h" #ifdef BN_MP_RAND_C -/* LibTomMath, multiple-precision integer library -- Tom St Denis - * - * LibTomMath is a library that provides multiple-precision - * integer arithmetic as well as number theoretic functionality. - * - * The library was designed directly after the MPI library by - * Michael Fromberger but has been written from scratch with - * additional optimizations in place. - * - * The library is free for all purposes without any express - * guarantee it works. - * - * Tom St Denis, tomstdenis@gmail.com, http://libtom.org - */ - -/* makes a pseudo-random int of a given size */ -int -mp_rand (mp_int * a, int digits) +/* LibTomMath, multiple-precision integer library -- Tom St Denis */ +/* SPDX-License-Identifier: Unlicense */ + +mp_err(*s_mp_rand_source)(void *out, size_t size) = s_mp_rand_platform; + +void mp_rand_source(mp_err(*source)(void *out, size_t size)) { - int res; - mp_digit d; - - mp_zero (a); - if (digits <= 0) { - return MP_OKAY; - } - - /* first place a random non-zero digit */ - do { - d = ((mp_digit) labs (rand ())) & MP_MASK; - } while (d == 0); - - if ((res = mp_add_d (a, d, a)) != MP_OKAY) { - return res; - } - - while (--digits > 0) { - if ((res = mp_lshd (a, 1)) != MP_OKAY) { - return res; - } - - if ((res = mp_add_d (a, ((mp_digit) labs (rand ())), a)) != MP_OKAY) { - return res; - } - } - - return MP_OKAY; + s_mp_rand_source = (source == NULL) ? s_mp_rand_platform : source; } -#endif -/* $Source: /cvs/libtom/libtommath/bn_mp_rand.c,v $ */ -/* $Revision: 1.4 $ */ -/* $Date: 2006/12/28 01:25:13 $ */ +mp_err mp_rand(mp_int *a, int digits) +{ + int i; + mp_err err; + + mp_zero(a); + + if (digits <= 0) { + return MP_OKAY; + } + + if ((err = mp_grow(a, digits)) != MP_OKAY) { + return err; + } + + if ((err = s_mp_rand_source(a->dp, (size_t)digits * sizeof(mp_digit))) != MP_OKAY) { + return err; + } + + /* TODO: We ensure that the highest digit is nonzero. Should this be removed? */ + while ((a->dp[digits - 1] & MP_MASK) == 0u) { + if ((err = s_mp_rand_source(a->dp + digits - 1, sizeof(mp_digit))) != MP_OKAY) { + return err; + } + } + + a->used = digits; + for (i = 0; i < digits; ++i) { + a->dp[i] &= MP_MASK; + } + + return MP_OKAY; +} +#endif diff --git a/lib/hcrypto/libtommath/bn_mp_read_radix.c b/lib/hcrypto/libtommath/bn_mp_read_radix.c index 35ca886736a1..de18e06fc331 100644 --- a/lib/hcrypto/libtommath/bn_mp_read_radix.c +++ b/lib/hcrypto/libtommath/bn_mp_read_radix.c @@ -1,85 +1,79 @@ -#include <tommath.h> +#include "tommath_private.h" #ifdef BN_MP_READ_RADIX_C -/* LibTomMath, multiple-precision integer library -- Tom St Denis - * - * LibTomMath is a library that provides multiple-precision - * integer arithmetic as well as number theoretic functionality. - * - * The library was designed directly after the MPI library by - * Michael Fromberger but has been written from scratch with - * additional optimizations in place. - * - * The library is free for all purposes without any express - * guarantee it works. - * - * Tom St Denis, tomstdenis@gmail.com, http://libtom.org - */ +/* LibTomMath, multiple-precision integer library -- Tom St Denis */ +/* SPDX-License-Identifier: Unlicense */ + +#define MP_TOUPPER(c) ((((c) >= 'a') && ((c) <= 'z')) ? (((c) + 'A') - 'a') : (c)) /* read a string [ASCII] in a given radix */ -int mp_read_radix (mp_int * a, const char *str, int radix) +mp_err mp_read_radix(mp_int *a, const char *str, int radix) { - int y, res, neg; - char ch; + mp_err err; + int y; + mp_sign neg; + unsigned pos; + char ch; - /* zero the digit bignum */ - mp_zero(a); + /* zero the digit bignum */ + mp_zero(a); - /* make sure the radix is ok */ - if (radix < 2 || radix > 64) { - return MP_VAL; - } + /* make sure the radix is ok */ + if ((radix < 2) || (radix > 64)) { + return MP_VAL; + } - /* if the leading digit is a - * minus set the sign to negative. - */ - if (*str == '-') { - ++str; - neg = MP_NEG; - } else { - neg = MP_ZPOS; - } + /* if the leading digit is a + * minus set the sign to negative. + */ + if (*str == '-') { + ++str; + neg = MP_NEG; + } else { + neg = MP_ZPOS; + } - /* set the integer to the default of zero */ - mp_zero (a); + /* set the integer to the default of zero */ + mp_zero(a); - /* process each digit of the string */ - while (*str) { - /* if the radix < 36 the conversion is case insensitive - * this allows numbers like 1AB and 1ab to represent the same value - * [e.g. in hex] - */ - ch = (char) ((radix < 36) ? toupper (*str) : *str); - for (y = 0; y < 64; y++) { - if (ch == mp_s_rmap[y]) { + /* process each digit of the string */ + while (*str != '\0') { + /* if the radix <= 36 the conversion is case insensitive + * this allows numbers like 1AB and 1ab to represent the same value + * [e.g. in hex] + */ + ch = (radix <= 36) ? (char)MP_TOUPPER((int)*str) : *str; + pos = (unsigned)(ch - '('); + if (mp_s_rmap_reverse_sz < pos) { break; } - } + y = (int)mp_s_rmap_reverse[pos]; - /* if the char was found in the map - * and is less than the given radix add it - * to the number, otherwise exit the loop. - */ - if (y < radix) { - if ((res = mp_mul_d (a, (mp_digit) radix, a)) != MP_OKAY) { - return res; + /* if the char was found in the map + * and is less than the given radix add it + * to the number, otherwise exit the loop. + */ + if ((y == 0xff) || (y >= radix)) { + break; + } + if ((err = mp_mul_d(a, (mp_digit)radix, a)) != MP_OKAY) { + return err; } - if ((res = mp_add_d (a, (mp_digit) y, a)) != MP_OKAY) { - return res; + if ((err = mp_add_d(a, (mp_digit)y, a)) != MP_OKAY) { + return err; } - } else { - break; - } - ++str; - } + ++str; + } - /* set the sign only if a != 0 */ - if (mp_iszero(a) != 1) { - a->sign = neg; - } - return MP_OKAY; + /* if an illegal character was found, fail. */ + if (!((*str == '\0') || (*str == '\r') || (*str == '\n'))) { + mp_zero(a); + return MP_VAL; + } + + /* set the sign only if a != 0 */ + if (!MP_IS_ZERO(a)) { + a->sign = neg; + } + return MP_OKAY; } #endif - -/* $Source: /cvs/libtom/libtommath/bn_mp_read_radix.c,v $ */ -/* $Revision: 1.5 $ */ -/* $Date: 2006/12/28 01:25:13 $ */ diff --git a/lib/hcrypto/libtommath/bn_mp_read_signed_bin.c b/lib/hcrypto/libtommath/bn_mp_read_signed_bin.c deleted file mode 100644 index 8da651ce30fc..000000000000 --- a/lib/hcrypto/libtommath/bn_mp_read_signed_bin.c +++ /dev/null @@ -1,41 +0,0 @@ -#include <tommath.h> -#ifdef BN_MP_READ_SIGNED_BIN_C -/* LibTomMath, multiple-precision integer library -- Tom St Denis - * - * LibTomMath is a library that provides multiple-precision - * integer arithmetic as well as number theoretic functionality. - * - * The library was designed directly after the MPI library by - * Michael Fromberger but has been written from scratch with - * additional optimizations in place. - * - * The library is free for all purposes without any express - * guarantee it works. - * - * Tom St Denis, tomstdenis@gmail.com, http://libtom.org - */ - -/* read signed bin, big endian, first byte is 0==positive or 1==negative */ -int mp_read_signed_bin (mp_int * a, const unsigned char *b, int c) -{ - int res; - - /* read magnitude */ - if ((res = mp_read_unsigned_bin (a, b + 1, c - 1)) != MP_OKAY) { - return res; - } - - /* first byte is 0 for positive, non-zero for negative */ - if (b[0] == 0) { - a->sign = MP_ZPOS; - } else { - a->sign = MP_NEG; - } - - return MP_OKAY; -} -#endif - -/* $Source: /cvs/libtom/libtommath/bn_mp_read_signed_bin.c,v $ */ -/* $Revision: 1.5 $ */ -/* $Date: 2006/12/28 01:25:13 $ */ diff --git a/lib/hcrypto/libtommath/bn_mp_read_unsigned_bin.c b/lib/hcrypto/libtommath/bn_mp_read_unsigned_bin.c deleted file mode 100644 index 1ebba13a02c0..000000000000 --- a/lib/hcrypto/libtommath/bn_mp_read_unsigned_bin.c +++ /dev/null @@ -1,55 +0,0 @@ -#include <tommath.h> -#ifdef BN_MP_READ_UNSIGNED_BIN_C -/* LibTomMath, multiple-precision integer library -- Tom St Denis - * - * LibTomMath is a library that provides multiple-precision - * integer arithmetic as well as number theoretic functionality. - * - * The library was designed directly after the MPI library by - * Michael Fromberger but has been written from scratch with - * additional optimizations in place. - * - * The library is free for all purposes without any express - * guarantee it works. - * - * Tom St Denis, tomstdenis@gmail.com, http://libtom.org - */ - -/* reads a unsigned char array, assumes the msb is stored first [big endian] */ -int mp_read_unsigned_bin (mp_int * a, const unsigned char *b, int c) -{ - int res; - - /* make sure there are at least two digits */ - if (a->alloc < 2) { - if ((res = mp_grow(a, 2)) != MP_OKAY) { - return res; - } - } - - /* zero the int */ - mp_zero (a); - - /* read the bytes in */ - while (c-- > 0) { - if ((res = mp_mul_2d (a, 8, a)) != MP_OKAY) { - return res; - } - -#ifndef MP_8BIT - a->dp[0] |= *b++; - a->used += 1; -#else - a->dp[0] = (*b & MP_MASK); - a->dp[1] |= ((*b++ >> 7U) & 1); - a->used += 2; -#endif - } - mp_clamp (a); - return MP_OKAY; -} -#endif - -/* $Source: /cvs/libtom/libtommath/bn_mp_read_unsigned_bin.c,v $ */ -/* $Revision: 1.5 $ */ -/* $Date: 2006/12/28 01:25:13 $ */ diff --git a/lib/hcrypto/libtommath/bn_mp_reduce.c b/lib/hcrypto/libtommath/bn_mp_reduce.c index ae57a6a00334..3c669d491def 100644 --- a/lib/hcrypto/libtommath/bn_mp_reduce.c +++ b/lib/hcrypto/libtommath/bn_mp_reduce.c @@ -1,100 +1,83 @@ -#include <tommath.h> +#include "tommath_private.h" #ifdef BN_MP_REDUCE_C -/* LibTomMath, multiple-precision integer library -- Tom St Denis - * - * LibTomMath is a library that provides multiple-precision - * integer arithmetic as well as number theoretic functionality. - * - * The library was designed directly after the MPI library by - * Michael Fromberger but has been written from scratch with - * additional optimizations in place. - * - * The library is free for all purposes without any express - * guarantee it works. - * - * Tom St Denis, tomstdenis@gmail.com, http://libtom.org - */ +/* LibTomMath, multiple-precision integer library -- Tom St Denis */ +/* SPDX-License-Identifier: Unlicense */ /* reduces x mod m, assumes 0 < x < m**2, mu is * precomputed via mp_reduce_setup. * From HAC pp.604 Algorithm 14.42 */ -int mp_reduce (mp_int * x, mp_int * m, mp_int * mu) +mp_err mp_reduce(mp_int *x, const mp_int *m, const mp_int *mu) { - mp_int q; - int res, um = m->used; + mp_int q; + mp_err err; + int um = m->used; - /* q = x */ - if ((res = mp_init_copy (&q, x)) != MP_OKAY) { - return res; - } + /* q = x */ + if ((err = mp_init_copy(&q, x)) != MP_OKAY) { + return err; + } - /* q1 = x / b**(k-1) */ - mp_rshd (&q, um - 1); + /* q1 = x / b**(k-1) */ + mp_rshd(&q, um - 1); - /* according to HAC this optimization is ok */ - if (((unsigned long) um) > (((mp_digit)1) << (DIGIT_BIT - 1))) { - if ((res = mp_mul (&q, mu, &q)) != MP_OKAY) { - goto CLEANUP; - } - } else { -#ifdef BN_S_MP_MUL_HIGH_DIGS_C - if ((res = s_mp_mul_high_digs (&q, mu, &q, um)) != MP_OKAY) { - goto CLEANUP; - } -#elif defined(BN_FAST_S_MP_MUL_HIGH_DIGS_C) - if ((res = fast_s_mp_mul_high_digs (&q, mu, &q, um)) != MP_OKAY) { + /* according to HAC this optimization is ok */ + if ((mp_digit)um > ((mp_digit)1 << (MP_DIGIT_BIT - 1))) { + if ((err = mp_mul(&q, mu, &q)) != MP_OKAY) { + goto CLEANUP; + } + } else if (MP_HAS(S_MP_MUL_HIGH_DIGS)) { + if ((err = s_mp_mul_high_digs(&q, mu, &q, um)) != MP_OKAY) { + goto CLEANUP; + } + } else if (MP_HAS(S_MP_MUL_HIGH_DIGS_FAST)) { + if ((err = s_mp_mul_high_digs_fast(&q, mu, &q, um)) != MP_OKAY) { + goto CLEANUP; + } + } else { + err = MP_VAL; goto CLEANUP; - } -#else - { - res = MP_VAL; - goto CLEANUP; - } -#endif - } - - /* q3 = q2 / b**(k+1) */ - mp_rshd (&q, um + 1); + } - /* x = x mod b**(k+1), quick (no division) */ - if ((res = mp_mod_2d (x, DIGIT_BIT * (um + 1), x)) != MP_OKAY) { - goto CLEANUP; - } + /* q3 = q2 / b**(k+1) */ + mp_rshd(&q, um + 1); - /* q = q * m mod b**(k+1), quick (no division) */ - if ((res = s_mp_mul_digs (&q, m, &q, um + 1)) != MP_OKAY) { - goto CLEANUP; - } - - /* x = x - q */ - if ((res = mp_sub (x, &q, x)) != MP_OKAY) { - goto CLEANUP; - } - - /* If x < 0, add b**(k+1) to it */ - if (mp_cmp_d (x, 0) == MP_LT) { - mp_set (&q, 1); - if ((res = mp_lshd (&q, um + 1)) != MP_OKAY) + /* x = x mod b**(k+1), quick (no division) */ + if ((err = mp_mod_2d(x, MP_DIGIT_BIT * (um + 1), x)) != MP_OKAY) { goto CLEANUP; - if ((res = mp_add (x, &q, x)) != MP_OKAY) + } + + /* q = q * m mod b**(k+1), quick (no division) */ + if ((err = s_mp_mul_digs(&q, m, &q, um + 1)) != MP_OKAY) { goto CLEANUP; - } + } - /* Back off if it's too big */ - while (mp_cmp (x, m) != MP_LT) { - if ((res = s_mp_sub (x, m, x)) != MP_OKAY) { + /* x = x - q */ + if ((err = mp_sub(x, &q, x)) != MP_OKAY) { goto CLEANUP; - } - } + } + + /* If x < 0, add b**(k+1) to it */ + if (mp_cmp_d(x, 0uL) == MP_LT) { + mp_set(&q, 1uL); + if ((err = mp_lshd(&q, um + 1)) != MP_OKAY) { + goto CLEANUP; + } + if ((err = mp_add(x, &q, x)) != MP_OKAY) { + goto CLEANUP; + } + } + + /* Back off if it's too big */ + while (mp_cmp(x, m) != MP_LT) { + if ((err = s_mp_sub(x, m, x)) != MP_OKAY) { + goto CLEANUP; + } + } CLEANUP: - mp_clear (&q); + mp_clear(&q); - return res; + return err; } #endif - -/* $Source: /cvs/libtom/libtommath/bn_mp_reduce.c,v $ */ -/* $Revision: 1.4 $ */ -/* $Date: 2006/12/28 01:25:13 $ */ diff --git a/lib/hcrypto/libtommath/bn_mp_reduce_2k.c b/lib/hcrypto/libtommath/bn_mp_reduce_2k.c index 1c4a751dda5a..1cea6cb212e9 100644 --- a/lib/hcrypto/libtommath/bn_mp_reduce_2k.c +++ b/lib/hcrypto/libtommath/bn_mp_reduce_2k.c @@ -1,61 +1,48 @@ -#include <tommath.h> +#include "tommath_private.h" #ifdef BN_MP_REDUCE_2K_C -/* LibTomMath, multiple-precision integer library -- Tom St Denis - * - * LibTomMath is a library that provides multiple-precision - * integer arithmetic as well as number theoretic functionality. - * - * The library was designed directly after the MPI library by - * Michael Fromberger but has been written from scratch with - * additional optimizations in place. - * - * The library is free for all purposes without any express - * guarantee it works. - * - * Tom St Denis, tomstdenis@gmail.com, http://libtom.org - */ +/* LibTomMath, multiple-precision integer library -- Tom St Denis */ +/* SPDX-License-Identifier: Unlicense */ /* reduces a modulo n where n is of the form 2**p - d */ -int mp_reduce_2k(mp_int *a, mp_int *n, mp_digit d) +mp_err mp_reduce_2k(mp_int *a, const mp_int *n, mp_digit d) { mp_int q; - int p, res; + mp_err err; + int p; - if ((res = mp_init(&q)) != MP_OKAY) { - return res; + if ((err = mp_init(&q)) != MP_OKAY) { + return err; } p = mp_count_bits(n); top: /* q = a/2**p, a = a mod 2**p */ - if ((res = mp_div_2d(a, p, &q, a)) != MP_OKAY) { - goto ERR; + if ((err = mp_div_2d(a, p, &q, a)) != MP_OKAY) { + goto LBL_ERR; } - if (d != 1) { + if (d != 1u) { /* q = q * d */ - if ((res = mp_mul_d(&q, d, &q)) != MP_OKAY) { - goto ERR; + if ((err = mp_mul_d(&q, d, &q)) != MP_OKAY) { + goto LBL_ERR; } } /* a = a + q */ - if ((res = s_mp_add(a, &q, a)) != MP_OKAY) { - goto ERR; + if ((err = s_mp_add(a, &q, a)) != MP_OKAY) { + goto LBL_ERR; } if (mp_cmp_mag(a, n) != MP_LT) { - s_mp_sub(a, n, a); + if ((err = s_mp_sub(a, n, a)) != MP_OKAY) { + goto LBL_ERR; + } goto top; } -ERR: +LBL_ERR: mp_clear(&q); - return res; + return err; } #endif - -/* $Source: /cvs/libtom/libtommath/bn_mp_reduce_2k.c,v $ */ -/* $Revision: 1.4 $ */ -/* $Date: 2006/12/28 01:25:13 $ */ diff --git a/lib/hcrypto/libtommath/bn_mp_reduce_2k_l.c b/lib/hcrypto/libtommath/bn_mp_reduce_2k_l.c index 71abeaebba72..6a9f3d31b03d 100644 --- a/lib/hcrypto/libtommath/bn_mp_reduce_2k_l.c +++ b/lib/hcrypto/libtommath/bn_mp_reduce_2k_l.c @@ -1,62 +1,49 @@ -#include <tommath.h> +#include "tommath_private.h" #ifdef BN_MP_REDUCE_2K_L_C -/* LibTomMath, multiple-precision integer library -- Tom St Denis - * - * LibTomMath is a library that provides multiple-precision - * integer arithmetic as well as number theoretic functionality. - * - * The library was designed directly after the MPI library by - * Michael Fromberger but has been written from scratch with - * additional optimizations in place. - * - * The library is free for all purposes without any express - * guarantee it works. - * - * Tom St Denis, tomstdenis@gmail.com, http://libtom.org - */ +/* LibTomMath, multiple-precision integer library -- Tom St Denis */ +/* SPDX-License-Identifier: Unlicense */ /* reduces a modulo n where n is of the form 2**p - d This differs from reduce_2k since "d" can be larger than a single digit. */ -int mp_reduce_2k_l(mp_int *a, mp_int *n, mp_int *d) +mp_err mp_reduce_2k_l(mp_int *a, const mp_int *n, const mp_int *d) { mp_int q; - int p, res; + mp_err err; + int p; - if ((res = mp_init(&q)) != MP_OKAY) { - return res; + if ((err = mp_init(&q)) != MP_OKAY) { + return err; } p = mp_count_bits(n); top: /* q = a/2**p, a = a mod 2**p */ - if ((res = mp_div_2d(a, p, &q, a)) != MP_OKAY) { - goto ERR; + if ((err = mp_div_2d(a, p, &q, a)) != MP_OKAY) { + goto LBL_ERR; } /* q = q * d */ - if ((res = mp_mul(&q, d, &q)) != MP_OKAY) { - goto ERR; + if ((err = mp_mul(&q, d, &q)) != MP_OKAY) { + goto LBL_ERR; } /* a = a + q */ - if ((res = s_mp_add(a, &q, a)) != MP_OKAY) { - goto ERR; + if ((err = s_mp_add(a, &q, a)) != MP_OKAY) { + goto LBL_ERR; } if (mp_cmp_mag(a, n) != MP_LT) { - s_mp_sub(a, n, a); + if ((err = s_mp_sub(a, n, a)) != MP_OKAY) { + goto LBL_ERR; + } goto top; } -ERR: +LBL_ERR: mp_clear(&q); - return res; + return err; } #endif - -/* $Source: /cvs/libtom/libtommath/bn_mp_reduce_2k_l.c,v $ */ -/* $Revision: 1.4 $ */ -/* $Date: 2006/12/28 01:25:13 $ */ diff --git a/lib/hcrypto/libtommath/bn_mp_reduce_2k_setup.c b/lib/hcrypto/libtommath/bn_mp_reduce_2k_setup.c index dca723c81568..2eaf7addf6c7 100644 --- a/lib/hcrypto/libtommath/bn_mp_reduce_2k_setup.c +++ b/lib/hcrypto/libtommath/bn_mp_reduce_2k_setup.c @@ -1,39 +1,28 @@ -#include <tommath.h> +#include "tommath_private.h" #ifdef BN_MP_REDUCE_2K_SETUP_C -/* LibTomMath, multiple-precision integer library -- Tom St Denis - * - * LibTomMath is a library that provides multiple-precision - * integer arithmetic as well as number theoretic functionality. - * - * The library was designed directly after the MPI library by - * Michael Fromberger but has been written from scratch with - * additional optimizations in place. - * - * The library is free for all purposes without any express - * guarantee it works. - * - * Tom St Denis, tomstdenis@gmail.com, http://libtom.org - */ +/* LibTomMath, multiple-precision integer library -- Tom St Denis */ +/* SPDX-License-Identifier: Unlicense */ /* determines the setup value */ -int mp_reduce_2k_setup(mp_int *a, mp_digit *d) +mp_err mp_reduce_2k_setup(const mp_int *a, mp_digit *d) { - int res, p; + mp_err err; mp_int tmp; + int p; - if ((res = mp_init(&tmp)) != MP_OKAY) { - return res; + if ((err = mp_init(&tmp)) != MP_OKAY) { + return err; } p = mp_count_bits(a); - if ((res = mp_2expt(&tmp, p)) != MP_OKAY) { + if ((err = mp_2expt(&tmp, p)) != MP_OKAY) { mp_clear(&tmp); - return res; + return err; } - if ((res = s_mp_sub(&tmp, a, &tmp)) != MP_OKAY) { + if ((err = s_mp_sub(&tmp, a, &tmp)) != MP_OKAY) { mp_clear(&tmp); - return res; + return err; } *d = tmp.dp[0]; @@ -41,7 +30,3 @@ int mp_reduce_2k_setup(mp_int *a, mp_digit *d) return MP_OKAY; } #endif - -/* $Source: /cvs/libtom/libtommath/bn_mp_reduce_2k_setup.c,v $ */ -/* $Revision: 1.4 $ */ -/* $Date: 2006/12/28 01:25:13 $ */ diff --git a/lib/hcrypto/libtommath/bn_mp_reduce_2k_setup_l.c b/lib/hcrypto/libtommath/bn_mp_reduce_2k_setup_l.c index cc59a6e71585..4f9aa14d1841 100644 --- a/lib/hcrypto/libtommath/bn_mp_reduce_2k_setup_l.c +++ b/lib/hcrypto/libtommath/bn_mp_reduce_2k_setup_l.c @@ -1,44 +1,28 @@ -#include <tommath.h> +#include "tommath_private.h" #ifdef BN_MP_REDUCE_2K_SETUP_L_C -/* LibTomMath, multiple-precision integer library -- Tom St Denis - * - * LibTomMath is a library that provides multiple-precision - * integer arithmetic as well as number theoretic functionality. - * - * The library was designed directly after the MPI library by - * Michael Fromberger but has been written from scratch with - * additional optimizations in place. - * - * The library is free for all purposes without any express - * guarantee it works. - * - * Tom St Denis, tomstdenis@gmail.com, http://libtom.org - */ +/* LibTomMath, multiple-precision integer library -- Tom St Denis */ +/* SPDX-License-Identifier: Unlicense */ /* determines the setup value */ -int mp_reduce_2k_setup_l(mp_int *a, mp_int *d) +mp_err mp_reduce_2k_setup_l(const mp_int *a, mp_int *d) { - int res; + mp_err err; mp_int tmp; - if ((res = mp_init(&tmp)) != MP_OKAY) { - return res; + if ((err = mp_init(&tmp)) != MP_OKAY) { + return err; } - if ((res = mp_2expt(&tmp, mp_count_bits(a))) != MP_OKAY) { - goto ERR; + if ((err = mp_2expt(&tmp, mp_count_bits(a))) != MP_OKAY) { + goto LBL_ERR; } - if ((res = s_mp_sub(&tmp, a, d)) != MP_OKAY) { - goto ERR; + if ((err = s_mp_sub(&tmp, a, d)) != MP_OKAY) { + goto LBL_ERR; } -ERR: +LBL_ERR: mp_clear(&tmp); - return res; + return err; } #endif - -/* $Source: /cvs/libtom/libtommath/bn_mp_reduce_2k_setup_l.c,v $ */ -/* $Revision: 1.4 $ */ -/* $Date: 2006/12/28 01:25:13 $ */ diff --git a/lib/hcrypto/libtommath/bn_mp_reduce_is_2k.c b/lib/hcrypto/libtommath/bn_mp_reduce_is_2k.c index c8d25d83e226..a9f4f9f2b6a1 100644 --- a/lib/hcrypto/libtommath/bn_mp_reduce_is_2k.c +++ b/lib/hcrypto/libtommath/bn_mp_reduce_is_2k.c @@ -1,22 +1,10 @@ -#include <tommath.h> +#include "tommath_private.h" #ifdef BN_MP_REDUCE_IS_2K_C -/* LibTomMath, multiple-precision integer library -- Tom St Denis - * - * LibTomMath is a library that provides multiple-precision - * integer arithmetic as well as number theoretic functionality. - * - * The library was designed directly after the MPI library by - * Michael Fromberger but has been written from scratch with - * additional optimizations in place. - * - * The library is free for all purposes without any express - * guarantee it works. - * - * Tom St Denis, tomstdenis@gmail.com, http://libtom.org - */ +/* LibTomMath, multiple-precision integer library -- Tom St Denis */ +/* SPDX-License-Identifier: Unlicense */ /* determines if mp_reduce_2k can be used */ -int mp_reduce_is_2k(mp_int *a) +mp_bool mp_reduce_is_2k(const mp_int *a) { int ix, iy, iw; mp_digit iz; @@ -31,22 +19,20 @@ int mp_reduce_is_2k(mp_int *a) iw = 1; /* Test every bit from the second digit up, must be 1 */ - for (ix = DIGIT_BIT; ix < iy; ix++) { - if ((a->dp[iw] & iz) == 0) { - return MP_NO; - } - iz <<= 1; - if (iz > (mp_digit)MP_MASK) { - ++iw; - iz = 1; - } + for (ix = MP_DIGIT_BIT; ix < iy; ix++) { + if ((a->dp[iw] & iz) == 0u) { + return MP_NO; + } + iz <<= 1; + if (iz > MP_DIGIT_MAX) { + ++iw; + iz = 1; + } } + return MP_YES; + } else { + return MP_YES; } - return MP_YES; } #endif - -/* $Source: /cvs/libtom/libtommath/bn_mp_reduce_is_2k.c,v $ */ -/* $Revision: 1.4 $ */ -/* $Date: 2006/12/28 01:25:13 $ */ diff --git a/lib/hcrypto/libtommath/bn_mp_reduce_is_2k_l.c b/lib/hcrypto/libtommath/bn_mp_reduce_is_2k_l.c index ad006f39c50e..4bc69bef85b1 100644 --- a/lib/hcrypto/libtommath/bn_mp_reduce_is_2k_l.c +++ b/lib/hcrypto/libtommath/bn_mp_reduce_is_2k_l.c @@ -1,22 +1,10 @@ -#include <tommath.h> +#include "tommath_private.h" #ifdef BN_MP_REDUCE_IS_2K_L_C -/* LibTomMath, multiple-precision integer library -- Tom St Denis - * - * LibTomMath is a library that provides multiple-precision - * integer arithmetic as well as number theoretic functionality. - * - * The library was designed directly after the MPI library by - * Michael Fromberger but has been written from scratch with - * additional optimizations in place. - * - * The library is free for all purposes without any express - * guarantee it works. - * - * Tom St Denis, tomstdenis@gmail.com, http://libtom.org - */ +/* LibTomMath, multiple-precision integer library -- Tom St Denis */ +/* SPDX-License-Identifier: Unlicense */ /* determines if reduce_2k_l can be used */ -int mp_reduce_is_2k_l(mp_int *a) +mp_bool mp_reduce_is_2k_l(const mp_int *a) { int ix, iy; @@ -27,18 +15,14 @@ int mp_reduce_is_2k_l(mp_int *a) } else if (a->used > 1) { /* if more than half of the digits are -1 we're sold */ for (iy = ix = 0; ix < a->used; ix++) { - if (a->dp[ix] == MP_MASK) { - ++iy; - } + if (a->dp[ix] == MP_DIGIT_MAX) { + ++iy; + } } return (iy >= (a->used/2)) ? MP_YES : MP_NO; - + } else { + return MP_NO; } - return MP_NO; } #endif - -/* $Source: /cvs/libtom/libtommath/bn_mp_reduce_is_2k_l.c,v $ */ -/* $Revision: 1.4 $ */ -/* $Date: 2006/12/28 01:25:13 $ */ diff --git a/lib/hcrypto/libtommath/bn_mp_reduce_setup.c b/lib/hcrypto/libtommath/bn_mp_reduce_setup.c index 035419bf3472..f02160fa52e5 100644 --- a/lib/hcrypto/libtommath/bn_mp_reduce_setup.c +++ b/lib/hcrypto/libtommath/bn_mp_reduce_setup.c @@ -1,34 +1,17 @@ -#include <tommath.h> +#include "tommath_private.h" #ifdef BN_MP_REDUCE_SETUP_C -/* LibTomMath, multiple-precision integer library -- Tom St Denis - * - * LibTomMath is a library that provides multiple-precision - * integer arithmetic as well as number theoretic functionality. - * - * The library was designed directly after the MPI library by - * Michael Fromberger but has been written from scratch with - * additional optimizations in place. - * - * The library is free for all purposes without any express - * guarantee it works. - * - * Tom St Denis, tomstdenis@gmail.com, http://libtom.org - */ +/* LibTomMath, multiple-precision integer library -- Tom St Denis */ +/* SPDX-License-Identifier: Unlicense */ /* pre-calculate the value required for Barrett reduction * For a given modulus "b" it calulates the value required in "a" */ -int mp_reduce_setup (mp_int * a, mp_int * b) +mp_err mp_reduce_setup(mp_int *a, const mp_int *b) { - int res; - - if ((res = mp_2expt (a, b->used * 2 * DIGIT_BIT)) != MP_OKAY) { - return res; - } - return mp_div (a, b, a, NULL); + mp_err err; + if ((err = mp_2expt(a, b->used * 2 * MP_DIGIT_BIT)) != MP_OKAY) { + return err; + } + return mp_div(a, b, a, NULL); } #endif - -/* $Source: /cvs/libtom/libtommath/bn_mp_reduce_setup.c,v $ */ -/* $Revision: 1.4 $ */ -/* $Date: 2006/12/28 01:25:13 $ */ diff --git a/lib/hcrypto/libtommath/bn_mp_root_u32.c b/lib/hcrypto/libtommath/bn_mp_root_u32.c new file mode 100644 index 000000000000..97b1b2ea4824 --- /dev/null +++ b/lib/hcrypto/libtommath/bn_mp_root_u32.c @@ -0,0 +1,142 @@ +#include "tommath_private.h" +#ifdef BN_MP_ROOT_U32_C +/* LibTomMath, multiple-precision integer library -- Tom St Denis */ +/* SPDX-License-Identifier: Unlicense */ + +/* find the n'th root of an integer + * + * Result found such that (c)**b <= a and (c+1)**b > a + * + * This algorithm uses Newton's approximation + * x[i+1] = x[i] - f(x[i])/f'(x[i]) + * which will find the root in log(N) time where + * each step involves a fair bit. + */ +mp_err mp_root_u32(const mp_int *a, uint32_t b, mp_int *c) +{ + mp_int t1, t2, t3, a_; + mp_ord cmp; + int ilog2; + mp_err err; + + /* input must be positive if b is even */ + if (((b & 1u) == 0u) && (a->sign == MP_NEG)) { + return MP_VAL; + } + if (b == 0) { + return MP_VAL; + } + + if ((err = mp_init_multi(&t1, &t2, &t3, NULL)) != MP_OKAY) { + return err; + } + + /* if a is negative fudge the sign but keep track */ + a_ = *a; + a_.sign = MP_ZPOS; + + /* Compute seed: 2^(log_2(n)/b + 2)*/ + ilog2 = mp_count_bits(a); + + /* + If "b" is larger than INT_MAX it is also larger than + log_2(n) because the bit-length of the "n" is measured + with an int and hence the root is always < 2 (two). + */ + if (b > (uint32_t)(INT_MAX/2)) { + mp_set(c, 1uL); + c->sign = a->sign; + err = MP_OKAY; + goto LBL_ERR; + } + + /* "b" is smaller than INT_MAX, we can cast safely */ + if (ilog2 < (int)b) { + mp_set(c, 1uL); + c->sign = a->sign; + err = MP_OKAY; + goto LBL_ERR; + } + ilog2 = ilog2 / ((int)b); + if (ilog2 == 0) { + mp_set(c, 1uL); + c->sign = a->sign; + err = MP_OKAY; + goto LBL_ERR; + } + /* Start value must be larger than root */ + ilog2 += 2; + if ((err = mp_2expt(&t2,ilog2)) != MP_OKAY) goto LBL_ERR; + do { + /* t1 = t2 */ + if ((err = mp_copy(&t2, &t1)) != MP_OKAY) goto LBL_ERR; + + /* t2 = t1 - ((t1**b - a) / (b * t1**(b-1))) */ + + /* t3 = t1**(b-1) */ + if ((err = mp_expt_u32(&t1, b - 1u, &t3)) != MP_OKAY) goto LBL_ERR; + + /* numerator */ + /* t2 = t1**b */ + if ((err = mp_mul(&t3, &t1, &t2)) != MP_OKAY) goto LBL_ERR; + + /* t2 = t1**b - a */ + if ((err = mp_sub(&t2, &a_, &t2)) != MP_OKAY) goto LBL_ERR; + + /* denominator */ + /* t3 = t1**(b-1) * b */ + if ((err = mp_mul_d(&t3, b, &t3)) != MP_OKAY) goto LBL_ERR; + + /* t3 = (t1**b - a)/(b * t1**(b-1)) */ + if ((err = mp_div(&t2, &t3, &t3, NULL)) != MP_OKAY) goto LBL_ERR; + + if ((err = mp_sub(&t1, &t3, &t2)) != MP_OKAY) goto LBL_ERR; + + /* + Number of rounds is at most log_2(root). If it is more it + got stuck, so break out of the loop and do the rest manually. + */ + if (ilog2-- == 0) { + break; + } + } while (mp_cmp(&t1, &t2) != MP_EQ); + + /* result can be off by a few so check */ + /* Loop beneath can overshoot by one if found root is smaller than actual root */ + for (;;) { + if ((err = mp_expt_u32(&t1, b, &t2)) != MP_OKAY) goto LBL_ERR; + cmp = mp_cmp(&t2, &a_); + if (cmp == MP_EQ) { + err = MP_OKAY; + goto LBL_ERR; + } + if (cmp == MP_LT) { + if ((err = mp_add_d(&t1, 1uL, &t1)) != MP_OKAY) goto LBL_ERR; + } else { + break; + } + } + /* correct overshoot from above or from recurrence */ + for (;;) { + if ((err = mp_expt_u32(&t1, b, &t2)) != MP_OKAY) goto LBL_ERR; + if (mp_cmp(&t2, &a_) == MP_GT) { + if ((err = mp_sub_d(&t1, 1uL, &t1)) != MP_OKAY) goto LBL_ERR; + } else { + break; + } + } + + /* set the result */ + mp_exch(&t1, c); + + /* set the sign of the result */ + c->sign = a->sign; + + err = MP_OKAY; + +LBL_ERR: + mp_clear_multi(&t1, &t2, &t3, NULL); + return err; +} + +#endif diff --git a/lib/hcrypto/libtommath/bn_mp_rshd.c b/lib/hcrypto/libtommath/bn_mp_rshd.c index ed13ce59a492..bb8743e3bc51 100644 --- a/lib/hcrypto/libtommath/bn_mp_rshd.c +++ b/lib/hcrypto/libtommath/bn_mp_rshd.c @@ -1,72 +1,51 @@ -#include <tommath.h> +#include "tommath_private.h" #ifdef BN_MP_RSHD_C -/* LibTomMath, multiple-precision integer library -- Tom St Denis - * - * LibTomMath is a library that provides multiple-precision - * integer arithmetic as well as number theoretic functionality. - * - * The library was designed directly after the MPI library by - * Michael Fromberger but has been written from scratch with - * additional optimizations in place. - * - * The library is free for all purposes without any express - * guarantee it works. - * - * Tom St Denis, tomstdenis@gmail.com, http://libtom.org - */ +/* LibTomMath, multiple-precision integer library -- Tom St Denis */ +/* SPDX-License-Identifier: Unlicense */ /* shift right a certain amount of digits */ -void mp_rshd (mp_int * a, int b) +void mp_rshd(mp_int *a, int b) { - int x; - - /* if b <= 0 then ignore it */ - if (b <= 0) { - return; - } - - /* if b > used then simply zero it and return */ - if (a->used <= b) { - mp_zero (a); - return; - } - - { - register mp_digit *bottom, *top; - - /* shift the digits down */ - - /* bottom */ - bottom = a->dp; - - /* top [offset into digits] */ - top = a->dp + b; - - /* this is implemented as a sliding window where - * the window is b-digits long and digits from - * the top of the window are copied to the bottom - * - * e.g. - - b-2 | b-1 | b0 | b1 | b2 | ... | bb | ----> - /\ | ----> - \-------------------/ ----> - */ - for (x = 0; x < (a->used - b); x++) { + int x; + mp_digit *bottom, *top; + + /* if b <= 0 then ignore it */ + if (b <= 0) { + return; + } + + /* if b > used then simply zero it and return */ + if (a->used <= b) { + mp_zero(a); + return; + } + + /* shift the digits down */ + + /* bottom */ + bottom = a->dp; + + /* top [offset into digits] */ + top = a->dp + b; + + /* this is implemented as a sliding window where + * the window is b-digits long and digits from + * the top of the window are copied to the bottom + * + * e.g. + + b-2 | b-1 | b0 | b1 | b2 | ... | bb | ----> + /\ | ----> + \-------------------/ ----> + */ + for (x = 0; x < (a->used - b); x++) { *bottom++ = *top++; - } + } - /* zero the top digits */ - for (; x < a->used; x++) { - *bottom++ = 0; - } - } + /* zero the top digits */ + MP_ZERO_DIGITS(bottom, a->used - x); - /* remove excess digits */ - a->used -= b; + /* remove excess digits */ + a->used -= b; } #endif - -/* $Source: /cvs/libtom/libtommath/bn_mp_rshd.c,v $ */ -/* $Revision: 1.4 $ */ -/* $Date: 2006/12/28 01:25:13 $ */ diff --git a/lib/hcrypto/libtommath/bn_mp_sbin_size.c b/lib/hcrypto/libtommath/bn_mp_sbin_size.c new file mode 100644 index 000000000000..e0993d690079 --- /dev/null +++ b/lib/hcrypto/libtommath/bn_mp_sbin_size.c @@ -0,0 +1,11 @@ +#include "tommath_private.h" +#ifdef BN_MP_SBIN_SIZE_C +/* LibTomMath, multiple-precision integer library -- Tom St Denis */ +/* SPDX-License-Identifier: Unlicense */ + +/* get the size for an signed equivalent */ +size_t mp_sbin_size(const mp_int *a) +{ + return 1u + mp_ubin_size(a); +} +#endif diff --git a/lib/hcrypto/libtommath/bn_mp_set.c b/lib/hcrypto/libtommath/bn_mp_set.c index 174adcbc6d6b..44ac6df571c0 100644 --- a/lib/hcrypto/libtommath/bn_mp_set.c +++ b/lib/hcrypto/libtommath/bn_mp_set.c @@ -1,29 +1,14 @@ -#include <tommath.h> +#include "tommath_private.h" #ifdef BN_MP_SET_C -/* LibTomMath, multiple-precision integer library -- Tom St Denis - * - * LibTomMath is a library that provides multiple-precision - * integer arithmetic as well as number theoretic functionality. - * - * The library was designed directly after the MPI library by - * Michael Fromberger but has been written from scratch with - * additional optimizations in place. - * - * The library is free for all purposes without any express - * guarantee it works. - * - * Tom St Denis, tomstdenis@gmail.com, http://libtom.org - */ +/* LibTomMath, multiple-precision integer library -- Tom St Denis */ +/* SPDX-License-Identifier: Unlicense */ /* set to a digit */ -void mp_set (mp_int * a, mp_digit b) +void mp_set(mp_int *a, mp_digit b) { - mp_zero (a); - a->dp[0] = b & MP_MASK; - a->used = (a->dp[0] != 0) ? 1 : 0; + a->dp[0] = b & MP_MASK; + a->sign = MP_ZPOS; + a->used = (a->dp[0] != 0u) ? 1 : 0; + MP_ZERO_DIGITS(a->dp + a->used, a->alloc - a->used); } #endif - -/* $Source: /cvs/libtom/libtommath/bn_mp_set.c,v $ */ -/* $Revision: 1.4 $ */ -/* $Date: 2006/12/28 01:25:13 $ */ diff --git a/lib/hcrypto/libtommath/bn_mp_set_double.c b/lib/hcrypto/libtommath/bn_mp_set_double.c new file mode 100644 index 000000000000..6f91b64f5034 --- /dev/null +++ b/lib/hcrypto/libtommath/bn_mp_set_double.c @@ -0,0 +1,47 @@ +#include "tommath_private.h" +#ifdef BN_MP_SET_DOUBLE_C +/* LibTomMath, multiple-precision integer library -- Tom St Denis */ +/* SPDX-License-Identifier: Unlicense */ + +#if defined(__STDC_IEC_559__) || defined(__GCC_IEC_559) || defined(__x86_64__) || defined(_M_X64) || defined(_M_AMD64) || defined(__i386__) || defined(_M_X86) || defined(__aarch64__) || defined(__arm__) +mp_err mp_set_double(mp_int *a, double b) +{ + uint64_t frac; + int exp; + mp_err err; + union { + double dbl; + uint64_t bits; + } cast; + cast.dbl = b; + + exp = (int)((unsigned)(cast.bits >> 52) & 0x7FFu); + frac = (cast.bits & ((1uLL << 52) - 1uLL)) | (1uLL << 52); + + if (exp == 0x7FF) { /* +-inf, NaN */ + return MP_VAL; + } + exp -= 1023 + 52; + + mp_set_u64(a, frac); + + err = (exp < 0) ? mp_div_2d(a, -exp, a, NULL) : mp_mul_2d(a, exp, a); + if (err != MP_OKAY) { + return err; + } + + if (((cast.bits >> 63) != 0uLL) && !MP_IS_ZERO(a)) { + a->sign = MP_NEG; + } + + return MP_OKAY; +} +#else +/* pragma message() not supported by several compilers (in mostly older but still used versions) */ +# ifdef _MSC_VER +# pragma message("mp_set_double implementation is only available on platforms with IEEE754 floating point format") +# else +# warning "mp_set_double implementation is only available on platforms with IEEE754 floating point format" +# endif +#endif +#endif diff --git a/lib/hcrypto/libtommath/bn_mp_set_i32.c b/lib/hcrypto/libtommath/bn_mp_set_i32.c new file mode 100644 index 000000000000..df4513d3755e --- /dev/null +++ b/lib/hcrypto/libtommath/bn_mp_set_i32.c @@ -0,0 +1,7 @@ +#include "tommath_private.h" +#ifdef BN_MP_SET_I32_C +/* LibTomMath, multiple-precision integer library -- Tom St Denis */ +/* SPDX-License-Identifier: Unlicense */ + +MP_SET_SIGNED(mp_set_i32, mp_set_u32, int32_t, uint32_t) +#endif diff --git a/lib/hcrypto/libtommath/bn_mp_set_i64.c b/lib/hcrypto/libtommath/bn_mp_set_i64.c new file mode 100644 index 000000000000..395103bf5e2f --- /dev/null +++ b/lib/hcrypto/libtommath/bn_mp_set_i64.c @@ -0,0 +1,7 @@ +#include "tommath_private.h" +#ifdef BN_MP_SET_I64_C +/* LibTomMath, multiple-precision integer library -- Tom St Denis */ +/* SPDX-License-Identifier: Unlicense */ + +MP_SET_SIGNED(mp_set_i64, mp_set_u64, int64_t, uint64_t) +#endif diff --git a/lib/hcrypto/libtommath/bn_mp_set_int.c b/lib/hcrypto/libtommath/bn_mp_set_int.c deleted file mode 100644 index 3072e76e1c43..000000000000 --- a/lib/hcrypto/libtommath/bn_mp_set_int.c +++ /dev/null @@ -1,48 +0,0 @@ -#include <tommath.h> -#ifdef BN_MP_SET_INT_C -/* LibTomMath, multiple-precision integer library -- Tom St Denis - * - * LibTomMath is a library that provides multiple-precision - * integer arithmetic as well as number theoretic functionality. - * - * The library was designed directly after the MPI library by - * Michael Fromberger but has been written from scratch with - * additional optimizations in place. - * - * The library is free for all purposes without any express - * guarantee it works. - * - * Tom St Denis, tomstdenis@gmail.com, http://libtom.org - */ - -/* set a 32-bit const */ -int mp_set_int (mp_int * a, unsigned long b) -{ - int x, res; - - mp_zero (a); - - /* set four bits at a time */ - for (x = 0; x < 8; x++) { - /* shift the number up four bits */ - if ((res = mp_mul_2d (a, 4, a)) != MP_OKAY) { - return res; - } - - /* OR in the top four bits of the source */ - a->dp[0] |= (b >> 28) & 15; - - /* shift the source up to the next four bits */ - b <<= 4; - - /* ensure that digits are not clamped off */ - a->used += 1; - } - mp_clamp (a); - return MP_OKAY; -} -#endif - -/* $Source: /cvs/libtom/libtommath/bn_mp_set_int.c,v $ */ -/* $Revision: 1.4 $ */ -/* $Date: 2006/12/28 01:25:13 $ */ diff --git a/lib/hcrypto/libtommath/bn_mp_set_l.c b/lib/hcrypto/libtommath/bn_mp_set_l.c new file mode 100644 index 000000000000..1e445fb62a0c --- /dev/null +++ b/lib/hcrypto/libtommath/bn_mp_set_l.c @@ -0,0 +1,7 @@ +#include "tommath_private.h" +#ifdef BN_MP_SET_L_C +/* LibTomMath, multiple-precision integer library -- Tom St Denis */ +/* SPDX-License-Identifier: Unlicense */ + +MP_SET_SIGNED(mp_set_l, mp_set_ul, long, unsigned long) +#endif diff --git a/lib/hcrypto/libtommath/bn_mp_set_ll.c b/lib/hcrypto/libtommath/bn_mp_set_ll.c new file mode 100644 index 000000000000..3e2324f32994 --- /dev/null +++ b/lib/hcrypto/libtommath/bn_mp_set_ll.c @@ -0,0 +1,7 @@ +#include "tommath_private.h" +#ifdef BN_MP_SET_LL_C +/* LibTomMath, multiple-precision integer library -- Tom St Denis */ +/* SPDX-License-Identifier: Unlicense */ + +MP_SET_SIGNED(mp_set_ll, mp_set_ull, long long, unsigned long long) +#endif diff --git a/lib/hcrypto/libtommath/bn_mp_set_u32.c b/lib/hcrypto/libtommath/bn_mp_set_u32.c new file mode 100644 index 000000000000..18ba5e14c0d0 --- /dev/null +++ b/lib/hcrypto/libtommath/bn_mp_set_u32.c @@ -0,0 +1,7 @@ +#include "tommath_private.h" +#ifdef BN_MP_SET_U32_C +/* LibTomMath, multiple-precision integer library -- Tom St Denis */ +/* SPDX-License-Identifier: Unlicense */ + +MP_SET_UNSIGNED(mp_set_u32, uint32_t) +#endif diff --git a/lib/hcrypto/libtommath/bn_mp_set_u64.c b/lib/hcrypto/libtommath/bn_mp_set_u64.c new file mode 100644 index 000000000000..88fab6c54a2f --- /dev/null +++ b/lib/hcrypto/libtommath/bn_mp_set_u64.c @@ -0,0 +1,7 @@ +#include "tommath_private.h" +#ifdef BN_MP_SET_U64_C +/* LibTomMath, multiple-precision integer library -- Tom St Denis */ +/* SPDX-License-Identifier: Unlicense */ + +MP_SET_UNSIGNED(mp_set_u64, uint64_t) +#endif diff --git a/lib/hcrypto/libtommath/bn_mp_set_ul.c b/lib/hcrypto/libtommath/bn_mp_set_ul.c new file mode 100644 index 000000000000..adfd85c7f8e8 --- /dev/null +++ b/lib/hcrypto/libtommath/bn_mp_set_ul.c @@ -0,0 +1,7 @@ +#include "tommath_private.h" +#ifdef BN_MP_SET_UL_C +/* LibTomMath, multiple-precision integer library -- Tom St Denis */ +/* SPDX-License-Identifier: Unlicense */ + +MP_SET_UNSIGNED(mp_set_ul, unsigned long) +#endif diff --git a/lib/hcrypto/libtommath/bn_mp_set_ull.c b/lib/hcrypto/libtommath/bn_mp_set_ull.c new file mode 100644 index 000000000000..8fbc1bd2cd0b --- /dev/null +++ b/lib/hcrypto/libtommath/bn_mp_set_ull.c @@ -0,0 +1,7 @@ +#include "tommath_private.h" +#ifdef BN_MP_SET_ULL_C +/* LibTomMath, multiple-precision integer library -- Tom St Denis */ +/* SPDX-License-Identifier: Unlicense */ + +MP_SET_UNSIGNED(mp_set_ull, unsigned long long) +#endif diff --git a/lib/hcrypto/libtommath/bn_mp_shrink.c b/lib/hcrypto/libtommath/bn_mp_shrink.c index c600efc58164..cf27ed9ec385 100644 --- a/lib/hcrypto/libtommath/bn_mp_shrink.c +++ b/lib/hcrypto/libtommath/bn_mp_shrink.c @@ -1,40 +1,22 @@ -#include <tommath.h> +#include "tommath_private.h" #ifdef BN_MP_SHRINK_C -/* LibTomMath, multiple-precision integer library -- Tom St Denis - * - * LibTomMath is a library that provides multiple-precision - * integer arithmetic as well as number theoretic functionality. - * - * The library was designed directly after the MPI library by - * Michael Fromberger but has been written from scratch with - * additional optimizations in place. - * - * The library is free for all purposes without any express - * guarantee it works. - * - * Tom St Denis, tomstdenis@gmail.com, http://libtom.org - */ +/* LibTomMath, multiple-precision integer library -- Tom St Denis */ +/* SPDX-License-Identifier: Unlicense */ /* shrink a bignum */ -int mp_shrink (mp_int * a) +mp_err mp_shrink(mp_int *a) { - mp_digit *tmp; - int used = 1; - - if(a->used > 0) - used = a->used; - - if (a->alloc != used) { - if ((tmp = OPT_CAST(mp_digit) XREALLOC (a->dp, sizeof (mp_digit) * used)) == NULL) { - return MP_MEM; - } - a->dp = tmp; - a->alloc = used; - } - return MP_OKAY; + mp_digit *tmp; + int alloc = MP_MAX(MP_MIN_PREC, a->used); + if (a->alloc != alloc) { + if ((tmp = (mp_digit *) MP_REALLOC(a->dp, + (size_t)a->alloc * sizeof(mp_digit), + (size_t)alloc * sizeof(mp_digit))) == NULL) { + return MP_MEM; + } + a->dp = tmp; + a->alloc = alloc; + } + return MP_OKAY; } #endif - -/* $Source: /cvs/libtom/libtommath/bn_mp_shrink.c,v $ */ -/* $Revision: 1.4 $ */ -/* $Date: 2006/12/28 01:25:13 $ */ diff --git a/lib/hcrypto/libtommath/bn_mp_signed_bin_size.c b/lib/hcrypto/libtommath/bn_mp_signed_bin_size.c deleted file mode 100644 index 6739d19e2bcc..000000000000 --- a/lib/hcrypto/libtommath/bn_mp_signed_bin_size.c +++ /dev/null @@ -1,27 +0,0 @@ -#include <tommath.h> -#ifdef BN_MP_SIGNED_BIN_SIZE_C -/* LibTomMath, multiple-precision integer library -- Tom St Denis - * - * LibTomMath is a library that provides multiple-precision - * integer arithmetic as well as number theoretic functionality. - * - * The library was designed directly after the MPI library by - * Michael Fromberger but has been written from scratch with - * additional optimizations in place. - * - * The library is free for all purposes without any express - * guarantee it works. - * - * Tom St Denis, tomstdenis@gmail.com, http://libtom.org - */ - -/* get the size for an signed equivalent */ -int mp_signed_bin_size (mp_int * a) -{ - return 1 + mp_unsigned_bin_size (a); -} -#endif - -/* $Source: /cvs/libtom/libtommath/bn_mp_signed_bin_size.c,v $ */ -/* $Revision: 1.4 $ */ -/* $Date: 2006/12/28 01:25:13 $ */ diff --git a/lib/hcrypto/libtommath/bn_mp_signed_rsh.c b/lib/hcrypto/libtommath/bn_mp_signed_rsh.c new file mode 100644 index 000000000000..8d8d8414dd70 --- /dev/null +++ b/lib/hcrypto/libtommath/bn_mp_signed_rsh.c @@ -0,0 +1,22 @@ +#include "tommath_private.h" +#ifdef BN_MP_SIGNED_RSH_C +/* LibTomMath, multiple-precision integer library -- Tom St Denis */ +/* SPDX-License-Identifier: Unlicense */ + +/* shift right by a certain bit count with sign extension */ +mp_err mp_signed_rsh(const mp_int *a, int b, mp_int *c) +{ + mp_err res; + if (a->sign == MP_ZPOS) { + return mp_div_2d(a, b, c, NULL); + } + + res = mp_add_d(a, 1uL, c); + if (res != MP_OKAY) { + return res; + } + + res = mp_div_2d(c, b, c, NULL); + return (res == MP_OKAY) ? mp_sub_d(c, 1uL, c) : res; +} +#endif diff --git a/lib/hcrypto/libtommath/bn_mp_sqr.c b/lib/hcrypto/libtommath/bn_mp_sqr.c index 90f4dd6d7273..e0d0a73e4483 100644 --- a/lib/hcrypto/libtommath/bn_mp_sqr.c +++ b/lib/hcrypto/libtommath/bn_mp_sqr.c @@ -1,58 +1,28 @@ -#include <tommath.h> +#include "tommath_private.h" #ifdef BN_MP_SQR_C -/* LibTomMath, multiple-precision integer library -- Tom St Denis - * - * LibTomMath is a library that provides multiple-precision - * integer arithmetic as well as number theoretic functionality. - * - * The library was designed directly after the MPI library by - * Michael Fromberger but has been written from scratch with - * additional optimizations in place. - * - * The library is free for all purposes without any express - * guarantee it works. - * - * Tom St Denis, tomstdenis@gmail.com, http://libtom.org - */ +/* LibTomMath, multiple-precision integer library -- Tom St Denis */ +/* SPDX-License-Identifier: Unlicense */ /* computes b = a*a */ -int -mp_sqr (mp_int * a, mp_int * b) +mp_err mp_sqr(const mp_int *a, mp_int *b) { - int res; - -#ifdef BN_MP_TOOM_SQR_C - /* use Toom-Cook? */ - if (a->used >= TOOM_SQR_CUTOFF) { - res = mp_toom_sqr(a, b); - /* Karatsuba? */ - } else -#endif -#ifdef BN_MP_KARATSUBA_SQR_C -if (a->used >= KARATSUBA_SQR_CUTOFF) { - res = mp_karatsuba_sqr (a, b); - } else -#endif - { -#ifdef BN_FAST_S_MP_SQR_C - /* can we use the fast comba multiplier? */ - if ((a->used * 2 + 1) < MP_WARRAY && - a->used < - (1 << (sizeof(mp_word) * CHAR_BIT - 2*DIGIT_BIT - 1))) { - res = fast_s_mp_sqr (a, b); - } else -#endif -#ifdef BN_S_MP_SQR_C - res = s_mp_sqr (a, b); -#else - res = MP_VAL; -#endif - } - b->sign = MP_ZPOS; - return res; + mp_err err; + if (MP_HAS(S_MP_TOOM_SQR) && /* use Toom-Cook? */ + (a->used >= MP_TOOM_SQR_CUTOFF)) { + err = s_mp_toom_sqr(a, b); + } else if (MP_HAS(S_MP_KARATSUBA_SQR) && /* Karatsuba? */ + (a->used >= MP_KARATSUBA_SQR_CUTOFF)) { + err = s_mp_karatsuba_sqr(a, b); + } else if (MP_HAS(S_MP_SQR_FAST) && /* can we use the fast comba multiplier? */ + (((a->used * 2) + 1) < MP_WARRAY) && + (a->used < (MP_MAXFAST / 2))) { + err = s_mp_sqr_fast(a, b); + } else if (MP_HAS(S_MP_SQR)) { + err = s_mp_sqr(a, b); + } else { + err = MP_VAL; + } + b->sign = MP_ZPOS; + return err; } #endif - -/* $Source: /cvs/libtom/libtommath/bn_mp_sqr.c,v $ */ -/* $Revision: 1.4 $ */ -/* $Date: 2006/12/28 01:25:13 $ */ diff --git a/lib/hcrypto/libtommath/bn_mp_sqrmod.c b/lib/hcrypto/libtommath/bn_mp_sqrmod.c index 161cbbb30dd3..626ea2c299c5 100644 --- a/lib/hcrypto/libtommath/bn_mp_sqrmod.c +++ b/lib/hcrypto/libtommath/bn_mp_sqrmod.c @@ -1,41 +1,25 @@ -#include <tommath.h> +#include "tommath_private.h" #ifdef BN_MP_SQRMOD_C -/* LibTomMath, multiple-precision integer library -- Tom St Denis - * - * LibTomMath is a library that provides multiple-precision - * integer arithmetic as well as number theoretic functionality. - * - * The library was designed directly after the MPI library by - * Michael Fromberger but has been written from scratch with - * additional optimizations in place. - * - * The library is free for all purposes without any express - * guarantee it works. - * - * Tom St Denis, tomstdenis@gmail.com, http://libtom.org - */ +/* LibTomMath, multiple-precision integer library -- Tom St Denis */ +/* SPDX-License-Identifier: Unlicense */ /* c = a * a (mod b) */ -int -mp_sqrmod (mp_int * a, mp_int * b, mp_int * c) +mp_err mp_sqrmod(const mp_int *a, const mp_int *b, mp_int *c) { - int res; - mp_int t; + mp_err err; + mp_int t; - if ((res = mp_init (&t)) != MP_OKAY) { - return res; - } + if ((err = mp_init(&t)) != MP_OKAY) { + return err; + } - if ((res = mp_sqr (a, &t)) != MP_OKAY) { - mp_clear (&t); - return res; - } - res = mp_mod (&t, b, c); - mp_clear (&t); - return res; + if ((err = mp_sqr(a, &t)) != MP_OKAY) { + goto LBL_ERR; + } + err = mp_mod(&t, b, c); + +LBL_ERR: + mp_clear(&t); + return err; } #endif - -/* $Source: /cvs/libtom/libtommath/bn_mp_sqrmod.c,v $ */ -/* $Revision: 1.4 $ */ -/* $Date: 2006/12/28 01:25:13 $ */ diff --git a/lib/hcrypto/libtommath/bn_mp_sqrt.c b/lib/hcrypto/libtommath/bn_mp_sqrt.c index 8391297f7e52..82d682467b9c 100644 --- a/lib/hcrypto/libtommath/bn_mp_sqrt.c +++ b/lib/hcrypto/libtommath/bn_mp_sqrt.c @@ -1,81 +1,67 @@ -#include <tommath.h> +#include "tommath_private.h" #ifdef BN_MP_SQRT_C -/* LibTomMath, multiple-precision integer library -- Tom St Denis - * - * LibTomMath is a library that provides multiple-precision - * integer arithmetic as well as number theoretic functionality. - * - * The library was designed directly after the MPI library by - * Michael Fromberger but has been written from scratch with - * additional optimizations in place. - * - * The library is free for all purposes without any express - * guarantee it works. - * - * Tom St Denis, tomstdenis@gmail.com, http://libtom.org - */ +/* LibTomMath, multiple-precision integer library -- Tom St Denis */ +/* SPDX-License-Identifier: Unlicense */ /* this function is less generic than mp_n_root, simpler and faster */ -int mp_sqrt(mp_int *arg, mp_int *ret) +mp_err mp_sqrt(const mp_int *arg, mp_int *ret) { - int res; - mp_int t1,t2; + mp_err err; + mp_int t1, t2; - /* must be positive */ - if (arg->sign == MP_NEG) { - return MP_VAL; - } + /* must be positive */ + if (arg->sign == MP_NEG) { + return MP_VAL; + } - /* easy out */ - if (mp_iszero(arg) == MP_YES) { - mp_zero(ret); - return MP_OKAY; - } + /* easy out */ + if (MP_IS_ZERO(arg)) { + mp_zero(ret); + return MP_OKAY; + } - if ((res = mp_init_copy(&t1, arg)) != MP_OKAY) { - return res; - } + if ((err = mp_init_copy(&t1, arg)) != MP_OKAY) { + return err; + } - if ((res = mp_init(&t2)) != MP_OKAY) { - goto E2; - } + if ((err = mp_init(&t2)) != MP_OKAY) { + goto E2; + } - /* First approx. (not very bad for large arg) */ - mp_rshd (&t1,t1.used/2); + /* First approx. (not very bad for large arg) */ + mp_rshd(&t1, t1.used/2); - /* t1 > 0 */ - if ((res = mp_div(arg,&t1,&t2,NULL)) != MP_OKAY) { - goto E1; - } - if ((res = mp_add(&t1,&t2,&t1)) != MP_OKAY) { - goto E1; - } - if ((res = mp_div_2(&t1,&t1)) != MP_OKAY) { - goto E1; - } - /* And now t1 > sqrt(arg) */ - do { - if ((res = mp_div(arg,&t1,&t2,NULL)) != MP_OKAY) { + /* t1 > 0 */ + if ((err = mp_div(arg, &t1, &t2, NULL)) != MP_OKAY) { goto E1; - } - if ((res = mp_add(&t1,&t2,&t1)) != MP_OKAY) { + } + if ((err = mp_add(&t1, &t2, &t1)) != MP_OKAY) { goto E1; - } - if ((res = mp_div_2(&t1,&t1)) != MP_OKAY) { + } + if ((err = mp_div_2(&t1, &t1)) != MP_OKAY) { goto E1; - } - /* t1 >= sqrt(arg) >= t2 at this point */ - } while (mp_cmp_mag(&t1,&t2) == MP_GT); + } + /* And now t1 > sqrt(arg) */ + do { + if ((err = mp_div(arg, &t1, &t2, NULL)) != MP_OKAY) { + goto E1; + } + if ((err = mp_add(&t1, &t2, &t1)) != MP_OKAY) { + goto E1; + } + if ((err = mp_div_2(&t1, &t1)) != MP_OKAY) { + goto E1; + } + /* t1 >= sqrt(arg) >= t2 at this point */ + } while (mp_cmp_mag(&t1, &t2) == MP_GT); - mp_exch(&t1,ret); + mp_exch(&t1, ret); -E1: mp_clear(&t2); -E2: mp_clear(&t1); - return res; +E1: + mp_clear(&t2); +E2: + mp_clear(&t1); + return err; } #endif - -/* $Source: /cvs/libtom/libtommath/bn_mp_sqrt.c,v $ */ -/* $Revision: 1.4 $ */ -/* $Date: 2006/12/28 01:25:13 $ */ diff --git a/lib/hcrypto/libtommath/bn_mp_sqrtmod_prime.c b/lib/hcrypto/libtommath/bn_mp_sqrtmod_prime.c new file mode 100644 index 000000000000..a833ed7c1704 --- /dev/null +++ b/lib/hcrypto/libtommath/bn_mp_sqrtmod_prime.c @@ -0,0 +1,118 @@ +#include "tommath_private.h" +#ifdef BN_MP_SQRTMOD_PRIME_C +/* LibTomMath, multiple-precision integer library -- Tom St Denis */ +/* SPDX-License-Identifier: Unlicense */ + +/* Tonelli-Shanks algorithm + * https://en.wikipedia.org/wiki/Tonelli%E2%80%93Shanks_algorithm + * https://gmplib.org/list-archives/gmp-discuss/2013-April/005300.html + * + */ + +mp_err mp_sqrtmod_prime(const mp_int *n, const mp_int *prime, mp_int *ret) +{ + mp_err err; + int legendre; + mp_int t1, C, Q, S, Z, M, T, R, two; + mp_digit i; + + /* first handle the simple cases */ + if (mp_cmp_d(n, 0uL) == MP_EQ) { + mp_zero(ret); + return MP_OKAY; + } + if (mp_cmp_d(prime, 2uL) == MP_EQ) return MP_VAL; /* prime must be odd */ + if ((err = mp_kronecker(n, prime, &legendre)) != MP_OKAY) return err; + if (legendre == -1) return MP_VAL; /* quadratic non-residue mod prime */ + + if ((err = mp_init_multi(&t1, &C, &Q, &S, &Z, &M, &T, &R, &two, NULL)) != MP_OKAY) { + return err; + } + + /* SPECIAL CASE: if prime mod 4 == 3 + * compute directly: err = n^(prime+1)/4 mod prime + * Handbook of Applied Cryptography algorithm 3.36 + */ + if ((err = mp_mod_d(prime, 4uL, &i)) != MP_OKAY) goto cleanup; + if (i == 3u) { + if ((err = mp_add_d(prime, 1uL, &t1)) != MP_OKAY) goto cleanup; + if ((err = mp_div_2(&t1, &t1)) != MP_OKAY) goto cleanup; + if ((err = mp_div_2(&t1, &t1)) != MP_OKAY) goto cleanup; + if ((err = mp_exptmod(n, &t1, prime, ret)) != MP_OKAY) goto cleanup; + err = MP_OKAY; + goto cleanup; + } + + /* NOW: Tonelli-Shanks algorithm */ + + /* factor out powers of 2 from prime-1, defining Q and S as: prime-1 = Q*2^S */ + if ((err = mp_copy(prime, &Q)) != MP_OKAY) goto cleanup; + if ((err = mp_sub_d(&Q, 1uL, &Q)) != MP_OKAY) goto cleanup; + /* Q = prime - 1 */ + mp_zero(&S); + /* S = 0 */ + while (MP_IS_EVEN(&Q)) { + if ((err = mp_div_2(&Q, &Q)) != MP_OKAY) goto cleanup; + /* Q = Q / 2 */ + if ((err = mp_add_d(&S, 1uL, &S)) != MP_OKAY) goto cleanup; + /* S = S + 1 */ + } + + /* find a Z such that the Legendre symbol (Z|prime) == -1 */ + mp_set_u32(&Z, 2u); + /* Z = 2 */ + for (;;) { + if ((err = mp_kronecker(&Z, prime, &legendre)) != MP_OKAY) goto cleanup; + if (legendre == -1) break; + if ((err = mp_add_d(&Z, 1uL, &Z)) != MP_OKAY) goto cleanup; + /* Z = Z + 1 */ + } + + if ((err = mp_exptmod(&Z, &Q, prime, &C)) != MP_OKAY) goto cleanup; + /* C = Z ^ Q mod prime */ + if ((err = mp_add_d(&Q, 1uL, &t1)) != MP_OKAY) goto cleanup; + if ((err = mp_div_2(&t1, &t1)) != MP_OKAY) goto cleanup; + /* t1 = (Q + 1) / 2 */ + if ((err = mp_exptmod(n, &t1, prime, &R)) != MP_OKAY) goto cleanup; + /* R = n ^ ((Q + 1) / 2) mod prime */ + if ((err = mp_exptmod(n, &Q, prime, &T)) != MP_OKAY) goto cleanup; + /* T = n ^ Q mod prime */ + if ((err = mp_copy(&S, &M)) != MP_OKAY) goto cleanup; + /* M = S */ + mp_set_u32(&two, 2u); + + for (;;) { + if ((err = mp_copy(&T, &t1)) != MP_OKAY) goto cleanup; + i = 0; + for (;;) { + if (mp_cmp_d(&t1, 1uL) == MP_EQ) break; + if ((err = mp_exptmod(&t1, &two, prime, &t1)) != MP_OKAY) goto cleanup; + i++; + } + if (i == 0u) { + if ((err = mp_copy(&R, ret)) != MP_OKAY) goto cleanup; + err = MP_OKAY; + goto cleanup; + } + if ((err = mp_sub_d(&M, i, &t1)) != MP_OKAY) goto cleanup; + if ((err = mp_sub_d(&t1, 1uL, &t1)) != MP_OKAY) goto cleanup; + if ((err = mp_exptmod(&two, &t1, prime, &t1)) != MP_OKAY) goto cleanup; + /* t1 = 2 ^ (M - i - 1) */ + if ((err = mp_exptmod(&C, &t1, prime, &t1)) != MP_OKAY) goto cleanup; + /* t1 = C ^ (2 ^ (M - i - 1)) mod prime */ + if ((err = mp_sqrmod(&t1, prime, &C)) != MP_OKAY) goto cleanup; + /* C = (t1 * t1) mod prime */ + if ((err = mp_mulmod(&R, &t1, prime, &R)) != MP_OKAY) goto cleanup; + /* R = (R * t1) mod prime */ + if ((err = mp_mulmod(&T, &C, prime, &T)) != MP_OKAY) goto cleanup; + /* T = (T * C) mod prime */ + mp_set(&M, i); + /* M = i */ + } + +cleanup: + mp_clear_multi(&t1, &C, &Q, &S, &Z, &M, &T, &R, &two, NULL); + return err; +} + +#endif diff --git a/lib/hcrypto/libtommath/bn_mp_sub.c b/lib/hcrypto/libtommath/bn_mp_sub.c index f5015cce45e9..c1ea39e1144c 100644 --- a/lib/hcrypto/libtommath/bn_mp_sub.c +++ b/lib/hcrypto/libtommath/bn_mp_sub.c @@ -1,59 +1,40 @@ -#include <tommath.h> +#include "tommath_private.h" #ifdef BN_MP_SUB_C -/* LibTomMath, multiple-precision integer library -- Tom St Denis - * - * LibTomMath is a library that provides multiple-precision - * integer arithmetic as well as number theoretic functionality. - * - * The library was designed directly after the MPI library by - * Michael Fromberger but has been written from scratch with - * additional optimizations in place. - * - * The library is free for all purposes without any express - * guarantee it works. - * - * Tom St Denis, tomstdenis@gmail.com, http://libtom.org - */ +/* LibTomMath, multiple-precision integer library -- Tom St Denis */ +/* SPDX-License-Identifier: Unlicense */ /* high level subtraction (handles signs) */ -int -mp_sub (mp_int * a, mp_int * b, mp_int * c) +mp_err mp_sub(const mp_int *a, const mp_int *b, mp_int *c) { - int sa, sb, res; + mp_sign sa = a->sign, sb = b->sign; + mp_err err; - sa = a->sign; - sb = b->sign; - - if (sa != sb) { - /* subtract a negative from a positive, OR */ - /* subtract a positive from a negative. */ - /* In either case, ADD their magnitudes, */ - /* and use the sign of the first number. */ - c->sign = sa; - res = s_mp_add (a, b, c); - } else { - /* subtract a positive from a positive, OR */ - /* subtract a negative from a negative. */ - /* First, take the difference between their */ - /* magnitudes, then... */ - if (mp_cmp_mag (a, b) != MP_LT) { - /* Copy the sign from the first */ + if (sa != sb) { + /* subtract a negative from a positive, OR */ + /* subtract a positive from a negative. */ + /* In either case, ADD their magnitudes, */ + /* and use the sign of the first number. */ c->sign = sa; - /* The first has a larger or equal magnitude */ - res = s_mp_sub (a, b, c); - } else { - /* The result has the *opposite* sign from */ - /* the first number. */ - c->sign = (sa == MP_ZPOS) ? MP_NEG : MP_ZPOS; - /* The second has a larger magnitude */ - res = s_mp_sub (b, a, c); - } - } - return res; + err = s_mp_add(a, b, c); + } else { + /* subtract a positive from a positive, OR */ + /* subtract a negative from a negative. */ + /* First, take the difference between their */ + /* magnitudes, then... */ + if (mp_cmp_mag(a, b) != MP_LT) { + /* Copy the sign from the first */ + c->sign = sa; + /* The first has a larger or equal magnitude */ + err = s_mp_sub(a, b, c); + } else { + /* The result has the *opposite* sign from */ + /* the first number. */ + c->sign = (sa == MP_ZPOS) ? MP_NEG : MP_ZPOS; + /* The second has a larger magnitude */ + err = s_mp_sub(b, a, c); + } + } + return err; } #endif - -/* $Source: /cvs/libtom/libtommath/bn_mp_sub.c,v $ */ -/* $Revision: 1.4 $ */ -/* $Date: 2006/12/28 01:25:13 $ */ diff --git a/lib/hcrypto/libtommath/bn_mp_sub_d.c b/lib/hcrypto/libtommath/bn_mp_sub_d.c index 06cdca636d93..3ebf9b48520e 100644 --- a/lib/hcrypto/libtommath/bn_mp_sub_d.c +++ b/lib/hcrypto/libtommath/bn_mp_sub_d.c @@ -1,93 +1,74 @@ -#include <tommath.h> +#include "tommath_private.h" #ifdef BN_MP_SUB_D_C -/* LibTomMath, multiple-precision integer library -- Tom St Denis - * - * LibTomMath is a library that provides multiple-precision - * integer arithmetic as well as number theoretic functionality. - * - * The library was designed directly after the MPI library by - * Michael Fromberger but has been written from scratch with - * additional optimizations in place. - * - * The library is free for all purposes without any express - * guarantee it works. - * - * Tom St Denis, tomstdenis@gmail.com, http://libtom.org - */ +/* LibTomMath, multiple-precision integer library -- Tom St Denis */ +/* SPDX-License-Identifier: Unlicense */ /* single digit subtraction */ -int -mp_sub_d (mp_int * a, mp_digit b, mp_int * c) +mp_err mp_sub_d(const mp_int *a, mp_digit b, mp_int *c) { - mp_digit *tmpa, *tmpc, mu; - int res, ix, oldused; + mp_digit *tmpa, *tmpc; + mp_err err; + int ix, oldused; - /* grow c as required */ - if (c->alloc < a->used + 1) { - if ((res = mp_grow(c, a->used + 1)) != MP_OKAY) { - return res; - } - } + /* grow c as required */ + if (c->alloc < (a->used + 1)) { + if ((err = mp_grow(c, a->used + 1)) != MP_OKAY) { + return err; + } + } - /* if a is negative just do an unsigned - * addition [with fudged signs] - */ - if (a->sign == MP_NEG) { - a->sign = MP_ZPOS; - res = mp_add_d(a, b, c); - a->sign = c->sign = MP_NEG; + /* if a is negative just do an unsigned + * addition [with fudged signs] + */ + if (a->sign == MP_NEG) { + mp_int a_ = *a; + a_.sign = MP_ZPOS; + err = mp_add_d(&a_, b, c); + c->sign = MP_NEG; - /* clamp */ - mp_clamp(c); + /* clamp */ + mp_clamp(c); - return res; - } + return err; + } - /* setup regs */ - oldused = c->used; - tmpa = a->dp; - tmpc = c->dp; + /* setup regs */ + oldused = c->used; + tmpa = a->dp; + tmpc = c->dp; - /* if a <= b simply fix the single digit */ - if ((a->used == 1 && a->dp[0] <= b) || a->used == 0) { - if (a->used == 1) { - *tmpc++ = b - *tmpa; - } else { - *tmpc++ = b; - } - ix = 1; + /* if a <= b simply fix the single digit */ + if (((a->used == 1) && (a->dp[0] <= b)) || (a->used == 0)) { + if (a->used == 1) { + *tmpc++ = b - *tmpa; + } else { + *tmpc++ = b; + } + ix = 1; - /* negative/1digit */ - c->sign = MP_NEG; - c->used = 1; - } else { - /* positive/size */ - c->sign = MP_ZPOS; - c->used = a->used; + /* negative/1digit */ + c->sign = MP_NEG; + c->used = 1; + } else { + mp_digit mu = b; - /* subtract first digit */ - *tmpc = *tmpa++ - b; - mu = *tmpc >> (sizeof(mp_digit) * CHAR_BIT - 1); - *tmpc++ &= MP_MASK; + /* positive/size */ + c->sign = MP_ZPOS; + c->used = a->used; - /* handle rest of the digits */ - for (ix = 1; ix < a->used; ix++) { - *tmpc = *tmpa++ - mu; - mu = *tmpc >> (sizeof(mp_digit) * CHAR_BIT - 1); - *tmpc++ &= MP_MASK; - } - } + /* subtract digits, mu is carry */ + for (ix = 0; ix < a->used; ix++) { + *tmpc = *tmpa++ - mu; + mu = *tmpc >> (MP_SIZEOF_BITS(mp_digit) - 1u); + *tmpc++ &= MP_MASK; + } + } - /* zero excess digits */ - while (ix++ < oldused) { - *tmpc++ = 0; - } - mp_clamp(c); - return MP_OKAY; + /* zero excess digits */ + MP_ZERO_DIGITS(tmpc, oldused - ix); + + mp_clamp(c); + return MP_OKAY; } #endif - -/* $Source: /cvs/libtom/libtommath/bn_mp_sub_d.c,v $ */ -/* $Revision: 1.6 $ */ -/* $Date: 2006/12/28 01:25:13 $ */ diff --git a/lib/hcrypto/libtommath/bn_mp_submod.c b/lib/hcrypto/libtommath/bn_mp_submod.c index 869e23cded54..5ebd374986ad 100644 --- a/lib/hcrypto/libtommath/bn_mp_submod.c +++ b/lib/hcrypto/libtommath/bn_mp_submod.c @@ -1,42 +1,25 @@ -#include <tommath.h> +#include "tommath_private.h" #ifdef BN_MP_SUBMOD_C -/* LibTomMath, multiple-precision integer library -- Tom St Denis - * - * LibTomMath is a library that provides multiple-precision - * integer arithmetic as well as number theoretic functionality. - * - * The library was designed directly after the MPI library by - * Michael Fromberger but has been written from scratch with - * additional optimizations in place. - * - * The library is free for all purposes without any express - * guarantee it works. - * - * Tom St Denis, tomstdenis@gmail.com, http://libtom.org - */ +/* LibTomMath, multiple-precision integer library -- Tom St Denis */ +/* SPDX-License-Identifier: Unlicense */ /* d = a - b (mod c) */ -int -mp_submod (mp_int * a, mp_int * b, mp_int * c, mp_int * d) +mp_err mp_submod(const mp_int *a, const mp_int *b, const mp_int *c, mp_int *d) { - int res; - mp_int t; + mp_err err; + mp_int t; + if ((err = mp_init(&t)) != MP_OKAY) { + return err; + } - if ((res = mp_init (&t)) != MP_OKAY) { - return res; - } + if ((err = mp_sub(a, b, &t)) != MP_OKAY) { + goto LBL_ERR; + } + err = mp_mod(&t, c, d); - if ((res = mp_sub (a, b, &t)) != MP_OKAY) { - mp_clear (&t); - return res; - } - res = mp_mod (&t, c, d); - mp_clear (&t); - return res; +LBL_ERR: + mp_clear(&t); + return err; } #endif - -/* $Source: /cvs/libtom/libtommath/bn_mp_submod.c,v $ */ -/* $Revision: 1.4 $ */ -/* $Date: 2006/12/28 01:25:13 $ */ diff --git a/lib/hcrypto/libtommath/bn_mp_to_radix.c b/lib/hcrypto/libtommath/bn_mp_to_radix.c new file mode 100644 index 000000000000..7fa86cae1dab --- /dev/null +++ b/lib/hcrypto/libtommath/bn_mp_to_radix.c @@ -0,0 +1,84 @@ +#include "tommath_private.h" +#ifdef BN_MP_TO_RADIX_C +/* LibTomMath, multiple-precision integer library -- Tom St Denis */ +/* SPDX-License-Identifier: Unlicense */ + +/* stores a bignum as a ASCII string in a given radix (2..64) + * + * Stores upto "size - 1" chars and always a NULL byte, puts the number of characters + * written, including the '\0', in "written". + */ +mp_err mp_to_radix(const mp_int *a, char *str, size_t maxlen, size_t *written, int radix) +{ + size_t digs; + mp_err err; + mp_int t; + mp_digit d; + char *_s = str; + + /* check range of radix and size*/ + if (maxlen < 2u) { + return MP_BUF; + } + if ((radix < 2) || (radix > 64)) { + return MP_VAL; + } + + /* quick out if its zero */ + if (MP_IS_ZERO(a)) { + *str++ = '0'; + *str = '\0'; + if (written != NULL) { + *written = 2u; + } + return MP_OKAY; + } + + if ((err = mp_init_copy(&t, a)) != MP_OKAY) { + return err; + } + + /* if it is negative output a - */ + if (t.sign == MP_NEG) { + /* we have to reverse our digits later... but not the - sign!! */ + ++_s; + + /* store the flag and mark the number as positive */ + *str++ = '-'; + t.sign = MP_ZPOS; + + /* subtract a char */ + --maxlen; + } + digs = 0u; + while (!MP_IS_ZERO(&t)) { + if (--maxlen < 1u) { + /* no more room */ + err = MP_BUF; + goto LBL_ERR; + } + if ((err = mp_div_d(&t, (mp_digit)radix, &t, &d)) != MP_OKAY) { + goto LBL_ERR; + } + *str++ = mp_s_rmap[d]; + ++digs; + } + /* reverse the digits of the string. In this case _s points + * to the first digit [exluding the sign] of the number + */ + s_mp_reverse((unsigned char *)_s, digs); + + /* append a NULL so the string is properly terminated */ + *str = '\0'; + digs++; + + if (written != NULL) { + *written = (a->sign == MP_NEG) ? (digs + 1u): digs; + } + +LBL_ERR: + mp_clear(&t); + return err; +} + +#endif diff --git a/lib/hcrypto/libtommath/bn_mp_to_sbin.c b/lib/hcrypto/libtommath/bn_mp_to_sbin.c new file mode 100644 index 000000000000..dbaf53e1f987 --- /dev/null +++ b/lib/hcrypto/libtommath/bn_mp_to_sbin.c @@ -0,0 +1,22 @@ +#include "tommath_private.h" +#ifdef BN_MP_TO_SBIN_C +/* LibTomMath, multiple-precision integer library -- Tom St Denis */ +/* SPDX-License-Identifier: Unlicense */ + +/* store in signed [big endian] format */ +mp_err mp_to_sbin(const mp_int *a, unsigned char *buf, size_t maxlen, size_t *written) +{ + mp_err err; + if (maxlen == 0u) { + return MP_BUF; + } + if ((err = mp_to_ubin(a, buf + 1, maxlen - 1u, written)) != MP_OKAY) { + return err; + } + if (written != NULL) { + (*written)++; + } + buf[0] = (a->sign == MP_ZPOS) ? (unsigned char)0 : (unsigned char)1; + return MP_OKAY; +} +#endif diff --git a/lib/hcrypto/libtommath/bn_mp_to_signed_bin.c b/lib/hcrypto/libtommath/bn_mp_to_signed_bin.c deleted file mode 100644 index 9df83ca52666..000000000000 --- a/lib/hcrypto/libtommath/bn_mp_to_signed_bin.c +++ /dev/null @@ -1,33 +0,0 @@ -#include <tommath.h> -#ifdef BN_MP_TO_SIGNED_BIN_C -/* LibTomMath, multiple-precision integer library -- Tom St Denis - * - * LibTomMath is a library that provides multiple-precision - * integer arithmetic as well as number theoretic functionality. - * - * The library was designed directly after the MPI library by - * Michael Fromberger but has been written from scratch with - * additional optimizations in place. - * - * The library is free for all purposes without any express - * guarantee it works. - * - * Tom St Denis, tomstdenis@gmail.com, http://libtom.org - */ - -/* store in signed [big endian] format */ -int mp_to_signed_bin (mp_int * a, unsigned char *b) -{ - int res; - - if ((res = mp_to_unsigned_bin (a, b + 1)) != MP_OKAY) { - return res; - } - b[0] = (unsigned char) ((a->sign == MP_ZPOS) ? 0 : 1); - return MP_OKAY; -} -#endif - -/* $Source: /cvs/libtom/libtommath/bn_mp_to_signed_bin.c,v $ */ -/* $Revision: 1.4 $ */ -/* $Date: 2006/12/28 01:25:13 $ */ diff --git a/lib/hcrypto/libtommath/bn_mp_to_signed_bin_n.c b/lib/hcrypto/libtommath/bn_mp_to_signed_bin_n.c deleted file mode 100644 index 677f827d4f40..000000000000 --- a/lib/hcrypto/libtommath/bn_mp_to_signed_bin_n.c +++ /dev/null @@ -1,31 +0,0 @@ -#include <tommath.h> -#ifdef BN_MP_TO_SIGNED_BIN_N_C -/* LibTomMath, multiple-precision integer library -- Tom St Denis - * - * LibTomMath is a library that provides multiple-precision - * integer arithmetic as well as number theoretic functionality. - * - * The library was designed directly after the MPI library by - * Michael Fromberger but has been written from scratch with - * additional optimizations in place. - * - * The library is free for all purposes without any express - * guarantee it works. - * - * Tom St Denis, tomstdenis@gmail.com, http://libtom.org - */ - -/* store in signed [big endian] format */ -int mp_to_signed_bin_n (mp_int * a, unsigned char *b, unsigned long *outlen) -{ - if (*outlen < (unsigned long)mp_signed_bin_size(a)) { - return MP_VAL; - } - *outlen = mp_signed_bin_size(a); - return mp_to_signed_bin(a, b); -} -#endif - -/* $Source: /cvs/libtom/libtommath/bn_mp_to_signed_bin_n.c,v $ */ -/* $Revision: 1.4 $ */ -/* $Date: 2006/12/28 01:25:13 $ */ diff --git a/lib/hcrypto/libtommath/bn_mp_to_ubin.c b/lib/hcrypto/libtommath/bn_mp_to_ubin.c new file mode 100644 index 000000000000..1681ca7ce9a9 --- /dev/null +++ b/lib/hcrypto/libtommath/bn_mp_to_ubin.c @@ -0,0 +1,41 @@ +#include "tommath_private.h" +#ifdef BN_MP_TO_UBIN_C +/* LibTomMath, multiple-precision integer library -- Tom St Denis */ +/* SPDX-License-Identifier: Unlicense */ + +/* store in unsigned [big endian] format */ +mp_err mp_to_ubin(const mp_int *a, unsigned char *buf, size_t maxlen, size_t *written) +{ + size_t x, count; + mp_err err; + mp_int t; + + count = mp_ubin_size(a); + if (count > maxlen) { + return MP_BUF; + } + + if ((err = mp_init_copy(&t, a)) != MP_OKAY) { + return err; + } + + for (x = count; x --> 0u;) { +#ifndef MP_8BIT + buf[x] = (unsigned char)(t.dp[0] & 255u); +#else + buf[x] = (unsigned char)(t.dp[0] | ((t.dp[1] & 1u) << 7)); +#endif + if ((err = mp_div_2d(&t, 8, &t, NULL)) != MP_OKAY) { + goto LBL_ERR; + } + } + + if (written != NULL) { + *written = count; + } + +LBL_ERR: + mp_clear(&t); + return err; +} +#endif diff --git a/lib/hcrypto/libtommath/bn_mp_to_unsigned_bin.c b/lib/hcrypto/libtommath/bn_mp_to_unsigned_bin.c deleted file mode 100644 index c137f104ac79..000000000000 --- a/lib/hcrypto/libtommath/bn_mp_to_unsigned_bin.c +++ /dev/null @@ -1,48 +0,0 @@ -#include <tommath.h> -#ifdef BN_MP_TO_UNSIGNED_BIN_C -/* LibTomMath, multiple-precision integer library -- Tom St Denis - * - * LibTomMath is a library that provides multiple-precision - * integer arithmetic as well as number theoretic functionality. - * - * The library was designed directly after the MPI library by - * Michael Fromberger but has been written from scratch with - * additional optimizations in place. - * - * The library is free for all purposes without any express - * guarantee it works. - * - * Tom St Denis, tomstdenis@gmail.com, http://libtom.org - */ - -/* store in unsigned [big endian] format */ -int mp_to_unsigned_bin (mp_int * a, unsigned char *b) -{ - int x, res; - mp_int t; - - if ((res = mp_init_copy (&t, a)) != MP_OKAY) { - return res; - } - - x = 0; - while (mp_iszero (&t) == 0) { -#ifndef MP_8BIT - b[x++] = (unsigned char) (t.dp[0] & 255); -#else - b[x++] = (unsigned char) (t.dp[0] | ((t.dp[1] & 0x01) << 7)); -#endif - if ((res = mp_div_2d (&t, 8, &t, NULL)) != MP_OKAY) { - mp_clear (&t); - return res; - } - } - bn_reverse (b, x); - mp_clear (&t); - return MP_OKAY; -} -#endif - -/* $Source: /cvs/libtom/libtommath/bn_mp_to_unsigned_bin.c,v $ */ -/* $Revision: 1.4 $ */ -/* $Date: 2006/12/28 01:25:13 $ */ diff --git a/lib/hcrypto/libtommath/bn_mp_to_unsigned_bin_n.c b/lib/hcrypto/libtommath/bn_mp_to_unsigned_bin_n.c deleted file mode 100644 index 0dc00c623d31..000000000000 --- a/lib/hcrypto/libtommath/bn_mp_to_unsigned_bin_n.c +++ /dev/null @@ -1,31 +0,0 @@ -#include <tommath.h> -#ifdef BN_MP_TO_UNSIGNED_BIN_N_C -/* LibTomMath, multiple-precision integer library -- Tom St Denis - * - * LibTomMath is a library that provides multiple-precision - * integer arithmetic as well as number theoretic functionality. - * - * The library was designed directly after the MPI library by - * Michael Fromberger but has been written from scratch with - * additional optimizations in place. - * - * The library is free for all purposes without any express - * guarantee it works. - * - * Tom St Denis, tomstdenis@gmail.com, http://libtom.org - */ - -/* store in unsigned [big endian] format */ -int mp_to_unsigned_bin_n (mp_int * a, unsigned char *b, unsigned long *outlen) -{ - if (*outlen < (unsigned long)mp_unsigned_bin_size(a)) { - return MP_VAL; - } - *outlen = mp_unsigned_bin_size(a); - return mp_to_unsigned_bin(a, b); -} -#endif - -/* $Source: /cvs/libtom/libtommath/bn_mp_to_unsigned_bin_n.c,v $ */ -/* $Revision: 1.4 $ */ -/* $Date: 2006/12/28 01:25:13 $ */ diff --git a/lib/hcrypto/libtommath/bn_mp_toom_mul.c b/lib/hcrypto/libtommath/bn_mp_toom_mul.c deleted file mode 100644 index b996342466c2..000000000000 --- a/lib/hcrypto/libtommath/bn_mp_toom_mul.c +++ /dev/null @@ -1,284 +0,0 @@ -#include <tommath.h> -#ifdef BN_MP_TOOM_MUL_C -/* LibTomMath, multiple-precision integer library -- Tom St Denis - * - * LibTomMath is a library that provides multiple-precision - * integer arithmetic as well as number theoretic functionality. - * - * The library was designed directly after the MPI library by - * Michael Fromberger but has been written from scratch with - * additional optimizations in place. - * - * The library is free for all purposes without any express - * guarantee it works. - * - * Tom St Denis, tomstdenis@gmail.com, http://libtom.org - */ - -/* multiplication using the Toom-Cook 3-way algorithm - * - * Much more complicated than Karatsuba but has a lower - * asymptotic running time of O(N**1.464). This algorithm is - * only particularly useful on VERY large inputs - * (we're talking 1000s of digits here...). -*/ -int mp_toom_mul(mp_int *a, mp_int *b, mp_int *c) -{ - mp_int w0, w1, w2, w3, w4, tmp1, tmp2, a0, a1, a2, b0, b1, b2; - int res, B; - - /* init temps */ - if ((res = mp_init_multi(&w0, &w1, &w2, &w3, &w4, - &a0, &a1, &a2, &b0, &b1, - &b2, &tmp1, &tmp2, NULL)) != MP_OKAY) { - return res; - } - - /* B */ - B = MIN(a->used, b->used) / 3; - - /* a = a2 * B**2 + a1 * B + a0 */ - if ((res = mp_mod_2d(a, DIGIT_BIT * B, &a0)) != MP_OKAY) { - goto ERR; - } - - if ((res = mp_copy(a, &a1)) != MP_OKAY) { - goto ERR; - } - mp_rshd(&a1, B); - mp_mod_2d(&a1, DIGIT_BIT * B, &a1); - - if ((res = mp_copy(a, &a2)) != MP_OKAY) { - goto ERR; - } - mp_rshd(&a2, B*2); - - /* b = b2 * B**2 + b1 * B + b0 */ - if ((res = mp_mod_2d(b, DIGIT_BIT * B, &b0)) != MP_OKAY) { - goto ERR; - } - - if ((res = mp_copy(b, &b1)) != MP_OKAY) { - goto ERR; - } - mp_rshd(&b1, B); - mp_mod_2d(&b1, DIGIT_BIT * B, &b1); - - if ((res = mp_copy(b, &b2)) != MP_OKAY) { - goto ERR; - } - mp_rshd(&b2, B*2); - - /* w0 = a0*b0 */ - if ((res = mp_mul(&a0, &b0, &w0)) != MP_OKAY) { - goto ERR; - } - - /* w4 = a2 * b2 */ - if ((res = mp_mul(&a2, &b2, &w4)) != MP_OKAY) { - goto ERR; - } - - /* w1 = (a2 + 2(a1 + 2a0))(b2 + 2(b1 + 2b0)) */ - if ((res = mp_mul_2(&a0, &tmp1)) != MP_OKAY) { - goto ERR; - } - if ((res = mp_add(&tmp1, &a1, &tmp1)) != MP_OKAY) { - goto ERR; - } - if ((res = mp_mul_2(&tmp1, &tmp1)) != MP_OKAY) { - goto ERR; - } - if ((res = mp_add(&tmp1, &a2, &tmp1)) != MP_OKAY) { - goto ERR; - } - - if ((res = mp_mul_2(&b0, &tmp2)) != MP_OKAY) { - goto ERR; - } - if ((res = mp_add(&tmp2, &b1, &tmp2)) != MP_OKAY) { - goto ERR; - } - if ((res = mp_mul_2(&tmp2, &tmp2)) != MP_OKAY) { - goto ERR; - } - if ((res = mp_add(&tmp2, &b2, &tmp2)) != MP_OKAY) { - goto ERR; - } - - if ((res = mp_mul(&tmp1, &tmp2, &w1)) != MP_OKAY) { - goto ERR; - } - - /* w3 = (a0 + 2(a1 + 2a2))(b0 + 2(b1 + 2b2)) */ - if ((res = mp_mul_2(&a2, &tmp1)) != MP_OKAY) { - goto ERR; - } - if ((res = mp_add(&tmp1, &a1, &tmp1)) != MP_OKAY) { - goto ERR; - } - if ((res = mp_mul_2(&tmp1, &tmp1)) != MP_OKAY) { - goto ERR; - } - if ((res = mp_add(&tmp1, &a0, &tmp1)) != MP_OKAY) { - goto ERR; - } - - if ((res = mp_mul_2(&b2, &tmp2)) != MP_OKAY) { - goto ERR; - } - if ((res = mp_add(&tmp2, &b1, &tmp2)) != MP_OKAY) { - goto ERR; - } - if ((res = mp_mul_2(&tmp2, &tmp2)) != MP_OKAY) { - goto ERR; - } - if ((res = mp_add(&tmp2, &b0, &tmp2)) != MP_OKAY) { - goto ERR; - } - - if ((res = mp_mul(&tmp1, &tmp2, &w3)) != MP_OKAY) { - goto ERR; - } - - - /* w2 = (a2 + a1 + a0)(b2 + b1 + b0) */ - if ((res = mp_add(&a2, &a1, &tmp1)) != MP_OKAY) { - goto ERR; - } - if ((res = mp_add(&tmp1, &a0, &tmp1)) != MP_OKAY) { - goto ERR; - } - if ((res = mp_add(&b2, &b1, &tmp2)) != MP_OKAY) { - goto ERR; - } - if ((res = mp_add(&tmp2, &b0, &tmp2)) != MP_OKAY) { - goto ERR; - } - if ((res = mp_mul(&tmp1, &tmp2, &w2)) != MP_OKAY) { - goto ERR; - } - - /* now solve the matrix - - 0 0 0 0 1 - 1 2 4 8 16 - 1 1 1 1 1 - 16 8 4 2 1 - 1 0 0 0 0 - - using 12 subtractions, 4 shifts, - 2 small divisions and 1 small multiplication - */ - - /* r1 - r4 */ - if ((res = mp_sub(&w1, &w4, &w1)) != MP_OKAY) { - goto ERR; - } - /* r3 - r0 */ - if ((res = mp_sub(&w3, &w0, &w3)) != MP_OKAY) { - goto ERR; - } - /* r1/2 */ - if ((res = mp_div_2(&w1, &w1)) != MP_OKAY) { - goto ERR; - } - /* r3/2 */ - if ((res = mp_div_2(&w3, &w3)) != MP_OKAY) { - goto ERR; - } - /* r2 - r0 - r4 */ - if ((res = mp_sub(&w2, &w0, &w2)) != MP_OKAY) { - goto ERR; - } - if ((res = mp_sub(&w2, &w4, &w2)) != MP_OKAY) { - goto ERR; - } - /* r1 - r2 */ - if ((res = mp_sub(&w1, &w2, &w1)) != MP_OKAY) { - goto ERR; - } - /* r3 - r2 */ - if ((res = mp_sub(&w3, &w2, &w3)) != MP_OKAY) { - goto ERR; - } - /* r1 - 8r0 */ - if ((res = mp_mul_2d(&w0, 3, &tmp1)) != MP_OKAY) { - goto ERR; - } - if ((res = mp_sub(&w1, &tmp1, &w1)) != MP_OKAY) { - goto ERR; - } - /* r3 - 8r4 */ - if ((res = mp_mul_2d(&w4, 3, &tmp1)) != MP_OKAY) { - goto ERR; - } - if ((res = mp_sub(&w3, &tmp1, &w3)) != MP_OKAY) { - goto ERR; - } - /* 3r2 - r1 - r3 */ - if ((res = mp_mul_d(&w2, 3, &w2)) != MP_OKAY) { - goto ERR; - } - if ((res = mp_sub(&w2, &w1, &w2)) != MP_OKAY) { - goto ERR; - } - if ((res = mp_sub(&w2, &w3, &w2)) != MP_OKAY) { - goto ERR; - } - /* r1 - r2 */ - if ((res = mp_sub(&w1, &w2, &w1)) != MP_OKAY) { - goto ERR; - } - /* r3 - r2 */ - if ((res = mp_sub(&w3, &w2, &w3)) != MP_OKAY) { - goto ERR; - } - /* r1/3 */ - if ((res = mp_div_3(&w1, &w1, NULL)) != MP_OKAY) { - goto ERR; - } - /* r3/3 */ - if ((res = mp_div_3(&w3, &w3, NULL)) != MP_OKAY) { - goto ERR; - } - - /* at this point shift W[n] by B*n */ - if ((res = mp_lshd(&w1, 1*B)) != MP_OKAY) { - goto ERR; - } - if ((res = mp_lshd(&w2, 2*B)) != MP_OKAY) { - goto ERR; - } - if ((res = mp_lshd(&w3, 3*B)) != MP_OKAY) { - goto ERR; - } - if ((res = mp_lshd(&w4, 4*B)) != MP_OKAY) { - goto ERR; - } - - if ((res = mp_add(&w0, &w1, c)) != MP_OKAY) { - goto ERR; - } - if ((res = mp_add(&w2, &w3, &tmp1)) != MP_OKAY) { - goto ERR; - } - if ((res = mp_add(&w4, &tmp1, &tmp1)) != MP_OKAY) { - goto ERR; - } - if ((res = mp_add(&tmp1, c, c)) != MP_OKAY) { - goto ERR; - } - -ERR: - mp_clear_multi(&w0, &w1, &w2, &w3, &w4, - &a0, &a1, &a2, &b0, &b1, - &b2, &tmp1, &tmp2, NULL); - return res; -} - -#endif - -/* $Source: /cvs/libtom/libtommath/bn_mp_toom_mul.c,v $ */ -/* $Revision: 1.4 $ */ -/* $Date: 2006/12/28 01:25:13 $ */ diff --git a/lib/hcrypto/libtommath/bn_mp_toom_sqr.c b/lib/hcrypto/libtommath/bn_mp_toom_sqr.c deleted file mode 100644 index 48880d0350c1..000000000000 --- a/lib/hcrypto/libtommath/bn_mp_toom_sqr.c +++ /dev/null @@ -1,226 +0,0 @@ -#include <tommath.h> -#ifdef BN_MP_TOOM_SQR_C -/* LibTomMath, multiple-precision integer library -- Tom St Denis - * - * LibTomMath is a library that provides multiple-precision - * integer arithmetic as well as number theoretic functionality. - * - * The library was designed directly after the MPI library by - * Michael Fromberger but has been written from scratch with - * additional optimizations in place. - * - * The library is free for all purposes without any express - * guarantee it works. - * - * Tom St Denis, tomstdenis@gmail.com, http://libtom.org - */ - -/* squaring using Toom-Cook 3-way algorithm */ -int -mp_toom_sqr(mp_int *a, mp_int *b) -{ - mp_int w0, w1, w2, w3, w4, tmp1, a0, a1, a2; - int res, B; - - /* init temps */ - if ((res = mp_init_multi(&w0, &w1, &w2, &w3, &w4, &a0, &a1, &a2, &tmp1, NULL)) != MP_OKAY) { - return res; - } - - /* B */ - B = a->used / 3; - - /* a = a2 * B**2 + a1 * B + a0 */ - if ((res = mp_mod_2d(a, DIGIT_BIT * B, &a0)) != MP_OKAY) { - goto ERR; - } - - if ((res = mp_copy(a, &a1)) != MP_OKAY) { - goto ERR; - } - mp_rshd(&a1, B); - mp_mod_2d(&a1, DIGIT_BIT * B, &a1); - - if ((res = mp_copy(a, &a2)) != MP_OKAY) { - goto ERR; - } - mp_rshd(&a2, B*2); - - /* w0 = a0*a0 */ - if ((res = mp_sqr(&a0, &w0)) != MP_OKAY) { - goto ERR; - } - - /* w4 = a2 * a2 */ - if ((res = mp_sqr(&a2, &w4)) != MP_OKAY) { - goto ERR; - } - - /* w1 = (a2 + 2(a1 + 2a0))**2 */ - if ((res = mp_mul_2(&a0, &tmp1)) != MP_OKAY) { - goto ERR; - } - if ((res = mp_add(&tmp1, &a1, &tmp1)) != MP_OKAY) { - goto ERR; - } - if ((res = mp_mul_2(&tmp1, &tmp1)) != MP_OKAY) { - goto ERR; - } - if ((res = mp_add(&tmp1, &a2, &tmp1)) != MP_OKAY) { - goto ERR; - } - - if ((res = mp_sqr(&tmp1, &w1)) != MP_OKAY) { - goto ERR; - } - - /* w3 = (a0 + 2(a1 + 2a2))**2 */ - if ((res = mp_mul_2(&a2, &tmp1)) != MP_OKAY) { - goto ERR; - } - if ((res = mp_add(&tmp1, &a1, &tmp1)) != MP_OKAY) { - goto ERR; - } - if ((res = mp_mul_2(&tmp1, &tmp1)) != MP_OKAY) { - goto ERR; - } - if ((res = mp_add(&tmp1, &a0, &tmp1)) != MP_OKAY) { - goto ERR; - } - - if ((res = mp_sqr(&tmp1, &w3)) != MP_OKAY) { - goto ERR; - } - - - /* w2 = (a2 + a1 + a0)**2 */ - if ((res = mp_add(&a2, &a1, &tmp1)) != MP_OKAY) { - goto ERR; - } - if ((res = mp_add(&tmp1, &a0, &tmp1)) != MP_OKAY) { - goto ERR; - } - if ((res = mp_sqr(&tmp1, &w2)) != MP_OKAY) { - goto ERR; - } - - /* now solve the matrix - - 0 0 0 0 1 - 1 2 4 8 16 - 1 1 1 1 1 - 16 8 4 2 1 - 1 0 0 0 0 - - using 12 subtractions, 4 shifts, 2 small divisions and 1 small multiplication. - */ - - /* r1 - r4 */ - if ((res = mp_sub(&w1, &w4, &w1)) != MP_OKAY) { - goto ERR; - } - /* r3 - r0 */ - if ((res = mp_sub(&w3, &w0, &w3)) != MP_OKAY) { - goto ERR; - } - /* r1/2 */ - if ((res = mp_div_2(&w1, &w1)) != MP_OKAY) { - goto ERR; - } - /* r3/2 */ - if ((res = mp_div_2(&w3, &w3)) != MP_OKAY) { - goto ERR; - } - /* r2 - r0 - r4 */ - if ((res = mp_sub(&w2, &w0, &w2)) != MP_OKAY) { - goto ERR; - } - if ((res = mp_sub(&w2, &w4, &w2)) != MP_OKAY) { - goto ERR; - } - /* r1 - r2 */ - if ((res = mp_sub(&w1, &w2, &w1)) != MP_OKAY) { - goto ERR; - } - /* r3 - r2 */ - if ((res = mp_sub(&w3, &w2, &w3)) != MP_OKAY) { - goto ERR; - } - /* r1 - 8r0 */ - if ((res = mp_mul_2d(&w0, 3, &tmp1)) != MP_OKAY) { - goto ERR; - } - if ((res = mp_sub(&w1, &tmp1, &w1)) != MP_OKAY) { - goto ERR; - } - /* r3 - 8r4 */ - if ((res = mp_mul_2d(&w4, 3, &tmp1)) != MP_OKAY) { - goto ERR; - } - if ((res = mp_sub(&w3, &tmp1, &w3)) != MP_OKAY) { - goto ERR; - } - /* 3r2 - r1 - r3 */ - if ((res = mp_mul_d(&w2, 3, &w2)) != MP_OKAY) { - goto ERR; - } - if ((res = mp_sub(&w2, &w1, &w2)) != MP_OKAY) { - goto ERR; - } - if ((res = mp_sub(&w2, &w3, &w2)) != MP_OKAY) { - goto ERR; - } - /* r1 - r2 */ - if ((res = mp_sub(&w1, &w2, &w1)) != MP_OKAY) { - goto ERR; - } - /* r3 - r2 */ - if ((res = mp_sub(&w3, &w2, &w3)) != MP_OKAY) { - goto ERR; - } - /* r1/3 */ - if ((res = mp_div_3(&w1, &w1, NULL)) != MP_OKAY) { - goto ERR; - } - /* r3/3 */ - if ((res = mp_div_3(&w3, &w3, NULL)) != MP_OKAY) { - goto ERR; - } - - /* at this point shift W[n] by B*n */ - if ((res = mp_lshd(&w1, 1*B)) != MP_OKAY) { - goto ERR; - } - if ((res = mp_lshd(&w2, 2*B)) != MP_OKAY) { - goto ERR; - } - if ((res = mp_lshd(&w3, 3*B)) != MP_OKAY) { - goto ERR; - } - if ((res = mp_lshd(&w4, 4*B)) != MP_OKAY) { - goto ERR; - } - - if ((res = mp_add(&w0, &w1, b)) != MP_OKAY) { - goto ERR; - } - if ((res = mp_add(&w2, &w3, &tmp1)) != MP_OKAY) { - goto ERR; - } - if ((res = mp_add(&w4, &tmp1, &tmp1)) != MP_OKAY) { - goto ERR; - } - if ((res = mp_add(&tmp1, b, b)) != MP_OKAY) { - goto ERR; - } - -ERR: - mp_clear_multi(&w0, &w1, &w2, &w3, &w4, &a0, &a1, &a2, &tmp1, NULL); - return res; -} - -#endif - -/* $Source: /cvs/libtom/libtommath/bn_mp_toom_sqr.c,v $ */ -/* $Revision: 1.4 $ */ -/* $Date: 2006/12/28 01:25:13 $ */ diff --git a/lib/hcrypto/libtommath/bn_mp_toradix.c b/lib/hcrypto/libtommath/bn_mp_toradix.c deleted file mode 100644 index 0adc28d2fdb8..000000000000 --- a/lib/hcrypto/libtommath/bn_mp_toradix.c +++ /dev/null @@ -1,75 +0,0 @@ -#include <tommath.h> -#ifdef BN_MP_TORADIX_C -/* LibTomMath, multiple-precision integer library -- Tom St Denis - * - * LibTomMath is a library that provides multiple-precision - * integer arithmetic as well as number theoretic functionality. - * - * The library was designed directly after the MPI library by - * Michael Fromberger but has been written from scratch with - * additional optimizations in place. - * - * The library is free for all purposes without any express - * guarantee it works. - * - * Tom St Denis, tomstdenis@gmail.com, http://libtom.org - */ - -/* stores a bignum as a ASCII string in a given radix (2..64) */ -int mp_toradix (mp_int * a, char *str, int radix) -{ - int res, digs; - mp_int t; - mp_digit d; - char *_s = str; - - /* check range of the radix */ - if (radix < 2 || radix > 64) { - return MP_VAL; - } - - /* quick out if its zero */ - if (mp_iszero(a) == 1) { - *str++ = '0'; - *str = '\0'; - return MP_OKAY; - } - - if ((res = mp_init_copy (&t, a)) != MP_OKAY) { - return res; - } - - /* if it is negative output a - */ - if (t.sign == MP_NEG) { - ++_s; - *str++ = '-'; - t.sign = MP_ZPOS; - } - - digs = 0; - while (mp_iszero (&t) == 0) { - if ((res = mp_div_d (&t, (mp_digit) radix, &t, &d)) != MP_OKAY) { - mp_clear (&t); - return res; - } - *str++ = mp_s_rmap[d]; - ++digs; - } - - /* reverse the digits of the string. In this case _s points - * to the first digit [exluding the sign] of the number] - */ - bn_reverse ((unsigned char *)_s, digs); - - /* append a NULL so the string is properly terminated */ - *str = '\0'; - - mp_clear (&t); - return MP_OKAY; -} - -#endif - -/* $Source: /cvs/libtom/libtommath/bn_mp_toradix.c,v $ */ -/* $Revision: 1.4 $ */ -/* $Date: 2006/12/28 01:25:13 $ */ diff --git a/lib/hcrypto/libtommath/bn_mp_toradix_n.c b/lib/hcrypto/libtommath/bn_mp_toradix_n.c deleted file mode 100644 index 28085124ea99..000000000000 --- a/lib/hcrypto/libtommath/bn_mp_toradix_n.c +++ /dev/null @@ -1,88 +0,0 @@ -#include <tommath.h> -#ifdef BN_MP_TORADIX_N_C -/* LibTomMath, multiple-precision integer library -- Tom St Denis - * - * LibTomMath is a library that provides multiple-precision - * integer arithmetic as well as number theoretic functionality. - * - * The library was designed directly after the MPI library by - * Michael Fromberger but has been written from scratch with - * additional optimizations in place. - * - * The library is free for all purposes without any express - * guarantee it works. - * - * Tom St Denis, tomstdenis@gmail.com, http://libtom.org - */ - -/* stores a bignum as a ASCII string in a given radix (2..64) - * - * Stores upto maxlen-1 chars and always a NULL byte - */ -int mp_toradix_n(mp_int * a, char *str, int radix, int maxlen) -{ - int res, digs; - mp_int t; - mp_digit d; - char *_s = str; - - /* check range of the maxlen, radix */ - if (maxlen < 2 || radix < 2 || radix > 64) { - return MP_VAL; - } - - /* quick out if its zero */ - if (mp_iszero(a) == MP_YES) { - *str++ = '0'; - *str = '\0'; - return MP_OKAY; - } - - if ((res = mp_init_copy (&t, a)) != MP_OKAY) { - return res; - } - - /* if it is negative output a - */ - if (t.sign == MP_NEG) { - /* we have to reverse our digits later... but not the - sign!! */ - ++_s; - - /* store the flag and mark the number as positive */ - *str++ = '-'; - t.sign = MP_ZPOS; - - /* subtract a char */ - --maxlen; - } - - digs = 0; - while (mp_iszero (&t) == 0) { - if (--maxlen < 1) { - /* no more room */ - break; - } - if ((res = mp_div_d (&t, (mp_digit) radix, &t, &d)) != MP_OKAY) { - mp_clear (&t); - return res; - } - *str++ = mp_s_rmap[d]; - ++digs; - } - - /* reverse the digits of the string. In this case _s points - * to the first digit [exluding the sign] of the number - */ - bn_reverse ((unsigned char *)_s, digs); - - /* append a NULL so the string is properly terminated */ - *str = '\0'; - - mp_clear (&t); - return MP_OKAY; -} - -#endif - -/* $Source: /cvs/libtom/libtommath/bn_mp_toradix_n.c,v $ */ -/* $Revision: 1.5 $ */ -/* $Date: 2006/12/28 01:25:13 $ */ diff --git a/lib/hcrypto/libtommath/bn_mp_ubin_size.c b/lib/hcrypto/libtommath/bn_mp_ubin_size.c new file mode 100644 index 000000000000..21230b48c9a9 --- /dev/null +++ b/lib/hcrypto/libtommath/bn_mp_ubin_size.c @@ -0,0 +1,12 @@ +#include "tommath_private.h" +#ifdef BN_MP_UBIN_SIZE_C +/* LibTomMath, multiple-precision integer library -- Tom St Denis */ +/* SPDX-License-Identifier: Unlicense */ + +/* get the size for an unsigned equivalent */ +size_t mp_ubin_size(const mp_int *a) +{ + size_t size = (size_t)mp_count_bits(a); + return (size / 8u) + (((size & 7u) != 0u) ? 1u : 0u); +} +#endif diff --git a/lib/hcrypto/libtommath/bn_mp_unpack.c b/lib/hcrypto/libtommath/bn_mp_unpack.c new file mode 100644 index 000000000000..d4eb90e0cfd6 --- /dev/null +++ b/lib/hcrypto/libtommath/bn_mp_unpack.c @@ -0,0 +1,49 @@ +#include "tommath_private.h" +#ifdef BN_MP_UNPACK_C +/* LibTomMath, multiple-precision integer library -- Tom St Denis */ +/* SPDX-License-Identifier: Unlicense */ + +/* based on gmp's mpz_import. + * see http://gmplib.org/manual/Integer-Import-and-Export.html + */ +mp_err mp_unpack(mp_int *rop, size_t count, mp_order order, size_t size, + mp_endian endian, size_t nails, const void *op) +{ + mp_err err; + size_t odd_nails, nail_bytes, i, j; + unsigned char odd_nail_mask; + + mp_zero(rop); + + if (endian == MP_NATIVE_ENDIAN) { + MP_GET_ENDIANNESS(endian); + } + + odd_nails = (nails % 8u); + odd_nail_mask = 0xff; + for (i = 0; i < odd_nails; ++i) { + odd_nail_mask ^= (unsigned char)(1u << (7u - i)); + } + nail_bytes = nails / 8u; + + for (i = 0; i < count; ++i) { + for (j = 0; j < (size - nail_bytes); ++j) { + unsigned char byte = *((const unsigned char *)op + + (((order == MP_MSB_FIRST) ? i : ((count - 1u) - i)) * size) + + ((endian == MP_BIG_ENDIAN) ? (j + nail_bytes) : (((size - 1u) - j) - nail_bytes))); + + if ((err = mp_mul_2d(rop, (j == 0u) ? (int)(8u - odd_nails) : 8, rop)) != MP_OKAY) { + return err; + } + + rop->dp[0] |= (j == 0u) ? (mp_digit)(byte & odd_nail_mask) : (mp_digit)byte; + rop->used += 1; + } + } + + mp_clamp(rop); + + return MP_OKAY; +} + +#endif diff --git a/lib/hcrypto/libtommath/bn_mp_unsigned_bin_size.c b/lib/hcrypto/libtommath/bn_mp_unsigned_bin_size.c deleted file mode 100644 index 6dc3bd5fc1bf..000000000000 --- a/lib/hcrypto/libtommath/bn_mp_unsigned_bin_size.c +++ /dev/null @@ -1,28 +0,0 @@ -#include <tommath.h> -#ifdef BN_MP_UNSIGNED_BIN_SIZE_C -/* LibTomMath, multiple-precision integer library -- Tom St Denis - * - * LibTomMath is a library that provides multiple-precision - * integer arithmetic as well as number theoretic functionality. - * - * The library was designed directly after the MPI library by - * Michael Fromberger but has been written from scratch with - * additional optimizations in place. - * - * The library is free for all purposes without any express - * guarantee it works. - * - * Tom St Denis, tomstdenis@gmail.com, http://libtom.org - */ - -/* get the size for an unsigned equivalent */ -int mp_unsigned_bin_size (mp_int * a) -{ - int size = mp_count_bits (a); - return (size / 8 + ((size & 7) != 0 ? 1 : 0)); -} -#endif - -/* $Source: /cvs/libtom/libtommath/bn_mp_unsigned_bin_size.c,v $ */ -/* $Revision: 1.4 $ */ -/* $Date: 2006/12/28 01:25:13 $ */ diff --git a/lib/hcrypto/libtommath/bn_mp_xor.c b/lib/hcrypto/libtommath/bn_mp_xor.c index 59ff2e183207..71e7ca1878e9 100644 --- a/lib/hcrypto/libtommath/bn_mp_xor.c +++ b/lib/hcrypto/libtommath/bn_mp_xor.c @@ -1,51 +1,56 @@ -#include <tommath.h> +#include "tommath_private.h" #ifdef BN_MP_XOR_C -/* LibTomMath, multiple-precision integer library -- Tom St Denis - * - * LibTomMath is a library that provides multiple-precision - * integer arithmetic as well as number theoretic functionality. - * - * The library was designed directly after the MPI library by - * Michael Fromberger but has been written from scratch with - * additional optimizations in place. - * - * The library is free for all purposes without any express - * guarantee it works. - * - * Tom St Denis, tomstdenis@gmail.com, http://libtom.org - */ - -/* XOR two ints together */ -int -mp_xor (mp_int * a, mp_int * b, mp_int * c) +/* LibTomMath, multiple-precision integer library -- Tom St Denis */ +/* SPDX-License-Identifier: Unlicense */ + +/* two complement xor */ +mp_err mp_xor(const mp_int *a, const mp_int *b, mp_int *c) { - int res, ix, px; - mp_int t, *x; - - if (a->used > b->used) { - if ((res = mp_init_copy (&t, a)) != MP_OKAY) { - return res; - } - px = b->used; - x = b; - } else { - if ((res = mp_init_copy (&t, b)) != MP_OKAY) { - return res; - } - px = a->used; - x = a; - } - - for (ix = 0; ix < px; ix++) { - t.dp[ix] ^= x->dp[ix]; - } - mp_clamp (&t); - mp_exch (c, &t); - mp_clear (&t); - return MP_OKAY; + int used = MP_MAX(a->used, b->used) + 1, i; + mp_err err; + mp_digit ac = 1, bc = 1, cc = 1; + mp_sign csign = (a->sign != b->sign) ? MP_NEG : MP_ZPOS; + + if (c->alloc < used) { + if ((err = mp_grow(c, used)) != MP_OKAY) { + return err; + } + } + + for (i = 0; i < used; i++) { + mp_digit x, y; + + /* convert to two complement if negative */ + if (a->sign == MP_NEG) { + ac += (i >= a->used) ? MP_MASK : (~a->dp[i] & MP_MASK); + x = ac & MP_MASK; + ac >>= MP_DIGIT_BIT; + } else { + x = (i >= a->used) ? 0uL : a->dp[i]; + } + + /* convert to two complement if negative */ + if (b->sign == MP_NEG) { + bc += (i >= b->used) ? MP_MASK : (~b->dp[i] & MP_MASK); + y = bc & MP_MASK; + bc >>= MP_DIGIT_BIT; + } else { + y = (i >= b->used) ? 0uL : b->dp[i]; + } + + c->dp[i] = x ^ y; + + /* convert to to sign-magnitude if negative */ + if (csign == MP_NEG) { + cc += ~c->dp[i] & MP_MASK; + c->dp[i] = cc & MP_MASK; + cc >>= MP_DIGIT_BIT; + } + } + + c->used = used; + c->sign = csign; + mp_clamp(c); + return MP_OKAY; } #endif - -/* $Source: /cvs/libtom/libtommath/bn_mp_xor.c,v $ */ -/* $Revision: 1.4 $ */ -/* $Date: 2006/12/28 01:25:13 $ */ diff --git a/lib/hcrypto/libtommath/bn_mp_zero.c b/lib/hcrypto/libtommath/bn_mp_zero.c index b0977d443164..72a255efcca2 100644 --- a/lib/hcrypto/libtommath/bn_mp_zero.c +++ b/lib/hcrypto/libtommath/bn_mp_zero.c @@ -1,36 +1,13 @@ -#include <tommath.h> +#include "tommath_private.h" #ifdef BN_MP_ZERO_C -/* LibTomMath, multiple-precision integer library -- Tom St Denis - * - * LibTomMath is a library that provides multiple-precision - * integer arithmetic as well as number theoretic functionality. - * - * The library was designed directly after the MPI library by - * Michael Fromberger but has been written from scratch with - * additional optimizations in place. - * - * The library is free for all purposes without any express - * guarantee it works. - * - * Tom St Denis, tomstdenis@gmail.com, http://libtom.org - */ +/* LibTomMath, multiple-precision integer library -- Tom St Denis */ +/* SPDX-License-Identifier: Unlicense */ /* set to zero */ -void mp_zero (mp_int * a) +void mp_zero(mp_int *a) { - int n; - mp_digit *tmp; - - a->sign = MP_ZPOS; - a->used = 0; - - tmp = a->dp; - for (n = 0; n < a->alloc; n++) { - *tmp++ = 0; - } + a->sign = MP_ZPOS; + a->used = 0; + MP_ZERO_DIGITS(a->dp, a->alloc); } #endif - -/* $Source: /cvs/libtom/libtommath/bn_mp_zero.c,v $ */ -/* $Revision: 1.4 $ */ -/* $Date: 2006/12/28 01:25:13 $ */ diff --git a/lib/hcrypto/libtommath/bn_mp_zero_multi.c b/lib/hcrypto/libtommath/bn_mp_zero_multi.c deleted file mode 100644 index 339a75fbf85d..000000000000 --- a/lib/hcrypto/libtommath/bn_mp_zero_multi.c +++ /dev/null @@ -1,35 +0,0 @@ -#include <tommath.h> -#ifdef BN_MP_ZERO_MULTI_C -/* LibTomMath, multiple-precision integer library -- Tom St Denis - * - * LibTomMath is a library that provides multiple-precision - * integer arithmetic as well as number theoretic functionality. - * - * The library was designed directly after the MPI library by - * Michael Fromberger but has been written from scratch with - * additional optimizations in place. - * - * The library is free for all purposes without any express - * guarantee it works. - * - * Tom St Denis, tomstdenis@gmail.com, http://libtom.org - */ -#include <stdarg.h> - -/* set to zero */ -void mp_zero_multi (mp_int * mp, ...) -{ - mp_int* next_mp = mp; - va_list args; - va_start(args, mp); - while (next_mp != NULL) { - mp_zero(next_mp); - next_mp = va_arg(args, mp_int*); - } - va_end(args); -} -#endif - -/* $Source: /cvs/libtom/libtommath/bn_mp_zero.c,v $ */ -/* $Revision: 1.4 $ */ -/* $Date: 2006/12/28 01:25:13 $ */ diff --git a/lib/hcrypto/libtommath/bn_prime_tab.c b/lib/hcrypto/libtommath/bn_prime_tab.c index bd252477ec6a..a6c07f8da25e 100644 --- a/lib/hcrypto/libtommath/bn_prime_tab.c +++ b/lib/hcrypto/libtommath/bn_prime_tab.c @@ -1,61 +1,61 @@ -#include <tommath.h> +#include "tommath_private.h" #ifdef BN_PRIME_TAB_C -/* LibTomMath, multiple-precision integer library -- Tom St Denis - * - * LibTomMath is a library that provides multiple-precision - * integer arithmetic as well as number theoretic functionality. - * - * The library was designed directly after the MPI library by - * Michael Fromberger but has been written from scratch with - * additional optimizations in place. - * - * The library is free for all purposes without any express - * guarantee it works. - * - * Tom St Denis, tomstdenis@gmail.com, http://libtom.org - */ +/* LibTomMath, multiple-precision integer library -- Tom St Denis */ +/* SPDX-License-Identifier: Unlicense */ + const mp_digit ltm_prime_tab[] = { - 0x0002, 0x0003, 0x0005, 0x0007, 0x000B, 0x000D, 0x0011, 0x0013, - 0x0017, 0x001D, 0x001F, 0x0025, 0x0029, 0x002B, 0x002F, 0x0035, - 0x003B, 0x003D, 0x0043, 0x0047, 0x0049, 0x004F, 0x0053, 0x0059, - 0x0061, 0x0065, 0x0067, 0x006B, 0x006D, 0x0071, 0x007F, + 0x0002, 0x0003, 0x0005, 0x0007, 0x000B, 0x000D, 0x0011, 0x0013, + 0x0017, 0x001D, 0x001F, 0x0025, 0x0029, 0x002B, 0x002F, 0x0035, + 0x003B, 0x003D, 0x0043, 0x0047, 0x0049, 0x004F, 0x0053, 0x0059, + 0x0061, 0x0065, 0x0067, 0x006B, 0x006D, 0x0071, 0x007F, #ifndef MP_8BIT - 0x0083, - 0x0089, 0x008B, 0x0095, 0x0097, 0x009D, 0x00A3, 0x00A7, 0x00AD, - 0x00B3, 0x00B5, 0x00BF, 0x00C1, 0x00C5, 0x00C7, 0x00D3, 0x00DF, - 0x00E3, 0x00E5, 0x00E9, 0x00EF, 0x00F1, 0x00FB, 0x0101, 0x0107, - 0x010D, 0x010F, 0x0115, 0x0119, 0x011B, 0x0125, 0x0133, 0x0137, + 0x0083, + 0x0089, 0x008B, 0x0095, 0x0097, 0x009D, 0x00A3, 0x00A7, 0x00AD, + 0x00B3, 0x00B5, 0x00BF, 0x00C1, 0x00C5, 0x00C7, 0x00D3, 0x00DF, + 0x00E3, 0x00E5, 0x00E9, 0x00EF, 0x00F1, 0x00FB, 0x0101, 0x0107, + 0x010D, 0x010F, 0x0115, 0x0119, 0x011B, 0x0125, 0x0133, 0x0137, - 0x0139, 0x013D, 0x014B, 0x0151, 0x015B, 0x015D, 0x0161, 0x0167, - 0x016F, 0x0175, 0x017B, 0x017F, 0x0185, 0x018D, 0x0191, 0x0199, - 0x01A3, 0x01A5, 0x01AF, 0x01B1, 0x01B7, 0x01BB, 0x01C1, 0x01C9, - 0x01CD, 0x01CF, 0x01D3, 0x01DF, 0x01E7, 0x01EB, 0x01F3, 0x01F7, - 0x01FD, 0x0209, 0x020B, 0x021D, 0x0223, 0x022D, 0x0233, 0x0239, - 0x023B, 0x0241, 0x024B, 0x0251, 0x0257, 0x0259, 0x025F, 0x0265, - 0x0269, 0x026B, 0x0277, 0x0281, 0x0283, 0x0287, 0x028D, 0x0293, - 0x0295, 0x02A1, 0x02A5, 0x02AB, 0x02B3, 0x02BD, 0x02C5, 0x02CF, + 0x0139, 0x013D, 0x014B, 0x0151, 0x015B, 0x015D, 0x0161, 0x0167, + 0x016F, 0x0175, 0x017B, 0x017F, 0x0185, 0x018D, 0x0191, 0x0199, + 0x01A3, 0x01A5, 0x01AF, 0x01B1, 0x01B7, 0x01BB, 0x01C1, 0x01C9, + 0x01CD, 0x01CF, 0x01D3, 0x01DF, 0x01E7, 0x01EB, 0x01F3, 0x01F7, + 0x01FD, 0x0209, 0x020B, 0x021D, 0x0223, 0x022D, 0x0233, 0x0239, + 0x023B, 0x0241, 0x024B, 0x0251, 0x0257, 0x0259, 0x025F, 0x0265, + 0x0269, 0x026B, 0x0277, 0x0281, 0x0283, 0x0287, 0x028D, 0x0293, + 0x0295, 0x02A1, 0x02A5, 0x02AB, 0x02B3, 0x02BD, 0x02C5, 0x02CF, - 0x02D7, 0x02DD, 0x02E3, 0x02E7, 0x02EF, 0x02F5, 0x02F9, 0x0301, - 0x0305, 0x0313, 0x031D, 0x0329, 0x032B, 0x0335, 0x0337, 0x033B, - 0x033D, 0x0347, 0x0355, 0x0359, 0x035B, 0x035F, 0x036D, 0x0371, - 0x0373, 0x0377, 0x038B, 0x038F, 0x0397, 0x03A1, 0x03A9, 0x03AD, - 0x03B3, 0x03B9, 0x03C7, 0x03CB, 0x03D1, 0x03D7, 0x03DF, 0x03E5, - 0x03F1, 0x03F5, 0x03FB, 0x03FD, 0x0407, 0x0409, 0x040F, 0x0419, - 0x041B, 0x0425, 0x0427, 0x042D, 0x043F, 0x0443, 0x0445, 0x0449, - 0x044F, 0x0455, 0x045D, 0x0463, 0x0469, 0x047F, 0x0481, 0x048B, + 0x02D7, 0x02DD, 0x02E3, 0x02E7, 0x02EF, 0x02F5, 0x02F9, 0x0301, + 0x0305, 0x0313, 0x031D, 0x0329, 0x032B, 0x0335, 0x0337, 0x033B, + 0x033D, 0x0347, 0x0355, 0x0359, 0x035B, 0x035F, 0x036D, 0x0371, + 0x0373, 0x0377, 0x038B, 0x038F, 0x0397, 0x03A1, 0x03A9, 0x03AD, + 0x03B3, 0x03B9, 0x03C7, 0x03CB, 0x03D1, 0x03D7, 0x03DF, 0x03E5, + 0x03F1, 0x03F5, 0x03FB, 0x03FD, 0x0407, 0x0409, 0x040F, 0x0419, + 0x041B, 0x0425, 0x0427, 0x042D, 0x043F, 0x0443, 0x0445, 0x0449, + 0x044F, 0x0455, 0x045D, 0x0463, 0x0469, 0x047F, 0x0481, 0x048B, - 0x0493, 0x049D, 0x04A3, 0x04A9, 0x04B1, 0x04BD, 0x04C1, 0x04C7, - 0x04CD, 0x04CF, 0x04D5, 0x04E1, 0x04EB, 0x04FD, 0x04FF, 0x0503, - 0x0509, 0x050B, 0x0511, 0x0515, 0x0517, 0x051B, 0x0527, 0x0529, - 0x052F, 0x0551, 0x0557, 0x055D, 0x0565, 0x0577, 0x0581, 0x058F, - 0x0593, 0x0595, 0x0599, 0x059F, 0x05A7, 0x05AB, 0x05AD, 0x05B3, - 0x05BF, 0x05C9, 0x05CB, 0x05CF, 0x05D1, 0x05D5, 0x05DB, 0x05E7, - 0x05F3, 0x05FB, 0x0607, 0x060D, 0x0611, 0x0617, 0x061F, 0x0623, - 0x062B, 0x062F, 0x063D, 0x0641, 0x0647, 0x0649, 0x064D, 0x0653 + 0x0493, 0x049D, 0x04A3, 0x04A9, 0x04B1, 0x04BD, 0x04C1, 0x04C7, + 0x04CD, 0x04CF, 0x04D5, 0x04E1, 0x04EB, 0x04FD, 0x04FF, 0x0503, + 0x0509, 0x050B, 0x0511, 0x0515, 0x0517, 0x051B, 0x0527, 0x0529, + 0x052F, 0x0551, 0x0557, 0x055D, 0x0565, 0x0577, 0x0581, 0x058F, + 0x0593, 0x0595, 0x0599, 0x059F, 0x05A7, 0x05AB, 0x05AD, 0x05B3, + 0x05BF, 0x05C9, 0x05CB, 0x05CF, 0x05D1, 0x05D5, 0x05DB, 0x05E7, + 0x05F3, 0x05FB, 0x0607, 0x060D, 0x0611, 0x0617, 0x061F, 0x0623, + 0x062B, 0x062F, 0x063D, 0x0641, 0x0647, 0x0649, 0x064D, 0x0653 #endif }; + +#if defined(__GNUC__) && __GNUC__ >= 4 +#pragma GCC diagnostic push +#pragma GCC diagnostic ignored "-Wdeprecated-declarations" +const mp_digit *s_mp_prime_tab = ltm_prime_tab; +#pragma GCC diagnostic pop +#elif defined(_MSC_VER) && _MSC_VER >= 1500 +#pragma warning(push) +#pragma warning(disable: 4996) +const mp_digit *s_mp_prime_tab = ltm_prime_tab; +#pragma warning(pop) +#else +const mp_digit *s_mp_prime_tab = ltm_prime_tab; #endif -/* $Source: /cvs/libtom/libtommath/bn_prime_tab.c,v $ */ -/* $Revision: 1.4 $ */ -/* $Date: 2006/12/28 01:25:13 $ */ +#endif diff --git a/lib/hcrypto/libtommath/bn_reverse.c b/lib/hcrypto/libtommath/bn_reverse.c deleted file mode 100644 index ddfa827a09f5..000000000000 --- a/lib/hcrypto/libtommath/bn_reverse.c +++ /dev/null @@ -1,39 +0,0 @@ -#include <tommath.h> -#ifdef BN_REVERSE_C -/* LibTomMath, multiple-precision integer library -- Tom St Denis - * - * LibTomMath is a library that provides multiple-precision - * integer arithmetic as well as number theoretic functionality. - * - * The library was designed directly after the MPI library by - * Michael Fromberger but has been written from scratch with - * additional optimizations in place. - * - * The library is free for all purposes without any express - * guarantee it works. - * - * Tom St Denis, tomstdenis@gmail.com, http://libtom.org - */ - -/* reverse an array, used for radix code */ -void -bn_reverse (unsigned char *s, int len) -{ - int ix, iy; - unsigned char t; - - ix = 0; - iy = len - 1; - while (ix < iy) { - t = s[ix]; - s[ix] = s[iy]; - s[iy] = t; - ++ix; - --iy; - } -} -#endif - -/* $Source: /cvs/libtom/libtommath/bn_reverse.c,v $ */ -/* $Revision: 1.4 $ */ -/* $Date: 2006/12/28 01:25:13 $ */ diff --git a/lib/hcrypto/libtommath/bn_s_mp_add.c b/lib/hcrypto/libtommath/bn_s_mp_add.c index e7f54f4cf1e4..c946aa80d26a 100644 --- a/lib/hcrypto/libtommath/bn_s_mp_add.c +++ b/lib/hcrypto/libtommath/bn_s_mp_add.c @@ -1,109 +1,91 @@ -#include <tommath.h> +#include "tommath_private.h" #ifdef BN_S_MP_ADD_C -/* LibTomMath, multiple-precision integer library -- Tom St Denis - * - * LibTomMath is a library that provides multiple-precision - * integer arithmetic as well as number theoretic functionality. - * - * The library was designed directly after the MPI library by - * Michael Fromberger but has been written from scratch with - * additional optimizations in place. - * - * The library is free for all purposes without any express - * guarantee it works. - * - * Tom St Denis, tomstdenis@gmail.com, http://libtom.org - */ +/* LibTomMath, multiple-precision integer library -- Tom St Denis */ +/* SPDX-License-Identifier: Unlicense */ /* low level addition, based on HAC pp.594, Algorithm 14.7 */ -int -s_mp_add (mp_int * a, mp_int * b, mp_int * c) +mp_err s_mp_add(const mp_int *a, const mp_int *b, mp_int *c) { - mp_int *x; - int olduse, res, min, max; - - /* find sizes, we let |a| <= |b| which means we have to sort - * them. "x" will point to the input with the most digits - */ - if (a->used > b->used) { - min = b->used; - max = a->used; - x = a; - } else { - min = a->used; - max = b->used; - x = b; - } - - /* init result */ - if (c->alloc < max + 1) { - if ((res = mp_grow (c, max + 1)) != MP_OKAY) { - return res; - } - } - - /* get old used digit count and set new one */ - olduse = c->used; - c->used = max + 1; - - { - register mp_digit u, *tmpa, *tmpb, *tmpc; - register int i; - - /* alias for digit pointers */ - - /* first input */ - tmpa = a->dp; - - /* second input */ - tmpb = b->dp; - - /* destination */ - tmpc = c->dp; - - /* zero the carry */ - u = 0; - for (i = 0; i < min; i++) { - /* Compute the sum at one digit, T[i] = A[i] + B[i] + U */ - *tmpc = *tmpa++ + *tmpb++ + u; - - /* U = carry bit of T[i] */ - u = *tmpc >> ((mp_digit)DIGIT_BIT); - - /* take away carry bit from T[i] */ - *tmpc++ &= MP_MASK; - } - - /* now copy higher words if any, that is in A+B - * if A or B has more digits add those in - */ - if (min != max) { - for (; i < max; i++) { - /* T[i] = X[i] + U */ - *tmpc = x->dp[i] + u; - - /* U = carry bit of T[i] */ - u = *tmpc >> ((mp_digit)DIGIT_BIT); - - /* take away carry bit from T[i] */ - *tmpc++ &= MP_MASK; + const mp_int *x; + mp_err err; + int olduse, min, max; + + /* find sizes, we let |a| <= |b| which means we have to sort + * them. "x" will point to the input with the most digits + */ + if (a->used > b->used) { + min = b->used; + max = a->used; + x = a; + } else { + min = a->used; + max = b->used; + x = b; + } + + /* init result */ + if (c->alloc < (max + 1)) { + if ((err = mp_grow(c, max + 1)) != MP_OKAY) { + return err; } - } + } - /* add carry */ - *tmpc++ = u; + /* get old used digit count and set new one */ + olduse = c->used; + c->used = max + 1; - /* clear digits above oldused */ - for (i = c->used; i < olduse; i++) { - *tmpc++ = 0; - } - } + { + mp_digit u, *tmpa, *tmpb, *tmpc; + int i; - mp_clamp (c); - return MP_OKAY; + /* alias for digit pointers */ + + /* first input */ + tmpa = a->dp; + + /* second input */ + tmpb = b->dp; + + /* destination */ + tmpc = c->dp; + + /* zero the carry */ + u = 0; + for (i = 0; i < min; i++) { + /* Compute the sum at one digit, T[i] = A[i] + B[i] + U */ + *tmpc = *tmpa++ + *tmpb++ + u; + + /* U = carry bit of T[i] */ + u = *tmpc >> (mp_digit)MP_DIGIT_BIT; + + /* take away carry bit from T[i] */ + *tmpc++ &= MP_MASK; + } + + /* now copy higher words if any, that is in A+B + * if A or B has more digits add those in + */ + if (min != max) { + for (; i < max; i++) { + /* T[i] = X[i] + U */ + *tmpc = x->dp[i] + u; + + /* U = carry bit of T[i] */ + u = *tmpc >> (mp_digit)MP_DIGIT_BIT; + + /* take away carry bit from T[i] */ + *tmpc++ &= MP_MASK; + } + } + + /* add carry */ + *tmpc++ = u; + + /* clear digits above oldused */ + MP_ZERO_DIGITS(tmpc, olduse - c->used); + } + + mp_clamp(c); + return MP_OKAY; } #endif - -/* $Source: /cvs/libtom/libtommath/bn_s_mp_add.c,v $ */ -/* $Revision: 1.4 $ */ -/* $Date: 2006/12/28 01:25:13 $ */ diff --git a/lib/hcrypto/libtommath/bn_s_mp_balance_mul.c b/lib/hcrypto/libtommath/bn_s_mp_balance_mul.c new file mode 100644 index 000000000000..7ece5d794278 --- /dev/null +++ b/lib/hcrypto/libtommath/bn_s_mp_balance_mul.c @@ -0,0 +1,81 @@ +#include "tommath_private.h" +#ifdef BN_S_MP_BALANCE_MUL_C +/* LibTomMath, multiple-precision integer library -- Tom St Denis */ +/* SPDX-License-Identifier: Unlicense */ + +/* single-digit multiplication with the smaller number as the single-digit */ +mp_err s_mp_balance_mul(const mp_int *a, const mp_int *b, mp_int *c) +{ + int count, len_a, len_b, nblocks, i, j, bsize; + mp_int a0, tmp, A, B, r; + mp_err err; + + len_a = a->used; + len_b = b->used; + + nblocks = MP_MAX(a->used, b->used) / MP_MIN(a->used, b->used); + bsize = MP_MIN(a->used, b->used) ; + + if ((err = mp_init_size(&a0, bsize + 2)) != MP_OKAY) { + return err; + } + if ((err = mp_init_multi(&tmp, &r, NULL)) != MP_OKAY) { + mp_clear(&a0); + return err; + } + + /* Make sure that A is the larger one*/ + if (len_a < len_b) { + B = *a; + A = *b; + } else { + A = *a; + B = *b; + } + + for (i = 0, j=0; i < nblocks; i++) { + /* Cut a slice off of a */ + a0.used = 0; + for (count = 0; count < bsize; count++) { + a0.dp[count] = A.dp[ j++ ]; + a0.used++; + } + mp_clamp(&a0); + /* Multiply with b */ + if ((err = mp_mul(&a0, &B, &tmp)) != MP_OKAY) { + goto LBL_ERR; + } + /* Shift tmp to the correct position */ + if ((err = mp_lshd(&tmp, bsize * i)) != MP_OKAY) { + goto LBL_ERR; + } + /* Add to output. No carry needed */ + if ((err = mp_add(&r, &tmp, &r)) != MP_OKAY) { + goto LBL_ERR; + } + } + /* The left-overs; there are always left-overs */ + if (j < A.used) { + a0.used = 0; + for (count = 0; j < A.used; count++) { + a0.dp[count] = A.dp[ j++ ]; + a0.used++; + } + mp_clamp(&a0); + if ((err = mp_mul(&a0, &B, &tmp)) != MP_OKAY) { + goto LBL_ERR; + } + if ((err = mp_lshd(&tmp, bsize * i)) != MP_OKAY) { + goto LBL_ERR; + } + if ((err = mp_add(&r, &tmp, &r)) != MP_OKAY) { + goto LBL_ERR; + } + } + + mp_exch(&r,c); +LBL_ERR: + mp_clear_multi(&a0, &tmp, &r,NULL); + return err; +} +#endif diff --git a/lib/hcrypto/libtommath/bn_s_mp_exptmod.c b/lib/hcrypto/libtommath/bn_s_mp_exptmod.c index deb4b4ddb161..c3bfa95e8344 100644 --- a/lib/hcrypto/libtommath/bn_s_mp_exptmod.c +++ b/lib/hcrypto/libtommath/bn_s_mp_exptmod.c @@ -1,252 +1,198 @@ -#include <tommath.h> +#include "tommath_private.h" #ifdef BN_S_MP_EXPTMOD_C -/* LibTomMath, multiple-precision integer library -- Tom St Denis - * - * LibTomMath is a library that provides multiple-precision - * integer arithmetic as well as number theoretic functionality. - * - * The library was designed directly after the MPI library by - * Michael Fromberger but has been written from scratch with - * additional optimizations in place. - * - * The library is free for all purposes without any express - * guarantee it works. - * - * Tom St Denis, tomstdenis@gmail.com, http://libtom.org - */ +/* LibTomMath, multiple-precision integer library -- Tom St Denis */ +/* SPDX-License-Identifier: Unlicense */ + #ifdef MP_LOW_MEM - #define TAB_SIZE 32 +# define TAB_SIZE 32 +# define MAX_WINSIZE 5 #else - #define TAB_SIZE 256 +# define TAB_SIZE 256 +# define MAX_WINSIZE 0 #endif -int s_mp_exptmod (mp_int * G, mp_int * X, mp_int * P, mp_int * Y, int redmode) +mp_err s_mp_exptmod(const mp_int *G, const mp_int *X, const mp_int *P, mp_int *Y, int redmode) { - mp_int M[TAB_SIZE], res, mu; - mp_digit buf; - int err, bitbuf, bitcpy, bitcnt, mode, digidx, x, y, winsize; - int (*redux)(mp_int*,mp_int*,mp_int*); - - /* find window size */ - x = mp_count_bits (X); - if (x <= 7) { - winsize = 2; - } else if (x <= 36) { - winsize = 3; - } else if (x <= 140) { - winsize = 4; - } else if (x <= 450) { - winsize = 5; - } else if (x <= 1303) { - winsize = 6; - } else if (x <= 3529) { - winsize = 7; - } else { - winsize = 8; - } - -#ifdef MP_LOW_MEM - if (winsize > 5) { - winsize = 5; - } -#endif - - /* init M array */ - /* init first cell */ - if ((err = mp_init(&M[1])) != MP_OKAY) { - return err; - } - - /* now init the second half of the array */ - for (x = 1<<(winsize-1); x < (1 << winsize); x++) { - if ((err = mp_init(&M[x])) != MP_OKAY) { - for (y = 1<<(winsize-1); y < x; y++) { - mp_clear (&M[y]); - } - mp_clear(&M[1]); + mp_int M[TAB_SIZE], res, mu; + mp_digit buf; + mp_err err; + int bitbuf, bitcpy, bitcnt, mode, digidx, x, y, winsize; + mp_err(*redux)(mp_int *x, const mp_int *m, const mp_int *mu); + + /* find window size */ + x = mp_count_bits(X); + if (x <= 7) { + winsize = 2; + } else if (x <= 36) { + winsize = 3; + } else if (x <= 140) { + winsize = 4; + } else if (x <= 450) { + winsize = 5; + } else if (x <= 1303) { + winsize = 6; + } else if (x <= 3529) { + winsize = 7; + } else { + winsize = 8; + } + + winsize = MAX_WINSIZE ? MP_MIN(MAX_WINSIZE, winsize) : winsize; + + /* init M array */ + /* init first cell */ + if ((err = mp_init(&M[1])) != MP_OKAY) { return err; - } - } - - /* create mu, used for Barrett reduction */ - if ((err = mp_init (&mu)) != MP_OKAY) { - goto LBL_M; - } - - if (redmode == 0) { - if ((err = mp_reduce_setup (&mu, P)) != MP_OKAY) { - goto LBL_MU; - } - redux = mp_reduce; - } else { - if ((err = mp_reduce_2k_setup_l (P, &mu)) != MP_OKAY) { - goto LBL_MU; - } - redux = mp_reduce_2k_l; - } - - /* create M table - * - * The M table contains powers of the base, - * e.g. M[x] = G**x mod P - * - * The first half of the table is not - * computed though accept for M[0] and M[1] - */ - if ((err = mp_mod (G, P, &M[1])) != MP_OKAY) { - goto LBL_MU; - } - - /* compute the value at M[1<<(winsize-1)] by squaring - * M[1] (winsize-1) times - */ - if ((err = mp_copy (&M[1], &M[1 << (winsize - 1)])) != MP_OKAY) { - goto LBL_MU; - } - - for (x = 0; x < (winsize - 1); x++) { - /* square it */ - if ((err = mp_sqr (&M[1 << (winsize - 1)], - &M[1 << (winsize - 1)])) != MP_OKAY) { - goto LBL_MU; - } - - /* reduce modulo P */ - if ((err = redux (&M[1 << (winsize - 1)], P, &mu)) != MP_OKAY) { - goto LBL_MU; - } - } - - /* create upper table, that is M[x] = M[x-1] * M[1] (mod P) - * for x = (2**(winsize - 1) + 1) to (2**winsize - 1) - */ - for (x = (1 << (winsize - 1)) + 1; x < (1 << winsize); x++) { - if ((err = mp_mul (&M[x - 1], &M[1], &M[x])) != MP_OKAY) { - goto LBL_MU; - } - if ((err = redux (&M[x], P, &mu)) != MP_OKAY) { - goto LBL_MU; - } - } - - /* setup result */ - if ((err = mp_init (&res)) != MP_OKAY) { - goto LBL_MU; - } - mp_set (&res, 1); - - /* set initial mode and bit cnt */ - mode = 0; - bitcnt = 1; - buf = 0; - digidx = X->used - 1; - bitcpy = 0; - bitbuf = 0; - - for (;;) { - /* grab next digit as required */ - if (--bitcnt == 0) { - /* if digidx == -1 we are out of digits */ - if (digidx == -1) { - break; - } - /* read next digit and reset the bitcnt */ - buf = X->dp[digidx--]; - bitcnt = (int) DIGIT_BIT; - } - - /* grab the next msb from the exponent */ - y = (buf >> (mp_digit)(DIGIT_BIT - 1)) & 1; - buf <<= (mp_digit)1; - - /* if the bit is zero and mode == 0 then we ignore it - * These represent the leading zero bits before the first 1 bit - * in the exponent. Technically this opt is not required but it - * does lower the # of trivial squaring/reductions used - */ - if (mode == 0 && y == 0) { - continue; - } - - /* if the bit is zero and mode == 1 then we square */ - if (mode == 1 && y == 0) { - if ((err = mp_sqr (&res, &res)) != MP_OKAY) { - goto LBL_RES; + } + + /* now init the second half of the array */ + for (x = 1<<(winsize-1); x < (1 << winsize); x++) { + if ((err = mp_init(&M[x])) != MP_OKAY) { + for (y = 1<<(winsize-1); y < x; y++) { + mp_clear(&M[y]); + } + mp_clear(&M[1]); + return err; } - if ((err = redux (&res, P, &mu)) != MP_OKAY) { - goto LBL_RES; - } - continue; - } - - /* else we add it to the window */ - bitbuf |= (y << (winsize - ++bitcpy)); - mode = 2; - - if (bitcpy == winsize) { - /* ok window is filled so square as required and multiply */ - /* square first */ - for (x = 0; x < winsize; x++) { - if ((err = mp_sqr (&res, &res)) != MP_OKAY) { - goto LBL_RES; - } - if ((err = redux (&res, P, &mu)) != MP_OKAY) { - goto LBL_RES; - } + } + + /* create mu, used for Barrett reduction */ + if ((err = mp_init(&mu)) != MP_OKAY) goto LBL_M; + + if (redmode == 0) { + if ((err = mp_reduce_setup(&mu, P)) != MP_OKAY) goto LBL_MU; + redux = mp_reduce; + } else { + if ((err = mp_reduce_2k_setup_l(P, &mu)) != MP_OKAY) goto LBL_MU; + redux = mp_reduce_2k_l; + } + + /* create M table + * + * The M table contains powers of the base, + * e.g. M[x] = G**x mod P + * + * The first half of the table is not + * computed though accept for M[0] and M[1] + */ + if ((err = mp_mod(G, P, &M[1])) != MP_OKAY) goto LBL_MU; + + /* compute the value at M[1<<(winsize-1)] by squaring + * M[1] (winsize-1) times + */ + if ((err = mp_copy(&M[1], &M[(size_t)1 << (winsize - 1)])) != MP_OKAY) goto LBL_MU; + + for (x = 0; x < (winsize - 1); x++) { + /* square it */ + if ((err = mp_sqr(&M[(size_t)1 << (winsize - 1)], + &M[(size_t)1 << (winsize - 1)])) != MP_OKAY) goto LBL_MU; + + /* reduce modulo P */ + if ((err = redux(&M[(size_t)1 << (winsize - 1)], P, &mu)) != MP_OKAY) goto LBL_MU; + } + + /* create upper table, that is M[x] = M[x-1] * M[1] (mod P) + * for x = (2**(winsize - 1) + 1) to (2**winsize - 1) + */ + for (x = (1 << (winsize - 1)) + 1; x < (1 << winsize); x++) { + if ((err = mp_mul(&M[x - 1], &M[1], &M[x])) != MP_OKAY) goto LBL_MU; + if ((err = redux(&M[x], P, &mu)) != MP_OKAY) goto LBL_MU; + } + + /* setup result */ + if ((err = mp_init(&res)) != MP_OKAY) goto LBL_MU; + mp_set(&res, 1uL); + + /* set initial mode and bit cnt */ + mode = 0; + bitcnt = 1; + buf = 0; + digidx = X->used - 1; + bitcpy = 0; + bitbuf = 0; + + for (;;) { + /* grab next digit as required */ + if (--bitcnt == 0) { + /* if digidx == -1 we are out of digits */ + if (digidx == -1) { + break; + } + /* read next digit and reset the bitcnt */ + buf = X->dp[digidx--]; + bitcnt = (int)MP_DIGIT_BIT; } - /* then multiply */ - if ((err = mp_mul (&res, &M[bitbuf], &res)) != MP_OKAY) { - goto LBL_RES; - } - if ((err = redux (&res, P, &mu)) != MP_OKAY) { - goto LBL_RES; + /* grab the next msb from the exponent */ + y = (buf >> (mp_digit)(MP_DIGIT_BIT - 1)) & 1uL; + buf <<= (mp_digit)1; + + /* if the bit is zero and mode == 0 then we ignore it + * These represent the leading zero bits before the first 1 bit + * in the exponent. Technically this opt is not required but it + * does lower the # of trivial squaring/reductions used + */ + if ((mode == 0) && (y == 0)) { + continue; } - /* empty window and reset */ - bitcpy = 0; - bitbuf = 0; - mode = 1; - } - } - - /* if bits remain then square/multiply */ - if (mode == 2 && bitcpy > 0) { - /* square then multiply if the bit is set */ - for (x = 0; x < bitcpy; x++) { - if ((err = mp_sqr (&res, &res)) != MP_OKAY) { - goto LBL_RES; - } - if ((err = redux (&res, P, &mu)) != MP_OKAY) { - goto LBL_RES; + /* if the bit is zero and mode == 1 then we square */ + if ((mode == 1) && (y == 0)) { + if ((err = mp_sqr(&res, &res)) != MP_OKAY) goto LBL_RES; + if ((err = redux(&res, P, &mu)) != MP_OKAY) goto LBL_RES; + continue; } - bitbuf <<= 1; - if ((bitbuf & (1 << winsize)) != 0) { - /* then multiply */ - if ((err = mp_mul (&res, &M[1], &res)) != MP_OKAY) { - goto LBL_RES; - } - if ((err = redux (&res, P, &mu)) != MP_OKAY) { - goto LBL_RES; - } + /* else we add it to the window */ + bitbuf |= (y << (winsize - ++bitcpy)); + mode = 2; + + if (bitcpy == winsize) { + /* ok window is filled so square as required and multiply */ + /* square first */ + for (x = 0; x < winsize; x++) { + if ((err = mp_sqr(&res, &res)) != MP_OKAY) goto LBL_RES; + if ((err = redux(&res, P, &mu)) != MP_OKAY) goto LBL_RES; + } + + /* then multiply */ + if ((err = mp_mul(&res, &M[bitbuf], &res)) != MP_OKAY) goto LBL_RES; + if ((err = redux(&res, P, &mu)) != MP_OKAY) goto LBL_RES; + + /* empty window and reset */ + bitcpy = 0; + bitbuf = 0; + mode = 1; } - } - } - - mp_exch (&res, Y); - err = MP_OKAY; -LBL_RES:mp_clear (&res); -LBL_MU:mp_clear (&mu); + } + + /* if bits remain then square/multiply */ + if ((mode == 2) && (bitcpy > 0)) { + /* square then multiply if the bit is set */ + for (x = 0; x < bitcpy; x++) { + if ((err = mp_sqr(&res, &res)) != MP_OKAY) goto LBL_RES; + if ((err = redux(&res, P, &mu)) != MP_OKAY) goto LBL_RES; + + bitbuf <<= 1; + if ((bitbuf & (1 << winsize)) != 0) { + /* then multiply */ + if ((err = mp_mul(&res, &M[1], &res)) != MP_OKAY) goto LBL_RES; + if ((err = redux(&res, P, &mu)) != MP_OKAY) goto LBL_RES; + } + } + } + + mp_exch(&res, Y); + err = MP_OKAY; +LBL_RES: + mp_clear(&res); +LBL_MU: + mp_clear(&mu); LBL_M: - mp_clear(&M[1]); - for (x = 1<<(winsize-1); x < (1 << winsize); x++) { - mp_clear (&M[x]); - } - return err; + mp_clear(&M[1]); + for (x = 1<<(winsize-1); x < (1 << winsize); x++) { + mp_clear(&M[x]); + } + return err; } #endif - -/* $Source: /cvs/libtom/libtommath/bn_s_mp_exptmod.c,v $ */ -/* $Revision: 1.5 $ */ -/* $Date: 2006/12/28 01:25:13 $ */ diff --git a/lib/hcrypto/libtommath/bn_s_mp_exptmod_fast.c b/lib/hcrypto/libtommath/bn_s_mp_exptmod_fast.c new file mode 100644 index 000000000000..682ded84505e --- /dev/null +++ b/lib/hcrypto/libtommath/bn_s_mp_exptmod_fast.c @@ -0,0 +1,254 @@ +#include "tommath_private.h" +#ifdef BN_S_MP_EXPTMOD_FAST_C +/* LibTomMath, multiple-precision integer library -- Tom St Denis */ +/* SPDX-License-Identifier: Unlicense */ + +/* computes Y == G**X mod P, HAC pp.616, Algorithm 14.85 + * + * Uses a left-to-right k-ary sliding window to compute the modular exponentiation. + * The value of k changes based on the size of the exponent. + * + * Uses Montgomery or Diminished Radix reduction [whichever appropriate] + */ + +#ifdef MP_LOW_MEM +# define TAB_SIZE 32 +# define MAX_WINSIZE 5 +#else +# define TAB_SIZE 256 +# define MAX_WINSIZE 0 +#endif + +mp_err s_mp_exptmod_fast(const mp_int *G, const mp_int *X, const mp_int *P, mp_int *Y, int redmode) +{ + mp_int M[TAB_SIZE], res; + mp_digit buf, mp; + int bitbuf, bitcpy, bitcnt, mode, digidx, x, y, winsize; + mp_err err; + + /* use a pointer to the reduction algorithm. This allows us to use + * one of many reduction algorithms without modding the guts of + * the code with if statements everywhere. + */ + mp_err(*redux)(mp_int *x, const mp_int *n, mp_digit rho); + + /* find window size */ + x = mp_count_bits(X); + if (x <= 7) { + winsize = 2; + } else if (x <= 36) { + winsize = 3; + } else if (x <= 140) { + winsize = 4; + } else if (x <= 450) { + winsize = 5; + } else if (x <= 1303) { + winsize = 6; + } else if (x <= 3529) { + winsize = 7; + } else { + winsize = 8; + } + + winsize = MAX_WINSIZE ? MP_MIN(MAX_WINSIZE, winsize) : winsize; + + /* init M array */ + /* init first cell */ + if ((err = mp_init_size(&M[1], P->alloc)) != MP_OKAY) { + return err; + } + + /* now init the second half of the array */ + for (x = 1<<(winsize-1); x < (1 << winsize); x++) { + if ((err = mp_init_size(&M[x], P->alloc)) != MP_OKAY) { + for (y = 1<<(winsize-1); y < x; y++) { + mp_clear(&M[y]); + } + mp_clear(&M[1]); + return err; + } + } + + /* determine and setup reduction code */ + if (redmode == 0) { + if (MP_HAS(MP_MONTGOMERY_SETUP)) { + /* now setup montgomery */ + if ((err = mp_montgomery_setup(P, &mp)) != MP_OKAY) goto LBL_M; + } else { + err = MP_VAL; + goto LBL_M; + } + + /* automatically pick the comba one if available (saves quite a few calls/ifs) */ + if (MP_HAS(S_MP_MONTGOMERY_REDUCE_FAST) && + (((P->used * 2) + 1) < MP_WARRAY) && + (P->used < MP_MAXFAST)) { + redux = s_mp_montgomery_reduce_fast; + } else if (MP_HAS(MP_MONTGOMERY_REDUCE)) { + /* use slower baseline Montgomery method */ + redux = mp_montgomery_reduce; + } else { + err = MP_VAL; + goto LBL_M; + } + } else if (redmode == 1) { + if (MP_HAS(MP_DR_SETUP) && MP_HAS(MP_DR_REDUCE)) { + /* setup DR reduction for moduli of the form B**k - b */ + mp_dr_setup(P, &mp); + redux = mp_dr_reduce; + } else { + err = MP_VAL; + goto LBL_M; + } + } else if (MP_HAS(MP_REDUCE_2K_SETUP) && MP_HAS(MP_REDUCE_2K)) { + /* setup DR reduction for moduli of the form 2**k - b */ + if ((err = mp_reduce_2k_setup(P, &mp)) != MP_OKAY) goto LBL_M; + redux = mp_reduce_2k; + } else { + err = MP_VAL; + goto LBL_M; + } + + /* setup result */ + if ((err = mp_init_size(&res, P->alloc)) != MP_OKAY) goto LBL_M; + + /* create M table + * + + * + * The first half of the table is not computed though accept for M[0] and M[1] + */ + + if (redmode == 0) { + if (MP_HAS(MP_MONTGOMERY_CALC_NORMALIZATION)) { + /* now we need R mod m */ + if ((err = mp_montgomery_calc_normalization(&res, P)) != MP_OKAY) goto LBL_RES; + + /* now set M[1] to G * R mod m */ + if ((err = mp_mulmod(G, &res, P, &M[1])) != MP_OKAY) goto LBL_RES; + } else { + err = MP_VAL; + goto LBL_RES; + } + } else { + mp_set(&res, 1uL); + if ((err = mp_mod(G, P, &M[1])) != MP_OKAY) goto LBL_RES; + } + + /* compute the value at M[1<<(winsize-1)] by squaring M[1] (winsize-1) times */ + if ((err = mp_copy(&M[1], &M[(size_t)1 << (winsize - 1)])) != MP_OKAY) goto LBL_RES; + + for (x = 0; x < (winsize - 1); x++) { + if ((err = mp_sqr(&M[(size_t)1 << (winsize - 1)], &M[(size_t)1 << (winsize - 1)])) != MP_OKAY) goto LBL_RES; + if ((err = redux(&M[(size_t)1 << (winsize - 1)], P, mp)) != MP_OKAY) goto LBL_RES; + } + + /* create upper table */ + for (x = (1 << (winsize - 1)) + 1; x < (1 << winsize); x++) { + if ((err = mp_mul(&M[x - 1], &M[1], &M[x])) != MP_OKAY) goto LBL_RES; + if ((err = redux(&M[x], P, mp)) != MP_OKAY) goto LBL_RES; + } + + /* set initial mode and bit cnt */ + mode = 0; + bitcnt = 1; + buf = 0; + digidx = X->used - 1; + bitcpy = 0; + bitbuf = 0; + + for (;;) { + /* grab next digit as required */ + if (--bitcnt == 0) { + /* if digidx == -1 we are out of digits so break */ + if (digidx == -1) { + break; + } + /* read next digit and reset bitcnt */ + buf = X->dp[digidx--]; + bitcnt = (int)MP_DIGIT_BIT; + } + + /* grab the next msb from the exponent */ + y = (mp_digit)(buf >> (MP_DIGIT_BIT - 1)) & 1uL; + buf <<= (mp_digit)1; + + /* if the bit is zero and mode == 0 then we ignore it + * These represent the leading zero bits before the first 1 bit + * in the exponent. Technically this opt is not required but it + * does lower the # of trivial squaring/reductions used + */ + if ((mode == 0) && (y == 0)) { + continue; + } + + /* if the bit is zero and mode == 1 then we square */ + if ((mode == 1) && (y == 0)) { + if ((err = mp_sqr(&res, &res)) != MP_OKAY) goto LBL_RES; + if ((err = redux(&res, P, mp)) != MP_OKAY) goto LBL_RES; + continue; + } + + /* else we add it to the window */ + bitbuf |= (y << (winsize - ++bitcpy)); + mode = 2; + + if (bitcpy == winsize) { + /* ok window is filled so square as required and multiply */ + /* square first */ + for (x = 0; x < winsize; x++) { + if ((err = mp_sqr(&res, &res)) != MP_OKAY) goto LBL_RES; + if ((err = redux(&res, P, mp)) != MP_OKAY) goto LBL_RES; + } + + /* then multiply */ + if ((err = mp_mul(&res, &M[bitbuf], &res)) != MP_OKAY) goto LBL_RES; + if ((err = redux(&res, P, mp)) != MP_OKAY) goto LBL_RES; + + /* empty window and reset */ + bitcpy = 0; + bitbuf = 0; + mode = 1; + } + } + + /* if bits remain then square/multiply */ + if ((mode == 2) && (bitcpy > 0)) { + /* square then multiply if the bit is set */ + for (x = 0; x < bitcpy; x++) { + if ((err = mp_sqr(&res, &res)) != MP_OKAY) goto LBL_RES; + if ((err = redux(&res, P, mp)) != MP_OKAY) goto LBL_RES; + + /* get next bit of the window */ + bitbuf <<= 1; + if ((bitbuf & (1 << winsize)) != 0) { + /* then multiply */ + if ((err = mp_mul(&res, &M[1], &res)) != MP_OKAY) goto LBL_RES; + if ((err = redux(&res, P, mp)) != MP_OKAY) goto LBL_RES; + } + } + } + + if (redmode == 0) { + /* fixup result if Montgomery reduction is used + * recall that any value in a Montgomery system is + * actually multiplied by R mod n. So we have + * to reduce one more time to cancel out the factor + * of R. + */ + if ((err = redux(&res, P, mp)) != MP_OKAY) goto LBL_RES; + } + + /* swap res with Y */ + mp_exch(&res, Y); + err = MP_OKAY; +LBL_RES: + mp_clear(&res); +LBL_M: + mp_clear(&M[1]); + for (x = 1<<(winsize-1); x < (1 << winsize); x++) { + mp_clear(&M[x]); + } + return err; +} +#endif diff --git a/lib/hcrypto/libtommath/bn_s_mp_get_bit.c b/lib/hcrypto/libtommath/bn_s_mp_get_bit.c new file mode 100644 index 000000000000..28598dfec558 --- /dev/null +++ b/lib/hcrypto/libtommath/bn_s_mp_get_bit.c @@ -0,0 +1,21 @@ +#include "tommath_private.h" +#ifdef BN_S_MP_GET_BIT_C + +/* LibTomMath, multiple-precision integer library -- Tom St Denis */ +/* SPDX-License-Identifier: Unlicense */ + +/* Get bit at position b and return MP_YES if the bit is 1, MP_NO if it is 0 */ +mp_bool s_mp_get_bit(const mp_int *a, unsigned int b) +{ + mp_digit bit; + int limb = (int)(b / MP_DIGIT_BIT); + + if (limb >= a->used) { + return MP_NO; + } + + bit = (mp_digit)1 << (b % MP_DIGIT_BIT); + return ((a->dp[limb] & bit) != 0u) ? MP_YES : MP_NO; +} + +#endif diff --git a/lib/hcrypto/libtommath/bn_s_mp_invmod_fast.c b/lib/hcrypto/libtommath/bn_s_mp_invmod_fast.c new file mode 100644 index 000000000000..677d7ab696c6 --- /dev/null +++ b/lib/hcrypto/libtommath/bn_s_mp_invmod_fast.c @@ -0,0 +1,118 @@ +#include "tommath_private.h" +#ifdef BN_S_MP_INVMOD_FAST_C +/* LibTomMath, multiple-precision integer library -- Tom St Denis */ +/* SPDX-License-Identifier: Unlicense */ + +/* computes the modular inverse via binary extended euclidean algorithm, + * that is c = 1/a mod b + * + * Based on slow invmod except this is optimized for the case where b is + * odd as per HAC Note 14.64 on pp. 610 + */ +mp_err s_mp_invmod_fast(const mp_int *a, const mp_int *b, mp_int *c) +{ + mp_int x, y, u, v, B, D; + mp_sign neg; + mp_err err; + + /* 2. [modified] b must be odd */ + if (MP_IS_EVEN(b)) { + return MP_VAL; + } + + /* init all our temps */ + if ((err = mp_init_multi(&x, &y, &u, &v, &B, &D, NULL)) != MP_OKAY) { + return err; + } + + /* x == modulus, y == value to invert */ + if ((err = mp_copy(b, &x)) != MP_OKAY) goto LBL_ERR; + + /* we need y = |a| */ + if ((err = mp_mod(a, b, &y)) != MP_OKAY) goto LBL_ERR; + + /* if one of x,y is zero return an error! */ + if (MP_IS_ZERO(&x) || MP_IS_ZERO(&y)) { + err = MP_VAL; + goto LBL_ERR; + } + + /* 3. u=x, v=y, A=1, B=0, C=0,D=1 */ + if ((err = mp_copy(&x, &u)) != MP_OKAY) goto LBL_ERR; + if ((err = mp_copy(&y, &v)) != MP_OKAY) goto LBL_ERR; + mp_set(&D, 1uL); + +top: + /* 4. while u is even do */ + while (MP_IS_EVEN(&u)) { + /* 4.1 u = u/2 */ + if ((err = mp_div_2(&u, &u)) != MP_OKAY) goto LBL_ERR; + + /* 4.2 if B is odd then */ + if (MP_IS_ODD(&B)) { + if ((err = mp_sub(&B, &x, &B)) != MP_OKAY) goto LBL_ERR; + } + /* B = B/2 */ + if ((err = mp_div_2(&B, &B)) != MP_OKAY) goto LBL_ERR; + } + + /* 5. while v is even do */ + while (MP_IS_EVEN(&v)) { + /* 5.1 v = v/2 */ + if ((err = mp_div_2(&v, &v)) != MP_OKAY) goto LBL_ERR; + + /* 5.2 if D is odd then */ + if (MP_IS_ODD(&D)) { + /* D = (D-x)/2 */ + if ((err = mp_sub(&D, &x, &D)) != MP_OKAY) goto LBL_ERR; + } + /* D = D/2 */ + if ((err = mp_div_2(&D, &D)) != MP_OKAY) goto LBL_ERR; + } + + /* 6. if u >= v then */ + if (mp_cmp(&u, &v) != MP_LT) { + /* u = u - v, B = B - D */ + if ((err = mp_sub(&u, &v, &u)) != MP_OKAY) goto LBL_ERR; + + if ((err = mp_sub(&B, &D, &B)) != MP_OKAY) goto LBL_ERR; + } else { + /* v - v - u, D = D - B */ + if ((err = mp_sub(&v, &u, &v)) != MP_OKAY) goto LBL_ERR; + + if ((err = mp_sub(&D, &B, &D)) != MP_OKAY) goto LBL_ERR; + } + + /* if not zero goto step 4 */ + if (!MP_IS_ZERO(&u)) { + goto top; + } + + /* now a = C, b = D, gcd == g*v */ + + /* if v != 1 then there is no inverse */ + if (mp_cmp_d(&v, 1uL) != MP_EQ) { + err = MP_VAL; + goto LBL_ERR; + } + + /* b is now the inverse */ + neg = a->sign; + while (D.sign == MP_NEG) { + if ((err = mp_add(&D, b, &D)) != MP_OKAY) goto LBL_ERR; + } + + /* too big */ + while (mp_cmp_mag(&D, b) != MP_LT) { + if ((err = mp_sub(&D, b, &D)) != MP_OKAY) goto LBL_ERR; + } + + mp_exch(&D, c); + c->sign = neg; + err = MP_OKAY; + +LBL_ERR: + mp_clear_multi(&x, &y, &u, &v, &B, &D, NULL); + return err; +} +#endif diff --git a/lib/hcrypto/libtommath/bn_s_mp_invmod_slow.c b/lib/hcrypto/libtommath/bn_s_mp_invmod_slow.c new file mode 100644 index 000000000000..4c5db3300ba8 --- /dev/null +++ b/lib/hcrypto/libtommath/bn_s_mp_invmod_slow.c @@ -0,0 +1,119 @@ +#include "tommath_private.h" +#ifdef BN_S_MP_INVMOD_SLOW_C +/* LibTomMath, multiple-precision integer library -- Tom St Denis */ +/* SPDX-License-Identifier: Unlicense */ + +/* hac 14.61, pp608 */ +mp_err s_mp_invmod_slow(const mp_int *a, const mp_int *b, mp_int *c) +{ + mp_int x, y, u, v, A, B, C, D; + mp_err err; + + /* b cannot be negative */ + if ((b->sign == MP_NEG) || MP_IS_ZERO(b)) { + return MP_VAL; + } + + /* init temps */ + if ((err = mp_init_multi(&x, &y, &u, &v, + &A, &B, &C, &D, NULL)) != MP_OKAY) { + return err; + } + + /* x = a, y = b */ + if ((err = mp_mod(a, b, &x)) != MP_OKAY) goto LBL_ERR; + if ((err = mp_copy(b, &y)) != MP_OKAY) goto LBL_ERR; + + /* 2. [modified] if x,y are both even then return an error! */ + if (MP_IS_EVEN(&x) && MP_IS_EVEN(&y)) { + err = MP_VAL; + goto LBL_ERR; + } + + /* 3. u=x, v=y, A=1, B=0, C=0,D=1 */ + if ((err = mp_copy(&x, &u)) != MP_OKAY) goto LBL_ERR; + if ((err = mp_copy(&y, &v)) != MP_OKAY) goto LBL_ERR; + mp_set(&A, 1uL); + mp_set(&D, 1uL); + +top: + /* 4. while u is even do */ + while (MP_IS_EVEN(&u)) { + /* 4.1 u = u/2 */ + if ((err = mp_div_2(&u, &u)) != MP_OKAY) goto LBL_ERR; + + /* 4.2 if A or B is odd then */ + if (MP_IS_ODD(&A) || MP_IS_ODD(&B)) { + /* A = (A+y)/2, B = (B-x)/2 */ + if ((err = mp_add(&A, &y, &A)) != MP_OKAY) goto LBL_ERR; + if ((err = mp_sub(&B, &x, &B)) != MP_OKAY) goto LBL_ERR; + } + /* A = A/2, B = B/2 */ + if ((err = mp_div_2(&A, &A)) != MP_OKAY) goto LBL_ERR; + if ((err = mp_div_2(&B, &B)) != MP_OKAY) goto LBL_ERR; + } + + /* 5. while v is even do */ + while (MP_IS_EVEN(&v)) { + /* 5.1 v = v/2 */ + if ((err = mp_div_2(&v, &v)) != MP_OKAY) goto LBL_ERR; + + /* 5.2 if C or D is odd then */ + if (MP_IS_ODD(&C) || MP_IS_ODD(&D)) { + /* C = (C+y)/2, D = (D-x)/2 */ + if ((err = mp_add(&C, &y, &C)) != MP_OKAY) goto LBL_ERR; + if ((err = mp_sub(&D, &x, &D)) != MP_OKAY) goto LBL_ERR; + } + /* C = C/2, D = D/2 */ + if ((err = mp_div_2(&C, &C)) != MP_OKAY) goto LBL_ERR; + if ((err = mp_div_2(&D, &D)) != MP_OKAY) goto LBL_ERR; + } + + /* 6. if u >= v then */ + if (mp_cmp(&u, &v) != MP_LT) { + /* u = u - v, A = A - C, B = B - D */ + if ((err = mp_sub(&u, &v, &u)) != MP_OKAY) goto LBL_ERR; + + if ((err = mp_sub(&A, &C, &A)) != MP_OKAY) goto LBL_ERR; + + if ((err = mp_sub(&B, &D, &B)) != MP_OKAY) goto LBL_ERR; + } else { + /* v - v - u, C = C - A, D = D - B */ + if ((err = mp_sub(&v, &u, &v)) != MP_OKAY) goto LBL_ERR; + + if ((err = mp_sub(&C, &A, &C)) != MP_OKAY) goto LBL_ERR; + + if ((err = mp_sub(&D, &B, &D)) != MP_OKAY) goto LBL_ERR; + } + + /* if not zero goto step 4 */ + if (!MP_IS_ZERO(&u)) { + goto top; + } + + /* now a = C, b = D, gcd == g*v */ + + /* if v != 1 then there is no inverse */ + if (mp_cmp_d(&v, 1uL) != MP_EQ) { + err = MP_VAL; + goto LBL_ERR; + } + + /* if its too low */ + while (mp_cmp_d(&C, 0uL) == MP_LT) { + if ((err = mp_add(&C, b, &C)) != MP_OKAY) goto LBL_ERR; + } + + /* too big */ + while (mp_cmp_mag(&C, b) != MP_LT) { + if ((err = mp_sub(&C, b, &C)) != MP_OKAY) goto LBL_ERR; + } + + /* C is now the inverse */ + mp_exch(&C, c); + err = MP_OKAY; +LBL_ERR: + mp_clear_multi(&x, &y, &u, &v, &A, &B, &C, &D, NULL); + return err; +} +#endif diff --git a/lib/hcrypto/libtommath/bn_s_mp_karatsuba_mul.c b/lib/hcrypto/libtommath/bn_s_mp_karatsuba_mul.c new file mode 100644 index 000000000000..85899fb873e1 --- /dev/null +++ b/lib/hcrypto/libtommath/bn_s_mp_karatsuba_mul.c @@ -0,0 +1,174 @@ +#include "tommath_private.h" +#ifdef BN_S_MP_KARATSUBA_MUL_C +/* LibTomMath, multiple-precision integer library -- Tom St Denis */ +/* SPDX-License-Identifier: Unlicense */ + +/* c = |a| * |b| using Karatsuba Multiplication using + * three half size multiplications + * + * Let B represent the radix [e.g. 2**MP_DIGIT_BIT] and + * let n represent half of the number of digits in + * the min(a,b) + * + * a = a1 * B**n + a0 + * b = b1 * B**n + b0 + * + * Then, a * b => + a1b1 * B**2n + ((a1 + a0)(b1 + b0) - (a0b0 + a1b1)) * B + a0b0 + * + * Note that a1b1 and a0b0 are used twice and only need to be + * computed once. So in total three half size (half # of + * digit) multiplications are performed, a0b0, a1b1 and + * (a1+b1)(a0+b0) + * + * Note that a multiplication of half the digits requires + * 1/4th the number of single precision multiplications so in + * total after one call 25% of the single precision multiplications + * are saved. Note also that the call to mp_mul can end up back + * in this function if the a0, a1, b0, or b1 are above the threshold. + * This is known as divide-and-conquer and leads to the famous + * O(N**lg(3)) or O(N**1.584) work which is asymptopically lower than + * the standard O(N**2) that the baseline/comba methods use. + * Generally though the overhead of this method doesn't pay off + * until a certain size (N ~ 80) is reached. + */ +mp_err s_mp_karatsuba_mul(const mp_int *a, const mp_int *b, mp_int *c) +{ + mp_int x0, x1, y0, y1, t1, x0y0, x1y1; + int B; + mp_err err = MP_MEM; /* default the return code to an error */ + + /* min # of digits */ + B = MP_MIN(a->used, b->used); + + /* now divide in two */ + B = B >> 1; + + /* init copy all the temps */ + if (mp_init_size(&x0, B) != MP_OKAY) { + goto LBL_ERR; + } + if (mp_init_size(&x1, a->used - B) != MP_OKAY) { + goto X0; + } + if (mp_init_size(&y0, B) != MP_OKAY) { + goto X1; + } + if (mp_init_size(&y1, b->used - B) != MP_OKAY) { + goto Y0; + } + + /* init temps */ + if (mp_init_size(&t1, B * 2) != MP_OKAY) { + goto Y1; + } + if (mp_init_size(&x0y0, B * 2) != MP_OKAY) { + goto T1; + } + if (mp_init_size(&x1y1, B * 2) != MP_OKAY) { + goto X0Y0; + } + + /* now shift the digits */ + x0.used = y0.used = B; + x1.used = a->used - B; + y1.used = b->used - B; + + { + int x; + mp_digit *tmpa, *tmpb, *tmpx, *tmpy; + + /* we copy the digits directly instead of using higher level functions + * since we also need to shift the digits + */ + tmpa = a->dp; + tmpb = b->dp; + + tmpx = x0.dp; + tmpy = y0.dp; + for (x = 0; x < B; x++) { + *tmpx++ = *tmpa++; + *tmpy++ = *tmpb++; + } + + tmpx = x1.dp; + for (x = B; x < a->used; x++) { + *tmpx++ = *tmpa++; + } + + tmpy = y1.dp; + for (x = B; x < b->used; x++) { + *tmpy++ = *tmpb++; + } + } + + /* only need to clamp the lower words since by definition the + * upper words x1/y1 must have a known number of digits + */ + mp_clamp(&x0); + mp_clamp(&y0); + + /* now calc the products x0y0 and x1y1 */ + /* after this x0 is no longer required, free temp [x0==t2]! */ + if (mp_mul(&x0, &y0, &x0y0) != MP_OKAY) { + goto X1Y1; /* x0y0 = x0*y0 */ + } + if (mp_mul(&x1, &y1, &x1y1) != MP_OKAY) { + goto X1Y1; /* x1y1 = x1*y1 */ + } + + /* now calc x1+x0 and y1+y0 */ + if (s_mp_add(&x1, &x0, &t1) != MP_OKAY) { + goto X1Y1; /* t1 = x1 - x0 */ + } + if (s_mp_add(&y1, &y0, &x0) != MP_OKAY) { + goto X1Y1; /* t2 = y1 - y0 */ + } + if (mp_mul(&t1, &x0, &t1) != MP_OKAY) { + goto X1Y1; /* t1 = (x1 + x0) * (y1 + y0) */ + } + + /* add x0y0 */ + if (mp_add(&x0y0, &x1y1, &x0) != MP_OKAY) { + goto X1Y1; /* t2 = x0y0 + x1y1 */ + } + if (s_mp_sub(&t1, &x0, &t1) != MP_OKAY) { + goto X1Y1; /* t1 = (x1+x0)*(y1+y0) - (x1y1 + x0y0) */ + } + + /* shift by B */ + if (mp_lshd(&t1, B) != MP_OKAY) { + goto X1Y1; /* t1 = (x0y0 + x1y1 - (x1-x0)*(y1-y0))<<B */ + } + if (mp_lshd(&x1y1, B * 2) != MP_OKAY) { + goto X1Y1; /* x1y1 = x1y1 << 2*B */ + } + + if (mp_add(&x0y0, &t1, &t1) != MP_OKAY) { + goto X1Y1; /* t1 = x0y0 + t1 */ + } + if (mp_add(&t1, &x1y1, c) != MP_OKAY) { + goto X1Y1; /* t1 = x0y0 + t1 + x1y1 */ + } + + /* Algorithm succeeded set the return code to MP_OKAY */ + err = MP_OKAY; + +X1Y1: + mp_clear(&x1y1); +X0Y0: + mp_clear(&x0y0); +T1: + mp_clear(&t1); +Y1: + mp_clear(&y1); +Y0: + mp_clear(&y0); +X1: + mp_clear(&x1); +X0: + mp_clear(&x0); +LBL_ERR: + return err; +} +#endif diff --git a/lib/hcrypto/libtommath/bn_s_mp_karatsuba_sqr.c b/lib/hcrypto/libtommath/bn_s_mp_karatsuba_sqr.c new file mode 100644 index 000000000000..f132d071975e --- /dev/null +++ b/lib/hcrypto/libtommath/bn_s_mp_karatsuba_sqr.c @@ -0,0 +1,110 @@ +#include "tommath_private.h" +#ifdef BN_S_MP_KARATSUBA_SQR_C +/* LibTomMath, multiple-precision integer library -- Tom St Denis */ +/* SPDX-License-Identifier: Unlicense */ + +/* Karatsuba squaring, computes b = a*a using three + * half size squarings + * + * See comments of karatsuba_mul for details. It + * is essentially the same algorithm but merely + * tuned to perform recursive squarings. + */ +mp_err s_mp_karatsuba_sqr(const mp_int *a, mp_int *b) +{ + mp_int x0, x1, t1, t2, x0x0, x1x1; + int B; + mp_err err = MP_MEM; + + /* min # of digits */ + B = a->used; + + /* now divide in two */ + B = B >> 1; + + /* init copy all the temps */ + if (mp_init_size(&x0, B) != MP_OKAY) + goto LBL_ERR; + if (mp_init_size(&x1, a->used - B) != MP_OKAY) + goto X0; + + /* init temps */ + if (mp_init_size(&t1, a->used * 2) != MP_OKAY) + goto X1; + if (mp_init_size(&t2, a->used * 2) != MP_OKAY) + goto T1; + if (mp_init_size(&x0x0, B * 2) != MP_OKAY) + goto T2; + if (mp_init_size(&x1x1, (a->used - B) * 2) != MP_OKAY) + goto X0X0; + + { + int x; + mp_digit *dst, *src; + + src = a->dp; + + /* now shift the digits */ + dst = x0.dp; + for (x = 0; x < B; x++) { + *dst++ = *src++; + } + + dst = x1.dp; + for (x = B; x < a->used; x++) { + *dst++ = *src++; + } + } + + x0.used = B; + x1.used = a->used - B; + + mp_clamp(&x0); + + /* now calc the products x0*x0 and x1*x1 */ + if (mp_sqr(&x0, &x0x0) != MP_OKAY) + goto X1X1; /* x0x0 = x0*x0 */ + if (mp_sqr(&x1, &x1x1) != MP_OKAY) + goto X1X1; /* x1x1 = x1*x1 */ + + /* now calc (x1+x0)**2 */ + if (s_mp_add(&x1, &x0, &t1) != MP_OKAY) + goto X1X1; /* t1 = x1 - x0 */ + if (mp_sqr(&t1, &t1) != MP_OKAY) + goto X1X1; /* t1 = (x1 - x0) * (x1 - x0) */ + + /* add x0y0 */ + if (s_mp_add(&x0x0, &x1x1, &t2) != MP_OKAY) + goto X1X1; /* t2 = x0x0 + x1x1 */ + if (s_mp_sub(&t1, &t2, &t1) != MP_OKAY) + goto X1X1; /* t1 = (x1+x0)**2 - (x0x0 + x1x1) */ + + /* shift by B */ + if (mp_lshd(&t1, B) != MP_OKAY) + goto X1X1; /* t1 = (x0x0 + x1x1 - (x1-x0)*(x1-x0))<<B */ + if (mp_lshd(&x1x1, B * 2) != MP_OKAY) + goto X1X1; /* x1x1 = x1x1 << 2*B */ + + if (mp_add(&x0x0, &t1, &t1) != MP_OKAY) + goto X1X1; /* t1 = x0x0 + t1 */ + if (mp_add(&t1, &x1x1, b) != MP_OKAY) + goto X1X1; /* t1 = x0x0 + t1 + x1x1 */ + + err = MP_OKAY; + +X1X1: + mp_clear(&x1x1); +X0X0: + mp_clear(&x0x0); +T2: + mp_clear(&t2); +T1: + mp_clear(&t1); +X1: + mp_clear(&x1); +X0: + mp_clear(&x0); +LBL_ERR: + return err; +} +#endif diff --git a/lib/hcrypto/libtommath/bn_s_mp_montgomery_reduce_fast.c b/lib/hcrypto/libtommath/bn_s_mp_montgomery_reduce_fast.c new file mode 100644 index 000000000000..3f0c672ac868 --- /dev/null +++ b/lib/hcrypto/libtommath/bn_s_mp_montgomery_reduce_fast.c @@ -0,0 +1,159 @@ +#include "tommath_private.h" +#ifdef BN_S_MP_MONTGOMERY_REDUCE_FAST_C +/* LibTomMath, multiple-precision integer library -- Tom St Denis */ +/* SPDX-License-Identifier: Unlicense */ + +/* computes xR**-1 == x (mod N) via Montgomery Reduction + * + * This is an optimized implementation of montgomery_reduce + * which uses the comba method to quickly calculate the columns of the + * reduction. + * + * Based on Algorithm 14.32 on pp.601 of HAC. +*/ +mp_err s_mp_montgomery_reduce_fast(mp_int *x, const mp_int *n, mp_digit rho) +{ + int ix, olduse; + mp_err err; + mp_word W[MP_WARRAY]; + + if (x->used > MP_WARRAY) { + return MP_VAL; + } + + /* get old used count */ + olduse = x->used; + + /* grow a as required */ + if (x->alloc < (n->used + 1)) { + if ((err = mp_grow(x, n->used + 1)) != MP_OKAY) { + return err; + } + } + + /* first we have to get the digits of the input into + * an array of double precision words W[...] + */ + { + mp_word *_W; + mp_digit *tmpx; + + /* alias for the W[] array */ + _W = W; + + /* alias for the digits of x*/ + tmpx = x->dp; + + /* copy the digits of a into W[0..a->used-1] */ + for (ix = 0; ix < x->used; ix++) { + *_W++ = *tmpx++; + } + + /* zero the high words of W[a->used..m->used*2] */ + if (ix < ((n->used * 2) + 1)) { + MP_ZERO_BUFFER(_W, sizeof(mp_word) * (size_t)(((n->used * 2) + 1) - ix)); + } + } + + /* now we proceed to zero successive digits + * from the least significant upwards + */ + for (ix = 0; ix < n->used; ix++) { + /* mu = ai * m' mod b + * + * We avoid a double precision multiplication (which isn't required) + * by casting the value down to a mp_digit. Note this requires + * that W[ix-1] have the carry cleared (see after the inner loop) + */ + mp_digit mu; + mu = ((W[ix] & MP_MASK) * rho) & MP_MASK; + + /* a = a + mu * m * b**i + * + * This is computed in place and on the fly. The multiplication + * by b**i is handled by offseting which columns the results + * are added to. + * + * Note the comba method normally doesn't handle carries in the + * inner loop In this case we fix the carry from the previous + * column since the Montgomery reduction requires digits of the + * result (so far) [see above] to work. This is + * handled by fixing up one carry after the inner loop. The + * carry fixups are done in order so after these loops the + * first m->used words of W[] have the carries fixed + */ + { + int iy; + mp_digit *tmpn; + mp_word *_W; + + /* alias for the digits of the modulus */ + tmpn = n->dp; + + /* Alias for the columns set by an offset of ix */ + _W = W + ix; + + /* inner loop */ + for (iy = 0; iy < n->used; iy++) { + *_W++ += (mp_word)mu * (mp_word)*tmpn++; + } + } + + /* now fix carry for next digit, W[ix+1] */ + W[ix + 1] += W[ix] >> (mp_word)MP_DIGIT_BIT; + } + + /* now we have to propagate the carries and + * shift the words downward [all those least + * significant digits we zeroed]. + */ + { + mp_digit *tmpx; + mp_word *_W, *_W1; + + /* nox fix rest of carries */ + + /* alias for current word */ + _W1 = W + ix; + + /* alias for next word, where the carry goes */ + _W = W + ++ix; + + for (; ix < ((n->used * 2) + 1); ix++) { + *_W++ += *_W1++ >> (mp_word)MP_DIGIT_BIT; + } + + /* copy out, A = A/b**n + * + * The result is A/b**n but instead of converting from an + * array of mp_word to mp_digit than calling mp_rshd + * we just copy them in the right order + */ + + /* alias for destination word */ + tmpx = x->dp; + + /* alias for shifted double precision result */ + _W = W + n->used; + + for (ix = 0; ix < (n->used + 1); ix++) { + *tmpx++ = *_W++ & (mp_word)MP_MASK; + } + + /* zero oldused digits, if the input a was larger than + * m->used+1 we'll have to clear the digits + */ + MP_ZERO_DIGITS(tmpx, olduse - ix); + } + + /* set the max used and clamp */ + x->used = n->used + 1; + mp_clamp(x); + + /* if A >= m then A = A - m */ + if (mp_cmp_mag(x, n) != MP_LT) { + return s_mp_sub(x, n, x); + } + return MP_OKAY; +} +#endif diff --git a/lib/hcrypto/libtommath/bn_s_mp_mul_digs.c b/lib/hcrypto/libtommath/bn_s_mp_mul_digs.c index c5892181f9f1..64509d4cb931 100644 --- a/lib/hcrypto/libtommath/bn_s_mp_mul_digs.c +++ b/lib/hcrypto/libtommath/bn_s_mp_mul_digs.c @@ -1,90 +1,74 @@ -#include <tommath.h> +#include "tommath_private.h" #ifdef BN_S_MP_MUL_DIGS_C -/* LibTomMath, multiple-precision integer library -- Tom St Denis - * - * LibTomMath is a library that provides multiple-precision - * integer arithmetic as well as number theoretic functionality. - * - * The library was designed directly after the MPI library by - * Michael Fromberger but has been written from scratch with - * additional optimizations in place. - * - * The library is free for all purposes without any express - * guarantee it works. - * - * Tom St Denis, tomstdenis@gmail.com, http://libtom.org - */ +/* LibTomMath, multiple-precision integer library -- Tom St Denis */ +/* SPDX-License-Identifier: Unlicense */ /* multiplies |a| * |b| and only computes upto digs digits of result * HAC pp. 595, Algorithm 14.12 Modified so you can control how * many digits of output are created. */ -int s_mp_mul_digs (mp_int * a, mp_int * b, mp_int * c, int digs) +mp_err s_mp_mul_digs(const mp_int *a, const mp_int *b, mp_int *c, int digs) { - mp_int t; - int res, pa, pb, ix, iy; - mp_digit u; - mp_word r; - mp_digit tmpx, *tmpt, *tmpy; + mp_int t; + mp_err err; + int pa, pb, ix, iy; + mp_digit u; + mp_word r; + mp_digit tmpx, *tmpt, *tmpy; - /* can we use the fast multiplier? */ - if (((digs) < MP_WARRAY) && - MIN (a->used, b->used) < - (1 << ((CHAR_BIT * sizeof (mp_word)) - (2 * DIGIT_BIT)))) { - return fast_s_mp_mul_digs (a, b, c, digs); - } + /* can we use the fast multiplier? */ + if ((digs < MP_WARRAY) && + (MP_MIN(a->used, b->used) < MP_MAXFAST)) { + return s_mp_mul_digs_fast(a, b, c, digs); + } - if ((res = mp_init_size (&t, digs)) != MP_OKAY) { - return res; - } - t.used = digs; + if ((err = mp_init_size(&t, digs)) != MP_OKAY) { + return err; + } + t.used = digs; - /* compute the digits of the product directly */ - pa = a->used; - for (ix = 0; ix < pa; ix++) { - /* set the carry to zero */ - u = 0; + /* compute the digits of the product directly */ + pa = a->used; + for (ix = 0; ix < pa; ix++) { + /* set the carry to zero */ + u = 0; - /* limit ourselves to making digs digits of output */ - pb = MIN (b->used, digs - ix); + /* limit ourselves to making digs digits of output */ + pb = MP_MIN(b->used, digs - ix); - /* setup some aliases */ - /* copy of the digit from a used within the nested loop */ - tmpx = a->dp[ix]; + /* setup some aliases */ + /* copy of the digit from a used within the nested loop */ + tmpx = a->dp[ix]; - /* an alias for the destination shifted ix places */ - tmpt = t.dp + ix; + /* an alias for the destination shifted ix places */ + tmpt = t.dp + ix; - /* an alias for the digits of b */ - tmpy = b->dp; + /* an alias for the digits of b */ + tmpy = b->dp; - /* compute the columns of the output and propagate the carry */ - for (iy = 0; iy < pb; iy++) { - /* compute the column as a mp_word */ - r = ((mp_word)*tmpt) + - ((mp_word)tmpx) * ((mp_word)*tmpy++) + - ((mp_word) u); + /* compute the columns of the output and propagate the carry */ + for (iy = 0; iy < pb; iy++) { + /* compute the column as a mp_word */ + r = (mp_word)*tmpt + + ((mp_word)tmpx * (mp_word)*tmpy++) + + (mp_word)u; - /* the new column is the lower part of the result */ - *tmpt++ = (mp_digit) (r & ((mp_word) MP_MASK)); + /* the new column is the lower part of the result */ + *tmpt++ = (mp_digit)(r & (mp_word)MP_MASK); - /* get the carry word from the result */ - u = (mp_digit) (r >> ((mp_word) DIGIT_BIT)); - } - /* set carry if it is placed below digs */ - if (ix + iy < digs) { - *tmpt = u; - } - } + /* get the carry word from the result */ + u = (mp_digit)(r >> (mp_word)MP_DIGIT_BIT); + } + /* set carry if it is placed below digs */ + if ((ix + iy) < digs) { + *tmpt = u; + } + } - mp_clamp (&t); - mp_exch (&t, c); + mp_clamp(&t); + mp_exch(&t, c); - mp_clear (&t); - return MP_OKAY; + mp_clear(&t); + return MP_OKAY; } #endif - -/* $Source: /cvs/libtom/libtommath/bn_s_mp_mul_digs.c,v $ */ -/* $Revision: 1.4 $ */ -/* $Date: 2006/12/28 01:25:13 $ */ diff --git a/lib/hcrypto/libtommath/bn_s_mp_mul_digs_fast.c b/lib/hcrypto/libtommath/bn_s_mp_mul_digs_fast.c new file mode 100644 index 000000000000..b2a287b027b6 --- /dev/null +++ b/lib/hcrypto/libtommath/bn_s_mp_mul_digs_fast.c @@ -0,0 +1,90 @@ +#include "tommath_private.h" +#ifdef BN_S_MP_MUL_DIGS_FAST_C +/* LibTomMath, multiple-precision integer library -- Tom St Denis */ +/* SPDX-License-Identifier: Unlicense */ + +/* Fast (comba) multiplier + * + * This is the fast column-array [comba] multiplier. It is + * designed to compute the columns of the product first + * then handle the carries afterwards. This has the effect + * of making the nested loops that compute the columns very + * simple and schedulable on super-scalar processors. + * + * This has been modified to produce a variable number of + * digits of output so if say only a half-product is required + * you don't have to compute the upper half (a feature + * required for fast Barrett reduction). + * + * Based on Algorithm 14.12 on pp.595 of HAC. + * + */ +mp_err s_mp_mul_digs_fast(const mp_int *a, const mp_int *b, mp_int *c, int digs) +{ + int olduse, pa, ix, iz; + mp_err err; + mp_digit W[MP_WARRAY]; + mp_word _W; + + /* grow the destination as required */ + if (c->alloc < digs) { + if ((err = mp_grow(c, digs)) != MP_OKAY) { + return err; + } + } + + /* number of output digits to produce */ + pa = MP_MIN(digs, a->used + b->used); + + /* clear the carry */ + _W = 0; + for (ix = 0; ix < pa; ix++) { + int tx, ty; + int iy; + mp_digit *tmpx, *tmpy; + + /* get offsets into the two bignums */ + ty = MP_MIN(b->used-1, ix); + tx = ix - ty; + + /* setup temp aliases */ + tmpx = a->dp + tx; + tmpy = b->dp + ty; + + /* this is the number of times the loop will iterrate, essentially + while (tx++ < a->used && ty-- >= 0) { ... } + */ + iy = MP_MIN(a->used-tx, ty+1); + + /* execute loop */ + for (iz = 0; iz < iy; ++iz) { + _W += (mp_word)*tmpx++ * (mp_word)*tmpy--; + + } + + /* store term */ + W[ix] = (mp_digit)_W & MP_MASK; + + /* make next carry */ + _W = _W >> (mp_word)MP_DIGIT_BIT; + } + + /* setup dest */ + olduse = c->used; + c->used = pa; + + { + mp_digit *tmpc; + tmpc = c->dp; + for (ix = 0; ix < pa; ix++) { + /* now extract the previous digit [below the carry] */ + *tmpc++ = W[ix]; + } + + /* clear unused digits [that existed in the old copy of c] */ + MP_ZERO_DIGITS(tmpc, olduse - ix); + } + mp_clamp(c); + return MP_OKAY; +} +#endif diff --git a/lib/hcrypto/libtommath/bn_s_mp_mul_high_digs.c b/lib/hcrypto/libtommath/bn_s_mp_mul_high_digs.c index 2b718f23ccfc..2bb2a50985f8 100644 --- a/lib/hcrypto/libtommath/bn_s_mp_mul_high_digs.c +++ b/lib/hcrypto/libtommath/bn_s_mp_mul_high_digs.c @@ -1,81 +1,64 @@ -#include <tommath.h> +#include "tommath_private.h" #ifdef BN_S_MP_MUL_HIGH_DIGS_C -/* LibTomMath, multiple-precision integer library -- Tom St Denis - * - * LibTomMath is a library that provides multiple-precision - * integer arithmetic as well as number theoretic functionality. - * - * The library was designed directly after the MPI library by - * Michael Fromberger but has been written from scratch with - * additional optimizations in place. - * - * The library is free for all purposes without any express - * guarantee it works. - * - * Tom St Denis, tomstdenis@gmail.com, http://libtom.org - */ +/* LibTomMath, multiple-precision integer library -- Tom St Denis */ +/* SPDX-License-Identifier: Unlicense */ /* multiplies |a| * |b| and does not compute the lower digs digits * [meant to get the higher part of the product] */ -int -s_mp_mul_high_digs (mp_int * a, mp_int * b, mp_int * c, int digs) +mp_err s_mp_mul_high_digs(const mp_int *a, const mp_int *b, mp_int *c, int digs) { - mp_int t; - int res, pa, pb, ix, iy; - mp_digit u; - mp_word r; - mp_digit tmpx, *tmpt, *tmpy; + mp_int t; + int pa, pb, ix, iy; + mp_err err; + mp_digit u; + mp_word r; + mp_digit tmpx, *tmpt, *tmpy; - /* can we use the fast multiplier? */ -#ifdef BN_FAST_S_MP_MUL_HIGH_DIGS_C - if (((a->used + b->used + 1) < MP_WARRAY) - && MIN (a->used, b->used) < (1 << ((CHAR_BIT * sizeof (mp_word)) - (2 * DIGIT_BIT)))) { - return fast_s_mp_mul_high_digs (a, b, c, digs); - } -#endif + /* can we use the fast multiplier? */ + if (MP_HAS(S_MP_MUL_HIGH_DIGS_FAST) + && ((a->used + b->used + 1) < MP_WARRAY) + && (MP_MIN(a->used, b->used) < MP_MAXFAST)) { + return s_mp_mul_high_digs_fast(a, b, c, digs); + } - if ((res = mp_init_size (&t, a->used + b->used + 1)) != MP_OKAY) { - return res; - } - t.used = a->used + b->used + 1; + if ((err = mp_init_size(&t, a->used + b->used + 1)) != MP_OKAY) { + return err; + } + t.used = a->used + b->used + 1; - pa = a->used; - pb = b->used; - for (ix = 0; ix < pa; ix++) { - /* clear the carry */ - u = 0; + pa = a->used; + pb = b->used; + for (ix = 0; ix < pa; ix++) { + /* clear the carry */ + u = 0; - /* left hand side of A[ix] * B[iy] */ - tmpx = a->dp[ix]; + /* left hand side of A[ix] * B[iy] */ + tmpx = a->dp[ix]; - /* alias to the address of where the digits will be stored */ - tmpt = &(t.dp[digs]); + /* alias to the address of where the digits will be stored */ + tmpt = &(t.dp[digs]); - /* alias for where to read the right hand side from */ - tmpy = b->dp + (digs - ix); + /* alias for where to read the right hand side from */ + tmpy = b->dp + (digs - ix); - for (iy = digs - ix; iy < pb; iy++) { - /* calculate the double precision result */ - r = ((mp_word)*tmpt) + - ((mp_word)tmpx) * ((mp_word)*tmpy++) + - ((mp_word) u); + for (iy = digs - ix; iy < pb; iy++) { + /* calculate the double precision result */ + r = (mp_word)*tmpt + + ((mp_word)tmpx * (mp_word)*tmpy++) + + (mp_word)u; - /* get the lower part */ - *tmpt++ = (mp_digit) (r & ((mp_word) MP_MASK)); + /* get the lower part */ + *tmpt++ = (mp_digit)(r & (mp_word)MP_MASK); - /* carry the carry */ - u = (mp_digit) (r >> ((mp_word) DIGIT_BIT)); - } - *tmpt = u; - } - mp_clamp (&t); - mp_exch (&t, c); - mp_clear (&t); - return MP_OKAY; + /* carry the carry */ + u = (mp_digit)(r >> (mp_word)MP_DIGIT_BIT); + } + *tmpt = u; + } + mp_clamp(&t); + mp_exch(&t, c); + mp_clear(&t); + return MP_OKAY; } #endif - -/* $Source: /cvs/libtom/libtommath/bn_s_mp_mul_high_digs.c,v $ */ -/* $Revision: 1.4 $ */ -/* $Date: 2006/12/28 01:25:13 $ */ diff --git a/lib/hcrypto/libtommath/bn_s_mp_mul_high_digs_fast.c b/lib/hcrypto/libtommath/bn_s_mp_mul_high_digs_fast.c new file mode 100644 index 000000000000..a2c4fb6924a2 --- /dev/null +++ b/lib/hcrypto/libtommath/bn_s_mp_mul_high_digs_fast.c @@ -0,0 +1,81 @@ +#include "tommath_private.h" +#ifdef BN_S_MP_MUL_HIGH_DIGS_FAST_C +/* LibTomMath, multiple-precision integer library -- Tom St Denis */ +/* SPDX-License-Identifier: Unlicense */ + +/* this is a modified version of fast_s_mul_digs that only produces + * output digits *above* digs. See the comments for fast_s_mul_digs + * to see how it works. + * + * This is used in the Barrett reduction since for one of the multiplications + * only the higher digits were needed. This essentially halves the work. + * + * Based on Algorithm 14.12 on pp.595 of HAC. + */ +mp_err s_mp_mul_high_digs_fast(const mp_int *a, const mp_int *b, mp_int *c, int digs) +{ + int olduse, pa, ix, iz; + mp_err err; + mp_digit W[MP_WARRAY]; + mp_word _W; + + /* grow the destination as required */ + pa = a->used + b->used; + if (c->alloc < pa) { + if ((err = mp_grow(c, pa)) != MP_OKAY) { + return err; + } + } + + /* number of output digits to produce */ + pa = a->used + b->used; + _W = 0; + for (ix = digs; ix < pa; ix++) { + int tx, ty, iy; + mp_digit *tmpx, *tmpy; + + /* get offsets into the two bignums */ + ty = MP_MIN(b->used-1, ix); + tx = ix - ty; + + /* setup temp aliases */ + tmpx = a->dp + tx; + tmpy = b->dp + ty; + + /* this is the number of times the loop will iterrate, essentially its + while (tx++ < a->used && ty-- >= 0) { ... } + */ + iy = MP_MIN(a->used-tx, ty+1); + + /* execute loop */ + for (iz = 0; iz < iy; iz++) { + _W += (mp_word)*tmpx++ * (mp_word)*tmpy--; + } + + /* store term */ + W[ix] = (mp_digit)_W & MP_MASK; + + /* make next carry */ + _W = _W >> (mp_word)MP_DIGIT_BIT; + } + + /* setup dest */ + olduse = c->used; + c->used = pa; + + { + mp_digit *tmpc; + + tmpc = c->dp + digs; + for (ix = digs; ix < pa; ix++) { + /* now extract the previous digit [below the carry] */ + *tmpc++ = W[ix]; + } + + /* clear unused digits [that existed in the old copy of c] */ + MP_ZERO_DIGITS(tmpc, olduse - ix); + } + mp_clamp(c); + return MP_OKAY; +} +#endif diff --git a/lib/hcrypto/libtommath/bn_s_mp_prime_is_divisible.c b/lib/hcrypto/libtommath/bn_s_mp_prime_is_divisible.c new file mode 100644 index 000000000000..ffd5093e6e1e --- /dev/null +++ b/lib/hcrypto/libtommath/bn_s_mp_prime_is_divisible.c @@ -0,0 +1,35 @@ +#include "tommath_private.h" +#ifdef BN_S_MP_PRIME_IS_DIVISIBLE_C +/* LibTomMath, multiple-precision integer library -- Tom St Denis */ +/* SPDX-License-Identifier: Unlicense */ + +/* determines if an integers is divisible by one + * of the first PRIME_SIZE primes or not + * + * sets result to 0 if not, 1 if yes + */ +mp_err s_mp_prime_is_divisible(const mp_int *a, mp_bool *result) +{ + int ix; + mp_err err; + mp_digit res; + + /* default to not */ + *result = MP_NO; + + for (ix = 0; ix < PRIVATE_MP_PRIME_TAB_SIZE; ix++) { + /* what is a mod LBL_prime_tab[ix] */ + if ((err = mp_mod_d(a, s_mp_prime_tab[ix], &res)) != MP_OKAY) { + return err; + } + + /* is the residue zero? */ + if (res == 0u) { + *result = MP_YES; + return MP_OKAY; + } + } + + return MP_OKAY; +} +#endif diff --git a/lib/hcrypto/libtommath/bn_s_mp_rand_jenkins.c b/lib/hcrypto/libtommath/bn_s_mp_rand_jenkins.c new file mode 100644 index 000000000000..da0771c5f4c1 --- /dev/null +++ b/lib/hcrypto/libtommath/bn_s_mp_rand_jenkins.c @@ -0,0 +1,52 @@ +#include "tommath_private.h" +#ifdef BN_S_MP_RAND_JENKINS_C +/* LibTomMath, multiple-precision integer library -- Tom St Denis */ +/* SPDX-License-Identifier: Unlicense */ + +/* Bob Jenkins' http://burtleburtle.net/bob/rand/smallprng.html */ +/* Chosen for speed and a good "mix" */ +typedef struct { + uint64_t a; + uint64_t b; + uint64_t c; + uint64_t d; +} ranctx; + +static ranctx jenkins_x; + +#define rot(x,k) (((x)<<(k))|((x)>>(64-(k)))) +static uint64_t s_rand_jenkins_val(void) +{ + uint64_t e = jenkins_x.a - rot(jenkins_x.b, 7); + jenkins_x.a = jenkins_x.b ^ rot(jenkins_x.c, 13); + jenkins_x.b = jenkins_x.c + rot(jenkins_x.d, 37); + jenkins_x.c = jenkins_x.d + e; + jenkins_x.d = e + jenkins_x.a; + return jenkins_x.d; +} + +void s_mp_rand_jenkins_init(uint64_t seed) +{ + uint64_t i; + jenkins_x.a = 0xf1ea5eedULL; + jenkins_x.b = jenkins_x.c = jenkins_x.d = seed; + for (i = 0uLL; i < 20uLL; ++i) { + (void)s_rand_jenkins_val(); + } +} + +mp_err s_mp_rand_jenkins(void *p, size_t n) +{ + char *q = (char *)p; + while (n > 0u) { + int i; + uint64_t x = s_rand_jenkins_val(); + for (i = 0; (i < 8) && (n > 0u); ++i, --n) { + *q++ = (char)(x & 0xFFuLL); + x >>= 8; + } + } + return MP_OKAY; +} + +#endif diff --git a/lib/hcrypto/libtommath/bn_s_mp_rand_platform.c b/lib/hcrypto/libtommath/bn_s_mp_rand_platform.c new file mode 100644 index 000000000000..79879c35039a --- /dev/null +++ b/lib/hcrypto/libtommath/bn_s_mp_rand_platform.c @@ -0,0 +1,168 @@ +#include "tommath_private.h" +#ifdef BN_S_MP_RAND_PLATFORM_C +/* LibTomMath, multiple-precision integer library -- Tom St Denis */ +/* SPDX-License-Identifier: Unlicense */ + +/* First the OS-specific special cases + * - *BSD + * - Windows + */ +#if defined(__FreeBSD__) || defined(__OpenBSD__) || defined(__NetBSD__) || defined(__DragonFly__) +#define BN_S_READ_ARC4RANDOM_C +static mp_err s_read_arc4random(void *p, size_t n) +{ + arc4random_buf(p, n); + return MP_OKAY; +} +#endif + +#if defined(_WIN32) || defined(_WIN32_WCE) +#define BN_S_READ_WINCSP_C + +#ifndef _WIN32_WINNT +#define _WIN32_WINNT 0x0400 +#endif +#ifdef _WIN32_WCE +#define UNDER_CE +#define ARM +#endif + +#define WIN32_LEAN_AND_MEAN +#include <windows.h> +#include <wincrypt.h> + +static mp_err s_read_wincsp(void *p, size_t n) +{ + static HCRYPTPROV hProv = 0; + if (hProv == 0) { + HCRYPTPROV h = 0; + if (!CryptAcquireContext(&h, NULL, MS_DEF_PROV, PROV_RSA_FULL, + (CRYPT_VERIFYCONTEXT | CRYPT_MACHINE_KEYSET)) && + !CryptAcquireContext(&h, NULL, MS_DEF_PROV, PROV_RSA_FULL, + CRYPT_VERIFYCONTEXT | CRYPT_MACHINE_KEYSET | CRYPT_NEWKEYSET)) { + return MP_ERR; + } + hProv = h; + } + return CryptGenRandom(hProv, (DWORD)n, (BYTE *)p) == TRUE ? MP_OKAY : MP_ERR; +} +#endif /* WIN32 */ + +#if !defined(BN_S_READ_WINCSP_C) && defined(__linux__) && defined(__GLIBC_PREREQ) +#if __GLIBC_PREREQ(2, 25) +#define BN_S_READ_GETRANDOM_C +#include <sys/random.h> +#include <errno.h> + +static mp_err s_read_getrandom(void *p, size_t n) +{ + char *q = (char *)p; + while (n > 0u) { + ssize_t ret = getrandom(q, n, 0); + if (ret < 0) { + if (errno == EINTR) { + continue; + } + return MP_ERR; + } + q += ret; + n -= (size_t)ret; + } + return MP_OKAY; +} +#endif +#endif + +/* We assume all platforms besides windows provide "/dev/urandom". + * In case yours doesn't, define MP_NO_DEV_URANDOM at compile-time. + */ +#if !defined(BN_S_READ_WINCSP_C) && !defined(MP_NO_DEV_URANDOM) +#define BN_S_READ_URANDOM_C +#ifndef MP_DEV_URANDOM +#define MP_DEV_URANDOM "/dev/urandom" +#endif +#include <fcntl.h> +#include <errno.h> +#include <unistd.h> + +static mp_err s_read_urandom(void *p, size_t n) +{ + int fd; + char *q = (char *)p; + + do { + fd = open(MP_DEV_URANDOM, O_RDONLY); + } while ((fd == -1) && (errno == EINTR)); + if (fd == -1) return MP_ERR; + + while (n > 0u) { + ssize_t ret = read(fd, q, n); + if (ret < 0) { + if (errno == EINTR) { + continue; + } + close(fd); + return MP_ERR; + } + q += ret; + n -= (size_t)ret; + } + + close(fd); + return MP_OKAY; +} +#endif + +#if defined(MP_PRNG_ENABLE_LTM_RNG) +#define BN_S_READ_LTM_RNG +unsigned long (*ltm_rng)(unsigned char *out, unsigned long outlen, void (*callback)(void)); +void (*ltm_rng_callback)(void); + +static mp_err s_read_ltm_rng(void *p, size_t n) +{ + unsigned long res; + if (ltm_rng == NULL) return MP_ERR; + res = ltm_rng(p, n, ltm_rng_callback); + if (res != n) return MP_ERR; + return MP_OKAY; +} +#endif + +#ifdef BN_S_READ_ARC4RANDOM_C +mp_err s_read_arc4random(void *p, size_t n); +#endif +#ifdef BN_S_READ_WINCSP_C +mp_err s_read_wincsp(void *p, size_t n); +#endif +#ifdef BN_S_READ_GETRANDOM_C +mp_err s_read_getrandom(void *p, size_t n); +#endif +#ifdef BN_S_READ_URANDOM_C +mp_err s_read_urandom(void *p, size_t n); +#endif +#ifdef BN_S_READ_LTM_RNG +mp_err s_read_ltm_rng(void *p, size_t n); +#endif + +mp_err s_mp_rand_platform(void *p, size_t n) +{ + mp_err err = MP_ERR; +#ifdef BN_S_READ_ARC4RANDOM_C + if ((err != MP_OKAY) && MP_HAS(S_READ_ARC4RANDOM)) err = s_read_arc4random(p, n); +#endif +#ifdef BN_S_READ_WINCSP_C + if ((err != MP_OKAY) && MP_HAS(S_READ_WINCSP)) err = s_read_wincsp(p, n); +#endif +#ifdef BN_S_READ_GETRANDOM_C + if ((err != MP_OKAY) && MP_HAS(S_READ_GETRANDOM)) err = s_read_getrandom(p, n); +#endif +#ifdef BN_S_READ_URANDOM_C + if ((err != MP_OKAY) && MP_HAS(S_READ_URANDOM)) err = s_read_urandom(p, n); +#endif +#ifdef BN_S_READ_LTM_RNG + if ((err != MP_OKAY) && MP_HAS(S_READ_LTM_RNG)) err = s_read_ltm_rng(p, n); +#endif + return err; +} + +#endif diff --git a/lib/hcrypto/libtommath/bn_s_mp_reverse.c b/lib/hcrypto/libtommath/bn_s_mp_reverse.c new file mode 100644 index 000000000000..c549e605e717 --- /dev/null +++ b/lib/hcrypto/libtommath/bn_s_mp_reverse.c @@ -0,0 +1,22 @@ +#include "tommath_private.h" +#ifdef BN_S_MP_REVERSE_C +/* LibTomMath, multiple-precision integer library -- Tom St Denis */ +/* SPDX-License-Identifier: Unlicense */ + +/* reverse an array, used for radix code */ +void s_mp_reverse(unsigned char *s, size_t len) +{ + size_t ix, iy; + unsigned char t; + + ix = 0u; + iy = len - 1u; + while (ix < iy) { + t = s[ix]; + s[ix] = s[iy]; + s[iy] = t; + ++ix; + --iy; + } +} +#endif diff --git a/lib/hcrypto/libtommath/bn_s_mp_sqr.c b/lib/hcrypto/libtommath/bn_s_mp_sqr.c index c1c3826db5f5..505c9f0533f6 100644 --- a/lib/hcrypto/libtommath/bn_s_mp_sqr.c +++ b/lib/hcrypto/libtommath/bn_s_mp_sqr.c @@ -1,84 +1,69 @@ -#include <tommath.h> +#include "tommath_private.h" #ifdef BN_S_MP_SQR_C -/* LibTomMath, multiple-precision integer library -- Tom St Denis - * - * LibTomMath is a library that provides multiple-precision - * integer arithmetic as well as number theoretic functionality. - * - * The library was designed directly after the MPI library by - * Michael Fromberger but has been written from scratch with - * additional optimizations in place. - * - * The library is free for all purposes without any express - * guarantee it works. - * - * Tom St Denis, tomstdenis@gmail.com, http://libtom.org - */ +/* LibTomMath, multiple-precision integer library -- Tom St Denis */ +/* SPDX-License-Identifier: Unlicense */ /* low level squaring, b = a*a, HAC pp.596-597, Algorithm 14.16 */ -int s_mp_sqr (mp_int * a, mp_int * b) +mp_err s_mp_sqr(const mp_int *a, mp_int *b) { - mp_int t; - int res, ix, iy, pa; - mp_word r; - mp_digit u, tmpx, *tmpt; + mp_int t; + int ix, iy, pa; + mp_err err; + mp_word r; + mp_digit u, tmpx, *tmpt; - pa = a->used; - if ((res = mp_init_size (&t, 2*pa + 1)) != MP_OKAY) { - return res; - } + pa = a->used; + if ((err = mp_init_size(&t, (2 * pa) + 1)) != MP_OKAY) { + return err; + } - /* default used is maximum possible size */ - t.used = 2*pa + 1; + /* default used is maximum possible size */ + t.used = (2 * pa) + 1; - for (ix = 0; ix < pa; ix++) { - /* first calculate the digit at 2*ix */ - /* calculate double precision result */ - r = ((mp_word) t.dp[2*ix]) + - ((mp_word)a->dp[ix])*((mp_word)a->dp[ix]); + for (ix = 0; ix < pa; ix++) { + /* first calculate the digit at 2*ix */ + /* calculate double precision result */ + r = (mp_word)t.dp[2*ix] + + ((mp_word)a->dp[ix] * (mp_word)a->dp[ix]); - /* store lower part in result */ - t.dp[ix+ix] = (mp_digit) (r & ((mp_word) MP_MASK)); + /* store lower part in result */ + t.dp[ix+ix] = (mp_digit)(r & (mp_word)MP_MASK); - /* get the carry */ - u = (mp_digit)(r >> ((mp_word) DIGIT_BIT)); + /* get the carry */ + u = (mp_digit)(r >> (mp_word)MP_DIGIT_BIT); - /* left hand side of A[ix] * A[iy] */ - tmpx = a->dp[ix]; + /* left hand side of A[ix] * A[iy] */ + tmpx = a->dp[ix]; - /* alias for where to store the results */ - tmpt = t.dp + (2*ix + 1); + /* alias for where to store the results */ + tmpt = t.dp + ((2 * ix) + 1); - for (iy = ix + 1; iy < pa; iy++) { - /* first calculate the product */ - r = ((mp_word)tmpx) * ((mp_word)a->dp[iy]); + for (iy = ix + 1; iy < pa; iy++) { + /* first calculate the product */ + r = (mp_word)tmpx * (mp_word)a->dp[iy]; - /* now calculate the double precision result, note we use - * addition instead of *2 since it's easier to optimize - */ - r = ((mp_word) *tmpt) + r + r + ((mp_word) u); + /* now calculate the double precision result, note we use + * addition instead of *2 since it's easier to optimize + */ + r = (mp_word)*tmpt + r + r + (mp_word)u; - /* store lower part */ - *tmpt++ = (mp_digit) (r & ((mp_word) MP_MASK)); + /* store lower part */ + *tmpt++ = (mp_digit)(r & (mp_word)MP_MASK); - /* get carry */ - u = (mp_digit)(r >> ((mp_word) DIGIT_BIT)); - } - /* propagate upwards */ - while (u != ((mp_digit) 0)) { - r = ((mp_word) *tmpt) + ((mp_word) u); - *tmpt++ = (mp_digit) (r & ((mp_word) MP_MASK)); - u = (mp_digit)(r >> ((mp_word) DIGIT_BIT)); - } - } + /* get carry */ + u = (mp_digit)(r >> (mp_word)MP_DIGIT_BIT); + } + /* propagate upwards */ + while (u != 0uL) { + r = (mp_word)*tmpt + (mp_word)u; + *tmpt++ = (mp_digit)(r & (mp_word)MP_MASK); + u = (mp_digit)(r >> (mp_word)MP_DIGIT_BIT); + } + } - mp_clamp (&t); - mp_exch (&t, b); - mp_clear (&t); - return MP_OKAY; + mp_clamp(&t); + mp_exch(&t, b); + mp_clear(&t); + return MP_OKAY; } #endif - -/* $Source: /cvs/libtom/libtommath/bn_s_mp_sqr.c,v $ */ -/* $Revision: 1.4 $ */ -/* $Date: 2006/12/28 01:25:13 $ */ diff --git a/lib/hcrypto/libtommath/bn_s_mp_sqr_fast.c b/lib/hcrypto/libtommath/bn_s_mp_sqr_fast.c new file mode 100644 index 000000000000..4a8a8912f3fa --- /dev/null +++ b/lib/hcrypto/libtommath/bn_s_mp_sqr_fast.c @@ -0,0 +1,97 @@ +#include "tommath_private.h" +#ifdef BN_S_MP_SQR_FAST_C +/* LibTomMath, multiple-precision integer library -- Tom St Denis */ +/* SPDX-License-Identifier: Unlicense */ + +/* the jist of squaring... + * you do like mult except the offset of the tmpx [one that + * starts closer to zero] can't equal the offset of tmpy. + * So basically you set up iy like before then you min it with + * (ty-tx) so that it never happens. You double all those + * you add in the inner loop + +After that loop you do the squares and add them in. +*/ + +mp_err s_mp_sqr_fast(const mp_int *a, mp_int *b) +{ + int olduse, pa, ix, iz; + mp_digit W[MP_WARRAY], *tmpx; + mp_word W1; + mp_err err; + + /* grow the destination as required */ + pa = a->used + a->used; + if (b->alloc < pa) { + if ((err = mp_grow(b, pa)) != MP_OKAY) { + return err; + } + } + + /* number of output digits to produce */ + W1 = 0; + for (ix = 0; ix < pa; ix++) { + int tx, ty, iy; + mp_word _W; + mp_digit *tmpy; + + /* clear counter */ + _W = 0; + + /* get offsets into the two bignums */ + ty = MP_MIN(a->used-1, ix); + tx = ix - ty; + + /* setup temp aliases */ + tmpx = a->dp + tx; + tmpy = a->dp + ty; + + /* this is the number of times the loop will iterrate, essentially + while (tx++ < a->used && ty-- >= 0) { ... } + */ + iy = MP_MIN(a->used-tx, ty+1); + + /* now for squaring tx can never equal ty + * we halve the distance since they approach at a rate of 2x + * and we have to round because odd cases need to be executed + */ + iy = MP_MIN(iy, ((ty-tx)+1)>>1); + + /* execute loop */ + for (iz = 0; iz < iy; iz++) { + _W += (mp_word)*tmpx++ * (mp_word)*tmpy--; + } + + /* double the inner product and add carry */ + _W = _W + _W + W1; + + /* even columns have the square term in them */ + if (((unsigned)ix & 1u) == 0u) { + _W += (mp_word)a->dp[ix>>1] * (mp_word)a->dp[ix>>1]; + } + + /* store it */ + W[ix] = (mp_digit)_W & MP_MASK; + + /* make next carry */ + W1 = _W >> (mp_word)MP_DIGIT_BIT; + } + + /* setup dest */ + olduse = b->used; + b->used = a->used+a->used; + + { + mp_digit *tmpb; + tmpb = b->dp; + for (ix = 0; ix < pa; ix++) { + *tmpb++ = W[ix] & MP_MASK; + } + + /* clear unused digits [that existed in the old copy of c] */ + MP_ZERO_DIGITS(tmpb, olduse - ix); + } + mp_clamp(b); + return MP_OKAY; +} +#endif diff --git a/lib/hcrypto/libtommath/bn_s_mp_sub.c b/lib/hcrypto/libtommath/bn_s_mp_sub.c index 6a60c3932c44..5672dab51ede 100644 --- a/lib/hcrypto/libtommath/bn_s_mp_sub.c +++ b/lib/hcrypto/libtommath/bn_s_mp_sub.c @@ -1,89 +1,71 @@ -#include <tommath.h> +#include "tommath_private.h" #ifdef BN_S_MP_SUB_C -/* LibTomMath, multiple-precision integer library -- Tom St Denis - * - * LibTomMath is a library that provides multiple-precision - * integer arithmetic as well as number theoretic functionality. - * - * The library was designed directly after the MPI library by - * Michael Fromberger but has been written from scratch with - * additional optimizations in place. - * - * The library is free for all purposes without any express - * guarantee it works. - * - * Tom St Denis, tomstdenis@gmail.com, http://libtom.org - */ +/* LibTomMath, multiple-precision integer library -- Tom St Denis */ +/* SPDX-License-Identifier: Unlicense */ /* low level subtraction (assumes |a| > |b|), HAC pp.595 Algorithm 14.9 */ -int -s_mp_sub (mp_int * a, mp_int * b, mp_int * c) +mp_err s_mp_sub(const mp_int *a, const mp_int *b, mp_int *c) { - int olduse, res, min, max; + int olduse, min, max; + mp_err err; - /* find sizes */ - min = b->used; - max = a->used; + /* find sizes */ + min = b->used; + max = a->used; - /* init result */ - if (c->alloc < max) { - if ((res = mp_grow (c, max)) != MP_OKAY) { - return res; - } - } - olduse = c->used; - c->used = max; + /* init result */ + if (c->alloc < max) { + if ((err = mp_grow(c, max)) != MP_OKAY) { + return err; + } + } + olduse = c->used; + c->used = max; - { - register mp_digit u, *tmpa, *tmpb, *tmpc; - register int i; + { + mp_digit u, *tmpa, *tmpb, *tmpc; + int i; - /* alias for digit pointers */ - tmpa = a->dp; - tmpb = b->dp; - tmpc = c->dp; + /* alias for digit pointers */ + tmpa = a->dp; + tmpb = b->dp; + tmpc = c->dp; - /* set carry to zero */ - u = 0; - for (i = 0; i < min; i++) { - /* T[i] = A[i] - B[i] - U */ - *tmpc = *tmpa++ - *tmpb++ - u; + /* set carry to zero */ + u = 0; + for (i = 0; i < min; i++) { + /* T[i] = A[i] - B[i] - U */ + *tmpc = (*tmpa++ - *tmpb++) - u; - /* U = carry bit of T[i] - * Note this saves performing an AND operation since - * if a carry does occur it will propagate all the way to the - * MSB. As a result a single shift is enough to get the carry - */ - u = *tmpc >> ((mp_digit)(CHAR_BIT * sizeof (mp_digit) - 1)); + /* U = carry bit of T[i] + * Note this saves performing an AND operation since + * if a carry does occur it will propagate all the way to the + * MSB. As a result a single shift is enough to get the carry + */ + u = *tmpc >> (MP_SIZEOF_BITS(mp_digit) - 1u); - /* Clear carry from T[i] */ - *tmpc++ &= MP_MASK; - } + /* Clear carry from T[i] */ + *tmpc++ &= MP_MASK; + } - /* now copy higher words if any, e.g. if A has more digits than B */ - for (; i < max; i++) { - /* T[i] = A[i] - U */ - *tmpc = *tmpa++ - u; + /* now copy higher words if any, e.g. if A has more digits than B */ + for (; i < max; i++) { + /* T[i] = A[i] - U */ + *tmpc = *tmpa++ - u; - /* U = carry bit of T[i] */ - u = *tmpc >> ((mp_digit)(CHAR_BIT * sizeof (mp_digit) - 1)); + /* U = carry bit of T[i] */ + u = *tmpc >> (MP_SIZEOF_BITS(mp_digit) - 1u); - /* Clear carry from T[i] */ - *tmpc++ &= MP_MASK; - } + /* Clear carry from T[i] */ + *tmpc++ &= MP_MASK; + } - /* clear digits above used (since we may not have grown result above) */ - for (i = c->used; i < olduse; i++) { - *tmpc++ = 0; - } - } + /* clear digits above used (since we may not have grown result above) */ + MP_ZERO_DIGITS(tmpc, olduse - c->used); + } - mp_clamp (c); - return MP_OKAY; + mp_clamp(c); + return MP_OKAY; } #endif - -/* $Source: /cvs/libtom/libtommath/bn_s_mp_sub.c,v $ */ -/* $Revision: 1.4 $ */ -/* $Date: 2006/12/28 01:25:13 $ */ diff --git a/lib/hcrypto/libtommath/bn_s_mp_toom_mul.c b/lib/hcrypto/libtommath/bn_s_mp_toom_mul.c new file mode 100644 index 000000000000..86901b074c33 --- /dev/null +++ b/lib/hcrypto/libtommath/bn_s_mp_toom_mul.c @@ -0,0 +1,215 @@ +#include "tommath_private.h" +#ifdef BN_S_MP_TOOM_MUL_C +/* LibTomMath, multiple-precision integer library -- Tom St Denis */ +/* SPDX-License-Identifier: Unlicense */ + +/* multiplication using the Toom-Cook 3-way algorithm + * + * Much more complicated than Karatsuba but has a lower + * asymptotic running time of O(N**1.464). This algorithm is + * only particularly useful on VERY large inputs + * (we're talking 1000s of digits here...). +*/ + +/* + This file contains code from J. Arndt's book "Matters Computational" + and the accompanying FXT-library with permission of the author. +*/ + +/* + Setup from + + Chung, Jaewook, and M. Anwar Hasan. "Asymmetric squaring formulae." + 18th IEEE Symposium on Computer Arithmetic (ARITH'07). IEEE, 2007. + + The interpolation from above needed one temporary variable more + than the interpolation here: + + Bodrato, Marco, and Alberto Zanoni. "What about Toom-Cook matrices optimality." + Centro Vito Volterra Universita di Roma Tor Vergata (2006) +*/ + +mp_err s_mp_toom_mul(const mp_int *a, const mp_int *b, mp_int *c) +{ + mp_int S1, S2, T1, a0, a1, a2, b0, b1, b2; + int B, count; + mp_err err; + + /* init temps */ + if ((err = mp_init_multi(&S1, &S2, &T1, NULL)) != MP_OKAY) { + return err; + } + + /* B */ + B = MP_MIN(a->used, b->used) / 3; + + /** a = a2 * x^2 + a1 * x + a0; */ + if ((err = mp_init_size(&a0, B)) != MP_OKAY) goto LBL_ERRa0; + + for (count = 0; count < B; count++) { + a0.dp[count] = a->dp[count]; + a0.used++; + } + mp_clamp(&a0); + if ((err = mp_init_size(&a1, B)) != MP_OKAY) goto LBL_ERRa1; + for (; count < (2 * B); count++) { + a1.dp[count - B] = a->dp[count]; + a1.used++; + } + mp_clamp(&a1); + if ((err = mp_init_size(&a2, B + (a->used - (3 * B)))) != MP_OKAY) goto LBL_ERRa2; + for (; count < a->used; count++) { + a2.dp[count - (2 * B)] = a->dp[count]; + a2.used++; + } + mp_clamp(&a2); + + /** b = b2 * x^2 + b1 * x + b0; */ + if ((err = mp_init_size(&b0, B)) != MP_OKAY) goto LBL_ERRb0; + for (count = 0; count < B; count++) { + b0.dp[count] = b->dp[count]; + b0.used++; + } + mp_clamp(&b0); + if ((err = mp_init_size(&b1, B)) != MP_OKAY) goto LBL_ERRb1; + for (; count < (2 * B); count++) { + b1.dp[count - B] = b->dp[count]; + b1.used++; + } + mp_clamp(&b1); + if ((err = mp_init_size(&b2, B + (b->used - (3 * B)))) != MP_OKAY) goto LBL_ERRb2; + for (; count < b->used; count++) { + b2.dp[count - (2 * B)] = b->dp[count]; + b2.used++; + } + mp_clamp(&b2); + + /** \\ S1 = (a2+a1+a0) * (b2+b1+b0); */ + /** T1 = a2 + a1; */ + if ((err = mp_add(&a2, &a1, &T1)) != MP_OKAY) goto LBL_ERR; + + /** S2 = T1 + a0; */ + if ((err = mp_add(&T1, &a0, &S2)) != MP_OKAY) goto LBL_ERR; + + /** c = b2 + b1; */ + if ((err = mp_add(&b2, &b1, c)) != MP_OKAY) goto LBL_ERR; + + /** S1 = c + b0; */ + if ((err = mp_add(c, &b0, &S1)) != MP_OKAY) goto LBL_ERR; + + /** S1 = S1 * S2; */ + if ((err = mp_mul(&S1, &S2, &S1)) != MP_OKAY) goto LBL_ERR; + + /** \\S2 = (4*a2+2*a1+a0) * (4*b2+2*b1+b0); */ + /** T1 = T1 + a2; */ + if ((err = mp_add(&T1, &a2, &T1)) != MP_OKAY) goto LBL_ERR; + + /** T1 = T1 << 1; */ + if ((err = mp_mul_2(&T1, &T1)) != MP_OKAY) goto LBL_ERR; + + /** T1 = T1 + a0; */ + if ((err = mp_add(&T1, &a0, &T1)) != MP_OKAY) goto LBL_ERR; + + /** c = c + b2; */ + if ((err = mp_add(c, &b2, c)) != MP_OKAY) goto LBL_ERR; + + /** c = c << 1; */ + if ((err = mp_mul_2(c, c)) != MP_OKAY) goto LBL_ERR; + + /** c = c + b0; */ + if ((err = mp_add(c, &b0, c)) != MP_OKAY) goto LBL_ERR; + + /** S2 = T1 * c; */ + if ((err = mp_mul(&T1, c, &S2)) != MP_OKAY) goto LBL_ERR; + + /** \\S3 = (a2-a1+a0) * (b2-b1+b0); */ + /** a1 = a2 - a1; */ + if ((err = mp_sub(&a2, &a1, &a1)) != MP_OKAY) goto LBL_ERR; + + /** a1 = a1 + a0; */ + if ((err = mp_add(&a1, &a0, &a1)) != MP_OKAY) goto LBL_ERR; + + /** b1 = b2 - b1; */ + if ((err = mp_sub(&b2, &b1, &b1)) != MP_OKAY) goto LBL_ERR; + + /** b1 = b1 + b0; */ + if ((err = mp_add(&b1, &b0, &b1)) != MP_OKAY) goto LBL_ERR; + + /** a1 = a1 * b1; */ + if ((err = mp_mul(&a1, &b1, &a1)) != MP_OKAY) goto LBL_ERR; + + /** b1 = a2 * b2; */ + if ((err = mp_mul(&a2, &b2, &b1)) != MP_OKAY) goto LBL_ERR; + + /** \\S2 = (S2 - S3)/3; */ + /** S2 = S2 - a1; */ + if ((err = mp_sub(&S2, &a1, &S2)) != MP_OKAY) goto LBL_ERR; + + /** S2 = S2 / 3; \\ this is an exact division */ + if ((err = mp_div_3(&S2, &S2, NULL)) != MP_OKAY) goto LBL_ERR; + + /** a1 = S1 - a1; */ + if ((err = mp_sub(&S1, &a1, &a1)) != MP_OKAY) goto LBL_ERR; + + /** a1 = a1 >> 1; */ + if ((err = mp_div_2(&a1, &a1)) != MP_OKAY) goto LBL_ERR; + + /** a0 = a0 * b0; */ + if ((err = mp_mul(&a0, &b0, &a0)) != MP_OKAY) goto LBL_ERR; + + /** S1 = S1 - a0; */ + if ((err = mp_sub(&S1, &a0, &S1)) != MP_OKAY) goto LBL_ERR; + + /** S2 = S2 - S1; */ + if ((err = mp_sub(&S2, &S1, &S2)) != MP_OKAY) goto LBL_ERR; + + /** S2 = S2 >> 1; */ + if ((err = mp_div_2(&S2, &S2)) != MP_OKAY) goto LBL_ERR; + + /** S1 = S1 - a1; */ + if ((err = mp_sub(&S1, &a1, &S1)) != MP_OKAY) goto LBL_ERR; + + /** S1 = S1 - b1; */ + if ((err = mp_sub(&S1, &b1, &S1)) != MP_OKAY) goto LBL_ERR; + + /** T1 = b1 << 1; */ + if ((err = mp_mul_2(&b1, &T1)) != MP_OKAY) goto LBL_ERR; + + /** S2 = S2 - T1; */ + if ((err = mp_sub(&S2, &T1, &S2)) != MP_OKAY) goto LBL_ERR; + + /** a1 = a1 - S2; */ + if ((err = mp_sub(&a1, &S2, &a1)) != MP_OKAY) goto LBL_ERR; + + + /** P = b1*x^4+ S2*x^3+ S1*x^2+ a1*x + a0; */ + if ((err = mp_lshd(&b1, 4 * B)) != MP_OKAY) goto LBL_ERR; + if ((err = mp_lshd(&S2, 3 * B)) != MP_OKAY) goto LBL_ERR; + if ((err = mp_add(&b1, &S2, &b1)) != MP_OKAY) goto LBL_ERR; + if ((err = mp_lshd(&S1, 2 * B)) != MP_OKAY) goto LBL_ERR; + if ((err = mp_add(&b1, &S1, &b1)) != MP_OKAY) goto LBL_ERR; + if ((err = mp_lshd(&a1, 1 * B)) != MP_OKAY) goto LBL_ERR; + if ((err = mp_add(&b1, &a1, &b1)) != MP_OKAY) goto LBL_ERR; + if ((err = mp_add(&b1, &a0, c)) != MP_OKAY) goto LBL_ERR; + + /** a * b - P */ + + +LBL_ERR: + mp_clear(&b2); +LBL_ERRb2: + mp_clear(&b1); +LBL_ERRb1: + mp_clear(&b0); +LBL_ERRb0: + mp_clear(&a2); +LBL_ERRa2: + mp_clear(&a1); +LBL_ERRa1: + mp_clear(&a0); +LBL_ERRa0: + mp_clear_multi(&S1, &S2, &T1, NULL); + return err; +} + +#endif diff --git a/lib/hcrypto/libtommath/bn_s_mp_toom_sqr.c b/lib/hcrypto/libtommath/bn_s_mp_toom_sqr.c new file mode 100644 index 000000000000..f2ffb30c2985 --- /dev/null +++ b/lib/hcrypto/libtommath/bn_s_mp_toom_sqr.c @@ -0,0 +1,147 @@ +#include "tommath_private.h" +#ifdef BN_S_MP_TOOM_SQR_C +/* LibTomMath, multiple-precision integer library -- Tom St Denis */ +/* SPDX-License-Identifier: Unlicense */ + +/* squaring using Toom-Cook 3-way algorithm */ + +/* + This file contains code from J. Arndt's book "Matters Computational" + and the accompanying FXT-library with permission of the author. +*/ + +/* squaring using Toom-Cook 3-way algorithm */ +/* + Setup and interpolation from algorithm SQR_3 in + + Chung, Jaewook, and M. Anwar Hasan. "Asymmetric squaring formulae." + 18th IEEE Symposium on Computer Arithmetic (ARITH'07). IEEE, 2007. + +*/ +mp_err s_mp_toom_sqr(const mp_int *a, mp_int *b) +{ + mp_int S0, a0, a1, a2; + mp_digit *tmpa, *tmpc; + int B, count; + mp_err err; + + + /* init temps */ + if ((err = mp_init(&S0)) != MP_OKAY) { + return err; + } + + /* B */ + B = a->used / 3; + + /** a = a2 * x^2 + a1 * x + a0; */ + if ((err = mp_init_size(&a0, B)) != MP_OKAY) goto LBL_ERRa0; + + a0.used = B; + if ((err = mp_init_size(&a1, B)) != MP_OKAY) goto LBL_ERRa1; + a1.used = B; + if ((err = mp_init_size(&a2, B + (a->used - (3 * B)))) != MP_OKAY) goto LBL_ERRa2; + + tmpa = a->dp; + tmpc = a0.dp; + for (count = 0; count < B; count++) { + *tmpc++ = *tmpa++; + } + tmpc = a1.dp; + for (; count < (2 * B); count++) { + *tmpc++ = *tmpa++; + } + tmpc = a2.dp; + for (; count < a->used; count++) { + *tmpc++ = *tmpa++; + a2.used++; + } + mp_clamp(&a0); + mp_clamp(&a1); + mp_clamp(&a2); + + /** S0 = a0^2; */ + if ((err = mp_sqr(&a0, &S0)) != MP_OKAY) goto LBL_ERR; + + /** \\S1 = (a2 + a1 + a0)^2 */ + /** \\S2 = (a2 - a1 + a0)^2 */ + /** \\S1 = a0 + a2; */ + /** a0 = a0 + a2; */ + if ((err = mp_add(&a0, &a2, &a0)) != MP_OKAY) goto LBL_ERR; + /** \\S2 = S1 - a1; */ + /** b = a0 - a1; */ + if ((err = mp_sub(&a0, &a1, b)) != MP_OKAY) goto LBL_ERR; + /** \\S1 = S1 + a1; */ + /** a0 = a0 + a1; */ + if ((err = mp_add(&a0, &a1, &a0)) != MP_OKAY) goto LBL_ERR; + /** \\S1 = S1^2; */ + /** a0 = a0^2; */ + if ((err = mp_sqr(&a0, &a0)) != MP_OKAY) goto LBL_ERR; + /** \\S2 = S2^2; */ + /** b = b^2; */ + if ((err = mp_sqr(b, b)) != MP_OKAY) goto LBL_ERR; + + /** \\ S3 = 2 * a1 * a2 */ + /** \\S3 = a1 * a2; */ + /** a1 = a1 * a2; */ + if ((err = mp_mul(&a1, &a2, &a1)) != MP_OKAY) goto LBL_ERR; + /** \\S3 = S3 << 1; */ + /** a1 = a1 << 1; */ + if ((err = mp_mul_2(&a1, &a1)) != MP_OKAY) goto LBL_ERR; + + /** \\S4 = a2^2; */ + /** a2 = a2^2; */ + if ((err = mp_sqr(&a2, &a2)) != MP_OKAY) goto LBL_ERR; + + /** \\ tmp = (S1 + S2)/2 */ + /** \\tmp = S1 + S2; */ + /** b = a0 + b; */ + if ((err = mp_add(&a0, b, b)) != MP_OKAY) goto LBL_ERR; + /** \\tmp = tmp >> 1; */ + /** b = b >> 1; */ + if ((err = mp_div_2(b, b)) != MP_OKAY) goto LBL_ERR; + + /** \\ S1 = S1 - tmp - S3 */ + /** \\S1 = S1 - tmp; */ + /** a0 = a0 - b; */ + if ((err = mp_sub(&a0, b, &a0)) != MP_OKAY) goto LBL_ERR; + /** \\S1 = S1 - S3; */ + /** a0 = a0 - a1; */ + if ((err = mp_sub(&a0, &a1, &a0)) != MP_OKAY) goto LBL_ERR; + + /** \\S2 = tmp - S4 -S0 */ + /** \\S2 = tmp - S4; */ + /** b = b - a2; */ + if ((err = mp_sub(b, &a2, b)) != MP_OKAY) goto LBL_ERR; + /** \\S2 = S2 - S0; */ + /** b = b - S0; */ + if ((err = mp_sub(b, &S0, b)) != MP_OKAY) goto LBL_ERR; + + + /** \\P = S4*x^4 + S3*x^3 + S2*x^2 + S1*x + S0; */ + /** P = a2*x^4 + a1*x^3 + b*x^2 + a0*x + S0; */ + + if ((err = mp_lshd(&a2, 4 * B)) != MP_OKAY) goto LBL_ERR; + if ((err = mp_lshd(&a1, 3 * B)) != MP_OKAY) goto LBL_ERR; + if ((err = mp_lshd(b, 2 * B)) != MP_OKAY) goto LBL_ERR; + if ((err = mp_lshd(&a0, 1 * B)) != MP_OKAY) goto LBL_ERR; + if ((err = mp_add(&a2, &a1, &a2)) != MP_OKAY) goto LBL_ERR; + if ((err = mp_add(&a2, b, b)) != MP_OKAY) goto LBL_ERR; + if ((err = mp_add(b, &a0, b)) != MP_OKAY) goto LBL_ERR; + if ((err = mp_add(b, &S0, b)) != MP_OKAY) goto LBL_ERR; + /** a^2 - P */ + + +LBL_ERR: + mp_clear(&a2); +LBL_ERRa2: + mp_clear(&a1); +LBL_ERRa1: + mp_clear(&a0); +LBL_ERRa0: + mp_clear(&S0); + + return err; +} + +#endif diff --git a/lib/hcrypto/libtommath/bncore.c b/lib/hcrypto/libtommath/bncore.c deleted file mode 100644 index 919e3b33b02e..000000000000 --- a/lib/hcrypto/libtommath/bncore.c +++ /dev/null @@ -1,36 +0,0 @@ -#include <tommath.h> -#ifdef BNCORE_C -/* LibTomMath, multiple-precision integer library -- Tom St Denis - * - * LibTomMath is a library that provides multiple-precision - * integer arithmetic as well as number theoretic functionality. - * - * The library was designed directly after the MPI library by - * Michael Fromberger but has been written from scratch with - * additional optimizations in place. - * - * The library is free for all purposes without any express - * guarantee it works. - * - * Tom St Denis, tomstdenis@gmail.com, http://libtom.org - */ - -/* Known optimal configurations - - CPU /Compiler /MUL CUTOFF/SQR CUTOFF -------------------------------------------------------------- - Intel P4 Northwood /GCC v3.4.1 / 88/ 128/LTM 0.32 ;-) - AMD Athlon64 /GCC v3.4.4 / 80/ 120/LTM 0.35 - -*/ - -int KARATSUBA_MUL_CUTOFF = 80, /* Min. number of digits before Karatsuba multiplication is used. */ - KARATSUBA_SQR_CUTOFF = 120, /* Min. number of digits before Karatsuba squaring is used. */ - - TOOM_MUL_CUTOFF = 350, /* no optimal values of these are known yet so set em high */ - TOOM_SQR_CUTOFF = 400; -#endif - -/* $Source: /cvs/libtom/libtommath/bncore.c,v $ */ -/* $Revision: 1.5 $ */ -/* $Date: 2006/12/28 01:25:13 $ */ diff --git a/lib/hcrypto/libtommath/changes.txt b/lib/hcrypto/libtommath/changes.txt new file mode 100644 index 000000000000..ebf7382a0837 --- /dev/null +++ b/lib/hcrypto/libtommath/changes.txt @@ -0,0 +1,497 @@ +XXX XXth, 2019 +v1.2.0 + -- A huge refactoring of the library happened - renaming, + deprecating and replacing existing functions by improved API's. + + All deprecated functions, macros and symbols are only marked as such + so this version is still API and ABI compatible to v1.x. + + -- Daniel Mendler was pushing for those changes and contributing a load of patches, + refactorings, code reviews and whatnotelse. + -- Christoph Zurnieden re-worked internals of the library, improved the performance, + did code reviews and wrote documentation. + -- Francois Perrad did some refactoring and took again care of linting the sources and + provided all fixes. + -- Jan Nijtmans, Karel Miko and Joachim Breitner contributed various patches. + + -- Private symbols can now be hidden for the shared library builds, disabled by default. + -- All API's follow a single code style, are prefixed the same etc. + -- Unified, safer and improved API's + -- Less magic numbers - return values (where appropriate) and most flags are now enums, + this was implemented in a backwards compatible way where return values were int. + -- API's with return values are now by default marked as "warn on unsused result", this + can be disabled if required (which will most likely hide bugs), c.f. MP_WUR in tommath.h + -- Provide a whole set of setters&getters for different primitive types (long, uint32_t, etc.) + -- All those primitive setters are now optimized. + -- It's possible to automatically tune the cutoff values for Karatsuba&Toom-Cook + -- The custom allocators which were formerly known as XMALLOC(), XFREE() etc. are now available + as MP_MALLOC(), MP_REALLOC(), MP_CALLOC() and MP_FREE(). MP_REALLOC() and MP_FREE() now also + provide the allocated size to ease the usage of simple allocators without tracking. + -- Building is now also possible with MSVC 2015, 2017 and 2019 (use makefile.msvc) + -- Added mp_decr() and mp_incr() + -- Added mp_log_u32() + -- Improved prime-checking + -- Improved Toom-Cook multiplication + -- Removed the LTM book (`make docs` now builds the user manual) + + +Jan 28th, 2019 +v1.1.0 + -- Christoph Zurnieden contributed FIPS 186.4 compliant + prime-checking (PR #113), several other fixes and a load of documentation + -- Daniel Mendler provided two's-complement functions (PR #124) + and mp_{set,get}_double() (PR #123) + -- Francois Perrad took care of linting the sources, provided all fixes and + a astylerc to auto-format the sources. + -- A bunch of patches by Kevin B Kenny have been back-ported from TCL + -- Jan Nijtmans provided the patches to `const`ify all API + function arguments (also from TCL) + -- mp_rand() has now several native random provider implementations + and doesn't rely on `rand()` anymore + -- Karel Miko provided fixes when building for MS Windows + and re-worked the makefile generating process + -- The entire environment and build logic has been extended and improved + regarding auto-detection of platforms, libtool and a lot more + -- Prevent some potential BOF cases + -- Improved/fixed mp_lshd() and mp_invmod() + -- A load more bugs were fixed by various contributors + + +Aug 29th, 2017 +v1.0.1 + -- Dmitry Kovalenko provided fixes to mp_add_d() and mp_init_copy() + -- Matt Johnston contributed some improvements to mp_div_2d(), + mp_exptmod_fast(), mp_mod() and mp_mulmod() + -- Julien Nabet provided a fix to the error handling in mp_init_multi() + -- Ben Gardner provided a fix regarding usage of reserved keywords + -- Fixed mp_rand() to fill the correct number of bits + -- Fixed mp_invmod() + -- Use the same 64-bit detection code as in libtomcrypt + -- Correct usage of DESTDIR, PREFIX, etc. when installing the library + -- Francois Perrad updated all the perl scripts to an actual perl version + + +Feb 5th, 2016 +v1.0 + -- Bump to 1.0 + -- Dirkjan Bussink provided a faster version of mp_expt_d() + -- Moritz Lenz contributed a fix to mp_mod() + and provided mp_get_long() and mp_set_long() + -- Fixed bugs in mp_read_radix(), mp_radix_size + Thanks to shameister, Gerhard R, + -- Christopher Brown provided mp_export() and mp_import() + -- Improvements in the code of mp_init_copy() + Thanks to ramkumarkoppu, + -- lomereiter provided mp_balance_mul() + -- Alexander Boström from the heimdal project contributed patches to + mp_prime_next_prime() and mp_invmod() and added a mp_isneg() macro + -- Fix build issues for Linux x32 ABI + -- Added mp_get_long_long() and mp_set_long_long() + -- Carlin provided a patch to use arc4random() instead of rand() + on platforms where it is supported + -- Karel Miko provided mp_sqrtmod_prime() + + +July 23rd, 2010 +v0.42.0 + -- Fix for mp_prime_next_prime() bug when checking generated prime + -- allow mp_shrink to shrink initialized, but empty MPI's + -- Added project and solution files for Visual Studio 2005 and Visual Studio 2008. + +March 10th, 2007 +v0.41 -- Wolfgang Ehrhardt suggested a quick fix to mp_div_d() which makes the detection of powers of two quicker. + -- [CRI] Added libtommath.dsp for Visual C++ users. + +December 24th, 2006 +v0.40 -- Updated makefile to properly support LIBNAME + -- Fixed bug in fast_s_mp_mul_high_digs() which overflowed (line 83), thanks Valgrind! + +April 4th, 2006 +v0.39 -- Jim Wigginton pointed out my Montgomery examples in figures 6.4 and 6.6 were off by one, k should be 9 not 8 + -- Bruce Guenter suggested I use --tag=CC for libtool builds where the compiler may think it's C++. + -- "mm" from sci.crypt pointed out that my mp_gcd was sub-optimal (I also updated and corrected the book) + -- updated some of the @@ tags in tommath.src to reflect source changes. + -- updated email and url info in all source files + +Jan 26th, 2006 +v0.38 -- broken makefile.shared fixed + -- removed some carry stores that were not required [updated text] + +November 18th, 2005 +v0.37 -- [Don Porter] reported on a TCL list [HEY SEND ME BUGREPORTS ALREADY!!!] that mp_add_d() would compute -0 with some inputs. Fixed. + -- [rinick@gmail.com] reported the makefile.bcc was messed up. Fixed. + -- [Kevin Kenny] reported some issues with mp_toradix_n(). Now it doesn't require a min of 3 chars of output. + -- Made the make command renamable. Wee + +August 1st, 2005 +v0.36 -- LTM_PRIME_2MSB_ON was fixed and the "OFF" flag was removed. + -- [Peter LaDow] found a typo in the XREALLOC macro + -- [Peter LaDow] pointed out that mp_read_(un)signed_bin should have "const" on the input + -- Ported LTC patch to fix the prime_random_ex() function to get the bitsize correct [and the maskOR flags] + -- Kevin Kenny pointed out a stray // + -- David Hulton pointed out a typo in the textbook [mp_montgomery_setup() pseudo-code] + -- Neal Hamilton (Elliptic Semiconductor) pointed out that my Karatsuba notation was backwards and that I could use + unsigned operations in the routine. + -- Paul Schmidt pointed out a linking error in mp_exptmod() when BN_S_MP_EXPTMOD_C is undefined (and another for read_radix) + -- Updated makefiles to be way more flexible + +March 12th, 2005 +v0.35 -- Stupid XOR function missing line again... oops. + -- Fixed bug in invmod not handling negative inputs correctly [Wolfgang Ehrhardt] + -- Made exteuclid always give positive u3 output...[ Wolfgang Ehrhardt ] + -- [Wolfgang Ehrhardt] Suggested a fix for mp_reduce() which avoided underruns. ;-) + -- mp_rand() would emit one too many digits and it was possible to get a 0 out of it ... oops + -- Added montgomery to the testing to make sure it handles 1..10 digit moduli correctly + -- Fixed bug in comba that would lead to possible erroneous outputs when "pa < digs" + -- Fixed bug in mp_toradix_size for "0" [Kevin Kenny] + -- Updated chapters 1-5 of the textbook ;-) It now talks about the new comba code! + +February 12th, 2005 +v0.34 -- Fixed two more small errors in mp_prime_random_ex() + -- Fixed overflow in mp_mul_d() [Kevin Kenny] + -- Added mp_to_(un)signed_bin_n() functions which do bounds checking for ya [and report the size] + -- Added "large" diminished radix support. Speeds up things like DSA where the moduli is of the form 2^k - P for some P < 2^(k/2) or so + Actually is faster than Montgomery on my AMD64 (and probably much faster on a P4) + -- Updated the manual a bit + -- Ok so I haven't done the textbook work yet... My current freelance gig has landed me in France till the + end of Feb/05. Once I get back I'll have tons of free time and I plan to go to town on the book. + As of this release the API will freeze. At least until the book catches up with all the changes. I welcome + bug reports but new algorithms will have to wait. + +December 23rd, 2004 +v0.33 -- Fixed "small" variant for mp_div() which would munge with negative dividends... + -- Fixed bug in mp_prime_random_ex() which would set the most significant byte to zero when + no special flags were set + -- Fixed overflow [minor] bug in fast_s_mp_sqr() + -- Made the makefiles easier to configure the group/user that ltm will install as + -- Fixed "final carry" bug in comba multipliers. (Volkan Ceylan) + -- Matt Johnston pointed out a missing semi-colon in mp_exptmod + +October 29th, 2004 +v0.32 -- Added "makefile.shared" for shared object support + -- Added more to the build options/configs in the manual + -- Started the Depends framework, wrote dep.pl to scan deps and + produce "callgraph.txt" ;-) + -- Wrote SC_RSA_1 which will enable close to the minimum required to perform + RSA on 32-bit [or 64-bit] platforms with LibTomCrypt + -- Merged in the small/slower mp_div replacement. You can now toggle which + you want to use as your mp_div() at build time. Saves roughly 8KB or so. + -- Renamed a few files and changed some comments to make depends system work better. + (No changes to function names) + -- Merged in new Combas that perform 2 reads per inner loop instead of the older + 3reads/2writes per inner loop of the old code. Really though if you want speed + learn to use TomsFastMath ;-) + +August 9th, 2004 +v0.31 -- "profiled" builds now :-) new timings for Intel Northwoods + -- Added "pretty" build target + -- Update mp_init() to actually assign 0's instead of relying on calloc() + -- "Wolfgang Ehrhardt" <Wolfgang.Ehrhardt@munich.netsurf.de> found a bug in mp_mul() where if + you multiply a negative by zero you get negative zero as the result. Oops. + -- J Harper from PeerSec let me toy with his AMD64 and I got 60-bit digits working properly + [this also means that I fixed a bug where if sizeof(int) < sizeof(mp_digit) it would bug] + +April 11th, 2004 +v0.30 -- Added "mp_toradix_n" which stores upto "n-1" least significant digits of an mp_int + -- Johan Lindh sent a patch so MSVC wouldn't whine about redefining malloc [in weird dll modes] + -- Henrik Goldman spotted a missing OPT_CAST in mp_fwrite() + -- Tuned tommath.h so that when MP_LOW_MEM is defined MP_PREC shall be reduced. + [I also allow MP_PREC to be externally defined now] + -- Sped up mp_cnt_lsb() by using a 4x4 table [e.g. 4x speedup] + -- Added mp_prime_random_ex() which is a more versatile prime generator accurate to + exact bit lengths (unlike the deprecated but still available mp_prime_random() which + is only accurate to byte lengths). See the new LTM_PRIME_* flags ;-) + -- Alex Polushin contributed an optimized mp_sqrt() as well as mp_get_int() and mp_is_square(). + I've cleaned them all up to be a little more consistent [along with one bug fix] for this release. + -- Added mp_init_set and mp_init_set_int to initialize and set small constants with one function + call. + -- Removed /etclib directory [um LibTomPoly deprecates this]. + -- Fixed mp_mod() so the sign of the result agrees with the sign of the modulus. + ++ N.B. My semester is almost up so expect updates to the textbook to be posted to the libtomcrypt.org + website. + +Jan 25th, 2004 +v0.29 ++ Note: "Henrik" from the v0.28 changelog refers to Henrik Goldman ;-) + -- Added fix to mp_shrink to prevent a realloc when used == 0 [e.g. realloc zero bytes???] + -- Made the mp_prime_rabin_miller_trials() function internal table smaller and also + set the minimum number of tests to two (sounds a bit safer). + -- Added a mp_exteuclid() which computes the extended euclidean algorithm. + -- Fixed a memory leak in s_mp_exptmod() [called when Barrett reduction is to be used] which would arise + if a multiplication or subsequent reduction failed [would not free the temp result]. + -- Made an API change to mp_radix_size(). It now returns an error code and stores the required size + through an "int star" passed to it. + +Dec 24th, 2003 +v0.28 -- Henrik Goldman suggested I add casts to the montomgery code [stores into mu...] so compilers wouldn't + spew [erroneous] diagnostics... fixed. + -- Henrik Goldman also spotted two typos. One in mp_radix_size() and another in mp_toradix(). + -- Added fix to mp_shrink() to avoid a memory leak. + -- Added mp_prime_random() which requires a callback to make truly random primes of a given nature + (idea from chat with Niels Ferguson at Crypto'03) + -- Picked up a second wind. I'm filled with Gooo. Mission Gooo! + -- Removed divisions from mp_reduce_is_2k() + -- Sped up mp_div_d() [general case] to use only one division per digit instead of two. + -- Added the heap macros from LTC to LTM. Now you can easily [by editing four lines of tommath.h] + change the name of the heap functions used in LTM [also compatible with LTC via MPI mode] + -- Added bn_prime_rabin_miller_trials() which gives the number of Rabin-Miller trials to achieve + a failure rate of less than 2^-96 + -- fixed bug in fast_mp_invmod(). The initial testing logic was wrong. An invalid input is not when + "a" and "b" are even it's when "b" is even [the algo is for odd moduli only]. + -- Started a new manual [finally]. It is incomplete and will be finished as time goes on. I had to stop + adding full demos around half way in chapter three so I could at least get a good portion of the + manual done. If you really need help using the library you can always email me! + -- My Textbook is now included as part of the package [all Public Domain] + +Sept 19th, 2003 +v0.27 -- Removed changes.txt~ which was made by accident since "kate" decided it was + a good time to re-enable backups... [kde is fun!] + -- In mp_grow() "a->dp" is not overwritten by realloc call [re: memory leak] + Now if mp_grow() fails the mp_int is still valid and can be cleared via + mp_clear() to reclaim the memory. + -- Henrik Goldman found a buffer overflow bug in mp_add_d(). Fixed. + -- Cleaned up mp_mul_d() to be much easier to read and follow. + +Aug 29th, 2003 +v0.26 -- Fixed typo that caused warning with GCC 3.2 + -- Martin Marcel noticed a bug in mp_neg() that allowed negative zeroes. + Also, Martin is the fellow who noted the bugs in mp_gcd() of 0.24/0.25. + -- Martin Marcel noticed an optimization [and slight bug] in mp_lcm(). + -- Added fix to mp_read_unsigned_bin to prevent a buffer overflow. + -- Beefed up the comments in the baseline multipliers [and montgomery] + -- Added "mont" demo to the makefile.msvc in etc/ + -- Optimized sign compares in mp_cmp from 4 to 2 cases. + +Aug 4th, 2003 +v0.25 -- Fix to mp_gcd again... oops (0,-a) == (-a, 0) == a + -- Fix to mp_clear which didn't reset the sign [Greg Rose] + -- Added mp_error_to_string() to convert return codes to strings. [Greg Rose] + -- Optimized fast_mp_invmod() to do the test for invalid inputs [both even] + first so temps don't have to be initialized if it's going to fail. + -- Optimized mp_gcd() by removing mp_div_2d calls for when one of the inputs + is odd. + -- Tons of new comments, some indentation fixups, etc. + -- mp_jacobi() returns MP_VAL if the modulus is less than or equal to zero. + -- fixed two typos in the header of each file :-) + -- LibTomMath is officially Public Domain [see LICENSE] + +July 15th, 2003 +v0.24 -- Optimized mp_add_d and mp_sub_d to not allocate temporary variables + -- Fixed mp_gcd() so the gcd of 0,0 is 0. Allows the gcd operation to be chained + e.g. (0,0,a) == a [instead of 1] + -- Should be one of the last release for a while. Working on LibTomMath book now. + -- optimized the pprime demo [/etc/pprime.c] to first make a huge table of single + digit primes then it reads them randomly instead of randomly choosing/testing single + digit primes. + +July 12th, 2003 +v0.23 -- Optimized mp_prime_next_prime() to not use mp_mod [via is_divisible()] in each + iteration. Instead now a smaller table is kept of the residues which can be updated + without division. + -- Fixed a bug in next_prime() where an input of zero would be treated as odd and + have two added to it [to move to the next odd]. + -- fixed a bug in prime_fermat() and prime_miller_rabin() which allowed the base + to be negative, zero or one. Normally the test is only valid if the base is + greater than one. + -- changed the next_prime() prototype to accept a new parameter "bbs_style" which + will find the next prime congruent to 3 mod 4. The default [bbs_style==0] will + make primes which are either congruent to 1 or 3 mod 4. + -- fixed mp_read_unsigned_bin() so that it doesn't include both code for + the case DIGIT_BIT < 8 and >= 8 + -- optimized div_d() to easy out on division by 1 [or if a == 0] and use + logical shifts if the divisor is a power of two. + -- the default DIGIT_BIT type was not int for non-default builds. Fixed. + +July 2nd, 2003 +v0.22 -- Fixed up mp_invmod so the result is properly in range now [was always congruent to the inverse...] + -- Fixed up s_mp_exptmod and mp_exptmod_fast so the lower half of the pre-computed table isn't allocated + which makes the algorithm use half as much ram. + -- Fixed the install script not to make the book :-) [which isn't included anyways] + -- added mp_cnt_lsb() which counts how many of the lsbs are zero + -- optimized mp_gcd() to use the new mp_cnt_lsb() to replace multiple divisions by two by a single division. + -- applied similar optimization to mp_prime_miller_rabin(). + -- Fixed a bug in both mp_invmod() and fast_mp_invmod() which tested for odd + via "mp_iseven() == 0" which is not valid [since zero is not even either]. + +June 19th, 2003 +v0.21 -- Fixed bug in mp_mul_d which would not handle sign correctly [would not always forward it] + -- Removed the #line lines from gen.pl [was in violation of ISO C] + +June 8th, 2003 +v0.20 -- Removed the book from the package. Added the TDCAL license document. + -- This release is officially pure-bred TDCAL again [last officially TDCAL based release was v0.16] + +June 6th, 2003 +v0.19 -- Fixed a bug in mp_montgomery_reduce() which was introduced when I tweaked mp_rshd() in the previous release. + Essentially the digits were not trimmed before the compare which cause a subtraction to occur all the time. + -- Fixed up etc/tune.c a bit to stop testing new cutoffs after 16 failures [to find more optimal points]. + Brute force ho! + + +May 29th, 2003 +v0.18 -- Fixed a bug in s_mp_sqr which would handle carries properly just not very elegantly. + (e.g. correct result, just bad looking code) + -- Fixed bug in mp_sqr which still had a 512 constant instead of MP_WARRAY + -- Added Toom-Cook multipliers [needs tuning!] + -- Added efficient divide by 3 algorithm mp_div_3 + -- Re-wrote mp_div_d to be faster than calling mp_div + -- Added in a donated BCC makefile and a single page LTM poster (ahalhabsi@sbcglobal.net) + -- Added mp_reduce_2k which reduces an input modulo n = 2**p - k for any single digit k + -- Made the exptmod system be aware of the 2k reduction algorithms. + -- Rewrote mp_dr_reduce to be smaller, simpler and easier to understand. + +May 17th, 2003 +v0.17 -- Benjamin Goldberg submitted optimized mp_add and mp_sub routines. A new gen.pl as well + as several smaller suggestions. Thanks! + -- removed call to mp_cmp in inner loop of mp_div and put mp_cmp_mag in its place :-) + -- Fixed bug in mp_exptmod that would cause it to fail for odd moduli when DIGIT_BIT != 28 + -- mp_exptmod now also returns errors if the modulus is negative and will handle negative exponents + -- mp_prime_is_prime will now return true if the input is one of the primes in the prime table + -- Damian M Gryski (dgryski@uwaterloo.ca) found a index out of bounds error in the + mp_fast_s_mp_mul_high_digs function which didn't come up before. (fixed) + -- Refactored the DR reduction code so there is only one function per file. + -- Fixed bug in the mp_mul() which would erroneously avoid the faster multiplier [comba] when it was + allowed. The bug would not cause the incorrect value to be produced just less efficient (fixed) + -- Fixed similar bug in the Montgomery reduction code. + -- Added tons of (mp_digit) casts so the 7/15/28/31 bit digit code will work flawlessly out of the box. + Also added limited support for 64-bit machines with a 60-bit digit. Both thanks to Tom Wu (tom@arcot.com) + -- Added new comments here and there, cleaned up some code [style stuff] + -- Fixed a lingering typo in mp_exptmod* that would set bitcnt to zero then one. Very silly stuff :-) + -- Fixed up mp_exptmod_fast so it would set "redux" to the comba Montgomery reduction if allowed. This + saves quite a few calls and if statements. + -- Added etc/mont.c a test of the Montgomery reduction [assuming all else works :-| ] + -- Fixed up etc/tune.c to use a wider test range [more appropriate] also added a x86 based addition which + uses RDTSC for high precision timing. + -- Updated demo/demo.c to remove MPI stuff [won't work anyways], made the tests run for 2 seconds each so its + not so insanely slow. Also made the output space delimited [and fixed up various errors] + -- Added logs directory, logs/graph.dem which will use gnuplot to make a series of PNG files + that go with the pre-made index.html. You have to build [via make timing] and run ltmtest first in the + root of the package. + -- Fixed a bug in mp_sub and mp_add where "-a - -a" or "-a + a" would produce -0 as the result [obviously invalid]. + -- Fixed a bug in mp_rshd. If the count == a.used it should zero/return [instead of shifting] + -- Fixed a "off-by-one" bug in mp_mul2d. The initial size check on alloc would be off by one if the residue + shifting caused a carry. + -- Fixed a bug where s_mp_mul_digs() would not call the Comba based routine if allowed. This made Barrett reduction + slower than it had to be. + +Mar 29th, 2003 +v0.16 -- Sped up mp_div by making normalization one shift call + -- Sped up mp_mul_2d/mp_div_2d by aliasing pointers :-) + -- Cleaned up mp_gcd to use the macros for odd/even detection + -- Added comments here and there, mostly there but occasionally here too. + +Mar 22nd, 2003 +v0.15 -- Added series of prime testing routines to lib + -- Fixed up etc/tune.c + -- Added DR reduction algorithm + -- Beefed up the manual more. + -- Fixed up demo/demo.c so it doesn't have so many warnings and it does the full series of + tests + -- Added "pre-gen" directory which will hold a "gen.pl"'ed copy of the entire lib [done at + zipup time so its always the latest] + -- Added conditional casts for C++ users [boo!] + +Mar 15th, 2003 +v0.14 -- Tons of manual updates + -- cleaned up the directory + -- added MSVC makefiles + -- source changes [that I don't recall] + -- Fixed up the lshd/rshd code to use pointer aliasing + -- Fixed up the mul_2d and div_2d to not call rshd/lshd unless needed + -- Fixed up etc/tune.c a tad + -- fixed up demo/demo.c to output comma-delimited results of timing + also fixed up timing demo to use a finer granularity for various functions + -- fixed up demo/demo.c testing to pause during testing so my Duron won't catch on fire + [stays around 31-35C during testing :-)] + +Feb 13th, 2003 +v0.13 -- tons of minor speed-ups in low level add, sub, mul_2 and div_2 which propagate + to other functions like mp_invmod, mp_div, etc... + -- Sped up mp_exptmod_fast by using new code to find R mod m [e.g. B^n mod m] + -- minor fixes + +Jan 17th, 2003 +v0.12 -- re-wrote the majority of the makefile so its more portable and will + install via "make install" on most *nix platforms + -- Re-packaged all the source as seperate files. Means the library a single + file packagage any more. Instead of just adding "bn.c" you have to add + libtommath.a + -- Renamed "bn.h" to "tommath.h" + -- Changes to the manual to reflect all of this + -- Used GNU Indent to clean up the source + +Jan 15th, 2003 +v0.11 -- More subtle fixes + -- Moved to gentoo linux [hurrah!] so made *nix specific fixes to the make process + -- Sped up the montgomery reduction code quite a bit + -- fixed up demo so when building timing for the x86 it assumes ELF format now + +Jan 9th, 2003 +v0.10 -- Pekka Riikonen suggested fixes to the radix conversion code. + -- Added baseline montgomery and comba montgomery reductions, sped up exptmods + [to a point, see bn.h for MONTGOMERY_EXPT_CUTOFF] + +Jan 6th, 2003 +v0.09 -- Updated the manual to reflect recent changes. :-) + -- Added Jacobi function (mp_jacobi) to supplement the number theory side of the lib + -- Added a Mersenne prime finder demo in ./etc/mersenne.c + +Jan 2nd, 2003 +v0.08 -- Sped up the multipliers by moving the inner loop variables into a smaller scope + -- Corrected a bunch of small "warnings" + -- Added more comments + -- Made "mtest" be able to use /dev/random, /dev/urandom or stdin for RNG data + -- Corrected some bugs where error messages were potentially ignored + -- add etc/pprime.c program which makes numbers which are provably prime. + +Jan 1st, 2003 +v0.07 -- Removed alot of heap operations from core functions to speed them up + -- Added a root finding function [and mp_sqrt macro like from MPI] + -- Added more to manual + +Dec 31st, 2002 +v0.06 -- Sped up the s_mp_add, s_mp_sub which inturn sped up mp_invmod, mp_exptmod, etc... + -- Cleaned up the header a bit more + +Dec 30th, 2002 +v0.05 -- Builds with MSVC out of the box + -- Fixed a bug in mp_invmod w.r.t. even moduli + -- Made mp_toradix and mp_read_radix use char instead of unsigned char arrays + -- Fixed up exptmod to use fewer multiplications + -- Fixed up mp_init_size to use only one heap operation + -- Note there is a slight "off-by-one" bug in the library somewhere + without the padding (see the source for comment) the library + crashes in libtomcrypt. Anyways a reasonable workaround is to pad the + numbers which will always correct it since as the numbers grow the padding + will still be beyond the end of the number + -- Added more to the manual + +Dec 29th, 2002 +v0.04 -- Fixed a memory leak in mp_to_unsigned_bin + -- optimized invmod code + -- Fixed bug in mp_div + -- use exchange instead of copy for results + -- added a bit more to the manual + +Dec 27th, 2002 +v0.03 -- Sped up s_mp_mul_high_digs by not computing the carries of the lower digits + -- Fixed a bug where mp_set_int wouldn't zero the value first and set the used member. + -- fixed a bug in s_mp_mul_high_digs where the limit placed on the result digits was not calculated properly + -- fixed bugs in add/sub/mul/sqr_mod functions where if the modulus and dest were the same it wouldn't work + -- fixed a bug in mp_mod and mp_mod_d concerning negative inputs + -- mp_mul_d didn't preserve sign + -- Many many many many fixes + -- Works in LibTomCrypt now :-) + -- Added iterations to the timing demos... more accurate. + -- Tom needs a job. + +Dec 26th, 2002 +v0.02 -- Fixed a few "slips" in the manual. This is "LibTomMath" afterall :-) + -- Added mp_cmp_mag, mp_neg, mp_abs and mp_radix_size that were missing. + -- Sped up the fast [comba] multipliers more [yahoo!] + +Dec 25th,2002 +v0.01 -- Initial release. Gimme a break. + -- Todo list, + add details to manual [e.g. algorithms] + more comments in code + example programs diff --git a/lib/hcrypto/libtommath/demo/mtest_opponent.c b/lib/hcrypto/libtommath/demo/mtest_opponent.c new file mode 100644 index 000000000000..7fbd35ebcc1e --- /dev/null +++ b/lib/hcrypto/libtommath/demo/mtest_opponent.c @@ -0,0 +1,402 @@ +#include "shared.h" + +#ifdef LTM_MTEST_REAL_RAND +#define LTM_MTEST_RAND_SEED time(NULL) +#else +#define LTM_MTEST_RAND_SEED 23 +#endif + +static void draw(mp_int *a) +{ + ndraw(a, ""); +} + +#define FGETS(str, size, stream) \ + { \ + char *ret = fgets(str, size, stream); \ + if (!ret) { fprintf(stderr, "\n%d: fgets failed\n", __LINE__); goto LBL_ERR; } \ + } + +static int mtest_opponent(void) +{ + char cmd[4096]; + char buf[4096]; + int ix; + unsigned rr; + mp_int a, b, c, d, e, f; + unsigned long expt_n, add_n, sub_n, mul_n, div_n, sqr_n, mul2d_n, div2d_n, + gcd_n, lcm_n, inv_n, div2_n, mul2_n, add_d_n, sub_d_n; + + srand(LTM_MTEST_RAND_SEED); + + if (mp_init_multi(&a, &b, &c, &d, &e, &f, NULL)!= MP_OKAY) + return EXIT_FAILURE; + + div2_n = mul2_n = inv_n = expt_n = lcm_n = gcd_n = add_n = + sub_n = mul_n = div_n = sqr_n = mul2d_n = div2d_n = add_d_n = sub_d_n = 0; + +#ifndef MP_FIXED_CUTOFFS + /* force KARA and TOOM to enable despite cutoffs */ + KARATSUBA_SQR_CUTOFF = KARATSUBA_MUL_CUTOFF = 8; + TOOM_SQR_CUTOFF = TOOM_MUL_CUTOFF = 16; +#endif + + for (;;) { + /* randomly clear and re-init one variable, this has the affect of triming the alloc space */ + switch (abs(rand()) % 7) { + case 0: + mp_clear(&a); + mp_init(&a); + break; + case 1: + mp_clear(&b); + mp_init(&b); + break; + case 2: + mp_clear(&c); + mp_init(&c); + break; + case 3: + mp_clear(&d); + mp_init(&d); + break; + case 4: + mp_clear(&e); + mp_init(&e); + break; + case 5: + mp_clear(&f); + mp_init(&f); + break; + case 6: + break; /* don't clear any */ + } + + + printf("%4lu/%4lu/%4lu/%4lu/%4lu/%4lu/%4lu/%4lu/%4lu/%4lu/%4lu/%4lu/%4lu/%4lu/%4lu ", + add_n, sub_n, mul_n, div_n, sqr_n, mul2d_n, div2d_n, gcd_n, lcm_n, + expt_n, inv_n, div2_n, mul2_n, add_d_n, sub_d_n); + FGETS(cmd, 4095, stdin); + cmd[strlen(cmd) - 1u] = '\0'; + printf("%-6s ]\r", cmd); + fflush(stdout); + if (strcmp(cmd, "mul2d") == 0) { + ++mul2d_n; + FGETS(buf, 4095, stdin); + mp_read_radix(&a, buf, 64); + FGETS(buf, 4095, stdin); + sscanf(buf, "%u", &rr); + FGETS(buf, 4095, stdin); + mp_read_radix(&b, buf, 64); + + mp_mul_2d(&a, (int)rr, &a); + a.sign = b.sign; + if (mp_cmp(&a, &b) != MP_EQ) { + printf("mul2d failed, rr == %u\n", rr); + draw(&a); + draw(&b); + goto LBL_ERR; + } + } else if (strcmp(cmd, "div2d") == 0) { + ++div2d_n; + FGETS(buf, 4095, stdin); + mp_read_radix(&a, buf, 64); + FGETS(buf, 4095, stdin); + sscanf(buf, "%u", &rr); + FGETS(buf, 4095, stdin); + mp_read_radix(&b, buf, 64); + + mp_div_2d(&a, (int)rr, &a, &e); + a.sign = b.sign; + if ((a.used == b.used) && (a.used == 0)) { + a.sign = b.sign = MP_ZPOS; + } + if (mp_cmp(&a, &b) != MP_EQ) { + printf("div2d failed, rr == %u\n", rr); + draw(&a); + draw(&b); + goto LBL_ERR; + } + } else if (strcmp(cmd, "add") == 0) { + ++add_n; + FGETS(buf, 4095, stdin); + mp_read_radix(&a, buf, 64); + FGETS(buf, 4095, stdin); + mp_read_radix(&b, buf, 64); + FGETS(buf, 4095, stdin); + mp_read_radix(&c, buf, 64); + mp_copy(&a, &d); + mp_add(&d, &b, &d); + if (mp_cmp(&c, &d) != MP_EQ) { + printf("add %lu failure!\n", add_n); + draw(&a); + draw(&b); + draw(&c); + draw(&d); + goto LBL_ERR; + } + + /* test the sign/unsigned storage functions */ + + rr = (unsigned)mp_sbin_size(&c); + mp_to_sbin(&c, (unsigned char *) cmd, (size_t)rr, NULL); + memset(cmd + rr, rand() & 0xFF, sizeof(cmd) - rr); + mp_from_sbin(&d, (unsigned char *) cmd, (size_t)rr); + if (mp_cmp(&c, &d) != MP_EQ) { + printf("mp_signed_bin failure!\n"); + draw(&c); + draw(&d); + goto LBL_ERR; + } + + rr = (unsigned)mp_ubin_size(&c); + mp_to_ubin(&c, (unsigned char *) cmd, (size_t)rr, NULL); + memset(cmd + rr, rand() & 0xFF, sizeof(cmd) - rr); + mp_from_ubin(&d, (unsigned char *) cmd, (size_t)rr); + if (mp_cmp_mag(&c, &d) != MP_EQ) { + printf("mp_unsigned_bin failure!\n"); + draw(&c); + draw(&d); + goto LBL_ERR; + } + + } else if (strcmp(cmd, "sub") == 0) { + ++sub_n; + FGETS(buf, 4095, stdin); + mp_read_radix(&a, buf, 64); + FGETS(buf, 4095, stdin); + mp_read_radix(&b, buf, 64); + FGETS(buf, 4095, stdin); + mp_read_radix(&c, buf, 64); + mp_copy(&a, &d); + mp_sub(&d, &b, &d); + if (mp_cmp(&c, &d) != MP_EQ) { + printf("sub %lu failure!\n", sub_n); + draw(&a); + draw(&b); + draw(&c); + draw(&d); + goto LBL_ERR; + } + } else if (strcmp(cmd, "mul") == 0) { + ++mul_n; + FGETS(buf, 4095, stdin); + mp_read_radix(&a, buf, 64); + FGETS(buf, 4095, stdin); + mp_read_radix(&b, buf, 64); + FGETS(buf, 4095, stdin); + mp_read_radix(&c, buf, 64); + mp_copy(&a, &d); + mp_mul(&d, &b, &d); + if (mp_cmp(&c, &d) != MP_EQ) { + printf("mul %lu failure!\n", mul_n); + draw(&a); + draw(&b); + draw(&c); + draw(&d); + goto LBL_ERR; + } + } else if (strcmp(cmd, "div") == 0) { + ++div_n; + FGETS(buf, 4095, stdin); + mp_read_radix(&a, buf, 64); + FGETS(buf, 4095, stdin); + mp_read_radix(&b, buf, 64); + FGETS(buf, 4095, stdin); + mp_read_radix(&c, buf, 64); + FGETS(buf, 4095, stdin); + mp_read_radix(&d, buf, 64); + + mp_div(&a, &b, &e, &f); + if ((mp_cmp(&c, &e) != MP_EQ) || (mp_cmp(&d, &f) != MP_EQ)) { + printf("div %lu %d, %d, failure!\n", div_n, mp_cmp(&c, &e), + mp_cmp(&d, &f)); + draw(&a); + draw(&b); + draw(&c); + draw(&d); + draw(&e); + draw(&f); + goto LBL_ERR; + } + + } else if (strcmp(cmd, "sqr") == 0) { + ++sqr_n; + FGETS(buf, 4095, stdin); + mp_read_radix(&a, buf, 64); + FGETS(buf, 4095, stdin); + mp_read_radix(&b, buf, 64); + mp_copy(&a, &c); + mp_sqr(&c, &c); + if (mp_cmp(&b, &c) != MP_EQ) { + printf("sqr %lu failure!\n", sqr_n); + draw(&a); + draw(&b); + draw(&c); + goto LBL_ERR; + } + } else if (strcmp(cmd, "gcd") == 0) { + ++gcd_n; + FGETS(buf, 4095, stdin); + mp_read_radix(&a, buf, 64); + FGETS(buf, 4095, stdin); + mp_read_radix(&b, buf, 64); + FGETS(buf, 4095, stdin); + mp_read_radix(&c, buf, 64); + mp_copy(&a, &d); + mp_gcd(&d, &b, &d); + d.sign = c.sign; + if (mp_cmp(&c, &d) != MP_EQ) { + printf("gcd %lu failure!\n", gcd_n); + draw(&a); + draw(&b); + draw(&c); + draw(&d); + goto LBL_ERR; + } + } else if (strcmp(cmd, "lcm") == 0) { + ++lcm_n; + FGETS(buf, 4095, stdin); + mp_read_radix(&a, buf, 64); + FGETS(buf, 4095, stdin); + mp_read_radix(&b, buf, 64); + FGETS(buf, 4095, stdin); + mp_read_radix(&c, buf, 64); + mp_copy(&a, &d); + mp_lcm(&d, &b, &d); + d.sign = c.sign; + if (mp_cmp(&c, &d) != MP_EQ) { + printf("lcm %lu failure!\n", lcm_n); + draw(&a); + draw(&b); + draw(&c); + draw(&d); + goto LBL_ERR; + } + } else if (strcmp(cmd, "expt") == 0) { + ++expt_n; + FGETS(buf, 4095, stdin); + mp_read_radix(&a, buf, 64); + FGETS(buf, 4095, stdin); + mp_read_radix(&b, buf, 64); + FGETS(buf, 4095, stdin); + mp_read_radix(&c, buf, 64); + FGETS(buf, 4095, stdin); + mp_read_radix(&d, buf, 64); + mp_copy(&a, &e); + mp_exptmod(&e, &b, &c, &e); + if (mp_cmp(&d, &e) != MP_EQ) { + printf("expt %lu failure!\n", expt_n); + draw(&a); + draw(&b); + draw(&c); + draw(&d); + draw(&e); + goto LBL_ERR; + } + } else if (strcmp(cmd, "invmod") == 0) { + ++inv_n; + FGETS(buf, 4095, stdin); + mp_read_radix(&a, buf, 64); + FGETS(buf, 4095, stdin); + mp_read_radix(&b, buf, 64); + FGETS(buf, 4095, stdin); + mp_read_radix(&c, buf, 64); + mp_invmod(&a, &b, &d); + mp_mulmod(&d, &a, &b, &e); + if (mp_cmp_d(&e, 1uL) != MP_EQ) { + printf("inv [wrong value from MPI?!] failure\n"); + draw(&a); + draw(&b); + draw(&c); + draw(&d); + draw(&e); + mp_gcd(&a, &b, &e); + draw(&e); + goto LBL_ERR; + } + + } else if (strcmp(cmd, "div2") == 0) { + ++div2_n; + FGETS(buf, 4095, stdin); + mp_read_radix(&a, buf, 64); + FGETS(buf, 4095, stdin); + mp_read_radix(&b, buf, 64); + mp_div_2(&a, &c); + if (mp_cmp(&c, &b) != MP_EQ) { + printf("div_2 %lu failure\n", div2_n); + draw(&a); + draw(&b); + draw(&c); + goto LBL_ERR; + } + } else if (strcmp(cmd, "mul2") == 0) { + ++mul2_n; + FGETS(buf, 4095, stdin); + mp_read_radix(&a, buf, 64); + FGETS(buf, 4095, stdin); + mp_read_radix(&b, buf, 64); + mp_mul_2(&a, &c); + if (mp_cmp(&c, &b) != MP_EQ) { + printf("mul_2 %lu failure\n", mul2_n); + draw(&a); + draw(&b); + draw(&c); + goto LBL_ERR; + } + } else if (strcmp(cmd, "add_d") == 0) { + ++add_d_n; + FGETS(buf, 4095, stdin); + mp_read_radix(&a, buf, 64); + FGETS(buf, 4095, stdin); + sscanf(buf, "%d", &ix); + FGETS(buf, 4095, stdin); + mp_read_radix(&b, buf, 64); + mp_add_d(&a, (mp_digit)ix, &c); + if (mp_cmp(&b, &c) != MP_EQ) { + printf("add_d %lu failure\n", add_d_n); + draw(&a); + draw(&b); + draw(&c); + printf("d == %d\n", ix); + goto LBL_ERR; + } + } else if (strcmp(cmd, "sub_d") == 0) { + ++sub_d_n; + FGETS(buf, 4095, stdin); + mp_read_radix(&a, buf, 64); + FGETS(buf, 4095, stdin); + sscanf(buf, "%d", &ix); + FGETS(buf, 4095, stdin); + mp_read_radix(&b, buf, 64); + mp_sub_d(&a, (mp_digit)ix, &c); + if (mp_cmp(&b, &c) != MP_EQ) { + printf("sub_d %lu failure\n", sub_d_n); + draw(&a); + draw(&b); + draw(&c); + printf("d == %d\n", ix); + goto LBL_ERR; + } + } else if (strcmp(cmd, "exit") == 0) { + printf("\nokay, exiting now\n"); + break; + } + } + + mp_clear_multi(&a, &b, &c, &d, &e, &f, NULL); + printf("\n"); + return 0; + +LBL_ERR: + mp_clear_multi(&a, &b, &c, &d, &e, &f, NULL); + printf("\n"); + return EXIT_FAILURE; +} + +int main(void) +{ + print_header(); + + return mtest_opponent(); +} diff --git a/lib/hcrypto/libtommath/demo/shared.c b/lib/hcrypto/libtommath/demo/shared.c new file mode 100644 index 000000000000..dc8e05a6a1b2 --- /dev/null +++ b/lib/hcrypto/libtommath/demo/shared.c @@ -0,0 +1,42 @@ +#include "shared.h" + +void ndraw(mp_int *a, const char *name) +{ + char *buf = NULL; + int size; + + mp_radix_size(a, 10, &size); + buf = (char *)malloc((size_t) size); + if (buf == NULL) { + fprintf(stderr, "\nndraw: malloc(%d) failed\n", size); + exit(EXIT_FAILURE); + } + + printf("%s: ", name); + mp_to_decimal(a, buf, (size_t) size); + printf("%s\n", buf); + mp_to_hex(a, buf, (size_t) size); + printf("0x%s\n", buf); + + free(buf); +} + +void print_header(void) +{ +#ifdef MP_8BIT + printf("Digit size 8 Bit \n"); +#endif +#ifdef MP_16BIT + printf("Digit size 16 Bit \n"); +#endif +#ifdef MP_32BIT + printf("Digit size 32 Bit \n"); +#endif +#ifdef MP_64BIT + printf("Digit size 64 Bit \n"); +#endif + printf("Size of mp_digit: %u\n", (unsigned int)sizeof(mp_digit)); + printf("Size of mp_word: %u\n", (unsigned int)sizeof(mp_word)); + printf("MP_DIGIT_BIT: %d\n", MP_DIGIT_BIT); + printf("MP_PREC: %d\n", MP_PREC); +} diff --git a/lib/hcrypto/libtommath/demo/shared.h b/lib/hcrypto/libtommath/demo/shared.h new file mode 100644 index 000000000000..4d5eb53b2f43 --- /dev/null +++ b/lib/hcrypto/libtommath/demo/shared.h @@ -0,0 +1,21 @@ +#include <string.h> +#include <stdlib.h> +#include <time.h> + +/* + * Configuration + */ +#ifndef LTM_DEMO_TEST_REDUCE_2K_L +/* This test takes a moment so we disable it by default, but it can be: + * 0 to disable testing + * 1 to make the test with P = 2^1024 - 0x2A434 B9FDEC95 D8F9D550 FFFFFFFF FFFFFFFF + * 2 to make the test with P = 2^2048 - 0x1 00000000 00000000 00000000 00000000 4945DDBF 8EA2A91D 5776399B B83E188F + */ +#define LTM_DEMO_TEST_REDUCE_2K_L 0 +#endif + +#define MP_WUR /* TODO: result checks disabled for now */ +#include "tommath_private.h" + +extern void ndraw(mp_int* a, const char* name); +extern void print_header(void); diff --git a/lib/hcrypto/libtommath/demo/test.c b/lib/hcrypto/libtommath/demo/test.c new file mode 100644 index 000000000000..9049fa81f91a --- /dev/null +++ b/lib/hcrypto/libtommath/demo/test.c @@ -0,0 +1,2522 @@ +#include <inttypes.h> +#include "shared.h" + +static long rand_long(void) +{ + long x; + if (s_mp_rand_source(&x, sizeof(x)) != MP_OKAY) { + fprintf(stderr, "s_mp_rand_source failed\n"); + exit(EXIT_FAILURE); + } + return x; +} + +static int rand_int(void) +{ + int x; + if (s_mp_rand_source(&x, sizeof(x)) != MP_OKAY) { + fprintf(stderr, "s_mp_rand_source failed\n"); + exit(EXIT_FAILURE); + } + return x; +} + +static int32_t rand_int32(void) +{ + int32_t x; + if (s_mp_rand_source(&x, sizeof(x)) != MP_OKAY) { + fprintf(stderr, "s_mp_rand_source failed\n"); + exit(EXIT_FAILURE); + } + return x; +} + +static int64_t rand_int64(void) +{ + int64_t x; + if (s_mp_rand_source(&x, sizeof(x)) != MP_OKAY) { + fprintf(stderr, "s_mp_rand_source failed\n"); + exit(EXIT_FAILURE); + } + return x; +} + +static uint32_t uabs32(int32_t x) +{ + return x > 0 ? (uint32_t)x : -(uint32_t)x; +} + +static uint64_t uabs64(int64_t x) +{ + return x > 0 ? (uint64_t)x : -(uint64_t)x; +} + +/* This function prototype is needed + * to test dead code elimination + * which is used for feature detection. + * + * If the feature detection does not + * work as desired we will get a linker error. + */ +void does_not_exist(void); + +static int test_feature_detection(void) +{ +#define BN_TEST_FEATURE1_C + if (!MP_HAS(TEST_FEATURE1)) { + does_not_exist(); + return EXIT_FAILURE; + } + +#define BN_TEST_FEATURE2_C 1 + if (MP_HAS(TEST_FEATURE2)) { + does_not_exist(); + return EXIT_FAILURE; + } + +#define BN_TEST_FEATURE3_C 0 + if (MP_HAS(TEST_FEATURE3)) { + does_not_exist(); + return EXIT_FAILURE; + } + +#define BN_TEST_FEATURE4_C something + if (MP_HAS(TEST_FEATURE4)) { + does_not_exist(); + return EXIT_FAILURE; + } + + if (MP_HAS(TEST_FEATURE5)) { + does_not_exist(); + return EXIT_FAILURE; + } + + return EXIT_SUCCESS; +} + +static int test_trivial_stuff(void) +{ + mp_int a, b, c, d; + mp_err e; + if ((e = mp_init_multi(&a, &b, &c, &d, NULL)) != MP_OKAY) { + return EXIT_FAILURE; + } + (void)mp_error_to_string(e); + + /* a: 0->5 */ + mp_set(&a, 5u); + /* a: 5-> b: -5 */ + mp_neg(&a, &b); + if (mp_cmp(&a, &b) != MP_GT) { + goto LBL_ERR; + } + if (mp_cmp(&b, &a) != MP_LT) { + goto LBL_ERR; + } + /* a: 5-> a: -5 */ + mp_neg(&a, &a); + if (mp_cmp(&b, &a) != MP_EQ) { + goto LBL_ERR; + } + /* a: -5-> b: 5 */ + mp_abs(&a, &b); + if (mp_isneg(&b) != MP_NO) { + goto LBL_ERR; + } + /* a: -5-> b: -4 */ + mp_add_d(&a, 1uL, &b); + if (mp_isneg(&b) != MP_YES) { + goto LBL_ERR; + } + if (mp_get_i32(&b) != -4) { + goto LBL_ERR; + } + if (mp_get_u32(&b) != (uint32_t)-4) { + goto LBL_ERR; + } + if (mp_get_mag_u32(&b) != 4) { + goto LBL_ERR; + } + /* a: -5-> b: 1 */ + mp_add_d(&a, 6uL, &b); + if (mp_get_u32(&b) != 1) { + goto LBL_ERR; + } + /* a: -5-> a: 1 */ + mp_add_d(&a, 6uL, &a); + if (mp_get_u32(&a) != 1) { + goto LBL_ERR; + } + mp_zero(&a); + /* a: 0-> a: 6 */ + mp_add_d(&a, 6uL, &a); + if (mp_get_u32(&a) != 6) { + goto LBL_ERR; + } + + mp_set(&a, 42u); + mp_set(&b, 1u); + mp_neg(&b, &b); + mp_set(&c, 1u); + mp_exptmod(&a, &b, &c, &d); + + mp_set(&c, 7u); + mp_exptmod(&a, &b, &c, &d); + + if (mp_iseven(&a) == mp_isodd(&a)) { + goto LBL_ERR; + } + + mp_clear_multi(&a, &b, &c, &d, NULL); + return EXIT_SUCCESS; +LBL_ERR: + mp_clear_multi(&a, &b, &c, &d, NULL); + return EXIT_FAILURE; +} + +static int check_get_set_i32(mp_int *a, int32_t b) +{ + mp_clear(a); + if (mp_shrink(a) != MP_OKAY) return EXIT_FAILURE; + + mp_set_i32(a, b); + if (mp_shrink(a) != MP_OKAY) return EXIT_FAILURE; + if (mp_get_i32(a) != b) return EXIT_FAILURE; + if (mp_get_u32(a) != (uint32_t)b) return EXIT_FAILURE; + if (mp_get_mag_u32(a) != uabs32(b)) return EXIT_FAILURE; + + mp_set_u32(a, (uint32_t)b); + if (mp_get_u32(a) != (uint32_t)b) return EXIT_FAILURE; + if (mp_get_i32(a) != (int32_t)(uint32_t)b) return EXIT_FAILURE; + + return EXIT_SUCCESS; +} + +static int test_mp_get_set_i32(void) +{ + int i; + mp_int a; + + if (mp_init(&a) != MP_OKAY) { + return EXIT_FAILURE; + } + + check_get_set_i32(&a, 0); + check_get_set_i32(&a, -1); + check_get_set_i32(&a, 1); + check_get_set_i32(&a, INT32_MIN); + check_get_set_i32(&a, INT32_MAX); + + for (i = 0; i < 1000; ++i) { + int32_t b = rand_int32(); + if (check_get_set_i32(&a, b) != EXIT_SUCCESS) { + goto LBL_ERR; + } + } + + mp_clear(&a); + return EXIT_SUCCESS; +LBL_ERR: + mp_clear(&a); + return EXIT_FAILURE; +} + +static int check_get_set_i64(mp_int *a, int64_t b) +{ + mp_clear(a); + if (mp_shrink(a) != MP_OKAY) return EXIT_FAILURE; + + mp_set_i64(a, b); + if (mp_shrink(a) != MP_OKAY) return EXIT_FAILURE; + if (mp_get_i64(a) != b) return EXIT_FAILURE; + if (mp_get_u64(a) != (uint64_t)b) return EXIT_FAILURE; + if (mp_get_mag_u64(a) != uabs64(b)) return EXIT_FAILURE; + + mp_set_u64(a, (uint64_t)b); + if (mp_get_u64(a) != (uint64_t)b) return EXIT_FAILURE; + if (mp_get_i64(a) != (int64_t)(uint64_t)b) return EXIT_FAILURE; + + return EXIT_SUCCESS; +} + +static int test_mp_get_set_i64(void) +{ + int i; + mp_int a; + + if (mp_init(&a) != MP_OKAY) { + return EXIT_FAILURE; + } + + check_get_set_i64(&a, 0); + check_get_set_i64(&a, -1); + check_get_set_i64(&a, 1); + check_get_set_i64(&a, INT64_MIN); + check_get_set_i64(&a, INT64_MAX); + + for (i = 0; i < 1000; ++i) { + int64_t b = rand_int64(); + if (check_get_set_i64(&a, b) != EXIT_SUCCESS) { + goto LBL_ERR; + } + } + + mp_clear(&a); + return EXIT_SUCCESS; +LBL_ERR: + mp_clear(&a); + return EXIT_FAILURE; +} + +static int test_mp_fread_fwrite(void) +{ + mp_int a, b; + mp_err e; + FILE *tmp = NULL; + if ((e = mp_init_multi(&a, &b, NULL)) != MP_OKAY) { + return EXIT_FAILURE; + } + + mp_set_ul(&a, 123456uL); + tmp = tmpfile(); + if ((e = mp_fwrite(&a, 64, tmp)) != MP_OKAY) { + goto LBL_ERR; + } + rewind(tmp); + if ((e = mp_fread(&b, 64, tmp)) != MP_OKAY) { + goto LBL_ERR; + } + if (mp_get_u32(&b) != 123456uL) { + goto LBL_ERR; + } + fclose(tmp); + + mp_clear_multi(&a, &b, NULL); + return EXIT_SUCCESS; +LBL_ERR: + if (tmp != NULL) fclose(tmp); + mp_clear_multi(&a, &b, NULL); + return EXIT_FAILURE; +} + +static mp_err very_random_source(void *out, size_t size) +{ + memset(out, 0xff, size); + return MP_OKAY; +} + +static int test_mp_rand(void) +{ + mp_int a, b; + int n; + mp_err err; + if (mp_init_multi(&a, &b, NULL)!= MP_OKAY) { + return EXIT_FAILURE; + } + mp_rand_source(very_random_source); + for (n = 1; n < 1024; ++n) { + if ((err = mp_rand(&a, n)) != MP_OKAY) { + printf("Failed mp_rand() %s.\n", mp_error_to_string(err)); + break; + } + if ((err = mp_incr(&a)) != MP_OKAY) { + printf("Failed mp_incr() %s.\n", mp_error_to_string(err)); + break; + } + if ((err = mp_div_2d(&a, n * MP_DIGIT_BIT, &b, NULL)) != MP_OKAY) { + printf("Failed mp_div_2d() %s.\n", mp_error_to_string(err)); + break; + } + if (mp_cmp_d(&b, 1) != MP_EQ) { + ndraw(&a, "mp_rand() a"); + ndraw(&b, "mp_rand() b"); + err = MP_ERR; + break; + } + } + mp_rand_source(s_mp_rand_jenkins); + mp_clear_multi(&a, &b, NULL); + return err == MP_OKAY ? EXIT_SUCCESS : EXIT_FAILURE; +} + +static int test_mp_kronecker(void) +{ + struct mp_kronecker_st { + long n; + int c[21]; + }; + static struct mp_kronecker_st kronecker[] = { + /*-10, -9, -8, -7,-6, -5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10*/ + { -10, { 0, -1, 0, -1, 0, 0, 0, 1, 0, -1, 0, 1, 0, -1, 0, 0, 0, 1, 0, 1, 0 } }, + { -9, { -1, 0, -1, 1, 0, -1, -1, 0, -1, -1, 0, 1, 1, 0, 1, 1, 0, -1, 1, 0, 1 } }, + { -8, { 0, -1, 0, 1, 0, 1, 0, -1, 0, -1, 0, 1, 0, 1, 0, -1, 0, -1, 0, 1, 0 } }, + { -7, { 1, -1, -1, 0, 1, 1, -1, 1, -1, -1, 0, 1, 1, -1, 1, -1, -1, 0, 1, 1, -1 } }, + { -6, { 0, 0, 0, -1, 0, -1, 0, 0, 0, -1, 0, 1, 0, 0, 0, 1, 0, 1, 0, 0, 0 } }, + { -5, { 0, -1, 1, -1, 1, 0, -1, -1, 1, -1, 0, 1, -1, 1, 1, 0, -1, 1, -1, 1, 0 } }, + { -4, { 0, -1, 0, 1, 0, -1, 0, 1, 0, -1, 0, 1, 0, -1, 0, 1, 0, -1, 0, 1, 0 } }, + { -3, { -1, 0, 1, -1, 0, 1, -1, 0, 1, -1, 0, 1, -1, 0, 1, -1, 0, 1, -1, 0, 1 } }, + { -2, { 0, -1, 0, 1, 0, 1, 0, -1, 0, -1, 0, 1, 0, 1, 0, -1, 0, -1, 0, 1, 0 } }, + { -1, { -1, -1, -1, 1, 1, -1, -1, 1, -1, -1, 1, 1, 1, -1, 1, 1, -1, -1, 1, 1, 1 } }, + { 0, { 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0 } }, + { 1, { 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1 } }, + { 2, { 0, 1, 0, 1, 0, -1, 0, -1, 0, 1, 0, 1, 0, -1, 0, -1, 0, 1, 0, 1, 0 } }, + { 3, { 1, 0, -1, -1, 0, -1, 1, 0, -1, 1, 0, 1, -1, 0, 1, -1, 0, -1, -1, 0, 1 } }, + { 4, { 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0 } }, + { 5, { 0, 1, -1, -1, 1, 0, 1, -1, -1, 1, 0, 1, -1, -1, 1, 0, 1, -1, -1, 1, 0 } }, + { 6, { 0, 0, 0, -1, 0, 1, 0, 0, 0, 1, 0, 1, 0, 0, 0, 1, 0, -1, 0, 0, 0 } }, + { 7, { -1, 1, 1, 0, 1, -1, 1, 1, 1, 1, 0, 1, 1, 1, 1, -1, 1, 0, 1, 1, -1 } }, + { 8, { 0, 1, 0, 1, 0, -1, 0, -1, 0, 1, 0, 1, 0, -1, 0, -1, 0, 1, 0, 1, 0 } }, + { 9, { 1, 0, 1, 1, 0, 1, 1, 0, 1, 1, 0, 1, 1, 0, 1, 1, 0, 1, 1, 0, 1 } }, + { 10, { 0, 1, 0, -1, 0, 0, 0, 1, 0, 1, 0, 1, 0, 1, 0, 0, 0, -1, 0, 1, 0 } } + }; + + long k, m; + int i, cnt; + mp_err err; + mp_int a, b; + if (mp_init_multi(&a, &b, NULL)!= MP_OKAY) { + return EXIT_FAILURE; + } + + mp_set_ul(&a, 0uL); + mp_set_ul(&b, 1uL); + if ((err = mp_kronecker(&a, &b, &i)) != MP_OKAY) { + printf("Failed executing mp_kronecker(0 | 1) %s.\n", mp_error_to_string(err)); + goto LBL_ERR; + } + if (i != 1) { + printf("Failed trivial mp_kronecker(0 | 1) %d != 1\n", i); + goto LBL_ERR; + } + for (cnt = 0; cnt < (int)(sizeof(kronecker)/sizeof(kronecker[0])); ++cnt) { + k = kronecker[cnt].n; + mp_set_l(&a, k); + /* only test positive values of a */ + for (m = -10; m <= 10; m++) { + mp_set_l(&b, m); + if ((err = mp_kronecker(&a, &b, &i)) != MP_OKAY) { + printf("Failed executing mp_kronecker(%ld | %ld) %s.\n", kronecker[cnt].n, m, mp_error_to_string(err)); + goto LBL_ERR; + } + if ((err == MP_OKAY) && (i != kronecker[cnt].c[m + 10])) { + printf("Failed trivial mp_kronecker(%ld | %ld) %d != %d\n", kronecker[cnt].n, m, i, kronecker[cnt].c[m + 10]); + goto LBL_ERR; + } + } + } + + mp_clear_multi(&a, &b, NULL); + return EXIT_SUCCESS; +LBL_ERR: + mp_clear_multi(&a, &b, NULL); + return EXIT_FAILURE; +} + +static int test_mp_complement(void) +{ + int i; + + mp_int a, b, c; + if (mp_init_multi(&a, &b, &c, NULL)!= MP_OKAY) { + return EXIT_FAILURE; + } + + for (i = 0; i < 1000; ++i) { + long l = rand_long(); + mp_set_l(&a, l); + mp_complement(&a, &b); + + l = ~l; + mp_set_l(&c, l); + + if (mp_cmp(&b, &c) != MP_EQ) { + printf("\nmp_complement() bad result!"); + goto LBL_ERR; + } + } + + mp_clear_multi(&a, &b, &c, NULL); + return EXIT_SUCCESS; +LBL_ERR: + mp_clear_multi(&a, &b, &c, NULL); + return EXIT_FAILURE; +} + +static int test_mp_signed_rsh(void) +{ + int i; + + mp_int a, b, d; + if (mp_init_multi(&a, &b, &d, NULL)!= MP_OKAY) { + return EXIT_FAILURE; + } + + for (i = 0; i < 1000; ++i) { + long l; + int em; + + l = rand_long(); + mp_set_l(&a, l); + + em = abs(rand_int()) % 32; + + mp_set_l(&d, l >> em); + + mp_signed_rsh(&a, em, &b); + if (mp_cmp(&b, &d) != MP_EQ) { + printf("\nmp_signed_rsh() bad result!"); + goto LBL_ERR; + } + } + + mp_clear_multi(&a, &b, &d, NULL); + return EXIT_SUCCESS; +LBL_ERR: + mp_clear_multi(&a, &b, &d, NULL); + return EXIT_FAILURE; + +} + +static int test_mp_xor(void) +{ + int i; + + mp_int a, b, c, d; + if (mp_init_multi(&a, &b, &c, &d, NULL)!= MP_OKAY) { + return EXIT_FAILURE; + } + + for (i = 0; i < 1000; ++i) { + long l, em; + + l = rand_long(); + mp_set_l(&a,l); + + em = rand_long(); + mp_set_l(&b, em); + + mp_set_l(&d, l ^ em); + + mp_xor(&a, &b, &c); + if (mp_cmp(&c, &d) != MP_EQ) { + printf("\nmp_xor() bad result!"); + goto LBL_ERR; + } + } + + mp_clear_multi(&a, &b, &c, &d, NULL); + return EXIT_SUCCESS; +LBL_ERR: + mp_clear_multi(&a, &b, &c, &d, NULL); + return EXIT_FAILURE; + +} + +static int test_mp_or(void) +{ + int i; + + mp_int a, b, c, d; + if (mp_init_multi(&a, &b, &c, &d, NULL)!= MP_OKAY) { + return EXIT_FAILURE; + } + + for (i = 0; i < 1000; ++i) { + long l, em; + + l = rand_long(); + mp_set_l(&a, l); + + em = rand_long(); + mp_set_l(&b, em); + + mp_set_l(&d, l | em); + + mp_or(&a, &b, &c); + if (mp_cmp(&c, &d) != MP_EQ) { + printf("\nmp_or() bad result!"); + goto LBL_ERR; + } + } + + mp_clear_multi(&a, &b, &c, &d, NULL); + return EXIT_SUCCESS; +LBL_ERR: + mp_clear_multi(&a, &b, &c, &d, NULL); + return EXIT_FAILURE; +} + +static int test_mp_and(void) +{ + int i; + + mp_int a, b, c, d; + if (mp_init_multi(&a, &b, &c, &d, NULL)!= MP_OKAY) { + return EXIT_FAILURE; + } + + for (i = 0; i < 1000; ++i) { + long l, em; + + l = rand_long(); + mp_set_l(&a, l); + + em = rand_long(); + mp_set_l(&b, em); + + mp_set_l(&d, l & em); + + mp_and(&a, &b, &c); + if (mp_cmp(&c, &d) != MP_EQ) { + printf("\nmp_and() bad result!"); + goto LBL_ERR; + } + } + + mp_clear_multi(&a, &b, &c, &d, NULL); + return EXIT_SUCCESS; +LBL_ERR: + mp_clear_multi(&a, &b, &c, &d, NULL); + return EXIT_FAILURE; +} + +static int test_mp_invmod(void) +{ + mp_int a, b, c, d; + if (mp_init_multi(&a, &b, &c, &d, NULL)!= MP_OKAY) { + return EXIT_FAILURE; + } + + /* mp_invmod corner-case of https://github.com/libtom/libtommath/issues/118 */ + { + const char *a_ = "47182BB8DF0FFE9F61B1F269BACC066B48BA145D35137D426328DC3F88A5EA44"; + const char *b_ = "FFFFFFFEFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF00000000FFFFFFFFFFFFFFFF"; + const char *should_ = "0521A82E10376F8E4FDEF9A32A427AC2A0FFF686E00290D39E3E4B5522409596"; + + if (mp_read_radix(&a, a_, 16) != MP_OKAY) { + printf("\nmp_read_radix(a) failed!"); + goto LBL_ERR; + } + if (mp_read_radix(&b, b_, 16) != MP_OKAY) { + printf("\nmp_read_radix(b) failed!"); + goto LBL_ERR; + } + if (mp_read_radix(&c, should_, 16) != MP_OKAY) { + printf("\nmp_read_radix(should) failed!"); + goto LBL_ERR; + } + + if (mp_invmod(&a, &b, &d) != MP_OKAY) { + printf("\nmp_invmod() failed!"); + goto LBL_ERR; + } + + if (mp_cmp(&c, &d) != MP_EQ) { + printf("\nmp_invmod() bad result!"); + goto LBL_ERR; + } + } + + mp_clear_multi(&a, &b, &c, &d, NULL); + return EXIT_SUCCESS; +LBL_ERR: + mp_clear_multi(&a, &b, &c, &d, NULL); + return EXIT_FAILURE; + +} + +#if defined(__STDC_IEC_559__) || defined(__GCC_IEC_559) || defined(__x86_64__) || defined(_M_X64) || defined(_M_AMD64) || defined(__i386__) || defined(_M_X86) || defined(__aarch64__) || defined(__arm__) +static int test_mp_set_double(void) +{ + int i; + + mp_int a, b; + if (mp_init_multi(&a, &b, NULL)!= MP_OKAY) { + return EXIT_FAILURE; + } + + /* test mp_get_double/mp_set_double */ + if (mp_set_double(&a, +1.0/0.0) != MP_VAL) { + printf("\nmp_set_double should return MP_VAL for +inf"); + goto LBL_ERR; + } + if (mp_set_double(&a, -1.0/0.0) != MP_VAL) { + printf("\nmp_set_double should return MP_VAL for -inf"); + goto LBL_ERR; + } + if (mp_set_double(&a, +0.0/0.0) != MP_VAL) { + printf("\nmp_set_double should return MP_VAL for NaN"); + goto LBL_ERR; + } + if (mp_set_double(&a, -0.0/0.0) != MP_VAL) { + printf("\nmp_set_double should return MP_VAL for NaN"); + goto LBL_ERR; + } + + for (i = 0; i < 1000; ++i) { + int tmp = rand_int(); + double dbl = (double)tmp * rand_int() + 1; + if (mp_set_double(&a, dbl) != MP_OKAY) { + printf("\nmp_set_double() failed"); + goto LBL_ERR; + } + if (dbl != mp_get_double(&a)) { + printf("\nmp_get_double() bad result!"); + goto LBL_ERR; + } + if (mp_set_double(&a, -dbl) != MP_OKAY) { + printf("\nmp_set_double() failed"); + goto LBL_ERR; + } + if (-dbl != mp_get_double(&a)) { + printf("\nmp_get_double() bad result!"); + goto LBL_ERR; + } + } + + mp_clear_multi(&a, &b, NULL); + return EXIT_SUCCESS; +LBL_ERR: + mp_clear_multi(&a, &b, NULL); + return EXIT_FAILURE; + +} +#endif + +static int test_mp_get_u32(void) +{ + unsigned long t; + int i; + + mp_int a, b; + if (mp_init_multi(&a, &b, NULL)!= MP_OKAY) { + return EXIT_FAILURE; + } + + for (i = 0; i < 1000; ++i) { + t = (unsigned long)rand_long() & 0xFFFFFFFFuL; + mp_set_ul(&a, t); + if (t != mp_get_u32(&a)) { + printf("\nmp_get_u32() bad result!"); + goto LBL_ERR; + } + } + mp_set_ul(&a, 0uL); + if (mp_get_u32(&a) != 0) { + printf("\nmp_get_u32() bad result!"); + goto LBL_ERR; + } + mp_set_ul(&a, 0xFFFFFFFFuL); + if (mp_get_u32(&a) != 0xFFFFFFFFuL) { + printf("\nmp_get_u32() bad result!"); + goto LBL_ERR; + } + + mp_clear_multi(&a, &b, NULL); + return EXIT_SUCCESS; +LBL_ERR: + mp_clear_multi(&a, &b, NULL); + return EXIT_FAILURE; +} + +static int test_mp_get_ul(void) +{ + unsigned long s, t; + int i; + + mp_int a, b; + if (mp_init_multi(&a, &b, NULL)!= MP_OKAY) { + return EXIT_FAILURE; + } + + for (i = 0; i < ((int)MP_SIZEOF_BITS(unsigned long) - 1); ++i) { + t = (1UL << (i+1)) - 1; + if (!t) + t = ~0UL; + printf(" t = 0x%lx i = %d\r", t, i); + do { + mp_set_ul(&a, t); + s = mp_get_ul(&a); + if (s != t) { + printf("\nmp_get_ul() bad result! 0x%lx != 0x%lx", s, t); + goto LBL_ERR; + } + t <<= 1; + } while (t != 0uL); + } + + mp_clear_multi(&a, &b, NULL); + return EXIT_SUCCESS; +LBL_ERR: + mp_clear_multi(&a, &b, NULL); + return EXIT_FAILURE; +} + +static int test_mp_get_u64(void) +{ + unsigned long long q, r; + int i; + + mp_int a, b; + if (mp_init_multi(&a, &b, NULL)!= MP_OKAY) { + return EXIT_FAILURE; + } + + for (i = 0; i < (int)(MP_SIZEOF_BITS(unsigned long long) - 1); ++i) { + r = (1ULL << (i+1)) - 1; + if (!r) + r = ~0ULL; + printf(" r = 0x%llx i = %d\r", r, i); + do { + mp_set_u64(&a, r); + q = mp_get_u64(&a); + if (q != r) { + printf("\nmp_get_u64() bad result! 0x%llx != 0x%llx", q, r); + goto LBL_ERR; + } + r <<= 1; + } while (r != 0uLL); + } + + mp_clear_multi(&a, &b, NULL); + return EXIT_SUCCESS; +LBL_ERR: + mp_clear_multi(&a, &b, NULL); + return EXIT_FAILURE; + +} + +static int test_mp_sqrt(void) +{ + int i, n; + + mp_int a, b, c; + if (mp_init_multi(&a, &b, &c, NULL)!= MP_OKAY) { + return EXIT_FAILURE; + } + + for (i = 0; i < 1000; ++i) { + printf("%6d\r", i); + fflush(stdout); + n = (rand_int() & 15) + 1; + mp_rand(&a, n); + if (mp_sqrt(&a, &b) != MP_OKAY) { + printf("\nmp_sqrt() error!"); + goto LBL_ERR; + } + mp_root_u32(&a, 2uL, &c); + if (mp_cmp_mag(&b, &c) != MP_EQ) { + printf("mp_sqrt() bad result!\n"); + goto LBL_ERR; + } + } + + mp_clear_multi(&a, &b, &c, NULL); + return EXIT_SUCCESS; +LBL_ERR: + mp_clear_multi(&a, &b, &c, NULL); + return EXIT_FAILURE; +} + +static int test_mp_is_square(void) +{ + int i, n; + + mp_int a, b; + mp_bool res; + + if (mp_init_multi(&a, &b, NULL)!= MP_OKAY) { + return EXIT_FAILURE; + } + + for (i = 0; i < 1000; ++i) { + printf("%6d\r", i); + fflush(stdout); + + /* test mp_is_square false negatives */ + n = (rand_int() & 7) + 1; + mp_rand(&a, n); + mp_sqr(&a, &a); + if (mp_is_square(&a, &res) != MP_OKAY) { + printf("\nfn:mp_is_square() error!"); + goto LBL_ERR; + } + if (res == MP_NO) { + printf("\nfn:mp_is_square() bad result!"); + goto LBL_ERR; + } + + /* test for false positives */ + mp_add_d(&a, 1uL, &a); + if (mp_is_square(&a, &res) != MP_OKAY) { + printf("\nfp:mp_is_square() error!"); + goto LBL_ERR; + } + if (res == MP_YES) { + printf("\nfp:mp_is_square() bad result!"); + goto LBL_ERR; + } + + } + printf("\n\n"); + + mp_clear_multi(&a, &b, NULL); + return EXIT_SUCCESS; +LBL_ERR: + mp_clear_multi(&a, &b, NULL); + return EXIT_FAILURE; +} + +static int test_mp_sqrtmod_prime(void) +{ + struct mp_sqrtmod_prime_st { + unsigned long p; + unsigned long n; + mp_digit r; + }; + + static struct mp_sqrtmod_prime_st sqrtmod_prime[] = { + { 5, 14, 3 }, + { 7, 9, 4 }, + { 113, 2, 62 } + }; + int i; + + mp_int a, b, c; + if (mp_init_multi(&a, &b, &c, NULL)!= MP_OKAY) { + return EXIT_FAILURE; + } + + /* r^2 = n (mod p) */ + for (i = 0; i < (int)(sizeof(sqrtmod_prime)/sizeof(sqrtmod_prime[0])); ++i) { + mp_set_ul(&a, sqrtmod_prime[i].p); + mp_set_ul(&b, sqrtmod_prime[i].n); + if (mp_sqrtmod_prime(&b, &a, &c) != MP_OKAY) { + printf("Failed executing %d. mp_sqrtmod_prime\n", (i+1)); + goto LBL_ERR; + } + if (mp_cmp_d(&c, sqrtmod_prime[i].r) != MP_EQ) { + printf("Failed %d. trivial mp_sqrtmod_prime\n", (i+1)); + ndraw(&c, "r"); + goto LBL_ERR; + } + } + + mp_clear_multi(&a, &b, &c, NULL); + return EXIT_SUCCESS; +LBL_ERR: + mp_clear_multi(&a, &b, &c, NULL); + return EXIT_FAILURE; +} + +static int test_mp_prime_rand(void) +{ + int ix; + mp_err err; + mp_int a, b; + if (mp_init_multi(&a, &b, NULL)!= MP_OKAY) { + return EXIT_FAILURE; + } + + /* test for size */ + for (ix = 10; ix < 128; ix++) { + printf("Testing (not safe-prime): %9d bits \r", ix); + fflush(stdout); + err = mp_prime_rand(&a, 8, ix, (rand_int() & 1) ? 0 : MP_PRIME_2MSB_ON); + if (err != MP_OKAY) { + printf("\nfailed with error: %s\n", mp_error_to_string(err)); + goto LBL_ERR; + } + if (mp_count_bits(&a) != ix) { + printf("Prime is %d not %d bits!!!\n", mp_count_bits(&a), ix); + goto LBL_ERR; + } + } + printf("\n"); + + mp_clear_multi(&a, &b, NULL); + return EXIT_SUCCESS; +LBL_ERR: + mp_clear_multi(&a, &b, NULL); + return EXIT_FAILURE; +} + +static int test_mp_prime_is_prime(void) +{ + int ix; + mp_err err; + mp_bool cnt, fu; + + mp_int a, b; + if (mp_init_multi(&a, &b, NULL)!= MP_OKAY) { + return EXIT_FAILURE; + } + + /* strong Miller-Rabin pseudoprime to the first 200 primes (F. Arnault) */ + puts("Testing mp_prime_is_prime() with Arnault's pseudoprime 803...901 \n"); + mp_read_radix(&a, + "91xLNF3roobhzgTzoFIG6P13ZqhOVYSN60Fa7Cj2jVR1g0k89zdahO9/kAiRprpfO1VAp1aBHucLFV/qLKLFb+zonV7R2Vxp1K13ClwUXStpV0oxTNQVjwybmFb5NBEHImZ6V7P6+udRJuH8VbMEnS0H8/pSqQrg82OoQQ2fPpAk6G1hkjqoCv5s/Yr", + 64); + mp_prime_is_prime(&a, mp_prime_rabin_miller_trials(mp_count_bits(&a)), &cnt); + if (cnt == MP_YES) { + printf("Arnault's pseudoprime is not prime but mp_prime_is_prime says it is.\n"); + goto LBL_ERR; + } + /* About the same size as Arnault's pseudoprime */ + puts("Testing mp_prime_is_prime() with certified prime 2^1119 + 53\n"); + mp_set(&a, 1uL); + mp_mul_2d(&a,1119,&a); + mp_add_d(&a, 53uL, &a); + err = mp_prime_is_prime(&a, mp_prime_rabin_miller_trials(mp_count_bits(&a)), &cnt); + /* small problem */ + if (err != MP_OKAY) { + printf("\nfailed with error: %s\n", mp_error_to_string(err)); + } + /* large problem */ + if (cnt == MP_NO) { + printf("A certified prime is a prime but mp_prime_is_prime says it is not.\n"); + } + if ((err != MP_OKAY) || (cnt == MP_NO)) { + printf("prime tested was: 0x"); + mp_fwrite(&a,16,stdout); + putchar('\n'); + goto LBL_ERR; + } + for (ix = 16; ix < 128; ix++) { + printf("Testing ( safe-prime): %9d bits \r", ix); + fflush(stdout); + err = mp_prime_rand(&a, 8, ix, ((rand_int() & 1) ? 0 : MP_PRIME_2MSB_ON) | MP_PRIME_SAFE); + if (err != MP_OKAY) { + printf("\nfailed with error: %s\n", mp_error_to_string(err)); + goto LBL_ERR; + } + if (mp_count_bits(&a) != ix) { + printf("Prime is %d not %d bits!!!\n", mp_count_bits(&a), ix); + goto LBL_ERR; + } + /* let's see if it's really a safe prime */ + mp_sub_d(&a, 1uL, &b); + mp_div_2(&b, &b); + err = mp_prime_is_prime(&b, mp_prime_rabin_miller_trials(mp_count_bits(&b)), &cnt); + /* small problem */ + if (err != MP_OKAY) { + printf("\nfailed with error: %s\n", mp_error_to_string(err)); + } + /* large problem */ + if (cnt == MP_NO) { + printf("\nsub is not prime!\n"); + } + mp_prime_frobenius_underwood(&b, &fu); + if (fu == MP_NO) { + printf("\nfrobenius-underwood says sub is not prime!\n"); + } + if ((err != MP_OKAY) || (cnt == MP_NO)) { + printf("prime tested was: 0x"); + mp_fwrite(&a,16,stdout); + putchar('\n'); + printf("sub tested was: 0x"); + mp_fwrite(&b,16,stdout); + putchar('\n'); + goto LBL_ERR; + } + + } + /* Check regarding problem #143 */ +#ifndef MP_8BIT + mp_read_radix(&a, + "FFFFFFFFFFFFFFFFC90FDAA22168C234C4C6628B80DC1CD129024E088A67CC74020BBEA63B139B22514A08798E3404DDEF9519B3CD3A431B302B0A6DF25F14374FE1356D6D51C245E485B576625E7EC6F44C42E9A63A3620FFFFFFFFFFFFFFFF", + 16); + err = mp_prime_strong_lucas_selfridge(&a, &cnt); + /* small problem */ + if (err != MP_OKAY) { + printf("\nmp_prime_strong_lucas_selfridge failed with error: %s\n", mp_error_to_string(err)); + } + /* large problem */ + if (cnt == MP_NO) { + printf("\n\nissue #143 - mp_prime_strong_lucas_selfridge FAILED!\n"); + } + if ((err != MP_OKAY) || (cnt == MP_NO)) { + printf("prime tested was: 0x"); + mp_fwrite(&a,16,stdout); + putchar('\n'); + goto LBL_ERR; + } +#endif + + printf("\n\n"); + + mp_clear_multi(&a, &b, NULL); + return EXIT_SUCCESS; +LBL_ERR: + mp_clear_multi(&a, &b, NULL); + return EXIT_FAILURE; + +} + + +static int test_mp_prime_next_prime(void) +{ + mp_err err; + mp_int a, b, c; + + mp_init_multi(&a, &b, &c, NULL); + + + /* edge cases */ + mp_set(&a, 0u); + if ((err = mp_prime_next_prime(&a, 5, 0)) != MP_OKAY) { + goto LBL_ERR; + } + if (mp_cmp_d(&a, 2u) != MP_EQ) { + printf("mp_prime_next_prime: output should have been 2 but was: "); + mp_fwrite(&a,10,stdout); + putchar('\n'); + goto LBL_ERR; + } + + mp_set(&a, 0u); + if ((err = mp_prime_next_prime(&a, 5, 1)) != MP_OKAY) { + goto LBL_ERR; + } + if (mp_cmp_d(&a, 3u) != MP_EQ) { + printf("mp_prime_next_prime: output should have been 3 but was: "); + mp_fwrite(&a,10,stdout); + putchar('\n'); + goto LBL_ERR; + } + + mp_set(&a, 2u); + if ((err = mp_prime_next_prime(&a, 5, 0)) != MP_OKAY) { + goto LBL_ERR; + } + if (mp_cmp_d(&a, 3u) != MP_EQ) { + printf("mp_prime_next_prime: output should have been 3 but was: "); + mp_fwrite(&a,10,stdout); + putchar('\n'); + goto LBL_ERR; + } + + mp_set(&a, 2u); + if ((err = mp_prime_next_prime(&a, 5, 1)) != MP_OKAY) { + goto LBL_ERR; + } + if (mp_cmp_d(&a, 3u) != MP_EQ) { + printf("mp_prime_next_prime: output should have been 3 but was: "); + mp_fwrite(&a,10,stdout); + putchar('\n'); + goto LBL_ERR; + } + mp_set(&a, 8); + if ((err = mp_prime_next_prime(&a, 5, 1)) != MP_OKAY) { + goto LBL_ERR; + } + if (mp_cmp_d(&a, 11u) != MP_EQ) { + printf("mp_prime_next_prime: output should have been 11 but was: "); + mp_fwrite(&a,10,stdout); + putchar('\n'); + goto LBL_ERR; + } + /* 2^300 + 157 is a 300 bit large prime to guarantee a multi-limb bigint */ + if ((err = mp_2expt(&a, 300)) != MP_OKAY) { + goto LBL_ERR; + } + mp_set_u32(&b, 157); + if ((err = mp_add(&a, &b, &a)) != MP_OKAY) { + goto LBL_ERR; + } + if ((err = mp_copy(&a, &b)) != MP_OKAY) { + goto LBL_ERR; + } + + /* 2^300 + 385 is the next prime */ + mp_set_u32(&c, 228); + if ((err = mp_add(&b, &c, &b)) != MP_OKAY) { + goto LBL_ERR; + } + if ((err = mp_prime_next_prime(&a, 5, 0)) != MP_OKAY) { + goto LBL_ERR; + } + if (mp_cmp(&a, &b) != MP_EQ) { + printf("mp_prime_next_prime: output should have been\n"); + mp_fwrite(&b,10,stdout); + putchar('\n'); + printf("but was:\n"); + mp_fwrite(&a,10,stdout); + putchar('\n'); + goto LBL_ERR; + } + + /* Use another temporary variable or recompute? Mmh... */ + if ((err = mp_2expt(&a, 300)) != MP_OKAY) { + goto LBL_ERR; + } + mp_set_u32(&b, 157); + if ((err = mp_add(&a, &b, &a)) != MP_OKAY) { + goto LBL_ERR; + } + if ((err = mp_copy(&a, &b)) != MP_OKAY) { + goto LBL_ERR; + } + + /* 2^300 + 631 is the next prime congruent to 3 mod 4*/ + mp_set_u32(&c, 474); + if ((err = mp_add(&b, &c, &b)) != MP_OKAY) { + goto LBL_ERR; + } + if ((err = mp_prime_next_prime(&a, 5, 1)) != MP_OKAY) { + goto LBL_ERR; + } + if (mp_cmp(&a, &b) != MP_EQ) { + printf("mp_prime_next_prime (bbs): output should have been\n"); + mp_fwrite(&b,10,stdout); + putchar('\n'); + printf("but was:\n"); + mp_fwrite(&a,10,stdout); + putchar('\n'); + goto LBL_ERR; + } + + mp_clear_multi(&a, &b, &c, NULL); + return EXIT_SUCCESS; +LBL_ERR: + mp_clear_multi(&a, &b, &c, NULL); + return EXIT_FAILURE; +} + +static int test_mp_montgomery_reduce(void) +{ + mp_digit mp; + int ix, i, n; + char buf[4096]; + + /* size_t written; */ + + mp_int a, b, c, d, e; + if (mp_init_multi(&a, &b, &c, &d, &e, NULL)!= MP_OKAY) { + return EXIT_FAILURE; + } + + /* test montgomery */ + for (i = 1; i <= 10; i++) { + if (i == 10) + i = 1000; + printf(" digit size: %2d\r", i); + fflush(stdout); + for (n = 0; n < 1000; n++) { + mp_rand(&a, i); + a.dp[0] |= 1; + + /* let's see if R is right */ + mp_montgomery_calc_normalization(&b, &a); + mp_montgomery_setup(&a, &mp); + + /* now test a random reduction */ + for (ix = 0; ix < 100; ix++) { + mp_rand(&c, 1 + abs(rand_int()) % (2*i)); + mp_copy(&c, &d); + mp_copy(&c, &e); + + mp_mod(&d, &a, &d); + mp_montgomery_reduce(&c, &a, mp); + mp_mulmod(&c, &b, &a, &c); + + if (mp_cmp(&c, &d) != MP_EQ) { +/* *INDENT-OFF* */ + printf("d = e mod a, c = e MOD a\n"); + mp_to_decimal(&a, buf, sizeof(buf)); printf("a = %s\n", buf); + mp_to_decimal(&e, buf, sizeof(buf)); printf("e = %s\n", buf); + mp_to_decimal(&d, buf, sizeof(buf)); printf("d = %s\n", buf); + mp_to_decimal(&c, buf, sizeof(buf)); printf("c = %s\n", buf); + + printf("compare no compare!\n"); goto LBL_ERR; +/* *INDENT-ON* */ + } + /* only one big montgomery reduction */ + if (i > 10) { + n = 1000; + ix = 100; + } + } + } + } + + printf("\n\n"); + + mp_clear_multi(&a, &b, &c, &d, &e, NULL); + return EXIT_SUCCESS; +LBL_ERR: + mp_clear_multi(&a, &b, &c, &d, &e, NULL); + return EXIT_FAILURE; + +} + +static int test_mp_read_radix(void) +{ + char buf[4096]; + size_t written; + mp_err err; + + mp_int a; + if (mp_init_multi(&a, NULL)!= MP_OKAY) goto LTM_ERR; + + if ((err = mp_read_radix(&a, "123456", 10)) != MP_OKAY) goto LTM_ERR; + + if ((err = mp_to_radix(&a, buf, SIZE_MAX, &written, 10)) != MP_OKAY) goto LTM_ERR; + printf(" '123456' a == %s, length = %zu\n", buf, written); + + /* See comment in bn_mp_to_radix.c */ + /* + if( (err = mp_to_radix(&a, buf, 3u, &written, 10) ) != MP_OKAY) goto LTM_ERR; + printf(" '56' a == %s, length = %zu\n", buf, written); + + if( (err = mp_to_radix(&a, buf, 4u, &written, 10) ) != MP_OKAY) goto LTM_ERR; + printf(" '456' a == %s, length = %zu\n", buf, written); + if( (err = mp_to_radix(&a, buf, 30u, &written, 10) ) != MP_OKAY) goto LTM_ERR; + printf(" '123456' a == %s, length = %zu, error = %s\n", + buf, written, mp_error_to_string(err)); + */ + if ((err = mp_read_radix(&a, "-123456", 10)) != MP_OKAY) goto LTM_ERR; + if ((err = mp_to_radix(&a, buf, SIZE_MAX, &written, 10)) != MP_OKAY) goto LTM_ERR; + printf(" '-123456' a == %s, length = %zu\n", buf, written); + + if ((err = mp_read_radix(&a, "0", 10)) != MP_OKAY) goto LTM_ERR; + if ((err = mp_to_radix(&a, buf, SIZE_MAX, &written, 10)) != MP_OKAY) goto LTM_ERR; + printf(" '0' a == %s, length = %zu\n", buf, written); + + + + /* Although deprecated it needs to function as long as it isn't dropped */ + /* + printf("Testing deprecated mp_toradix_n\n"); + if( (err = mp_read_radix(&a, "-123456", 10) ) != MP_OKAY) goto LTM_ERR; + if( (err = mp_toradix_n(&a, buf, 10, 3) ) != MP_OKAY) goto LTM_ERR; + printf("a == %s\n", buf); + if( (err = mp_toradix_n(&a, buf, 10, 4) ) != MP_OKAY) goto LTM_ERR; + printf("a == %s\n", buf); + if( (err = mp_toradix_n(&a, buf, 10, 30) ) != MP_OKAY) goto LTM_ERR; + printf("a == %s\n", buf); + */ + + + while (0) { + char *s = fgets(buf, sizeof(buf), stdin); + if (s != buf) break; + mp_read_radix(&a, buf, 10); + mp_prime_next_prime(&a, 5, 1); + mp_to_radix(&a, buf, sizeof(buf), NULL, 10); + printf("%s, %lu\n", buf, (unsigned long)a.dp[0] & 3uL); + } + + mp_clear(&a); + return EXIT_SUCCESS; +LTM_ERR: + mp_clear(&a); + return EXIT_FAILURE; +} + +static int test_mp_cnt_lsb(void) +{ + int ix; + + mp_int a, b; + if (mp_init_multi(&a, &b, NULL)!= MP_OKAY) { + return EXIT_FAILURE; + } + + mp_set(&a, 1uL); + for (ix = 0; ix < 1024; ix++) { + if (mp_cnt_lsb(&a) != ix) { + printf("Failed at %d, %d\n", ix, mp_cnt_lsb(&a)); + goto LBL_ERR; + } + mp_mul_2(&a, &a); + } + + mp_clear_multi(&a, &b, NULL); + return EXIT_SUCCESS; +LBL_ERR: + mp_clear_multi(&a, &b, NULL); + return EXIT_FAILURE; + +} + +static int test_mp_reduce_2k(void) +{ + int ix, cnt; + + mp_int a, b, c, d; + if (mp_init_multi(&a, &b, &c, &d, NULL)!= MP_OKAY) { + return EXIT_FAILURE; + } + + /* test mp_reduce_2k */ + for (cnt = 3; cnt <= 128; ++cnt) { + mp_digit tmp; + + mp_2expt(&a, cnt); + mp_sub_d(&a, 2uL, &a); /* a = 2**cnt - 2 */ + + printf("\r %4d bits", cnt); + printf("(%d)", mp_reduce_is_2k(&a)); + mp_reduce_2k_setup(&a, &tmp); + printf("(%lu)", (unsigned long) tmp); + for (ix = 0; ix < 1000; ix++) { + if (!(ix & 127)) { + printf("."); + fflush(stdout); + } + mp_rand(&b, (cnt / MP_DIGIT_BIT + 1) * 2); + mp_copy(&c, &b); + mp_mod(&c, &a, &c); + mp_reduce_2k(&b, &a, 2uL); + if (mp_cmp(&c, &b) != MP_EQ) { + printf("FAILED\n"); + goto LBL_ERR; + } + } + } + + mp_clear_multi(&a, &b, &c, &d, NULL); + return EXIT_SUCCESS; +LBL_ERR: + mp_clear_multi(&a, &b, &c, &d, NULL); + return EXIT_FAILURE; +} + +static int test_mp_div_3(void) +{ + int cnt; + + mp_int a, b, c, d, e; + if (mp_init_multi(&a, &b, &c, &d, &e, NULL)!= MP_OKAY) { + return EXIT_FAILURE; + } + + /* test mp_div_3 */ + mp_set(&d, 3uL); + for (cnt = 0; cnt < 10000;) { + mp_digit r2; + + if (!(++cnt & 127)) { + printf("%9d\r", cnt); + fflush(stdout); + } + mp_rand(&a, abs(rand_int()) % 128 + 1); + mp_div(&a, &d, &b, &e); + mp_div_3(&a, &c, &r2); + + if (mp_cmp(&b, &c) || mp_cmp_d(&e, r2)) { + printf("\nmp_div_3 => Failure\n"); + goto LBL_ERR; + } + } + printf("\nPassed div_3 testing"); + + mp_clear_multi(&a, &b, &c, &d, &e, NULL); + return EXIT_SUCCESS; +LBL_ERR: + mp_clear_multi(&a, &b, &c, &d, &e, NULL); + return EXIT_FAILURE; +} + +static int test_mp_dr_reduce(void) +{ + mp_digit mp; + int cnt; + unsigned rr; + int ix; + + mp_int a, b, c; + if (mp_init_multi(&a, &b, &c, NULL)!= MP_OKAY) { + return EXIT_FAILURE; + } + + /* test the DR reduction */ + for (cnt = 2; cnt < 32; cnt++) { + printf("\r%d digit modulus", cnt); + mp_grow(&a, cnt); + mp_zero(&a); + for (ix = 1; ix < cnt; ix++) { + a.dp[ix] = MP_MASK; + } + a.used = cnt; + a.dp[0] = 3; + + mp_rand(&b, cnt - 1); + mp_copy(&b, &c); + + rr = 0; + do { + if (!(rr & 127)) { + printf("."); + fflush(stdout); + } + mp_sqr(&b, &b); + mp_add_d(&b, 1uL, &b); + mp_copy(&b, &c); + + mp_mod(&b, &a, &b); + mp_dr_setup(&a, &mp); + mp_dr_reduce(&c, &a, mp); + + if (mp_cmp(&b, &c) != MP_EQ) { + printf("Failed on trial %u\n", rr); + goto LBL_ERR; + } + } while (++rr < 500); + printf(" passed"); + fflush(stdout); + } + + mp_clear_multi(&a, &b, &c, NULL); + return EXIT_SUCCESS; +LBL_ERR: + mp_clear_multi(&a, &b, &c, NULL); + return EXIT_FAILURE; +} + +static int test_mp_reduce_2k_l(void) +{ +# if LTM_DEMO_TEST_REDUCE_2K_L + mp_int a, b, c, d; + int cnt; + char buf[4096]; + size_t length[1]; + if (mp_init_multi(&a, &b, NULL)!= MP_OKAY) { + return EXIT_FAILURE; + } + /* test the mp_reduce_2k_l code */ +# if LTM_DEMO_TEST_REDUCE_2K_L == 1 + /* first load P with 2^1024 - 0x2A434 B9FDEC95 D8F9D550 FFFFFFFF FFFFFFFF */ + mp_2expt(&a, 1024); + mp_read_radix(&b, "2A434B9FDEC95D8F9D550FFFFFFFFFFFFFFFF", 16); + mp_sub(&a, &b, &a); +# elif LTM_DEMO_TEST_REDUCE_2K_L == 2 + /* p = 2^2048 - 0x1 00000000 00000000 00000000 00000000 4945DDBF 8EA2A91D 5776399B B83E188F */ + mp_2expt(&a, 2048); + mp_read_radix(&b, + "1000000000000000000000000000000004945DDBF8EA2A91D5776399BB83E188F", + 16); + mp_sub(&a, &b, &a); +# else +# error oops +# endif + *length = sizeof(buf); + mp_to_radix(&a, buf, length, 10); + printf("\n\np==%s, length = %zu\n", buf, *length); + /* now mp_reduce_is_2k_l() should return */ + if (mp_reduce_is_2k_l(&a) != 1) { + printf("mp_reduce_is_2k_l() return 0, should be 1\n"); + goto LBL_ERR; + } + mp_reduce_2k_setup_l(&a, &d); + /* now do a million square+1 to see if it varies */ + mp_rand(&b, 64); + mp_mod(&b, &a, &b); + mp_copy(&b, &c); + printf("Testing: mp_reduce_2k_l..."); + fflush(stdout); + for (cnt = 0; cnt < (int)(1uL << 20); cnt++) { + mp_sqr(&b, &b); + mp_add_d(&b, 1uL, &b); + mp_reduce_2k_l(&b, &a, &d); + mp_sqr(&c, &c); + mp_add_d(&c, 1uL, &c); + mp_mod(&c, &a, &c); + if (mp_cmp(&b, &c) != MP_EQ) { + printf("mp_reduce_2k_l() failed at step %d\n", cnt); + mp_to_hex(&b, buf, sizeof(buf)); + printf("b == %s\n", buf); + mp_to_hex(&c, buf, sizeof(buf)); + printf("c == %s\n", buf); + goto LBL_ERR; + } + } + + mp_clear_multi(&a, &b, NULL); + return EXIT_SUCCESS; +LBL_ERR: + mp_clear_multi(&a, &b, NULL); + return EXIT_FAILURE; +#else + return EXIT_SUCCESS; +# endif /* LTM_DEMO_TEST_REDUCE_2K_L */ +} +/* stripped down version of mp_radix_size. The faster version can be off by up t +o +3 */ +/* TODO: This function should be removed, replaced by mp_radix_size, mp_radix_size_overestimate in 2.0 */ +static mp_err s_rs(const mp_int *a, int radix, uint32_t *size) +{ + mp_err res; + uint32_t digs = 0u; + mp_int t; + mp_digit d; + *size = 0u; + if (mp_iszero(a) == MP_YES) { + *size = 2u; + return MP_OKAY; + } + if (radix == 2) { + *size = (uint32_t)mp_count_bits(a) + 1u; + return MP_OKAY; + } + if ((res = mp_init_copy(&t, a)) != MP_OKAY) { + return res; + } + t.sign = MP_ZPOS; + while (mp_iszero(&t) == MP_NO) { + if ((res = mp_div_d(&t, (mp_digit)radix, &t, &d)) != MP_OKAY) { + mp_clear(&t); + return res; + } + ++digs; + } + mp_clear(&t); + *size = digs + 1; + return MP_OKAY; +} +static int test_mp_log_u32(void) +{ + mp_int a; + mp_digit d; + uint32_t base, lb, size; + const uint32_t max_base = MP_MIN(UINT32_MAX, MP_DIGIT_MAX); + + if (mp_init(&a) != MP_OKAY) { + goto LBL_ERR; + } + + /* + base a result + 0 x MP_VAL + 1 x MP_VAL + */ + mp_set(&a, 42uL); + base = 0u; + if (mp_log_u32(&a, base, &lb) != MP_VAL) { + goto LBL_ERR; + } + base = 1u; + if (mp_log_u32(&a, base, &lb) != MP_VAL) { + goto LBL_ERR; + } + /* + base a result + 2 0 MP_VAL + 2 1 0 + 2 2 1 + 2 3 1 + */ + base = 2u; + mp_zero(&a); + if (mp_log_u32(&a, base, &lb) != MP_VAL) { + goto LBL_ERR; + } + + for (d = 1; d < 4; d++) { + mp_set(&a, d); + if (mp_log_u32(&a, base, &lb) != MP_OKAY) { + goto LBL_ERR; + } + if (lb != ((d == 1)?0uL:1uL)) { + goto LBL_ERR; + } + } + /* + base a result + 3 0 MP_VAL + 3 1 0 + 3 2 0 + 3 3 1 + */ + base = 3u; + mp_zero(&a); + if (mp_log_u32(&a, base, &lb) != MP_VAL) { + goto LBL_ERR; + } + for (d = 1; d < 4; d++) { + mp_set(&a, d); + if (mp_log_u32(&a, base, &lb) != MP_OKAY) { + goto LBL_ERR; + } + if (lb != ((d < base)?0uL:1uL)) { + goto LBL_ERR; + } + } + + /* + bases 2..64 with "a" a random large constant. + The range of bases tested allows to check with + radix_size. + */ + if (mp_rand(&a, 10) != MP_OKAY) { + goto LBL_ERR; + } + for (base = 2u; base < 65u; base++) { + if (mp_log_u32(&a, base, &lb) != MP_OKAY) { + goto LBL_ERR; + } + if (s_rs(&a,(int)base, &size) != MP_OKAY) { + goto LBL_ERR; + } + /* radix_size includes the memory needed for '\0', too*/ + size -= 2; + if (lb != size) { + goto LBL_ERR; + } + } + + /* + bases 2..64 with "a" a random small constant to + test the part of mp_ilogb that uses native types. + */ + if (mp_rand(&a, 1) != MP_OKAY) { + goto LBL_ERR; + } + for (base = 2u; base < 65u; base++) { + if (mp_log_u32(&a, base, &lb) != MP_OKAY) { + goto LBL_ERR; + } + if (s_rs(&a,(int)base, &size) != MP_OKAY) { + goto LBL_ERR; + } + size -= 2; + if (lb != size) { + goto LBL_ERR; + } + } + + /*Test upper edgecase with base UINT32_MAX and number (UINT32_MAX/2)*UINT32_MAX^10 */ + mp_set(&a, max_base); + if (mp_expt_u32(&a, 10uL, &a) != MP_OKAY) { + goto LBL_ERR; + } + if (mp_add_d(&a, max_base / 2, &a) != MP_OKAY) { + goto LBL_ERR; + } + if (mp_log_u32(&a, max_base, &lb) != MP_OKAY) { + goto LBL_ERR; + } + if (lb != 10u) { + goto LBL_ERR; + } + + mp_clear(&a); + return EXIT_SUCCESS; +LBL_ERR: + mp_clear(&a); + return EXIT_FAILURE; +} + +static int test_mp_incr(void) +{ + mp_int a, b; + mp_err e = MP_OKAY; + + if ((e = mp_init_multi(&a, &b, NULL)) != MP_OKAY) { + goto LTM_ERR; + } + + /* Does it increment inside the limits of a MP_xBIT limb? */ + mp_set(&a, MP_MASK/2); + if ((e = mp_incr(&a)) != MP_OKAY) { + goto LTM_ERR; + } + if (mp_cmp_d(&a, (MP_MASK/2uL) + 1uL) != MP_EQ) { + goto LTM_ERR; + } + + /* Does it increment outside of the limits of a MP_xBIT limb? */ + mp_set(&a, MP_MASK); + mp_set(&b, MP_MASK); + if ((e = mp_incr(&a)) != MP_OKAY) { + goto LTM_ERR; + } + if ((e = mp_add_d(&b, 1uL, &b)) != MP_OKAY) { + goto LTM_ERR; + } + if (mp_cmp(&a, &b) != MP_EQ) { + goto LTM_ERR; + } + + /* Does it increment from -1 to 0? */ + mp_set(&a, 1uL); + a.sign = MP_NEG; + if ((e = mp_incr(&a)) != MP_OKAY) { + goto LTM_ERR; + } + if (mp_cmp_d(&a, 0uL) != MP_EQ) { + goto LTM_ERR; + } + + /* Does it increment from -(MP_MASK + 1) to -MP_MASK? */ + mp_set(&a, MP_MASK); + if ((e = mp_add_d(&a, 1uL, &a)) != MP_OKAY) { + goto LTM_ERR; + } + a.sign = MP_NEG; + if ((e = mp_incr(&a)) != MP_OKAY) { + goto LTM_ERR; + } + if (a.sign != MP_NEG) { + goto LTM_ERR; + } + a.sign = MP_ZPOS; + if (mp_cmp_d(&a, MP_MASK) != MP_EQ) { + goto LTM_ERR; + } + + mp_clear_multi(&a, &b, NULL); + return EXIT_SUCCESS; +LTM_ERR: + mp_clear_multi(&a, &b, NULL); + return EXIT_FAILURE; +} + +static int test_mp_decr(void) +{ + mp_int a, b; + mp_err e = MP_OKAY; + + if ((e = mp_init_multi(&a, &b, NULL)) != MP_OKAY) { + goto LTM_ERR; + } + + /* Does it decrement inside the limits of a MP_xBIT limb? */ + mp_set(&a, MP_MASK/2); + if ((e = mp_decr(&a)) != MP_OKAY) { + goto LTM_ERR; + } + if (mp_cmp_d(&a, (MP_MASK/2uL) - 1uL) != MP_EQ) { + goto LTM_ERR; + } + + /* Does it decrement outside of the limits of a MP_xBIT limb? */ + mp_set(&a, MP_MASK); + if ((e = mp_add_d(&a, 1uL, &a)) != MP_OKAY) { + goto LTM_ERR; + } + if ((e = mp_decr(&a)) != MP_OKAY) { + goto LTM_ERR; + } + if (mp_cmp_d(&a, MP_MASK) != MP_EQ) { + goto LTM_ERR; + } + + /* Does it decrement from 0 to -1? */ + mp_zero(&a); + if ((e = mp_decr(&a)) != MP_OKAY) { + goto LTM_ERR; + } + if (a.sign == MP_NEG) { + a.sign = MP_ZPOS; + if (mp_cmp_d(&a, 1uL) != MP_EQ) { + goto LTM_ERR; + } + } else { + goto LTM_ERR; + } + + + /* Does it decrement from -MP_MASK to -(MP_MASK + 1)? */ + mp_set(&a, MP_MASK); + a.sign = MP_NEG; + mp_set(&b, MP_MASK); + b.sign = MP_NEG; + if ((e = mp_sub_d(&b, 1uL, &b)) != MP_OKAY) { + goto LTM_ERR; + } + if ((e = mp_decr(&a)) != MP_OKAY) { + goto LTM_ERR; + } + if (mp_cmp(&a, &b) != MP_EQ) { + goto LTM_ERR; + } + + mp_clear_multi(&a, &b, NULL); + return EXIT_SUCCESS; +LTM_ERR: + mp_clear_multi(&a, &b, NULL); + return EXIT_FAILURE; +} + +/* + Cannot test mp_exp(_d) without mp_root and vice versa. + So one of the two has to be tested from scratch. + + Numbers generated by + for i in {1..10} + do + seed=$(head -c 10000 /dev/urandom | tr -dc '[:digit:]' | head -c 120); + echo $seed; + convertbase $seed 10 64; + done + + (The program "convertbase" uses libtommath's to/from_radix functions) + + Roots were precalculated with Pari/GP + + default(realprecision,1000); + for(n=3,100,r = floor(a^(1/n));printf("\"" r "\", ")) + + All numbers as strings to simplifiy things, especially for the + low-mp branch. +*/ + +static int test_mp_root_u32(void) +{ + mp_int a, c, r; + mp_err e; + int i, j; + + const char *input[] = { + "4n9cbk886QtLQmofprid3l2Q0GD8Yv979Lh8BdZkFE8g2pDUUSMBET/+M/YFyVZ3mBp", + "5NlgzHhmIX05O5YoW5yW5reAlVNtRAlIcN2dfoATnNdc1Cw5lHZUTwNthmK6/ZLKfY6", + "3gweiHDX+ji5utraSe46IJX+uuh7iggs63xIpMP5MriU4Np+LpHI5are8RzS9pKh9xP", + "5QOJUSKMrfe7LkeyJOlupS8h7bjT+TXmZkDzOjZtfj7mdA7cbg0lRX3CuafhjIrpK8S", + "4HtYFldVkyVbrlg/s7kmaA7j45PvLQm+1bbn6ehgP8tVoBmGbv2yDQI1iQQze4AlHyN", + "3bwCUx79NAR7c68OPSp5ZabhZ9aBEr7rWNTO2oMY7zhbbbw7p6shSMxqE9K9nrTNucf", + "4j5RGb78TfuYSzrXn0z6tiAoWiRI81hGY3el9AEa9S+gN4x/AmzotHT2Hvj6lyBpE7q", + "4lwg30SXqZhEHNsl5LIXdyu7UNt0VTWebP3m7+WUL+hsnFW9xJe7UnzYngZsvWh14IE", + "1+tcqFeRuGqjRADRoRUJ8gL4UUSFQVrVVoV6JpwVcKsuBq5G0pABn0dLcQQQMViiVRj", + "hXwxuFySNSFcmbrs/coz4FUAaUYaOEt+l4V5V8vY71KyBvQPxRq/6lsSrG2FHvWDax" + }; + /* roots 3-100 of the above */ + const char *root[10][100] = { + { + "9163694094944489658600517465135586130944", + "936597377180979771960755204040", "948947857956884030956907", + "95727185767390496595", "133844854039712620", "967779611885360", + "20926191452627", "974139547476", "79203891950", "9784027073", + "1667309744", "365848129", "98268452", "31109156", "11275351", + "4574515", "2040800", "986985", "511525", "281431", "163096", + "98914", "62437", "40832", "27556", "19127", "13614", "9913", + "7367", "5577", "4294", "3357", "2662", "2138", "1738", "1428", + "1185", "993", "839", "715", "613", "530", "461", "403", "355", + "314", "279", "249", "224", "202", "182", "166", "151", "138", + "126", "116", "107", "99", "92", "85", "79", "74", "69", "65", "61", + "57", "54", "51", "48", "46", "43", "41", "39", "37", "36", "34", + "32", "31", "30", "28", "27", "26", "25", "24", "23", "23", "22", + "21", "20", "20", "19", "18", "18", "17", "17", "16", "16", "15" + }, { + "9534798256755061606359588498764080011382", + "964902943621813525741417593772", "971822399862464674540423", + "97646291566833512831", "136141536090599560", "982294733581430", + "21204945933335", "985810529393", "80066084985", "9881613813", + "1682654547", "368973625", "99051783", "31341581", "11354620", + "4604882", "2053633", "992879", "514434", "282959", "163942", + "99406", "62736", "41020", "27678", "19208", "13670", "9952", + "7395", "5598", "4310", "3369", "2671", "2145", "1744", "1433", + "1189", "996", "842", "717", "615", "531", "462", "404", "356", + "315", "280", "250", "224", "202", "183", "166", "151", "138", + "127", "116", "107", "99", "92", "85", "80", "74", "70", "65", "61", + "58", "54", "51", "48", "46", "43", "41", "39", "37", "36", "34", + "32", "31", "30", "29", "27", "26", "25", "24", "23", "23", "22", + "21", "20", "20", "19", "18", "18", "17", "17", "16", "16", "15" + }, { + "8398539113202579297642815367509019445624", + "877309458945432597462853440936", "900579899458998599215071", + "91643543761699761637", "128935656335800903", "936647990947203", + "20326748623514", "948988882684", "77342677787", "9573063447", + "1634096832", "359076114", "96569670", "30604705", "11103188", + "4508519", "2012897", "974160", "505193", "278105", "161251", + "97842", "61788", "40423", "27291", "18949", "13492", "9826", + "7305", "5532", "4260", "3332", "2642", "2123", "1726", "1418", + "1177", "986", "834", "710", "610", "527", "458", "401", "353", + "312", "278", "248", "223", "201", "181", "165", "150", "137", + "126", "116", "107", "99", "91", "85", "79", "74", "69", "65", "61", + "57", "54", "51", "48", "46", "43", "41", "39", "37", "35", "34", + "32", "31", "30", "28", "27", "26", "25", "24", "23", "22", "22", + "21", "20", "20", "19", "18", "18", "17", "17", "16", "16", "15" + }, { + "9559098494021810340217797724866627755195", + "966746709063325235560830083787", "973307706084821682248292", + "97770642291138756434", "136290128605981259", "983232784778520", + "21222944848922", "986563584410", "80121684894", "9887903837", + "1683643206", "369174929", "99102220", "31356542", "11359721", + "4606836", "2054458", "993259", "514621", "283057", "163997", + "99437", "62755", "41032", "27686", "19213", "13674", "9955", + "7397", "5599", "4311", "3370", "2672", "2146", "1744", "1433", + "1189", "996", "842", "717", "615", "532", "462", "404", "356", + "315", "280", "250", "224", "202", "183", "166", "151", "138", + "127", "116", "107", "99", "92", "86", "80", "74", "70", "65", "61", + "58", "54", "51", "48", "46", "43", "41", "39", "37", "36", "34", + "32", "31", "30", "29", "27", "26", "25", "24", "23", "23", "22", + "21", "20", "20", "19", "18", "18", "17", "17", "16", "16", "15" + }, { + "8839202025813295923132694443541993309220", + "911611499784863252820288596270", "928640961450376817534853", + "94017030509441723821", "131792686685970629", "954783483196511", + "20676214073400", "963660189823", "78428929840", "9696237956", + "1653495486", "363032624", "97562430", "30899570", "11203842", + "4547110", "2029216", "981661", "508897", "280051", "162331", + "98469", "62168", "40663", "27446", "19053", "13563", "9877", + "7341", "5558", "4280", "3347", "2654", "2132", "1733", "1424", + "1182", "990", "837", "713", "612", "529", "460", "402", "354", + "313", "279", "249", "223", "201", "182", "165", "150", "138", + "126", "116", "107", "99", "92", "85", "79", "74", "69", "65", "61", + "57", "54", "51", "48", "46", "43", "41", "39", "37", "36", "34", + "32", "31", "30", "28", "27", "26", "25", "24", "23", "23", "22", + "21", "20", "20", "19", "18", "18", "17", "17", "16", "16", "15" + }, { + "8338442683973420410660145045849076963795", + "872596990706967613912664152945", "896707843885562730147307", + "91315073695274540969", "128539440806486007", "934129001105825", + "20278149285734", "946946589774", "77191347471", "9555892093", + "1631391010", "358523975", "96431070", "30563524", "11089126", + "4503126", "2010616", "973111", "504675", "277833", "161100", + "97754", "61734", "40390", "27269", "18934", "13482", "9819", + "7300", "5528", "4257", "3330", "2641", "2122", "1725", "1417", + "1177", "986", "833", "710", "609", "527", "458", "401", "353", + "312", "278", "248", "222", "200", "181", "165", "150", "137", + "126", "116", "107", "99", "91", "85", "79", "74", "69", "65", "61", + "57", "54", "51", "48", "46", "43", "41", "39", "37", "35", "34", + "32", "31", "30", "28", "27", "26", "25", "24", "23", "22", "22", + "21", "20", "20", "19", "18", "18", "17", "17", "16", "16", "15" + }, { + "9122818552483814953977703257848970704164", + "933462289569511464780529972314", "946405863353935713909178", + "95513446972056321834", "133588658082928446", + "966158521967027", "20895030642048", "972833934108", + "79107381638", "9773098125", "1665590516", "365497822", + "98180628", "31083090", "11266459", "4571108", "2039360", + "986323", "511198", "281260", "163001", "98858", + "62404", "40811", "27543", "19117", "13608", "9908", + "7363", "5575", "4292", "3356", "2661", "2138", + "1737", "1428", "1185", "993", "839", "714", "613", + "530", "461", "403", "355", "314", "279", "249", + "224", "202", "182", "165", "151", "138", "126", + "116", "107", "99", "92", "85", "79", "74", "69", + "65", "61", "57", "54", "51", "48", "46", "43", + "41", "39", "37", "36", "34", "32", "31", "30", + "28", "27", "26", "25", "24", "23", "23", "22", + "21", "20", "20", "19", "18", "18", "17", "17", + "16", "16", "15" + }, { + "9151329724083804100369546479681933027521", + "935649419557299174433860420387", "948179413831316112751907", + "95662582675170358900", "133767426788182384", + "967289728859610", "20916775466497", "973745045600", + "79174731802", "9780725058", "1666790321", "365742295", + "98241919", "31101281", "11272665", "4573486", "2040365", + "986785", "511426", "281380", "163067", "98897", + "62427", "40826", "27552", "19124", "13612", "9911", + "7366", "5576", "4294", "3357", "2662", "2138", + "1738", "1428", "1185", "993", "839", "715", "613", + "530", "461", "403", "355", "314", "279", "249", + "224", "202", "182", "165", "151", "138", "126", + "116", "107", "99", "92", "85", "79", "74", "69", + "65", "61", "57", "54", "51", "48", "46", "43", + "41", "39", "37", "36", "34", "32", "31", "30", + "28", "27", "26", "25", "24", "23", "23", "22", + "21", "20", "20", "19", "18", "18", "17", "17", + "16", "16", "15" + }, { + "6839396355168045468586008471269923213531", + "752078770083218822016981965090", "796178899357307807726034", + "82700643015444840424", "118072966296549115", + "867224751770392", "18981881485802", "892288574037", + "73130030771", "9093989389", "1558462688", "343617470", + "92683740", "29448679", "10708016", "4356820", "1948676", + "944610", "490587", "270425", "156989", "95362", + "60284", "39477", "26675", "18536", "13208", "9627", + "7161", "5426", "4181", "3272", "2596", "2087", + "1697", "1395", "1159", "971", "821", "700", "601", + "520", "452", "396", "348", "308", "274", "245", + "220", "198", "179", "163", "148", "136", "124", + "114", "106", "98", "91", "84", "78", "73", "68", + "64", "60", "57", "53", "50", "48", "45", "43", + "41", "39", "37", "35", "34", "32", "31", "29", + "28", "27", "26", "25", "24", "23", "22", "22", + "21", "20", "19", "19", "18", "18", "17", "17", + "16", "16", "15" + }, { + "4788090721380022347683138981782307670424", + "575601315594614059890185238256", "642831903229558719812840", + "69196031110028430211", "101340693763170691", + "758683936560287", "16854690815260", "801767985909", + "66353290503", "8318415180", "1435359033", "318340531", + "86304307", "27544217", "10054988", "4105446", "1841996", + "895414", "466223", "257591", "149855", "91205", + "57758", "37886", "25639", "17842", "12730", "9290", + "6918", "5248", "4048", "3170", "2518", "2026", + "1649", "1357", "1128", "946", "800", "682", "586", + "507", "441", "387", "341", "302", "268", "240", + "215", "194", "176", "160", "146", "133", "122", + "112", "104", "96", "89", "83", "77", "72", "67", + "63", "59", "56", "53", "50", "47", "45", "42", + "40", "38", "36", "35", "33", "32", "30", "29", + "28", "27", "26", "25", "24", "23", "22", "21", + "21", "20", "19", "19", "18", "17", "17", "16", + "16", "15", "15" + } + }; + + if ((e = mp_init_multi(&a, &c, &r, NULL)) != MP_OKAY) { + return EXIT_FAILURE; + } +#ifdef MP_8BIT + for (i = 0; i < 1; i++) { +#else + for (i = 0; i < 10; i++) { +#endif + mp_read_radix(&a, input[i], 64); +#ifdef MP_8BIT + for (j = 3; j < 10; j++) { +#else + for (j = 3; j < 100; j++) { +#endif + mp_root_u32(&a, (uint32_t)j, &c); + mp_read_radix(&r, root[i][j-3], 10); + if (mp_cmp(&r, &c) != MP_EQ) { + fprintf(stderr, "mp_root_u32 failed at input #%d, root #%d\n", i, j); + goto LTM_ERR; + } + } + } + mp_clear_multi(&a, &c, &r, NULL); + return EXIT_SUCCESS; +LTM_ERR: + mp_clear_multi(&a, &c, &r, NULL); + return EXIT_FAILURE; +} + +static int test_s_mp_balance_mul(void) +{ + mp_int a, b, c; + mp_err e = MP_OKAY; + + const char *na = + "4b0I5uMTujCysw+1OOuOyH2FX2WymrHUqi8BBDb7XpkV/4i7vXTbEYUy/kdIfCKu5jT5JEqYkdmnn3jAYo8XShPzNLxZx9yoLjxYRyptSuOI2B1DspvbIVYXY12sxPZ4/HCJ4Usm2MU5lO/006KnDMxuxiv1rm6YZJZ0eZU"; + const char *nb = "3x9vs0yVi4hIq7poAeVcggC3WoRt0zRLKO"; + const char *nc = + "HzrSq9WVt1jDTVlwUxSKqxctu2GVD+N8+SVGaPFRqdxyld6IxDBbj27BPJzYUdR96k3sWpkO8XnDBvupGPnehpQe4KlO/KmN1PjFov/UTZYM+LYzkFcBPyV6hkkL8ePC1rlFLAHzgJMBCXVp4mRqtkQrDsZXXlcqlbTFu69wF6zDEysiX2cAtn/kP9ldblJiwYPCD8hG"; + + if ((e = mp_init_multi(&a, &b, &c, NULL)) != MP_OKAY) { + goto LTM_ERR; + } + + if ((e = mp_read_radix(&a, na, 64)) != MP_OKAY) { + goto LTM_ERR; + } + if ((e = mp_read_radix(&b, nb, 64)) != MP_OKAY) { + goto LTM_ERR; + } + + if ((e = s_mp_balance_mul(&a, &b, &c)) != MP_OKAY) { + goto LTM_ERR; + } + + if ((e = mp_read_radix(&b, nc, 64)) != MP_OKAY) { + goto LTM_ERR; + } + + if (mp_cmp(&b, &c) != MP_EQ) { + goto LTM_ERR; + } + + mp_clear_multi(&a, &b, &c, NULL); + return EXIT_SUCCESS; +LTM_ERR: + mp_clear_multi(&a, &b, &c, NULL); + return EXIT_FAILURE; +} + +#define s_mp_mul(a, b, c) s_mp_mul_digs(a, b, c, (a)->used + (b)->used + 1) +static int test_s_mp_karatsuba_mul(void) +{ + mp_int a, b, c, d; + int size, err; + + if ((err = mp_init_multi(&a, &b, &c, &d, NULL)) != MP_OKAY) { + goto LTM_ERR; + } + for (size = MP_KARATSUBA_MUL_CUTOFF; size < MP_KARATSUBA_MUL_CUTOFF + 20; size++) { + if ((err = mp_rand(&a, size)) != MP_OKAY) { + goto LTM_ERR; + } + if ((err = mp_rand(&b, size)) != MP_OKAY) { + goto LTM_ERR; + } + if ((err = s_mp_karatsuba_mul(&a, &b, &c)) != MP_OKAY) { + goto LTM_ERR; + } + if ((err = s_mp_mul(&a,&b,&d)) != MP_OKAY) { + goto LTM_ERR; + } + if (mp_cmp(&c, &d) != MP_EQ) { + fprintf(stderr, "Karatsuba multiplication failed at size %d\n", size); + goto LTM_ERR; + } + } + + mp_clear_multi(&a, &b, &c, &d, NULL); + return EXIT_SUCCESS; +LTM_ERR: + mp_clear_multi(&a, &b, &c, &d, NULL); + return EXIT_FAILURE; +} + +static int test_s_mp_karatsuba_sqr(void) +{ + mp_int a, b, c; + int size, err; + + if ((err = mp_init_multi(&a, &b, &c, NULL)) != MP_OKAY) { + goto LTM_ERR; + } + for (size = MP_KARATSUBA_SQR_CUTOFF; size < MP_KARATSUBA_SQR_CUTOFF + 20; size++) { + if ((err = mp_rand(&a, size)) != MP_OKAY) { + goto LTM_ERR; + } + if ((err = s_mp_karatsuba_sqr(&a, &b)) != MP_OKAY) { + goto LTM_ERR; + } + if ((err = s_mp_sqr(&a, &c)) != MP_OKAY) { + goto LTM_ERR; + } + if (mp_cmp(&b, &c) != MP_EQ) { + fprintf(stderr, "Karatsuba squaring failed at size %d\n", size); + goto LTM_ERR; + } + } + + mp_clear_multi(&a, &b, &c, NULL); + return EXIT_SUCCESS; +LTM_ERR: + mp_clear_multi(&a, &b, &c, NULL); + return EXIT_FAILURE; +} + +static int test_s_mp_toom_mul(void) +{ + mp_int a, b, c, d; + int size, err; + +#if (MP_DIGIT_BIT == 60) + int tc_cutoff; +#endif + + if ((err = mp_init_multi(&a, &b, &c, &d, NULL)) != MP_OKAY) { + goto LTM_ERR; + } + /* This number construction is limb-size specific */ +#if (MP_DIGIT_BIT == 60) + if ((err = mp_rand(&a, 1196)) != MP_OKAY) { + goto LTM_ERR; + } + if ((err = mp_mul_2d(&a,71787 - mp_count_bits(&a), &a)) != MP_OKAY) { + goto LTM_ERR; + } + + if ((err = mp_rand(&b, 1338)) != MP_OKAY) { + goto LTM_ERR; + } + if ((err = mp_mul_2d(&b, 80318 - mp_count_bits(&b), &b)) != MP_OKAY) { + goto LTM_ERR; + } + if ((err = mp_mul_2d(&b, 6310, &b)) != MP_OKAY) { + goto LTM_ERR; + } + if ((err = mp_2expt(&c, 99000 - 1000)) != MP_OKAY) { + goto LTM_ERR; + } + if ((err = mp_add(&b, &c, &b)) != MP_OKAY) { + goto LTM_ERR; + } + + tc_cutoff = TOOM_MUL_CUTOFF; + TOOM_MUL_CUTOFF = INT_MAX; + if ((err = mp_mul(&a, &b, &c)) != MP_OKAY) { + goto LTM_ERR; + } + TOOM_MUL_CUTOFF = tc_cutoff; + if ((err = mp_mul(&a, &b, &d)) != MP_OKAY) { + goto LTM_ERR; + } + if (mp_cmp(&c, &d) != MP_EQ) { + fprintf(stderr, "Toom-Cook 3-way multiplication failed for edgecase f1 * f2\n"); + goto LTM_ERR; + } +#endif + + for (size = MP_TOOM_MUL_CUTOFF; size < MP_TOOM_MUL_CUTOFF + 20; size++) { + if ((err = mp_rand(&a, size)) != MP_OKAY) { + goto LTM_ERR; + } + if ((err = mp_rand(&b, size)) != MP_OKAY) { + goto LTM_ERR; + } + if ((err = s_mp_toom_mul(&a, &b, &c)) != MP_OKAY) { + goto LTM_ERR; + } + if ((err = s_mp_mul(&a,&b,&d)) != MP_OKAY) { + goto LTM_ERR; + } + if (mp_cmp(&c, &d) != MP_EQ) { + fprintf(stderr, "Toom-Cook 3-way multiplication failed at size %d\n", size); + goto LTM_ERR; + } + } + + mp_clear_multi(&a, &b, &c, &d, NULL); + return EXIT_SUCCESS; +LTM_ERR: + mp_clear_multi(&a, &b, &c, &d, NULL); + return EXIT_FAILURE; +} + +static int test_s_mp_toom_sqr(void) +{ + mp_int a, b, c; + int size, err; + + if ((err = mp_init_multi(&a, &b, &c, NULL)) != MP_OKAY) { + goto LTM_ERR; + } + for (size = MP_TOOM_SQR_CUTOFF; size < MP_TOOM_SQR_CUTOFF + 20; size++) { + if ((err = mp_rand(&a, size)) != MP_OKAY) { + goto LTM_ERR; + } + if ((err = s_mp_toom_sqr(&a, &b)) != MP_OKAY) { + goto LTM_ERR; + } + if ((err = s_mp_sqr(&a, &c)) != MP_OKAY) { + goto LTM_ERR; + } + if (mp_cmp(&b, &c) != MP_EQ) { + fprintf(stderr, "Toom-Cook 3-way squaring failed at size %d\n", size); + goto LTM_ERR; + } + } + + mp_clear_multi(&a, &b, &c, NULL); + return EXIT_SUCCESS; +LTM_ERR: + mp_clear_multi(&a, &b, &c, NULL); + return EXIT_FAILURE; +} + +static int test_mp_read_write_ubin(void) +{ + mp_int a, b, c; + int err; + size_t size, len; + unsigned char *buf = NULL; + + if ((err = mp_init_multi(&a, &b, &c, NULL)) != MP_OKAY) { + goto LTM_ERR; + } + + if ((err = mp_rand(&a, 15)) != MP_OKAY) goto LTM_ERR; + if ((err = mp_neg(&a, &b)) != MP_OKAY) goto LTM_ERR; + + size = mp_ubin_size(&a); + printf("mp_to_ubin_size %zu\n", size); + buf = malloc(sizeof(*buf) * size); + if (buf == NULL) { + fprintf(stderr, "test_read_write_binaries (u) failed to allocate %zu bytes\n", + sizeof(*buf) * size); + goto LTM_ERR; + } + + if ((err = mp_to_ubin(&a, buf, size, &len)) != MP_OKAY) goto LTM_ERR; + printf("mp_to_ubin len = %zu\n", len); + + if ((err = mp_from_ubin(&c, buf, len)) != MP_OKAY) goto LTM_ERR; + + if (mp_cmp(&a, &c) != MP_EQ) { + fprintf(stderr, "to/from ubin cycle failed\n"); + goto LTM_ERR; + } + free(buf); + mp_clear_multi(&a, &b, &c, NULL); + return EXIT_SUCCESS; +LTM_ERR: + free(buf); + mp_clear_multi(&a, &b, &c, NULL); + return EXIT_FAILURE; +} + +static int test_mp_read_write_sbin(void) +{ + mp_int a, b, c; + int err; + size_t size, len; + unsigned char *buf = NULL; + + if ((err = mp_init_multi(&a, &b, &c, NULL)) != MP_OKAY) { + goto LTM_ERR; + } + + if ((err = mp_rand(&a, 15)) != MP_OKAY) goto LTM_ERR; + if ((err = mp_neg(&a, &b)) != MP_OKAY) goto LTM_ERR; + + size = mp_sbin_size(&a); + printf("mp_to_sbin_size %zu\n", size); + buf = malloc(sizeof(*buf) * size); + if (buf == NULL) { + fprintf(stderr, "test_read_write_binaries (s) failed to allocate %zu bytes\n", + sizeof(*buf) * size); + goto LTM_ERR; + } + + if ((err = mp_to_sbin(&b, buf, size, &len)) != MP_OKAY) goto LTM_ERR; + printf("mp_to_sbin len = %zu\n", len); + + if ((err = mp_from_sbin(&c, buf, len)) != MP_OKAY) goto LTM_ERR; + + if (mp_cmp(&b, &c) != MP_EQ) { + fprintf(stderr, "to/from ubin cycle failed\n"); + goto LTM_ERR; + } + + free(buf); + mp_clear_multi(&a, &b, &c, NULL); + return EXIT_SUCCESS; +LTM_ERR: + free(buf); + mp_clear_multi(&a, &b, &c, NULL); + return EXIT_FAILURE; +} + +static int test_mp_pack_unpack(void) +{ + mp_int a, b; + int err; + size_t written, count; + unsigned char *buf = NULL; + + mp_order order = MP_LSB_FIRST; + mp_endian endianess = MP_NATIVE_ENDIAN; + + if ((err = mp_init_multi(&a, &b, NULL)) != MP_OKAY) goto LTM_ERR; + if ((err = mp_rand(&a, 15)) != MP_OKAY) goto LTM_ERR; + + count = mp_pack_count(&a, 0, 1); + + buf = malloc(count); + if (buf == NULL) { + fprintf(stderr, "test_pack_unpack failed to allocate\n"); + goto LTM_ERR; + } + + if ((err = mp_pack((void *)buf, count, &written, order, 1, + endianess, 0, &a)) != MP_OKAY) goto LTM_ERR; + if ((err = mp_unpack(&b, count, order, 1, + endianess, 0, (const void *)buf)) != MP_OKAY) goto LTM_ERR; + + if (mp_cmp(&a, &b) != MP_EQ) { + fprintf(stderr, "pack/unpack cycle failed\n"); + goto LTM_ERR; + } + + free(buf); + mp_clear_multi(&a, &b, NULL); + return EXIT_SUCCESS; +LTM_ERR: + free(buf); + mp_clear_multi(&a, &b, NULL); + return EXIT_FAILURE; +} + +static int unit_tests(int argc, char **argv) +{ + static const struct { + const char *name; + int (*fn)(void); + } test[] = { +#define T0(n) { #n, test_##n } +#define T1(n, o) { #n, MP_HAS(o) ? test_##n : NULL } +#define T2(n, o1, o2) { #n, MP_HAS(o1) && MP_HAS(o2) ? test_##n : NULL } + T0(feature_detection), + T0(trivial_stuff), + T2(mp_get_set_i32, MP_GET_I32, MP_GET_MAG_U32), + T2(mp_get_set_i64, MP_GET_I64, MP_GET_MAG_U64), + T1(mp_and, MP_AND), + T1(mp_cnt_lsb, MP_CNT_LSB), + T1(mp_complement, MP_COMPLEMENT), + T1(mp_decr, MP_DECR), + T1(mp_div_3, MP_DIV_3), + T1(mp_dr_reduce, MP_DR_REDUCE), + T2(mp_pack_unpack,MP_PACK, MP_UNPACK), + T2(mp_fread_fwrite, MP_FREAD, MP_FWRITE), + T1(mp_get_u32, MP_GET_I32), + T1(mp_get_u64, MP_GET_I64), + T1(mp_get_ul, MP_GET_L), + T1(mp_log_u32, MP_LOG_U32), + T1(mp_incr, MP_INCR), + T1(mp_invmod, MP_INVMOD), + T1(mp_is_square, MP_IS_SQUARE), + T1(mp_kronecker, MP_KRONECKER), + T1(mp_montgomery_reduce, MP_MONTGOMERY_REDUCE), + T1(mp_root_u32, MP_ROOT_U32), + T1(mp_or, MP_OR), + T1(mp_prime_is_prime, MP_PRIME_IS_PRIME), + T1(mp_prime_next_prime, MP_PRIME_NEXT_PRIME), + T1(mp_prime_rand, MP_PRIME_RAND), + T1(mp_rand, MP_RAND), + T1(mp_read_radix, MP_READ_RADIX), + T1(mp_read_write_ubin, MP_TO_UBIN), + T1(mp_read_write_sbin, MP_TO_SBIN), + T1(mp_reduce_2k, MP_REDUCE_2K), + T1(mp_reduce_2k_l, MP_REDUCE_2K_L), +#if defined(__STDC_IEC_559__) || defined(__GCC_IEC_559) + T1(mp_set_double, MP_SET_DOUBLE), +#endif + T1(mp_signed_rsh, MP_SIGNED_RSH), + T1(mp_sqrt, MP_SQRT), + T1(mp_sqrtmod_prime, MP_SQRTMOD_PRIME), + T1(mp_xor, MP_XOR), + T1(s_mp_balance_mul, S_MP_BALANCE_MUL), + T1(s_mp_karatsuba_mul, S_MP_KARATSUBA_MUL), + T1(s_mp_karatsuba_sqr, S_MP_KARATSUBA_SQR), + T1(s_mp_toom_mul, S_MP_TOOM_MUL), + T1(s_mp_toom_sqr, S_MP_TOOM_SQR) +#undef T2 +#undef T1 + }; + unsigned long i, ok, fail, nop; + uint64_t t; + int j; + + ok = fail = nop = 0; + + t = (uint64_t)time(NULL); + printf("SEED: 0x%"PRIx64"\n\n", t); + s_mp_rand_jenkins_init(t); + mp_rand_source(s_mp_rand_jenkins); + + for (i = 0; i < sizeof(test) / sizeof(test[0]); ++i) { + if (argc > 1) { + for (j = 1; j < argc; ++j) { + if (strstr(test[i].name, argv[j]) != NULL) { + break; + } + } + if (j == argc) continue; + } + printf("TEST %s\n\n", test[i].name); + if (test[i].fn == NULL) { + nop++; + printf("NOP %s\n\n", test[i].name); + } else if (test[i].fn() == EXIT_SUCCESS) { + ok++; + printf("\n\n"); + } else { + fail++; + printf("\n\nFAIL %s\n\n", test[i].name); + } + } + printf("Tests OK/NOP/FAIL: %lu/%lu/%lu\n", ok, nop, fail); + + if (fail != 0) return EXIT_FAILURE; + else return EXIT_SUCCESS; +} + +int main(int argc, char **argv) +{ + print_header(); + + return unit_tests(argc, argv); +} diff --git a/lib/hcrypto/libtommath/demo/timing.c b/lib/hcrypto/libtommath/demo/timing.c new file mode 100644 index 000000000000..f620b8cd4dde --- /dev/null +++ b/lib/hcrypto/libtommath/demo/timing.c @@ -0,0 +1,406 @@ +#include <time.h> +#include <string.h> +#include <stdlib.h> +#include <unistd.h> +#include <inttypes.h> + +#define MP_WUR +#include <tommath.h> + +#ifdef IOWNANATHLON +#include <unistd.h> +#define SLEEP sleep(4) +#else +#define SLEEP +#endif + +#ifdef LTM_TIMING_REAL_RAND +#define LTM_TIMING_RAND_SEED time(NULL) +#else +#define LTM_TIMING_RAND_SEED 23 +#endif + + +static void ndraw(mp_int *a, const char *name) +{ + char buf[4096]; + + printf("%s: ", name); + mp_to_radix(a, buf, sizeof(buf), NULL, 64); + printf("%s\n", buf); +} + +static void draw(mp_int *a) +{ + ndraw(a, ""); +} + + +static unsigned long lfsr = 0xAAAAAAAAuL; + +static unsigned int lbit(void) +{ + if ((lfsr & 0x80000000uL) != 0uL) { + lfsr = ((lfsr << 1) ^ 0x8000001BuL) & 0xFFFFFFFFuL; + return 1u; + } else { + lfsr <<= 1; + return 0u; + } +} + +/* RDTSC from Scott Duplichan */ +static uint64_t TIMFUNC(void) +{ +#if defined __GNUC__ +#if defined(__i386__) || defined(__x86_64__) + /* version from http://www.mcs.anl.gov/~kazutomo/rdtsc.html + * the old code always got a warning issued by gcc, clang did not complain... + */ + unsigned hi, lo; + __asm__ __volatile__("rdtsc" : "=a"(lo), "=d"(hi)); + return ((uint64_t)lo)|(((uint64_t)hi)<<32); +#else /* gcc-IA64 version */ + unsigned long result; + __asm__ __volatile__("mov %0=ar.itc":"=r"(result)::"memory"); + + while (__builtin_expect((int) result == -1, 0)) + __asm__ __volatile__("mov %0=ar.itc":"=r"(result)::"memory"); + + return result; +#endif + + /* Microsoft and Intel Windows compilers */ +#elif defined _M_IX86 + __asm rdtsc +#elif defined _M_AMD64 + return __rdtsc(); +#elif defined _M_IA64 +#if defined __INTEL_COMPILER +#include <ia64intrin.h> +#endif + return __getReg(3116); +#else +#error need rdtsc function for this build +#endif +} + +#if 1 +#define DO(x) x; x; +#else +#define DO2(x) x; x; +#define DO4(x) DO2(x); DO2(x); +#define DO8(x) DO4(x); DO4(x); +#define DO(x) DO8(x); DO8(x); +#endif + +#ifdef TIMING_NO_LOGS +#define FOPEN(a, b) NULL +#define FPRINTF(a,b,c,d) +#define FFLUSH(a) +#define FCLOSE(a) (void)(a) +#else +#define FOPEN(a,b) fopen(a,b) +#define FPRINTF(a,b,c,d) fprintf(a,b,c,d) +#define FFLUSH(a) fflush(a) +#define FCLOSE(a) fclose(a) +#endif + +static int should_test(const char *test, int argc, char **argv) +{ + int j; + if (argc > 1) { + for (j = 1; j < argc; ++j) { + if (strstr(test, argv[j]) != NULL) { + return 1; + } + } + if (j == argc) return 0; + } + return 1; +} + +int main(int argc, char **argv) +{ + uint64_t tt, gg, CLK_PER_SEC; + FILE *log, *logb, *logc, *logd; + mp_int a, b, c, d, e, f; +#ifdef LTM_TIMING_PRIME_IS_PRIME + const char *name; + int m; +#endif + int n, cnt, ix, old_kara_m, old_kara_s, old_toom_m, old_toom_s; + unsigned rr; + + mp_init(&a); + mp_init(&b); + mp_init(&c); + mp_init(&d); + mp_init(&e); + mp_init(&f); + + srand(LTM_TIMING_RAND_SEED); + + + CLK_PER_SEC = TIMFUNC(); + sleep(1); + CLK_PER_SEC = TIMFUNC() - CLK_PER_SEC; + + printf("CLK_PER_SEC == %" PRIu64 "\n", CLK_PER_SEC); + +#ifdef LTM_TIMING_PRIME_IS_PRIME + if (should_test("prime", argc, argv)) { + for (m = 0; m < 2; ++m) { + if (m == 0) { + name = " Arnault"; + mp_read_radix(&a, + "91xLNF3roobhzgTzoFIG6P13ZqhOVYSN60Fa7Cj2jVR1g0k89zdahO9/kAiRprpfO1VAp1aBHucLFV/qLKLFb+zonV7R2Vxp1K13ClwUXStpV0oxTNQVjwybmFb5NBEHImZ6V7P6+udRJuH8VbMEnS0H8/pSqQrg82OoQQ2fPpAk6G1hkjqoCv5s/Yr", + 64); + } else { + name = "2^1119 + 53"; + mp_set(&a,1u); + mp_mul_2d(&a,1119,&a); + mp_add_d(&a,53,&a); + } + cnt = mp_prime_rabin_miller_trials(mp_count_bits(&a)); + ix = -cnt; + for (; cnt >= ix; cnt += ix) { + rr = 0u; + tt = UINT64_MAX; + do { + gg = TIMFUNC(); + DO(mp_prime_is_prime(&a, cnt, &n)); + gg = (TIMFUNC() - gg) >> 1; + if (tt > gg) + tt = gg; + if ((m == 0) && (n == MP_YES)) { + printf("Arnault's pseudoprime is not prime but mp_prime_is_prime says it is.\n"); + return EXIT_FAILURE; + } + } while (++rr < 100u); + printf("Prime-check\t%s(%2d) => %9" PRIu64 "/sec, %9" PRIu64 " cycles\n", + name, cnt, CLK_PER_SEC / tt, tt); + } + } + } +#endif + + if (should_test("add", argc, argv)) { + log = FOPEN("logs/add.log", "w"); + for (cnt = 8; cnt <= 128; cnt += 8) { + SLEEP; + mp_rand(&a, cnt); + mp_rand(&b, cnt); + rr = 0u; + tt = UINT64_MAX; + do { + gg = TIMFUNC(); + DO(mp_add(&a, &b, &c)); + gg = (TIMFUNC() - gg) >> 1; + if (tt > gg) + tt = gg; + } while (++rr < 100000u); + printf("Adding\t\t%4d-bit => %9" PRIu64 "/sec, %9" PRIu64 " cycles\n", + mp_count_bits(&a), CLK_PER_SEC / tt, tt); + FPRINTF(log, "%6d %9" PRIu64 "\n", cnt * MP_DIGIT_BIT, tt); + FFLUSH(log); + } + FCLOSE(log); + } + + if (should_test("sub", argc, argv)) { + log = FOPEN("logs/sub.log", "w"); + for (cnt = 8; cnt <= 128; cnt += 8) { + SLEEP; + mp_rand(&a, cnt); + mp_rand(&b, cnt); + rr = 0u; + tt = UINT64_MAX; + do { + gg = TIMFUNC(); + DO(mp_sub(&a, &b, &c)); + gg = (TIMFUNC() - gg) >> 1; + if (tt > gg) + tt = gg; + } while (++rr < 100000u); + + printf("Subtracting\t\t%4d-bit => %9" PRIu64 "/sec, %9" PRIu64 " cycles\n", + mp_count_bits(&a), CLK_PER_SEC / tt, tt); + FPRINTF(log, "%6d %9" PRIu64 "\n", cnt * MP_DIGIT_BIT, tt); + FFLUSH(log); + } + FCLOSE(log); + } + + if (should_test("mulsqr", argc, argv)) { + /* do mult/square twice, first without karatsuba and second with */ + old_kara_m = KARATSUBA_MUL_CUTOFF; + old_kara_s = KARATSUBA_SQR_CUTOFF; + /* currently toom-cook cut-off is too high to kick in, so we just use the karatsuba values */ + old_toom_m = old_kara_m; + old_toom_s = old_kara_s; + for (ix = 0; ix < 3; ix++) { + printf("With%s Karatsuba, With%s Toom\n", (ix == 1) ? "" : "out", (ix == 2) ? "" : "out"); + + KARATSUBA_MUL_CUTOFF = (ix == 1) ? old_kara_m : 9999; + KARATSUBA_SQR_CUTOFF = (ix == 1) ? old_kara_s : 9999; + TOOM_MUL_CUTOFF = (ix == 2) ? old_toom_m : 9999; + TOOM_SQR_CUTOFF = (ix == 2) ? old_toom_s : 9999; + + log = FOPEN((ix == 0) ? "logs/mult.log" : (ix == 1) ? "logs/mult_kara.log" : "logs/mult_toom.log", "w"); + for (cnt = 4; cnt <= (10240 / MP_DIGIT_BIT); cnt += 2) { + SLEEP; + mp_rand(&a, cnt); + mp_rand(&b, cnt); + rr = 0u; + tt = UINT64_MAX; + do { + gg = TIMFUNC(); + DO(mp_mul(&a, &b, &c)); + gg = (TIMFUNC() - gg) >> 1; + if (tt > gg) + tt = gg; + } while (++rr < 100u); + printf("Multiplying\t%4d-bit => %9" PRIu64 "/sec, %9" PRIu64 " cycles\n", + mp_count_bits(&a), CLK_PER_SEC / tt, tt); + FPRINTF(log, "%6d %9" PRIu64 "\n", mp_count_bits(&a), tt); + FFLUSH(log); + } + FCLOSE(log); + + log = FOPEN((ix == 0) ? "logs/sqr.log" : (ix == 1) ? "logs/sqr_kara.log" : "logs/sqr_toom.log", "w"); + for (cnt = 4; cnt <= (10240 / MP_DIGIT_BIT); cnt += 2) { + SLEEP; + mp_rand(&a, cnt); + rr = 0u; + tt = UINT64_MAX; + do { + gg = TIMFUNC(); + DO(mp_sqr(&a, &b)); + gg = (TIMFUNC() - gg) >> 1; + if (tt > gg) + tt = gg; + } while (++rr < 100u); + printf("Squaring\t%4d-bit => %9" PRIu64 "/sec, %9" PRIu64 " cycles\n", + mp_count_bits(&a), CLK_PER_SEC / tt, tt); + FPRINTF(log, "%6d %9" PRIu64 "\n", mp_count_bits(&a), tt); + FFLUSH(log); + } + FCLOSE(log); + + } + } + + if (should_test("expt", argc, argv)) { + const char *primes[] = { + /* 2K large moduli */ + "179769313486231590772930519078902473361797697894230657273430081157732675805500963132708477322407536021120113879871393357658789768814416622492847430639474124377767893424865485276302219601246094119453082952085005768838150682342462881473913110540827237163350510684586239334100047359817950870678242457666208137217", + "32317006071311007300714876688669951960444102669715484032130345427524655138867890893197201411522913463688717960921898019494119559150490921095088152386448283120630877367300996091750197750389652106796057638384067568276792218642619756161838094338476170470581645852036305042887575891541065808607552399123930385521914333389668342420684974786564569494856176035326322058077805659331026192708460314150258592864177116725943603718461857357598351152301645904403697613233287231227125684710820209725157101726931323469678542580656697935045997268352998638099733077152121140120031150424541696791951097529546801429027668869927491725169", + "1044388881413152506691752710716624382579964249047383780384233483283953907971557456848826811934997558340890106714439262837987573438185793607263236087851365277945956976543709998340361590134383718314428070011855946226376318839397712745672334684344586617496807908705803704071284048740118609114467977783598029006686938976881787785946905630190260940599579453432823469303026696443059025015972399867714215541693835559885291486318237914434496734087811872639496475100189041349008417061675093668333850551032972088269550769983616369411933015213796825837188091833656751221318492846368125550225998300412344784862595674492194617023806505913245610825731835380087608622102834270197698202313169017678006675195485079921636419370285375124784014907159135459982790513399611551794271106831134090584272884279791554849782954323534517065223269061394905987693002122963395687782878948440616007412945674919823050571642377154816321380631045902916136926708342856440730447899971901781465763473223850267253059899795996090799469201774624817718449867455659250178329070473119433165550807568221846571746373296884912819520317457002440926616910874148385078411929804522981857338977648103126085902995208257421855249796721729039744118165938433694823325696642096892124547425283", + /* 2K moduli mersenne primes */ + "6864797660130609714981900799081393217269435300143305409394463459185543183397656052122559640661454554977296311391480858037121987999716643812574028291115057151", + "531137992816767098689588206552468627329593117727031923199444138200403559860852242739162502265229285668889329486246501015346579337652707239409519978766587351943831270835393219031728127", + "10407932194664399081925240327364085538615262247266704805319112350403608059673360298012239441732324184842421613954281007791383566248323464908139906605677320762924129509389220345773183349661583550472959420547689811211693677147548478866962501384438260291732348885311160828538416585028255604666224831890918801847068222203140521026698435488732958028878050869736186900714720710555703168729087", + "1475979915214180235084898622737381736312066145333169775147771216478570297878078949377407337049389289382748507531496480477281264838760259191814463365330269540496961201113430156902396093989090226259326935025281409614983499388222831448598601834318536230923772641390209490231836446899608210795482963763094236630945410832793769905399982457186322944729636418890623372171723742105636440368218459649632948538696905872650486914434637457507280441823676813517852099348660847172579408422316678097670224011990280170474894487426924742108823536808485072502240519452587542875349976558572670229633962575212637477897785501552646522609988869914013540483809865681250419497686697771007", + "259117086013202627776246767922441530941818887553125427303974923161874019266586362086201209516800483406550695241733194177441689509238807017410377709597512042313066624082916353517952311186154862265604547691127595848775610568757931191017711408826252153849035830401185072116424747461823031471398340229288074545677907941037288235820705892351068433882986888616658650280927692080339605869308790500409503709875902119018371991620994002568935113136548829739112656797303241986517250116412703509705427773477972349821676443446668383119322540099648994051790241624056519054483690809616061625743042361721863339415852426431208737266591962061753535748892894599629195183082621860853400937932839420261866586142503251450773096274235376822938649407127700846077124211823080804139298087057504713825264571448379371125032081826126566649084251699453951887789613650248405739378594599444335231188280123660406262468609212150349937584782292237144339628858485938215738821232393687046160677362909315071", + "190797007524439073807468042969529173669356994749940177394741882673528979787005053706368049835514900244303495954950709725762186311224148828811920216904542206960744666169364221195289538436845390250168663932838805192055137154390912666527533007309292687539092257043362517857366624699975402375462954490293259233303137330643531556539739921926201438606439020075174723029056838272505051571967594608350063404495977660656269020823960825567012344189908927956646011998057988548630107637380993519826582389781888135705408653045219655801758081251164080554609057468028203308718724654081055323215860189611391296030471108443146745671967766308925858547271507311563765171008318248647110097614890313562856541784154881743146033909602737947385055355960331855614540900081456378659068370317267696980001187750995491090350108417050917991562167972281070161305972518044872048331306383715094854938415738549894606070722584737978176686422134354526989443028353644037187375385397838259511833166416134323695660367676897722287918773420968982326089026150031515424165462111337527431154890666327374921446276833564519776797633875503548665093914556482031482248883127023777039667707976559857333357013727342079099064400455741830654320379350833236245819348824064783585692924881021978332974949906122664421376034687815350484991", + + /* DR moduli */ + "14059105607947488696282932836518693308967803494693489478439861164411992439598399594747002144074658928593502845729752797260025831423419686528151609940203368612079", + "101745825697019260773923519755878567461315282017759829107608914364075275235254395622580447400994175578963163918967182013639660669771108475957692810857098847138903161308502419410142185759152435680068435915159402496058513611411688900243039", + "736335108039604595805923406147184530889923370574768772191969612422073040099331944991573923112581267542507986451953227192970402893063850485730703075899286013451337291468249027691733891486704001513279827771740183629161065194874727962517148100775228363421083691764065477590823919364012917984605619526140821797602431", + "38564998830736521417281865696453025806593491967131023221754800625044118265468851210705360385717536794615180260494208076605798671660719333199513807806252394423283413430106003596332513246682903994829528690198205120921557533726473585751382193953592127439965050261476810842071573684505878854588706623484573925925903505747545471088867712185004135201289273405614415899438276535626346098904241020877974002916168099951885406379295536200413493190419727789712076165162175783", + "542189391331696172661670440619180536749994166415993334151601745392193484590296600979602378676624808129613777993466242203025054573692562689251250471628358318743978285860720148446448885701001277560572526947619392551574490839286458454994488665744991822837769918095117129546414124448777033941223565831420390846864429504774477949153794689948747680362212954278693335653935890352619041936727463717926744868338358149568368643403037768649616778526013610493696186055899318268339432671541328195724261329606699831016666359440874843103020666106568222401047720269951530296879490444224546654729111504346660859907296364097126834834235287147", + "1487259134814709264092032648525971038895865645148901180585340454985524155135260217788758027400478312256339496385275012465661575576202252063145698732079880294664220579764848767704076761853197216563262660046602703973050798218246170835962005598561669706844469447435461092542265792444947706769615695252256130901271870341005768912974433684521436211263358097522726462083917939091760026658925757076733484173202927141441492573799914240222628795405623953109131594523623353044898339481494120112723445689647986475279242446083151413667587008191682564376412347964146113898565886683139407005941383669325997475076910488086663256335689181157957571445067490187939553165903773554290260531009121879044170766615232300936675369451260747671432073394867530820527479172464106442450727640226503746586340279816318821395210726268291535648506190714616083163403189943334431056876038286530365757187367147446004855912033137386225053275419626102417236133948503", + "1095121115716677802856811290392395128588168592409109494900178008967955253005183831872715423151551999734857184538199864469605657805519106717529655044054833197687459782636297255219742994736751541815269727940751860670268774903340296040006114013971309257028332849679096824800250742691718610670812374272414086863715763724622797509437062518082383056050144624962776302147890521249477060215148275163688301275847155316042279405557632639366066847442861422164832655874655824221577849928863023018366835675399949740429332468186340518172487073360822220449055340582568461568645259954873303616953776393853174845132081121976327462740354930744487429617202585015510744298530101547706821590188733515880733527449780963163909830077616357506845523215289297624086914545378511082534229620116563260168494523906566709418166011112754529766183554579321224940951177394088465596712620076240067370589036924024728375076210477267488679008016579588696191194060127319035195370137160936882402244399699172017835144537488486396906144217720028992863941288217185353914991583400421682751000603596655790990815525126154394344641336397793791497068253936771017031980867706707490224041075826337383538651825493679503771934836094655802776331664261631740148281763487765852746577808019633679", + + /* generic unrestricted moduli */ + "17933601194860113372237070562165128350027320072176844226673287945873370751245439587792371960615073855669274087805055507977323024886880985062002853331424203", + "2893527720709661239493896562339544088620375736490408468011883030469939904368086092336458298221245707898933583190713188177399401852627749210994595974791782790253946539043962213027074922559572312141181787434278708783207966459019479487", + "347743159439876626079252796797422223177535447388206607607181663903045907591201940478223621722118173270898487582987137708656414344685816179420855160986340457973820182883508387588163122354089264395604796675278966117567294812714812796820596564876450716066283126720010859041484786529056457896367683122960411136319", + "47266428956356393164697365098120418976400602706072312735924071745438532218237979333351774907308168340693326687317443721193266215155735814510792148768576498491199122744351399489453533553203833318691678263241941706256996197460424029012419012634671862283532342656309677173602509498417976091509154360039893165037637034737020327399910409885798185771003505320583967737293415979917317338985837385734747478364242020380416892056650841470869294527543597349250299539682430605173321029026555546832473048600327036845781970289288898317888427517364945316709081173840186150794397479045034008257793436817683392375274635794835245695887", + "436463808505957768574894870394349739623346440601945961161254440072143298152040105676491048248110146278752857839930515766167441407021501229924721335644557342265864606569000117714935185566842453630868849121480179691838399545644365571106757731317371758557990781880691336695584799313313687287468894148823761785582982549586183756806449017542622267874275103877481475534991201849912222670102069951687572917937634467778042874315463238062009202992087620963771759666448266532858079402669920025224220613419441069718482837399612644978839925207109870840278194042158748845445131729137117098529028886770063736487420613144045836803985635654192482395882603511950547826439092832800532152534003936926017612446606135655146445620623395788978726744728503058670046885876251527122350275750995227", + "11424167473351836398078306042624362277956429440521137061889702611766348760692206243140413411077394583180726863277012016602279290144126785129569474909173584789822341986742719230331946072730319555984484911716797058875905400999504305877245849119687509023232790273637466821052576859232452982061831009770786031785669030271542286603956118755585683996118896215213488875253101894663403069677745948305893849505434201763745232895780711972432011344857521691017896316861403206449421332243658855453435784006517202894181640562433575390821384210960117518650374602256601091379644034244332285065935413233557998331562749140202965844219336298970011513882564935538704289446968322281451907487362046511461221329799897350993370560697505809686438782036235372137015731304779072430260986460269894522159103008260495503005267165927542949439526272736586626709581721032189532726389643625590680105784844246152702670169304203783072275089194754889511973916207", + 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+ NULL + }; + log = FOPEN("logs/expt.log", "w"); + logb = FOPEN("logs/expt_dr.log", "w"); + logc = FOPEN("logs/expt_2k.log", "w"); + logd = FOPEN("logs/expt_2kl.log", "w"); + for (n = 0; primes[n] != NULL; n++) { + SLEEP; + mp_read_radix(&a, primes[n], 10); + mp_zero(&b); + for (rr = 0; rr < (unsigned) mp_count_bits(&a); rr++) { + mp_mul_2(&b, &b); + b.dp[0] |= lbit(); + b.used += 1; + } + mp_sub_d(&a, 1uL, &c); + mp_mod(&b, &c, &b); + mp_set(&c, 3uL); + rr = 0u; + tt = UINT64_MAX; + do { + gg = TIMFUNC(); + DO(mp_exptmod(&c, &b, &a, &d)); + gg = (TIMFUNC() - gg) >> 1; + if (tt > gg) + tt = gg; + } while (++rr < 10u); + mp_sub_d(&a, 1uL, &e); + mp_sub(&e, &b, &b); + mp_exptmod(&c, &b, &a, &e); /* c^(p-1-b) mod a */ + mp_mulmod(&e, &d, &a, &d); /* c^b * c^(p-1-b) == c^p-1 == 1 */ + if (mp_cmp_d(&d, 1uL) != MP_EQ) { + printf("Different (%d)!!!\n", mp_count_bits(&a)); + draw(&d); + exit(0); + } + printf("Exponentiating\t%4d-bit => %9" PRIu64 "/sec, %9" PRIu64 " cycles\n", + mp_count_bits(&a), CLK_PER_SEC / tt, tt); + FPRINTF((n < 3) ? logd : (n < 9) ? logc : (n < 16) ? logb : log, + "%6d %9" PRIu64 "\n", mp_count_bits(&a), tt); + } + FCLOSE(log); + FCLOSE(logb); + FCLOSE(logc); + FCLOSE(logd); + } + + if (should_test("invmod", argc, argv)) { + log = FOPEN("logs/invmod.log", "w"); + for (cnt = 4; cnt <= 32; cnt += 4) { + SLEEP; + mp_rand(&a, cnt); + mp_rand(&b, cnt); + + do { + mp_add_d(&b, 1uL, &b); + mp_gcd(&a, &b, &c); + } while (mp_cmp_d(&c, 1uL) != MP_EQ); + + rr = 0u; + tt = UINT64_MAX; + do { + gg = TIMFUNC(); + DO(mp_invmod(&b, &a, &c)); + gg = (TIMFUNC() - gg) >> 1; + if (tt > gg) + tt = gg; + } while (++rr < 1000u); + mp_mulmod(&b, &c, &a, &d); + if (mp_cmp_d(&d, 1uL) != MP_EQ) { + printf("Failed to invert\n"); + return 0; + } + printf("Inverting mod\t%4d-bit => %9" PRIu64 "/sec, %9" PRIu64 " cycles\n", + mp_count_bits(&a), CLK_PER_SEC / tt, tt); + FPRINTF(log, "%6d %9" PRIu64 "\n", cnt * MP_DIGIT_BIT, tt); + } + FCLOSE(log); + } + + return 0; +} diff --git a/lib/hcrypto/libtommath/doc/bn.pdf b/lib/hcrypto/libtommath/doc/bn.pdf Binary files differnew file mode 100644 index 000000000000..fbf05ead115a --- /dev/null +++ b/lib/hcrypto/libtommath/doc/bn.pdf diff --git a/lib/hcrypto/libtommath/doc/bn.tex b/lib/hcrypto/libtommath/doc/bn.tex new file mode 100644 index 000000000000..5937feef1a4c --- /dev/null +++ b/lib/hcrypto/libtommath/doc/bn.tex @@ -0,0 +1,2507 @@ +\documentclass[synpaper]{book} +\usepackage{hyperref} +\usepackage{makeidx} +\usepackage{amssymb} +\usepackage{color} +\usepackage{alltt} +\usepackage{graphicx} +\usepackage{layout} +\usepackage{appendix} +\def\union{\cup} +\def\intersect{\cap} +\def\getsrandom{\stackrel{\rm R}{\gets}} +\def\cross{\times} +\def\cat{\hspace{0.5em} \| \hspace{0.5em}} +\def\catn{$\|$} +\def\divides{\hspace{0.3em} | \hspace{0.3em}} +\def\nequiv{\not\equiv} +\def\approx{\raisebox{0.2ex}{\mbox{\small $\sim$}}} +\def\lcm{{\rm lcm}} +\def\gcd{{\rm gcd}} +\def\log{{\rm log}} +\def\ord{{\rm ord}} +\def\abs{{\mathit abs}} +\def\rep{{\mathit rep}} +\def\mod{{\mathit\ mod\ }} +\renewcommand{\pmod}[1]{\ ({\rm mod\ }{#1})} +\newcommand{\floor}[1]{\left\lfloor{#1}\right\rfloor} +\newcommand{\ceil}[1]{\left\lceil{#1}\right\rceil} +\def\Or{{\rm\ or\ }} +\def\And{{\rm\ and\ }} +\def\iff{\hspace{1em}\Longleftrightarrow\hspace{1em}} +\def\implies{\Rightarrow} +\def\undefined{{\rm ``undefined"}} +\def\Proof{\vspace{1ex}\noindent {\bf Proof:}\hspace{1em}} +\let\oldphi\phi +\def\phi{\varphi} +\def\Pr{{\rm Pr}} +\newcommand{\str}[1]{{\mathbf{#1}}} +\def\F{{\mathbb F}} +\def\N{{\mathbb N}} +\def\Z{{\mathbb Z}} +\def\R{{\mathbb R}} +\def\C{{\mathbb C}} +\def\Q{{\mathbb Q}} +\definecolor{DGray}{gray}{0.5} +\newcommand{\emailaddr}[1]{\mbox{$<${#1}$>$}} +\def\twiddle{\raisebox{0.3ex}{\mbox{\tiny $\sim$}}} +\def\gap{\vspace{0.5ex}} +\makeindex +\begin{document} +\frontmatter +\pagestyle{empty} +\title{LibTomMath User Manual \\ v1.2.0} +\author{LibTom Projects \\ www.libtom.net} +\maketitle +This text, the library and the accompanying textbook are all hereby placed in the public domain. This book has been +formatted for B5 [176x250] paper using the \LaTeX{} {\em book} macro package. + +\vspace{10cm} + +\begin{flushright}Open Source. Open Academia. Open Minds. + +\mbox{ } +LibTom Projects + +\& originally + +Tom St Denis, + +Ontario, Canada +\end{flushright} + +\tableofcontents +\listoffigures +\mainmatter +\pagestyle{headings} +\chapter{Introduction} +\section{What is LibTomMath?} +LibTomMath is a library of source code which provides a series of efficient and carefully written functions for manipulating +large integer numbers. It was written in portable ISO C source code so that it will build on any platform with a conforming +C compiler. + +In a nutshell the library was written from scratch with verbose comments to help instruct computer science students how +to implement ``bignum'' math. However, the resulting code has proven to be very useful. It has been used by numerous +universities, commercial and open source software developers. It has been used on a variety of platforms ranging from +Linux and Windows based x86 to ARM based Gameboys and PPC based MacOS machines. + +\section{License} +As of the v0.25 the library source code has been placed in the public domain with every new release. As of the v0.28 +release the textbook ``Implementing Multiple Precision Arithmetic'' has been placed in the public domain with every new +release as well. This textbook is meant to compliment the project by providing a more solid walkthrough of the development +algorithms used in the library. + +Since both\footnote{Note that the MPI files under mtest/ are copyrighted by Michael Fromberger. They are not required to use LibTomMath.} are in the +public domain everyone is entitled to do with them as they see fit. + +\section{Building LibTomMath} + +LibTomMath is meant to be very ``GCC friendly'' as it comes with a makefile well suited for GCC. However, the library will +also build in MSVC, Borland C out of the box. For any other ISO C compiler a makefile will have to be made by the end +developer. Please consider to commit such a makefile to the LibTomMath developers, currently residing at +\url{http://github.com/libtom/libtommath}, if successfully done so. + +Intel's C-compiler (ICC) is sufficiently compatible with GCC, at least the newer versions, to replace GCC for building the static and the shared library. Editing the makefiles is not needed, just set the shell variable \texttt{CC} as shown below. +\begin{alltt} +CC=/home/czurnieden/intel/bin/icc make +\end{alltt} + +ICC does not know all options available for GCC and LibTomMath uses two diagnostics \texttt{-Wbad-function-cast} and \texttt{-Wcast-align} that are not supported by ICC resulting in the warnings: +\begin{alltt} +icc: command line warning #10148: option '-Wbad-function-cast' not supported +icc: command line warning #10148: option '-Wcast-align' not supported +\end{alltt} +It is possible to mute this ICC warning with the compiler flag \texttt{-diag-disable=10148}\footnote{It is not recommended to suppress warnings without a very good reason but there is no harm in doing so in this very special case.}. + +\subsection{Static Libraries} +To build as a static library for GCC issue the following +\begin{alltt} +make +\end{alltt} + +command. This will build the library and archive the object files in ``libtommath.a''. Now you link against +that and include ``tommath.h'' within your programs. Alternatively to build with MSVC issue the following +\begin{alltt} +nmake -f makefile.msvc +\end{alltt} + +This will build the library and archive the object files in ``tommath.lib''. This has been tested with MSVC +version 6.00 with service pack 5. + +To run a program to adapt the Toom-Cook cut-off values to your architecture type +\begin{alltt} +make tune +\end{alltt} +This will take some time. + +\subsection{Shared Libraries} +\subsubsection{GNU based Operating Systems} +To build as a shared library for GCC issue the following +\begin{alltt} +make -f makefile.shared +\end{alltt} +This requires the ``libtool'' package (common on most Linux/BSD systems). It will build LibTomMath as both shared +and static then install (by default) into /usr/lib as well as install the header files in /usr/include. The shared +library (resource) will be called ``libtommath.la'' while the static library called ``libtommath.a''. Generally +you use libtool to link your application against the shared object. + +To run a program to adapt the Toom-Cook cut-off values to your architecture type +\begin{alltt} +make -f makefile.shared tune +\end{alltt} +This will take some time. + +\subsubsection{Microsoft Windows based Operating Systems} +There is limited support for making a ``DLL'' in windows via the ``makefile.cygwin\_dll'' makefile. It requires +Cygwin to work with since it requires the auto-export/import functionality. The resulting DLL and import library +``libtommath.dll.a'' can be used to link LibTomMath dynamically to any Windows program using Cygwin. +\subsubsection{OpenBSD} +OpenBSD replaced some of their GNU-tools, especially \texttt{libtool} with their own, slightly different versions. To ease the workload of LibTomMath's developer team, only a static library can be build with the included \texttt{makefile.unix}. + +The wrong \texttt{make} will result in errors like: +\begin{alltt} +*** Parse error in /home/user/GITHUB/libtommath: Need an operator in 'LIBNAME' ) +*** Parse error: Need an operator in 'endif' (makefile.shared:8) +*** Parse error: Need an operator in 'CROSS_COMPILE' (makefile_include.mk:16) +*** Parse error: Need an operator in 'endif' (makefile_include.mk:18) +*** Parse error: Missing dependency operator (makefile_include.mk:22) +*** Parse error: Missing dependency operator (makefile_include.mk:23) +... +\end{alltt} +The wrong \texttt{libtool} will build it all fine but when it comes to the final linking fails with +\begin{alltt} +... +cc -I./ -Wall -Wsign-compare -Wextra -Wshadow -Wsystem-headers -Wdeclaration-afo... +cc -I./ -Wall -Wsign-compare -Wextra -Wshadow -Wsystem-headers -Wdeclaration-afo... +cc -I./ -Wall -Wsign-compare -Wextra -Wshadow -Wsystem-headers -Wdeclaration-afo... +libtool --mode=link --tag=CC cc bn_error.lo bn_s_mp_invmod_fast.lo bn_fast_mp_mo +libtool: link: cc bn_error.lo bn_s_mp_invmod_fast.lo bn_s_mp_montgomery_reduce_fast0 +bn_error.lo: file not recognized: File format not recognized +cc: error: linker command failed with exit code 1 (use -v to see invocation) +Error while executing cc bn_error.lo bn_s_mp_invmod_fast.lo bn_fast_mp_montgomery0 +gmake: *** [makefile.shared:64: libtommath.la] Error 1 +\end{alltt} + +To build a shared library with OpenBSD\footnote{Tested with OpenBSD version 6.4} the GNU versions of \texttt{make} and \texttt{libtool} are needed. +\begin{alltt} +$ sudo pkg_add gmake libtool +\end{alltt} +At this time two versions of \texttt{libtool} are installed and both are named \texttt{libtool}, unfortunately but GNU \texttt{libtool} has been placed in \texttt{/usr/local/bin/} and the native version in \texttt{/usr/bin/}. The path might be different in other versions of OpenBSD but both programms differ in the output of \texttt{libtool --version} +\begin{alltt} +$ /usr/local/bin/libtool --version +libtool (GNU libtool) 2.4.2 +Written by Gordon Matzigkeit <gord@gnu.ai.mit.edu>, 1996 + +Copyright (C) 2011 Free Software Foundation, Inc. +This is free software; see the source for copying conditions. There is NO +warranty; not even for MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. +$ libtool --version +libtool (not (GNU libtool)) 1.5.26 +\end{alltt} + +The shared library should build now with +\begin{alltt} +LIBTOOL="/usr/local/bin/libtool" gmake -f makefile.shared +\end{alltt} +You might need to run a \texttt{gmake -f makefile.shared clean} first. + +\subsubsection{NetBSD} +NetBSD is not as strict as OpenBSD but still needs \texttt{gmake} to build the shared library. \texttt{libtool} may also not exist in a fresh install. +\begin{alltt} +pkg_add gmake libtool +\end{alltt} +Please check with \texttt{libtool --version} that installed libtool is indeed a GNU libtool. +Build the shared library by typing: +\begin{alltt} +gmake -f makefile.shared +\end{alltt} + +\subsection{Testing} +To build the library and the test harness type + +\begin{alltt} +make test +\end{alltt} + +This will build the library, ``test'' and ``mtest/mtest''. The ``test'' program will accept test vectors and verify the +results. ``mtest/mtest'' will generate test vectors using the MPI library by Michael Fromberger\footnote{A copy of MPI +is included in the package}. Simply pipe mtest into test using + +\begin{alltt} +mtest/mtest | test +\end{alltt} + +If you do not have a ``/dev/urandom'' style RNG source you will have to write your own PRNG and simply pipe that into +mtest. For example, if your PRNG program is called ``myprng'' simply invoke + +\begin{alltt} +myprng | mtest/mtest | test +\end{alltt} + +This will output a row of numbers that are increasing. Each column is a different test (such as addition, multiplication, etc) +that is being performed. The numbers represent how many times the test was invoked. If an error is detected the program +will exit with a dump of the relevant numbers it was working with. + +\section{Build Configuration} +LibTomMath can configured at build time in three phases we shall call ``depends'', ``tweaks'' and ``trims''. +Each phase changes how the library is built and they are applied one after another respectively. + +To make the system more powerful you can tweak the build process. Classes are defined in the file +``tommath\_superclass.h''. By default, the symbol ``LTM\_ALL'' shall be defined which simply +instructs the system to build all of the functions. This is how LibTomMath used to be packaged. This will give you +access to every function LibTomMath offers. + +However, there are cases where such a build is not optional. For instance, you want to perform RSA operations. You +don't need the vast majority of the library to perform these operations. Aside from LTM\_ALL there is +another pre--defined class ``SC\_RSA\_1'' which works in conjunction with the RSA from LibTomCrypt. Additional +classes can be defined base on the need of the user. + +\subsection{Build Depends} +In the file tommath\_class.h you will see a large list of C ``defines'' followed by a series of ``ifdefs'' +which further define symbols. All of the symbols (technically they're macros $\ldots$) represent a given C source +file. For instance, BN\_MP\_ADD\_C represents the file ``bn\_mp\_add.c''. When a define has been enabled the +function in the respective file will be compiled and linked into the library. Accordingly when the define +is absent the file will not be compiled and not contribute any size to the library. + +You will also note that the header tommath\_class.h is actually recursively included (it includes itself twice). +This is to help resolve as many dependencies as possible. In the last pass the symbol LTM\_LAST will be defined. +This is useful for ``trims''. + +\subsection{Build Tweaks} +A tweak is an algorithm ``alternative''. For example, to provide tradeoffs (usually between size and space). +They can be enabled at any pass of the configuration phase. + +\begin{small} +\begin{center} +\begin{tabular}{|l|l|} +\hline \textbf{Define} & \textbf{Purpose} \\ +\hline BN\_MP\_DIV\_SMALL & Enables a slower, smaller and equally \\ + & functional mp\_div() function \\ +\hline +\end{tabular} +\end{center} +\end{small} + +\subsection{Build Trims} +A trim is a manner of removing functionality from a function that is not required. For instance, to perform +RSA cryptography you only require exponentiation with odd moduli so even moduli support can be safely removed. +Build trims are meant to be defined on the last pass of the configuration which means they are to be defined +only if LTM\_LAST has been defined. + +\subsubsection{Moduli Related} +\begin{small} +\begin{center} +\begin{tabular}{|l|l|} +\hline \textbf{Restriction} & \textbf{Undefine} \\ +\hline Exponentiation with odd moduli only & BN\_S\_MP\_EXPTMOD\_C \\ + & BN\_MP\_REDUCE\_C \\ + & BN\_MP\_REDUCE\_SETUP\_C \\ + & BN\_S\_MP\_MUL\_HIGH\_DIGS\_C \\ + & BN\_FAST\_S\_MP\_MUL\_HIGH\_DIGS\_C \\ +\hline Exponentiation with random odd moduli & (The above plus the following) \\ + & BN\_MP\_REDUCE\_2K\_C \\ + & BN\_MP\_REDUCE\_2K\_SETUP\_C \\ + & BN\_MP\_REDUCE\_IS\_2K\_C \\ + & BN\_MP\_DR\_IS\_MODULUS\_C \\ + & BN\_MP\_DR\_REDUCE\_C \\ + & BN\_MP\_DR\_SETUP\_C \\ +\hline Modular inverse odd moduli only & BN\_MP\_INVMOD\_SLOW\_C \\ +\hline Modular inverse (both, smaller/slower) & BN\_FAST\_MP\_INVMOD\_C \\ +\hline +\end{tabular} +\end{center} +\end{small} + +\subsubsection{Operand Size Related} +\begin{small} +\begin{center} +\begin{tabular}{|l|l|} +\hline \textbf{Restriction} & \textbf{Undefine} \\ +\hline Moduli $\le 2560$ bits & BN\_MP\_MONTGOMERY\_REDUCE\_C \\ + & BN\_S\_MP\_MUL\_DIGS\_C \\ + & BN\_S\_MP\_MUL\_HIGH\_DIGS\_C \\ + & BN\_S\_MP\_SQR\_C \\ +\hline Polynomial Schmolynomial & BN\_MP\_KARATSUBA\_MUL\_C \\ + & BN\_MP\_KARATSUBA\_SQR\_C \\ + & BN\_MP\_TOOM\_MUL\_C \\ + & BN\_MP\_TOOM\_SQR\_C \\ + +\hline +\end{tabular} +\end{center} +\end{small} + + +\section{Purpose of LibTomMath} +Unlike GNU MP (GMP) Library, LIP, OpenSSL or various other commercial kits (Miracl), LibTomMath was not written with +bleeding edge performance in mind. First and foremost LibTomMath was written to be entirely open. Not only is the +source code public domain (unlike various other GPL/etc licensed code), not only is the code freely downloadable but the +source code is also accessible for computer science students attempting to learn ``BigNum'' or multiple precision +arithmetic techniques. + +LibTomMath was written to be an instructive collection of source code. This is why there are many comments, only one +function per source file and often I use a ``middle-road'' approach where I don't cut corners for an extra 2\% speed +increase. + +Source code alone cannot really teach how the algorithms work which is why I also wrote a textbook that accompanies +the library (beat that!). + +So you may be thinking ``should I use LibTomMath?'' and the answer is a definite maybe. Let me tabulate what I think +are the pros and cons of LibTomMath by comparing it to the math routines from GnuPG\footnote{GnuPG v1.2.3 versus LibTomMath v0.28}. + +\newpage\begin{figure}[h] +\begin{small} +\begin{center} +\begin{tabular}{|l|c|c|l|} +\hline \textbf{Criteria} & \textbf{Pro} & \textbf{Con} & \textbf{Notes} \\ +\hline Few lines of code per file & X & & GnuPG $ = 300.9$, LibTomMath $ = 71.97$ \\ +\hline Commented function prototypes & X && GnuPG function names are cryptic. \\ +\hline Speed && X & LibTomMath is slower. \\ +\hline Totally free & X & & GPL has unfavourable restrictions.\\ +\hline Large function base & X & & GnuPG is barebones. \\ +\hline Five modular reduction algorithms & X & & Faster modular exponentiation for a variety of moduli. \\ +\hline Portable & X & & GnuPG requires configuration to build. \\ +\hline +\end{tabular} +\end{center} +\end{small} +\caption{LibTomMath Valuation} +\end{figure} + +It may seem odd to compare LibTomMath to GnuPG since the math in GnuPG is only a small portion of the entire application. +However, LibTomMath was written with cryptography in mind. It provides essentially all of the functions a cryptosystem +would require when working with large integers. + +So it may feel tempting to just rip the math code out of GnuPG (or GnuMP where it was taken from originally) in your +own application but I think there are reasons not to. While LibTomMath is slower than libraries such as GnuMP it is +not normally significantly slower. On x86 machines the difference is normally a factor of two when performing modular +exponentiations. It depends largely on the processor, compiler and the moduli being used. + +Essentially the only time you wouldn't use LibTomMath is when blazing speed is the primary concern. However, +on the other side of the coin LibTomMath offers you a totally free (public domain) well structured math library +that is very flexible, complete and performs well in resource constrained environments. Fast RSA for example can +be performed with as little as 8KB of ram for data (again depending on build options). + +\chapter{Getting Started with LibTomMath} +\section{Building Programs} +In order to use LibTomMath you must include ``tommath.h'' and link against the appropriate library file (typically +libtommath.a). There is no library initialization required and the entire library is thread safe. + +\section{Return Codes} +There are three possible return codes a function may return. + +\index{MP\_OKAY}\index{MP\_YES}\index{MP\_NO}\index{MP\_VAL}\index{MP\_MEM} +\begin{figure}[h!] +\begin{center} +\begin{small} +\begin{tabular}{|l|l|} +\hline \textbf{Code} & \textbf{Meaning} \\ +\hline MP\_OKAY & The function succeeded. \\ +\hline MP\_VAL & The function input was invalid. \\ +\hline MP\_MEM & Heap memory exhausted. \\ +\hline &\\ +\hline MP\_YES & Response is yes. \\ +\hline MP\_NO & Response is no. \\ +\hline +\end{tabular} +\end{small} +\end{center} +\caption{Return Codes} +\end{figure} + +The last two codes listed are not actually ``return'ed'' by a function. They are placed in an integer (the caller must +provide the address of an integer it can store to) which the caller can access. To convert one of the three return codes +to a string use the following function. + +\index{mp\_error\_to\_string} +\begin{alltt} +char *mp_error_to_string(int code); +\end{alltt} + +This will return a pointer to a string which describes the given error code. It will not work for the return codes +MP\_YES and MP\_NO. + +\section{Data Types} +The basic ``multiple precision integer'' type is known as the ``mp\_int'' within LibTomMath. This data type is used to +organize all of the data required to manipulate the integer it represents. Within LibTomMath it has been prototyped +as the following. + +\index{mp\_int} +\begin{alltt} +typedef struct \{ + int used, alloc, sign; + mp_digit *dp; +\} mp_int; +\end{alltt} + +Where ``mp\_digit'' is a data type that represents individual digits of the integer. By default, an mp\_digit is the +ISO C ``unsigned long'' data type and each digit is $28-$bits long. The mp\_digit type can be configured to suit other +platforms by defining the appropriate macros. + +All LTM functions that use the mp\_int type will expect a pointer to mp\_int structure. You must allocate memory to +hold the structure itself by yourself (whether off stack or heap it doesn't matter). The very first thing that must be +done to use an mp\_int is that it must be initialized. + +\section{Function Organization} + +The arithmetic functions of the library are all organized to have the same style prototype. That is source operands +are passed on the left and the destination is on the right. For instance, + +\begin{alltt} +mp_add(&a, &b, &c); /* c = a + b */ +mp_mul(&a, &a, &c); /* c = a * a */ +mp_div(&a, &b, &c, &d); /* c = [a/b], d = a mod b */ +\end{alltt} + +Another feature of the way the functions have been implemented is that source operands can be destination operands as well. +For instance, + +\begin{alltt} +mp_add(&a, &b, &b); /* b = a + b */ +mp_div(&a, &b, &a, &c); /* a = [a/b], c = a mod b */ +\end{alltt} + +This allows operands to be re-used which can make programming simpler. + +\section{Initialization} +\subsection{Single Initialization} +A single mp\_int can be initialized with the ``mp\_init'' function. + +\index{mp\_init} +\begin{alltt} +int mp_init (mp_int * a); +\end{alltt} + +This function expects a pointer to an mp\_int structure and will initialize the members of the structure so the mp\_int +represents the default integer which is zero. If the functions returns MP\_OKAY then the mp\_int is ready to be used +by the other LibTomMath functions. + +\begin{small} \begin{alltt} +int main(void) +\{ + mp_int number; + int result; + + if ((result = mp_init(&number)) != MP_OKAY) \{ + printf("Error initializing the number. \%s", + mp_error_to_string(result)); + return EXIT_FAILURE; + \} + + /* use the number */ + + return EXIT_SUCCESS; +\} +\end{alltt} \end{small} + +\subsection{Single Free} +When you are finished with an mp\_int it is ideal to return the heap it used back to the system. The following function +provides this functionality. + +\index{mp\_clear} +\begin{alltt} +void mp_clear (mp_int * a); +\end{alltt} + +The function expects a pointer to a previously initialized mp\_int structure and frees the heap it uses. It sets the +pointer\footnote{The ``dp'' member.} within the mp\_int to \textbf{NULL} which is used to prevent double free situations. +Is is legal to call mp\_clear() twice on the same mp\_int in a row. + +\begin{small} \begin{alltt} +int main(void) +\{ + mp_int number; + int result; + + if ((result = mp_init(&number)) != MP_OKAY) \{ + printf("Error initializing the number. \%s", + mp_error_to_string(result)); + return EXIT_FAILURE; + \} + + /* use the number */ + + /* We're done with it. */ + mp_clear(&number); + + return EXIT_SUCCESS; +\} +\end{alltt} \end{small} + +\subsection{Multiple Initializations} +Certain algorithms require more than one large integer. In these instances it is ideal to initialize all of the mp\_int +variables in an ``all or nothing'' fashion. That is, they are either all initialized successfully or they are all +not initialized. + +The mp\_init\_multi() function provides this functionality. + +\index{mp\_init\_multi} \index{mp\_clear\_multi} +\begin{alltt} +int mp_init_multi(mp_int *mp, ...); +\end{alltt} + +It accepts a \textbf{NULL} terminated list of pointers to mp\_int structures. It will attempt to initialize them all +at once. If the function returns MP\_OKAY then all of the mp\_int variables are ready to use, otherwise none of them +are available for use. A complementary mp\_clear\_multi() function allows multiple mp\_int variables to be free'd +from the heap at the same time. + +\begin{small} \begin{alltt} +int main(void) +\{ + mp_int num1, num2, num3; + int result; + + if ((result = mp_init_multi(&num1, + &num2, + &num3, NULL)) != MP\_OKAY) \{ + printf("Error initializing the numbers. \%s", + mp_error_to_string(result)); + return EXIT_FAILURE; + \} + + /* use the numbers */ + + /* We're done with them. */ + mp_clear_multi(&num1, &num2, &num3, NULL); + + return EXIT_SUCCESS; +\} +\end{alltt} \end{small} + +\subsection{Other Initializers} +To initialized and make a copy of an mp\_int the mp\_init\_copy() function has been provided. + +\index{mp\_init\_copy} +\begin{alltt} +int mp_init_copy (mp_int * a, mp_int * b); +\end{alltt} + +This function will initialize $a$ and make it a copy of $b$ if all goes well. + +\begin{small} \begin{alltt} +int main(void) +\{ + mp_int num1, num2; + int result; + + /* initialize and do work on num1 ... */ + + /* We want a copy of num1 in num2 now */ + if ((result = mp_init_copy(&num2, &num1)) != MP_OKAY) \{ + printf("Error initializing the copy. \%s", + mp_error_to_string(result)); + return EXIT_FAILURE; + \} + + /* now num2 is ready and contains a copy of num1 */ + + /* We're done with them. */ + mp_clear_multi(&num1, &num2, NULL); + + return EXIT_SUCCESS; +\} +\end{alltt} \end{small} + +Another less common initializer is mp\_init\_size() which allows the user to initialize an mp\_int with a given +default number of digits. By default, all initializers allocate \textbf{MP\_PREC} digits. This function lets +you override this behaviour. + +\index{mp\_init\_size} +\begin{alltt} +int mp_init_size (mp_int * a, int size); +\end{alltt} + +The $size$ parameter must be greater than zero. If the function succeeds the mp\_int $a$ will be initialized +to have $size$ digits (which are all initially zero). + +\begin{small} \begin{alltt} +int main(void) +\{ + mp_int number; + int result; + + /* we need a 60-digit number */ + if ((result = mp_init_size(&number, 60)) != MP_OKAY) \{ + printf("Error initializing the number. \%s", + mp_error_to_string(result)); + return EXIT_FAILURE; + \} + + /* use the number */ + + return EXIT_SUCCESS; +\} +\end{alltt} \end{small} + +\section{Maintenance Functions} +\subsection{Clear Leading Zeros} + +This is used to ensure that leading zero digits are trimed and the leading "used" digit will be non-zero. +It also fixes the sign if there are no more leading digits. + +\index{mp\_clamp} +\begin{alltt} +void mp_clamp(mp_int *a); +\end{alltt} + +\subsection{Zero Out} + +This function will set the ``bigint'' to zeros without changing the amount of allocated memory. + +\index{mp\_zero} +\begin{alltt} +void mp_zero(mp_int *a); +\end{alltt} + + +\subsection{Reducing Memory Usage} +When an mp\_int is in a state where it won't be changed again\footnote{A Diffie-Hellman modulus for instance.} excess +digits can be removed to return memory to the heap with the mp\_shrink() function. + +\index{mp\_shrink} +\begin{alltt} +int mp_shrink (mp_int * a); +\end{alltt} + +This will remove excess digits of the mp\_int $a$. If the operation fails the mp\_int should be intact without the +excess digits being removed. Note that you can use a shrunk mp\_int in further computations, however, such operations +will require heap operations which can be slow. It is not ideal to shrink mp\_int variables that you will further +modify in the system (unless you are seriously low on memory). + +\begin{small} \begin{alltt} +int main(void) +\{ + mp_int number; + int result; + + if ((result = mp_init(&number)) != MP_OKAY) \{ + printf("Error initializing the number. \%s", + mp_error_to_string(result)); + return EXIT_FAILURE; + \} + + /* use the number [e.g. pre-computation] */ + + /* We're done with it for now. */ + if ((result = mp_shrink(&number)) != MP_OKAY) \{ + printf("Error shrinking the number. \%s", + mp_error_to_string(result)); + return EXIT_FAILURE; + \} + + /* use it .... */ + + + /* we're done with it. */ + mp_clear(&number); + + return EXIT_SUCCESS; +\} +\end{alltt} \end{small} + +\subsection{Adding additional digits} + +Within the mp\_int structure are two parameters which control the limitations of the array of digits that represent +the integer the mp\_int is meant to equal. The \textit{used} parameter dictates how many digits are significant, that is, +contribute to the value of the mp\_int. The \textit{alloc} parameter dictates how many digits are currently available in +the array. If you need to perform an operation that requires more digits you will have to mp\_grow() the mp\_int to +your desired size. + +\index{mp\_grow} +\begin{alltt} +int mp_grow (mp_int * a, int size); +\end{alltt} + +This will grow the array of digits of $a$ to $size$. If the \textit{alloc} parameter is already bigger than +$size$ the function will not do anything. + +\begin{small} \begin{alltt} +int main(void) +\{ + mp_int number; + int result; + + if ((result = mp_init(&number)) != MP_OKAY) \{ + printf("Error initializing the number. \%s", + mp_error_to_string(result)); + return EXIT_FAILURE; + \} + + /* use the number */ + + /* We need to add 20 digits to the number */ + if ((result = mp_grow(&number, number.alloc + 20)) != MP_OKAY) \{ + printf("Error growing the number. \%s", + mp_error_to_string(result)); + return EXIT_FAILURE; + \} + + + /* use the number */ + + /* we're done with it. */ + mp_clear(&number); + + return EXIT_SUCCESS; +\} +\end{alltt} \end{small} + +\chapter{Basic Operations} +\section{Copying} + +A so called ``deep copy'', where new memory is allocated and all contents of $a$ are copied verbatim into $b$ such that $b = a$ at the end. + +\index{mp\_copy} +\begin{alltt} +int mp_copy (mp_int * a, mp_int *b); +\end{alltt} + +You can also just swap $a$ and $b$. It does the normal pointer changing with a temporary pointer variable, just that you do not have to. + +\index{mp\_exch} +\begin{alltt} +void mp_exch (mp_int * a, mp_int *b); +\end{alltt} + +\section{Bit Counting} + +To get the position of the lowest bit set (LSB, the Lowest Significant Bit; the number of bits which are zero before the first zero bit ) + +\index{mp\_cnt\_lsb} +\begin{alltt} +int mp_cnt_lsb(const mp_int *a); +\end{alltt} + +To get the position of the highest bit set (MSB, the Most Significant Bit; the number of bits in teh ``bignum'') + +\index{mp\_count\_bits} +\begin{alltt} +int mp_count_bits(const mp_int *a); +\end{alltt} + + +\section{Small Constants} +Setting mp\_ints to small constants is a relatively common operation. To accommodate these instances there is a +small constant assignment function. This function is used to set a single digit constant. +The reason for this function is efficiency. Setting a single digit is quick but the +domain of a digit can change (it's always at least $0 \ldots 127$). + +\subsection{Single Digit} + +Setting a single digit can be accomplished with the following function. + +\index{mp\_set} +\begin{alltt} +void mp_set (mp_int * a, mp_digit b); +\end{alltt} + +This will zero the contents of $a$ and make it represent an integer equal to the value of $b$. Note that this +function has a return type of \textbf{void}. It cannot cause an error so it is safe to assume the function +succeeded. + +\begin{small} \begin{alltt} +int main(void) +\{ + mp_int number; + int result; + + if ((result = mp_init(&number)) != MP_OKAY) \{ + printf("Error initializing the number. \%s", + mp_error_to_string(result)); + return EXIT_FAILURE; + \} + + /* set the number to 5 */ + mp_set(&number, 5); + + /* we're done with it. */ + mp_clear(&number); + + return EXIT_SUCCESS; +\} +\end{alltt} \end{small} + +\subsection{Int32 and Int64 Constants} + +These functions can be used to set a constant with 32 or 64 bits. + +\index{mp\_set\_i32} \index{mp\_set\_u32} +\index{mp\_set\_i64} \index{mp\_set\_u64} +\begin{alltt} +void mp_set_i32 (mp_int * a, int32_t b); +void mp_set_u32 (mp_int * a, uint32_t b); +void mp_set_i64 (mp_int * a, int64_t b); +void mp_set_u64 (mp_int * a, uint64_t b); +\end{alltt} + +These functions assign the sign and value of the input \texttt{b} to \texttt{mp\_int a}. +The value can be obtained again by calling the following functions. + +\index{mp\_get\_i32} \index{mp\_get\_u32} \index{mp\_get\_mag\_u32} +\index{mp\_get\_i64} \index{mp\_get\_u64} \index{mp\_get\_mag\_u64} +\begin{alltt} +int32_t mp_get_i32 (mp_int * a); +uint32_t mp_get_u32 (mp_int * a); +uint32_t mp_get_mag_u32 (mp_int * a); +int64_t mp_get_i64 (mp_int * a); +uint64_t mp_get_u64 (mp_int * a); +uint64_t mp_get_mag_u64 (mp_int * a); +\end{alltt} + +These functions return the 32 or 64 least significant bits of $a$ respectively. The unsigned functions +return negative values in a twos complement representation. The absolute value or magnitude can be obtained using the mp\_get\_mag functions. + +\begin{small} \begin{alltt} +int main(void) +\{ + mp_int number; + int result; + + if ((result = mp_init(&number)) != MP_OKAY) \{ + printf("Error initializing the number. \%s", + mp_error_to_string(result)); + return EXIT_FAILURE; + \} + + /* set the number to 654321 (note this is bigger than 127) */ + mp_set_u32(&number, 654321); + + printf("number == \%" PRIi32, mp_get_i32(&number)); + + /* we're done with it. */ + mp_clear(&number); + + return EXIT_SUCCESS; +\} +\end{alltt} \end{small} + +This should output the following if the program succeeds. + +\begin{alltt} +number == 654321 +\end{alltt} + +\subsection{Long Constants - platform dependant} + +\index{mp\_set\_l} \index{mp\_set\_ul} +\begin{alltt} +void mp_set_l (mp_int * a, long b); +void mp_set_ul (mp_int * a, unsigned long b); +\end{alltt} + +This will assign the value of the platform-dependent sized variable $b$ to the mp\_int $a$. + +To retrieve the value, the following functions can be used. + +\index{mp\_get\_l} \index{mp\_get\_ul} \index{mp\_get\_mag\_ul} +\begin{alltt} +long mp_get_l (mp_int * a); +unsigned long mp_get_ul (mp_int * a); +unsigned long mp_get_mag_ul (mp_int * a); +\end{alltt} + +This will return the least significant bits of the mp\_int $a$ that fit into a ``long''. + +\subsection{Long Long Constants - platform dependant} + +\index{mp\_set\_ll} \index{mp\_set\_ull} +\begin{alltt} +void mp_set_ll (mp_int * a, long long b); +void mp_set_ull (mp_int * a, unsigned long long b); +\end{alltt} + +This will assign the value of the platform-dependent sized variable $b$ to the mp\_int $a$. + +To retrieve the value, the following functions can be used. + +\index{mp\_get\_ll} +\index{mp\_get\_ull} +\index{mp\_get\_mag\_ull} +\begin{alltt} +long long mp_get_ll (mp_int * a); +unsigned long long mp_get_ull (mp_int * a); +unsigned long long mp_get_mag_ull (mp_int * a); +\end{alltt} + +This will return the least significant bits of the mp\_int $a$ that fit into a ``long long''. + +\subsection{Initialize and Setting Constants} +To both initialize and set small constants the following two functions are available. +\index{mp\_init\_set} \index{mp\_init\_set\_int} +\begin{alltt} +int mp_init_set (mp_int * a, mp_digit b); +int mp_init_i32 (mp_int * a, int32_t b); +int mp_init_u32 (mp_int * a, uint32_t b); +int mp_init_i64 (mp_int * a, int64_t b); +int mp_init_u64 (mp_int * a, uint64_t b); +int mp_init_l (mp_int * a, long b); +int mp_init_ul (mp_int * a, unsigned long b); +int mp_init_ll (mp_int * a, long long b); +int mp_init_ull (mp_int * a, unsigned long long b); +\end{alltt} + +Both functions work like the previous counterparts except they first mp\_init $a$ before setting the values. + +\begin{alltt} +int main(void) +\{ + mp_int number1, number2; + int result; + + /* initialize and set a single digit */ + if ((result = mp_init_set(&number1, 100)) != MP_OKAY) \{ + printf("Error setting number1: \%s", + mp_error_to_string(result)); + return EXIT_FAILURE; + \} + + /* initialize and set a long */ + if ((result = mp_init_l(&number2, 1023)) != MP_OKAY) \{ + printf("Error setting number2: \%s", + mp_error_to_string(result)); + return EXIT_FAILURE; + \} + + /* display */ + printf("Number1, Number2 == \%" PRIi32 ", \%" PRIi32, + mp_get_i32(&number1), mp_get_i32(&number2)); + + /* clear */ + mp_clear_multi(&number1, &number2, NULL); + + return EXIT_SUCCESS; +\} +\end{alltt} + +If this program succeeds it shall output. +\begin{alltt} +Number1, Number2 == 100, 1023 +\end{alltt} + +\section{Comparisons} + +Comparisons in LibTomMath are always performed in a ``left to right'' fashion. There are three possible return codes +for any comparison. + +\index{MP\_GT} \index{MP\_EQ} \index{MP\_LT} +\begin{figure}[h] +\begin{center} +\begin{tabular}{|c|c|} +\hline \textbf{Result Code} & \textbf{Meaning} \\ +\hline MP\_GT & $a > b$ \\ +\hline MP\_EQ & $a = b$ \\ +\hline MP\_LT & $a < b$ \\ +\hline +\end{tabular} +\end{center} +\caption{Comparison Codes for $a, b$} +\label{fig:CMP} +\end{figure} + +In figure \ref{fig:CMP} two integers $a$ and $b$ are being compared. In this case $a$ is said to be ``to the left'' of +$b$. + +\subsection{Unsigned comparison} + +An unsigned comparison considers only the digits themselves and not the associated \textit{sign} flag of the +mp\_int structures. This is analogous to an absolute comparison. The function mp\_cmp\_mag() will compare two +mp\_int variables based on their digits only. + +\index{mp\_cmp\_mag} +\begin{alltt} +int mp_cmp_mag(mp_int * a, mp_int * b); +\end{alltt} +This will compare $a$ to $b$ placing $a$ to the left of $b$. This function cannot fail and will return one of the +three compare codes listed in figure \ref{fig:CMP}. + +\begin{small} \begin{alltt} +int main(void) +\{ + mp_int number1, number2; + int result; + + if ((result = mp_init_multi(&number1, &number2, NULL)) != MP_OKAY) \{ + printf("Error initializing the numbers. \%s", + mp_error_to_string(result)); + return EXIT_FAILURE; + \} + + /* set the number1 to 5 */ + mp_set(&number1, 5); + + /* set the number2 to -6 */ + mp_set(&number2, 6); + if ((result = mp_neg(&number2, &number2)) != MP_OKAY) \{ + printf("Error negating number2. \%s", + mp_error_to_string(result)); + return EXIT_FAILURE; + \} + + switch(mp_cmp_mag(&number1, &number2)) \{ + case MP_GT: printf("|number1| > |number2|"); break; + case MP_EQ: printf("|number1| = |number2|"); break; + case MP_LT: printf("|number1| < |number2|"); break; + \} + + /* we're done with it. */ + mp_clear_multi(&number1, &number2, NULL); + + return EXIT_SUCCESS; +\} +\end{alltt} \end{small} + +If this program\footnote{This function uses the mp\_neg() function which is discussed in section \ref{sec:NEG}.} completes +successfully it should print the following. + +\begin{alltt} +|number1| < |number2| +\end{alltt} + +This is because $\vert -6 \vert = 6$ and obviously $5 < 6$. + +\subsection{Signed comparison} + +To compare two mp\_int variables based on their signed value the mp\_cmp() function is provided. + +\index{mp\_cmp} +\begin{alltt} +int mp_cmp(mp_int * a, mp_int * b); +\end{alltt} + +This will compare $a$ to the left of $b$. It will first compare the signs of the two mp\_int variables. If they +differ it will return immediately based on their signs. If the signs are equal then it will compare the digits +individually. This function will return one of the compare conditions codes listed in figure \ref{fig:CMP}. + +\begin{small} \begin{alltt} +int main(void) +\{ + mp_int number1, number2; + int result; + + if ((result = mp_init_multi(&number1, &number2, NULL)) != MP_OKAY) \{ + printf("Error initializing the numbers. \%s", + mp_error_to_string(result)); + return EXIT_FAILURE; + \} + + /* set the number1 to 5 */ + mp_set(&number1, 5); + + /* set the number2 to -6 */ + mp_set(&number2, 6); + if ((result = mp_neg(&number2, &number2)) != MP_OKAY) \{ + printf("Error negating number2. \%s", + mp_error_to_string(result)); + return EXIT_FAILURE; + \} + + switch(mp_cmp(&number1, &number2)) \{ + case MP_GT: printf("number1 > number2"); break; + case MP_EQ: printf("number1 = number2"); break; + case MP_LT: printf("number1 < number2"); break; + \} + + /* we're done with it. */ + mp_clear_multi(&number1, &number2, NULL); + + return EXIT_SUCCESS; +\} +\end{alltt} \end{small} + +If this program\footnote{This function uses the mp\_neg() function which is discussed in section \ref{sec:NEG}.} completes +successfully it should print the following. + +\begin{alltt} +number1 > number2 +\end{alltt} + +\subsection{Single Digit} + +To compare a single digit against an mp\_int the following function has been provided. + +\index{mp\_cmp\_d} +\begin{alltt} +int mp_cmp_d(mp_int * a, mp_digit b); +\end{alltt} + +This will compare $a$ to the left of $b$ using a signed comparison. Note that it will always treat $b$ as +positive. This function is rather handy when you have to compare against small values such as $1$ (which often +comes up in cryptography). The function cannot fail and will return one of the tree compare condition codes +listed in figure \ref{fig:CMP}. + + +\begin{small} \begin{alltt} +int main(void) +\{ + mp_int number; + int result; + + if ((result = mp_init(&number)) != MP_OKAY) \{ + printf("Error initializing the number. \%s", + mp_error_to_string(result)); + return EXIT_FAILURE; + \} + + /* set the number to 5 */ + mp_set(&number, 5); + + switch(mp_cmp_d(&number, 7)) \{ + case MP_GT: printf("number > 7"); break; + case MP_EQ: printf("number = 7"); break; + case MP_LT: printf("number < 7"); break; + \} + + /* we're done with it. */ + mp_clear(&number); + + return EXIT_SUCCESS; +\} +\end{alltt} \end{small} + +If this program functions properly it will print out the following. + +\begin{alltt} +number < 7 +\end{alltt} + +\section{Logical Operations} + +Logical operations are operations that can be performed either with simple shifts or boolean operators such as +AND, XOR and OR directly. These operations are very quick. + +\subsection{Multiplication by two} + +Multiplications and divisions by any power of two can be performed with quick logical shifts either left or +right depending on the operation. + +When multiplying or dividing by two a special case routine can be used which are as follows. +\index{mp\_mul\_2} \index{mp\_div\_2} +\begin{alltt} +int mp_mul_2(mp_int * a, mp_int * b); +int mp_div_2(mp_int * a, mp_int * b); +\end{alltt} + +The former will assign twice $a$ to $b$ while the latter will assign half $a$ to $b$. These functions are fast +since the shift counts and maskes are hardcoded into the routines. + +\begin{small} \begin{alltt} +int main(void) +\{ + mp_int number; + int result; + + if ((result = mp_init(&number)) != MP_OKAY) \{ + printf("Error initializing the number. \%s", + mp_error_to_string(result)); + return EXIT_FAILURE; + \} + + /* set the number to 5 */ + mp_set(&number, 5); + + /* multiply by two */ + if ((result = mp\_mul\_2(&number, &number)) != MP_OKAY) \{ + printf("Error multiplying the number. \%s", + mp_error_to_string(result)); + return EXIT_FAILURE; + \} + switch(mp_cmp_d(&number, 7)) \{ + case MP_GT: printf("2*number > 7"); break; + case MP_EQ: printf("2*number = 7"); break; + case MP_LT: printf("2*number < 7"); break; + \} + + /* now divide by two */ + if ((result = mp\_div\_2(&number, &number)) != MP_OKAY) \{ + printf("Error dividing the number. \%s", + mp_error_to_string(result)); + return EXIT_FAILURE; + \} + switch(mp_cmp_d(&number, 7)) \{ + case MP_GT: printf("2*number/2 > 7"); break; + case MP_EQ: printf("2*number/2 = 7"); break; + case MP_LT: printf("2*number/2 < 7"); break; + \} + + /* we're done with it. */ + mp_clear(&number); + + return EXIT_SUCCESS; +\} +\end{alltt} \end{small} + +If this program is successful it will print out the following text. + +\begin{alltt} +2*number > 7 +2*number/2 < 7 +\end{alltt} + +Since $10 > 7$ and $5 < 7$. + +To multiply by a power of two the following function can be used. + +\index{mp\_mul\_2d} +\begin{alltt} +int mp_mul_2d(mp_int * a, int b, mp_int * c); +\end{alltt} + +This will multiply $a$ by $2^b$ and store the result in ``c''. If the value of $b$ is less than or equal to +zero the function will copy $a$ to ``c'' without performing any further actions. The multiplication itself +is implemented as a right-shift operation of $a$ by $b$ bits. + +To divide by a power of two use the following. + +\index{mp\_div\_2d} +\begin{alltt} +int mp_div_2d (mp_int * a, int b, mp_int * c, mp_int * d); +\end{alltt} +Which will divide $a$ by $2^b$, store the quotient in ``c'' and the remainder in ``d'. If $b \le 0$ then the +function simply copies $a$ over to ``c'' and zeroes $d$. The variable $d$ may be passed as a \textbf{NULL} +value to signal that the remainder is not desired. The division itself is implemented as a left-shift +operation of $a$ by $b$ bits. + +It is also not very uncommon to need just the power of two $2^b$; for example the startvalue for the Newton method. + +\index{mp\_2expt} +\begin{alltt} +int mp_2expt(mp_int *a, int b); +\end{alltt} +It is faster than doing it by shifting $1$ with \texttt{mp\_mul\_2d}. + +\subsection{Polynomial Basis Operations} + +Strictly speaking the organization of the integers within the mp\_int structures is what is known as a +``polynomial basis''. This simply means a field element is stored by divisions of a radix. For example, if +$f(x) = \sum_{i=0}^{k} y_ix^k$ for any vector $\vec y$ then the array of digits in $\vec y$ are said to be +the polynomial basis representation of $z$ if $f(\beta) = z$ for a given radix $\beta$. + +To multiply by the polynomial $g(x) = x$ all you have todo is shift the digits of the basis left one place. The +following function provides this operation. + +\index{mp\_lshd} +\begin{alltt} +int mp_lshd (mp_int * a, int b); +\end{alltt} + +This will multiply $a$ in place by $x^b$ which is equivalent to shifting the digits left $b$ places and inserting zeroes +in the least significant digits. Similarly to divide by a power of $x$ the following function is provided. + +\index{mp\_rshd} +\begin{alltt} +void mp_rshd (mp_int * a, int b) +\end{alltt} +This will divide $a$ in place by $x^b$ and discard the remainder. This function cannot fail as it performs the operations +in place and no new digits are required to complete it. + +\subsection{AND, OR, XOR and COMPLEMENT Operations} + +While AND, OR and XOR operations compute arbitrary-precision bitwise operations. Negative numbers +are treated as if they are in two-complement representation, while internally they are sign-magnitude however. + +\index{mp\_or} \index{mp\_and} \index{mp\_xor} \index{mp\_complement} +\begin{alltt} +int mp_or (mp_int * a, mp_int * b, mp_int * c); +int mp_and (mp_int * a, mp_int * b, mp_int * c); +int mp_xor (mp_int * a, mp_int * b, mp_int * c); +int mp_complement(const mp_int *a, mp_int *b); +int mp_signed_rsh(mp_int * a, int b, mp_int * c, mp_int * d); +\end{alltt} + +The function \texttt{mp\_complement} computes a two-complement $b = \sim a$. The function \texttt{mp\_signed\_rsh} performs +sign extending right shift. For positive numbers it is equivalent to \texttt{mp\_div\_2d}. + +\subsection{Bit Picking} +\index{mp\_get\_bit} +\begin{alltt} +int mp_get_bit(mp_int *a, int b) +\end{alltt} + +Pick a bit: returns \texttt{MP\_YES} if the bit at position $b$ (0-index) is set, that is if it is 1 (one), \texttt{MP\_NO} +if the bit is 0 (zero) and \texttt{MP\_VAL} if $b < 0$. + +\section{Addition and Subtraction} + +To compute an addition or subtraction the following two functions can be used. + +\index{mp\_add} \index{mp\_sub} +\begin{alltt} +int mp_add (mp_int * a, mp_int * b, mp_int * c); +int mp_sub (mp_int * a, mp_int * b, mp_int * c) +\end{alltt} + +Which perform $c = a \odot b$ where $\odot$ is one of signed addition or subtraction. The operations are fully sign +aware. + +\section{Sign Manipulation} +\subsection{Negation} +\label{sec:NEG} +Simple integer negation can be performed with the following. + +\index{mp\_neg} +\begin{alltt} +int mp_neg (mp_int * a, mp_int * b); +\end{alltt} + +Which assigns $-a$ to $b$. + +\subsection{Absolute} +Simple integer absolutes can be performed with the following. + +\index{mp\_abs} +\begin{alltt} +int mp_abs (mp_int * a, mp_int * b); +\end{alltt} + +Which assigns $\vert a \vert$ to $b$. + +\section{Integer Division and Remainder} +To perform a complete and general integer division with remainder use the following function. + +\index{mp\_div} +\begin{alltt} +int mp_div (mp_int * a, mp_int * b, mp_int * c, mp_int * d); +\end{alltt} + +This divides $a$ by $b$ and stores the quotient in $c$ and $d$. The signed quotient is computed such that +$bc + d = a$. Note that either of $c$ or $d$ can be set to \textbf{NULL} if their value is not required. If +$b$ is zero the function returns \textbf{MP\_VAL}. + + +\chapter{Multiplication and Squaring} +\section{Multiplication} +A full signed integer multiplication can be performed with the following. +\index{mp\_mul} +\begin{alltt} +int mp_mul (mp_int * a, mp_int * b, mp_int * c); +\end{alltt} +Which assigns the full signed product $ab$ to $c$. This function actually breaks into one of four cases which are +specific multiplication routines optimized for given parameters. First there are the Toom-Cook multiplications which +should only be used with very large inputs. This is followed by the Karatsuba multiplications which are for moderate +sized inputs. Then followed by the Comba and baseline multipliers. + +Fortunately for the developer you don't really need to know this unless you really want to fine tune the system. mp\_mul() +will determine on its own\footnote{Some tweaking may be required but \texttt{make tune} will put some reasonable values in \texttt{bncore.c}} what routine to use automatically when it is called. + +\begin{alltt} +int main(void) +\{ + mp_int number1, number2; + int result; + + /* Initialize the numbers */ + if ((result = mp_init_multi(&number1, + &number2, NULL)) != MP_OKAY) \{ + printf("Error initializing the numbers. \%s", + mp_error_to_string(result)); + return EXIT_FAILURE; + \} + + /* set the terms */ + mp_set_i32(&number, 257); + mp_set_i32(&number2, 1023); + + /* multiply them */ + if ((result = mp_mul(&number1, &number2, + &number1)) != MP_OKAY) \{ + printf("Error multiplying terms. \%s", + mp_error_to_string(result)); + return EXIT_FAILURE; + \} + + /* display */ + printf("number1 * number2 == \%" PRIi32, mp_get_i32(&number1)); + + /* free terms and return */ + mp_clear_multi(&number1, &number2, NULL); + + return EXIT_SUCCESS; +\} +\end{alltt} + +If this program succeeds it shall output the following. + +\begin{alltt} +number1 * number2 == 262911 +\end{alltt} + +\section{Squaring} +Since squaring can be performed faster than multiplication it is performed it's own function instead of just using +mp\_mul(). + +\index{mp\_sqr} +\begin{alltt} +int mp_sqr (mp_int * a, mp_int * b); +\end{alltt} + +Will square $a$ and store it in $b$. Like the case of multiplication there are four different squaring +algorithms all which can be called from mp\_sqr(). It is ideal to use mp\_sqr over mp\_mul when squaring terms because +of the speed difference. + +\section{Tuning Polynomial Basis Routines} + +Both of the Toom-Cook and Karatsuba multiplication algorithms are faster than the traditional $O(n^2)$ approach that +the Comba and baseline algorithms use. At $O(n^{1.464973})$ and $O(n^{1.584962})$ running times respectively they require +considerably less work. For example, a 10000-digit multiplication would take roughly 724,000 single precision +multiplications with Toom-Cook or 100,000,000 single precision multiplications with the standard Comba (a factor +of 138). + +So why not always use Karatsuba or Toom-Cook? The simple answer is that they have so much overhead that they're not +actually faster than Comba until you hit distinct ``cutoff'' points. For Karatsuba with the default configuration, +GCC 3.3.1 and an Athlon XP processor the cutoff point is roughly 110 digits (about 70 for the Intel P4). That is, at +110 digits Karatsuba and Comba multiplications just about break even and for 110+ digits Karatsuba is faster. + +Toom-Cook has incredible overhead and is probably only useful for very large inputs. So far no known cutoff points +exist and for the most part I just set the cutoff points very high to make sure they're not called. + +To get reasonable values for the cut-off points for your architecture, type + +\begin{alltt} +make tune +\end{alltt} + +This will run a benchmark, computes the medians, rewrites \texttt{bncore.c}, and recompiles \texttt{bncore.c} and relinks the library. + +The benchmark itself can be fine-tuned in the file \texttt{etc/tune\_it.sh}. + +The program \texttt{etc/tune} is also able to print a list of values for printing curves with e.g.: \texttt{gnuplot}. type \texttt{./etc/tune -h} to get a list of all available options. + +\chapter{Modular Reduction} + +Modular reduction is process of taking the remainder of one quantity divided by another. Expressed +as (\ref{eqn:mod}) the modular reduction is equivalent to the remainder of $b$ divided by $c$. + +\begin{equation} +a \equiv b \mbox{ (mod }c\mbox{)} +\label{eqn:mod} +\end{equation} + +Of particular interest to cryptography are reductions where $b$ is limited to the range $0 \le b < c^2$ since particularly +fast reduction algorithms can be written for the limited range. + +Note that one of the four optimized reduction algorithms are automatically chosen in the modular exponentiation +algorithm mp\_exptmod when an appropriate modulus is detected. + +\section{Straight Division} +In order to effect an arbitrary modular reduction the following algorithm is provided. + +\index{mp\_mod} +\begin{alltt} +int mp_mod(mp_int *a, mp_int *b, mp_int *c); +\end{alltt} + +This reduces $a$ modulo $b$ and stores the result in $c$. The sign of $c$ shall agree with the sign +of $b$. This algorithm accepts an input $a$ of any range and is not limited by $0 \le a < b^2$. + +\section{Barrett Reduction} + +Barrett reduction is a generic optimized reduction algorithm that requires pre--computation to achieve +a decent speedup over straight division. First a $\mu$ value must be precomputed with the following function. + +\index{mp\_reduce\_setup} +\begin{alltt} +int mp_reduce_setup(mp_int *a, mp_int *b); +\end{alltt} + +Given a modulus in $b$ this produces the required $\mu$ value in $a$. For any given modulus this only has to +be computed once. Modular reduction can now be performed with the following. + +\index{mp\_reduce} +\begin{alltt} +int mp_reduce(mp_int *a, mp_int *b, mp_int *c); +\end{alltt} + +This will reduce $a$ in place modulo $b$ with the precomputed $\mu$ value in $c$. $a$ must be in the range +$0 \le a < b^2$. + +\begin{alltt} +int main(void) +\{ + mp_int a, b, c, mu; + int result; + + /* initialize a,b to desired values, mp_init mu, + * c and set c to 1...we want to compute a^3 mod b + */ + + /* get mu value */ + if ((result = mp_reduce_setup(&mu, b)) != MP_OKAY) \{ + printf("Error getting mu. \%s", + mp_error_to_string(result)); + return EXIT_FAILURE; + \} + + /* square a to get c = a^2 */ + if ((result = mp_sqr(&a, &c)) != MP_OKAY) \{ + printf("Error squaring. \%s", + mp_error_to_string(result)); + return EXIT_FAILURE; + \} + + /* now reduce `c' modulo b */ + if ((result = mp_reduce(&c, &b, &mu)) != MP_OKAY) \{ + printf("Error reducing. \%s", + mp_error_to_string(result)); + return EXIT_FAILURE; + \} + + /* multiply a to get c = a^3 */ + if ((result = mp_mul(&a, &c, &c)) != MP_OKAY) \{ + printf("Error reducing. \%s", + mp_error_to_string(result)); + return EXIT_FAILURE; + \} + + /* now reduce `c' modulo b */ + if ((result = mp_reduce(&c, &b, &mu)) != MP_OKAY) \{ + printf("Error reducing. \%s", + mp_error_to_string(result)); + return EXIT_FAILURE; + \} + + /* c now equals a^3 mod b */ + + return EXIT_SUCCESS; +\} +\end{alltt} + +This program will calculate $a^3 \mbox{ mod }b$ if all the functions succeed. + +\section{Montgomery Reduction} + +Montgomery is a specialized reduction algorithm for any odd moduli. Like Barrett reduction a pre--computation +step is required. This is accomplished with the following. + +\index{mp\_montgomery\_setup} +\begin{alltt} +int mp_montgomery_setup(mp_int *a, mp_digit *mp); +\end{alltt} + +For the given odd moduli $a$ the precomputation value is placed in $mp$. The reduction is computed with the +following. + +\index{mp\_montgomery\_reduce} +\begin{alltt} +int mp_montgomery_reduce(mp_int *a, mp_int *m, mp_digit mp); +\end{alltt} +This reduces $a$ in place modulo $m$ with the pre--computed value $mp$. $a$ must be in the range +$0 \le a < b^2$. + +Montgomery reduction is faster than Barrett reduction for moduli smaller than the ``comba'' limit. With the default +setup for instance, the limit is $127$ digits ($3556$--bits). Note that this function is not limited to +$127$ digits just that it falls back to a baseline algorithm after that point. + +An important observation is that this reduction does not return $a \mbox{ mod }m$ but $aR^{-1} \mbox{ mod }m$ +where $R = \beta^n$, $n$ is the n number of digits in $m$ and $\beta$ is radix used (default is $2^{28}$). + +To quickly calculate $R$ the following function was provided. + +\index{mp\_montgomery\_calc\_normalization} +\begin{alltt} +int mp_montgomery_calc_normalization(mp_int *a, mp_int *b); +\end{alltt} +Which calculates $a = R$ for the odd moduli $b$ without using multiplication or division. + +The normal modus operandi for Montgomery reductions is to normalize the integers before entering the system. For +example, to calculate $a^3 \mbox { mod }b$ using Montgomery reduction the value of $a$ can be normalized by +multiplying it by $R$. Consider the following code snippet. + +\begin{alltt} +int main(void) +\{ + mp_int a, b, c, R; + mp_digit mp; + int result; + + /* initialize a,b to desired values, + * mp_init R, c and set c to 1.... + */ + + /* get normalization */ + if ((result = mp_montgomery_calc_normalization(&R, b)) != MP_OKAY) \{ + printf("Error getting norm. \%s", + mp_error_to_string(result)); + return EXIT_FAILURE; + \} + + /* get mp value */ + if ((result = mp_montgomery_setup(&c, &mp)) != MP_OKAY) \{ + printf("Error setting up montgomery. \%s", + mp_error_to_string(result)); + return EXIT_FAILURE; + \} + + /* normalize `a' so now a is equal to aR */ + if ((result = mp_mulmod(&a, &R, &b, &a)) != MP_OKAY) \{ + printf("Error computing aR. \%s", + mp_error_to_string(result)); + return EXIT_FAILURE; + \} + + /* square a to get c = a^2R^2 */ + if ((result = mp_sqr(&a, &c)) != MP_OKAY) \{ + printf("Error squaring. \%s", + mp_error_to_string(result)); + return EXIT_FAILURE; + \} + + /* now reduce `c' back down to c = a^2R^2 * R^-1 == a^2R */ + if ((result = mp_montgomery_reduce(&c, &b, mp)) != MP_OKAY) \{ + printf("Error reducing. \%s", + mp_error_to_string(result)); + return EXIT_FAILURE; + \} + + /* multiply a to get c = a^3R^2 */ + if ((result = mp_mul(&a, &c, &c)) != MP_OKAY) \{ + printf("Error reducing. \%s", + mp_error_to_string(result)); + return EXIT_FAILURE; + \} + + /* now reduce `c' back down to c = a^3R^2 * R^-1 == a^3R */ + if ((result = mp_montgomery_reduce(&c, &b, mp)) != MP_OKAY) \{ + printf("Error reducing. \%s", + mp_error_to_string(result)); + return EXIT_FAILURE; + \} + + /* now reduce (again) `c' back down to c = a^3R * R^-1 == a^3 */ + if ((result = mp_montgomery_reduce(&c, &b, mp)) != MP_OKAY) \{ + printf("Error reducing. \%s", + mp_error_to_string(result)); + return EXIT_FAILURE; + \} + + /* c now equals a^3 mod b */ + + return EXIT_SUCCESS; +\} +\end{alltt} + +This particular example does not look too efficient but it demonstrates the point of the algorithm. By +normalizing the inputs the reduced results are always of the form $aR$ for some variable $a$. This allows +a single final reduction to correct for the normalization and the fast reduction used within the algorithm. + +For more details consider examining the file \textit{bn\_mp\_exptmod\_fast.c}. + +\section{Restricted Diminished Radix} + +``Diminished Radix'' reduction refers to reduction with respect to moduli that are amenable to simple +digit shifting and small multiplications. In this case the ``restricted'' variant refers to moduli of the +form $\beta^k - p$ for some $k \ge 0$ and $0 < p < \beta$ where $\beta$ is the radix (default to $2^{28}$). + +As in the case of Montgomery reduction there is a pre--computation phase required for a given modulus. + +\index{mp\_dr\_setup} +\begin{alltt} +void mp_dr_setup(mp_int *a, mp_digit *d); +\end{alltt} + +This computes the value required for the modulus $a$ and stores it in $d$. This function cannot fail +and does not return any error codes. After the pre--computation a reduction can be performed with the +following. + +\index{mp\_dr\_reduce} +\begin{alltt} +int mp_dr_reduce(mp_int *a, mp_int *b, mp_digit mp); +\end{alltt} + +This reduces $a$ in place modulo $b$ with the pre--computed value $mp$. $b$ must be of a restricted +diminished radix form and $a$ must be in the range $0 \le a < b^2$. Diminished radix reductions are +much faster than both Barrett and Montgomery reductions as they have a much lower asymptotic running time. + +Since the moduli are restricted this algorithm is not particularly useful for something like Rabin, RSA or +BBS cryptographic purposes. This reduction algorithm is useful for Diffie-Hellman and ECC where fixed +primes are acceptable. + +Note that unlike Montgomery reduction there is no normalization process. The result of this function is +equal to the correct residue. + +\section{Unrestricted Diminished Radix} + +Unrestricted reductions work much like the restricted counterparts except in this case the moduli is of the +form $2^k - p$ for $0 < p < \beta$. In this sense the unrestricted reductions are more flexible as they +can be applied to a wider range of numbers. + +\index{mp\_reduce\_2k\_setup} +\begin{alltt} +int mp_reduce_2k_setup(mp_int *a, mp_digit *d); +\end{alltt} + +This will compute the required $d$ value for the given moduli $a$. + +\index{mp\_reduce\_2k} +\begin{alltt} +int mp_reduce_2k(mp_int *a, mp_int *n, mp_digit d); +\end{alltt} + +This will reduce $a$ in place modulo $n$ with the pre--computed value $d$. From my experience this routine is +slower than mp\_dr\_reduce but faster for most moduli sizes than the Montgomery reduction. + +\section{Combined Modular Reduction} + +Some of the combinations of an arithmetic operations followed by a modular reduction can be done in a faster way. The ones implemented are: + +Addition $d = (a + b) \mod c$ +\index{mp\_addmod} +\begin{alltt} +int mp_addmod(const mp_int *a, const mp_int *b, const mp_int *c, mp_int *d); +\end{alltt} + +Subtraction $d = (a - b) \mod c$ +\begin{alltt} +int mp_submod(const mp_int *a, const mp_int *b, const mp_int *c, mp_int *d); +\end{alltt} + +Multiplication $d = (ab) \mod c$ +\begin{alltt} +int mp_mulmod(const mp_int *a, const mp_int *b, const mp_int *c, mp_int *d); +\end{alltt} + +Squaring $d = (a^2) \mod c$ +\begin{alltt} +int mp_sqrmod(const mp_int *a, const mp_int *b, const mp_int *c, mp_int *d); +\end{alltt} + + + +\chapter{Exponentiation} +\section{Single Digit Exponentiation} +\index{mp\_expt\_d} +\begin{alltt} +int mp_expt_d (mp_int * a, mp_digit b, mp_int * c) +\end{alltt} +This function computes $c = a^b$. + +\section{Modular Exponentiation} +\index{mp\_exptmod} +\begin{alltt} +int mp_exptmod (mp_int * G, mp_int * X, mp_int * P, mp_int * Y) +\end{alltt} +This computes $Y \equiv G^X \mbox{ (mod }P\mbox{)}$ using a variable width sliding window algorithm. This function +will automatically detect the fastest modular reduction technique to use during the operation. For negative values of +$X$ the operation is performed as $Y \equiv (G^{-1} \mbox{ mod }P)^{\vert X \vert} \mbox{ (mod }P\mbox{)}$ provided that +$gcd(G, P) = 1$. + +This function is actually a shell around the two internal exponentiation functions. This routine will automatically +detect when Barrett, Montgomery, Restricted and Unrestricted Diminished Radix based exponentiation can be used. Generally +moduli of the a ``restricted diminished radix'' form lead to the fastest modular exponentiations. Followed by Montgomery +and the other two algorithms. + +\section{Modulus a Power of Two} +\index{mp\_mod\_2d} +\begin{alltt} +int mp_mod_2d(const mp_int *a, int b, mp_int *c) +\end{alltt} +It calculates $c = a \mod 2^b$. + +\section{Root Finding} +\index{mp\_n\_root} +\begin{alltt} +int mp_n_root (mp_int * a, mp_digit b, mp_int * c) +\end{alltt} +This computes $c = a^{1/b}$ such that $c^b \le a$ and $(c+1)^b > a$. Will return a positive root only for even roots and return +a root with the sign of the input for odd roots. For example, performing $4^{1/2}$ will return $2$ whereas $(-8)^{1/3}$ +will return $-2$. + +This algorithm uses the ``Newton Approximation'' method and will converge on the correct root fairly quickly. + +The square root $c = a^{1/2}$ (with the same conditions $c^2 \le a$ and $(c+1)^2 > a$) is implemented with a faster algorithm. + +\index{mp\_sqrt} +\begin{alltt} +int mp_sqrt (mp_int * a, mp_digit b, mp_int * c) +\end{alltt} + + +\chapter{Logarithm} +\section{Integer Logarithm} +A logarithm function for positive integer input \texttt{a, base} computing $\floor{\log_bx}$ such that $(\log_b x)^b \le x$. +\index{mp\_ilogb} +\begin{alltt} +int mp_ilogb(mp_int *a, mp_digit base, mp_int *c) +\end{alltt} +\subsection{Example} +\begin{alltt} +#include <stdlib.h> +#include <stdio.h> +#include <errno.h> + +#include <tommath.h> + +int main(int argc, char **argv) +{ + mp_int x, output; + mp_digit base; + int e; + + if (argc != 3) { + fprintf(stderr,"Usage %s base x\textbackslash{}n", argv[0]); + exit(EXIT_FAILURE); + } + if ((e = mp_init_multi(&x, &output, NULL)) != MP_OKAY) { + fprintf(stderr,"mp_init failed: \textbackslash{}"%s\textbackslash{}"\textbackslash{}n", + mp_error_to_string(e)); + exit(EXIT_FAILURE); + } + errno = 0; +#ifdef MP_64BIT + base = (mp_digit)strtoull(argv[1], NULL, 10); +#else + base = (mp_digit)strtoul(argv[1], NULL, 10); +#endif + if ((errno == ERANGE) || (base > (base & MP_MASK))) { + fprintf(stderr,"strtoul(l) failed: input out of range\textbackslash{}n"); + exit(EXIT_FAILURE); + } + if ((e = mp_read_radix(&x, argv[2], 10)) != MP_OKAY) { + fprintf(stderr,"mp_read_radix failed: \textbackslash{}"%s\textbackslash{}"\textbackslash{}n", + mp_error_to_string(e)); + exit(EXIT_FAILURE); + } + if ((e = mp_ilogb(&x, base, &output)) != MP_OKAY) { + fprintf(stderr,"mp_ilogb failed: \textbackslash{}"%s\textbackslash{}"\textbackslash{}n", + mp_error_to_string(e)); + exit(EXIT_FAILURE); + } + + if ((e = mp_fwrite(&output, 10, stdout)) != MP_OKAY) { + fprintf(stderr,"mp_fwrite failed: \textbackslash{}"%s\textbackslash{}"\textbackslash{}n", + mp_error_to_string(e)); + exit(EXIT_FAILURE); + } + putchar('\textbackslash{}n'); + + mp_clear_multi(&x, &output, NULL); + exit(EXIT_SUCCESS); +} +\end{alltt} + + + +\chapter{Prime Numbers} +\section{Trial Division} +\index{mp\_prime\_is\_divisible} +\begin{alltt} +int mp_prime_is_divisible (mp_int * a, int *result) +\end{alltt} +This will attempt to evenly divide $a$ by a list of primes\footnote{Default is the first 256 primes.} and store the +outcome in ``result''. That is if $result = 0$ then $a$ is not divisible by the primes, otherwise it is. Note that +if the function does not return \textbf{MP\_OKAY} the value in ``result'' should be considered undefined\footnote{Currently +the default is to set it to zero first.}. + +\section{Fermat Test} +\index{mp\_prime\_fermat} +\begin{alltt} +int mp_prime_fermat (mp_int * a, mp_int * b, int *result) +\end{alltt} +Performs a Fermat primality test to the base $b$. That is it computes $b^a \mbox{ mod }a$ and tests whether the value is +equal to $b$ or not. If the values are equal then $a$ is probably prime and $result$ is set to one. Otherwise $result$ +is set to zero. + +\section{Miller-Rabin Test} +\index{mp\_prime\_miller\_rabin} +\begin{alltt} +int mp_prime_miller_rabin (mp_int * a, mp_int * b, int *result) +\end{alltt} +Performs a Miller-Rabin test to the base $b$ of $a$. This test is much stronger than the Fermat test and is very hard to +fool (besides with Carmichael numbers). If $a$ passes the test (therefore is probably prime) $result$ is set to one. +Otherwise $result$ is set to zero. + +Note that is suggested that you use the Miller-Rabin test instead of the Fermat test since all of the failures of +Miller-Rabin are a subset of the failures of the Fermat test. + +\subsection{Required Number of Tests} +Generally to ensure a number is very likely to be prime you have to perform the Miller-Rabin with at least a half-dozen +or so unique bases. However, it has been proven that the probability of failure goes down as the size of the input goes up. +This is why a simple function has been provided to help out. + +\index{mp\_prime\_rabin\_miller\_trials} +\begin{alltt} +int mp_prime_rabin_miller_trials(int size) +\end{alltt} +This returns the number of trials required for a low probability of failure for a given ``size'' expressed in bits. This comes in handy specially since larger numbers are slower to test. For example, a 512-bit number would require 18 tests for a probability of $2^{-160}$ whereas a 1024-bit number would only require 12 tests for a probability of $2^{-192}$. The exact values as implemented are listed in table \ref{table:millerrabinrunsimpl}. + +\begin{table}[h] +\begin{center} +\begin{tabular}{c c c} +\textbf{bits} & \textbf{Rounds} & \textbf{Error}\\ + 80 & -1 & Use deterministic algorithm for size <= 80 bits \\ + 81 & 37 & $2^{-96}$ \\ + 96 & 32 & $2^{-96}$ \\ + 128 & 40 & $2^{-112}$ \\ + 160 & 35 & $2^{-112}$ \\ + 256 & 27 & $2^{-128}$ \\ + 384 & 16 & $2^{-128}$ \\ + 512 & 18 & $2^{-160}$ \\ + 768 & 11 & $2^{-160}$ \\ + 896 & 10 & $2^{-160}$ \\ + 1024 & 12 & $2^{-192}$ \\ + 1536 & 8 & $2^{-192}$ \\ + 2048 & 6 & $2^{-192}$ \\ + 3072 & 4 & $2^{-192}$ \\ + 4096 & 5 & $2^{-256}$ \\ + 5120 & 4 & $2^{-256}$ \\ + 6144 & 4 & $2^{-256}$ \\ + 8192 & 3 & $2^{-256}$ \\ + 9216 & 3 & $2^{-256}$ \\ + 10240 & 2 & $2^{-256}$ +\end{tabular} +\caption{ Number of Miller-Rabin rounds as implemented } \label{table:millerrabinrunsimpl} +\end{center} +\end{table} + +You should always still perform a trial division before a Miller-Rabin test though. + +A small table, broke in two for typographical reasons, with the number of rounds of Miller-Rabin tests is shown below. The numbers have been compute with a PARI/GP script listed in appendix \ref{app:numberofmrcomp}. +The first column is the number of bits $b$ in the prime $p = 2^b$, the numbers in the first row represent the +probability that the number that all of the Miller-Rabin tests deemed a pseudoprime is actually a composite. There is a deterministic test for numbers smaller than $2^{80}$. + +\begin{table}[h] +\begin{center} +\begin{tabular}{c c c c c c c} +\textbf{bits} & $\mathbf{2^{-80}}$ & $\mathbf{2^{-96}}$ & $\mathbf{2^{-112}}$ & $\mathbf{2^{-128}}$ & $\mathbf{2^{-160}}$ & $\mathbf{2^{-192}}$ \\ +80 & 31 & 39 & 47 & 55 & 71 & 87 \\ +96 & 29 & 37 & 45 & 53 & 69 & 85 \\ +128 & 24 & 32 & 40 & 48 & 64 & 80 \\ +160 & 19 & 27 & 35 & 43 & 59 & 75 \\ +192 & 15 & 21 & 29 & 37 & 53 & 69 \\ +256 & 10 & 15 & 20 & 27 & 43 & 59 \\ +384 & 7 & 9 & 12 & 16 & 25 & 38 \\ +512 & 5 & 7 & 9 & 12 & 18 & 26 \\ +768 & 4 & 5 & 6 & 8 & 11 & 16 \\ +1024 & 3 & 4 & 5 & 6 & 9 & 12 \\ +1536 & 2 & 3 & 3 & 4 & 6 & 8 \\ +2048 & 2 & 2 & 3 & 3 & 4 & 6 \\ +3072 & 1 & 2 & 2 & 2 & 3 & 4 \\ +4096 & 1 & 1 & 2 & 2 & 2 & 3 \\ +6144 & 1 & 1 & 1 & 1 & 2 & 2 \\ +8192 & 1 & 1 & 1 & 1 & 2 & 2 \\ +12288 & 1 & 1 & 1 & 1 & 1 & 1 \\ +16384 & 1 & 1 & 1 & 1 & 1 & 1 \\ +24576 & 1 & 1 & 1 & 1 & 1 & 1 \\ +32768 & 1 & 1 & 1 & 1 & 1 & 1 +\end{tabular} +\caption{ Number of Miller-Rabin rounds. Part I } \label{table:millerrabinrunsp1} +\end{center} +\end{table} +\newpage +\begin{table}[h] +\begin{center} +\begin{tabular}{c c c c c c c c} +\textbf{bits} &$\mathbf{2^{-224}}$ & $\mathbf{2^{-256}}$ & $\mathbf{2^{-288}}$ & $\mathbf{2^{-320}}$ & $\mathbf{2^{-352}}$ & $\mathbf{2^{-384}}$ & $\mathbf{2^{-416}}$\\ +80 & 103 & 119 & 135 & 151 & 167 & 183 & 199 \\ +96 & 101 & 117 & 133 & 149 & 165 & 181 & 197 \\ +128 & 96 & 112 & 128 & 144 & 160 & 176 & 192 \\ +160 & 91 & 107 & 123 & 139 & 155 & 171 & 187 \\ +192 & 85 & 101 & 117 & 133 & 149 & 165 & 181 \\ +256 & 75 & 91 & 107 & 123 & 139 & 155 & 171 \\ +384 & 54 & 70 & 86 & 102 & 118 & 134 & 150 \\ +512 & 36 & 49 & 65 & 81 & 97 & 113 & 129 \\ +768 & 22 & 29 & 37 & 47 & 58 & 70 & 86 \\ +1024 & 16 & 21 & 26 & 33 & 40 & 48 & 58 \\ +1536 & 10 & 13 & 17 & 21 & 25 & 30 & 35 \\ +2048 & 8 & 10 & 13 & 15 & 18 & 22 & 26 \\ +3072 & 5 & 7 & 8 & 10 & 12 & 14 & 17 \\ +4096 & 4 & 5 & 6 & 8 & 9 & 11 & 12 \\ +6144 & 3 & 4 & 4 & 5 & 6 & 7 & 8 \\ +8192 & 2 & 3 & 3 & 4 & 5 & 6 & 6 \\ +12288 & 2 & 2 & 2 & 3 & 3 & 4 & 4 \\ +16384 & 1 & 2 & 2 & 2 & 3 & 3 & 3 \\ +24576 & 1 & 1 & 2 & 2 & 2 & 2 & 2 \\ +32768 & 1 & 1 & 1 & 1 & 2 & 2 & 2 +\end{tabular} +\caption{ Number of Miller-Rabin rounds. Part II } \label{table:millerrabinrunsp2} +\end{center} +\end{table} + +Determining the probability needed to pick the right column is a bit harder. Fips 186.4, for example has $2^{-80}$ for $512$ bit large numbers, $2^{-112}$ for $1024$ bits, and $2^{128}$ for $1536$ bits. It can be seen in table \ref{table:millerrabinrunsp1} that those combinations follow the diagonal from $(512,2^{-80})$ downwards and to the right to gain a lower probabilty of getting a composite declared a pseudoprime for the same amount of work or less. + +If this version of the library has the strong Lucas-Selfridge and/or the Frobenius-Underwood test implemented only one or two rounds of the Miller-Rabin test with a random base is necesssary for numbers larger than or equal to $1024$ bits. + +This function is meant for RSA. The number of rounds for DSA is $\lceil -log_2(p)/2\rceil$ with $p$ the probability which is just the half of the absolute value of $p$ if given as a power of two. E.g.: with $p = 2^{-128}$, $\lceil -log_2(p)/2\rceil = 64$. + +This function can be used to test a DSA prime directly if these rounds are followed by a Lucas test. + +See also table C.1 in FIPS 186-4. + +\section{Strong Lucas-Selfridge Test} +\index{mp\_prime\_strong\_lucas\_selfridge} +\begin{alltt} +int mp_prime_strong_lucas_selfridge(const mp_int *a, int *result) +\end{alltt} +Performs a strong Lucas-Selfridge test. The strong Lucas-Selfridge test together with the Rabin-Miler test with bases $2$ and $3$ resemble the BPSW test. The single internal use is a compile-time option in \texttt{mp\_prime\_is\_prime} and can be excluded +from the Libtommath build if not needed. + +\section{Frobenius (Underwood) Test} +\index{mp\_prime\_frobenius\_underwood} +\begin{alltt} +int mp_prime_frobenius_underwood(const mp_int *N, int *result) +\end{alltt} +Performs the variant of the Frobenius test as described by Paul Underwood. The single internal use is in +\texttt{mp\_prime\_is\_prime} for \texttt{MP\_8BIT} only but can be included at build-time for all other sizes +if the preprocessor macro \texttt{LTM\_USE\_FROBENIUS\_TEST} is defined. + +It returns \texttt{MP\_ITER} if the number of iterations is exhausted, assumes a composite as the input and sets \texttt{result} accordingly. This will reduce the set of available pseudoprimes by a very small amount: test with large datasets (more than $10^{10}$ numbers, both randomly chosen and sequences of odd numbers with a random start point) found only 31 (thirty-one) numbers with $a > 120$ and none at all with just an additional simple check for divisors $d < 2^8$. + +\section{Primality Testing} +Testing if a number is a square can be done a bit faster than just by calculating the square root. It is used by the primality testing function described below. +\index{mp\_is\_square} +\begin{alltt} +int mp_is_square(const mp_int *arg, int *ret); +\end{alltt} + + +\index{mp\_prime\_is\_prime} +\begin{alltt} +int mp_prime_is_prime (mp_int * a, int t, int *result) +\end{alltt} +This will perform a trial division followed by two rounds of Miller-Rabin with bases 2 and 3 and a Lucas-Selfridge test. The Lucas-Selfridge test is replaced with a Frobenius-Underwood for \texttt{MP\_8BIT}. The Frobenius-Underwood test for all other sizes is available as a compile-time option with the preprocessor macro \texttt{LTM\_USE\_FROBENIUS\_TEST}. See file +\texttt{bn\_mp\_prime\_is\_prime.c} for the necessary details. It shall be noted that both functions are much slower than +the Miller-Rabin test and if speed is an essential issue, the macro \texttt{LTM\_USE\_ONLY\_MR} switches both functions, the Frobenius-Underwood test and the Lucas-Selfridge test off and their code will not even be compiled into the library. + +If $t$ is set to a positive value $t$ additional rounds of the Miller-Rabin test with random bases will be performed to allow for Fips 186.4 (vid.~p.~126ff) compliance. The function \texttt{mp\_prime\_rabin\_miller\_trials} can be used to determine the number of rounds. It is vital that the function \texttt{mp\_rand()} has a cryptographically strong random number generator available. + +One Miller-Rabin tests with a random base will be run automatically, so by setting $t$ to a positive value this function will run $t + 1$ Miller-Rabin tests with random bases. + +If $t$ is set to a negative value the test will run the deterministic Miller-Rabin test for the primes up to $3317044064679887385961981$. That limit has to be checked by the caller. + +If $a$ passes all of the tests $result$ is set to one, otherwise it is set to zero. + +\section{Next Prime} +\index{mp\_prime\_next\_prime} +\begin{alltt} +int mp_prime_next_prime(mp_int *a, int t, int bbs_style) +\end{alltt} +This finds the next prime after $a$ that passes mp\_prime\_is\_prime() with $t$ tests but see the documentation for +mp\_prime\_is\_prime for details regarding the use of the argument $t$. Set $bbs\_style$ to one if you +want only the next prime congruent to $3 \mbox{ mod } 4$, otherwise set it to zero to find any next prime. + +\section{Random Primes} +\index{mp\_prime\_rand} +\begin{alltt} +int mp_prime_rand(mp_int *a, int t, + int size, int flags); +\end{alltt} +This will generate a prime in $a$ using $t$ tests of the primality testing algorithms. +See the documentation for mp\_prime\_is\_prime for details regarding the use of the argument $t$. +The variable $size$ specifies the bit length of the prime desired. +The variable $flags$ specifies one of several options available +(see fig. \ref{fig:primeopts}) which can be OR'ed together. + +The function mp\_prime\_rand() is suitable for generating primes which must be secret (as in the case of RSA) since there +is no skew on the least significant bits. + +\textit{Note:} This function replaces the deprecated mp\_prime\_random and mp\_prime\_random\_ex functions. + +\begin{figure}[h] +\begin{center} +\begin{small} +\begin{tabular}{|r|l|} +\hline \textbf{Flag} & \textbf{Meaning} \\ +\hline LTM\_PRIME\_BBS & Make the prime congruent to $3$ modulo $4$ \\ +\hline LTM\_PRIME\_SAFE & Make a prime $p$ such that $(p - 1)/2$ is also prime. \\ + & This option implies LTM\_PRIME\_BBS as well. \\ +\hline LTM\_PRIME\_2MSB\_OFF & Makes sure that the bit adjacent to the most significant bit \\ + & Is forced to zero. \\ +\hline LTM\_PRIME\_2MSB\_ON & Makes sure that the bit adjacent to the most significant bit \\ + & Is forced to one. \\ +\hline +\end{tabular} +\end{small} +\end{center} +\caption{Primality Generation Options} +\label{fig:primeopts} +\end{figure} + +\chapter{Random Number Generation} +\section{PRNG} +\index{mp\_rand\_digit} +\begin{alltt} +int mp_rand_digit(mp_digit *r) +\end{alltt} +This function generates a random number in \texttt{r} of the size given in \texttt{r} (that is, the variable is used for in- and output) but not more than \texttt{MP\_MASK} bits. + +\index{mp\_rand} +\begin{alltt} +int mp_rand(mp_int *a, int digits) +\end{alltt} +This function generates a random number of \texttt{digits} bits. + +The random number generated with these two functions is cryptographically secure if the source of random numbers the operating systems offers is cryptographically secure. It will use \texttt{arc4random()} if the OS is a BSD flavor, Wincrypt on Windows, or \texttt{/dev/urandom} on all operating systems that have it. + + +\chapter{Input and Output} +\section{ASCII Conversions} +\subsection{To ASCII} +\index{mp\_to\_radix} +\begin{alltt} +int mp_to_radix (mp_int *a, char *str, size_t maxlen, size_t *written, int radix); +\end{alltt} +This stores $a$ in \texttt{str} of maximum length \texttt{maxlen} as a base-\texttt{radix} string of ASCII chars and appends a \texttt{NUL} character to terminate the string. + +Valid values of \texttt{radix} line in the range $[2, 64]$. + +The exact number of characters in \texttt{str} plus the \texttt{NUL} will be put in \texttt{written} if that variable is not set to \texttt{NULL}. + +If \texttt{str} is not big enough to hold $a$, \texttt{str} will be filled with the least-significant digits +of length \texttt{maxlen-1}, then \texttt{str} will be \texttt{NUL} terminated and the error \texttt{MP\_VAL} is returned. + +Please be aware that this function cannot evaluate the actual size of the buffer, it relies on the correctness of \texttt{maxlen}! + + +\index{mp\_radix\_size} +\begin{alltt} +int mp_radix_size (mp_int * a, int radix, int *size) +\end{alltt} +This stores in ``size'' the number of characters (including space for the NUL terminator) required. Upon error this +function returns an error code and ``size'' will be zero. + +If \texttt{LTM\_NO\_FILE} is not defined a function to write to a file is also available. +\index{mp\_fwrite} +\begin{alltt} +int mp_fwrite(const mp_int *a, int radix, FILE *stream); +\end{alltt} + + +\subsection{From ASCII} +\index{mp\_read\_radix} +\begin{alltt} +int mp_read_radix (mp_int * a, char *str, int radix); +\end{alltt} +This will read the base-``radix'' NUL terminated string from ``str'' into $a$. It will stop reading when it reads a +character it does not recognize (which happens to include th NUL char... imagine that...). A single leading $-$ sign +can be used to denote a negative number. + +If \texttt{LTM\_NO\_FILE} is not defined a function to read from a file is also available. +\index{mp\_fread} +\begin{alltt} +int mp_fread(mp_int *a, int radix, FILE *stream); +\end{alltt} + + +\section{Binary Conversions} + +Converting an mp\_int to and from binary is another keen idea. + +\index{mp\_ubin\_size} +\begin{alltt} +size_t mp_ubin_size(mp_int *a); +\end{alltt} + +This will return the number of bytes (octets) required to store the unsigned copy of the integer $a$. + +\index{mp\_to\_ubin} +\begin{alltt} +int mp_to_unsigned_bin(mp_int *a, unsigned char *b, size_t maxlen, size_t *len); +\end{alltt} +This will store $a$ into the buffer $b$ of size \texttt{maxlen} in big--endian format storing the number of bytes written in \texttt{len}. Fortunately this is exactly what DER (or is it ASN?) requires. It does not store the sign of the integer. + +\index{mp\_from\_ubin} +\begin{alltt} +int mp_from_ubin(mp_int *a, unsigned char *b, size_t size); +\end{alltt} +This will read in an unsigned big--endian array of bytes (octets) from $b$ of length \texttt{size} into $a$. The resulting big-integer $a$ will always be positive. + +For those who acknowledge the existence of negative numbers (heretic!) there are ``signed'' versions of the +previous functions. +\index{mp\_signed\_bin\_size} \index{mp\_to\_signed\_bin} \index{mp\_read\_signed\_bin} +\begin{alltt} +int mp_sbin_size(mp_int *a); +int mp_from_sbin(mp_int *a, unsigned char *b, size_t size); +int mp_to_sbin(mp_int *a, unsigned char *b, size_t maxsize, size_t *len); +\end{alltt} +They operate essentially the same as the unsigned copies except they prefix the data with zero or non--zero +byte depending on the sign. If the sign is zpos (e.g. not negative) the prefix is zero, otherwise the prefix +is non--zero. + +The two functions \texttt{mp\_unpack} (get your gifts out of the box, import binary data) and \texttt{mp\_pack} (put your gifts into the box, export binary data) implement the similarly working GMP functions as described at \url{http://gmplib.org/manual/Integer-Import-and-Export.html} with the exception that \texttt{mp\_pack} will not allocate memory if \texttt{rop} is \texttt{NULL}. +\index{mp\_unpack} \index{mp\_pack} +\begin{alltt} +int mp_unpack(mp_int *rop, size_t count, mp_order order, size_t size, + mp_endian endian, size_t nails, const void *op, size_t maxsize); +int mp_pack(void *rop, size_t *countp, mp_order order, size_t size, + mp_endian endian, size_t nails, const mp_int *op); +\end{alltt} +The function \texttt{mp\_pack} has the additional variable \texttt{maxsize} which must hold the size of the buffer \texttt{rop} in bytes. Use +\begin{alltt} +/* Parameters "nails" and "size" are the same as in mp_pack */ +size_t mp_pack_size(mp_int *a, size_t nails, size_t size); +\end{alltt} +To get the size in bytes necessary to be put in \texttt{maxsize}). + +To enhance the readability of your code, the following enums have been wrought for your convenience. +\begin{alltt} +typedef enum { + MP_LSB_FIRST = -1, + MP_MSB_FIRST = 1 +} mp_order; +typedef enum { + MP_LITTLE_ENDIAN = -1, + MP_NATIVE_ENDIAN = 0, + MP_BIG_ENDIAN = 1 +} mp_endian; +\end{alltt} + +\chapter{Algebraic Functions} +\section{Extended Euclidean Algorithm} +\index{mp\_exteuclid} +\begin{alltt} +int mp_exteuclid(mp_int *a, mp_int *b, + mp_int *U1, mp_int *U2, mp_int *U3); +\end{alltt} + +This finds the triple U1/U2/U3 using the Extended Euclidean algorithm such that the following equation holds. + +\begin{equation} +a \cdot U1 + b \cdot U2 = U3 +\end{equation} + +Any of the U1/U2/U3 parameters can be set to \textbf{NULL} if they are not desired. + +\section{Greatest Common Divisor} +\index{mp\_gcd} +\begin{alltt} +int mp_gcd (mp_int * a, mp_int * b, mp_int * c) +\end{alltt} +This will compute the greatest common divisor of $a$ and $b$ and store it in $c$. + +\section{Least Common Multiple} +\index{mp\_lcm} +\begin{alltt} +int mp_lcm (mp_int * a, mp_int * b, mp_int * c) +\end{alltt} +This will compute the least common multiple of $a$ and $b$ and store it in $c$. + +\section{Jacobi Symbol} +\index{mp\_jacobi} +\begin{alltt} +int mp_jacobi (mp_int * a, mp_int * p, int *c) +\end{alltt} +This will compute the Jacobi symbol for $a$ with respect to $p$. If $p$ is prime this essentially computes the Legendre +symbol. The result is stored in $c$ and can take on one of three values $\lbrace -1, 0, 1 \rbrace$. If $p$ is prime +then the result will be $-1$ when $a$ is not a quadratic residue modulo $p$. The result will be $0$ if $a$ divides $p$ +and the result will be $1$ if $a$ is a quadratic residue modulo $p$. + +\section{Kronecker Symbol} +\index{mp\_kronecker} +\begin{alltt} +int mp_kronecker (mp_int * a, mp_int * p, int *c) +\end{alltt} +Extension of the Jacoby symbol to all $\lbrace a, p \rbrace \in \mathbb{Z}$ . + + +\section{Modular square root} +\index{mp\_sqrtmod\_prime} +\begin{alltt} +int mp_sqrtmod_prime(mp_int *n, mp_int *p, mp_int *r) +\end{alltt} + +This will solve the modular equatioon $r^2 = n \mod p$ where $p$ is a prime number greater than 2 (odd prime). +The result is returned in the third argument $r$, the function returns \textbf{MP\_OKAY} on success, +other return values indicate failure. + +The implementation is split for two different cases: + +1. if $p \mod 4 == 3$ we apply \href{http://cacr.uwaterloo.ca/hac/}{Handbook of Applied Cryptography algorithm 3.36} and compute $r$ directly as +$r = n^{(p+1)/4} \mod p$ + +2. otherwise we use \href{https://en.wikipedia.org/wiki/Tonelli-Shanks_algorithm}{Tonelli-Shanks algorithm} + +The function does not check the primality of parameter $p$ thus it is up to the caller to assure that this parameter +is a prime number. When $p$ is a composite the function behaviour is undefined, it may even return a false-positive +\textbf{MP\_OKAY}. + +\section{Modular Inverse} +\index{mp\_invmod} +\begin{alltt} +int mp_invmod (mp_int * a, mp_int * b, mp_int * c) +\end{alltt} +Computes the multiplicative inverse of $a$ modulo $b$ and stores the result in $c$ such that $ac \equiv 1 \mbox{ (mod }b\mbox{)}$. + +\section{Single Digit Functions} + +For those using small numbers (\textit{snicker snicker}) there are several ``helper'' functions + +\index{mp\_add\_d} \index{mp\_sub\_d} \index{mp\_mul\_d} \index{mp\_div\_d} \index{mp\_mod\_d} +\begin{alltt} +int mp_add_d(mp_int *a, mp_digit b, mp_int *c); +int mp_sub_d(mp_int *a, mp_digit b, mp_int *c); +int mp_mul_d(mp_int *a, mp_digit b, mp_int *c); +int mp_div_d(mp_int *a, mp_digit b, mp_int *c, mp_digit *d); +int mp_mod_d(mp_int *a, mp_digit b, mp_digit *c); +\end{alltt} + +These work like the full mp\_int capable variants except the second parameter $b$ is a mp\_digit. These +functions fairly handy if you have to work with relatively small numbers since you will not have to allocate +an entire mp\_int to store a number like $1$ or $2$. + +The functions \texttt{mp\_incr} and \texttt{mp\_decr} mimic the postfix operators \texttt{++} and \texttt{--} respectively, to increment the input by one. They call the full single-digit functions if the addition would carry. Both functions need to be included in a minimized library because they call each other in case of a negative input, These functions change the inputs! +\begin{alltt} +int mp_incr(mp_int *a); +int mp_decr(mp_int *a); +\end{alltt} + + +The division by three can be made faster by replacing the division with a multiplication by the multiplicative inverse of three. + +\index{mp\_div\_3} +\begin{alltt} +int mp_div_3(const mp_int *a, mp_int *c, mp_digit *d); +\end{alltt} + +\chapter{Little Helpers} +It is never wrong to have some useful little shortcuts at hand. +\section{Function Macros} +To make this overview simpler the macros are given as function prototypes. The return of logic macros is \texttt{MP\_NO} or \texttt{MP\_YES} respectively. + +\index{mp\_iseven} +\begin{alltt} +int mp_iseven(mp_int *a) +\end{alltt} +Checks if $a = 0 mod 2$ + +\index{mp\_isodd} +\begin{alltt} +int mp_isodd(mp_int *a) +\end{alltt} +Checks if $a = 1 mod 2$ + +\index{mp\_isneg} +\begin{alltt} +int mp_isneg(mp_int *a) +\end{alltt} +Checks if $a < 0$ + + +\index{mp\_iszero} +\begin{alltt} +int mp_iszero(mp_int *a) +\end{alltt} +Checks if $a = 0$. It does not check if the amount of memory allocated for $a$ is also minimal. + + +Other macros which are either shortcuts to normal functions or just other names for them do have their place in a programmer's life, too! + +\subsection{Renamings} +\index{mp\_mag\_size} +\begin{alltt} +#define mp_mag_size(mp) mp_unsigned_bin_size(mp) +\end{alltt} + + +\index{mp\_raw\_size} +\begin{alltt} +#define mp_raw_size(mp) mp_signed_bin_size(mp) +\end{alltt} + + +\index{mp\_read\_mag} +\begin{alltt} +#define mp_read_mag(mp, str, len) mp_read_unsigned_bin((mp), (str), (len)) +\end{alltt} + + +\index{mp\_read\_raw} +\begin{alltt} + #define mp_read_raw(mp, str, len) mp_read_signed_bin((mp), (str), (len)) +\end{alltt} + + +\index{mp\_tomag} +\begin{alltt} +#define mp_tomag(mp, str) mp_to_unsigned_bin((mp), (str)) +\end{alltt} + + +\index{mp\_toraw} +\begin{alltt} +#define mp_toraw(mp, str) mp_to_signed_bin((mp), (str)) +\end{alltt} + + + +\subsection{Shortcuts} + +\index{mp\_to\_binary} +\begin{alltt} +#define mp_to_binary(M, S, N) mp_to_radix((M), (S), (N), 2) +\end{alltt} + + +\index{mp\_to\_octal} +\begin{alltt} +#define mp_to_octal(M, S, N) mp_to_radix((M), (S), (N), 8) +\end{alltt} + + +\index{mp\_to\_decimal} +\begin{alltt} +#define mp_to_decimal(M, S, N) mp_to_radix((M), (S), (N), 10) +\end{alltt} + + +\index{mp\_to\_hex} +\begin{alltt} +#define mp_to_hex(M, S, N) mp_to_radix((M), (S), (N), 16) +\end{alltt} + +\begin{appendices} +\appendixpage +%\noappendicestocpagenum +\addappheadtotoc +\chapter{Computing Number of Miller-Rabin Trials}\label{app:numberofmrcomp} +The number of Miller-Rabin rounds in the tables \ref{millerrabinrunsimpl}, \ref{millerrabinrunsp1}, and \ref{millerrabinrunsp2} have been calculated with the formula in FIPS 186-4 appendix F.1 (page 117) implemented as a PARI/GP script. +\begin{alltt} +log2(x) = log(x)/log(2) + +fips_f1_sums(k, M, t) = { + local(s = 0); + s = sum(m=3,M, + 2^(m-t*(m-1)) * + sum(j=2,m, + 1/ ( 2^( j + (k-1)/j ) ) + ) + ); + return(s); +} + +fips_f1_2(k, t, M) = { + local(common_factor, t1, t2, f1, f2, ds, res); + + common_factor = 2.00743 * log(2) * k * 2^(-k); + t1 = 2^(k - 2 - M*t); + f1 = (8 * ((Pi^2) - 6))/3; + f2 = 2^(k - 2); + ds = t1 + f1 * f2 * fips_f1_sums(k, M, t); + res = common_factor * ds; + return(res); +} + +fips_f1_1(prime_length, ptarget)={ + local(t, t_end, M, M_end, pkt); + + t_end = ceil(-log2(ptarget)/2); + M_end = floor(2 * sqrt(prime_length-1) - 1); + + for(t = 1, t_end, + for(M = 3, M_end, + pkt = fips_f1_2(prime_length, t, M); + if(pkt <= ptarget, + return(t); + ); + ); + ); +} +\end{alltt} + +To get the number of rounds for a $1024$ bit large prime with a probability of $2^{-160}$: +\begin{alltt} +? fips_f1_1(1024,2^(-160)) +%1 = 9 +\end{alltt} +\end{appendices} +\input{bn.ind} + +\end{document} diff --git a/lib/hcrypto/libtommath/etc/2kprime.1 b/lib/hcrypto/libtommath/etc/2kprime.1 new file mode 100644 index 000000000000..c41ded1f9750 --- /dev/null +++ b/lib/hcrypto/libtommath/etc/2kprime.1 @@ -0,0 +1,2 @@ +256-bits (k = 36113) = 115792089237316195423570985008687907853269984665640564039457584007913129603823 +512-bits (k = 38117) = 13407807929942597099574024998205846127479365820592393377723561443721764030073546976801874298166903427690031858186486050853753882811946569946433649006045979 diff --git a/lib/hcrypto/libtommath/etc/2kprime.c b/lib/hcrypto/libtommath/etc/2kprime.c new file mode 100644 index 000000000000..95ed2de4227f --- /dev/null +++ b/lib/hcrypto/libtommath/etc/2kprime.c @@ -0,0 +1,81 @@ +/* Makes safe primes of a 2k nature */ +#include <tommath.h> +#include <time.h> + +static int sizes[] = {256, 512, 768, 1024, 1536, 2048, 3072, 4096}; + +int main(void) +{ + char buf[2000]; + size_t x; + mp_bool y; + mp_int q, p; + FILE *out; + clock_t t1; + mp_digit z; + + mp_init_multi(&q, &p, NULL); + + out = fopen("2kprime.1", "w"); + if (out != NULL) { + for (x = 0; x < (sizeof(sizes) / sizeof(sizes[0])); x++) { +top: + mp_2expt(&q, sizes[x]); + mp_add_d(&q, 3uL, &q); + z = -3; + + t1 = clock(); + for (;;) { + mp_sub_d(&q, 4uL, &q); + z += 4uL; + + if (z > MP_MASK) { + printf("No primes of size %d found\n", sizes[x]); + break; + } + + if ((clock() - t1) > CLOCKS_PER_SEC) { + printf("."); + fflush(stdout); + /* sleep((clock() - t1 + CLOCKS_PER_SEC/2)/CLOCKS_PER_SEC); */ + t1 = clock(); + } + + /* quick test on q */ + mp_prime_is_prime(&q, 1, &y); + if (y == MP_NO) { + continue; + } + + /* find (q-1)/2 */ + mp_sub_d(&q, 1uL, &p); + mp_div_2(&p, &p); + mp_prime_is_prime(&p, 3, &y); + if (y == MP_NO) { + continue; + } + + /* test on q */ + mp_prime_is_prime(&q, 3, &y); + if (y == MP_NO) { + continue; + } + + break; + } + + if (y == MP_NO) { + ++sizes[x]; + goto top; + } + + mp_to_decimal(&q, buf, sizeof(buf)); + printf("\n\n%d-bits (k = %lu) = %s\n", sizes[x], z, buf); + fprintf(out, "%d-bits (k = %lu) = %s\n", sizes[x], z, buf); + fflush(out); + } + fclose(out); + } + + return 0; +} diff --git a/lib/hcrypto/libtommath/etc/drprime.c b/lib/hcrypto/libtommath/etc/drprime.c new file mode 100644 index 000000000000..64e31ef10465 --- /dev/null +++ b/lib/hcrypto/libtommath/etc/drprime.c @@ -0,0 +1,67 @@ +/* Makes safe primes of a DR nature */ +#include <tommath.h> + +static int sizes[] = { 1+256/MP_DIGIT_BIT, 1+512/MP_DIGIT_BIT, 1+768/MP_DIGIT_BIT, 1+1024/MP_DIGIT_BIT, 1+2048/MP_DIGIT_BIT, 1+4096/MP_DIGIT_BIT }; + +int main(void) +{ + mp_bool res; + int x, y; + char buf[4096]; + FILE *out; + mp_int a, b; + + mp_init(&a); + mp_init(&b); + + out = fopen("drprimes.txt", "w"); + if (out != NULL) { + for (x = 0; x < (int)(sizeof(sizes)/sizeof(sizes[0])); x++) { +top: + printf("Seeking a %d-bit safe prime\n", sizes[x] * MP_DIGIT_BIT); + mp_grow(&a, sizes[x]); + mp_zero(&a); + for (y = 1; y < sizes[x]; y++) { + a.dp[y] = MP_MASK; + } + + /* make a DR modulus */ + a.dp[0] = -1; + a.used = sizes[x]; + + /* now loop */ + res = MP_NO; + for (;;) { + a.dp[0] += 4uL; + if (a.dp[0] >= MP_MASK) break; + mp_prime_is_prime(&a, 1, &res); + if (res == MP_NO) continue; + printf("."); + fflush(stdout); + mp_sub_d(&a, 1uL, &b); + mp_div_2(&b, &b); + mp_prime_is_prime(&b, 3, &res); + if (res == MP_NO) continue; + mp_prime_is_prime(&a, 3, &res); + if (res == MP_YES) break; + } + + if (res != MP_YES) { + printf("Error not DR modulus\n"); + sizes[x] += 1; + goto top; + } else { + mp_to_decimal(&a, buf, sizeof(buf)); + printf("\n\np == %s\n\n", buf); + fprintf(out, "%d-bit prime:\np == %s\n\n", mp_count_bits(&a), buf); + fflush(out); + } + } + fclose(out); + } + + mp_clear(&a); + mp_clear(&b); + + return 0; +} diff --git a/lib/hcrypto/libtommath/etc/drprimes.28 b/lib/hcrypto/libtommath/etc/drprimes.28 new file mode 100644 index 000000000000..9d438ad1dba5 --- /dev/null +++ b/lib/hcrypto/libtommath/etc/drprimes.28 @@ -0,0 +1,25 @@ +DR safe primes for 28-bit digits. + +224-bit prime: +p == 26959946667150639794667015087019630673637144422540572481103341844143 + +532-bit prime: +p == 14059105607947488696282932836518693308967803494693489478439861164411992439598399594747002144074658928593502845729752797260025831423419686528151609940203368691747 + +784-bit prime: +p == 101745825697019260773923519755878567461315282017759829107608914364075275235254395622580447400994175578963163918967182013639660669771108475957692810857098847138903161308502419410142185759152435680068435915159402496058513611411688900243039 + +1036-bit prime: +p == 736335108039604595805923406147184530889923370574768772191969612422073040099331944991573923112581267542507986451953227192970402893063850485730703075899286013451337291468249027691733891486704001513279827771740183629161065194874727962517148100775228363421083691764065477590823919364012917984605619526140821798437127 + +1540-bit prime: +p == 38564998830736521417281865696453025806593491967131023221754800625044118265468851210705360385717536794615180260494208076605798671660719333199513807806252394423283413430106003596332513246682903994829528690198205120921557533726473585751382193953592127439965050261476810842071573684505878854588706623484573925925903505747545471088867712185004135201289273405614415899438276535626346098904241020877974002916168099951885406379295536200413493190419727789712076165162175783 + +2072-bit prime: +p == 542189391331696172661670440619180536749994166415993334151601745392193484590296600979602378676624808129613777993466242203025054573692562689251250471628358318743978285860720148446448885701001277560572526947619392551574490839286458454994488665744991822837769918095117129546414124448777033941223565831420390846864429504774477949153794689948747680362212954278693335653935890352619041936727463717926744868338358149568368643403037768649616778526013610493696186055899318268339432671541328195724261329606699831016666359440874843103020666106568222401047720269951530296879490444224546654729111504346660859907296364097126834834235287147 + +3080-bit prime: +p == 1487259134814709264092032648525971038895865645148901180585340454985524155135260217788758027400478312256339496385275012465661575576202252063145698732079880294664220579764848767704076761853197216563262660046602703973050798218246170835962005598561669706844469447435461092542265792444947706769615695252256130901271870341005768912974433684521436211263358097522726462083917939091760026658925757076733484173202927141441492573799914240222628795405623953109131594523623353044898339481494120112723445689647986475279242446083151413667587008191682564376412347964146113898565886683139407005941383669325997475076910488086663256335689181157957571445067490187939553165903773554290260531009121879044170766615232300936675369451260747671432073394867530820527479172464106442450727640226503746586340279816318821395210726268291535648506190714616083163403189943334431056876038286530365757187367147446004855912033137386225053275419626102417236133948503 + +4116-bit prime: +p == 1095121115716677802856811290392395128588168592409109494900178008967955253005183831872715423151551999734857184538199864469605657805519106717529655044054833197687459782636297255219742994736751541815269727940751860670268774903340296040006114013971309257028332849679096824800250742691718610670812374272414086863715763724622797509437062518082383056050144624962776302147890521249477060215148275163688301275847155316042279405557632639366066847442861422164832655874655824221577849928863023018366835675399949740429332468186340518172487073360822220449055340582568461568645259954873303616953776393853174845132081121976327462740354930744487429617202585015510744298530101547706821590188733515880733527449780963163909830077616357506845523215289297624086914545378511082534229620116563260168494523906566709418166011112754529766183554579321224940951177394088465596712620076240067370589036924024728375076210477267488679008016579588696191194060127319035195370137160936882402244399699172017835144537488486396906144217720028992863941288217185353914991583400421682751000603596655790990815525126154394344641336397793791497068253936771017031980867706707490224041075826337383538651825493679503771934836094655802776331664261631740148281763487765852746577808019633679 diff --git a/lib/hcrypto/libtommath/etc/drprimes.txt b/lib/hcrypto/libtommath/etc/drprimes.txt new file mode 100644 index 000000000000..7c97f67b9c5f --- /dev/null +++ b/lib/hcrypto/libtommath/etc/drprimes.txt @@ -0,0 +1,9 @@ +300-bit prime: +p == 2037035976334486086268445688409378161051468393665936250636140449354381298610415201576637819 + +540-bit prime: +p == 3599131035634557106248430806148785487095757694641533306480604458089470064537190296255232548883112685719936728506816716098566612844395439751206810991770626477344739 + +780-bit prime: +p == 6359114106063703798370219984742410466332205126109989319225557147754704702203399726411277962562135973685197744935448875852478791860694279747355800678568677946181447581781401213133886609947027230004277244697462656003655947791725966271167 + diff --git a/lib/hcrypto/libtommath/etc/makefile b/lib/hcrypto/libtommath/etc/makefile new file mode 100644 index 000000000000..85bb09efc430 --- /dev/null +++ b/lib/hcrypto/libtommath/etc/makefile @@ -0,0 +1,44 @@ +LTM_CFLAGS += -Wall -W -Wextra -Wshadow -O3 -I../ +LTM_CFLAGS += $(CFLAGS) + +# default lib name (requires install with root) +# LIBNAME=-ltommath + +# libname when you can't install the lib with install +LIBNAME=../libtommath.a + +#provable primes +pprime: pprime.o + $(CC) $(LTM_CFLAGS) pprime.o $(LIBNAME) -o pprime + +# portable [well requires clock()] tuning app +tune: tune.o + $(CC) $(LTM_CFLAGS) tune.o $(LIBNAME) -o tune + ./tune_it.sh + +test_standalone: tune.o + # The benchmark program works as a testtool, too + $(CC) $(LTM_CFLAGS) tune.o $(LIBNAME) -o test + +# spits out mersenne primes +mersenne: mersenne.o + $(CC) $(LTM_CFLAGS) mersenne.o $(LIBNAME) -o mersenne + +# finds DR safe primes for the given config +drprime: drprime.o + $(CC) $(LTM_CFLAGS) drprime.o $(LIBNAME) -o drprime + +# finds 2k safe primes for the given config +2kprime: 2kprime.o + $(CC) $(LTM_CFLAGS) 2kprime.o $(LIBNAME) -o 2kprime + +mont: mont.o + $(CC) $(LTM_CFLAGS) mont.o $(LIBNAME) -o mont + + +clean: + rm -f *.log *.o *.obj *.exe pprime tune mersenne drprime mont 2kprime pprime.dat \ + tuning_list multiplying squaring test *.da *.dyn *.dpi *~ + rm -rf .libs + +.PHONY: tune diff --git a/lib/hcrypto/libtommath/etc/makefile.icc b/lib/hcrypto/libtommath/etc/makefile.icc new file mode 100644 index 000000000000..9217f7b1dc2d --- /dev/null +++ b/lib/hcrypto/libtommath/etc/makefile.icc @@ -0,0 +1,67 @@ +CC = icc + +CFLAGS += -I../ + +# optimize for SPEED +# +# -mcpu= can be pentium, pentiumpro (covers PII through PIII) or pentium4 +# -ax? specifies make code specifically for ? but compatible with IA-32 +# -x? specifies compile solely for ? [not specifically IA-32 compatible] +# +# where ? is +# K - PIII +# W - first P4 [Williamette] +# N - P4 Northwood +# P - P4 Prescott +# B - Blend of P4 and PM [mobile] +# +# Default to just generic max opts +CFLAGS += -O3 -xP -ip + +# default lib name (requires install with root) +# LIBNAME=-ltommath + +# libname when you can't install the lib with install +LIBNAME=../libtommath.a + +#provable primes +pprime: pprime.o + $(CC) pprime.o $(LIBNAME) -o pprime + +tune: tune.o + $(CC) $(CFLAGS) tune.o $(LIBNAME) -o tune + ./tune_it.sh + +# same app but using RDTSC for higher precision [requires 80586+], coff based gcc installs [e.g. ming, cygwin, djgpp] +tune86: tune.c + nasm -f coff timer.asm + $(CC) -DX86_TIMER $(CFLAGS) tune.c timer.o $(LIBNAME) -o tune86 + +# for cygwin +tune86c: tune.c + nasm -f gnuwin32 timer.asm + $(CC) -DX86_TIMER $(CFLAGS) tune.c timer.o $(LIBNAME) -o tune86 + +#make tune86 for linux or any ELF format +tune86l: tune.c + nasm -f elf -DUSE_ELF timer.asm + $(CC) -DX86_TIMER $(CFLAGS) tune.c timer.o $(LIBNAME) -o tune86l + +# spits out mersenne primes +mersenne: mersenne.o + $(CC) mersenne.o $(LIBNAME) -o mersenne + +# fines DR safe primes for the given config +drprime: drprime.o + $(CC) drprime.o $(LIBNAME) -o drprime + +# fines 2k safe primes for the given config +2kprime: 2kprime.o + $(CC) 2kprime.o $(LIBNAME) -o 2kprime + +mont: mont.o + $(CC) mont.o $(LIBNAME) -o mont + + +clean: + rm -f *.log *.o *.obj *.exe pprime tune mersenne drprime tune86 tune86l mont 2kprime pprime.dat *.il tuning_list diff --git a/lib/hcrypto/libtommath/etc/makefile.msvc b/lib/hcrypto/libtommath/etc/makefile.msvc new file mode 100644 index 000000000000..592a43715c1b --- /dev/null +++ b/lib/hcrypto/libtommath/etc/makefile.msvc @@ -0,0 +1,24 @@ +#MSVC Makefile +# +#Tom St Denis + +CFLAGS = /I../ /Ox /DWIN32 /W3 + +pprime: pprime.obj + cl pprime.obj ../tommath.lib + +mersenne: mersenne.obj + cl mersenne.obj ../tommath.lib + +tune: tune.obj + cl tune.obj ../tommath.lib + + +mont: mont.obj + cl mont.obj ../tommath.lib + +drprime: drprime.obj + cl drprime.obj ../tommath.lib + +2kprime: 2kprime.obj + cl 2kprime.obj ../tommath.lib diff --git a/lib/hcrypto/libtommath/etc/mersenne.c b/lib/hcrypto/libtommath/etc/mersenne.c new file mode 100644 index 000000000000..0c9f52fcf864 --- /dev/null +++ b/lib/hcrypto/libtommath/etc/mersenne.c @@ -0,0 +1,138 @@ +/* Finds Mersenne primes using the Lucas-Lehmer test + * + * Tom St Denis, tomstdenis@gmail.com + */ +#include <time.h> +#include <tommath.h> + +static mp_err is_mersenne(long s, mp_bool *pp) +{ + mp_int n, u; + mp_err res; + int k; + + *pp = MP_NO; + + if ((res = mp_init(&n)) != MP_OKAY) { + return res; + } + + if ((res = mp_init(&u)) != MP_OKAY) { + goto LBL_N; + } + + /* n = 2^s - 1 */ + if ((res = mp_2expt(&n, (int)s)) != MP_OKAY) { + goto LBL_MU; + } + if ((res = mp_sub_d(&n, 1uL, &n)) != MP_OKAY) { + goto LBL_MU; + } + + /* set u=4 */ + mp_set(&u, 4uL); + + /* for k=1 to s-2 do */ + for (k = 1; k <= (s - 2); k++) { + /* u = u^2 - 2 mod n */ + if ((res = mp_sqr(&u, &u)) != MP_OKAY) { + goto LBL_MU; + } + if ((res = mp_sub_d(&u, 2uL, &u)) != MP_OKAY) { + goto LBL_MU; + } + + /* make sure u is positive */ + while (u.sign == MP_NEG) { + if ((res = mp_add(&u, &n, &u)) != MP_OKAY) { + goto LBL_MU; + } + } + + /* reduce */ + if ((res = mp_reduce_2k(&u, &n, 1uL)) != MP_OKAY) { + goto LBL_MU; + } + } + + /* if u == 0 then its prime */ + if (mp_iszero(&u) == MP_YES) { + mp_prime_is_prime(&n, 8, pp); + if (*pp != MP_YES) printf("FAILURE\n"); + } + + res = MP_OKAY; +LBL_MU: + mp_clear(&u); +LBL_N: + mp_clear(&n); + return res; +} + +/* square root of a long < 65536 */ +static long i_sqrt(long x) +{ + long x1, x2; + + x2 = 16; + do { + x1 = x2; + x2 = x1 - ((x1 * x1) - x) / (2 * x1); + } while (x1 != x2); + + if ((x1 * x1) > x) { + --x1; + } + + return x1; +} + +/* is the long prime by brute force */ +static int isprime(long k) +{ + long y, z; + + y = i_sqrt(k); + for (z = 2; z <= y; z++) { + if ((k % z) == 0) + return 0; + } + return 1; +} + + +int main(void) +{ + mp_bool pp; + long k; + clock_t tt; + + k = 3; + + for (;;) { + /* start time */ + tt = clock(); + + /* test if 2^k - 1 is prime */ + if (is_mersenne(k, &pp) != MP_OKAY) { + printf("Whoa error\n"); + return -1; + } + + if (pp == MP_YES) { + /* count time */ + tt = clock() - tt; + + /* display if prime */ + printf("2^%-5ld - 1 is prime, test took %ld ticks\n", k, (long)tt); + } + + /* goto next odd exponent */ + k += 2; + + /* but make sure its prime */ + while (isprime(k) == 0) { + k += 2; + } + } +} diff --git a/lib/hcrypto/libtommath/etc/mont.c b/lib/hcrypto/libtommath/etc/mont.c new file mode 100644 index 000000000000..4652410d0c09 --- /dev/null +++ b/lib/hcrypto/libtommath/etc/mont.c @@ -0,0 +1,44 @@ +/* tests the montgomery routines */ +#include <tommath.h> +#include <stdlib.h> +#include <time.h> + +int main(void) +{ + mp_int modulus, R, p, pp; + mp_digit mp; + int x, y; + + srand(time(NULL)); + mp_init_multi(&modulus, &R, &p, &pp, NULL); + + /* loop through various sizes */ + for (x = 4; x < 256; x++) { + printf("DIGITS == %3d...", x); + fflush(stdout); + + /* make up the odd modulus */ + mp_rand(&modulus, x); + modulus.dp[0] |= 1uL; + + /* now find the R value */ + mp_montgomery_calc_normalization(&R, &modulus); + mp_montgomery_setup(&modulus, &mp); + + /* now run through a bunch tests */ + for (y = 0; y < 1000; y++) { + mp_rand(&p, x/2); /* p = random */ + mp_mul(&p, &R, &pp); /* pp = R * p */ + mp_montgomery_reduce(&pp, &modulus, mp); + + /* should be equal to p */ + if (mp_cmp(&pp, &p) != MP_EQ) { + printf("FAILURE!\n"); + exit(-1); + } + } + printf("PASSED\n"); + } + + return 0; +} diff --git a/lib/hcrypto/libtommath/etc/pprime.c b/lib/hcrypto/libtommath/etc/pprime.c new file mode 100644 index 000000000000..009a18cb9227 --- /dev/null +++ b/lib/hcrypto/libtommath/etc/pprime.c @@ -0,0 +1,411 @@ +/* Generates provable primes + * + * See http://gmail.com:8080/papers/pp.pdf for more info. + * + * Tom St Denis, tomstdenis@gmail.com, http://tom.gmail.com + */ +#include <stdlib.h> +#include <time.h> +#include "tommath.h" + +static int n_prime; +static FILE *primes; + +/* fast square root */ +static mp_digit i_sqrt(mp_word x) +{ + mp_word x1, x2; + + x2 = x; + do { + x1 = x2; + x2 = x1 - ((x1 * x1) - x) / (2u * x1); + } while (x1 != x2); + + if ((x1 * x1) > x) { + --x1; + } + + return x1; +} + + +/* generates a prime digit */ +static void gen_prime(void) +{ + mp_digit r, x, y, next; + FILE *out; + + out = fopen("pprime.dat", "wb"); + if (out != NULL) { + + /* write first set of primes */ + /* *INDENT-OFF* */ + r = 3uL; fwrite(&r, 1uL, sizeof(mp_digit), out); + r = 5uL; fwrite(&r, 1uL, sizeof(mp_digit), out); + r = 7uL; fwrite(&r, 1uL, sizeof(mp_digit), out); + r = 11uL; fwrite(&r, 1uL, sizeof(mp_digit), out); + r = 13uL; fwrite(&r, 1uL, sizeof(mp_digit), out); + r = 17uL; fwrite(&r, 1uL, sizeof(mp_digit), out); + r = 19uL; fwrite(&r, 1uL, sizeof(mp_digit), out); + r = 23uL; fwrite(&r, 1uL, sizeof(mp_digit), out); + r = 29uL; fwrite(&r, 1uL, sizeof(mp_digit), out); + r = 31uL; fwrite(&r, 1uL, sizeof(mp_digit), out); + /* *INDENT-ON* */ + + /* get square root, since if 'r' is composite its factors must be < than this */ + y = i_sqrt(r); + next = (y + 1uL) * (y + 1uL); + + for (;;) { + do { + r += 2uL; /* next candidate */ + r &= MP_MASK; + if (r < 31uL) break; + + /* update sqrt ? */ + if (next <= r) { + ++y; + next = (y + 1uL) * (y + 1uL); + } + + /* loop if divisible by 3,5,7,11,13,17,19,23,29 */ + if ((r % 3uL) == 0uL) { + x = 0uL; + continue; + } + if ((r % 5uL) == 0uL) { + x = 0uL; + continue; + } + if ((r % 7uL) == 0uL) { + x = 0uL; + continue; + } + if ((r % 11uL) == 0uL) { + x = 0uL; + continue; + } + if ((r % 13uL) == 0uL) { + x = 0uL; + continue; + } + if ((r % 17uL) == 0uL) { + x = 0uL; + continue; + } + if ((r % 19uL) == 0uL) { + x = 0uL; + continue; + } + if ((r % 23uL) == 0uL) { + x = 0uL; + continue; + } + if ((r % 29uL) == 0uL) { + x = 0uL; + continue; + } + + /* now check if r is divisible by x + k={1,7,11,13,17,19,23,29} */ + for (x = 30uL; x <= y; x += 30uL) { + if ((r % (x + 1uL)) == 0uL) { + x = 0uL; + break; + } + if ((r % (x + 7uL)) == 0uL) { + x = 0uL; + break; + } + if ((r % (x + 11uL)) == 0uL) { + x = 0uL; + break; + } + if ((r % (x + 13uL)) == 0uL) { + x = 0uL; + break; + } + if ((r % (x + 17uL)) == 0uL) { + x = 0uL; + break; + } + if ((r % (x + 19uL)) == 0uL) { + x = 0uL; + break; + } + if ((r % (x + 23uL)) == 0uL) { + x = 0uL; + break; + } + if ((r % (x + 29uL)) == 0uL) { + x = 0uL; + break; + } + } + } while (x == 0uL); + if (r > 31uL) { + fwrite(&r, 1uL, sizeof(mp_digit), out); + printf("%9lu\r", r); + fflush(stdout); + } + if (r < 31uL) break; + } + + fclose(out); + } +} + +static void load_tab(void) +{ + primes = fopen("pprime.dat", "rb"); + if (primes == NULL) { + gen_prime(); + primes = fopen("pprime.dat", "rb"); + } + fseek(primes, 0L, SEEK_END); + n_prime = ftell(primes) / sizeof(mp_digit); +} + +static mp_digit prime_digit(void) +{ + int n; + mp_digit d; + + n = abs(rand()) % n_prime; + fseek(primes, n * sizeof(mp_digit), SEEK_SET); + fread(&d, 1uL, sizeof(mp_digit), primes); + return d; +} + + +/* makes a prime of at least k bits */ +static mp_err pprime(int k, int li, mp_int *p, mp_int *q) +{ + mp_int a, b, c, n, x, y, z, v; + mp_err res; + int ii; + static const mp_digit bases[] = { 2, 3, 5, 7, 11, 13, 17, 19 }; + + /* single digit ? */ + if (k <= (int) MP_DIGIT_BIT) { + mp_set(p, prime_digit()); + return MP_OKAY; + } + + if ((res = mp_init(&c)) != MP_OKAY) { + return res; + } + + if ((res = mp_init(&v)) != MP_OKAY) { + goto LBL_C; + } + + /* product of first 50 primes */ + if ((res = + mp_read_radix(&v, + "19078266889580195013601891820992757757219839668357012055907516904309700014933909014729740190", + 10)) != MP_OKAY) { + goto LBL_V; + } + + if ((res = mp_init(&a)) != MP_OKAY) { + goto LBL_V; + } + + /* set the prime */ + mp_set(&a, prime_digit()); + + if ((res = mp_init(&b)) != MP_OKAY) { + goto LBL_A; + } + + if ((res = mp_init(&n)) != MP_OKAY) { + goto LBL_B; + } + + if ((res = mp_init(&x)) != MP_OKAY) { + goto LBL_N; + } + + if ((res = mp_init(&y)) != MP_OKAY) { + goto LBL_X; + } + + if ((res = mp_init(&z)) != MP_OKAY) { + goto LBL_Y; + } + + /* now loop making the single digit */ + while (mp_count_bits(&a) < k) { + fprintf(stderr, "prime has %4d bits left\r", k - mp_count_bits(&a)); + fflush(stderr); +top: + mp_set(&b, prime_digit()); + + /* now compute z = a * b * 2 */ + if ((res = mp_mul(&a, &b, &z)) != MP_OKAY) { /* z = a * b */ + goto LBL_Z; + } + + if ((res = mp_copy(&z, &c)) != MP_OKAY) { /* c = a * b */ + goto LBL_Z; + } + + if ((res = mp_mul_2(&z, &z)) != MP_OKAY) { /* z = 2 * a * b */ + goto LBL_Z; + } + + /* n = z + 1 */ + if ((res = mp_add_d(&z, 1uL, &n)) != MP_OKAY) { /* n = z + 1 */ + goto LBL_Z; + } + + /* check (n, v) == 1 */ + if ((res = mp_gcd(&n, &v, &y)) != MP_OKAY) { /* y = (n, v) */ + goto LBL_Z; + } + + if (mp_cmp_d(&y, 1uL) != MP_EQ) + goto top; + + /* now try base x=bases[ii] */ + for (ii = 0; ii < li; ii++) { + mp_set(&x, bases[ii]); + + /* compute x^a mod n */ + if ((res = mp_exptmod(&x, &a, &n, &y)) != MP_OKAY) { /* y = x^a mod n */ + goto LBL_Z; + } + + /* if y == 1 loop */ + if (mp_cmp_d(&y, 1uL) == MP_EQ) + continue; + + /* now x^2a mod n */ + if ((res = mp_sqrmod(&y, &n, &y)) != MP_OKAY) { /* y = x^2a mod n */ + goto LBL_Z; + } + + if (mp_cmp_d(&y, 1uL) == MP_EQ) + continue; + + /* compute x^b mod n */ + if ((res = mp_exptmod(&x, &b, &n, &y)) != MP_OKAY) { /* y = x^b mod n */ + goto LBL_Z; + } + + /* if y == 1 loop */ + if (mp_cmp_d(&y, 1uL) == MP_EQ) + continue; + + /* now x^2b mod n */ + if ((res = mp_sqrmod(&y, &n, &y)) != MP_OKAY) { /* y = x^2b mod n */ + goto LBL_Z; + } + + if (mp_cmp_d(&y, 1uL) == MP_EQ) + continue; + + /* compute x^c mod n == x^ab mod n */ + if ((res = mp_exptmod(&x, &c, &n, &y)) != MP_OKAY) { /* y = x^ab mod n */ + goto LBL_Z; + } + + /* if y == 1 loop */ + if (mp_cmp_d(&y, 1uL) == MP_EQ) + continue; + + /* now compute (x^c mod n)^2 */ + if ((res = mp_sqrmod(&y, &n, &y)) != MP_OKAY) { /* y = x^2ab mod n */ + goto LBL_Z; + } + + /* y should be 1 */ + if (mp_cmp_d(&y, 1uL) != MP_EQ) + continue; + break; + } + + /* no bases worked? */ + if (ii == li) + goto top; + + { + char buf[4096]; + + mp_to_decimal(&n, buf, sizeof(buf)); + printf("Certificate of primality for:\n%s\n\n", buf); + mp_to_decimal(&a, buf, sizeof(buf)); + printf("A == \n%s\n\n", buf); + mp_to_decimal(&b, buf, sizeof(buf)); + printf("B == \n%s\n\nG == %lu\n", buf, bases[ii]); + printf("----------------------------------------------------------------\n"); + } + + /* a = n */ + mp_copy(&n, &a); + } + + /* get q to be the order of the large prime subgroup */ + mp_sub_d(&n, 1uL, q); + mp_div_2(q, q); + mp_div(q, &b, q, NULL); + + mp_exch(&n, p); + + res = MP_OKAY; +LBL_Z: + mp_clear(&z); +LBL_Y: + mp_clear(&y); +LBL_X: + mp_clear(&x); +LBL_N: + mp_clear(&n); +LBL_B: + mp_clear(&b); +LBL_A: + mp_clear(&a); +LBL_V: + mp_clear(&v); +LBL_C: + mp_clear(&c); + return res; +} + + +int main(void) +{ + mp_int p, q; + char buf[4096]; + int k, li; + clock_t t1; + + srand(time(NULL)); + load_tab(); + + printf("Enter # of bits: \n"); + fgets(buf, sizeof(buf), stdin); + sscanf(buf, "%d", &k); + + printf("Enter number of bases to try (1 to 8):\n"); + fgets(buf, sizeof(buf), stdin); + sscanf(buf, "%d", &li); + + + mp_init(&p); + mp_init(&q); + + t1 = clock(); + pprime(k, li, &p, &q); + t1 = clock() - t1; + + printf("\n\nTook %d ticks, %d bits\n", t1, mp_count_bits(&p)); + + mp_to_decimal(&p, buf, sizeof(buf)); + printf("P == %s\n", buf); + mp_to_decimal(&q, buf, sizeof(buf)); + printf("Q == %s\n", buf); + + return 0; +} diff --git a/lib/hcrypto/libtommath/etc/prime.1024 b/lib/hcrypto/libtommath/etc/prime.1024 new file mode 100644 index 000000000000..5636e2da0985 --- /dev/null +++ b/lib/hcrypto/libtommath/etc/prime.1024 @@ -0,0 +1,414 @@ +Enter # of bits: +Enter number of bases to try (1 to 8): +Certificate of primality for: +36360080703173363 + +A == +89963569 + +B == +202082249 + +G == 2 +---------------------------------------------------------------- +Certificate of primality for: +4851595597739856136987139 + +A == +36360080703173363 + +B == +66715963 + +G == 2 +---------------------------------------------------------------- +Certificate of primality for: +19550639734462621430325731591027 + +A == +4851595597739856136987139 + +B == +2014867 + +G == 2 +---------------------------------------------------------------- +Certificate of primality for: +10409036141344317165691858509923818734539 + +A == +19550639734462621430325731591027 + +B == +266207047 + +G == 2 +---------------------------------------------------------------- +Certificate of primality for: +1049829549988285012736475602118094726647504414203 + +A == +10409036141344317165691858509923818734539 + +B == +50428759 + +G == 2 +---------------------------------------------------------------- +Certificate of primality for: +77194737385528288387712399596835459931920358844586615003 + +A == +1049829549988285012736475602118094726647504414203 + +B == +36765367 + +G == 2 +---------------------------------------------------------------- +Certificate of primality for: +35663756695365208574443215955488689578374232732893628896541201763 + +A == +77194737385528288387712399596835459931920358844586615003 + +B == +230998627 + +G == 2 +---------------------------------------------------------------- +Certificate of primality for: +16711831463502165169495622246023119698415848120292671294127567620396469803 + +A == +35663756695365208574443215955488689578374232732893628896541201763 + +B == +234297127 + +G == 2 +---------------------------------------------------------------- +Certificate of primality for: +6163534781560285962890718925972249753147470953579266394395432475622345597103528739 + +A == +16711831463502165169495622246023119698415848120292671294127567620396469803 + +B == +184406323 + +G == 2 +---------------------------------------------------------------- +Certificate of primality for: +814258256205243497704094951432575867360065658372158511036259934640748088306764553488803787 + +A == +6163534781560285962890718925972249753147470953579266394395432475622345597103528739 + +B == +66054487 + +G == 2 +---------------------------------------------------------------- +Certificate of primality for: +176469695533271657902814176811660357049007467856432383037590673407330246967781451723764079581998187 + +A == +814258256205243497704094951432575867360065658372158511036259934640748088306764553488803787 + +B == +108362239 + +G == 2 +---------------------------------------------------------------- +Certificate of primality for: +44924492859445516541759485198544012102424796403707253610035148063863073596051272171194806669756971406400419 + +A == +176469695533271657902814176811660357049007467856432383037590673407330246967781451723764079581998187 + +B == +127286707 + +G == 2 +---------------------------------------------------------------- +Certificate of primality for: +20600996927219343383225424320134474929609459588323857796871086845924186191561749519858600696159932468024710985371059 + +A == +44924492859445516541759485198544012102424796403707253610035148063863073596051272171194806669756971406400419 + +B == +229284691 + +G == 2 +---------------------------------------------------------------- +Certificate of primality for: +6295696427695493110141186605837397185848992307978456138112526915330347715236378041486547994708748840844217371233735072572979 + +A == +20600996927219343383225424320134474929609459588323857796871086845924186191561749519858600696159932468024710985371059 + +B == +152800771 + +G == 2 +---------------------------------------------------------------- +Certificate of primality for: +3104984078042317488749073016454213579257792635142218294052134804187631661145261015102617582090263808696699966840735333252107678792123 + +A == +6295696427695493110141186605837397185848992307978456138112526915330347715236378041486547994708748840844217371233735072572979 + +B == +246595759 + +G == 2 +---------------------------------------------------------------- +Certificate of primality for: +26405175827665701256325699315126705508919255051121452292124404943796947287968603975320562847910946802396632302209435206627913466015741799499 + +A == +3104984078042317488749073016454213579257792635142218294052134804187631661145261015102617582090263808696699966840735333252107678792123 + +B == +4252063 + +G == 2 +---------------------------------------------------------------- +Certificate of primality for: +11122146237908413610034600609460545703591095894418599759742741406628055069007082998134905595800236452010905900391505454890446585211975124558601770163 + +A == +26405175827665701256325699315126705508919255051121452292124404943796947287968603975320562847910946802396632302209435206627913466015741799499 + +B == +210605419 + +G == 2 +---------------------------------------------------------------- +Certificate of primality for: +1649861642047798890580354082088712649911849362201343649289384923147797960364736011515757482030049342943790127685185806092659832129486307035500638595572396187 + +A == +11122146237908413610034600609460545703591095894418599759742741406628055069007082998134905595800236452010905900391505454890446585211975124558601770163 + +B == +74170111 + +G == 2 +---------------------------------------------------------------- +Certificate of primality for: +857983367126266717607389719637086684134462613006415859877666235955788392464081914127715967940968197765042399904117392707518175220864852816390004264107201177394565363 + +A == +1649861642047798890580354082088712649911849362201343649289384923147797960364736011515757482030049342943790127685185806092659832129486307035500638595572396187 + +B == +260016763 + +G == 2 +---------------------------------------------------------------- +Certificate of primality for: +175995909353623703257072120479340610010337144085688850745292031336724691277374210929188442230237711063783727092685448718515661641054886101716698390145283196296702450566161283 + +A == +857983367126266717607389719637086684134462613006415859877666235955788392464081914127715967940968197765042399904117392707518175220864852816390004264107201177394565363 + +B == +102563707 + +G == 2 +---------------------------------------------------------------- +Certificate of primality for: +48486002551155667224487059713350447239190772068092630563272168418880661006593537218144160068395218642353495339720640699721703003648144463556291315694787862009052641640656933232794283 + +A == +175995909353623703257072120479340610010337144085688850745292031336724691277374210929188442230237711063783727092685448718515661641054886101716698390145283196296702450566161283 + +B == +137747527 + +G == 2 +---------------------------------------------------------------- +Certificate of primality for: +13156468011529105025061495011938518171328604045212410096476697450506055664012861932372156505805788068791146986282263016790631108386790291275939575123375304599622623328517354163964228279867403 + +A == +48486002551155667224487059713350447239190772068092630563272168418880661006593537218144160068395218642353495339720640699721703003648144463556291315694787862009052641640656933232794283 + +B == +135672847 + +G == 2 +---------------------------------------------------------------- +Certificate of primality for: +6355194692790533601105154341731997464407930009404822926832136060319955058388106456084549316415200519472481147942263916585428906582726749131479465958107142228236909665306781538860053107680830113869123 + +A == +13156468011529105025061495011938518171328604045212410096476697450506055664012861932372156505805788068791146986282263016790631108386790291275939575123375304599622623328517354163964228279867403 + +B == +241523587 + +G == 2 +---------------------------------------------------------------- +Certificate of primality for: +3157116676535430302794438027544146642863331358530722860333745617571010460905857862561870488000265751138954271040017454405707755458702044884023184574412221802502351503929935224995314581932097706874819348858083 + +A == +6355194692790533601105154341731997464407930009404822926832136060319955058388106456084549316415200519472481147942263916585428906582726749131479465958107142228236909665306781538860053107680830113869123 + +B == +248388667 + +G == 2 +---------------------------------------------------------------- +Certificate of primality for: +390533129219992506725320633489467713907837370444962163378727819939092929448752905310115311180032249230394348337568973177802874166228132778126338883671958897238722734394783244237133367055422297736215754829839364158067 + +A == +3157116676535430302794438027544146642863331358530722860333745617571010460905857862561870488000265751138954271040017454405707755458702044884023184574412221802502351503929935224995314581932097706874819348858083 + +B == +61849651 + +G == 2 +---------------------------------------------------------------- +Certificate of primality for: +48583654555070224891047847050732516652910250240135992225139515777200432486685999462997073444468380434359929499498804723793106565291183220444221080449740542884172281158126259373095216435009661050109711341419005972852770440739 + +A == +390533129219992506725320633489467713907837370444962163378727819939092929448752905310115311180032249230394348337568973177802874166228132778126338883671958897238722734394783244237133367055422297736215754829839364158067 + +B == +62201707 + +G == 2 +---------------------------------------------------------------- +Certificate of primality for: +25733035251905120039135866524384525138869748427727001128764704499071378939227862068500633813538831598776578372709963673670934388213622433800015759585470542686333039614931682098922935087822950084908715298627996115185849260703525317419 + +A == +48583654555070224891047847050732516652910250240135992225139515777200432486685999462997073444468380434359929499498804723793106565291183220444221080449740542884172281158126259373095216435009661050109711341419005972852770440739 + +B == +264832231 + +G == 2 +---------------------------------------------------------------- +Certificate of primality for: +2804594464939948901906623499531073917980499195397462605359913717827014360538186518540781517129548650937632008683280555602633122170458773895504894807182664540529077836857897972175530148107545939211339044386106111633510166695386323426241809387 + +A == +25733035251905120039135866524384525138869748427727001128764704499071378939227862068500633813538831598776578372709963673670934388213622433800015759585470542686333039614931682098922935087822950084908715298627996115185849260703525317419 + +B == +54494047 + +G == 2 +---------------------------------------------------------------- +Certificate of primality for: +738136612083433720096707308165797114449914259256979340471077690416567237592465306112484843530074782721390528773594351482384711900456440808251196845265132086486672447136822046628407467459921823150600138073268385534588238548865012638209515923513516547 + +A == +2804594464939948901906623499531073917980499195397462605359913717827014360538186518540781517129548650937632008683280555602633122170458773895504894807182664540529077836857897972175530148107545939211339044386106111633510166695386323426241809387 + +B == +131594179 + +G == 2 +---------------------------------------------------------------- +Certificate of primality for: +392847529056126766528615419937165193421166694172790666626558750047057558168124866940509180171236517681470100877687445134633784815352076138790217228749332398026714192707447855731679485746120589851992221508292976900578299504461333767437280988393026452846013683 + +A == +738136612083433720096707308165797114449914259256979340471077690416567237592465306112484843530074782721390528773594351482384711900456440808251196845265132086486672447136822046628407467459921823150600138073268385534588238548865012638209515923513516547 + +B == +266107603 + +G == 2 +---------------------------------------------------------------- +Certificate of primality for: +168459393231883505975876919268398655632763956627405508859662408056221544310200546265681845397346956580604208064328814319465940958080244889692368602591598503944015835190587740756859842792554282496742843600573336023639256008687581291233481455395123454655488735304365627 + +A == +392847529056126766528615419937165193421166694172790666626558750047057558168124866940509180171236517681470100877687445134633784815352076138790217228749332398026714192707447855731679485746120589851992221508292976900578299504461333767437280988393026452846013683 + +B == +214408111 + +G == 2 +---------------------------------------------------------------- +Certificate of primality for: +14865774288636941404884923981945833072113667565310054952177860608355263252462409554658728941191929400198053290113492910272458441655458514080123870132092365833472436407455910185221474386718838138135065780840839893113912689594815485706154461164071775481134379794909690501684643 + +A == +168459393231883505975876919268398655632763956627405508859662408056221544310200546265681845397346956580604208064328814319465940958080244889692368602591598503944015835190587740756859842792554282496742843600573336023639256008687581291233481455395123454655488735304365627 + +B == +44122723 + +G == 2 +---------------------------------------------------------------- +Certificate of primality for: +1213301773203241614897109856134894783021668292000023984098824423682568173639394290886185366993108292039068940333907505157813934962357206131450244004178619265868614859794316361031904412926604138893775068853175215502104744339658944443630407632290152772487455298652998368296998719996019 + +A == +14865774288636941404884923981945833072113667565310054952177860608355263252462409554658728941191929400198053290113492910272458441655458514080123870132092365833472436407455910185221474386718838138135065780840839893113912689594815485706154461164071775481134379794909690501684643 + +B == +40808563 + +G == 2 +---------------------------------------------------------------- +Certificate of primality for: +186935245989515158127969129347464851990429060640910951266513740972248428651109062997368144722015290092846666943896556191257222521203647606911446635194198213436423080005867489516421559330500722264446765608763224572386410155413161172707802334865729654109050873820610813855041667633843601286843 + +A == +1213301773203241614897109856134894783021668292000023984098824423682568173639394290886185366993108292039068940333907505157813934962357206131450244004178619265868614859794316361031904412926604138893775068853175215502104744339658944443630407632290152772487455298652998368296998719996019 + +B == +77035759 + +G == 2 +---------------------------------------------------------------- +Certificate of primality for: +83142661079751490510739960019112406284111408348732592580459037404394946037094409915127399165633756159385609671956087845517678367844901424617866988187132480585966721962585586730693443536100138246516868613250009028187662080828012497191775172228832247706080044971423654632146928165751885302331924491683 + +A == +186935245989515158127969129347464851990429060640910951266513740972248428651109062997368144722015290092846666943896556191257222521203647606911446635194198213436423080005867489516421559330500722264446765608763224572386410155413161172707802334865729654109050873820610813855041667633843601286843 + +B == +222383587 + +G == 2 +---------------------------------------------------------------- +Certificate of primality for: +3892354773803809855317742245039794448230625839512638747643814927766738642436392673485997449586432241626440927010641564064764336402368634186618250134234189066179771240232458249806850838490410473462391401438160528157981942499581634732706904411807195259620779379274017704050790865030808501633772117217899534443 + +A == +83142661079751490510739960019112406284111408348732592580459037404394946037094409915127399165633756159385609671956087845517678367844901424617866988187132480585966721962585586730693443536100138246516868613250009028187662080828012497191775172228832247706080044971423654632146928165751885302331924491683 + +B == +23407687 + +G == 2 +---------------------------------------------------------------- +Certificate of primality for: +1663606652988091811284014366560171522582683318514519379924950390627250155440313691226744227787921928894551755219495501365555370027257568506349958010457682898612082048959464465369892842603765280317696116552850664773291371490339084156052244256635115997453399761029567033971998617303988376172539172702246575225837054723 + +A == +3892354773803809855317742245039794448230625839512638747643814927766738642436392673485997449586432241626440927010641564064764336402368634186618250134234189066179771240232458249806850838490410473462391401438160528157981942499581634732706904411807195259620779379274017704050790865030808501633772117217899534443 + +B == +213701827 + +G == 2 +---------------------------------------------------------------- + + +Took 33057 ticks, 1048 bits +P == 1663606652988091811284014366560171522582683318514519379924950390627250155440313691226744227787921928894551755219495501365555370027257568506349958010457682898612082048959464465369892842603765280317696116552850664773291371490339084156052244256635115997453399761029567033971998617303988376172539172702246575225837054723 +Q == 3892354773803809855317742245039794448230625839512638747643814927766738642436392673485997449586432241626440927010641564064764336402368634186618250134234189066179771240232458249806850838490410473462391401438160528157981942499581634732706904411807195259620779379274017704050790865030808501633772117217899534443 diff --git a/lib/hcrypto/libtommath/etc/prime.512 b/lib/hcrypto/libtommath/etc/prime.512 new file mode 100644 index 000000000000..cb6ec302fb82 --- /dev/null +++ b/lib/hcrypto/libtommath/etc/prime.512 @@ -0,0 +1,205 @@ +Enter # of bits: +Enter number of bases to try (1 to 8): +Certificate of primality for: +85933926807634727 + +A == +253758023 + +B == +169322581 + +G == 5 +---------------------------------------------------------------- +Certificate of primality for: +23930198825086241462113799 + +A == +85933926807634727 + +B == +139236037 + +G == 11 +---------------------------------------------------------------- +Certificate of primality for: +6401844647261612602378676572510019 + +A == +23930198825086241462113799 + +B == +133760791 + +G == 2 +---------------------------------------------------------------- +Certificate of primality for: +269731366027728777712034888684015329354259 + +A == +6401844647261612602378676572510019 + +B == +21066691 + +G == 2 +---------------------------------------------------------------- +Certificate of primality for: +37942338209025571690075025099189467992329684223707 + +A == +269731366027728777712034888684015329354259 + +B == +70333567 + +G == 2 +---------------------------------------------------------------- +Certificate of primality for: +15306904714258982484473490774101705363308327436988160248323 + +A == +37942338209025571690075025099189467992329684223707 + +B == +201712723 + +G == 2 +---------------------------------------------------------------- +Certificate of primality for: +1616744757018513392810355191503853040357155275733333124624513530099 + +A == +15306904714258982484473490774101705363308327436988160248323 + +B == +52810963 + +G == 2 +---------------------------------------------------------------- +Certificate of primality for: +464222094814208047161771036072622485188658077940154689939306386289983787983 + +A == +1616744757018513392810355191503853040357155275733333124624513530099 + +B == +143566909 + +G == 5 +---------------------------------------------------------------- +Certificate of primality for: +187429931674053784626487560729643601208757374994177258429930699354770049369025096447 + +A == +464222094814208047161771036072622485188658077940154689939306386289983787983 + +B == +201875281 + +G == 5 +---------------------------------------------------------------- +Certificate of primality for: +100579220846502621074093727119851331775052664444339632682598589456666938521976625305832917563 + +A == +187429931674053784626487560729643601208757374994177258429930699354770049369025096447 + +B == +268311523 + +G == 2 +---------------------------------------------------------------- +Certificate of primality for: +1173616081309758475197022137833792133815753368965945885089720153370737965497134878651384030219765163 + +A == +100579220846502621074093727119851331775052664444339632682598589456666938521976625305832917563 + +B == +5834287 + +G == 2 +---------------------------------------------------------------- +Certificate of primality for: +191456913489905913185935197655672585713573070349044195411728114905691721186574907738081340754373032735283623 + +A == +1173616081309758475197022137833792133815753368965945885089720153370737965497134878651384030219765163 + +B == +81567097 + +G == 5 +---------------------------------------------------------------- +Certificate of primality for: +57856530489201750164178576399448868489243874083056587683743345599898489554401618943240901541005080049321706789987519 + +A == +191456913489905913185935197655672585713573070349044195411728114905691721186574907738081340754373032735283623 + +B == +151095433 + +G == 7 +---------------------------------------------------------------- +Certificate of primality for: +13790529750452576698109671710773784949185621244122040804792403407272729038377767162233653248852099545134831722512085881814803 + +A == +57856530489201750164178576399448868489243874083056587683743345599898489554401618943240901541005080049321706789987519 + +B == +119178679 + +G == 2 +---------------------------------------------------------------- +Certificate of primality for: +7075985989000817742677547821106534174334812111605018857703825637170140040509067704269696198231266351631132464035671858077052876058979 + +A == +13790529750452576698109671710773784949185621244122040804792403407272729038377767162233653248852099545134831722512085881814803 + +B == +256552363 + +G == 2 +---------------------------------------------------------------- +Certificate of primality for: +1227273006232588072907488910282307435921226646895131225407452056677899411162892829564455154080310937471747140942360789623819327234258162420463 + +A == +7075985989000817742677547821106534174334812111605018857703825637170140040509067704269696198231266351631132464035671858077052876058979 + +B == +86720989 + +G == 5 +---------------------------------------------------------------- +Certificate of primality for: +446764896913554613686067036908702877942872355053329937790398156069936255759889884246832779737114032666318220500106499161852193765380831330106375235763 + +A == +1227273006232588072907488910282307435921226646895131225407452056677899411162892829564455154080310937471747140942360789623819327234258162420463 + +B == +182015287 + +G == 2 +---------------------------------------------------------------- +Certificate of primality for: +5290203010849586596974953717018896543907195901082056939587768479377028575911127944611236020459652034082251335583308070846379514569838984811187823420951275243 + +A == +446764896913554613686067036908702877942872355053329937790398156069936255759889884246832779737114032666318220500106499161852193765380831330106375235763 + +B == +5920567 + +G == 2 +---------------------------------------------------------------- + + +Took 3454 ticks, 521 bits +P == 5290203010849586596974953717018896543907195901082056939587768479377028575911127944611236020459652034082251335583308070846379514569838984811187823420951275243 +Q == 446764896913554613686067036908702877942872355053329937790398156069936255759889884246832779737114032666318220500106499161852193765380831330106375235763 diff --git a/lib/hcrypto/libtommath/etc/timer.asm b/lib/hcrypto/libtommath/etc/timer.asm new file mode 100644 index 000000000000..35890d9852fd --- /dev/null +++ b/lib/hcrypto/libtommath/etc/timer.asm @@ -0,0 +1,37 @@ +; x86 timer in NASM
+;
+; Tom St Denis, tomstdenis@iahu.ca
+[bits 32]
+[section .data]
+time dd 0, 0
+
+[section .text]
+
+%ifdef USE_ELF
+[global t_start]
+t_start:
+%else
+[global _t_start]
+_t_start:
+%endif
+ push edx
+ push eax
+ rdtsc
+ mov [time+0],edx
+ mov [time+4],eax
+ pop eax
+ pop edx
+ ret
+
+%ifdef USE_ELF
+[global t_read]
+t_read:
+%else
+[global _t_read]
+_t_read:
+%endif
+ rdtsc
+ sub eax,[time+4]
+ sbb edx,[time+0]
+ ret
+
\ No newline at end of file diff --git a/lib/hcrypto/libtommath/etc/tune.c b/lib/hcrypto/libtommath/etc/tune.c new file mode 100644 index 000000000000..e7b99fce2895 --- /dev/null +++ b/lib/hcrypto/libtommath/etc/tune.c @@ -0,0 +1,542 @@ +/* Tune the Karatsuba parameters + * + * Tom St Denis, tstdenis82@gmail.com + */ +#include "../tommath.h" +#include "../tommath_private.h" +#include <time.h> +#include <inttypes.h> +#include <errno.h> + +/* + Please take in mind that both multiplicands are of the same size. The balancing + mechanism in mp_balance works well but has some overhead itself. You can test + the behaviour of it with the option "-o" followed by a (small) positive number 'x' + to generate ratios of the form 1:x. +*/ + +static uint64_t s_timer_function(void); +static void s_timer_start(void); +static uint64_t s_timer_stop(void); +static uint64_t s_time_mul(int size); +static uint64_t s_time_sqr(int size); +static void s_usage(char *s); + +static uint64_t s_timer_function(void) +{ +#if _POSIX_C_SOURCE >= 199309L +#define LTM_BILLION 1000000000 + struct timespec ts; + + /* TODO: Sets errno in case of error. Use? */ + clock_gettime(CLOCK_MONOTONIC, &ts); + return (((uint64_t)ts.tv_sec) * LTM_BILLION + (uint64_t)ts.tv_nsec); +#else + clock_t t; + t = clock(); + if (t < (clock_t)(0)) { + return (uint64_t)(0); + } + return (uint64_t)(t); +#endif +} + +/* generic ISO C timer */ +static uint64_t s_timer_tmp; +static void s_timer_start(void) +{ + s_timer_tmp = s_timer_function(); +} +static uint64_t s_timer_stop(void) +{ + return s_timer_function() - s_timer_tmp; +} + + +static int s_check_result; +static int s_number_of_test_loops; +static int s_stabilization_extra; +static int s_offset = 1; + +#define s_mp_mul(a, b, c) s_mp_mul_digs(a, b, c, (a)->used + (b)->used + 1) +static uint64_t s_time_mul(int size) +{ + int x; + mp_err e; + mp_int a, b, c, d; + uint64_t t1; + + if ((e = mp_init_multi(&a, &b, &c, &d, NULL)) != MP_OKAY) { + t1 = UINT64_MAX; + goto LTM_ERR; + } + + if ((e = mp_rand(&a, size * s_offset)) != MP_OKAY) { + t1 = UINT64_MAX; + goto LTM_ERR; + } + if ((e = mp_rand(&b, size)) != MP_OKAY) { + t1 = UINT64_MAX; + goto LTM_ERR; + } + + s_timer_start(); + for (x = 0; x < s_number_of_test_loops; x++) { + if ((e = mp_mul(&a,&b,&c)) != MP_OKAY) { + t1 = UINT64_MAX; + goto LTM_ERR; + } + if (s_check_result == 1) { + if ((e = s_mp_mul(&a,&b,&d)) != MP_OKAY) { + t1 = UINT64_MAX; + goto LTM_ERR; + } + if (mp_cmp(&c, &d) != MP_EQ) { + /* Time of 0 cannot happen (famous last words?) */ + t1 = 0uLL; + goto LTM_ERR; + } + } + } + + t1 = s_timer_stop(); +LTM_ERR: + mp_clear_multi(&a, &b, &c, &d, NULL); + return t1; +} + +static uint64_t s_time_sqr(int size) +{ + int x; + mp_err e; + mp_int a, b, c; + uint64_t t1; + + if ((e = mp_init_multi(&a, &b, &c, NULL)) != MP_OKAY) { + t1 = UINT64_MAX; + goto LTM_ERR; + } + + if ((e = mp_rand(&a, size)) != MP_OKAY) { + t1 = UINT64_MAX; + goto LTM_ERR; + } + + s_timer_start(); + for (x = 0; x < s_number_of_test_loops; x++) { + if ((e = mp_sqr(&a,&b)) != MP_OKAY) { + t1 = UINT64_MAX; + goto LTM_ERR; + } + if (s_check_result == 1) { + if ((e = s_mp_sqr(&a,&c)) != MP_OKAY) { + t1 = UINT64_MAX; + goto LTM_ERR; + } + if (mp_cmp(&c, &b) != MP_EQ) { + t1 = 0uLL; + goto LTM_ERR; + } + } + } + + t1 = s_timer_stop(); +LTM_ERR: + mp_clear_multi(&a, &b, &c, NULL); + return t1; +} + +struct tune_args { + int testmode; + int verbose; + int print; + int bncore; + int terse; + int upper_limit_print; + int increment_print; +} args; + +static void s_run(const char *name, uint64_t (*op)(int), int *cutoff) +{ + int x, count = 0; + uint64_t t1, t2; + if ((args.verbose == 1) || (args.testmode == 1)) { + printf("# %s.\n", name); + } + for (x = 8; x < args.upper_limit_print; x += args.increment_print) { + *cutoff = INT_MAX; + t1 = op(x); + if ((t1 == 0uLL) || (t1 == UINT64_MAX)) { + fprintf(stderr,"%s failed at x = INT_MAX (%s)\n", name, + (t1 == 0uLL)?"wrong result":"internal error"); + exit(EXIT_FAILURE); + } + *cutoff = x; + t2 = op(x); + if ((t2 == 0uLL) || (t2 == UINT64_MAX)) { + fprintf(stderr,"%s failed (%s)\n", name, + (t2 == 0uLL)?"wrong result":"internal error"); + exit(EXIT_FAILURE); + } + if (args.verbose == 1) { + printf("%d: %9"PRIu64" %9"PRIu64", %9"PRIi64"\n", x, t1, t2, (int64_t)t2 - (int64_t)t1); + } + if (t2 < t1) { + if (count == s_stabilization_extra) { + count = 0; + break; + } else if (count < s_stabilization_extra) { + count++; + } + } else if (count > 0) { + count--; + } + } + *cutoff = x - s_stabilization_extra * args.increment_print; +} + +static long s_strtol(const char *str, char **endptr, const char *err) +{ + const int base = 10; + char *_endptr; + long val; + errno = 0; + val = strtol(str, &_endptr, base); + if ((val > INT_MAX || val < 0) || (errno != 0)) { + fprintf(stderr, "Value %s not usable\n", str); + exit(EXIT_FAILURE); + } + if (_endptr == str) { + fprintf(stderr, "%s\n", err); + exit(EXIT_FAILURE); + } + if (endptr) *endptr = _endptr; + return val; +} + +static int s_exit_code = EXIT_FAILURE; +static void s_usage(char *s) +{ + fprintf(stderr,"Usage: %s [TvcpGbtrSLFfMmosh]\n",s); + fprintf(stderr," -T testmode, for use with testme.sh\n"); + fprintf(stderr," -v verbose, print all timings\n"); + fprintf(stderr," -c check results\n"); + fprintf(stderr," -p print benchmark of final cutoffs in files \"multiplying\"\n"); + fprintf(stderr," and \"squaring\"\n"); + fprintf(stderr," -G [string] suffix for the filenames listed above\n"); + fprintf(stderr," Implies '-p'\n"); + fprintf(stderr," -b print benchmark of bncore.c\n"); + fprintf(stderr," -t prints space (0x20) separated results\n"); + fprintf(stderr," -r [64] number of rounds\n"); + fprintf(stderr," -S [0xdeadbeef] seed for PRNG\n"); + fprintf(stderr," -L [3] number of negative values accumulated until the result is accepted\n"); + fprintf(stderr," -M [3000] upper limit of T-C tests/prints\n"); + fprintf(stderr," -m [1] increment of T-C tests/prints\n"); + fprintf(stderr," -o [1] multiplier for the second multiplicand\n"); + fprintf(stderr," (Not for computing the cut-offs!)\n"); + fprintf(stderr," -s 'preset' use values in 'preset' for printing.\n"); + fprintf(stderr," 'preset' is a comma separated string with cut-offs for\n"); + fprintf(stderr," ksm, kss, tc3m, tc3s in that order\n"); + fprintf(stderr," ksm = karatsuba multiplication\n"); + fprintf(stderr," kss = karatsuba squaring\n"); + fprintf(stderr," tc3m = Toom-Cook 3-way multiplication\n"); + fprintf(stderr," tc3s = Toom-Cook 3-way squaring\n"); + fprintf(stderr," Implies '-p'\n"); + fprintf(stderr," -h this message\n"); + exit(s_exit_code); +} + +struct cutoffs { + int KARATSUBA_MUL, KARATSUBA_SQR; + int TOOM_MUL, TOOM_SQR; +}; + +const struct cutoffs max_cutoffs = +{ INT_MAX, INT_MAX, INT_MAX, INT_MAX }; + +static void set_cutoffs(const struct cutoffs *c) +{ + KARATSUBA_MUL_CUTOFF = c->KARATSUBA_MUL; + KARATSUBA_SQR_CUTOFF = c->KARATSUBA_SQR; + TOOM_MUL_CUTOFF = c->TOOM_MUL; + TOOM_SQR_CUTOFF = c->TOOM_SQR; +} + +static void get_cutoffs(struct cutoffs *c) +{ + c->KARATSUBA_MUL = KARATSUBA_MUL_CUTOFF; + c->KARATSUBA_SQR = KARATSUBA_SQR_CUTOFF; + c->TOOM_MUL = TOOM_MUL_CUTOFF; + c->TOOM_SQR = TOOM_SQR_CUTOFF; + +} + +int main(int argc, char **argv) +{ + uint64_t t1, t2; + int x, i, j; + size_t n; + + int printpreset = 0; + /*int preset[8];*/ + char *endptr, *str; + + uint64_t seed = 0xdeadbeef; + + int opt; + struct cutoffs orig, updated; + + FILE *squaring, *multiplying; + char mullog[256] = "multiplying"; + char sqrlog[256] = "squaring"; + s_number_of_test_loops = 64; + s_stabilization_extra = 3; + + MP_ZERO_BUFFER(&args, sizeof(args)); + + args.testmode = 0; + args.verbose = 0; + args.print = 0; + args.bncore = 0; + args.terse = 0; + + args.upper_limit_print = 3000; + args.increment_print = 1; + + /* Very simple option parser, please treat it nicely. */ + if (argc != 1) { + for (opt = 1; (opt < argc) && (argv[opt][0] == '-'); opt++) { + switch (argv[opt][1]) { + case 'T': + args.testmode = 1; + s_check_result = 1; + args.upper_limit_print = 1000; + args.increment_print = 11; + s_number_of_test_loops = 1; + s_stabilization_extra = 1; + s_offset = 1; + break; + case 'v': + args.verbose = 1; + break; + case 'c': + s_check_result = 1; + break; + case 'p': + args.print = 1; + break; + case 'G': + args.print = 1; + opt++; + if (opt >= argc) { + s_usage(argv[0]); + } + /* manual strcat() */ + for (i = 0; i < 255; i++) { + if (mullog[i] == '\0') { + break; + } + } + for (j = 0; i < 255; j++, i++) { + mullog[i] = argv[opt][j]; + if (argv[opt][j] == '\0') { + break; + } + } + for (i = 0; i < 255; i++) { + if (sqrlog[i] == '\0') { + break; + } + } + for (j = 0; i < 255; j++, i++) { + sqrlog[i] = argv[opt][j]; + if (argv[opt][j] == '\0') { + break; + } + } + break; + case 'b': + args.bncore = 1; + break; + case 't': + args.terse = 1; + break; + case 'S': + opt++; + if (opt >= argc) { + s_usage(argv[0]); + } + str = argv[opt]; + errno = 0; + seed = (uint64_t)s_strtol(argv[opt], NULL, "No seed given?\n"); + break; + case 'L': + opt++; + if (opt >= argc) { + s_usage(argv[0]); + } + s_stabilization_extra = (int)s_strtol(argv[opt], NULL, "No value for option \"-L\"given"); + break; + case 'o': + opt++; + if (opt >= argc) { + s_usage(argv[0]); + } + s_offset = (int)s_strtol(argv[opt], NULL, "No value for the offset given"); + break; + case 'r': + opt++; + if (opt >= argc) { + s_usage(argv[0]); + } + s_number_of_test_loops = (int)s_strtol(argv[opt], NULL, "No value for the number of rounds given"); + break; + + case 'M': + opt++; + if (opt >= argc) { + s_usage(argv[0]); + } + args.upper_limit_print = (int)s_strtol(argv[opt], NULL, "No value for the upper limit of T-C tests given"); + break; + case 'm': + opt++; + if (opt >= argc) { + s_usage(argv[0]); + } + args.increment_print = (int)s_strtol(argv[opt], NULL, "No value for the increment for the T-C tests given"); + break; + case 's': + printpreset = 1; + args.print = 1; + opt++; + if (opt >= argc) { + s_usage(argv[0]); + } + str = argv[opt]; + KARATSUBA_MUL_CUTOFF = (int)s_strtol(str, &endptr, "[1/4] No value for KARATSUBA_MUL_CUTOFF given"); + str = endptr + 1; + KARATSUBA_SQR_CUTOFF = (int)s_strtol(str, &endptr, "[2/4] No value for KARATSUBA_SQR_CUTOFF given"); + str = endptr + 1; + TOOM_MUL_CUTOFF = (int)s_strtol(str, &endptr, "[3/4] No value for TOOM_MUL_CUTOFF given"); + str = endptr + 1; + TOOM_SQR_CUTOFF = (int)s_strtol(str, &endptr, "[4/4] No value for TOOM_SQR_CUTOFF given"); + break; + case 'h': + s_exit_code = EXIT_SUCCESS; + /* FALLTHROUGH */ + default: + s_usage(argv[0]); + } + } + } + + /* + mp_rand uses the cryptographically secure + source of the OS by default. That is too expensive, too slow and + most important for a benchmark: it is not repeatable. + */ + s_mp_rand_jenkins_init(seed); + mp_rand_source(s_mp_rand_jenkins); + + get_cutoffs(&orig); + + updated = max_cutoffs; + if ((args.bncore == 0) && (printpreset == 0)) { + struct { + const char *name; + int *cutoff, *update; + uint64_t (*fn)(int); + } test[] = { +#define T_MUL_SQR(n, o, f) { #n, &o##_CUTOFF, &(updated.o), MP_HAS(S_MP_##o) ? f : NULL } + /* + The influence of the Comba multiplication cannot be + eradicated programmatically. It depends on the size + of the macro MP_WPARRAY in tommath.h which needs to + be changed manually (to 0 (zero)). + */ + T_MUL_SQR("Karatsuba multiplication", KARATSUBA_MUL, s_time_mul), + T_MUL_SQR("Karatsuba squaring", KARATSUBA_SQR, s_time_sqr), + T_MUL_SQR("Toom-Cook 3-way multiplying", TOOM_MUL, s_time_mul), + T_MUL_SQR("Toom-Cook 3-way squaring", TOOM_SQR, s_time_sqr), +#undef T_MUL_SQR + }; + /* Turn all limits from bncore.c to the max */ + set_cutoffs(&max_cutoffs); + for (n = 0; n < sizeof(test)/sizeof(test[0]); ++n) { + if (test[n].fn) { + s_run(test[n].name, test[n].fn, test[n].cutoff); + *test[n].update = *test[n].cutoff; + *test[n].cutoff = INT_MAX; + } + } + } + if (args.terse == 1) { + printf("%d %d %d %d\n", + updated.KARATSUBA_MUL, + updated.KARATSUBA_SQR, + updated.TOOM_MUL, + updated.TOOM_SQR); + } else { + printf("KARATSUBA_MUL_CUTOFF = %d\n", updated.KARATSUBA_MUL); + printf("KARATSUBA_SQR_CUTOFF = %d\n", updated.KARATSUBA_SQR); + printf("TOOM_MUL_CUTOFF = %d\n", updated.TOOM_MUL); + printf("TOOM_SQR_CUTOFF = %d\n", updated.TOOM_SQR); + } + + if (args.print == 1) { + printf("Printing data for graphing to \"%s\" and \"%s\"\n",mullog, sqrlog); + + multiplying = fopen(mullog, "w+"); + if (multiplying == NULL) { + fprintf(stderr, "Opening file \"%s\" failed\n", mullog); + exit(EXIT_FAILURE); + } + + squaring = fopen(sqrlog, "w+"); + if (squaring == NULL) { + fprintf(stderr, "Opening file \"%s\" failed\n",sqrlog); + exit(EXIT_FAILURE); + } + + for (x = 8; x < args.upper_limit_print; x += args.increment_print) { + set_cutoffs(&max_cutoffs); + t1 = s_time_mul(x); + set_cutoffs(&orig); + t2 = s_time_mul(x); + fprintf(multiplying, "%d: %9"PRIu64" %9"PRIu64", %9"PRIi64"\n", x, t1, t2, (int64_t)t2 - (int64_t)t1); + fflush(multiplying); + if (args.verbose == 1) { + printf("MUL %d: %9"PRIu64" %9"PRIu64", %9"PRIi64"\n", x, t1, t2, (int64_t)t2 - (int64_t)t1); + fflush(stdout); + } + set_cutoffs(&max_cutoffs); + t1 = s_time_sqr(x); + set_cutoffs(&orig); + t2 = s_time_sqr(x); + fprintf(squaring,"%d: %9"PRIu64" %9"PRIu64", %9"PRIi64"\n", x, t1, t2, (int64_t)t2 - (int64_t)t1); + fflush(squaring); + if (args.verbose == 1) { + printf("SQR %d: %9"PRIu64" %9"PRIu64", %9"PRIi64"\n", x, t1, t2, (int64_t)t2 - (int64_t)t1); + fflush(stdout); + } + } + printf("Finished. Data for graphing in \"%s\" and \"%s\"\n",mullog, sqrlog); + if (args.verbose == 1) { + set_cutoffs(&orig); + if (args.terse == 1) { + printf("%d %d %d %d\n", + KARATSUBA_MUL_CUTOFF, + KARATSUBA_SQR_CUTOFF, + TOOM_MUL_CUTOFF, + TOOM_SQR_CUTOFF); + } else { + printf("KARATSUBA_MUL_CUTOFF = %d\n", KARATSUBA_MUL_CUTOFF); + printf("KARATSUBA_SQR_CUTOFF = %d\n", KARATSUBA_SQR_CUTOFF); + printf("TOOM_MUL_CUTOFF = %d\n", TOOM_MUL_CUTOFF); + printf("TOOM_SQR_CUTOFF = %d\n", TOOM_SQR_CUTOFF); + } + } + } + exit(EXIT_SUCCESS); +} diff --git a/lib/hcrypto/libtommath/etc/tune_it.sh b/lib/hcrypto/libtommath/etc/tune_it.sh new file mode 100755 index 000000000000..5e0fe7c3e374 --- /dev/null +++ b/lib/hcrypto/libtommath/etc/tune_it.sh @@ -0,0 +1,107 @@ +#!/bin/sh + +die() { + echo "$1 failed" + echo "Exiting" + exit $2 +} +# A linear congruential generator is sufficient for the purpose. +SEED=3735928559 +LCG() { + SEED=$(((1103515245 * $SEED + 12345) % 2147483648)) + echo $SEED +} +median() { +# read everything besides the header from file $1 +# | cut-out the required column $2 +# | sort all the entries numerically +# | show only the first $3 entries +# | show only the last entry + tail -n +2 $1 | cut -d' ' -f$2 | sort -n | head -n $3 | tail -n 1 +} + +MPWD=$(dirname $(readlink -f "$0")) +FILE_NAME="tuning_list" +TOMMATH_CUTOFFS_H="$MPWD/../tommath_cutoffs.h" +BACKUP_SUFFIX=".orig" +RNUM=0 + +############################################################################# +# It would be a good idea to isolate these processes (with e.g.: cpuset) # +# # +# It is not a good idea to e.g: watch high resolution videos while this # +# test are running if you do not have enough memory to avoid page faults. # +############################################################################# + +# Number of rounds overall. +LIMIT=100 +# Number of loops for each input. +RLOOPS=10 +# Offset ( > 0 ) . Runs tests with asymmetric input of the form 1:OFFSET +# Please use another destination for TOMMATH_CUTOFFS_H if you change OFFSET, because the numbers +# with an offset different from 1 (one) are not usable as the general cut-off values +# in "tommath_cutoffs.h". +OFFSET=1 +# Number ( >= 3 ) of positive results (TC-is-faster) accumulated until it is accepted. +# Due to the algorithm used to compute the median in this Posix compliant shell script +# the value needs to be 3 (three), not less, to keep the variation small. +LAG=3 +# Keep the temporary file $FILE_NAME. Set to 0 (zero) to remove it at the end. +# The file is in a format fit to feed into R directly. If you do it and find the median +# of this program to be off by more than a couple: please contact the authors and report +# the numbers from this program and R and the standard deviation. This program is known +# to get larger errors if the standard deviation is larger than ~50. +KEEP_TEMP=1 + +echo "You might like to watch the numbers go up to $LIMIT but it will take a long time!" + +# Might not have sufficient rights or disc full. +echo "km ks tc3m tc3s" > $FILE_NAME || die "Writing header to $FILE_NAME" $? +i=1 +while [ $i -le $LIMIT ]; do + RNUM=$(LCG) + printf "\r%d" $i + "$MPWD"/tune -t -r $RLOOPS -L $LAG -S "$RNUM" -o $OFFSET >> $FILE_NAME || die "tune" $? + i=$((i + 1)) +done + +if [ $KEEP_TEMP -eq 0 ]; then + rm -v $FILE_NAME || die "Removing $KEEP_TEMP" $? +fi + +echo "Writing cut-off values to \"$TOMMATH_CUTOFFS_H\"." +echo "In case of failure: a copy of \"$TOMMATH_CUTOFFS_H\" is in \"$TOMMATH_CUTOFFS_H$BACKUP_SUFFIX\"" + +cp -v $TOMMATH_CUTOFFS_H $TOMMATH_CUTOFFS_H$BACKUP_SUFFIX || die "Making backup copy of $TOMMATH_CUTOFFS_H" $? + +cat << END_OF_INPUT > $TOMMATH_CUTOFFS_H || die "Writing header to $TOMMATH_CUTOFFS_H" $? +/* LibTomMath, multiple-precision integer library -- Tom St Denis */ +/* SPDX-License-Identifier: Unlicense */ +/* + Current values evaluated on an AMD A8-6600K (64-bit). + Type "make tune" to optimize them for your machine but + be aware that it may take a long time. It took 2:30 minutes + on the aforementioned machine for example. + */ +END_OF_INPUT + +# The Posix shell does not offer an array data type so we create +# the median with 'standard tools'^TM + +# read the file (without the first line) and count the lines +i=$(tail -n +2 $FILE_NAME | wc -l) +# our median point will be at $i entries +i=$(( (i / 2) + 1 )) +TMP=$(median $FILE_NAME 1 $i) +echo "#define MP_DEFAULT_KARATSUBA_MUL_CUTOFF $TMP" +echo "#define MP_DEFAULT_KARATSUBA_MUL_CUTOFF $TMP" >> $TOMMATH_CUTOFFS_H || die "(km) Appending to $TOMMATH_CUTOFFS_H" $? +TMP=$(median $FILE_NAME 2 $i) +echo "#define MP_DEFAULT_KARATSUBA_SQR_CUTOFF $TMP" +echo "#define MP_DEFAULT_KARATSUBA_SQR_CUTOFF $TMP" >> $TOMMATH_CUTOFFS_H || die "(ks) Appending to $TOMMATH_CUTOFFS_H" $? +TMP=$(median $FILE_NAME 3 $i) +echo "#define MP_DEFAULT_TOOM_MUL_CUTOFF $TMP" +echo "#define MP_DEFAULT_TOOM_MUL_CUTOFF $TMP" >> $TOMMATH_CUTOFFS_H || die "(tc3m) Appending to $TOMMATH_CUTOFFS_H" $? +TMP=$(median $FILE_NAME 4 $i) +echo "#define MP_DEFAULT_TOOM_SQR_CUTOFF $TMP" +echo "#define MP_DEFAULT_TOOM_SQR_CUTOFF $TMP" >> $TOMMATH_CUTOFFS_H || die "(tc3s) Appending to $TOMMATH_CUTOFFS_H" $? + diff --git a/lib/hcrypto/libtommath/gen.pl b/lib/hcrypto/libtommath/gen.pl new file mode 100644 index 000000000000..332994d5cb68 --- /dev/null +++ b/lib/hcrypto/libtommath/gen.pl @@ -0,0 +1,20 @@ +#!/usr/bin/perl -w +# +# Generates a "single file" you can use to quickly +# add the whole source without any makefile troubles +# +use strict; +use warnings; + +open(my $out, '>', 'mpi.c') or die "Couldn't open mpi.c for writing: $!"; +foreach my $filename (glob 'bn*.c') { + open(my $src, '<', $filename) or die "Couldn't open $filename for reading: $!"; + print {$out} "/* Start: $filename */\n"; + print {$out} $_ while <$src>; + print {$out} "\n/* End: $filename */\n\n"; + close $src or die "Error closing $filename after reading: $!"; +} +print {$out} "\n/* EOF */\n"; +close $out or die "Error closing mpi.c after writing: $!"; + +system('perl -pli -e "s/\s*$//" mpi.c'); diff --git a/lib/hcrypto/libtommath/helper.pl b/lib/hcrypto/libtommath/helper.pl new file mode 100755 index 000000000000..e60c1a77511f --- /dev/null +++ b/lib/hcrypto/libtommath/helper.pl @@ -0,0 +1,482 @@ +#!/usr/bin/env perl + +use strict; +use warnings; + +use Getopt::Long; +use File::Find 'find'; +use File::Basename 'basename'; +use File::Glob 'bsd_glob'; + +sub read_file { + my $f = shift; + open my $fh, "<", $f or die "FATAL: read_rawfile() cannot open file '$f': $!"; + binmode $fh; + return do { local $/; <$fh> }; +} + +sub write_file { + my ($f, $data) = @_; + die "FATAL: write_file() no data" unless defined $data; + open my $fh, ">", $f or die "FATAL: write_file() cannot open file '$f': $!"; + binmode $fh; + print $fh $data or die "FATAL: write_file() cannot write to '$f': $!"; + close $fh or die "FATAL: write_file() cannot close '$f': $!"; + return; +} + +sub sanitize_comments { + my($content) = @_; + $content =~ s{/\*(.*?)\*/}{my $x=$1; $x =~ s/\w/x/g; "/*$x*/";}egs; + return $content; +} + +sub check_source { + my @all_files = ( + bsd_glob("makefile*"), + bsd_glob("*.{h,c,sh,pl}"), + bsd_glob("*/*.{h,c,sh,pl}"), + ); + + my $fails = 0; + for my $file (sort @all_files) { + my $troubles = {}; + my $lineno = 1; + my $content = read_file($file); + $content = sanitize_comments $content; + push @{$troubles->{crlf_line_end}}, '?' if $content =~ /\r/; + for my $l (split /\n/, $content) { + push @{$troubles->{merge_conflict}}, $lineno if $l =~ /^(<<<<<<<|=======|>>>>>>>)([^<=>]|$)/; + push @{$troubles->{trailing_space}}, $lineno if $l =~ / $/; + push @{$troubles->{tab}}, $lineno if $l =~ /\t/ && basename($file) !~ /^makefile/i; + push @{$troubles->{non_ascii_char}}, $lineno if $l =~ /[^[:ascii:]]/; + push @{$troubles->{cpp_comment}}, $lineno if $file =~ /\.(c|h)$/ && ($l =~ /\s\/\// || $l =~ /\/\/\s/); + # we prefer using XMALLOC, XFREE, XREALLOC, XCALLOC ... + push @{$troubles->{unwanted_malloc}}, $lineno if $file =~ /^[^\/]+\.c$/ && $l =~ /\bmalloc\s*\(/; + push @{$troubles->{unwanted_realloc}}, $lineno if $file =~ /^[^\/]+\.c$/ && $l =~ /\brealloc\s*\(/; + push @{$troubles->{unwanted_calloc}}, $lineno if $file =~ /^[^\/]+\.c$/ && $l =~ /\bcalloc\s*\(/; + push @{$troubles->{unwanted_free}}, $lineno if $file =~ /^[^\/]+\.c$/ && $l =~ /\bfree\s*\(/; + # and we probably want to also avoid the following + push @{$troubles->{unwanted_memcpy}}, $lineno if $file =~ /^[^\/]+\.c$/ && $l =~ /\bmemcpy\s*\(/; + push @{$troubles->{unwanted_memset}}, $lineno if $file =~ /^[^\/]+\.c$/ && $l =~ /\bmemset\s*\(/; + push @{$troubles->{unwanted_memcpy}}, $lineno if $file =~ /^[^\/]+\.c$/ && $l =~ /\bmemcpy\s*\(/; + push @{$troubles->{unwanted_memmove}}, $lineno if $file =~ /^[^\/]+\.c$/ && $l =~ /\bmemmove\s*\(/; + push @{$troubles->{unwanted_memcmp}}, $lineno if $file =~ /^[^\/]+\.c$/ && $l =~ /\bmemcmp\s*\(/; + push @{$troubles->{unwanted_strcmp}}, $lineno if $file =~ /^[^\/]+\.c$/ && $l =~ /\bstrcmp\s*\(/; + push @{$troubles->{unwanted_strcpy}}, $lineno if $file =~ /^[^\/]+\.c$/ && $l =~ /\bstrcpy\s*\(/; + push @{$troubles->{unwanted_strncpy}}, $lineno if $file =~ /^[^\/]+\.c$/ && $l =~ /\bstrncpy\s*\(/; + push @{$troubles->{unwanted_clock}}, $lineno if $file =~ /^[^\/]+\.c$/ && $l =~ /\bclock\s*\(/; + push @{$troubles->{unwanted_qsort}}, $lineno if $file =~ /^[^\/]+\.c$/ && $l =~ /\bqsort\s*\(/; + push @{$troubles->{sizeof_no_brackets}}, $lineno if $file =~ /^[^\/]+\.c$/ && $l =~ /\bsizeof\s*[^\(]/; + if ($file =~ m|^[^\/]+\.c$| && $l =~ /^static(\s+[a-zA-Z0-9_]+)+\s+([a-zA-Z0-9_]+)\s*\(/) { + my $funcname = $2; + # static functions should start with s_ + push @{$troubles->{staticfunc_name}}, "$lineno($funcname)" if $funcname !~ /^s_/; + } + $lineno++; + } + for my $k (sort keys %$troubles) { + warn "[$k] $file line:" . join(",", @{$troubles->{$k}}) . "\n"; + $fails++; + } + } + + warn( $fails > 0 ? "check-source: FAIL $fails\n" : "check-source: PASS\n" ); + return $fails; +} + +sub check_comments { + my $fails = 0; + my $first_comment = <<'MARKER'; +/* LibTomMath, multiple-precision integer library -- Tom St Denis */ +/* SPDX-License-Identifier: Unlicense */ +MARKER + #my @all_files = (bsd_glob("*.{h,c}"), bsd_glob("*/*.{h,c}")); + my @all_files = (bsd_glob("*.{h,c}")); + for my $f (@all_files) { + my $txt = read_file($f); + if ($txt !~ /\Q$first_comment\E/s) { + warn "[first_comment] $f\n"; + $fails++; + } + } + warn( $fails > 0 ? "check-comments: FAIL $fails\n" : "check-comments: PASS\n" ); + return $fails; +} + +sub check_doc { + my $fails = 0; + my $tex = read_file('doc/bn.tex'); + my $tmh = read_file('tommath.h'); + my @functions = $tmh =~ /\n\s*[a-zA-Z0-9_* ]+?(mp_[a-z0-9_]+)\s*\([^\)]+\)\s*;/sg; + my @macros = $tmh =~ /\n\s*#define\s+([a-z0-9_]+)\s*\([^\)]+\)/sg; + for my $n (sort @functions) { + (my $nn = $n) =~ s/_/\\_/g; # mp_sub_d >> mp\_sub\_d + if ($tex !~ /index\Q{$nn}\E/) { + warn "[missing_doc_for_function] $n\n"; + $fails++ + } + } + for my $n (sort @macros) { + (my $nn = $n) =~ s/_/\\_/g; # mp_iszero >> mp\_iszero + if ($tex !~ /index\Q{$nn}\E/) { + warn "[missing_doc_for_macro] $n\n"; + $fails++ + } + } + warn( $fails > 0 ? "check_doc: FAIL $fails\n" : "check-doc: PASS\n" ); + return $fails; +} + +sub prepare_variable { + my ($varname, @list) = @_; + my $output = "$varname="; + my $len = length($output); + foreach my $obj (sort @list) { + $len = $len + length $obj; + $obj =~ s/\*/\$/; + if ($len > 100) { + $output .= "\\\n"; + $len = length $obj; + } + $output .= $obj . ' '; + } + $output =~ s/ $//; + return $output; +} + +sub prepare_msvc_files_xml { + my ($all, $exclude_re, $targets) = @_; + my $last = []; + my $depth = 2; + + # sort files in the same order as visual studio (ugly, I know) + my @parts = (); + for my $orig (@$all) { + my $p = $orig; + $p =~ s|/|/~|g; + $p =~ s|/~([^/]+)$|/$1|g; + my @l = map { sprintf "% -99s", $_ } split /\//, $p; + push @parts, [ $orig, join(':', @l) ]; + } + my @sorted = map { $_->[0] } sort { $a->[1] cmp $b->[1] } @parts; + + my $files = "<Files>\r\n"; + for my $full (@sorted) { + my @items = split /\//, $full; # split by '/' + $full =~ s|/|\\|g; # replace '/' bt '\' + shift @items; # drop first one (src) + pop @items; # drop last one (filename.ext) + my $current = \@items; + if (join(':', @$current) ne join(':', @$last)) { + my $common = 0; + $common++ while ($last->[$common] && $current->[$common] && $last->[$common] eq $current->[$common]); + my $back = @$last - $common; + if ($back > 0) { + $files .= ("\t" x --$depth) . "</Filter>\r\n" for (1..$back); + } + my $fwd = [ @$current ]; splice(@$fwd, 0, $common); + for my $i (0..scalar(@$fwd) - 1) { + $files .= ("\t" x $depth) . "<Filter\r\n"; + $files .= ("\t" x $depth) . "\tName=\"$fwd->[$i]\"\r\n"; + $files .= ("\t" x $depth) . "\t>\r\n"; + $depth++; + } + $last = $current; + } + $files .= ("\t" x $depth) . "<File\r\n"; + $files .= ("\t" x $depth) . "\tRelativePath=\"$full\"\r\n"; + $files .= ("\t" x $depth) . "\t>\r\n"; + if ($full =~ $exclude_re) { + for (@$targets) { + $files .= ("\t" x $depth) . "\t<FileConfiguration\r\n"; + $files .= ("\t" x $depth) . "\t\tName=\"$_\"\r\n"; + $files .= ("\t" x $depth) . "\t\tExcludedFromBuild=\"true\"\r\n"; + $files .= ("\t" x $depth) . "\t\t>\r\n"; + $files .= ("\t" x $depth) . "\t\t<Tool\r\n"; + $files .= ("\t" x $depth) . "\t\t\tName=\"VCCLCompilerTool\"\r\n"; + $files .= ("\t" x $depth) . "\t\t\tAdditionalIncludeDirectories=\"\"\r\n"; + $files .= ("\t" x $depth) . "\t\t\tPreprocessorDefinitions=\"\"\r\n"; + $files .= ("\t" x $depth) . "\t\t/>\r\n"; + $files .= ("\t" x $depth) . "\t</FileConfiguration>\r\n"; + } + } + $files .= ("\t" x $depth) . "</File>\r\n"; + } + $files .= ("\t" x --$depth) . "</Filter>\r\n" for (@$last); + $files .= "\t</Files>"; + return $files; +} + +sub patch_file { + my ($content, @variables) = @_; + for my $v (@variables) { + if ($v =~ /^([A-Z0-9_]+)\s*=.*$/si) { + my $name = $1; + $content =~ s/\n\Q$name\E\b.*?[^\\]\n/\n$v\n/s; + } + else { + die "patch_file failed: " . substr($v, 0, 30) . ".."; + } + } + return $content; +} + +sub process_makefiles { + my $write = shift; + my $changed_count = 0; + my @o = map { my $x = $_; $x =~ s/\.c$/.o/; $x } bsd_glob("*.c"); + my @all = bsd_glob("*.{c,h}"); + + my $var_o = prepare_variable("OBJECTS", @o); + (my $var_obj = $var_o) =~ s/\.o\b/.obj/sg; + + # update MSVC project files + my $msvc_files = prepare_msvc_files_xml(\@all, qr/NOT_USED_HERE/, ['Debug|Win32', 'Release|Win32', 'Debug|x64', 'Release|x64']); + for my $m (qw/libtommath_VS2008.vcproj/) { + my $old = read_file($m); + my $new = $old; + $new =~ s|<Files>.*</Files>|$msvc_files|s; + if ($old ne $new) { + write_file($m, $new) if $write; + warn "changed: $m\n"; + $changed_count++; + } + } + + # update OBJECTS + HEADERS in makefile* + for my $m (qw/ makefile makefile.shared makefile_include.mk makefile.msvc makefile.unix makefile.mingw /) { + my $old = read_file($m); + my $new = $m eq 'makefile.msvc' ? patch_file($old, $var_obj) + : patch_file($old, $var_o); + if ($old ne $new) { + write_file($m, $new) if $write; + warn "changed: $m\n"; + $changed_count++; + } + } + + if ($write) { + return 0; # no failures + } + else { + warn( $changed_count > 0 ? "check-makefiles: FAIL $changed_count\n" : "check-makefiles: PASS\n" ); + return $changed_count; + } +} + +sub draw_func +{ + my ($deplist, $depmap, $out, $indent, $funcslist) = @_; + my @funcs = split ',', $funcslist; + # try this if you want to have a look at a minimized version of the callgraph without all the trivial functions + #if ($deplist =~ /$funcs[0]/ || $funcs[0] =~ /BN_MP_(ADD|SUB|CLEAR|CLEAR_\S+|DIV|MUL|COPY|ZERO|GROW|CLAMP|INIT|INIT_\S+|SET|ABS|CMP|CMP_D|EXCH)_C/) { + if ($deplist =~ /$funcs[0]/) { + return $deplist; + } else { + $deplist = $deplist . $funcs[0]; + } + if ($indent == 0) { + } elsif ($indent >= 1) { + print {$out} '| ' x ($indent - 1) . '+--->'; + } + print {$out} $funcs[0] . "\n"; + shift @funcs; + my $olddeplist = $deplist; + foreach my $i (@funcs) { + $deplist = draw_func($deplist, $depmap, $out, $indent + 1, ${$depmap}{$i}) if exists ${$depmap}{$i}; + } + return $olddeplist; +} + +sub update_dep +{ + #open class file and write preamble + open(my $class, '>', 'tommath_class.h') or die "Couldn't open tommath_class.h for writing\n"; + print {$class} << 'EOS'; +/* LibTomMath, multiple-precision integer library -- Tom St Denis */ +/* SPDX-License-Identifier: Unlicense */ + +#if !(defined(LTM1) && defined(LTM2) && defined(LTM3)) +#define LTM_INSIDE +#if defined(LTM2) +# define LTM3 +#endif +#if defined(LTM1) +# define LTM2 +#endif +#define LTM1 +#if defined(LTM_ALL) +EOS + + foreach my $filename (glob 'bn*.c') { + my $define = $filename; + + print "Processing $filename\n"; + + # convert filename to upper case so we can use it as a define + $define =~ tr/[a-z]/[A-Z]/; + $define =~ tr/\./_/; + print {$class} "# define $define\n"; + + # now copy text and apply #ifdef as required + my $apply = 0; + open(my $src, '<', $filename); + open(my $out, '>', 'tmp'); + + # first line will be the #ifdef + my $line = <$src>; + if ($line =~ /include/) { + print {$out} $line; + } else { + print {$out} << "EOS"; +#include "tommath_private.h" +#ifdef $define +/* LibTomMath, multiple-precision integer library -- Tom St Denis */ +/* SPDX-License-Identifier: Unlicense */ +$line +EOS + $apply = 1; + } + while (<$src>) { + if ($_ !~ /tommath\.h/) { + print {$out} $_; + } + } + if ($apply == 1) { + print {$out} "#endif\n"; + } + close $src; + close $out; + + unlink $filename; + rename 'tmp', $filename; + } + print {$class} "#endif\n#endif\n"; + + # now do classes + my %depmap; + foreach my $filename (glob 'bn*.c') { + my $content; + if ($filename =~ "bn_deprecated.c") { + open(my $src, '<', $filename) or die "Can't open source file!\n"; + read $src, $content, -s $src; + close $src; + } else { + my $cc = $ENV{'CC'} || 'gcc'; + $content = `$cc -E -x c -DLTM_ALL $filename`; + $content =~ s/^# 1 "$filename".*?^# 2 "$filename"//ms; + } + + # convert filename to upper case so we can use it as a define + $filename =~ tr/[a-z]/[A-Z]/; + $filename =~ tr/\./_/; + + print {$class} "#if defined($filename)\n"; + my $list = $filename; + + # strip comments + $content =~ s{/\*.*?\*/}{}gs; + + # scan for mp_* and make classes + my @deps = (); + foreach my $line (split /\n/, $content) { + while ($line =~ /(fast_)?(s_)?mp\_[a-z_0-9]*((?=\;)|(?=\())|(?<=\()mp\_[a-z_0-9]*(?=\()/g) { + my $a = $&; + next if $a eq "mp_err"; + $a =~ tr/[a-z]/[A-Z]/; + $a = 'BN_' . $a . '_C'; + push @deps, $a; + } + } + @deps = sort(@deps); + foreach my $a (@deps) { + if ($list !~ /$a/) { + print {$class} "# define $a\n"; + } + $list = $list . ',' . $a; + } + $depmap{$filename} = $list; + + print {$class} "#endif\n\n"; + } + + print {$class} << 'EOS'; +#ifdef LTM_INSIDE +#undef LTM_INSIDE +#ifdef LTM3 +# define LTM_LAST +#endif + +#include "tommath_superclass.h" +#include "tommath_class.h" +#else +# define LTM_LAST +#endif +EOS + close $class; + + #now let's make a cool call graph... + + open(my $out, '>', 'callgraph.txt'); + foreach (sort keys %depmap) { + draw_func("", \%depmap, $out, 0, $depmap{$_}); + print {$out} "\n\n"; + } + close $out; + + return 0; +} + +sub generate_def { + my @files = split /\n/, `git ls-files`; + @files = grep(/\.c/, @files); + @files = map { my $x = $_; $x =~ s/^bn_|\.c$//g; $x; } @files; + @files = grep(!/mp_radix_smap/, @files); + + push(@files, qw(mp_set_int mp_set_long mp_set_long_long mp_get_int mp_get_long mp_get_long_long mp_init_set_int)); + + my $files = join("\n ", sort(grep(/^mp_/, @files))); + write_file "tommath.def", "; libtommath +; +; Use this command to produce a 32-bit .lib file, for use in any MSVC version +; lib -machine:X86 -name:libtommath.dll -def:tommath.def -out:tommath.lib +; Use this command to produce a 64-bit .lib file, for use in any MSVC version +; lib -machine:X64 -name:libtommath.dll -def:tommath.def -out:tommath.lib +; +EXPORTS + $files +"; + return 0; +} + +sub die_usage { + die <<"MARKER"; +usage: $0 -s OR $0 --check-source + $0 -o OR $0 --check-comments + $0 -m OR $0 --check-makefiles + $0 -a OR $0 --check-all + $0 -u OR $0 --update-files +MARKER +} + +GetOptions( "s|check-source" => \my $check_source, + "o|check-comments" => \my $check_comments, + "m|check-makefiles" => \my $check_makefiles, + "d|check-doc" => \my $check_doc, + "a|check-all" => \my $check_all, + "u|update-files" => \my $update_files, + "h|help" => \my $help + ) or die_usage; + +my $failure; +$failure ||= check_source() if $check_all || $check_source; +$failure ||= check_comments() if $check_all || $check_comments; +$failure ||= check_doc() if $check_doc; # temporarily excluded from --check-all +$failure ||= process_makefiles(0) if $check_all || $check_makefiles; +$failure ||= process_makefiles(1) if $update_files; +$failure ||= update_dep() if $update_files; +$failure ||= generate_def() if $update_files; + +die_usage unless defined $failure; +exit $failure ? 1 : 0; diff --git a/lib/hcrypto/libtommath/libtommath.pc.in b/lib/hcrypto/libtommath/libtommath.pc.in new file mode 100644 index 000000000000..099b1cd74426 --- /dev/null +++ b/lib/hcrypto/libtommath/libtommath.pc.in @@ -0,0 +1,10 @@ +prefix=@to-be-replaced@ +exec_prefix=${prefix} +libdir=${exec_prefix}/lib +includedir=${prefix}/include + +Name: LibTomMath +Description: public domain library for manipulating large integer numbers +Version: @to-be-replaced@ +Libs: -L${libdir} -ltommath +Cflags: -I${includedir} diff --git a/lib/hcrypto/libtommath/libtommath_VS2008.sln b/lib/hcrypto/libtommath/libtommath_VS2008.sln new file mode 100644 index 000000000000..6bfc159b7b96 --- /dev/null +++ b/lib/hcrypto/libtommath/libtommath_VS2008.sln @@ -0,0 +1,29 @@ +
+Microsoft Visual Studio Solution File, Format Version 10.00
+# Visual Studio 2008
+Project("{8BC9CEB8-8B4A-11D0-8D11-00A0C91BC942}") = "tommath", "libtommath_VS2008.vcproj", "{42109FEE-B0B9-4FCD-9E56-2863BF8C55D2}"
+EndProject
+Global
+ GlobalSection(SolutionConfigurationPlatforms) = preSolution
+ Debug|Win32 = Debug|Win32
+ Debug|x64 = Debug|x64
+ Release|Win32 = Release|Win32
+ Release|x64 = Release|x64
+ EndGlobalSection
+ GlobalSection(ProjectConfigurationPlatforms) = postSolution
+ {42109FEE-B0B9-4FCD-9E56-2863BF8C55D2}.Debug|Win32.ActiveCfg = Debug|Win32
+ {42109FEE-B0B9-4FCD-9E56-2863BF8C55D2}.Debug|Win32.Build.0 = Debug|Win32
+ {42109FEE-B0B9-4FCD-9E56-2863BF8C55D2}.Debug|x64.ActiveCfg = Debug|x64
+ {42109FEE-B0B9-4FCD-9E56-2863BF8C55D2}.Debug|x64.Build.0 = Debug|x64
+ {42109FEE-B0B9-4FCD-9E56-2863BF8C55D2}.Release|Win32.ActiveCfg = Release|Win32
+ {42109FEE-B0B9-4FCD-9E56-2863BF8C55D2}.Release|Win32.Build.0 = Release|Win32
+ {42109FEE-B0B9-4FCD-9E56-2863BF8C55D2}.Release|x64.ActiveCfg = Release|x64
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+ </File>
+ </Files>
+ <Globals>
+ </Globals>
+</VisualStudioProject>
diff --git a/lib/hcrypto/libtommath/logs/README b/lib/hcrypto/libtommath/logs/README new file mode 100644 index 000000000000..ea20c8137985 --- /dev/null +++ b/lib/hcrypto/libtommath/logs/README @@ -0,0 +1,13 @@ +To use the pretty graphs you have to first build/run the ltmtest from the root directory of the package.
+Todo this type
+
+make timing ; ltmtest
+
+in the root. It will run for a while [about ten minutes on most PCs] and produce a series of .log files in logs/.
+
+After doing that run "gnuplot graphs.dem" to make the PNGs. If you managed todo that all so far just open index.html to view
+them all :-)
+
+Have fun
+
+Tom
\ No newline at end of file diff --git a/lib/hcrypto/libtommath/logs/add.log b/lib/hcrypto/libtommath/logs/add.log new file mode 100644 index 000000000000..0ed7b70d9eef --- /dev/null +++ b/lib/hcrypto/libtommath/logs/add.log @@ -0,0 +1,16 @@ + 480 48 + 960 61 + 1440 82 + 1920 97 + 2400 106 + 2880 112 + 3360 127 + 3840 130 + 4320 146 + 4800 157 + 5280 174 + 5760 185 + 6240 200 + 6720 214 + 7200 230 + 7680 244 diff --git a/lib/hcrypto/libtommath/logs/addsub.png b/lib/hcrypto/libtommath/logs/addsub.png Binary files differnew file mode 100644 index 000000000000..b8ffef74b320 --- /dev/null +++ b/lib/hcrypto/libtommath/logs/addsub.png diff --git a/lib/hcrypto/libtommath/logs/expt.log b/lib/hcrypto/libtommath/logs/expt.log new file mode 100644 index 000000000000..2e5ee308f934 --- /dev/null +++ b/lib/hcrypto/libtommath/logs/expt.log @@ -0,0 +1,7 @@ + 513 446633 + 769 1110301 + 1025 2414927 + 2049 14870787 + 2561 26299761 + 3073 44323310 + 4097 98934292 diff --git a/lib/hcrypto/libtommath/logs/expt.png b/lib/hcrypto/libtommath/logs/expt.png Binary files differnew file mode 100644 index 000000000000..27c53eecf1af --- /dev/null +++ b/lib/hcrypto/libtommath/logs/expt.png diff --git a/lib/hcrypto/libtommath/logs/expt_2k.log b/lib/hcrypto/libtommath/logs/expt_2k.log new file mode 100644 index 000000000000..140b92f2c4e2 --- /dev/null +++ b/lib/hcrypto/libtommath/logs/expt_2k.log @@ -0,0 +1,6 @@ + 521 533515 + 607 675230 + 1279 2560713 + 2203 7468422 + 3217 17314246 + 4253 33899969 diff --git a/lib/hcrypto/libtommath/logs/expt_2kl.log b/lib/hcrypto/libtommath/logs/expt_2kl.log new file mode 100644 index 000000000000..1dc495f9e41d --- /dev/null +++ b/lib/hcrypto/libtommath/logs/expt_2kl.log @@ -0,0 +1,3 @@ + 1024 2210287 + 2048 7940364 + 4096 35903891 diff --git a/lib/hcrypto/libtommath/logs/expt_dr.log b/lib/hcrypto/libtommath/logs/expt_dr.log new file mode 100644 index 000000000000..3752ea81aaf2 --- /dev/null +++ b/lib/hcrypto/libtommath/logs/expt_dr.log @@ -0,0 +1,7 @@ + 532 642330 + 784 1138699 + 1036 1972796 + 1540 3912241 + 2072 7075836 + 3080 16420867 + 4116 32477173 diff --git a/lib/hcrypto/libtommath/logs/graphs.dem b/lib/hcrypto/libtommath/logs/graphs.dem new file mode 100644 index 000000000000..538e5c075eef --- /dev/null +++ b/lib/hcrypto/libtommath/logs/graphs.dem @@ -0,0 +1,16 @@ +set terminal png +set ylabel "Cycles per Operation" +set xlabel "Operand size (bits)" + +set output "addsub.png" +plot 'add.log' smooth bezier title "Addition", 'sub.log' smooth bezier title "Subtraction" + +set output "mult.png" +plot 'sqr.log' smooth bezier title "Squaring (without Karatsuba)", 'sqr_kara.log' smooth bezier title "Squaring (Karatsuba)", 'mult.log' smooth bezier title "Multiplication (without Karatsuba)", 'mult_kara.log' smooth bezier title "Multiplication (Karatsuba)" + +set output "expt.png" +plot 'expt.log' smooth bezier title "Exptmod (Montgomery)", 'expt_dr.log' smooth bezier title "Exptmod (Dimminished Radix)", 'expt_2k.log' smooth bezier title "Exptmod (2k Reduction)" + +set output "invmod.png" +plot 'invmod.log' smooth bezier title "Modular Inverse" + diff --git a/lib/hcrypto/libtommath/logs/index.html b/lib/hcrypto/libtommath/logs/index.html new file mode 100644 index 000000000000..4b68c25a5103 --- /dev/null +++ b/lib/hcrypto/libtommath/logs/index.html @@ -0,0 +1,27 @@ +<html> +<head> +<title>LibTomMath Log Plots</title> +</head> +<body> + +<h1>Addition and Subtraction</h1> +<center><img src=addsub.png></center> +<hr> + +<h1>Multipliers</h1> +<center><img src=mult.png></center> +<hr> + +<h1>Exptmod</h1> +<center><img src=expt.png></center> +<hr> + +<h1>Modular Inverse</h1> +<center><img src=invmod.png></center> +<hr> + +</body> +</html> +/* $Source: /cvs/libtom/libtommath/logs/index.html,v $ */ +/* $Revision: 1.2 $ */ +/* $Date: 2005/05/05 14:38:47 $ */ diff --git a/lib/hcrypto/libtommath/logs/invmod.log b/lib/hcrypto/libtommath/logs/invmod.log new file mode 100644 index 000000000000..7d22449ef652 --- /dev/null +++ b/lib/hcrypto/libtommath/logs/invmod.log @@ -0,0 +1,8 @@ + 240 58197 + 480 86617 + 720 255279 + 960 399626 + 1200 533330 + 1440 470046 + 1680 906754 + 1920 1132009 diff --git a/lib/hcrypto/libtommath/logs/invmod.png b/lib/hcrypto/libtommath/logs/invmod.png Binary files differnew file mode 100644 index 000000000000..5c09e9012ada --- /dev/null +++ b/lib/hcrypto/libtommath/logs/invmod.png diff --git a/lib/hcrypto/libtommath/logs/mult.log b/lib/hcrypto/libtommath/logs/mult.log new file mode 100644 index 000000000000..841b40b96411 --- /dev/null +++ b/lib/hcrypto/libtommath/logs/mult.log @@ -0,0 +1,84 @@ + 240 114 + 360 182 + 480 273 + 600 364 + 717 471 + 840 597 + 960 737 + 1080 881 + 1196 1041 + 1318 1215 + 1438 1405 + 1559 1600 + 1679 1812 + 1800 2045 + 1918 2289 + 2040 2534 + 2160 2800 + 2280 3067 + 2397 3375 + 2520 3678 + 2640 4007 + 2759 4325 + 2880 4851 + 3000 5200 + 3117 5557 + 3239 5938 + 3356 6332 + 3480 6741 + 3600 7168 + 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b/lib/hcrypto/libtommath/logs/mult_kara.log new file mode 100644 index 000000000000..91b59cbfdabd --- /dev/null +++ b/lib/hcrypto/libtommath/logs/mult_kara.log @@ -0,0 +1,84 @@ + 240 133 + 360 250 + 474 396 + 599 585 + 720 637 + 840 1045 + 960 1212 + 1080 1543 + 1196 1780 + 1320 2005 + 1436 2274 + 1560 2446 + 1680 1985 + 1800 2368 + 1920 2791 + 2038 3620 + 2160 3763 + 2278 3444 + 2400 4158 + 2516 5869 + 2640 6368 + 2753 5384 + 2876 7449 + 3000 6471 + 3114 8540 + 3240 7217 + 3360 9685 + 3476 6759 + 3599 8518 + 3714 8911 + 3840 12345 + 3960 9787 + 4079 11018 + 4196 12033 + 4319 12740 + 4440 12471 + 4558 15251 + 4678 13353 + 4798 15998 + 4920 13395 + 5040 13699 + 5160 14552 + 5280 14972 + 5400 15825 + 5520 16512 + 5639 17379 + 5757 17596 + 5879 18350 + 6000 18976 + 6115 19601 + 6240 20076 + 6354 20515 + 6480 21670 + 6600 22312 + 6716 22647 + 6839 23437 + 6960 24164 + 7080 24723 + 7199 25454 + 7320 26092 + 7440 26912 + 7557 27521 + 7677 28015 + 7800 28885 + 7919 29483 + 8040 30115 + 8160 31236 + 8280 31975 + 8400 30835 + 8520 31565 + 8639 32380 + 8760 32760 + 8879 33590 + 8996 34553 + 9119 35185 + 9239 36146 + 9358 36815 + 9480 39630 + 9596 43022 + 9720 41219 + 9840 41596 + 9960 42354 + 10080 43352 + 10200 43915 diff --git a/lib/hcrypto/libtommath/logs/sqr.log b/lib/hcrypto/libtommath/logs/sqr.log new file mode 100644 index 000000000000..93234a1455e4 --- /dev/null +++ b/lib/hcrypto/libtommath/logs/sqr.log @@ -0,0 +1,84 @@ + 240 114 + 359 174 + 478 241 + 600 311 + 720 399 + 840 494 + 960 599 + 1080 799 + 1200 931 + 1320 911 + 1440 1016 + 1560 1143 + 1680 1281 + 1800 1459 + 1918 1617 + 2039 1763 + 2159 1913 + 2279 2071 + 2399 2240 + 2518 2412 + 2640 2600 + 2760 2792 + 2877 3008 + 2999 3220 + 3119 3405 + 3239 3637 + 3359 3859 + 3480 4094 + 3600 4328 + 3717 4571 + 3838 4840 + 3960 5098 + 4080 5349 + 4200 5617 + 4320 5891 + 4440 6147 + 4560 6444 + 4680 6745 + 4800 7057 + 4918 7317 + 5039 7637 + 5160 12833 + 5280 10098 + 5397 8666 + 5520 8999 + 5639 9376 + 5758 9727 + 5880 9996 + 6000 10427 + 6118 10868 + 6240 12218 + 6359 14010 + 6478 14838 + 6593 16135 + 6719 16503 + 6840 13267 + 6960 13648 + 7080 14118 + 7199 14525 + 7320 14803 + 7439 15378 + 7558 15871 + 7680 57530 + 7800 59550 + 7916 61091 + 8039 63004 + 8160 61136 + 8279 62803 + 8398 68671 + 8520 71001 + 8638 71537 + 8759 74757 + 8880 77164 + 9000 78963 + 9119 80982 + 9239 83142 + 9357 85292 + 9480 88190 + 9600 90343 + 9718 86710 + 9840 88818 + 9954 91034 + 10079 93350 + 10197 95592 diff --git a/lib/hcrypto/libtommath/logs/sqr_kara.log b/lib/hcrypto/libtommath/logs/sqr_kara.log new file mode 100644 index 000000000000..da108973f446 --- /dev/null +++ b/lib/hcrypto/libtommath/logs/sqr_kara.log @@ -0,0 +1,84 @@ + 240 115 + 360 175 + 480 241 + 600 312 + 719 397 + 839 494 + 960 597 + 1080 696 + 1200 794 + 1320 908 + 1439 1022 + 1560 1141 + 1678 1284 + 1797 1461 + 1918 1590 + 2040 1764 + 2160 1911 + 2278 2072 + 2399 2263 + 2516 2425 + 2640 2627 + 2756 2809 + 2880 3017 + 3000 3220 + 3119 3413 + 3239 3627 + 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2880 105 + 3360 118 + 3840 133 + 4320 146 + 4800 161 + 5280 182 + 5760 201 + 6240 201 + 6720 214 + 7200 228 + 7680 243 diff --git a/lib/hcrypto/libtommath/makefile b/lib/hcrypto/libtommath/makefile new file mode 100644 index 000000000000..be9fac6578fd --- /dev/null +++ b/lib/hcrypto/libtommath/makefile @@ -0,0 +1,165 @@ +#Makefile for GCC +# +#Tom St Denis + +ifeq ($V,1) +silent= +else +silent=@ +endif + +#default files to install +ifndef LIBNAME + LIBNAME=libtommath.a +endif + +coverage: LIBNAME:=-Wl,--whole-archive $(LIBNAME) -Wl,--no-whole-archive + +include makefile_include.mk + +%.o: %.c $(HEADERS) +ifneq ($V,1) + @echo " * ${CC} $@" +endif + ${silent} ${CC} -c ${LTM_CFLAGS} $< -o $@ + +LCOV_ARGS=--directory . + +#START_INS +OBJECTS=bn_cutoffs.o bn_deprecated.o bn_mp_2expt.o bn_mp_abs.o bn_mp_add.o bn_mp_add_d.o bn_mp_addmod.o \ +bn_mp_and.o bn_mp_clamp.o bn_mp_clear.o bn_mp_clear_multi.o bn_mp_cmp.o bn_mp_cmp_d.o bn_mp_cmp_mag.o \ +bn_mp_cnt_lsb.o bn_mp_complement.o bn_mp_copy.o bn_mp_count_bits.o bn_mp_decr.o bn_mp_div.o bn_mp_div_2.o \ +bn_mp_div_2d.o bn_mp_div_3.o bn_mp_div_d.o bn_mp_dr_is_modulus.o bn_mp_dr_reduce.o bn_mp_dr_setup.o \ +bn_mp_error_to_string.o bn_mp_exch.o bn_mp_expt_u32.o bn_mp_exptmod.o bn_mp_exteuclid.o bn_mp_fread.o \ +bn_mp_from_sbin.o bn_mp_from_ubin.o bn_mp_fwrite.o bn_mp_gcd.o bn_mp_get_double.o bn_mp_get_i32.o \ +bn_mp_get_i64.o bn_mp_get_l.o bn_mp_get_ll.o bn_mp_get_mag_u32.o bn_mp_get_mag_u64.o bn_mp_get_mag_ul.o \ +bn_mp_get_mag_ull.o bn_mp_grow.o bn_mp_incr.o bn_mp_init.o bn_mp_init_copy.o bn_mp_init_i32.o \ +bn_mp_init_i64.o bn_mp_init_l.o bn_mp_init_ll.o bn_mp_init_multi.o bn_mp_init_set.o bn_mp_init_size.o \ +bn_mp_init_u32.o bn_mp_init_u64.o bn_mp_init_ul.o bn_mp_init_ull.o bn_mp_invmod.o bn_mp_is_square.o \ +bn_mp_iseven.o bn_mp_isodd.o bn_mp_kronecker.o bn_mp_lcm.o bn_mp_log_u32.o bn_mp_lshd.o bn_mp_mod.o \ +bn_mp_mod_2d.o bn_mp_mod_d.o bn_mp_montgomery_calc_normalization.o bn_mp_montgomery_reduce.o \ +bn_mp_montgomery_setup.o bn_mp_mul.o bn_mp_mul_2.o bn_mp_mul_2d.o bn_mp_mul_d.o bn_mp_mulmod.o bn_mp_neg.o \ +bn_mp_or.o bn_mp_pack.o bn_mp_pack_count.o bn_mp_prime_fermat.o bn_mp_prime_frobenius_underwood.o \ +bn_mp_prime_is_prime.o bn_mp_prime_miller_rabin.o bn_mp_prime_next_prime.o \ +bn_mp_prime_rabin_miller_trials.o bn_mp_prime_rand.o bn_mp_prime_strong_lucas_selfridge.o \ +bn_mp_radix_size.o bn_mp_radix_smap.o bn_mp_rand.o bn_mp_read_radix.o bn_mp_reduce.o bn_mp_reduce_2k.o \ +bn_mp_reduce_2k_l.o bn_mp_reduce_2k_setup.o bn_mp_reduce_2k_setup_l.o bn_mp_reduce_is_2k.o \ +bn_mp_reduce_is_2k_l.o bn_mp_reduce_setup.o bn_mp_root_u32.o bn_mp_rshd.o bn_mp_sbin_size.o bn_mp_set.o \ +bn_mp_set_double.o bn_mp_set_i32.o bn_mp_set_i64.o bn_mp_set_l.o bn_mp_set_ll.o bn_mp_set_u32.o \ +bn_mp_set_u64.o bn_mp_set_ul.o bn_mp_set_ull.o bn_mp_shrink.o bn_mp_signed_rsh.o bn_mp_sqr.o \ +bn_mp_sqrmod.o bn_mp_sqrt.o bn_mp_sqrtmod_prime.o bn_mp_sub.o bn_mp_sub_d.o bn_mp_submod.o \ +bn_mp_to_radix.o bn_mp_to_sbin.o bn_mp_to_ubin.o bn_mp_ubin_size.o bn_mp_unpack.o bn_mp_xor.o bn_mp_zero.o \ +bn_prime_tab.o bn_s_mp_add.o bn_s_mp_balance_mul.o bn_s_mp_exptmod.o bn_s_mp_exptmod_fast.o \ +bn_s_mp_get_bit.o bn_s_mp_invmod_fast.o bn_s_mp_invmod_slow.o bn_s_mp_karatsuba_mul.o \ +bn_s_mp_karatsuba_sqr.o bn_s_mp_montgomery_reduce_fast.o bn_s_mp_mul_digs.o bn_s_mp_mul_digs_fast.o \ +bn_s_mp_mul_high_digs.o bn_s_mp_mul_high_digs_fast.o bn_s_mp_prime_is_divisible.o \ +bn_s_mp_rand_jenkins.o bn_s_mp_rand_platform.o bn_s_mp_reverse.o bn_s_mp_sqr.o bn_s_mp_sqr_fast.o \ +bn_s_mp_sub.o bn_s_mp_toom_mul.o bn_s_mp_toom_sqr.o + +#END_INS + +$(LIBNAME): $(OBJECTS) + $(AR) $(ARFLAGS) $@ $(OBJECTS) + $(RANLIB) $@ + +#make a profiled library (takes a while!!!) +# +# This will build the library with profile generation +# then run the test demo and rebuild the library. +# +# So far I've seen improvements in the MP math +profiled: + make CFLAGS="$(CFLAGS) -fprofile-arcs -DTESTING" timing + ./timing + rm -f *.a *.o timing + make CFLAGS="$(CFLAGS) -fbranch-probabilities" + +#make a single object profiled library +profiled_single: + perl gen.pl + $(CC) $(LTM_CFLAGS) -fprofile-arcs -DTESTING -c mpi.c -o mpi.o + $(CC) $(LTM_CFLAGS) -DTESTING -DTIMER demo/timing.c mpi.o -lgcov -o timing + ./timing + rm -f *.o timing + $(CC) $(LTM_CFLAGS) -fbranch-probabilities -DTESTING -c mpi.c -o mpi.o + $(AR) $(ARFLAGS) $(LIBNAME) mpi.o + ranlib $(LIBNAME) + +install: $(LIBNAME) + install -d $(DESTDIR)$(LIBPATH) + install -d $(DESTDIR)$(INCPATH) + install -m 644 $(LIBNAME) $(DESTDIR)$(LIBPATH) + install -m 644 $(HEADERS_PUB) $(DESTDIR)$(INCPATH) + +uninstall: + rm $(DESTDIR)$(LIBPATH)/$(LIBNAME) + rm $(HEADERS_PUB:%=$(DESTDIR)$(INCPATH)/%) + +test_standalone: test + @echo "test_standalone is deprecated, please use make-target 'test'" + +DEMOS=test mtest_opponent + +define DEMO_template +$(1): demo/$(1).o demo/shared.o $$(LIBNAME) + $$(CC) $$(LTM_CFLAGS) $$(LTM_LFLAGS) $$^ -o $$@ +endef + +$(foreach demo, $(strip $(DEMOS)), $(eval $(call DEMO_template,$(demo)))) + +.PHONY: mtest +mtest: + cd mtest ; $(CC) $(LTM_CFLAGS) -O0 mtest.c $(LTM_LFLAGS) -o mtest + +timing: $(LIBNAME) demo/timing.c + $(CC) $(LTM_CFLAGS) -DTIMER demo/timing.c $(LIBNAME) $(LTM_LFLAGS) -o timing + +tune: $(LIBNAME) + $(MAKE) -C etc tune CFLAGS="$(LTM_CFLAGS)" + $(MAKE) + +# You have to create a file .coveralls.yml with the content "repo_token: <the token>" +# in the base folder to be able to submit to coveralls +coveralls: lcov + coveralls-lcov + +docs manual: + $(MAKE) -C doc/ $@ V=$(V) + +.PHONY: pre_gen +pre_gen: + mkdir -p pre_gen + perl gen.pl + sed -e 's/[[:blank:]]*$$//' mpi.c > pre_gen/mpi.c + rm mpi.c + +zipup: clean astyle new_file docs + @# Update the index, so diff-index won't fail in case the pdf has been created. + @# As the pdf creation modifies the tex files, git sometimes detects the + @# modified files, but misses that it's put back to its original version. + @git update-index --refresh + @git diff-index --quiet HEAD -- || ( echo "FAILURE: uncommited changes or not a git" && exit 1 ) + rm -rf libtommath-$(VERSION) ltm-$(VERSION).* + @# files/dirs excluded from "git archive" are defined in .gitattributes + git archive --format=tar --prefix=libtommath-$(VERSION)/ HEAD | tar x + @echo 'fixme check' + -@(find libtommath-$(VERSION)/ -type f | xargs grep 'FIXM[E]') && echo '############## BEWARE: the "fixme" marker was found !!! ##############' || true + mkdir -p libtommath-$(VERSION)/doc + cp doc/bn.pdf libtommath-$(VERSION)/doc/ + $(MAKE) -C libtommath-$(VERSION)/ pre_gen + tar -c libtommath-$(VERSION)/ | xz -6e -c - > ltm-$(VERSION).tar.xz + zip -9rq ltm-$(VERSION).zip libtommath-$(VERSION) + cp doc/bn.pdf bn-$(VERSION).pdf + rm -rf libtommath-$(VERSION) + gpg -b -a ltm-$(VERSION).tar.xz + gpg -b -a ltm-$(VERSION).zip + +new_file: + perl helper.pl --update-files + +perlcritic: + perlcritic *.pl doc/*.pl + +astyle: + @echo " * run astyle on all sources" + @astyle --options=astylerc --formatted $(OBJECTS:.o=.c) tommath*.h demo/*.c etc/*.c mtest/mtest.c diff --git a/lib/hcrypto/libtommath/makefile.mingw b/lib/hcrypto/libtommath/makefile.mingw new file mode 100644 index 000000000000..7eee57dc4343 --- /dev/null +++ b/lib/hcrypto/libtommath/makefile.mingw @@ -0,0 +1,109 @@ +# MAKEFILE for MS Windows (mingw + gcc + gmake) +# +# BEWARE: variable OBJECTS is updated via helper.pl + +### USAGE: +# Open a command prompt with gcc + gmake in PATH and start: +# +# gmake -f makefile.mingw all +# test.exe +# gmake -f makefile.mingw PREFIX=c:\devel\libtom install + +#The following can be overridden from command line e.g. make -f makefile.mingw CC=gcc ARFLAGS=rcs +PREFIX = c:\mingw +CC = gcc +AR = ar +ARFLAGS = r +RANLIB = ranlib +STRIP = strip +CFLAGS = -O2 +LDFLAGS = + +#Compilation flags +LTM_CFLAGS = -I. $(CFLAGS) +LTM_LDFLAGS = $(LDFLAGS) -static-libgcc + +#Libraries to be created +LIBMAIN_S =libtommath.a +LIBMAIN_I =libtommath.dll.a +LIBMAIN_D =libtommath.dll + +#List of objects to compile (all goes to libtommath.a) +OBJECTS=bn_cutoffs.o bn_deprecated.o bn_mp_2expt.o bn_mp_abs.o bn_mp_add.o bn_mp_add_d.o bn_mp_addmod.o \ +bn_mp_and.o bn_mp_clamp.o bn_mp_clear.o bn_mp_clear_multi.o bn_mp_cmp.o bn_mp_cmp_d.o bn_mp_cmp_mag.o \ +bn_mp_cnt_lsb.o bn_mp_complement.o bn_mp_copy.o bn_mp_count_bits.o bn_mp_decr.o bn_mp_div.o bn_mp_div_2.o \ +bn_mp_div_2d.o bn_mp_div_3.o bn_mp_div_d.o bn_mp_dr_is_modulus.o bn_mp_dr_reduce.o bn_mp_dr_setup.o \ +bn_mp_error_to_string.o bn_mp_exch.o bn_mp_expt_u32.o bn_mp_exptmod.o bn_mp_exteuclid.o bn_mp_fread.o \ +bn_mp_from_sbin.o bn_mp_from_ubin.o bn_mp_fwrite.o bn_mp_gcd.o bn_mp_get_double.o bn_mp_get_i32.o \ +bn_mp_get_i64.o bn_mp_get_l.o bn_mp_get_ll.o bn_mp_get_mag_u32.o bn_mp_get_mag_u64.o bn_mp_get_mag_ul.o \ +bn_mp_get_mag_ull.o bn_mp_grow.o bn_mp_incr.o bn_mp_init.o bn_mp_init_copy.o bn_mp_init_i32.o \ +bn_mp_init_i64.o bn_mp_init_l.o bn_mp_init_ll.o bn_mp_init_multi.o bn_mp_init_set.o bn_mp_init_size.o \ +bn_mp_init_u32.o bn_mp_init_u64.o bn_mp_init_ul.o bn_mp_init_ull.o bn_mp_invmod.o bn_mp_is_square.o \ +bn_mp_iseven.o bn_mp_isodd.o bn_mp_kronecker.o bn_mp_lcm.o bn_mp_log_u32.o bn_mp_lshd.o bn_mp_mod.o \ +bn_mp_mod_2d.o bn_mp_mod_d.o bn_mp_montgomery_calc_normalization.o bn_mp_montgomery_reduce.o \ +bn_mp_montgomery_setup.o bn_mp_mul.o bn_mp_mul_2.o bn_mp_mul_2d.o bn_mp_mul_d.o bn_mp_mulmod.o bn_mp_neg.o \ +bn_mp_or.o bn_mp_pack.o bn_mp_pack_count.o bn_mp_prime_fermat.o bn_mp_prime_frobenius_underwood.o \ +bn_mp_prime_is_prime.o bn_mp_prime_miller_rabin.o bn_mp_prime_next_prime.o \ +bn_mp_prime_rabin_miller_trials.o bn_mp_prime_rand.o bn_mp_prime_strong_lucas_selfridge.o \ +bn_mp_radix_size.o bn_mp_radix_smap.o bn_mp_rand.o bn_mp_read_radix.o bn_mp_reduce.o bn_mp_reduce_2k.o \ +bn_mp_reduce_2k_l.o bn_mp_reduce_2k_setup.o bn_mp_reduce_2k_setup_l.o bn_mp_reduce_is_2k.o \ +bn_mp_reduce_is_2k_l.o bn_mp_reduce_setup.o bn_mp_root_u32.o bn_mp_rshd.o bn_mp_sbin_size.o bn_mp_set.o \ +bn_mp_set_double.o bn_mp_set_i32.o bn_mp_set_i64.o bn_mp_set_l.o bn_mp_set_ll.o bn_mp_set_u32.o \ +bn_mp_set_u64.o bn_mp_set_ul.o bn_mp_set_ull.o bn_mp_shrink.o bn_mp_signed_rsh.o bn_mp_sqr.o \ +bn_mp_sqrmod.o bn_mp_sqrt.o bn_mp_sqrtmod_prime.o bn_mp_sub.o bn_mp_sub_d.o bn_mp_submod.o \ +bn_mp_to_radix.o bn_mp_to_sbin.o bn_mp_to_ubin.o bn_mp_ubin_size.o bn_mp_unpack.o bn_mp_xor.o bn_mp_zero.o \ +bn_prime_tab.o bn_s_mp_add.o bn_s_mp_balance_mul.o bn_s_mp_exptmod.o bn_s_mp_exptmod_fast.o \ +bn_s_mp_get_bit.o bn_s_mp_invmod_fast.o bn_s_mp_invmod_slow.o bn_s_mp_karatsuba_mul.o \ +bn_s_mp_karatsuba_sqr.o bn_s_mp_montgomery_reduce_fast.o bn_s_mp_mul_digs.o bn_s_mp_mul_digs_fast.o \ +bn_s_mp_mul_high_digs.o bn_s_mp_mul_high_digs_fast.o bn_s_mp_prime_is_divisible.o \ +bn_s_mp_rand_jenkins.o bn_s_mp_rand_platform.o bn_s_mp_reverse.o bn_s_mp_sqr.o bn_s_mp_sqr_fast.o \ +bn_s_mp_sub.o bn_s_mp_toom_mul.o bn_s_mp_toom_sqr.o + +HEADERS_PUB=tommath.h +HEADERS=tommath_private.h tommath_class.h tommath_superclass.h tommath_cutoffs.h $(HEADERS_PUB) + +#The default rule for make builds the libtommath.a library (static) +default: $(LIBMAIN_S) + +#Dependencies on *.h +$(OBJECTS): $(HEADERS) + +.c.o: + $(CC) $(LTM_CFLAGS) -c $< -o $@ + +#Create libtommath.a +$(LIBMAIN_S): $(OBJECTS) + $(AR) $(ARFLAGS) $@ $(OBJECTS) + $(RANLIB) $@ + +#Create DLL + import library libtommath.dll.a +$(LIBMAIN_D) $(LIBMAIN_I): $(OBJECTS) + $(CC) -s -shared -o $(LIBMAIN_D) $^ -Wl,--enable-auto-import,--export-all -Wl,--out-implib=$(LIBMAIN_I) $(LTM_LDFLAGS) + $(STRIP) -S $(LIBMAIN_D) + +#Build test suite +test.exe: demo/shared.o demo/test.o $(LIBMAIN_S) + $(CC) $(LTM_CFLAGS) $(LTM_LDFLAGS) $^ -o $@ + @echo NOTICE: start the tests by launching test.exe + +test_standalone: test.exe + @echo test_standalone is deprecated, please use make-target 'test.exe' + +all: $(LIBMAIN_S) test.exe + +tune: $(LIBNAME_S) + $(MAKE) -C etc tune + $(MAKE) + +clean: + @-cmd /c del /Q /S *.o *.a *.exe *.dll 2>nul + +#Install the library + headers +install: $(LIBMAIN_S) $(LIBMAIN_I) $(LIBMAIN_D) + cmd /c if not exist "$(PREFIX)\bin" mkdir "$(PREFIX)\bin" + cmd /c if not exist "$(PREFIX)\lib" mkdir "$(PREFIX)\lib" + cmd /c if not exist "$(PREFIX)\include" mkdir "$(PREFIX)\include" + copy /Y $(LIBMAIN_S) "$(PREFIX)\lib" + copy /Y $(LIBMAIN_I) "$(PREFIX)\lib" + copy /Y $(LIBMAIN_D) "$(PREFIX)\bin" + copy /Y tommath*.h "$(PREFIX)\include" diff --git a/lib/hcrypto/libtommath/makefile.msvc b/lib/hcrypto/libtommath/makefile.msvc new file mode 100644 index 000000000000..aa8d8bec1881 --- /dev/null +++ b/lib/hcrypto/libtommath/makefile.msvc @@ -0,0 +1,93 @@ +# MAKEFILE for MS Windows (nmake + Windows SDK) +# +# BEWARE: variable OBJECTS is updated via helper.pl + +### USAGE: +# Open a command prompt with WinSDK variables set and start: +# +# nmake -f makefile.msvc all +# test.exe +# nmake -f makefile.msvc PREFIX=c:\devel\libtom install + +#The following can be overridden from command line e.g. make -f makefile.msvc CC=gcc ARFLAGS=rcs +PREFIX = c:\devel +CFLAGS = /Ox + +#Compilation flags +LTM_CFLAGS = /nologo /I./ /D_CRT_SECURE_NO_WARNINGS /D_CRT_NONSTDC_NO_DEPRECATE /D__STDC_WANT_SECURE_LIB__=1 /D_CRT_HAS_CXX17=0 /Wall /wd4146 /wd4127 /wd4668 /wd4710 /wd4711 /wd4820 /wd5045 /WX $(CFLAGS) +LTM_LDFLAGS = advapi32.lib + +#Libraries to be created (this makefile builds only static libraries) +LIBMAIN_S =tommath.lib + +#List of objects to compile (all goes to tommath.lib) +OBJECTS=bn_cutoffs.obj bn_deprecated.obj bn_mp_2expt.obj bn_mp_abs.obj bn_mp_add.obj bn_mp_add_d.obj bn_mp_addmod.obj \ +bn_mp_and.obj bn_mp_clamp.obj bn_mp_clear.obj bn_mp_clear_multi.obj bn_mp_cmp.obj bn_mp_cmp_d.obj bn_mp_cmp_mag.obj \ +bn_mp_cnt_lsb.obj bn_mp_complement.obj bn_mp_copy.obj bn_mp_count_bits.obj bn_mp_decr.obj bn_mp_div.obj bn_mp_div_2.obj \ +bn_mp_div_2d.obj bn_mp_div_3.obj bn_mp_div_d.obj bn_mp_dr_is_modulus.obj bn_mp_dr_reduce.obj bn_mp_dr_setup.obj \ +bn_mp_error_to_string.obj bn_mp_exch.obj bn_mp_expt_u32.obj bn_mp_exptmod.obj bn_mp_exteuclid.obj bn_mp_fread.obj \ +bn_mp_from_sbin.obj bn_mp_from_ubin.obj bn_mp_fwrite.obj bn_mp_gcd.obj bn_mp_get_double.obj bn_mp_get_i32.obj \ +bn_mp_get_i64.obj bn_mp_get_l.obj bn_mp_get_ll.obj bn_mp_get_mag_u32.obj bn_mp_get_mag_u64.obj bn_mp_get_mag_ul.obj \ +bn_mp_get_mag_ull.obj bn_mp_grow.obj bn_mp_incr.obj bn_mp_init.obj bn_mp_init_copy.obj bn_mp_init_i32.obj \ +bn_mp_init_i64.obj bn_mp_init_l.obj bn_mp_init_ll.obj bn_mp_init_multi.obj bn_mp_init_set.obj bn_mp_init_size.obj \ +bn_mp_init_u32.obj bn_mp_init_u64.obj bn_mp_init_ul.obj bn_mp_init_ull.obj bn_mp_invmod.obj bn_mp_is_square.obj \ +bn_mp_iseven.obj bn_mp_isodd.obj bn_mp_kronecker.obj bn_mp_lcm.obj bn_mp_log_u32.obj bn_mp_lshd.obj bn_mp_mod.obj \ +bn_mp_mod_2d.obj bn_mp_mod_d.obj bn_mp_montgomery_calc_normalization.obj bn_mp_montgomery_reduce.obj \ +bn_mp_montgomery_setup.obj bn_mp_mul.obj bn_mp_mul_2.obj bn_mp_mul_2d.obj bn_mp_mul_d.obj bn_mp_mulmod.obj bn_mp_neg.obj \ +bn_mp_or.obj bn_mp_pack.obj bn_mp_pack_count.obj bn_mp_prime_fermat.obj bn_mp_prime_frobenius_underwood.obj \ +bn_mp_prime_is_prime.obj bn_mp_prime_miller_rabin.obj bn_mp_prime_next_prime.obj \ +bn_mp_prime_rabin_miller_trials.obj bn_mp_prime_rand.obj bn_mp_prime_strong_lucas_selfridge.obj \ +bn_mp_radix_size.obj bn_mp_radix_smap.obj bn_mp_rand.obj bn_mp_read_radix.obj bn_mp_reduce.obj bn_mp_reduce_2k.obj \ +bn_mp_reduce_2k_l.obj bn_mp_reduce_2k_setup.obj bn_mp_reduce_2k_setup_l.obj bn_mp_reduce_is_2k.obj \ +bn_mp_reduce_is_2k_l.obj bn_mp_reduce_setup.obj bn_mp_root_u32.obj bn_mp_rshd.obj bn_mp_sbin_size.obj bn_mp_set.obj \ +bn_mp_set_double.obj bn_mp_set_i32.obj bn_mp_set_i64.obj bn_mp_set_l.obj bn_mp_set_ll.obj bn_mp_set_u32.obj \ +bn_mp_set_u64.obj bn_mp_set_ul.obj bn_mp_set_ull.obj bn_mp_shrink.obj bn_mp_signed_rsh.obj bn_mp_sqr.obj \ +bn_mp_sqrmod.obj bn_mp_sqrt.obj bn_mp_sqrtmod_prime.obj bn_mp_sub.obj bn_mp_sub_d.obj bn_mp_submod.obj \ +bn_mp_to_radix.obj bn_mp_to_sbin.obj bn_mp_to_ubin.obj bn_mp_ubin_size.obj bn_mp_unpack.obj bn_mp_xor.obj bn_mp_zero.obj \ +bn_prime_tab.obj bn_s_mp_add.obj bn_s_mp_balance_mul.obj bn_s_mp_exptmod.obj bn_s_mp_exptmod_fast.obj \ +bn_s_mp_get_bit.obj bn_s_mp_invmod_fast.obj bn_s_mp_invmod_slow.obj bn_s_mp_karatsuba_mul.obj \ +bn_s_mp_karatsuba_sqr.obj bn_s_mp_montgomery_reduce_fast.obj bn_s_mp_mul_digs.obj bn_s_mp_mul_digs_fast.obj \ +bn_s_mp_mul_high_digs.obj bn_s_mp_mul_high_digs_fast.obj bn_s_mp_prime_is_divisible.obj \ +bn_s_mp_rand_jenkins.obj bn_s_mp_rand_platform.obj bn_s_mp_reverse.obj bn_s_mp_sqr.obj bn_s_mp_sqr_fast.obj \ +bn_s_mp_sub.obj bn_s_mp_toom_mul.obj bn_s_mp_toom_sqr.obj + +HEADERS_PUB=tommath.h +HEADERS=tommath_private.h tommath_class.h tommath_superclass.h tommath_cutoffs.h $(HEADERS_PUB) + +#The default rule for make builds the tommath.lib library (static) +default: $(LIBMAIN_S) + +#Dependencies on *.h +$(OBJECTS): $(HEADERS) + +.c.obj: + $(CC) $(LTM_CFLAGS) /c $< /Fo$@ + +#Create tommath.lib +$(LIBMAIN_S): $(OBJECTS) + lib /out:$(LIBMAIN_S) $(OBJECTS) + +#Build test suite +test.exe: $(LIBMAIN_S) demo/shared.obj demo/test.obj + cl $(LTM_CFLAGS) $(TOBJECTS) $(LIBMAIN_S) $(LTM_LDFLAGS) demo/shared.c demo/test.c /Fe$@ + @echo NOTICE: start the tests by launching test.exe + +test_standalone: test.exe + @echo test_standalone is deprecated, please use make-target 'test.exe' + +all: $(LIBMAIN_S) test.exe + +tune: $(LIBMAIN_S) + $(MAKE) -C etc tune + $(MAKE) + +clean: + @-cmd /c del /Q /S *.OBJ *.LIB *.EXE *.DLL 2>nul + +#Install the library + headers +install: $(LIBMAIN_S) + cmd /c if not exist "$(PREFIX)\bin" mkdir "$(PREFIX)\bin" + cmd /c if not exist "$(PREFIX)\lib" mkdir "$(PREFIX)\lib" + cmd /c if not exist "$(PREFIX)\include" mkdir "$(PREFIX)\include" + copy /Y $(LIBMAIN_S) "$(PREFIX)\lib" + copy /Y tommath*.h "$(PREFIX)\include" diff --git a/lib/hcrypto/libtommath/makefile.shared b/lib/hcrypto/libtommath/makefile.shared new file mode 100644 index 000000000000..680210736390 --- /dev/null +++ b/lib/hcrypto/libtommath/makefile.shared @@ -0,0 +1,99 @@ +#Makefile for GCC +# +#Tom St Denis + +#default files to install +ifndef LIBNAME + LIBNAME=libtommath.la +endif + +include makefile_include.mk + + +ifndef LIBTOOL + ifeq ($(PLATFORM), Darwin) + LIBTOOL:=glibtool + else + LIBTOOL:=libtool + endif +endif +LTCOMPILE = $(LIBTOOL) --mode=compile --tag=CC $(CC) +LTLINK = $(LIBTOOL) --mode=link --tag=CC $(CC) + +LCOV_ARGS=--directory .libs --directory . + +#START_INS +OBJECTS=bn_cutoffs.o bn_deprecated.o bn_mp_2expt.o bn_mp_abs.o bn_mp_add.o bn_mp_add_d.o bn_mp_addmod.o \ +bn_mp_and.o bn_mp_clamp.o bn_mp_clear.o bn_mp_clear_multi.o bn_mp_cmp.o bn_mp_cmp_d.o bn_mp_cmp_mag.o \ +bn_mp_cnt_lsb.o bn_mp_complement.o bn_mp_copy.o bn_mp_count_bits.o bn_mp_decr.o bn_mp_div.o bn_mp_div_2.o \ +bn_mp_div_2d.o bn_mp_div_3.o bn_mp_div_d.o bn_mp_dr_is_modulus.o bn_mp_dr_reduce.o bn_mp_dr_setup.o \ +bn_mp_error_to_string.o bn_mp_exch.o bn_mp_expt_u32.o bn_mp_exptmod.o bn_mp_exteuclid.o bn_mp_fread.o \ +bn_mp_from_sbin.o bn_mp_from_ubin.o bn_mp_fwrite.o bn_mp_gcd.o bn_mp_get_double.o bn_mp_get_i32.o \ +bn_mp_get_i64.o bn_mp_get_l.o bn_mp_get_ll.o bn_mp_get_mag_u32.o bn_mp_get_mag_u64.o bn_mp_get_mag_ul.o \ +bn_mp_get_mag_ull.o bn_mp_grow.o bn_mp_incr.o bn_mp_init.o bn_mp_init_copy.o bn_mp_init_i32.o \ +bn_mp_init_i64.o bn_mp_init_l.o bn_mp_init_ll.o bn_mp_init_multi.o bn_mp_init_set.o bn_mp_init_size.o \ +bn_mp_init_u32.o bn_mp_init_u64.o bn_mp_init_ul.o bn_mp_init_ull.o bn_mp_invmod.o bn_mp_is_square.o \ +bn_mp_iseven.o bn_mp_isodd.o bn_mp_kronecker.o bn_mp_lcm.o bn_mp_log_u32.o bn_mp_lshd.o bn_mp_mod.o \ +bn_mp_mod_2d.o bn_mp_mod_d.o bn_mp_montgomery_calc_normalization.o bn_mp_montgomery_reduce.o \ +bn_mp_montgomery_setup.o bn_mp_mul.o bn_mp_mul_2.o bn_mp_mul_2d.o bn_mp_mul_d.o bn_mp_mulmod.o bn_mp_neg.o \ +bn_mp_or.o bn_mp_pack.o bn_mp_pack_count.o bn_mp_prime_fermat.o bn_mp_prime_frobenius_underwood.o \ +bn_mp_prime_is_prime.o bn_mp_prime_miller_rabin.o bn_mp_prime_next_prime.o \ +bn_mp_prime_rabin_miller_trials.o bn_mp_prime_rand.o bn_mp_prime_strong_lucas_selfridge.o \ +bn_mp_radix_size.o bn_mp_radix_smap.o bn_mp_rand.o bn_mp_read_radix.o bn_mp_reduce.o bn_mp_reduce_2k.o \ +bn_mp_reduce_2k_l.o bn_mp_reduce_2k_setup.o bn_mp_reduce_2k_setup_l.o bn_mp_reduce_is_2k.o \ +bn_mp_reduce_is_2k_l.o bn_mp_reduce_setup.o bn_mp_root_u32.o bn_mp_rshd.o bn_mp_sbin_size.o bn_mp_set.o \ +bn_mp_set_double.o bn_mp_set_i32.o bn_mp_set_i64.o bn_mp_set_l.o bn_mp_set_ll.o bn_mp_set_u32.o \ +bn_mp_set_u64.o bn_mp_set_ul.o bn_mp_set_ull.o bn_mp_shrink.o bn_mp_signed_rsh.o bn_mp_sqr.o \ +bn_mp_sqrmod.o bn_mp_sqrt.o bn_mp_sqrtmod_prime.o bn_mp_sub.o bn_mp_sub_d.o bn_mp_submod.o \ +bn_mp_to_radix.o bn_mp_to_sbin.o bn_mp_to_ubin.o bn_mp_ubin_size.o bn_mp_unpack.o bn_mp_xor.o bn_mp_zero.o \ +bn_prime_tab.o bn_s_mp_add.o bn_s_mp_balance_mul.o bn_s_mp_exptmod.o bn_s_mp_exptmod_fast.o \ +bn_s_mp_get_bit.o bn_s_mp_invmod_fast.o bn_s_mp_invmod_slow.o bn_s_mp_karatsuba_mul.o \ +bn_s_mp_karatsuba_sqr.o bn_s_mp_montgomery_reduce_fast.o bn_s_mp_mul_digs.o bn_s_mp_mul_digs_fast.o \ +bn_s_mp_mul_high_digs.o bn_s_mp_mul_high_digs_fast.o bn_s_mp_prime_is_divisible.o \ +bn_s_mp_rand_jenkins.o bn_s_mp_rand_platform.o bn_s_mp_reverse.o bn_s_mp_sqr.o bn_s_mp_sqr_fast.o \ +bn_s_mp_sub.o bn_s_mp_toom_mul.o bn_s_mp_toom_sqr.o + +#END_INS + +objs: $(OBJECTS) + +.c.o: $(HEADERS) + $(LTCOMPILE) $(LTM_CFLAGS) $(LTM_LDFLAGS) -o $@ -c $< + +LOBJECTS = $(OBJECTS:.o=.lo) + +$(LIBNAME): $(OBJECTS) + $(LTLINK) $(LTM_LDFLAGS) $(LOBJECTS) -o $(LIBNAME) -rpath $(LIBPATH) -version-info $(VERSION_SO) $(LTM_LIBTOOLFLAGS) + +install: $(LIBNAME) + install -d $(DESTDIR)$(LIBPATH) + install -d $(DESTDIR)$(INCPATH) + $(LIBTOOL) --mode=install install -m 644 $(LIBNAME) $(DESTDIR)$(LIBPATH)/$(LIBNAME) + install -m 644 $(HEADERS_PUB) $(DESTDIR)$(INCPATH) + sed -e 's,^prefix=.*,prefix=$(PREFIX),' -e 's,^Version:.*,Version: $(VERSION_PC),' libtommath.pc.in > libtommath.pc + install -d $(DESTDIR)$(LIBPATH)/pkgconfig + install -m 644 libtommath.pc $(DESTDIR)$(LIBPATH)/pkgconfig/ + +uninstall: + $(LIBTOOL) --mode=uninstall rm $(DESTDIR)$(LIBPATH)/$(LIBNAME) + rm $(HEADERS_PUB:%=$(DESTDIR)$(INCPATH)/%) + rm $(DESTDIR)$(LIBPATH)/pkgconfig/libtommath.pc + +test_standalone: test + @echo "test_standalone is deprecated, please use make-target 'test'" + +test mtest_opponent: demo/shared.o $(LIBNAME) | demo/test.o demo/mtest_opponent.o + $(LTLINK) $(LTM_LDFLAGS) demo/$@.o $^ -o $@ + +.PHONY: mtest +mtest: + cd mtest ; $(CC) $(LTM_CFLAGS) -O0 mtest.c $(LTM_LDFLAGS) -o mtest + +timing: $(LIBNAME) demo/timing.c + $(LTLINK) $(LTM_CFLAGS) $(LTM_LDFLAGS) -DTIMER demo/timing.c $(LIBNAME) -o timing + +tune: $(LIBNAME) + $(LTCOMPILE) $(LTM_CFLAGS) -c etc/tune.c -o etc/tune.o + $(LTLINK) $(LTM_LDFLAGS) -o etc/tune etc/tune.o $(LIBNAME) + cd etc/; /bin/sh tune_it.sh; cd .. + $(MAKE) -f makefile.shared diff --git a/lib/hcrypto/libtommath/makefile.unix b/lib/hcrypto/libtommath/makefile.unix new file mode 100644 index 000000000000..4cefc7e173db --- /dev/null +++ b/lib/hcrypto/libtommath/makefile.unix @@ -0,0 +1,106 @@ +# MAKEFILE that is intended to be compatible with any kind of make (GNU make, BSD make, ...) +# works on: Linux, *BSD, Cygwin, AIX, HP-UX and hopefully other UNIX systems +# +# Please do not use here neither any special make syntax nor any unusual tools/utilities! + +# using ICC compiler: +# make -f makefile.unix CC=icc CFLAGS="-O3 -xP -ip" + +# using Borland C++Builder: +# make -f makefile.unix CC=bcc32 + +#The following can be overridden from command line e.g. "make -f makefile.unix CC=gcc ARFLAGS=rcs" +DESTDIR = +PREFIX = /usr/local +LIBPATH = $(PREFIX)/lib +INCPATH = $(PREFIX)/include +CC = cc +AR = ar +ARFLAGS = r +RANLIB = ranlib +CFLAGS = -O2 +LDFLAGS = + +VERSION = 1.2.0 + +#Compilation flags +LTM_CFLAGS = -I. $(CFLAGS) +LTM_LDFLAGS = $(LDFLAGS) + +#Library to be created (this makefile builds only static library) +LIBMAIN_S = libtommath.a + +OBJECTS=bn_cutoffs.o bn_deprecated.o bn_mp_2expt.o bn_mp_abs.o bn_mp_add.o bn_mp_add_d.o bn_mp_addmod.o \ +bn_mp_and.o bn_mp_clamp.o bn_mp_clear.o bn_mp_clear_multi.o bn_mp_cmp.o bn_mp_cmp_d.o bn_mp_cmp_mag.o \ +bn_mp_cnt_lsb.o bn_mp_complement.o bn_mp_copy.o bn_mp_count_bits.o bn_mp_decr.o bn_mp_div.o bn_mp_div_2.o \ +bn_mp_div_2d.o bn_mp_div_3.o bn_mp_div_d.o bn_mp_dr_is_modulus.o bn_mp_dr_reduce.o bn_mp_dr_setup.o \ +bn_mp_error_to_string.o bn_mp_exch.o bn_mp_expt_u32.o bn_mp_exptmod.o bn_mp_exteuclid.o bn_mp_fread.o \ +bn_mp_from_sbin.o bn_mp_from_ubin.o bn_mp_fwrite.o bn_mp_gcd.o bn_mp_get_double.o bn_mp_get_i32.o \ +bn_mp_get_i64.o bn_mp_get_l.o bn_mp_get_ll.o bn_mp_get_mag_u32.o bn_mp_get_mag_u64.o bn_mp_get_mag_ul.o \ +bn_mp_get_mag_ull.o bn_mp_grow.o bn_mp_incr.o bn_mp_init.o bn_mp_init_copy.o bn_mp_init_i32.o \ +bn_mp_init_i64.o bn_mp_init_l.o bn_mp_init_ll.o bn_mp_init_multi.o bn_mp_init_set.o bn_mp_init_size.o \ +bn_mp_init_u32.o bn_mp_init_u64.o bn_mp_init_ul.o bn_mp_init_ull.o bn_mp_invmod.o bn_mp_is_square.o \ +bn_mp_iseven.o bn_mp_isodd.o bn_mp_kronecker.o bn_mp_lcm.o bn_mp_log_u32.o bn_mp_lshd.o bn_mp_mod.o \ +bn_mp_mod_2d.o bn_mp_mod_d.o bn_mp_montgomery_calc_normalization.o bn_mp_montgomery_reduce.o \ +bn_mp_montgomery_setup.o bn_mp_mul.o bn_mp_mul_2.o bn_mp_mul_2d.o bn_mp_mul_d.o bn_mp_mulmod.o bn_mp_neg.o \ +bn_mp_or.o bn_mp_pack.o bn_mp_pack_count.o bn_mp_prime_fermat.o bn_mp_prime_frobenius_underwood.o \ +bn_mp_prime_is_prime.o bn_mp_prime_miller_rabin.o bn_mp_prime_next_prime.o \ +bn_mp_prime_rabin_miller_trials.o bn_mp_prime_rand.o bn_mp_prime_strong_lucas_selfridge.o \ +bn_mp_radix_size.o bn_mp_radix_smap.o bn_mp_rand.o bn_mp_read_radix.o bn_mp_reduce.o bn_mp_reduce_2k.o \ +bn_mp_reduce_2k_l.o bn_mp_reduce_2k_setup.o bn_mp_reduce_2k_setup_l.o bn_mp_reduce_is_2k.o \ +bn_mp_reduce_is_2k_l.o bn_mp_reduce_setup.o bn_mp_root_u32.o bn_mp_rshd.o bn_mp_sbin_size.o bn_mp_set.o \ +bn_mp_set_double.o bn_mp_set_i32.o bn_mp_set_i64.o bn_mp_set_l.o bn_mp_set_ll.o bn_mp_set_u32.o \ +bn_mp_set_u64.o bn_mp_set_ul.o bn_mp_set_ull.o bn_mp_shrink.o bn_mp_signed_rsh.o bn_mp_sqr.o \ +bn_mp_sqrmod.o bn_mp_sqrt.o bn_mp_sqrtmod_prime.o bn_mp_sub.o bn_mp_sub_d.o bn_mp_submod.o \ +bn_mp_to_radix.o bn_mp_to_sbin.o bn_mp_to_ubin.o bn_mp_ubin_size.o bn_mp_unpack.o bn_mp_xor.o bn_mp_zero.o \ +bn_prime_tab.o bn_s_mp_add.o bn_s_mp_balance_mul.o bn_s_mp_exptmod.o bn_s_mp_exptmod_fast.o \ +bn_s_mp_get_bit.o bn_s_mp_invmod_fast.o bn_s_mp_invmod_slow.o bn_s_mp_karatsuba_mul.o \ +bn_s_mp_karatsuba_sqr.o bn_s_mp_montgomery_reduce_fast.o bn_s_mp_mul_digs.o bn_s_mp_mul_digs_fast.o \ +bn_s_mp_mul_high_digs.o bn_s_mp_mul_high_digs_fast.o bn_s_mp_prime_is_divisible.o \ +bn_s_mp_rand_jenkins.o bn_s_mp_rand_platform.o bn_s_mp_reverse.o bn_s_mp_sqr.o bn_s_mp_sqr_fast.o \ +bn_s_mp_sub.o bn_s_mp_toom_mul.o bn_s_mp_toom_sqr.o + +HEADERS_PUB=tommath.h +HEADERS=tommath_private.h tommath_class.h tommath_superclass.h tommath_cutoffs.h $(HEADERS_PUB) + +#The default rule for make builds the libtommath.a library (static) +default: $(LIBMAIN_S) + +#Dependencies on *.h +$(OBJECTS): $(HEADERS) + +#This is necessary for compatibility with BSD make (namely on OpenBSD) +.SUFFIXES: .o .c +.c.o: + $(CC) $(LTM_CFLAGS) -c $< -o $@ + +#Create libtommath.a +$(LIBMAIN_S): $(OBJECTS) + $(AR) $(ARFLAGS) $@ $(OBJECTS) + $(RANLIB) $@ + +#Build test_standalone suite +test: demo/shared.o demo/test.o $(LIBMAIN_S) + $(CC) $(LTM_CFLAGS) $(LTM_LDFLAGS) $^ -o $@ + @echo "NOTICE: start the tests by: ./test" + +test_standalone: test + @echo "test_standalone is deprecated, please use make-target 'test'" + +all: $(LIBMAIN_S) test + +tune: $(LIBMAIN_S) + $(MAKE) -C etc tune + $(MAKE) + +#NOTE: this makefile works also on cygwin, thus we need to delete *.exe +clean: + -@rm -f $(OBJECTS) $(LIBMAIN_S) + -@rm -f demo/main.o demo/opponent.o demo/test.o test test.exe + +#Install the library + headers +install: $(LIBMAIN_S) + @mkdir -p $(DESTDIR)$(INCPATH) $(DESTDIR)$(LIBPATH)/pkgconfig + @cp $(LIBMAIN_S) $(DESTDIR)$(LIBPATH)/ + @cp $(HEADERS_PUB) $(DESTDIR)$(INCPATH)/ + @sed -e 's,^prefix=.*,prefix=$(PREFIX),' -e 's,^Version:.*,Version: $(VERSION),' libtommath.pc.in > $(DESTDIR)$(LIBPATH)/pkgconfig/libtommath.pc diff --git a/lib/hcrypto/libtommath/makefile_include.mk b/lib/hcrypto/libtommath/makefile_include.mk new file mode 100644 index 000000000000..7b025e8e96bc --- /dev/null +++ b/lib/hcrypto/libtommath/makefile_include.mk @@ -0,0 +1,166 @@ +# +# Include makefile for libtommath +# + +#version of library +VERSION=1.2.0 +VERSION_PC=1.2.0 +VERSION_SO=3:0:2 + +PLATFORM := $(shell uname | sed -e 's/_.*//') + +# default make target +default: ${LIBNAME} + +# Compiler and Linker Names +ifndef CROSS_COMPILE + CROSS_COMPILE= +endif + +# We only need to go through this dance of determining the right compiler if we're using +# cross compilation, otherwise $(CC) is fine as-is. +ifneq (,$(CROSS_COMPILE)) +ifeq ($(origin CC),default) +CSTR := "\#ifdef __clang__\nCLANG\n\#endif\n" +ifeq ($(PLATFORM),FreeBSD) + # XXX: FreeBSD needs extra escaping for some reason + CSTR := $$$(CSTR) +endif +ifneq (,$(shell echo $(CSTR) | $(CC) -E - | grep CLANG)) + CC := $(CROSS_COMPILE)clang +else + CC := $(CROSS_COMPILE)gcc +endif # Clang +endif # cc is Make's default +endif # CROSS_COMPILE non-empty + +LD=$(CROSS_COMPILE)ld +AR=$(CROSS_COMPILE)ar +RANLIB=$(CROSS_COMPILE)ranlib + +ifndef MAKE +# BSDs refer to GNU Make as gmake +ifneq (,$(findstring $(PLATFORM),FreeBSD OpenBSD DragonFly NetBSD)) + MAKE=gmake +else + MAKE=make +endif +endif + +LTM_CFLAGS += -I./ -Wall -Wsign-compare -Wextra -Wshadow + +ifdef SANITIZER +LTM_CFLAGS += -fsanitize=undefined -fno-sanitize-recover=all -fno-sanitize=float-divide-by-zero +endif + +ifndef NO_ADDTL_WARNINGS +# additional warnings +LTM_CFLAGS += -Wdeclaration-after-statement -Wbad-function-cast -Wcast-align +LTM_CFLAGS += -Wstrict-prototypes -Wpointer-arith +endif + +ifdef CONV_WARNINGS +LTM_CFLAGS += -std=c89 -Wconversion -Wsign-conversion +ifeq ($(CONV_WARNINGS), strict) +LTM_CFLAGS += -DMP_USE_ENUMS -Wc++-compat +endif +else +LTM_CFLAGS += -Wsystem-headers +endif + +ifdef COMPILE_DEBUG +#debug +LTM_CFLAGS += -g3 +endif + +ifdef COMPILE_SIZE +#for size +LTM_CFLAGS += -Os +else + +ifndef IGNORE_SPEED +#for speed +LTM_CFLAGS += -O3 -funroll-loops + +#x86 optimizations [should be valid for any GCC install though] +LTM_CFLAGS += -fomit-frame-pointer +endif + +endif # COMPILE_SIZE + +ifneq ($(findstring clang,$(CC)),) +LTM_CFLAGS += -Wno-typedef-redefinition -Wno-tautological-compare -Wno-builtin-requires-header +endif +ifneq ($(findstring mingw,$(CC)),) +LTM_CFLAGS += -Wno-shadow +endif +ifeq ($(PLATFORM), Darwin) +LTM_CFLAGS += -Wno-nullability-completeness +endif +ifeq ($(PLATFORM), CYGWIN) +LIBTOOLFLAGS += -no-undefined +endif + +# add in the standard FLAGS +LTM_CFLAGS += $(CFLAGS) +LTM_LFLAGS += $(LFLAGS) +LTM_LDFLAGS += $(LDFLAGS) +LTM_LIBTOOLFLAGS += $(LIBTOOLFLAGS) + + +ifeq ($(PLATFORM),FreeBSD) + _ARCH := $(shell sysctl -b hw.machine_arch) +else + _ARCH := $(shell uname -m) +endif + +# adjust coverage set +ifneq ($(filter $(_ARCH), i386 i686 x86_64 amd64 ia64),) + COVERAGE = test_standalone timing + COVERAGE_APP = ./test && ./timing +else + COVERAGE = test_standalone + COVERAGE_APP = ./test +endif + +HEADERS_PUB=tommath.h +HEADERS=tommath_private.h tommath_class.h tommath_superclass.h tommath_cutoffs.h $(HEADERS_PUB) + +#LIBPATH The directory for libtommath to be installed to. +#INCPATH The directory to install the header files for libtommath. +#DATAPATH The directory to install the pdf docs. +DESTDIR ?= +PREFIX ?= /usr/local +LIBPATH ?= $(PREFIX)/lib +INCPATH ?= $(PREFIX)/include +DATAPATH ?= $(PREFIX)/share/doc/libtommath/pdf + +#make the code coverage of the library +# +coverage: LTM_CFLAGS += -fprofile-arcs -ftest-coverage -DTIMING_NO_LOGS +coverage: LTM_LFLAGS += -lgcov +coverage: LTM_LDFLAGS += -lgcov + +coverage: $(COVERAGE) + $(COVERAGE_APP) + +lcov: coverage + rm -f coverage.info + lcov --capture --no-external --no-recursion $(LCOV_ARGS) --output-file coverage.info -q + genhtml coverage.info --output-directory coverage -q + +# target that removes all coverage output +cleancov-clean: + rm -f `find . -type f -name "*.info" | xargs` + rm -rf coverage/ + +# cleans everything - coverage output and standard 'clean' +cleancov: cleancov-clean clean + +clean: + rm -f *.gcda *.gcno *.gcov *.bat *.o *.a *.obj *.lib *.exe *.dll etclib/*.o \ + demo/*.o test timing mtest_opponent mtest/mtest mtest/mtest.exe tuning_list \ + *.s mpi.c *.da *.dyn *.dpi tommath.tex `find . -type f | grep [~] | xargs` *.lo *.la + rm -rf .libs/ demo/.libs + ${MAKE} -C etc/ clean MAKE=${MAKE} + ${MAKE} -C doc/ clean MAKE=${MAKE} diff --git a/lib/hcrypto/libtommath/mtest/logtab.h b/lib/hcrypto/libtommath/mtest/logtab.h new file mode 100644 index 000000000000..dae3344d6893 --- /dev/null +++ b/lib/hcrypto/libtommath/mtest/logtab.h @@ -0,0 +1,24 @@ +const float s_logv_2[] = { + 0.000000000, 0.000000000, 1.000000000, 0.630929754, /* 0 1 2 3 */ + 0.500000000, 0.430676558, 0.386852807, 0.356207187, /* 4 5 6 7 */ + 0.333333333, 0.315464877, 0.301029996, 0.289064826, /* 8 9 10 11 */ + 0.278942946, 0.270238154, 0.262649535, 0.255958025, /* 12 13 14 15 */ + 0.250000000, 0.244650542, 0.239812467, 0.235408913, /* 16 17 18 19 */ + 0.231378213, 0.227670249, 0.224243824, 0.221064729, /* 20 21 22 23 */ + 0.218104292, 0.215338279, 0.212746054, 0.210309918, /* 24 25 26 27 */ + 0.208014598, 0.205846832, 0.203795047, 0.201849087, /* 28 29 30 31 */ + 0.200000000, 0.198239863, 0.196561632, 0.194959022, /* 32 33 34 35 */ + 0.193426404, 0.191958720, 0.190551412, 0.189200360, /* 36 37 38 39 */ + 0.187901825, 0.186652411, 0.185449023, 0.184288833, /* 40 41 42 43 */ + 0.183169251, 0.182087900, 0.181042597, 0.180031327, /* 44 45 46 47 */ + 0.179052232, 0.178103594, 0.177183820, 0.176291434, /* 48 49 50 51 */ + 0.175425064, 0.174583430, 0.173765343, 0.172969690, /* 52 53 54 55 */ + 0.172195434, 0.171441601, 0.170707280, 0.169991616, /* 56 57 58 59 */ + 0.169293808, 0.168613099, 0.167948779, 0.167300179, /* 60 61 62 63 */ + 0.166666667 +}; + + +/* $Source$ */ +/* $Revision$ */ +/* $Date$ */ diff --git a/lib/hcrypto/libtommath/mtest/mpi-config.h b/lib/hcrypto/libtommath/mtest/mpi-config.h new file mode 100644 index 000000000000..ea576e5638fb --- /dev/null +++ b/lib/hcrypto/libtommath/mtest/mpi-config.h @@ -0,0 +1,90 @@ +/* Default configuration for MPI library */ +/* $Id$ */ + +#ifndef MPI_CONFIG_H_ +#define MPI_CONFIG_H_ + +/* + For boolean options, + 0 = no + 1 = yes + + Other options are documented individually. + + */ + +#ifndef MP_IOFUNC +#define MP_IOFUNC 0 /* include mp_print() ? */ +#endif + +#ifndef MP_MODARITH +#define MP_MODARITH 1 /* include modular arithmetic ? */ +#endif + +#ifndef MP_NUMTH +#define MP_NUMTH 1 /* include number theoretic functions? */ +#endif + +#ifndef MP_LOGTAB +#define MP_LOGTAB 1 /* use table of logs instead of log()? */ +#endif + +#ifndef MP_MEMSET +#define MP_MEMSET 1 /* use memset() to zero buffers? */ +#endif + +#ifndef MP_MEMCPY +#define MP_MEMCPY 1 /* use memcpy() to copy buffers? */ +#endif + +#ifndef MP_CRYPTO +#define MP_CRYPTO 1 /* erase memory on free? */ +#endif + +#ifndef MP_ARGCHK +/* + 0 = no parameter checks + 1 = runtime checks, continue execution and return an error to caller + 2 = assertions; dump core on parameter errors + */ +#define MP_ARGCHK 2 /* how to check input arguments */ +#endif + +#ifndef MP_DEBUG +#define MP_DEBUG 0 /* print diagnostic output? */ +#endif + +#ifndef MP_DEFPREC +#define MP_DEFPREC 64 /* default precision, in digits */ +#endif + +#ifndef MP_MACRO +#define MP_MACRO 1 /* use macros for frequent calls? */ +#endif + +#ifndef MP_SQUARE +#define MP_SQUARE 1 /* use separate squaring code? */ +#endif + +#ifndef MP_PTAB_SIZE +/* + When building mpprime.c, we build in a table of small prime + values to use for primality testing. The more you include, + the more space they take up. See primes.c for the possible + values (currently 16, 32, 64, 128, 256, and 6542) + */ +#define MP_PTAB_SIZE 128 /* how many built-in primes? */ +#endif + +#ifndef MP_COMPAT_MACROS +#define MP_COMPAT_MACROS 1 /* define compatibility macros? */ +#endif + +#endif /* ifndef MPI_CONFIG_H_ */ + + +/* crc==3287762869, version==2, Sat Feb 02 06:43:53 2002 */ + +/* $Source$ */ +/* $Revision$ */ +/* $Date$ */ diff --git a/lib/hcrypto/libtommath/mtest/mpi-types.h b/lib/hcrypto/libtommath/mtest/mpi-types.h new file mode 100644 index 000000000000..f99d7eeae168 --- /dev/null +++ b/lib/hcrypto/libtommath/mtest/mpi-types.h @@ -0,0 +1,20 @@ +/* Type definitions generated by 'types.pl' */ +typedef char mp_sign; +typedef unsigned short mp_digit; /* 2 byte type */ +typedef unsigned int mp_word; /* 4 byte type */ +typedef unsigned int mp_size; +typedef int mp_err; + +#define MP_DIGIT_BIT (CHAR_BIT*sizeof(mp_digit)) +#define MP_DIGIT_MAX USHRT_MAX +#define MP_WORD_BIT (CHAR_BIT*sizeof(mp_word)) +#define MP_WORD_MAX UINT_MAX + +#define MP_DIGIT_SIZE 2 +#define DIGIT_FMT "%04X" +#define RADIX (MP_DIGIT_MAX+1) + + +/* $Source$ */ +/* $Revision$ */ +/* $Date$ */ diff --git a/lib/hcrypto/libtommath/mtest/mpi.c b/lib/hcrypto/libtommath/mtest/mpi.c new file mode 100644 index 000000000000..7e71ad609dc7 --- /dev/null +++ b/lib/hcrypto/libtommath/mtest/mpi.c @@ -0,0 +1,3987 @@ +/* + mpi.c + + by Michael J. Fromberger <sting@linguist.dartmouth.edu> + Copyright (C) 1998 Michael J. Fromberger + + Arbitrary precision integer arithmetic library + + SPDX-License-Identifier: Unlicense + + $Id$ + */ + +#include "mpi.h" +#include <stdlib.h> +#include <string.h> +#include <ctype.h> + +#if MP_DEBUG +#include <stdio.h> + +#define DIAG(T,V) {fprintf(stderr,T);mp_print(V,stderr);fputc('\n',stderr);} +#else +#define DIAG(T,V) +#endif + +/* + If MP_LOGTAB is not defined, use the math library to compute the + logarithms on the fly. Otherwise, use the static table below. + Pick which works best for your system. + */ +#if MP_LOGTAB + +/* {{{ s_logv_2[] - log table for 2 in various bases */ + +/* + A table of the logs of 2 for various bases (the 0 and 1 entries of + this table are meaningless and should not be referenced). + + This table is used to compute output lengths for the mp_toradix() + function. Since a number n in radix r takes up about log_r(n) + digits, we estimate the output size by taking the least integer + greater than log_r(n), where: + + log_r(n) = log_2(n) * log_r(2) + + This table, therefore, is a table of log_r(2) for 2 <= r <= 36, + which are the output bases supported. + */ + +#include "logtab.h" + +/* }}} */ +#define LOG_V_2(R) s_logv_2[(R)] + +#else + +#include <math.h> +#define LOG_V_2(R) (log(2.0)/log(R)) + +#endif + +/* Default precision for newly created mp_int's */ +static unsigned int s_mp_defprec = MP_DEFPREC; + +/* {{{ Digit arithmetic macros */ + +/* + When adding and multiplying digits, the results can be larger than + can be contained in an mp_digit. Thus, an mp_word is used. These + macros mask off the upper and lower digits of the mp_word (the + mp_word may be more than 2 mp_digits wide, but we only concern + ourselves with the low-order 2 mp_digits) + + If your mp_word DOES have more than 2 mp_digits, you need to + uncomment the first line, and comment out the second. + */ + +/* #define CARRYOUT(W) (((W)>>DIGIT_BIT)&MP_DIGIT_MAX) */ +#define CARRYOUT(W) ((W)>>DIGIT_BIT) +#define ACCUM(W) ((W)&MP_DIGIT_MAX) + +/* }}} */ + +/* {{{ Comparison constants */ + +#define MP_LT -1 +#define MP_EQ 0 +#define MP_GT 1 + +/* }}} */ + +/* {{{ Constant strings */ + +/* Constant strings returned by mp_strerror() */ +static const char *mp_err_string[] = { + "unknown result code", /* say what? */ + "boolean true", /* MP_OKAY, MP_YES */ + "boolean false", /* MP_NO */ + "out of memory", /* MP_MEM */ + "argument out of range", /* MP_RANGE */ + "invalid input parameter", /* MP_BADARG */ + "result is undefined" /* MP_UNDEF */ +}; + +/* Value to digit maps for radix conversion */ + +/* s_dmap_1 - standard digits and letters */ +static const char *s_dmap_1 = + "0123456789ABCDEFGHIJKLMNOPQRSTUVWXYZabcdefghijklmnopqrstuvwxyz+/"; + +#if 0 +/* s_dmap_2 - base64 ordering for digits */ +static const char *s_dmap_2 = + "ABCDEFGHIJKLMNOPQRSTUVWXYZabcdefghijklmnopqrstuvwxyz0123456789+/"; +#endif + +/* }}} */ + +/* {{{ Static function declarations */ + +/* + If MP_MACRO is false, these will be defined as actual functions; + otherwise, suitable macro definitions will be used. This works + around the fact that ANSI C89 doesn't support an 'inline' keyword + (although I hear C9x will ... about bloody time). At present, the + macro definitions are identical to the function bodies, but they'll + expand in place, instead of generating a function call. + + I chose these particular functions to be made into macros because + some profiling showed they are called a lot on a typical workload, + and yet they are primarily housekeeping. + */ +#if MP_MACRO == 0 + void s_mp_setz(mp_digit *dp, mp_size count); /* zero digits */ + void s_mp_copy(mp_digit *sp, mp_digit *dp, mp_size count); /* copy */ + void *s_mp_alloc(size_t nb, size_t ni); /* general allocator */ + void s_mp_free(void *ptr); /* general free function */ +#else + + /* Even if these are defined as macros, we need to respect the settings + of the MP_MEMSET and MP_MEMCPY configuration options... + */ + #if MP_MEMSET == 0 + #define s_mp_setz(dp, count) \ + {int ix;for(ix=0;ix<(count);ix++)(dp)[ix]=0;} + #else + #define s_mp_setz(dp, count) memset(dp, 0, (count) * sizeof(mp_digit)) + #endif /* MP_MEMSET */ + + #if MP_MEMCPY == 0 + #define s_mp_copy(sp, dp, count) \ + {int ix;for(ix=0;ix<(count);ix++)(dp)[ix]=(sp)[ix];} + #else + #define s_mp_copy(sp, dp, count) memcpy(dp, sp, (count) * sizeof(mp_digit)) + #endif /* MP_MEMCPY */ + + #define s_mp_alloc(nb, ni) calloc(nb, ni) + #define s_mp_free(ptr) {if(ptr) free(ptr);} +#endif /* MP_MACRO */ + +mp_err s_mp_grow(mp_int *mp, mp_size min); /* increase allocated size */ +mp_err s_mp_pad(mp_int *mp, mp_size min); /* left pad with zeroes */ + +void s_mp_clamp(mp_int *mp); /* clip leading zeroes */ + +void s_mp_exch(mp_int *a, mp_int *b); /* swap a and b in place */ + +mp_err s_mp_lshd(mp_int *mp, mp_size p); /* left-shift by p digits */ +void s_mp_rshd(mp_int *mp, mp_size p); /* right-shift by p digits */ +void s_mp_div_2d(mp_int *mp, mp_digit d); /* divide by 2^d in place */ +void s_mp_mod_2d(mp_int *mp, mp_digit d); /* modulo 2^d in place */ +mp_err s_mp_mul_2d(mp_int *mp, mp_digit d); /* multiply by 2^d in place*/ +void s_mp_div_2(mp_int *mp); /* divide by 2 in place */ +mp_err s_mp_mul_2(mp_int *mp); /* multiply by 2 in place */ +mp_digit s_mp_norm(mp_int *a, mp_int *b); /* normalize for division */ +mp_err s_mp_add_d(mp_int *mp, mp_digit d); /* unsigned digit addition */ +mp_err s_mp_sub_d(mp_int *mp, mp_digit d); /* unsigned digit subtract */ +mp_err s_mp_mul_d(mp_int *mp, mp_digit d); /* unsigned digit multiply */ +mp_err s_mp_div_d(mp_int *mp, mp_digit d, mp_digit *r); + /* unsigned digit divide */ +mp_err s_mp_reduce(mp_int *x, mp_int *m, mp_int *mu); + /* Barrett reduction */ +mp_err s_mp_add(mp_int *a, mp_int *b); /* magnitude addition */ +mp_err s_mp_sub(mp_int *a, mp_int *b); /* magnitude subtract */ +mp_err s_mp_mul(mp_int *a, mp_int *b); /* magnitude multiply */ +#if 0 +void s_mp_kmul(mp_digit *a, mp_digit *b, mp_digit *out, mp_size len); + /* multiply buffers in place */ +#endif +#if MP_SQUARE +mp_err s_mp_sqr(mp_int *a); /* magnitude square */ +#else +#define s_mp_sqr(a) s_mp_mul(a, a) +#endif +mp_err s_mp_div(mp_int *a, mp_int *b); /* magnitude divide */ +mp_err s_mp_2expt(mp_int *a, mp_digit k); /* a = 2^k */ +int s_mp_cmp(mp_int *a, mp_int *b); /* magnitude comparison */ +int s_mp_cmp_d(mp_int *a, mp_digit d); /* magnitude digit compare */ +int s_mp_ispow2(mp_int *v); /* is v a power of 2? */ +int s_mp_ispow2d(mp_digit d); /* is d a power of 2? */ + +int s_mp_tovalue(char ch, int r); /* convert ch to value */ +char s_mp_todigit(int val, int r, int low); /* convert val to digit */ +int s_mp_outlen(int bits, int r); /* output length in bytes */ + +/* }}} */ + +/* {{{ Default precision manipulation */ + +unsigned int mp_get_prec(void) +{ + return s_mp_defprec; + +} /* end mp_get_prec() */ + +void mp_set_prec(unsigned int prec) +{ + if(prec == 0) + s_mp_defprec = MP_DEFPREC; + else + s_mp_defprec = prec; + +} /* end mp_set_prec() */ + +/* }}} */ + +/*------------------------------------------------------------------------*/ +/* {{{ mp_init(mp) */ + +/* + mp_init(mp) + + Initialize a new zero-valued mp_int. Returns MP_OKAY if successful, + MP_MEM if memory could not be allocated for the structure. + */ + +mp_err mp_init(mp_int *mp) +{ + return mp_init_size(mp, s_mp_defprec); + +} /* end mp_init() */ + +/* }}} */ + +/* {{{ mp_init_array(mp[], count) */ + +mp_err mp_init_array(mp_int mp[], int count) +{ + mp_err res; + int pos; + + ARGCHK(mp !=NULL && count > 0, MP_BADARG); + + for(pos = 0; pos < count; ++pos) { + if((res = mp_init(&mp[pos])) != MP_OKAY) + goto CLEANUP; + } + + return MP_OKAY; + + CLEANUP: + while(--pos >= 0) + mp_clear(&mp[pos]); + + return res; + +} /* end mp_init_array() */ + +/* }}} */ + +/* {{{ mp_init_size(mp, prec) */ + +/* + mp_init_size(mp, prec) + + Initialize a new zero-valued mp_int with at least the given + precision; returns MP_OKAY if successful, or MP_MEM if memory could + not be allocated for the structure. + */ + +mp_err mp_init_size(mp_int *mp, mp_size prec) +{ + ARGCHK(mp != NULL && prec > 0, MP_BADARG); + + if((DIGITS(mp) = s_mp_alloc(prec, sizeof(mp_digit))) == NULL) + return MP_MEM; + + SIGN(mp) = MP_ZPOS; + USED(mp) = 1; + ALLOC(mp) = prec; + + return MP_OKAY; + +} /* end mp_init_size() */ + +/* }}} */ + +/* {{{ mp_init_copy(mp, from) */ + +/* + mp_init_copy(mp, from) + + Initialize mp as an exact copy of from. Returns MP_OKAY if + successful, MP_MEM if memory could not be allocated for the new + structure. + */ + +mp_err mp_init_copy(mp_int *mp, mp_int *from) +{ + ARGCHK(mp != NULL && from != NULL, MP_BADARG); + + if(mp == from) + return MP_OKAY; + + if((DIGITS(mp) = s_mp_alloc(USED(from), sizeof(mp_digit))) == NULL) + return MP_MEM; + + s_mp_copy(DIGITS(from), DIGITS(mp), USED(from)); + USED(mp) = USED(from); + ALLOC(mp) = USED(from); + SIGN(mp) = SIGN(from); + + return MP_OKAY; + +} /* end mp_init_copy() */ + +/* }}} */ + +/* {{{ mp_copy(from, to) */ + +/* + mp_copy(from, to) + + Copies the mp_int 'from' to the mp_int 'to'. It is presumed that + 'to' has already been initialized (if not, use mp_init_copy() + instead). If 'from' and 'to' are identical, nothing happens. + */ + +mp_err mp_copy(mp_int *from, mp_int *to) +{ + ARGCHK(from != NULL && to != NULL, MP_BADARG); + + if(from == to) + return MP_OKAY; + + { /* copy */ + mp_digit *tmp; + + /* + If the allocated buffer in 'to' already has enough space to hold + all the used digits of 'from', we'll re-use it to avoid hitting + the memory allocater more than necessary; otherwise, we'd have + to grow anyway, so we just allocate a hunk and make the copy as + usual + */ + if(ALLOC(to) >= USED(from)) { + s_mp_setz(DIGITS(to) + USED(from), ALLOC(to) - USED(from)); + s_mp_copy(DIGITS(from), DIGITS(to), USED(from)); + + } else { + if((tmp = s_mp_alloc(USED(from), sizeof(mp_digit))) == NULL) + return MP_MEM; + + s_mp_copy(DIGITS(from), tmp, USED(from)); + + if(DIGITS(to) != NULL) { +#if MP_CRYPTO + s_mp_setz(DIGITS(to), ALLOC(to)); +#endif + s_mp_free(DIGITS(to)); + } + + DIGITS(to) = tmp; + ALLOC(to) = USED(from); + } + + /* Copy the precision and sign from the original */ + USED(to) = USED(from); + SIGN(to) = SIGN(from); + } /* end copy */ + + return MP_OKAY; + +} /* end mp_copy() */ + +/* }}} */ + +/* {{{ mp_exch(mp1, mp2) */ + +/* + mp_exch(mp1, mp2) + + Exchange mp1 and mp2 without allocating any intermediate memory + (well, unless you count the stack space needed for this call and the + locals it creates...). This cannot fail. + */ + +void mp_exch(mp_int *mp1, mp_int *mp2) +{ +#if MP_ARGCHK == 2 + assert(mp1 != NULL && mp2 != NULL); +#else + if(mp1 == NULL || mp2 == NULL) + return; +#endif + + s_mp_exch(mp1, mp2); + +} /* end mp_exch() */ + +/* }}} */ + +/* {{{ mp_clear(mp) */ + +/* + mp_clear(mp) + + Release the storage used by an mp_int, and void its fields so that + if someone calls mp_clear() again for the same int later, we won't + get tollchocked. + */ + +void mp_clear(mp_int *mp) +{ + if(mp == NULL) + return; + + if(DIGITS(mp) != NULL) { +#if MP_CRYPTO + s_mp_setz(DIGITS(mp), ALLOC(mp)); +#endif + s_mp_free(DIGITS(mp)); + DIGITS(mp) = NULL; + } + + USED(mp) = 0; + ALLOC(mp) = 0; + +} /* end mp_clear() */ + +/* }}} */ + +/* {{{ mp_clear_array(mp[], count) */ + +void mp_clear_array(mp_int mp[], int count) +{ + ARGCHK(mp != NULL && count > 0, MP_BADARG); + + while(--count >= 0) + mp_clear(&mp[count]); + +} /* end mp_clear_array() */ + +/* }}} */ + +/* {{{ mp_zero(mp) */ + +/* + mp_zero(mp) + + Set mp to zero. Does not change the allocated size of the structure, + and therefore cannot fail (except on a bad argument, which we ignore) + */ +void mp_zero(mp_int *mp) +{ + if(mp == NULL) + return; + + s_mp_setz(DIGITS(mp), ALLOC(mp)); + USED(mp) = 1; + SIGN(mp) = MP_ZPOS; + +} /* end mp_zero() */ + +/* }}} */ + +/* {{{ mp_set(mp, d) */ + +void mp_set(mp_int *mp, mp_digit d) +{ + if(mp == NULL) + return; + + mp_zero(mp); + DIGIT(mp, 0) = d; + +} /* end mp_set() */ + +/* }}} */ + +/* {{{ mp_set_int(mp, z) */ + +mp_err mp_set_int(mp_int *mp, long z) +{ + int ix; + unsigned long v = labs(z); + mp_err res; + + ARGCHK(mp != NULL, MP_BADARG); + + mp_zero(mp); + if(z == 0) + return MP_OKAY; /* shortcut for zero */ + + for(ix = sizeof(long) - 1; ix >= 0; ix--) { + + if((res = s_mp_mul_2d(mp, CHAR_BIT)) != MP_OKAY) + return res; + + res = s_mp_add_d(mp, + (mp_digit)((v >> (ix * CHAR_BIT)) & UCHAR_MAX)); + if(res != MP_OKAY) + return res; + + } + + if(z < 0) + SIGN(mp) = MP_NEG; + + return MP_OKAY; + +} /* end mp_set_int() */ + +/* }}} */ + +/*------------------------------------------------------------------------*/ +/* {{{ Digit arithmetic */ + +/* {{{ mp_add_d(a, d, b) */ + +/* + mp_add_d(a, d, b) + + Compute the sum b = a + d, for a single digit d. Respects the sign of + its primary addend (single digits are unsigned anyway). + */ + +mp_err mp_add_d(mp_int *a, mp_digit d, mp_int *b) +{ + mp_err res = MP_OKAY; + + ARGCHK(a != NULL && b != NULL, MP_BADARG); + + if((res = mp_copy(a, b)) != MP_OKAY) + return res; + + if(SIGN(b) == MP_ZPOS) { + res = s_mp_add_d(b, d); + } else if(s_mp_cmp_d(b, d) >= 0) { + res = s_mp_sub_d(b, d); + } else { + SIGN(b) = MP_ZPOS; + + DIGIT(b, 0) = d - DIGIT(b, 0); + } + + return res; + +} /* end mp_add_d() */ + +/* }}} */ + +/* {{{ mp_sub_d(a, d, b) */ + +/* + mp_sub_d(a, d, b) + + Compute the difference b = a - d, for a single digit d. Respects the + sign of its subtrahend (single digits are unsigned anyway). + */ + +mp_err mp_sub_d(mp_int *a, mp_digit d, mp_int *b) +{ + mp_err res; + + ARGCHK(a != NULL && b != NULL, MP_BADARG); + + if((res = mp_copy(a, b)) != MP_OKAY) + return res; + + if(SIGN(b) == MP_NEG) { + if((res = s_mp_add_d(b, d)) != MP_OKAY) + return res; + + } else if(s_mp_cmp_d(b, d) >= 0) { + if((res = s_mp_sub_d(b, d)) != MP_OKAY) + return res; + + } else { + mp_neg(b, b); + + DIGIT(b, 0) = d - DIGIT(b, 0); + SIGN(b) = MP_NEG; + } + + if(s_mp_cmp_d(b, 0) == 0) + SIGN(b) = MP_ZPOS; + + return MP_OKAY; + +} /* end mp_sub_d() */ + +/* }}} */ + +/* {{{ mp_mul_d(a, d, b) */ + +/* + mp_mul_d(a, d, b) + + Compute the product b = a * d, for a single digit d. Respects the sign + of its multiplicand (single digits are unsigned anyway) + */ + +mp_err mp_mul_d(mp_int *a, mp_digit d, mp_int *b) +{ + mp_err res; + + ARGCHK(a != NULL && b != NULL, MP_BADARG); + + if(d == 0) { + mp_zero(b); + return MP_OKAY; + } + + if((res = mp_copy(a, b)) != MP_OKAY) + return res; + + res = s_mp_mul_d(b, d); + + return res; + +} /* end mp_mul_d() */ + +/* }}} */ + +/* {{{ mp_mul_2(a, c) */ + +mp_err mp_mul_2(mp_int *a, mp_int *c) +{ + mp_err res; + + ARGCHK(a != NULL && c != NULL, MP_BADARG); + + if((res = mp_copy(a, c)) != MP_OKAY) + return res; + + return s_mp_mul_2(c); + +} /* end mp_mul_2() */ + +/* }}} */ + +/* {{{ mp_div_d(a, d, q, r) */ + +/* + mp_div_d(a, d, q, r) + + Compute the quotient q = a / d and remainder r = a mod d, for a + single digit d. Respects the sign of its divisor (single digits are + unsigned anyway). + */ + +mp_err mp_div_d(mp_int *a, mp_digit d, mp_int *q, mp_digit *r) +{ + mp_err res; + mp_digit rem; + int pow; + + ARGCHK(a != NULL, MP_BADARG); + + if(d == 0) + return MP_RANGE; + + /* Shortcut for powers of two ... */ + if((pow = s_mp_ispow2d(d)) >= 0) { + mp_digit mask; + + mask = (1 << pow) - 1; + rem = DIGIT(a, 0) & mask; + + if(q) { + mp_copy(a, q); + s_mp_div_2d(q, pow); + } + + if(r) + *r = rem; + + return MP_OKAY; + } + + /* + If the quotient is actually going to be returned, we'll try to + avoid hitting the memory allocator by copying the dividend into it + and doing the division there. This can't be any _worse_ than + always copying, and will sometimes be better (since it won't make + another copy) + + If it's not going to be returned, we need to allocate a temporary + to hold the quotient, which will just be discarded. + */ + if(q) { + if((res = mp_copy(a, q)) != MP_OKAY) + return res; + + res = s_mp_div_d(q, d, &rem); + if(s_mp_cmp_d(q, 0) == MP_EQ) + SIGN(q) = MP_ZPOS; + + } else { + mp_int qp; + + if((res = mp_init_copy(&qp, a)) != MP_OKAY) + return res; + + res = s_mp_div_d(&qp, d, &rem); + if(s_mp_cmp_d(&qp, 0) == 0) + SIGN(&qp) = MP_ZPOS; + + mp_clear(&qp); + } + + if(r) + *r = rem; + + return res; + +} /* end mp_div_d() */ + +/* }}} */ + +/* {{{ mp_div_2(a, c) */ + +/* + mp_div_2(a, c) + + Compute c = a / 2, disregarding the remainder. + */ + +mp_err mp_div_2(mp_int *a, mp_int *c) +{ + mp_err res; + + ARGCHK(a != NULL && c != NULL, MP_BADARG); + + if((res = mp_copy(a, c)) != MP_OKAY) + return res; + + s_mp_div_2(c); + + return MP_OKAY; + +} /* end mp_div_2() */ + +/* }}} */ + +/* {{{ mp_expt_d(a, d, b) */ + +mp_err mp_expt_d(mp_int *a, mp_digit d, mp_int *c) +{ + mp_int s, x; + mp_err res; + + ARGCHK(a != NULL && c != NULL, MP_BADARG); + + if((res = mp_init(&s)) != MP_OKAY) + return res; + if((res = mp_init_copy(&x, a)) != MP_OKAY) + goto X; + + DIGIT(&s, 0) = 1; + + while(d != 0) { + if(d & 1) { + if((res = s_mp_mul(&s, &x)) != MP_OKAY) + goto CLEANUP; + } + + d >>= 1; + + if((res = s_mp_sqr(&x)) != MP_OKAY) + goto CLEANUP; + } + + s_mp_exch(&s, c); + +CLEANUP: + mp_clear(&x); +X: + mp_clear(&s); + + return res; + +} /* end mp_expt_d() */ + +/* }}} */ + +/* }}} */ + +/*------------------------------------------------------------------------*/ +/* {{{ Full arithmetic */ + +/* {{{ mp_abs(a, b) */ + +/* + mp_abs(a, b) + + Compute b = |a|. 'a' and 'b' may be identical. + */ + +mp_err mp_abs(mp_int *a, mp_int *b) +{ + mp_err res; + + ARGCHK(a != NULL && b != NULL, MP_BADARG); + + if((res = mp_copy(a, b)) != MP_OKAY) + return res; + + SIGN(b) = MP_ZPOS; + + return MP_OKAY; + +} /* end mp_abs() */ + +/* }}} */ + +/* {{{ mp_neg(a, b) */ + +/* + mp_neg(a, b) + + Compute b = -a. 'a' and 'b' may be identical. + */ + +mp_err mp_neg(mp_int *a, mp_int *b) +{ + mp_err res; + + ARGCHK(a != NULL && b != NULL, MP_BADARG); + + if((res = mp_copy(a, b)) != MP_OKAY) + return res; + + if(s_mp_cmp_d(b, 0) == MP_EQ) + SIGN(b) = MP_ZPOS; + else + SIGN(b) = (SIGN(b) == MP_NEG) ? MP_ZPOS : MP_NEG; + + return MP_OKAY; + +} /* end mp_neg() */ + +/* }}} */ + +/* {{{ mp_add(a, b, c) */ + +/* + mp_add(a, b, c) + + Compute c = a + b. All parameters may be identical. + */ + +mp_err mp_add(mp_int *a, mp_int *b, mp_int *c) +{ + mp_err res; + int cmp; + + ARGCHK(a != NULL && b != NULL && c != NULL, MP_BADARG); + + if(SIGN(a) == SIGN(b)) { /* same sign: add values, keep sign */ + + /* Commutativity of addition lets us do this in either order, + so we avoid having to use a temporary even if the result + is supposed to replace the output + */ + if(c == b) { + if((res = s_mp_add(c, a)) != MP_OKAY) + return res; + } else { + if(c != a && (res = mp_copy(a, c)) != MP_OKAY) + return res; + + if((res = s_mp_add(c, b)) != MP_OKAY) + return res; + } + + } else if((cmp = s_mp_cmp(a, b)) > 0) { /* different sign: a > b */ + + /* If the output is going to be clobbered, we will use a temporary + variable; otherwise, we'll do it without touching the memory + allocator at all, if possible + */ + if(c == b) { + mp_int tmp; + + if((res = mp_init_copy(&tmp, a)) != MP_OKAY) + return res; + if((res = s_mp_sub(&tmp, b)) != MP_OKAY) { + mp_clear(&tmp); + return res; + } + + s_mp_exch(&tmp, c); + mp_clear(&tmp); + + } else { + + if(c != a && (res = mp_copy(a, c)) != MP_OKAY) + return res; + if((res = s_mp_sub(c, b)) != MP_OKAY) + return res; + + } + + } else if(cmp == 0) { /* different sign, a == b */ + + mp_zero(c); + return MP_OKAY; + + } else { /* different sign: a < b */ + + /* See above... */ + if(c == a) { + mp_int tmp; + + if((res = mp_init_copy(&tmp, b)) != MP_OKAY) + return res; + if((res = s_mp_sub(&tmp, a)) != MP_OKAY) { + mp_clear(&tmp); + return res; + } + + s_mp_exch(&tmp, c); + mp_clear(&tmp); + + } else { + + if(c != b && (res = mp_copy(b, c)) != MP_OKAY) + return res; + if((res = s_mp_sub(c, a)) != MP_OKAY) + return res; + + } + } + + if(USED(c) == 1 && DIGIT(c, 0) == 0) + SIGN(c) = MP_ZPOS; + + return MP_OKAY; + +} /* end mp_add() */ + +/* }}} */ + +/* {{{ mp_sub(a, b, c) */ + +/* + mp_sub(a, b, c) + + Compute c = a - b. All parameters may be identical. + */ + +mp_err mp_sub(mp_int *a, mp_int *b, mp_int *c) +{ + mp_err res; + int cmp; + + ARGCHK(a != NULL && b != NULL && c != NULL, MP_BADARG); + + if(SIGN(a) != SIGN(b)) { + if(c == a) { + if((res = s_mp_add(c, b)) != MP_OKAY) + return res; + } else { + if(c != b && ((res = mp_copy(b, c)) != MP_OKAY)) + return res; + if((res = s_mp_add(c, a)) != MP_OKAY) + return res; + SIGN(c) = SIGN(a); + } + + } else if((cmp = s_mp_cmp(a, b)) > 0) { /* Same sign, a > b */ + if(c == b) { + mp_int tmp; + + if((res = mp_init_copy(&tmp, a)) != MP_OKAY) + return res; + if((res = s_mp_sub(&tmp, b)) != MP_OKAY) { + mp_clear(&tmp); + return res; + } + s_mp_exch(&tmp, c); + mp_clear(&tmp); + + } else { + if(c != a && ((res = mp_copy(a, c)) != MP_OKAY)) + return res; + + if((res = s_mp_sub(c, b)) != MP_OKAY) + return res; + } + + } else if(cmp == 0) { /* Same sign, equal magnitude */ + mp_zero(c); + return MP_OKAY; + + } else { /* Same sign, b > a */ + if(c == a) { + mp_int tmp; + + if((res = mp_init_copy(&tmp, b)) != MP_OKAY) + return res; + + if((res = s_mp_sub(&tmp, a)) != MP_OKAY) { + mp_clear(&tmp); + return res; + } + s_mp_exch(&tmp, c); + mp_clear(&tmp); + + } else { + if(c != b && ((res = mp_copy(b, c)) != MP_OKAY)) + return res; + + if((res = s_mp_sub(c, a)) != MP_OKAY) + return res; + } + + SIGN(c) = !SIGN(b); + } + + if(USED(c) == 1 && DIGIT(c, 0) == 0) + SIGN(c) = MP_ZPOS; + + return MP_OKAY; + +} /* end mp_sub() */ + +/* }}} */ + +/* {{{ mp_mul(a, b, c) */ + +/* + mp_mul(a, b, c) + + Compute c = a * b. All parameters may be identical. + */ + +mp_err mp_mul(mp_int *a, mp_int *b, mp_int *c) +{ + mp_err res; + mp_sign sgn; + + ARGCHK(a != NULL && b != NULL && c != NULL, MP_BADARG); + + sgn = (SIGN(a) == SIGN(b)) ? MP_ZPOS : MP_NEG; + + if(c == b) { + if((res = s_mp_mul(c, a)) != MP_OKAY) + return res; + + } else { + if((res = mp_copy(a, c)) != MP_OKAY) + return res; + + if((res = s_mp_mul(c, b)) != MP_OKAY) + return res; + } + + if(sgn == MP_ZPOS || s_mp_cmp_d(c, 0) == MP_EQ) + SIGN(c) = MP_ZPOS; + else + SIGN(c) = sgn; + + return MP_OKAY; + +} /* end mp_mul() */ + +/* }}} */ + +/* {{{ mp_mul_2d(a, d, c) */ + +/* + mp_mul_2d(a, d, c) + + Compute c = a * 2^d. a may be the same as c. + */ + +mp_err mp_mul_2d(mp_int *a, mp_digit d, mp_int *c) +{ + mp_err res; + + ARGCHK(a != NULL && c != NULL, MP_BADARG); + + if((res = mp_copy(a, c)) != MP_OKAY) + return res; + + if(d == 0) + return MP_OKAY; + + return s_mp_mul_2d(c, d); + +} /* end mp_mul() */ + +/* }}} */ + +/* {{{ mp_sqr(a, b) */ + +#if MP_SQUARE +mp_err mp_sqr(mp_int *a, mp_int *b) +{ + mp_err res; + + ARGCHK(a != NULL && b != NULL, MP_BADARG); + + if((res = mp_copy(a, b)) != MP_OKAY) + return res; + + if((res = s_mp_sqr(b)) != MP_OKAY) + return res; + + SIGN(b) = MP_ZPOS; + + return MP_OKAY; + +} /* end mp_sqr() */ +#endif + +/* }}} */ + +/* {{{ mp_div(a, b, q, r) */ + +/* + mp_div(a, b, q, r) + + Compute q = a / b and r = a mod b. Input parameters may be re-used + as output parameters. If q or r is NULL, that portion of the + computation will be discarded (although it will still be computed) + + Pay no attention to the hacker behind the curtain. + */ + +mp_err mp_div(mp_int *a, mp_int *b, mp_int *q, mp_int *r) +{ + mp_err res; + mp_int qtmp, rtmp; + int cmp; + + ARGCHK(a != NULL && b != NULL, MP_BADARG); + + if(mp_cmp_z(b) == MP_EQ) + return MP_RANGE; + + /* If a <= b, we can compute the solution without division, and + avoid any memory allocation + */ + if((cmp = s_mp_cmp(a, b)) < 0) { + if(r) { + if((res = mp_copy(a, r)) != MP_OKAY) + return res; + } + + if(q) + mp_zero(q); + + return MP_OKAY; + + } else if(cmp == 0) { + + /* Set quotient to 1, with appropriate sign */ + if(q) { + int qneg = (SIGN(a) != SIGN(b)); + + mp_set(q, 1); + if(qneg) + SIGN(q) = MP_NEG; + } + + if(r) + mp_zero(r); + + return MP_OKAY; + } + + /* If we get here, it means we actually have to do some division */ + + /* Set up some temporaries... */ + if((res = mp_init_copy(&qtmp, a)) != MP_OKAY) + return res; + if((res = mp_init_copy(&rtmp, b)) != MP_OKAY) + goto CLEANUP; + + if((res = s_mp_div(&qtmp, &rtmp)) != MP_OKAY) + goto CLEANUP; + + /* Compute the signs for the output */ + SIGN(&rtmp) = SIGN(a); /* Sr = Sa */ + if(SIGN(a) == SIGN(b)) + SIGN(&qtmp) = MP_ZPOS; /* Sq = MP_ZPOS if Sa = Sb */ + else + SIGN(&qtmp) = MP_NEG; /* Sq = MP_NEG if Sa != Sb */ + + if(s_mp_cmp_d(&qtmp, 0) == MP_EQ) + SIGN(&qtmp) = MP_ZPOS; + if(s_mp_cmp_d(&rtmp, 0) == MP_EQ) + SIGN(&rtmp) = MP_ZPOS; + + /* Copy output, if it is needed */ + if(q) + s_mp_exch(&qtmp, q); + + if(r) + s_mp_exch(&rtmp, r); + +CLEANUP: + mp_clear(&rtmp); + mp_clear(&qtmp); + + return res; + +} /* end mp_div() */ + +/* }}} */ + +/* {{{ mp_div_2d(a, d, q, r) */ + +mp_err mp_div_2d(mp_int *a, mp_digit d, mp_int *q, mp_int *r) +{ + mp_err res; + + ARGCHK(a != NULL, MP_BADARG); + + if(q) { + if((res = mp_copy(a, q)) != MP_OKAY) + return res; + + s_mp_div_2d(q, d); + } + + if(r) { + if((res = mp_copy(a, r)) != MP_OKAY) + return res; + + s_mp_mod_2d(r, d); + } + + return MP_OKAY; + +} /* end mp_div_2d() */ + +/* }}} */ + +/* {{{ mp_expt(a, b, c) */ + +/* + mp_expt(a, b, c) + + Compute c = a ** b, that is, raise a to the b power. Uses a + standard iterative square-and-multiply technique. + */ + +mp_err mp_expt(mp_int *a, mp_int *b, mp_int *c) +{ + mp_int s, x; + mp_err res; + mp_digit d; + unsigned int bit, dig; + + ARGCHK(a != NULL && b != NULL && c != NULL, MP_BADARG); + + if(mp_cmp_z(b) < 0) + return MP_RANGE; + + if((res = mp_init(&s)) != MP_OKAY) + return res; + + mp_set(&s, 1); + + if((res = mp_init_copy(&x, a)) != MP_OKAY) + goto X; + + /* Loop over low-order digits in ascending order */ + for(dig = 0; dig < (USED(b) - 1); dig++) { + d = DIGIT(b, dig); + + /* Loop over bits of each non-maximal digit */ + for(bit = 0; bit < DIGIT_BIT; bit++) { + if(d & 1) { + if((res = s_mp_mul(&s, &x)) != MP_OKAY) + goto CLEANUP; + } + + d >>= 1; + + if((res = s_mp_sqr(&x)) != MP_OKAY) + goto CLEANUP; + } + } + + /* Consider now the last digit... */ + d = DIGIT(b, dig); + + while(d) { + if(d & 1) { + if((res = s_mp_mul(&s, &x)) != MP_OKAY) + goto CLEANUP; + } + + d >>= 1; + + if((res = s_mp_sqr(&x)) != MP_OKAY) + goto CLEANUP; + } + + if(mp_iseven(b)) + SIGN(&s) = SIGN(a); + + res = mp_copy(&s, c); + +CLEANUP: + mp_clear(&x); +X: + mp_clear(&s); + + return res; + +} /* end mp_expt() */ + +/* }}} */ + +/* {{{ mp_2expt(a, k) */ + +/* Compute a = 2^k */ + +mp_err mp_2expt(mp_int *a, mp_digit k) +{ + ARGCHK(a != NULL, MP_BADARG); + + return s_mp_2expt(a, k); + +} /* end mp_2expt() */ + +/* }}} */ + +/* {{{ mp_mod(a, m, c) */ + +/* + mp_mod(a, m, c) + + Compute c = a (mod m). Result will always be 0 <= c < m. + */ + +mp_err mp_mod(mp_int *a, mp_int *m, mp_int *c) +{ + mp_err res; + int mag; + + ARGCHK(a != NULL && m != NULL && c != NULL, MP_BADARG); + + if(SIGN(m) == MP_NEG) + return MP_RANGE; + + /* + If |a| > m, we need to divide to get the remainder and take the + absolute value. + + If |a| < m, we don't need to do any division, just copy and adjust + the sign (if a is negative). + + If |a| == m, we can simply set the result to zero. + + This order is intended to minimize the average path length of the + comparison chain on common workloads -- the most frequent cases are + that |a| != m, so we do those first. + */ + if((mag = s_mp_cmp(a, m)) > 0) { + if((res = mp_div(a, m, NULL, c)) != MP_OKAY) + return res; + + if(SIGN(c) == MP_NEG) { + if((res = mp_add(c, m, c)) != MP_OKAY) + return res; + } + + } else if(mag < 0) { + if((res = mp_copy(a, c)) != MP_OKAY) + return res; + + if(mp_cmp_z(a) < 0) { + if((res = mp_add(c, m, c)) != MP_OKAY) + return res; + + } + + } else { + mp_zero(c); + + } + + return MP_OKAY; + +} /* end mp_mod() */ + +/* }}} */ + +/* {{{ mp_mod_d(a, d, c) */ + +/* + mp_mod_d(a, d, c) + + Compute c = a (mod d). Result will always be 0 <= c < d + */ +mp_err mp_mod_d(mp_int *a, mp_digit d, mp_digit *c) +{ + mp_err res; + mp_digit rem; + + ARGCHK(a != NULL && c != NULL, MP_BADARG); + + if(s_mp_cmp_d(a, d) > 0) { + if((res = mp_div_d(a, d, NULL, &rem)) != MP_OKAY) + return res; + + } else { + if(SIGN(a) == MP_NEG) + rem = d - DIGIT(a, 0); + else + rem = DIGIT(a, 0); + } + + if(c) + *c = rem; + + return MP_OKAY; + +} /* end mp_mod_d() */ + +/* }}} */ + +/* {{{ mp_sqrt(a, b) */ + +/* + mp_sqrt(a, b) + + Compute the integer square root of a, and store the result in b. + Uses an integer-arithmetic version of Newton's iterative linear + approximation technique to determine this value; the result has the + following two properties: + + b^2 <= a + (b+1)^2 >= a + + It is a range error to pass a negative value. + */ +mp_err mp_sqrt(mp_int *a, mp_int *b) +{ + mp_int x, t; + mp_err res; + + ARGCHK(a != NULL && b != NULL, MP_BADARG); + + /* Cannot take square root of a negative value */ + if(SIGN(a) == MP_NEG) + return MP_RANGE; + + /* Special cases for zero and one, trivial */ + if(mp_cmp_d(a, 0) == MP_EQ || mp_cmp_d(a, 1) == MP_EQ) + return mp_copy(a, b); + + /* Initialize the temporaries we'll use below */ + if((res = mp_init_size(&t, USED(a))) != MP_OKAY) + return res; + + /* Compute an initial guess for the iteration as a itself */ + if((res = mp_init_copy(&x, a)) != MP_OKAY) + goto X; + +s_mp_rshd(&x, (USED(&x)/2)+1); +mp_add_d(&x, 1, &x); + + for(;;) { + /* t = (x * x) - a */ + mp_copy(&x, &t); /* can't fail, t is big enough for original x */ + if((res = mp_sqr(&t, &t)) != MP_OKAY || + (res = mp_sub(&t, a, &t)) != MP_OKAY) + goto CLEANUP; + + /* t = t / 2x */ + s_mp_mul_2(&x); + if((res = mp_div(&t, &x, &t, NULL)) != MP_OKAY) + goto CLEANUP; + s_mp_div_2(&x); + + /* Terminate the loop, if the quotient is zero */ + if(mp_cmp_z(&t) == MP_EQ) + break; + + /* x = x - t */ + if((res = mp_sub(&x, &t, &x)) != MP_OKAY) + goto CLEANUP; + + } + + /* Copy result to output parameter */ + mp_sub_d(&x, 1, &x); + s_mp_exch(&x, b); + + CLEANUP: + mp_clear(&x); + X: + mp_clear(&t); + + return res; + +} /* end mp_sqrt() */ + +/* }}} */ + +/* }}} */ + +/*------------------------------------------------------------------------*/ +/* {{{ Modular arithmetic */ + +#if MP_MODARITH +/* {{{ mp_addmod(a, b, m, c) */ + +/* + mp_addmod(a, b, m, c) + + Compute c = (a + b) mod m + */ + +mp_err mp_addmod(mp_int *a, mp_int *b, mp_int *m, mp_int *c) +{ + mp_err res; + + ARGCHK(a != NULL && b != NULL && m != NULL && c != NULL, MP_BADARG); + + if((res = mp_add(a, b, c)) != MP_OKAY) + return res; + if((res = mp_mod(c, m, c)) != MP_OKAY) + return res; + + return MP_OKAY; + +} + +/* }}} */ + +/* {{{ mp_submod(a, b, m, c) */ + +/* + mp_submod(a, b, m, c) + + Compute c = (a - b) mod m + */ + +mp_err mp_submod(mp_int *a, mp_int *b, mp_int *m, mp_int *c) +{ + mp_err res; + + ARGCHK(a != NULL && b != NULL && m != NULL && c != NULL, MP_BADARG); + + if((res = mp_sub(a, b, c)) != MP_OKAY) + return res; + if((res = mp_mod(c, m, c)) != MP_OKAY) + return res; + + return MP_OKAY; + +} + +/* }}} */ + +/* {{{ mp_mulmod(a, b, m, c) */ + +/* + mp_mulmod(a, b, m, c) + + Compute c = (a * b) mod m + */ + +mp_err mp_mulmod(mp_int *a, mp_int *b, mp_int *m, mp_int *c) +{ + mp_err res; + + ARGCHK(a != NULL && b != NULL && m != NULL && c != NULL, MP_BADARG); + + if((res = mp_mul(a, b, c)) != MP_OKAY) + return res; + if((res = mp_mod(c, m, c)) != MP_OKAY) + return res; + + return MP_OKAY; + +} + +/* }}} */ + +/* {{{ mp_sqrmod(a, m, c) */ + +#if MP_SQUARE +mp_err mp_sqrmod(mp_int *a, mp_int *m, mp_int *c) +{ + mp_err res; + + ARGCHK(a != NULL && m != NULL && c != NULL, MP_BADARG); + + if((res = mp_sqr(a, c)) != MP_OKAY) + return res; + if((res = mp_mod(c, m, c)) != MP_OKAY) + return res; + + return MP_OKAY; + +} /* end mp_sqrmod() */ +#endif + +/* }}} */ + +/* {{{ mp_exptmod(a, b, m, c) */ + +/* + mp_exptmod(a, b, m, c) + + Compute c = (a ** b) mod m. Uses a standard square-and-multiply + method with modular reductions at each step. (This is basically the + same code as mp_expt(), except for the addition of the reductions) + + The modular reductions are done using Barrett's algorithm (see + s_mp_reduce() below for details) + */ + +mp_err mp_exptmod(mp_int *a, mp_int *b, mp_int *m, mp_int *c) +{ + mp_int s, x, mu; + mp_err res; + mp_digit d, *db = DIGITS(b); + mp_size ub = USED(b); + unsigned int bit, dig; + + ARGCHK(a != NULL && b != NULL && c != NULL, MP_BADARG); + + if(mp_cmp_z(b) < 0 || mp_cmp_z(m) <= 0) + return MP_RANGE; + + if((res = mp_init(&s)) != MP_OKAY) + return res; + if((res = mp_init_copy(&x, a)) != MP_OKAY) + goto X; + if((res = mp_mod(&x, m, &x)) != MP_OKAY || + (res = mp_init(&mu)) != MP_OKAY) + goto MU; + + mp_set(&s, 1); + + /* mu = b^2k / m */ + s_mp_add_d(&mu, 1); + s_mp_lshd(&mu, 2 * USED(m)); + if((res = mp_div(&mu, m, &mu, NULL)) != MP_OKAY) + goto CLEANUP; + + /* Loop over digits of b in ascending order, except highest order */ + for(dig = 0; dig < (ub - 1); dig++) { + d = *db++; + + /* Loop over the bits of the lower-order digits */ + for(bit = 0; bit < DIGIT_BIT; bit++) { + if(d & 1) { + if((res = s_mp_mul(&s, &x)) != MP_OKAY) + goto CLEANUP; + if((res = s_mp_reduce(&s, m, &mu)) != MP_OKAY) + goto CLEANUP; + } + + d >>= 1; + + if((res = s_mp_sqr(&x)) != MP_OKAY) + goto CLEANUP; + if((res = s_mp_reduce(&x, m, &mu)) != MP_OKAY) + goto CLEANUP; + } + } + + /* Now do the last digit... */ + d = *db; + + while(d) { + if(d & 1) { + if((res = s_mp_mul(&s, &x)) != MP_OKAY) + goto CLEANUP; + if((res = s_mp_reduce(&s, m, &mu)) != MP_OKAY) + goto CLEANUP; + } + + d >>= 1; + + if((res = s_mp_sqr(&x)) != MP_OKAY) + goto CLEANUP; + if((res = s_mp_reduce(&x, m, &mu)) != MP_OKAY) + goto CLEANUP; + } + + s_mp_exch(&s, c); + + CLEANUP: + mp_clear(&mu); + MU: + mp_clear(&x); + X: + mp_clear(&s); + + return res; + +} /* end mp_exptmod() */ + +/* }}} */ + +/* {{{ mp_exptmod_d(a, d, m, c) */ + +mp_err mp_exptmod_d(mp_int *a, mp_digit d, mp_int *m, mp_int *c) +{ + mp_int s, x; + mp_err res; + + ARGCHK(a != NULL && c != NULL, MP_BADARG); + + if((res = mp_init(&s)) != MP_OKAY) + return res; + if((res = mp_init_copy(&x, a)) != MP_OKAY) + goto X; + + mp_set(&s, 1); + + while(d != 0) { + if(d & 1) { + if((res = s_mp_mul(&s, &x)) != MP_OKAY || + (res = mp_mod(&s, m, &s)) != MP_OKAY) + goto CLEANUP; + } + + d /= 2; + + if((res = s_mp_sqr(&x)) != MP_OKAY || + (res = mp_mod(&x, m, &x)) != MP_OKAY) + goto CLEANUP; + } + + s_mp_exch(&s, c); + +CLEANUP: + mp_clear(&x); +X: + mp_clear(&s); + + return res; + +} /* end mp_exptmod_d() */ + +/* }}} */ +#endif /* if MP_MODARITH */ + +/* }}} */ + +/*------------------------------------------------------------------------*/ +/* {{{ Comparison functions */ + +/* {{{ mp_cmp_z(a) */ + +/* + mp_cmp_z(a) + + Compare a <=> 0. Returns <0 if a<0, 0 if a=0, >0 if a>0. + */ + +int mp_cmp_z(mp_int *a) +{ + if(SIGN(a) == MP_NEG) + return MP_LT; + else if(USED(a) == 1 && DIGIT(a, 0) == 0) + return MP_EQ; + else + return MP_GT; + +} /* end mp_cmp_z() */ + +/* }}} */ + +/* {{{ mp_cmp_d(a, d) */ + +/* + mp_cmp_d(a, d) + + Compare a <=> d. Returns <0 if a<d, 0 if a=d, >0 if a>d + */ + +int mp_cmp_d(mp_int *a, mp_digit d) +{ + ARGCHK(a != NULL, MP_EQ); + + if(SIGN(a) == MP_NEG) + return MP_LT; + + return s_mp_cmp_d(a, d); + +} /* end mp_cmp_d() */ + +/* }}} */ + +/* {{{ mp_cmp(a, b) */ + +int mp_cmp(mp_int *a, mp_int *b) +{ + ARGCHK(a != NULL && b != NULL, MP_EQ); + + if(SIGN(a) == SIGN(b)) { + int mag; + + if((mag = s_mp_cmp(a, b)) == MP_EQ) + return MP_EQ; + + if(SIGN(a) == MP_ZPOS) + return mag; + else + return -mag; + + } else if(SIGN(a) == MP_ZPOS) { + return MP_GT; + } else { + return MP_LT; + } + +} /* end mp_cmp() */ + +/* }}} */ + +/* {{{ mp_cmp_mag(a, b) */ + +/* + mp_cmp_mag(a, b) + + Compares |a| <=> |b|, and returns an appropriate comparison result + */ + +int mp_cmp_mag(mp_int *a, mp_int *b) +{ + ARGCHK(a != NULL && b != NULL, MP_EQ); + + return s_mp_cmp(a, b); + +} /* end mp_cmp_mag() */ + +/* }}} */ + +/* {{{ mp_cmp_int(a, z) */ + +/* + This just converts z to an mp_int, and uses the existing comparison + routines. This is sort of inefficient, but it's not clear to me how + frequently this wil get used anyway. For small positive constants, + you can always use mp_cmp_d(), and for zero, there is mp_cmp_z(). + */ +int mp_cmp_int(mp_int *a, long z) +{ + mp_int tmp; + int out; + + ARGCHK(a != NULL, MP_EQ); + + mp_init(&tmp); mp_set_int(&tmp, z); + out = mp_cmp(a, &tmp); + mp_clear(&tmp); + + return out; + +} /* end mp_cmp_int() */ + +/* }}} */ + +/* {{{ mp_isodd(a) */ + +/* + mp_isodd(a) + + Returns a true (non-zero) value if a is odd, false (zero) otherwise. + */ +int mp_isodd(mp_int *a) +{ + ARGCHK(a != NULL, 0); + + return (DIGIT(a, 0) & 1); + +} /* end mp_isodd() */ + +/* }}} */ + +/* {{{ mp_iseven(a) */ + +int mp_iseven(mp_int *a) +{ + return !mp_isodd(a); + +} /* end mp_iseven() */ + +/* }}} */ + +/* }}} */ + +/*------------------------------------------------------------------------*/ +/* {{{ Number theoretic functions */ + +#if MP_NUMTH +/* {{{ mp_gcd(a, b, c) */ + +/* + Like the old mp_gcd() function, except computes the GCD using the + binary algorithm due to Josef Stein in 1961 (via Knuth). + */ +mp_err mp_gcd(mp_int *a, mp_int *b, mp_int *c) +{ + mp_err res; + mp_int u, v, t; + mp_size k = 0; + + ARGCHK(a != NULL && b != NULL && c != NULL, MP_BADARG); + + if(mp_cmp_z(a) == MP_EQ && mp_cmp_z(b) == MP_EQ) + return MP_RANGE; + if(mp_cmp_z(a) == MP_EQ) { + return mp_copy(b, c); + } else if(mp_cmp_z(b) == MP_EQ) { + return mp_copy(a, c); + } + + if((res = mp_init(&t)) != MP_OKAY) + return res; + if((res = mp_init_copy(&u, a)) != MP_OKAY) + goto U; + if((res = mp_init_copy(&v, b)) != MP_OKAY) + goto V; + + SIGN(&u) = MP_ZPOS; + SIGN(&v) = MP_ZPOS; + + /* Divide out common factors of 2 until at least 1 of a, b is even */ + while(mp_iseven(&u) && mp_iseven(&v)) { + s_mp_div_2(&u); + s_mp_div_2(&v); + ++k; + } + + /* Initialize t */ + if(mp_isodd(&u)) { + if((res = mp_copy(&v, &t)) != MP_OKAY) + goto CLEANUP; + + /* t = -v */ + if(SIGN(&v) == MP_ZPOS) + SIGN(&t) = MP_NEG; + else + SIGN(&t) = MP_ZPOS; + + } else { + if((res = mp_copy(&u, &t)) != MP_OKAY) + goto CLEANUP; + + } + + for(;;) { + while(mp_iseven(&t)) { + s_mp_div_2(&t); + } + + if(mp_cmp_z(&t) == MP_GT) { + if((res = mp_copy(&t, &u)) != MP_OKAY) + goto CLEANUP; + + } else { + if((res = mp_copy(&t, &v)) != MP_OKAY) + goto CLEANUP; + + /* v = -t */ + if(SIGN(&t) == MP_ZPOS) + SIGN(&v) = MP_NEG; + else + SIGN(&v) = MP_ZPOS; + } + + if((res = mp_sub(&u, &v, &t)) != MP_OKAY) + goto CLEANUP; + + if(s_mp_cmp_d(&t, 0) == MP_EQ) + break; + } + + s_mp_2expt(&v, k); /* v = 2^k */ + res = mp_mul(&u, &v, c); /* c = u * v */ + + CLEANUP: + mp_clear(&v); + V: + mp_clear(&u); + U: + mp_clear(&t); + + return res; + +} /* end mp_bgcd() */ + +/* }}} */ + +/* {{{ mp_lcm(a, b, c) */ + +/* We compute the least common multiple using the rule: + + ab = [a, b](a, b) + + ... by computing the product, and dividing out the gcd. + */ + +mp_err mp_lcm(mp_int *a, mp_int *b, mp_int *c) +{ + mp_int gcd, prod; + mp_err res; + + ARGCHK(a != NULL && b != NULL && c != NULL, MP_BADARG); + + /* Set up temporaries */ + if((res = mp_init(&gcd)) != MP_OKAY) + return res; + if((res = mp_init(&prod)) != MP_OKAY) + goto GCD; + + if((res = mp_mul(a, b, &prod)) != MP_OKAY) + goto CLEANUP; + if((res = mp_gcd(a, b, &gcd)) != MP_OKAY) + goto CLEANUP; + + res = mp_div(&prod, &gcd, c, NULL); + + CLEANUP: + mp_clear(&prod); + GCD: + mp_clear(&gcd); + + return res; + +} /* end mp_lcm() */ + +/* }}} */ + +/* {{{ mp_xgcd(a, b, g, x, y) */ + +/* + mp_xgcd(a, b, g, x, y) + + Compute g = (a, b) and values x and y satisfying Bezout's identity + (that is, ax + by = g). This uses the extended binary GCD algorithm + based on the Stein algorithm used for mp_gcd() + */ + +mp_err mp_xgcd(mp_int *a, mp_int *b, mp_int *g, mp_int *x, mp_int *y) +{ + mp_int gx, xc, yc, u, v, A, B, C, D; + mp_int *clean[9]; + mp_err res; + int last = -1; + + if(mp_cmp_z(b) == 0) + return MP_RANGE; + + /* Initialize all these variables we need */ + if((res = mp_init(&u)) != MP_OKAY) goto CLEANUP; + clean[++last] = &u; + if((res = mp_init(&v)) != MP_OKAY) goto CLEANUP; + clean[++last] = &v; + if((res = mp_init(&gx)) != MP_OKAY) goto CLEANUP; + clean[++last] = &gx; + if((res = mp_init(&A)) != MP_OKAY) goto CLEANUP; + clean[++last] = &A; + if((res = mp_init(&B)) != MP_OKAY) goto CLEANUP; + clean[++last] = &B; + if((res = mp_init(&C)) != MP_OKAY) goto CLEANUP; + clean[++last] = &C; + if((res = mp_init(&D)) != MP_OKAY) goto CLEANUP; + clean[++last] = &D; + if((res = mp_init_copy(&xc, a)) != MP_OKAY) goto CLEANUP; + clean[++last] = &xc; + mp_abs(&xc, &xc); + if((res = mp_init_copy(&yc, b)) != MP_OKAY) goto CLEANUP; + clean[++last] = &yc; + mp_abs(&yc, &yc); + + mp_set(&gx, 1); + + /* Divide by two until at least one of them is even */ + while(mp_iseven(&xc) && mp_iseven(&yc)) { + s_mp_div_2(&xc); + s_mp_div_2(&yc); + if((res = s_mp_mul_2(&gx)) != MP_OKAY) + goto CLEANUP; + } + + mp_copy(&xc, &u); + mp_copy(&yc, &v); + mp_set(&A, 1); mp_set(&D, 1); + + /* Loop through binary GCD algorithm */ + for(;;) { + while(mp_iseven(&u)) { + s_mp_div_2(&u); + + if(mp_iseven(&A) && mp_iseven(&B)) { + s_mp_div_2(&A); s_mp_div_2(&B); + } else { + if((res = mp_add(&A, &yc, &A)) != MP_OKAY) goto CLEANUP; + s_mp_div_2(&A); + if((res = mp_sub(&B, &xc, &B)) != MP_OKAY) goto CLEANUP; + s_mp_div_2(&B); + } + } + + while(mp_iseven(&v)) { + s_mp_div_2(&v); + + if(mp_iseven(&C) && mp_iseven(&D)) { + s_mp_div_2(&C); s_mp_div_2(&D); + } else { + if((res = mp_add(&C, &yc, &C)) != MP_OKAY) goto CLEANUP; + s_mp_div_2(&C); + if((res = mp_sub(&D, &xc, &D)) != MP_OKAY) goto CLEANUP; + s_mp_div_2(&D); + } + } + + if(mp_cmp(&u, &v) >= 0) { + if((res = mp_sub(&u, &v, &u)) != MP_OKAY) goto CLEANUP; + if((res = mp_sub(&A, &C, &A)) != MP_OKAY) goto CLEANUP; + if((res = mp_sub(&B, &D, &B)) != MP_OKAY) goto CLEANUP; + + } else { + if((res = mp_sub(&v, &u, &v)) != MP_OKAY) goto CLEANUP; + if((res = mp_sub(&C, &A, &C)) != MP_OKAY) goto CLEANUP; + if((res = mp_sub(&D, &B, &D)) != MP_OKAY) goto CLEANUP; + + } + + /* If we're done, copy results to output */ + if(mp_cmp_z(&u) == 0) { + if(x) + if((res = mp_copy(&C, x)) != MP_OKAY) goto CLEANUP; + + if(y) + if((res = mp_copy(&D, y)) != MP_OKAY) goto CLEANUP; + + if(g) + if((res = mp_mul(&gx, &v, g)) != MP_OKAY) goto CLEANUP; + + break; + } + } + + CLEANUP: + while(last >= 0) + mp_clear(clean[last--]); + + return res; + +} /* end mp_xgcd() */ + +/* }}} */ + +/* {{{ mp_invmod(a, m, c) */ + +/* + mp_invmod(a, m, c) + + Compute c = a^-1 (mod m), if there is an inverse for a (mod m). + This is equivalent to the question of whether (a, m) = 1. If not, + MP_UNDEF is returned, and there is no inverse. + */ + +mp_err mp_invmod(mp_int *a, mp_int *m, mp_int *c) +{ + mp_int g, x; + mp_err res; + + ARGCHK(a && m && c, MP_BADARG); + + if(mp_cmp_z(a) == 0 || mp_cmp_z(m) == 0) + return MP_RANGE; + + if((res = mp_init(&g)) != MP_OKAY) + return res; + if((res = mp_init(&x)) != MP_OKAY) + goto X; + + if((res = mp_xgcd(a, m, &g, &x, NULL)) != MP_OKAY) + goto CLEANUP; + + if(mp_cmp_d(&g, 1) != MP_EQ) { + res = MP_UNDEF; + goto CLEANUP; + } + + res = mp_mod(&x, m, c); + SIGN(c) = SIGN(a); + +CLEANUP: + mp_clear(&x); +X: + mp_clear(&g); + + return res; + +} /* end mp_invmod() */ + +/* }}} */ +#endif /* if MP_NUMTH */ + +/* }}} */ + +/*------------------------------------------------------------------------*/ +/* {{{ mp_print(mp, ofp) */ + +#if MP_IOFUNC +/* + mp_print(mp, ofp) + + Print a textual representation of the given mp_int on the output + stream 'ofp'. Output is generated using the internal radix. + */ + +void mp_print(mp_int *mp, FILE *ofp) +{ + int ix; + + if(mp == NULL || ofp == NULL) + return; + + fputc((SIGN(mp) == MP_NEG) ? '-' : '+', ofp); + + for(ix = USED(mp) - 1; ix >= 0; ix--) { + fprintf(ofp, DIGIT_FMT, DIGIT(mp, ix)); + } + +} /* end mp_print() */ + +#endif /* if MP_IOFUNC */ + +/* }}} */ + +/*------------------------------------------------------------------------*/ +/* {{{ More I/O Functions */ + +/* {{{ mp_read_signed_bin(mp, str, len) */ + +/* + mp_read_signed_bin(mp, str, len) + + Read in a raw value (base 256) into the given mp_int + */ + +mp_err mp_read_signed_bin(mp_int *mp, unsigned char *str, int len) +{ + mp_err res; + + ARGCHK(mp != NULL && str != NULL && len > 0, MP_BADARG); + + if((res = mp_read_unsigned_bin(mp, str + 1, len - 1)) == MP_OKAY) { + /* Get sign from first byte */ + if(str[0]) + SIGN(mp) = MP_NEG; + else + SIGN(mp) = MP_ZPOS; + } + + return res; + +} /* end mp_read_signed_bin() */ + +/* }}} */ + +/* {{{ mp_signed_bin_size(mp) */ + +int mp_signed_bin_size(mp_int *mp) +{ + ARGCHK(mp != NULL, 0); + + return mp_unsigned_bin_size(mp) + 1; + +} /* end mp_signed_bin_size() */ + +/* }}} */ + +/* {{{ mp_to_signed_bin(mp, str) */ + +mp_err mp_to_signed_bin(mp_int *mp, unsigned char *str) +{ + ARGCHK(mp != NULL && str != NULL, MP_BADARG); + + /* Caller responsible for allocating enough memory (use mp_raw_size(mp)) */ + str[0] = (char)SIGN(mp); + + return mp_to_unsigned_bin(mp, str + 1); + +} /* end mp_to_signed_bin() */ + +/* }}} */ + +/* {{{ mp_read_unsigned_bin(mp, str, len) */ + +/* + mp_read_unsigned_bin(mp, str, len) + + Read in an unsigned value (base 256) into the given mp_int + */ + +mp_err mp_read_unsigned_bin(mp_int *mp, unsigned char *str, int len) +{ + int ix; + mp_err res; + + ARGCHK(mp != NULL && str != NULL && len > 0, MP_BADARG); + + mp_zero(mp); + + for(ix = 0; ix < len; ix++) { + if((res = s_mp_mul_2d(mp, CHAR_BIT)) != MP_OKAY) + return res; + + if((res = mp_add_d(mp, str[ix], mp)) != MP_OKAY) + return res; + } + + return MP_OKAY; + +} /* end mp_read_unsigned_bin() */ + +/* }}} */ + +/* {{{ mp_unsigned_bin_size(mp) */ + +int mp_unsigned_bin_size(mp_int *mp) +{ + mp_digit topdig; + int count; + + ARGCHK(mp != NULL, 0); + + /* Special case for the value zero */ + if(USED(mp) == 1 && DIGIT(mp, 0) == 0) + return 1; + + count = (USED(mp) - 1) * sizeof(mp_digit); + topdig = DIGIT(mp, USED(mp) - 1); + + while(topdig != 0) { + ++count; + topdig >>= CHAR_BIT; + } + + return count; + +} /* end mp_unsigned_bin_size() */ + +/* }}} */ + +/* {{{ mp_to_unsigned_bin(mp, str) */ + +mp_err mp_to_unsigned_bin(mp_int *mp, unsigned char *str) +{ + mp_digit *dp, *end, d; + unsigned char *spos; + + ARGCHK(mp != NULL && str != NULL, MP_BADARG); + + dp = DIGITS(mp); + end = dp + USED(mp) - 1; + spos = str; + + /* Special case for zero, quick test */ + if(dp == end && *dp == 0) { + *str = '\0'; + return MP_OKAY; + } + + /* Generate digits in reverse order */ + while(dp < end) { + unsigned int ix; + + d = *dp; + for(ix = 0; ix < sizeof(mp_digit); ++ix) { + *spos = d & UCHAR_MAX; + d >>= CHAR_BIT; + ++spos; + } + + ++dp; + } + + /* Now handle last digit specially, high order zeroes are not written */ + d = *end; + while(d != 0) { + *spos = d & UCHAR_MAX; + d >>= CHAR_BIT; + ++spos; + } + + /* Reverse everything to get digits in the correct order */ + while(--spos > str) { + unsigned char t = *str; + *str = *spos; + *spos = t; + + ++str; + } + + return MP_OKAY; + +} /* end mp_to_unsigned_bin() */ + +/* }}} */ + +/* {{{ mp_count_bits(mp) */ + +int mp_count_bits(mp_int *mp) +{ + int len; + mp_digit d; + + ARGCHK(mp != NULL, MP_BADARG); + + len = DIGIT_BIT * (USED(mp) - 1); + d = DIGIT(mp, USED(mp) - 1); + + while(d != 0) { + ++len; + d >>= 1; + } + + return len; + +} /* end mp_count_bits() */ + +/* }}} */ + +/* {{{ mp_read_radix(mp, str, radix) */ + +/* + mp_read_radix(mp, str, radix) + + Read an integer from the given string, and set mp to the resulting + value. The input is presumed to be in base 10. Leading non-digit + characters are ignored, and the function reads until a non-digit + character or the end of the string. + */ + +mp_err mp_read_radix(mp_int *mp, unsigned char *str, int radix) +{ + int ix = 0, val = 0; + mp_err res; + mp_sign sig = MP_ZPOS; + + ARGCHK(mp != NULL && str != NULL && radix >= 2 && radix <= MAX_RADIX, + MP_BADARG); + + mp_zero(mp); + + /* Skip leading non-digit characters until a digit or '-' or '+' */ + while(str[ix] && + (s_mp_tovalue(str[ix], radix) < 0) && + str[ix] != '-' && + str[ix] != '+') { + ++ix; + } + + if(str[ix] == '-') { + sig = MP_NEG; + ++ix; + } else if(str[ix] == '+') { + sig = MP_ZPOS; /* this is the default anyway... */ + ++ix; + } + + while((val = s_mp_tovalue(str[ix], radix)) >= 0) { + if((res = s_mp_mul_d(mp, radix)) != MP_OKAY) + return res; + if((res = s_mp_add_d(mp, val)) != MP_OKAY) + return res; + ++ix; + } + + if(s_mp_cmp_d(mp, 0) == MP_EQ) + SIGN(mp) = MP_ZPOS; + else + SIGN(mp) = sig; + + return MP_OKAY; + +} /* end mp_read_radix() */ + +/* }}} */ + +/* {{{ mp_radix_size(mp, radix) */ + +int mp_radix_size(mp_int *mp, int radix) +{ + int len; + ARGCHK(mp != NULL, 0); + + len = s_mp_outlen(mp_count_bits(mp), radix) + 1; /* for NUL terminator */ + + if(mp_cmp_z(mp) < 0) + ++len; /* for sign */ + + return len; + +} /* end mp_radix_size() */ + +/* }}} */ + +/* {{{ mp_value_radix_size(num, qty, radix) */ + +/* num = number of digits + qty = number of bits per digit + radix = target base + + Return the number of digits in the specified radix that would be + needed to express 'num' digits of 'qty' bits each. + */ +int mp_value_radix_size(int num, int qty, int radix) +{ + ARGCHK(num >= 0 && qty > 0 && radix >= 2 && radix <= MAX_RADIX, 0); + + return s_mp_outlen(num * qty, radix); + +} /* end mp_value_radix_size() */ + +/* }}} */ + +/* {{{ mp_toradix(mp, str, radix) */ + +mp_err mp_toradix(mp_int *mp, char *str, int radix) +{ + int ix, pos = 0; + + ARGCHK(mp != NULL && str != NULL, MP_BADARG); + ARGCHK(radix > 1 && radix <= MAX_RADIX, MP_RANGE); + + if(mp_cmp_z(mp) == MP_EQ) { + str[0] = '0'; + str[1] = '\0'; + } else { + mp_err res; + mp_int tmp; + mp_sign sgn; + mp_digit rem, rdx = (mp_digit)radix; + char ch; + + if((res = mp_init_copy(&tmp, mp)) != MP_OKAY) + return res; + + /* Save sign for later, and take absolute value */ + sgn = SIGN(&tmp); SIGN(&tmp) = MP_ZPOS; + + /* Generate output digits in reverse order */ + while(mp_cmp_z(&tmp) != 0) { + if((res = s_mp_div_d(&tmp, rdx, &rem)) != MP_OKAY) { + mp_clear(&tmp); + return res; + } + + /* Generate digits, use capital letters */ + ch = s_mp_todigit(rem, radix, 0); + + str[pos++] = ch; + } + + /* Add - sign if original value was negative */ + if(sgn == MP_NEG) + str[pos++] = '-'; + + /* Add trailing NUL to end the string */ + str[pos--] = '\0'; + + /* Reverse the digits and sign indicator */ + ix = 0; + while(ix < pos) { + char _tmp = str[ix]; + + str[ix] = str[pos]; + str[pos] = _tmp; + ++ix; + --pos; + } + + mp_clear(&tmp); + } + + return MP_OKAY; + +} /* end mp_toradix() */ + +/* }}} */ + +/* {{{ mp_char2value(ch, r) */ + +int mp_char2value(char ch, int r) +{ + return s_mp_tovalue(ch, r); + +} /* end mp_tovalue() */ + +/* }}} */ + +/* }}} */ + +/* {{{ mp_strerror(ec) */ + +/* + mp_strerror(ec) + + Return a string describing the meaning of error code 'ec'. The + string returned is allocated in static memory, so the caller should + not attempt to modify or free the memory associated with this + string. + */ +const char *mp_strerror(mp_err ec) +{ + int aec = (ec < 0) ? -ec : ec; + + /* Code values are negative, so the senses of these comparisons + are accurate */ + if(ec < MP_LAST_CODE || ec > MP_OKAY) { + return mp_err_string[0]; /* unknown error code */ + } else { + return mp_err_string[aec + 1]; + } + +} /* end mp_strerror() */ + +/* }}} */ + +/*========================================================================*/ +/*------------------------------------------------------------------------*/ +/* Static function definitions (internal use only) */ + +/* {{{ Memory management */ + +/* {{{ s_mp_grow(mp, min) */ + +/* Make sure there are at least 'min' digits allocated to mp */ +mp_err s_mp_grow(mp_int *mp, mp_size min) +{ + if(min > ALLOC(mp)) { + mp_digit *tmp; + + /* Set min to next nearest default precision block size */ + min = ((min + (s_mp_defprec - 1)) / s_mp_defprec) * s_mp_defprec; + + if((tmp = s_mp_alloc(min, sizeof(mp_digit))) == NULL) + return MP_MEM; + + s_mp_copy(DIGITS(mp), tmp, USED(mp)); + +#if MP_CRYPTO + s_mp_setz(DIGITS(mp), ALLOC(mp)); +#endif + s_mp_free(DIGITS(mp)); + DIGITS(mp) = tmp; + ALLOC(mp) = min; + } + + return MP_OKAY; + +} /* end s_mp_grow() */ + +/* }}} */ + +/* {{{ s_mp_pad(mp, min) */ + +/* Make sure the used size of mp is at least 'min', growing if needed */ +mp_err s_mp_pad(mp_int *mp, mp_size min) +{ + if(min > USED(mp)) { + mp_err res; + + /* Make sure there is room to increase precision */ + if(min > ALLOC(mp) && (res = s_mp_grow(mp, min)) != MP_OKAY) + return res; + + /* Increase precision; should already be 0-filled */ + USED(mp) = min; + } + + return MP_OKAY; + +} /* end s_mp_pad() */ + +/* }}} */ + +/* {{{ s_mp_setz(dp, count) */ + +#if MP_MACRO == 0 +/* Set 'count' digits pointed to by dp to be zeroes */ +void s_mp_setz(mp_digit *dp, mp_size count) +{ +#if MP_MEMSET == 0 + int ix; + + for(ix = 0; ix < count; ix++) + dp[ix] = 0; +#else + memset(dp, 0, count * sizeof(mp_digit)); +#endif + +} /* end s_mp_setz() */ +#endif + +/* }}} */ + +/* {{{ s_mp_copy(sp, dp, count) */ + +#if MP_MACRO == 0 +/* Copy 'count' digits from sp to dp */ +void s_mp_copy(mp_digit *sp, mp_digit *dp, mp_size count) +{ +#if MP_MEMCPY == 0 + int ix; + + for(ix = 0; ix < count; ix++) + dp[ix] = sp[ix]; +#else + memcpy(dp, sp, count * sizeof(mp_digit)); +#endif + +} /* end s_mp_copy() */ +#endif + +/* }}} */ + +/* {{{ s_mp_alloc(nb, ni) */ + +#if MP_MACRO == 0 +/* Allocate ni records of nb bytes each, and return a pointer to that */ +void *s_mp_alloc(size_t nb, size_t ni) +{ + return calloc(nb, ni); + +} /* end s_mp_alloc() */ +#endif + +/* }}} */ + +/* {{{ s_mp_free(ptr) */ + +#if MP_MACRO == 0 +/* Free the memory pointed to by ptr */ +void s_mp_free(void *ptr) +{ + if(ptr) + free(ptr); + +} /* end s_mp_free() */ +#endif + +/* }}} */ + +/* {{{ s_mp_clamp(mp) */ + +/* Remove leading zeroes from the given value */ +void s_mp_clamp(mp_int *mp) +{ + mp_size du = USED(mp); + mp_digit *zp = DIGITS(mp) + du - 1; + + while(du > 1 && !*zp--) + --du; + + USED(mp) = du; + +} /* end s_mp_clamp() */ + + +/* }}} */ + +/* {{{ s_mp_exch(a, b) */ + +/* Exchange the data for a and b; (b, a) = (a, b) */ +void s_mp_exch(mp_int *a, mp_int *b) +{ + mp_int tmp; + + tmp = *a; + *a = *b; + *b = tmp; + +} /* end s_mp_exch() */ + +/* }}} */ + +/* }}} */ + +/* {{{ Arithmetic helpers */ + +/* {{{ s_mp_lshd(mp, p) */ + +/* + Shift mp leftward by p digits, growing if needed, and zero-filling + the in-shifted digits at the right end. This is a convenient + alternative to multiplication by powers of the radix + */ + +mp_err s_mp_lshd(mp_int *mp, mp_size p) +{ + mp_err res; + mp_size pos; + mp_digit *dp; + int ix; + + if(p == 0) + return MP_OKAY; + + if((res = s_mp_pad(mp, USED(mp) + p)) != MP_OKAY) + return res; + + pos = USED(mp) - 1; + dp = DIGITS(mp); + + /* Shift all the significant figures over as needed */ + for(ix = pos - p; ix >= 0; ix--) + dp[ix + p] = dp[ix]; + + /* Fill the bottom digits with zeroes */ + for(ix = 0; (unsigned)ix < p; ix++) + dp[ix] = 0; + + return MP_OKAY; + +} /* end s_mp_lshd() */ + +/* }}} */ + +/* {{{ s_mp_rshd(mp, p) */ + +/* + Shift mp rightward by p digits. Maintains the invariant that + digits above the precision are all zero. Digits shifted off the + end are lost. Cannot fail. + */ + +void s_mp_rshd(mp_int *mp, mp_size p) +{ + mp_size ix; + mp_digit *dp; + + if(p == 0) + return; + + /* Shortcut when all digits are to be shifted off */ + if(p >= USED(mp)) { + s_mp_setz(DIGITS(mp), ALLOC(mp)); + USED(mp) = 1; + SIGN(mp) = MP_ZPOS; + return; + } + + /* Shift all the significant figures over as needed */ + dp = DIGITS(mp); + for(ix = p; ix < USED(mp); ix++) + dp[ix - p] = dp[ix]; + + /* Fill the top digits with zeroes */ + ix -= p; + while(ix < USED(mp)) + dp[ix++] = 0; + + /* Strip off any leading zeroes */ + s_mp_clamp(mp); + +} /* end s_mp_rshd() */ + +/* }}} */ + +/* {{{ s_mp_div_2(mp) */ + +/* Divide by two -- take advantage of radix properties to do it fast */ +void s_mp_div_2(mp_int *mp) +{ + s_mp_div_2d(mp, 1); + +} /* end s_mp_div_2() */ + +/* }}} */ + +/* {{{ s_mp_mul_2(mp) */ + +mp_err s_mp_mul_2(mp_int *mp) +{ + unsigned int ix; + mp_digit kin = 0, kout, *dp = DIGITS(mp); + mp_err res; + + /* Shift digits leftward by 1 bit */ + for(ix = 0; ix < USED(mp); ix++) { + kout = (dp[ix] >> (DIGIT_BIT - 1)) & 1; + dp[ix] = (dp[ix] << 1) | kin; + + kin = kout; + } + + /* Deal with rollover from last digit */ + if(kin) { + if(ix >= ALLOC(mp)) { + if((res = s_mp_grow(mp, ALLOC(mp) + 1)) != MP_OKAY) + return res; + dp = DIGITS(mp); + } + + dp[ix] = kin; + USED(mp) += 1; + } + + return MP_OKAY; + +} /* end s_mp_mul_2() */ + +/* }}} */ + +/* {{{ s_mp_mod_2d(mp, d) */ + +/* + Remainder the integer by 2^d, where d is a number of bits. This + amounts to a bitwise AND of the value, and does not require the full + division code + */ +void s_mp_mod_2d(mp_int *mp, mp_digit d) +{ + unsigned int ndig = (d / DIGIT_BIT), nbit = (d % DIGIT_BIT); + unsigned int ix; + mp_digit dmask, *dp = DIGITS(mp); + + if(ndig >= USED(mp)) + return; + + /* Flush all the bits above 2^d in its digit */ + dmask = (1 << nbit) - 1; + dp[ndig] &= dmask; + + /* Flush all digits above the one with 2^d in it */ + for(ix = ndig + 1; ix < USED(mp); ix++) + dp[ix] = 0; + + s_mp_clamp(mp); + +} /* end s_mp_mod_2d() */ + +/* }}} */ + +/* {{{ s_mp_mul_2d(mp, d) */ + +/* + Multiply by the integer 2^d, where d is a number of bits. This + amounts to a bitwise shift of the value, and does not require the + full multiplication code. + */ +mp_err s_mp_mul_2d(mp_int *mp, mp_digit d) +{ + mp_err res; + mp_digit save, next, mask, *dp; + mp_size used; + unsigned int ix; + + if((res = s_mp_lshd(mp, d / DIGIT_BIT)) != MP_OKAY) + return res; + + dp = DIGITS(mp); used = USED(mp); + d %= DIGIT_BIT; + + mask = (1 << d) - 1; + + /* If the shift requires another digit, make sure we've got one to + work with */ + if((dp[used - 1] >> (DIGIT_BIT - d)) & mask) { + if((res = s_mp_grow(mp, used + 1)) != MP_OKAY) + return res; + dp = DIGITS(mp); + } + + /* Do the shifting... */ + save = 0; + for(ix = 0; ix < used; ix++) { + next = (dp[ix] >> (DIGIT_BIT - d)) & mask; + dp[ix] = (dp[ix] << d) | save; + save = next; + } + + /* If, at this point, we have a nonzero carryout into the next + digit, we'll increase the size by one digit, and store it... + */ + if(save) { + dp[used] = save; + USED(mp) += 1; + } + + s_mp_clamp(mp); + return MP_OKAY; + +} /* end s_mp_mul_2d() */ + +/* }}} */ + +/* {{{ s_mp_div_2d(mp, d) */ + +/* + Divide the integer by 2^d, where d is a number of bits. This + amounts to a bitwise shift of the value, and does not require the + full division code (used in Barrett reduction, see below) + */ +void s_mp_div_2d(mp_int *mp, mp_digit d) +{ + int ix; + mp_digit save, next, mask, *dp = DIGITS(mp); + + s_mp_rshd(mp, d / DIGIT_BIT); + d %= DIGIT_BIT; + + mask = (1 << d) - 1; + + save = 0; + for(ix = USED(mp) - 1; ix >= 0; ix--) { + next = dp[ix] & mask; + dp[ix] = (dp[ix] >> d) | (save << (DIGIT_BIT - d)); + save = next; + } + + s_mp_clamp(mp); + +} /* end s_mp_div_2d() */ + +/* }}} */ + +/* {{{ s_mp_norm(a, b) */ + +/* + s_mp_norm(a, b) + + Normalize a and b for division, where b is the divisor. In order + that we might make good guesses for quotient digits, we want the + leading digit of b to be at least half the radix, which we + accomplish by multiplying a and b by a constant. This constant is + returned (so that it can be divided back out of the remainder at the + end of the division process). + + We multiply by the smallest power of 2 that gives us a leading digit + at least half the radix. By choosing a power of 2, we simplify the + multiplication and division steps to simple shifts. + */ +mp_digit s_mp_norm(mp_int *a, mp_int *b) +{ + mp_digit t, d = 0; + + t = DIGIT(b, USED(b) - 1); + while(t < (RADIX / 2)) { + t <<= 1; + ++d; + } + + if(d != 0) { + s_mp_mul_2d(a, d); + s_mp_mul_2d(b, d); + } + + return d; + +} /* end s_mp_norm() */ + +/* }}} */ + +/* }}} */ + +/* {{{ Primitive digit arithmetic */ + +/* {{{ s_mp_add_d(mp, d) */ + +/* Add d to |mp| in place */ +mp_err s_mp_add_d(mp_int *mp, mp_digit d) /* unsigned digit addition */ +{ + mp_word w, k = 0; + mp_size ix = 1, used = USED(mp); + mp_digit *dp = DIGITS(mp); + + w = dp[0] + d; + dp[0] = ACCUM(w); + k = CARRYOUT(w); + + while(ix < used && k) { + w = dp[ix] + k; + dp[ix] = ACCUM(w); + k = CARRYOUT(w); + ++ix; + } + + if(k != 0) { + mp_err res; + + if((res = s_mp_pad(mp, USED(mp) + 1)) != MP_OKAY) + return res; + + DIGIT(mp, ix) = k; + } + + return MP_OKAY; + +} /* end s_mp_add_d() */ + +/* }}} */ + +/* {{{ s_mp_sub_d(mp, d) */ + +/* Subtract d from |mp| in place, assumes |mp| > d */ +mp_err s_mp_sub_d(mp_int *mp, mp_digit d) /* unsigned digit subtract */ +{ + mp_word w, b = 0; + mp_size ix = 1, used = USED(mp); + mp_digit *dp = DIGITS(mp); + + /* Compute initial subtraction */ + w = (RADIX + dp[0]) - d; + b = CARRYOUT(w) ? 0 : 1; + dp[0] = ACCUM(w); + + /* Propagate borrows leftward */ + while(b && ix < used) { + w = (RADIX + dp[ix]) - b; + b = CARRYOUT(w) ? 0 : 1; + dp[ix] = ACCUM(w); + ++ix; + } + + /* Remove leading zeroes */ + s_mp_clamp(mp); + + /* If we have a borrow out, it's a violation of the input invariant */ + if(b) + return MP_RANGE; + else + return MP_OKAY; + +} /* end s_mp_sub_d() */ + +/* }}} */ + +/* {{{ s_mp_mul_d(a, d) */ + +/* Compute a = a * d, single digit multiplication */ +mp_err s_mp_mul_d(mp_int *a, mp_digit d) +{ + mp_word w, k = 0; + mp_size ix, max; + mp_err res; + mp_digit *dp = DIGITS(a); + + /* + Single-digit multiplication will increase the precision of the + output by at most one digit. However, we can detect when this + will happen -- if the high-order digit of a, times d, gives a + two-digit result, then the precision of the result will increase; + otherwise it won't. We use this fact to avoid calling s_mp_pad() + unless absolutely necessary. + */ + max = USED(a); + w = dp[max - 1] * d; + if(CARRYOUT(w) != 0) { + if((res = s_mp_pad(a, max + 1)) != MP_OKAY) + return res; + dp = DIGITS(a); + } + + for(ix = 0; ix < max; ix++) { + w = (dp[ix] * d) + k; + dp[ix] = ACCUM(w); + k = CARRYOUT(w); + } + + /* If there is a precision increase, take care of it here; the above + test guarantees we have enough storage to do this safely. + */ + if(k) { + dp[max] = k; + USED(a) = max + 1; + } + + s_mp_clamp(a); + + return MP_OKAY; + +} /* end s_mp_mul_d() */ + +/* }}} */ + +/* {{{ s_mp_div_d(mp, d, r) */ + +/* + s_mp_div_d(mp, d, r) + + Compute the quotient mp = mp / d and remainder r = mp mod d, for a + single digit d. If r is null, the remainder will be discarded. + */ + +mp_err s_mp_div_d(mp_int *mp, mp_digit d, mp_digit *r) +{ + mp_word w = 0, t; + mp_int quot; + mp_err res; + mp_digit *dp = DIGITS(mp), *qp; + int ix; + + if(d == 0) + return MP_RANGE; + + /* Make room for the quotient */ + if((res = mp_init_size(", USED(mp))) != MP_OKAY) + return res; + + USED(") = USED(mp); /* so clamping will work below */ + qp = DIGITS("); + + /* Divide without subtraction */ + for(ix = USED(mp) - 1; ix >= 0; ix--) { + w = (w << DIGIT_BIT) | dp[ix]; + + if(w >= d) { + t = w / d; + w = w % d; + } else { + t = 0; + } + + qp[ix] = t; + } + + /* Deliver the remainder, if desired */ + if(r) + *r = w; + + s_mp_clamp("); + mp_exch(", mp); + mp_clear("); + + return MP_OKAY; + +} /* end s_mp_div_d() */ + +/* }}} */ + +/* }}} */ + +/* {{{ Primitive full arithmetic */ + +/* {{{ s_mp_add(a, b) */ + +/* Compute a = |a| + |b| */ +mp_err s_mp_add(mp_int *a, mp_int *b) /* magnitude addition */ +{ + mp_word w = 0; + mp_digit *pa, *pb; + mp_size ix, used = USED(b); + mp_err res; + + /* Make sure a has enough precision for the output value */ + if((used > USED(a)) && (res = s_mp_pad(a, used)) != MP_OKAY) + return res; + + /* + Add up all digits up to the precision of b. If b had initially + the same precision as a, or greater, we took care of it by the + padding step above, so there is no problem. If b had initially + less precision, we'll have to make sure the carry out is duly + propagated upward among the higher-order digits of the sum. + */ + pa = DIGITS(a); + pb = DIGITS(b); + for(ix = 0; ix < used; ++ix) { + w += *pa + *pb++; + *pa++ = ACCUM(w); + w = CARRYOUT(w); + } + + /* If we run out of 'b' digits before we're actually done, make + sure the carries get propagated upward... + */ + used = USED(a); + while(w && ix < used) { + w += *pa; + *pa++ = ACCUM(w); + w = CARRYOUT(w); + ++ix; + } + + /* If there's an overall carry out, increase precision and include + it. We could have done this initially, but why touch the memory + allocator unless we're sure we have to? + */ + if(w) { + if((res = s_mp_pad(a, used + 1)) != MP_OKAY) + return res; + + DIGIT(a, ix) = w; /* pa may not be valid after s_mp_pad() call */ + } + + return MP_OKAY; + +} /* end s_mp_add() */ + +/* }}} */ + +/* {{{ s_mp_sub(a, b) */ + +/* Compute a = |a| - |b|, assumes |a| >= |b| */ +mp_err s_mp_sub(mp_int *a, mp_int *b) /* magnitude subtract */ +{ + mp_word w = 0; + mp_digit *pa, *pb; + mp_size ix, used = USED(b); + + /* + Subtract and propagate borrow. Up to the precision of b, this + accounts for the digits of b; after that, we just make sure the + carries get to the right place. This saves having to pad b out to + the precision of a just to make the loops work right... + */ + pa = DIGITS(a); + pb = DIGITS(b); + + for(ix = 0; ix < used; ++ix) { + w = (RADIX + *pa) - w - *pb++; + *pa++ = ACCUM(w); + w = CARRYOUT(w) ? 0 : 1; + } + + used = USED(a); + while(ix < used) { + w = RADIX + *pa - w; + *pa++ = ACCUM(w); + w = CARRYOUT(w) ? 0 : 1; + ++ix; + } + + /* Clobber any leading zeroes we created */ + s_mp_clamp(a); + + /* + If there was a borrow out, then |b| > |a| in violation + of our input invariant. We've already done the work, + but we'll at least complain about it... + */ + if(w) + return MP_RANGE; + else + return MP_OKAY; + +} /* end s_mp_sub() */ + +/* }}} */ + +mp_err s_mp_reduce(mp_int *x, mp_int *m, mp_int *mu) +{ + mp_int q; + mp_err res; + mp_size um = USED(m); + + if((res = mp_init_copy(&q, x)) != MP_OKAY) + return res; + + s_mp_rshd(&q, um - 1); /* q1 = x / b^(k-1) */ + s_mp_mul(&q, mu); /* q2 = q1 * mu */ + s_mp_rshd(&q, um + 1); /* q3 = q2 / b^(k+1) */ + + /* x = x mod b^(k+1), quick (no division) */ + s_mp_mod_2d(x, (mp_digit)(DIGIT_BIT * (um + 1))); + + /* q = q * m mod b^(k+1), quick (no division), uses the short multiplier */ +#ifndef SHRT_MUL + s_mp_mul(&q, m); + s_mp_mod_2d(&q, (mp_digit)(DIGIT_BIT * (um + 1))); +#else + s_mp_mul_dig(&q, m, um + 1); +#endif + + /* x = x - q */ + if((res = mp_sub(x, &q, x)) != MP_OKAY) + goto CLEANUP; + + /* If x < 0, add b^(k+1) to it */ + if(mp_cmp_z(x) < 0) { + mp_set(&q, 1); + if((res = s_mp_lshd(&q, um + 1)) != MP_OKAY) + goto CLEANUP; + if((res = mp_add(x, &q, x)) != MP_OKAY) + goto CLEANUP; + } + + /* Back off if it's too big */ + while(mp_cmp(x, m) >= 0) { + if((res = s_mp_sub(x, m)) != MP_OKAY) + break; + } + + CLEANUP: + mp_clear(&q); + + return res; + +} /* end s_mp_reduce() */ + + + +/* {{{ s_mp_mul(a, b) */ + +/* Compute a = |a| * |b| */ +mp_err s_mp_mul(mp_int *a, mp_int *b) +{ + mp_word w, k = 0; + mp_int tmp; + mp_err res; + mp_size ix, jx, ua = USED(a), ub = USED(b); + mp_digit *pa, *pb, *pt, *pbt; + + if((res = mp_init_size(&tmp, ua + ub)) != MP_OKAY) + return res; + + /* This has the effect of left-padding with zeroes... */ + USED(&tmp) = ua + ub; + + /* We're going to need the base value each iteration */ + pbt = DIGITS(&tmp); + + /* Outer loop: Digits of b */ + + pb = DIGITS(b); + for(ix = 0; ix < ub; ++ix, ++pb) { + if(*pb == 0) + continue; + + /* Inner product: Digits of a */ + pa = DIGITS(a); + for(jx = 0; jx < ua; ++jx, ++pa) { + pt = pbt + ix + jx; + w = *pb * *pa + k + *pt; + *pt = ACCUM(w); + k = CARRYOUT(w); + } + + pbt[ix + jx] = k; + k = 0; + } + + s_mp_clamp(&tmp); + s_mp_exch(&tmp, a); + + mp_clear(&tmp); + + return MP_OKAY; + +} /* end s_mp_mul() */ + +/* }}} */ + +/* {{{ s_mp_kmul(a, b, out, len) */ + +#if 0 +void s_mp_kmul(mp_digit *a, mp_digit *b, mp_digit *out, mp_size len) +{ + mp_word w, k = 0; + mp_size ix, jx; + mp_digit *pa, *pt; + + for(ix = 0; ix < len; ++ix, ++b) { + if(*b == 0) + continue; + + pa = a; + for(jx = 0; jx < len; ++jx, ++pa) { + pt = out + ix + jx; + w = *b * *pa + k + *pt; + *pt = ACCUM(w); + k = CARRYOUT(w); + } + + out[ix + jx] = k; + k = 0; + } + +} /* end s_mp_kmul() */ +#endif + +/* }}} */ + +/* {{{ s_mp_sqr(a) */ + +/* + Computes the square of a, in place. This can be done more + efficiently than a general multiplication, because many of the + computation steps are redundant when squaring. The inner product + step is a bit more complicated, but we save a fair number of + iterations of the multiplication loop. + */ +#if MP_SQUARE +mp_err s_mp_sqr(mp_int *a) +{ + mp_word w, k = 0; + mp_int tmp; + mp_err res; + mp_size ix, jx, kx, used = USED(a); + mp_digit *pa1, *pa2, *pt, *pbt; + + if((res = mp_init_size(&tmp, 2 * used)) != MP_OKAY) + return res; + + /* Left-pad with zeroes */ + USED(&tmp) = 2 * used; + + /* We need the base value each time through the loop */ + pbt = DIGITS(&tmp); + + pa1 = DIGITS(a); + for(ix = 0; ix < used; ++ix, ++pa1) { + if(*pa1 == 0) + continue; + + w = DIGIT(&tmp, ix + ix) + (*pa1 * *pa1); + + pbt[ix + ix] = ACCUM(w); + k = CARRYOUT(w); + + /* + The inner product is computed as: + + (C, S) = t[i,j] + 2 a[i] a[j] + C + + This can overflow what can be represented in an mp_word, and + since C arithmetic does not provide any way to check for + overflow, we have to check explicitly for overflow conditions + before they happen. + */ + for(jx = ix + 1, pa2 = DIGITS(a) + jx; jx < used; ++jx, ++pa2) { + mp_word u = 0, v; + + /* Store this in a temporary to avoid indirections later */ + pt = pbt + ix + jx; + + /* Compute the multiplicative step */ + w = *pa1 * *pa2; + + /* If w is more than half MP_WORD_MAX, the doubling will + overflow, and we need to record a carry out into the next + word */ + u = (w >> (MP_WORD_BIT - 1)) & 1; + + /* Double what we've got, overflow will be ignored as defined + for C arithmetic (we've already noted if it is to occur) + */ + w *= 2; + + /* Compute the additive step */ + v = *pt + k; + + /* If we do not already have an overflow carry, check to see + if the addition will cause one, and set the carry out if so + */ + u |= ((MP_WORD_MAX - v) < w); + + /* Add in the rest, again ignoring overflow */ + w += v; + + /* Set the i,j digit of the output */ + *pt = ACCUM(w); + + /* Save carry information for the next iteration of the loop. + This is why k must be an mp_word, instead of an mp_digit */ + k = CARRYOUT(w) | (u << DIGIT_BIT); + + } /* for(jx ...) */ + + /* Set the last digit in the cycle and reset the carry */ + k = DIGIT(&tmp, ix + jx) + k; + pbt[ix + jx] = ACCUM(k); + k = CARRYOUT(k); + + /* If we are carrying out, propagate the carry to the next digit + in the output. This may cascade, so we have to be somewhat + circumspect -- but we will have enough precision in the output + that we won't overflow + */ + kx = 1; + while(k) { + k = pbt[ix + jx + kx] + 1; + pbt[ix + jx + kx] = ACCUM(k); + k = CARRYOUT(k); + ++kx; + } + } /* for(ix ...) */ + + s_mp_clamp(&tmp); + s_mp_exch(&tmp, a); + + mp_clear(&tmp); + + return MP_OKAY; + +} /* end s_mp_sqr() */ +#endif + +/* }}} */ + +/* {{{ s_mp_div(a, b) */ + +/* + s_mp_div(a, b) + + Compute a = a / b and b = a mod b. Assumes b > a. + */ + +mp_err s_mp_div(mp_int *a, mp_int *b) +{ + mp_int quot, rem, t; + mp_word q; + mp_err res; + mp_digit d; + int ix; + + if(mp_cmp_z(b) == 0) + return MP_RANGE; + + /* Shortcut if b is power of two */ + if((ix = s_mp_ispow2(b)) >= 0) { + mp_copy(a, b); /* need this for remainder */ + s_mp_div_2d(a, (mp_digit)ix); + s_mp_mod_2d(b, (mp_digit)ix); + + return MP_OKAY; + } + + /* Allocate space to store the quotient */ + if((res = mp_init_size(", USED(a))) != MP_OKAY) + return res; + + /* A working temporary for division */ + if((res = mp_init_size(&t, USED(a))) != MP_OKAY) + goto T; + + /* Allocate space for the remainder */ + if((res = mp_init_size(&rem, USED(a))) != MP_OKAY) + goto REM; + + /* Normalize to optimize guessing */ + d = s_mp_norm(a, b); + + /* Perform the division itself...woo! */ + ix = USED(a) - 1; + + while(ix >= 0) { + /* Find a partial substring of a which is at least b */ + while(s_mp_cmp(&rem, b) < 0 && ix >= 0) { + if((res = s_mp_lshd(&rem, 1)) != MP_OKAY) + goto CLEANUP; + + if((res = s_mp_lshd(", 1)) != MP_OKAY) + goto CLEANUP; + + DIGIT(&rem, 0) = DIGIT(a, ix); + s_mp_clamp(&rem); + --ix; + } + + /* If we didn't find one, we're finished dividing */ + if(s_mp_cmp(&rem, b) < 0) + break; + + /* Compute a guess for the next quotient digit */ + q = DIGIT(&rem, USED(&rem) - 1); + if(q <= DIGIT(b, USED(b) - 1) && USED(&rem) > 1) + q = (q << DIGIT_BIT) | DIGIT(&rem, USED(&rem) - 2); + + q /= DIGIT(b, USED(b) - 1); + + /* The guess can be as much as RADIX + 1 */ + if(q >= RADIX) + q = RADIX - 1; + + /* See what that multiplies out to */ + mp_copy(b, &t); + if((res = s_mp_mul_d(&t, q)) != MP_OKAY) + goto CLEANUP; + + /* + If it's too big, back it off. We should not have to do this + more than once, or, in rare cases, twice. Knuth describes a + method by which this could be reduced to a maximum of once, but + I didn't implement that here. + */ + while(s_mp_cmp(&t, &rem) > 0) { + --q; + s_mp_sub(&t, b); + } + + /* At this point, q should be the right next digit */ + if((res = s_mp_sub(&rem, &t)) != MP_OKAY) + goto CLEANUP; + + /* + Include the digit in the quotient. We allocated enough memory + for any quotient we could ever possibly get, so we should not + have to check for failures here + */ + DIGIT(", 0) = q; + } + + /* Denormalize remainder */ + if(d != 0) + s_mp_div_2d(&rem, d); + + s_mp_clamp("); + s_mp_clamp(&rem); + + /* Copy quotient back to output */ + s_mp_exch(", a); + + /* Copy remainder back to output */ + s_mp_exch(&rem, b); + +CLEANUP: + mp_clear(&rem); +REM: + mp_clear(&t); +T: + mp_clear("); + + return res; + +} /* end s_mp_div() */ + +/* }}} */ + +/* {{{ s_mp_2expt(a, k) */ + +mp_err s_mp_2expt(mp_int *a, mp_digit k) +{ + mp_err res; + mp_size dig, bit; + + dig = k / DIGIT_BIT; + bit = k % DIGIT_BIT; + + mp_zero(a); + if((res = s_mp_pad(a, dig + 1)) != MP_OKAY) + return res; + + DIGIT(a, dig) |= (1 << bit); + + return MP_OKAY; + +} /* end s_mp_2expt() */ + +/* }}} */ + + +/* }}} */ + +/* }}} */ + +/* {{{ Primitive comparisons */ + +/* {{{ s_mp_cmp(a, b) */ + +/* Compare |a| <=> |b|, return 0 if equal, <0 if a<b, >0 if a>b */ +int s_mp_cmp(mp_int *a, mp_int *b) +{ + mp_size ua = USED(a), ub = USED(b); + + if(ua > ub) + return MP_GT; + else if(ua < ub) + return MP_LT; + else { + int ix = ua - 1; + mp_digit *ap = DIGITS(a) + ix, *bp = DIGITS(b) + ix; + + while(ix >= 0) { + if(*ap > *bp) + return MP_GT; + else if(*ap < *bp) + return MP_LT; + + --ap; --bp; --ix; + } + + return MP_EQ; + } + +} /* end s_mp_cmp() */ + +/* }}} */ + +/* {{{ s_mp_cmp_d(a, d) */ + +/* Compare |a| <=> d, return 0 if equal, <0 if a<d, >0 if a>d */ +int s_mp_cmp_d(mp_int *a, mp_digit d) +{ + mp_size ua = USED(a); + mp_digit *ap = DIGITS(a); + + if(ua > 1) + return MP_GT; + + if(*ap < d) + return MP_LT; + else if(*ap > d) + return MP_GT; + else + return MP_EQ; + +} /* end s_mp_cmp_d() */ + +/* }}} */ + +/* {{{ s_mp_ispow2(v) */ + +/* + Returns -1 if the value is not a power of two; otherwise, it returns + k such that v = 2^k, i.e. lg(v). + */ +int s_mp_ispow2(mp_int *v) +{ + mp_digit d, *dp; + mp_size uv = USED(v); + int extra = 0, ix; + + d = DIGIT(v, uv - 1); /* most significant digit of v */ + + while(d && ((d & 1) == 0)) { + d >>= 1; + ++extra; + } + + if(d == 1) { + ix = uv - 2; + dp = DIGITS(v) + ix; + + while(ix >= 0) { + if(*dp) + return -1; /* not a power of two */ + + --dp; --ix; + } + + return ((uv - 1) * DIGIT_BIT) + extra; + } + + return -1; + +} /* end s_mp_ispow2() */ + +/* }}} */ + +/* {{{ s_mp_ispow2d(d) */ + +int s_mp_ispow2d(mp_digit d) +{ + int pow = 0; + + while((d & 1) == 0) { + ++pow; d >>= 1; + } + + if(d == 1) + return pow; + + return -1; + +} /* end s_mp_ispow2d() */ + +/* }}} */ + +/* }}} */ + +/* {{{ Primitive I/O helpers */ + +/* {{{ s_mp_tovalue(ch, r) */ + +/* + Convert the given character to its digit value, in the given radix. + If the given character is not understood in the given radix, -1 is + returned. Otherwise the digit's numeric value is returned. + + The results will be odd if you use a radix < 2 or > 62, you are + expected to know what you're up to. + */ +int s_mp_tovalue(char ch, int r) +{ + int val, xch; + + if(r > 36) + xch = ch; + else + xch = toupper(ch); + + if(isdigit(xch)) + val = xch - '0'; + else if(isupper(xch)) + val = xch - 'A' + 10; + else if(islower(xch)) + val = xch - 'a' + 36; + else if(xch == '+') + val = 62; + else if(xch == '/') + val = 63; + else + return -1; + + if(val < 0 || val >= r) + return -1; + + return val; + +} /* end s_mp_tovalue() */ + +/* }}} */ + +/* {{{ s_mp_todigit(val, r, low) */ + +/* + Convert val to a radix-r digit, if possible. If val is out of range + for r, returns zero. Otherwise, returns an ASCII character denoting + the value in the given radix. + + The results may be odd if you use a radix < 2 or > 64, you are + expected to know what you're doing. + */ + +char s_mp_todigit(int val, int r, int low) +{ + char ch; + + if(val < 0 || val >= r) + return 0; + + ch = s_dmap_1[val]; + + if(r <= 36 && low) + ch = tolower(ch); + + return ch; + +} /* end s_mp_todigit() */ + +/* }}} */ + +/* {{{ s_mp_outlen(bits, radix) */ + +/* + Return an estimate for how long a string is needed to hold a radix + r representation of a number with 'bits' significant bits. + + Does not include space for a sign or a NUL terminator. + */ +int s_mp_outlen(int bits, int r) +{ + return (int)((double)bits * LOG_V_2(r)); + +} /* end s_mp_outlen() */ + +/* }}} */ + +/* }}} */ + +/*------------------------------------------------------------------------*/ +/* HERE THERE BE DRAGONS */ +/* crc==4242132123, version==2, Sat Feb 02 06:43:52 2002 */ + +/* $Source$ */ +/* $Revision$ */ +/* $Date$ */ diff --git a/lib/hcrypto/libtommath/mtest/mpi.h b/lib/hcrypto/libtommath/mtest/mpi.h new file mode 100644 index 000000000000..9a9cc410180a --- /dev/null +++ b/lib/hcrypto/libtommath/mtest/mpi.h @@ -0,0 +1,233 @@ +/* + mpi.h + + by Michael J. Fromberger <sting@linguist.dartmouth.edu> + Copyright (C) 1998 Michael J. Fromberger + + Arbitrary precision integer arithmetic library + + SPDX-License-Identifier: Unlicense + + $Id$ + */ + +#ifndef _H_MPI_ +#define _H_MPI_ + +#include "mpi-config.h" + +#define MP_LT -1 +#define MP_EQ 0 +#define MP_GT 1 + +#if MP_DEBUG +#undef MP_IOFUNC +#define MP_IOFUNC 1 +#endif + +#if MP_IOFUNC +#include <stdio.h> +#include <ctype.h> +#endif + +#include <limits.h> + +#define MP_NEG 1 +#define MP_ZPOS 0 + +/* Included for compatibility... */ +#define NEG MP_NEG +#define ZPOS MP_ZPOS + +#define MP_OKAY 0 /* no error, all is well */ +#define MP_YES 0 /* yes (boolean result) */ +#define MP_NO -1 /* no (boolean result) */ +#define MP_MEM -2 /* out of memory */ +#define MP_RANGE -3 /* argument out of range */ +#define MP_BADARG -4 /* invalid parameter */ +#define MP_UNDEF -5 /* answer is undefined */ +#define MP_LAST_CODE MP_UNDEF + +#include "mpi-types.h" + +/* Included for compatibility... */ +#define DIGIT_BIT MP_DIGIT_BIT +#define DIGIT_MAX MP_DIGIT_MAX + +/* Macros for accessing the mp_int internals */ +#define SIGN(MP) ((MP)->sign) +#define USED(MP) ((MP)->used) +#define ALLOC(MP) ((MP)->alloc) +#define DIGITS(MP) ((MP)->dp) +#define DIGIT(MP,N) (MP)->dp[(N)] + +#if MP_ARGCHK == 1 +#define ARGCHK(X,Y) {if(!(X)){return (Y);}} +#elif MP_ARGCHK == 2 +#include <assert.h> +#define ARGCHK(X,Y) assert(X) +#else +#define ARGCHK(X,Y) /* */ +#endif + +/* This defines the maximum I/O base (minimum is 2) */ +#define MAX_RADIX 64 + +typedef struct { + mp_sign sign; /* sign of this quantity */ + mp_size alloc; /* how many digits allocated */ + mp_size used; /* how many digits used */ + mp_digit *dp; /* the digits themselves */ +} mp_int; + +/*------------------------------------------------------------------------*/ +/* Default precision */ + +unsigned int mp_get_prec(void); +void mp_set_prec(unsigned int prec); + +/*------------------------------------------------------------------------*/ +/* Memory management */ + +mp_err mp_init(mp_int *mp); +mp_err mp_init_array(mp_int mp[], int count); +mp_err mp_init_size(mp_int *mp, mp_size prec); +mp_err mp_init_copy(mp_int *mp, mp_int *from); +mp_err mp_copy(mp_int *from, mp_int *to); +void mp_exch(mp_int *mp1, mp_int *mp2); +void mp_clear(mp_int *mp); +void mp_clear_array(mp_int mp[], int count); +void mp_zero(mp_int *mp); +void mp_set(mp_int *mp, mp_digit d); +mp_err mp_set_int(mp_int *mp, long z); +mp_err mp_shrink(mp_int *a); + + +/*------------------------------------------------------------------------*/ +/* Single digit arithmetic */ + +mp_err mp_add_d(mp_int *a, mp_digit d, mp_int *b); +mp_err mp_sub_d(mp_int *a, mp_digit d, mp_int *b); +mp_err mp_mul_d(mp_int *a, mp_digit d, mp_int *b); +mp_err mp_mul_2(mp_int *a, mp_int *c); +mp_err mp_div_d(mp_int *a, mp_digit d, mp_int *q, mp_digit *r); +mp_err mp_div_2(mp_int *a, mp_int *c); +mp_err mp_expt_d(mp_int *a, mp_digit d, mp_int *c); + +/*------------------------------------------------------------------------*/ +/* Sign manipulations */ + +mp_err mp_abs(mp_int *a, mp_int *b); +mp_err mp_neg(mp_int *a, mp_int *b); + +/*------------------------------------------------------------------------*/ +/* Full arithmetic */ + +mp_err mp_add(mp_int *a, mp_int *b, mp_int *c); +mp_err mp_sub(mp_int *a, mp_int *b, mp_int *c); +mp_err mp_mul(mp_int *a, mp_int *b, mp_int *c); +mp_err mp_mul_2d(mp_int *a, mp_digit d, mp_int *c); +#if MP_SQUARE +mp_err mp_sqr(mp_int *a, mp_int *b); +#else +#define mp_sqr(a, b) mp_mul(a, a, b) +#endif +mp_err mp_div(mp_int *a, mp_int *b, mp_int *q, mp_int *r); +mp_err mp_div_2d(mp_int *a, mp_digit d, mp_int *q, mp_int *r); +mp_err mp_expt(mp_int *a, mp_int *b, mp_int *c); +mp_err mp_2expt(mp_int *a, mp_digit k); +mp_err mp_sqrt(mp_int *a, mp_int *b); + +/*------------------------------------------------------------------------*/ +/* Modular arithmetic */ + +#if MP_MODARITH +mp_err mp_mod(mp_int *a, mp_int *m, mp_int *c); +mp_err mp_mod_d(mp_int *a, mp_digit d, mp_digit *c); +mp_err mp_addmod(mp_int *a, mp_int *b, mp_int *m, mp_int *c); +mp_err mp_submod(mp_int *a, mp_int *b, mp_int *m, mp_int *c); +mp_err mp_mulmod(mp_int *a, mp_int *b, mp_int *m, mp_int *c); +#if MP_SQUARE +mp_err mp_sqrmod(mp_int *a, mp_int *m, mp_int *c); +#else +#define mp_sqrmod(a, m, c) mp_mulmod(a, a, m, c) +#endif +mp_err mp_exptmod(mp_int *a, mp_int *b, mp_int *m, mp_int *c); +mp_err mp_exptmod_d(mp_int *a, mp_digit d, mp_int *m, mp_int *c); +#endif /* MP_MODARITH */ + +/*------------------------------------------------------------------------*/ +/* Comparisons */ + +int mp_cmp_z(mp_int *a); +int mp_cmp_d(mp_int *a, mp_digit d); +int mp_cmp(mp_int *a, mp_int *b); +int mp_cmp_mag(mp_int *a, mp_int *b); +int mp_cmp_int(mp_int *a, long z); +int mp_isodd(mp_int *a); +int mp_iseven(mp_int *a); + +/*------------------------------------------------------------------------*/ +/* Number theoretic */ + +#if MP_NUMTH +mp_err mp_gcd(mp_int *a, mp_int *b, mp_int *c); +mp_err mp_lcm(mp_int *a, mp_int *b, mp_int *c); +mp_err mp_xgcd(mp_int *a, mp_int *b, mp_int *g, mp_int *x, mp_int *y); +mp_err mp_invmod(mp_int *a, mp_int *m, mp_int *c); +#endif /* end MP_NUMTH */ + +/*------------------------------------------------------------------------*/ +/* Input and output */ + +#if MP_IOFUNC +void mp_print(mp_int *mp, FILE *ofp); +#endif /* end MP_IOFUNC */ + +/*------------------------------------------------------------------------*/ +/* Base conversion */ + +#define BITS 1 +#define BYTES CHAR_BIT + +mp_err mp_read_signed_bin(mp_int *mp, unsigned char *str, int len); +int mp_signed_bin_size(mp_int *mp); +mp_err mp_to_signed_bin(mp_int *mp, unsigned char *str); + +mp_err mp_read_unsigned_bin(mp_int *mp, unsigned char *str, int len); +int mp_unsigned_bin_size(mp_int *mp); +mp_err mp_to_unsigned_bin(mp_int *mp, unsigned char *str); + +int mp_count_bits(mp_int *mp); + +#if MP_COMPAT_MACROS +#define mp_read_raw(mp, str, len) mp_read_signed_bin((mp), (str), (len)) +#define mp_raw_size(mp) mp_signed_bin_size(mp) +#define mp_toraw(mp, str) mp_to_signed_bin((mp), (str)) +#define mp_read_mag(mp, str, len) mp_read_unsigned_bin((mp), (str), (len)) +#define mp_mag_size(mp) mp_unsigned_bin_size(mp) +#define mp_tomag(mp, str) mp_to_unsigned_bin((mp), (str)) +#endif + +mp_err mp_read_radix(mp_int *mp, unsigned char *str, int radix); +int mp_radix_size(mp_int *mp, int radix); +int mp_value_radix_size(int num, int qty, int radix); +mp_err mp_toradix(mp_int *mp, char *str, int radix); + +int mp_char2value(char ch, int r); + +#define mp_tobinary(M, S) mp_toradix((M), (S), 2) +#define mp_tooctal(M, S) mp_toradix((M), (S), 8) +#define mp_todecimal(M, S) mp_toradix((M), (S), 10) +#define mp_tohex(M, S) mp_toradix((M), (S), 16) + +/*------------------------------------------------------------------------*/ +/* Error strings */ + +const char *mp_strerror(mp_err ec); + +#endif /* end _H_MPI_ */ + +/* $Source$ */ +/* $Revision$ */ +/* $Date$ */ diff --git a/lib/hcrypto/libtommath/mtest/mtest.c b/lib/hcrypto/libtommath/mtest/mtest.c new file mode 100644 index 000000000000..06c9afb1ff50 --- /dev/null +++ b/lib/hcrypto/libtommath/mtest/mtest.c @@ -0,0 +1,374 @@ +/* makes a bignum test harness with NUM tests per operation + * + * the output is made in the following format [one parameter per line] + +operation +operand1 +operand2 +[... operandN] +result1 +result2 +[... resultN] + +So for example "a * b mod n" would be + +mulmod +a +b +n +a*b mod n + +e.g. if a=3, b=4 n=11 then + +mulmod +3 +4 +11 +1 + + */ + +#ifdef MP_8BIT +#define THE_MASK 127 +#else +#define THE_MASK 32767 +#endif + +#include <stdio.h> +#include <stdlib.h> +#include <time.h> +#include "mpi.c" + +#ifdef LTM_MTEST_REAL_RAND +#define getRandChar() fgetc(rng) +FILE *rng; +#else +#define getRandChar() (rand()&0xFF) +#endif + +void rand_num(mp_int *a) +{ + int size; + unsigned char buf[2048]; + size_t sz; + + size = 1 + ((getRandChar()<<8) + getRandChar()) % 101; + buf[0] = (getRandChar()&1)?1:0; +#ifdef LTM_MTEST_REAL_RAND + sz = fread(buf+1, 1, size, rng); +#else + sz = 1; + while (sz < (unsigned)size) { + buf[sz] = getRandChar(); + ++sz; + } +#endif + if (sz != (unsigned)size) { + fprintf(stderr, "\nWarning: fread failed\n\n"); + } + while (buf[1] == 0) buf[1] = getRandChar(); + mp_read_raw(a, buf, 1+size); +} + +void rand_num2(mp_int *a) +{ + int size; + unsigned char buf[2048]; + size_t sz; + + size = 10 + ((getRandChar()<<8) + getRandChar()) % 101; + buf[0] = (getRandChar()&1)?1:0; +#ifdef LTM_MTEST_REAL_RAND + sz = fread(buf+1, 1, size, rng); +#else + sz = 1; + while (sz < (unsigned)size) { + buf[sz] = getRandChar(); + ++sz; + } +#endif + if (sz != (unsigned)size) { + fprintf(stderr, "\nWarning: fread failed\n\n"); + } + while (buf[1] == 0) buf[1] = getRandChar(); + mp_read_raw(a, buf, 1+size); +} + +#define mp_to64(a, b) mp_toradix(a, b, 64) + +int main(int argc, char *argv[]) +{ + int n, tmp; + long long max; + mp_int a, b, c, d, e; +#ifdef MTEST_NO_FULLSPEED + clock_t t1; +#endif + char buf[4096]; + + mp_init(&a); + mp_init(&b); + mp_init(&c); + mp_init(&d); + mp_init(&e); + + if (argc > 1) { + max = strtol(argv[1], NULL, 0); + if (max < 0) { + if (max > -64) { + max = (1 << -(max)) + 1; + } else { + max = 1; + } + } else if (max == 0) { + max = 1; + } + } else { + max = 0; + } + + + /* initial (2^n - 1)^2 testing, makes sure the comba multiplier works [it has the new carry code] */ + /* + mp_set(&a, 1); + for (n = 1; n < 8192; n++) { + mp_mul(&a, &a, &c); + printf("mul\n"); + mp_to64(&a, buf); + printf("%s\n%s\n", buf, buf); + mp_to64(&c, buf); + printf("%s\n", buf); + + mp_add_d(&a, 1, &a); + mp_mul_2(&a, &a); + mp_sub_d(&a, 1, &a); + } + */ + +#ifdef LTM_MTEST_REAL_RAND + rng = fopen("/dev/urandom", "rb"); + if (rng == NULL) { + rng = fopen("/dev/random", "rb"); + if (rng == NULL) { + fprintf(stderr, "\nWarning: no /dev/[u]random available\n\n"); + printf("exit\n"); + return 1; + } + } +#else + srand(23); +#endif + +#ifdef MTEST_NO_FULLSPEED + t1 = clock(); +#endif + for (;;) { +#ifdef MTEST_NO_FULLSPEED + if (clock() - t1 > CLOCKS_PER_SEC) { + sleep(2); + t1 = clock(); + } +#endif + n = getRandChar() % 15; + + if (max != 0) { + --max; + if (max == 0) + n = 255; + } + + if (n == 0) { + /* add tests */ + rand_num(&a); + rand_num(&b); + mp_add(&a, &b, &c); + printf("add\n"); + mp_to64(&a, buf); + printf("%s\n", buf); + mp_to64(&b, buf); + printf("%s\n", buf); + mp_to64(&c, buf); + printf("%s\n", buf); + } else if (n == 1) { + /* sub tests */ + rand_num(&a); + rand_num(&b); + mp_sub(&a, &b, &c); + printf("sub\n"); + mp_to64(&a, buf); + printf("%s\n", buf); + mp_to64(&b, buf); + printf("%s\n", buf); + mp_to64(&c, buf); + printf("%s\n", buf); + } else if (n == 2) { + /* mul tests */ + rand_num(&a); + rand_num(&b); + mp_mul(&a, &b, &c); + printf("mul\n"); + mp_to64(&a, buf); + printf("%s\n", buf); + mp_to64(&b, buf); + printf("%s\n", buf); + mp_to64(&c, buf); + printf("%s\n", buf); + } else if (n == 3) { + /* div tests */ + rand_num(&a); + rand_num(&b); + mp_div(&a, &b, &c, &d); + printf("div\n"); + mp_to64(&a, buf); + printf("%s\n", buf); + mp_to64(&b, buf); + printf("%s\n", buf); + mp_to64(&c, buf); + printf("%s\n", buf); + mp_to64(&d, buf); + printf("%s\n", buf); + } else if (n == 4) { + /* sqr tests */ + rand_num(&a); + mp_sqr(&a, &b); + printf("sqr\n"); + mp_to64(&a, buf); + printf("%s\n", buf); + mp_to64(&b, buf); + printf("%s\n", buf); + } else if (n == 5) { + /* mul_2d test */ + rand_num(&a); + mp_copy(&a, &b); + n = getRandChar() & 63; + mp_mul_2d(&b, n, &b); + mp_to64(&a, buf); + printf("mul2d\n"); + printf("%s\n", buf); + printf("%d\n", n); + mp_to64(&b, buf); + printf("%s\n", buf); + } else if (n == 6) { + /* div_2d test */ + rand_num(&a); + mp_copy(&a, &b); + n = getRandChar() & 63; + mp_div_2d(&b, n, &b, NULL); + mp_to64(&a, buf); + printf("div2d\n"); + printf("%s\n", buf); + printf("%d\n", n); + mp_to64(&b, buf); + printf("%s\n", buf); + } else if (n == 7) { + /* gcd test */ + rand_num(&a); + rand_num(&b); + a.sign = MP_ZPOS; + b.sign = MP_ZPOS; + mp_gcd(&a, &b, &c); + printf("gcd\n"); + mp_to64(&a, buf); + printf("%s\n", buf); + mp_to64(&b, buf); + printf("%s\n", buf); + mp_to64(&c, buf); + printf("%s\n", buf); + } else if (n == 8) { + /* lcm test */ + rand_num(&a); + rand_num(&b); + a.sign = MP_ZPOS; + b.sign = MP_ZPOS; + mp_lcm(&a, &b, &c); + printf("lcm\n"); + mp_to64(&a, buf); + printf("%s\n", buf); + mp_to64(&b, buf); + printf("%s\n", buf); + mp_to64(&c, buf); + printf("%s\n", buf); + } else if (n == 9) { + /* exptmod test */ + rand_num2(&a); + rand_num2(&b); + rand_num2(&c); + /* if (c.dp[0]&1) mp_add_d(&c, 1, &c); */ + a.sign = b.sign = c.sign = 0; + mp_exptmod(&a, &b, &c, &d); + printf("expt\n"); + mp_to64(&a, buf); + printf("%s\n", buf); + mp_to64(&b, buf); + printf("%s\n", buf); + mp_to64(&c, buf); + printf("%s\n", buf); + mp_to64(&d, buf); + printf("%s\n", buf); + } else if (n == 10) { + /* invmod test */ + do { + rand_num2(&a); + rand_num2(&b); + b.sign = MP_ZPOS; + a.sign = MP_ZPOS; + mp_gcd(&a, &b, &c); + } while (mp_cmp_d(&c, 1) != 0 || mp_cmp_d(&b, 1) == 0); + mp_invmod(&a, &b, &c); + printf("invmod\n"); + mp_to64(&a, buf); + printf("%s\n", buf); + mp_to64(&b, buf); + printf("%s\n", buf); + mp_to64(&c, buf); + printf("%s\n", buf); + } else if (n == 11) { + rand_num(&a); + mp_mul_2(&a, &a); + mp_div_2(&a, &b); + printf("div2\n"); + mp_to64(&a, buf); + printf("%s\n", buf); + mp_to64(&b, buf); + printf("%s\n", buf); + } else if (n == 12) { + rand_num2(&a); + mp_mul_2(&a, &b); + printf("mul2\n"); + mp_to64(&a, buf); + printf("%s\n", buf); + mp_to64(&b, buf); + printf("%s\n", buf); + } else if (n == 13) { + rand_num2(&a); + tmp = abs(rand()) & THE_MASK; + mp_add_d(&a, tmp, &b); + printf("add_d\n"); + mp_to64(&a, buf); + printf("%s\n%d\n", buf, tmp); + mp_to64(&b, buf); + printf("%s\n", buf); + } else if (n == 14) { + rand_num2(&a); + tmp = abs(rand()) & THE_MASK; + mp_sub_d(&a, tmp, &b); + printf("sub_d\n"); + mp_to64(&a, buf); + printf("%s\n%d\n", buf, tmp); + mp_to64(&b, buf); + printf("%s\n", buf); + } else if (n == 255) { + printf("exit\n"); + break; + } + + } +#ifdef LTM_MTEST_REAL_RAND + fclose(rng); +#endif + return 0; +} + +/* $Source$ */ +/* $Revision$ */ +/* $Date$ */ diff --git a/lib/hcrypto/libtommath/pre_gen/mpi.c b/lib/hcrypto/libtommath/pre_gen/mpi.c new file mode 100644 index 000000000000..96f001d1fe51 --- /dev/null +++ b/lib/hcrypto/libtommath/pre_gen/mpi.c @@ -0,0 +1,9541 @@ +/* Start: bn_cutoffs.c */ +#include "tommath_private.h" +#ifdef BN_CUTOFFS_C +/* LibTomMath, multiple-precision integer library -- Tom St Denis */ +/* SPDX-License-Identifier: Unlicense */ + +#ifndef MP_FIXED_CUTOFFS +#include "tommath_cutoffs.h" +int KARATSUBA_MUL_CUTOFF = MP_DEFAULT_KARATSUBA_MUL_CUTOFF, + KARATSUBA_SQR_CUTOFF = MP_DEFAULT_KARATSUBA_SQR_CUTOFF, + TOOM_MUL_CUTOFF = MP_DEFAULT_TOOM_MUL_CUTOFF, + TOOM_SQR_CUTOFF = MP_DEFAULT_TOOM_SQR_CUTOFF; +#endif + +#endif + +/* End: bn_cutoffs.c */ + +/* Start: bn_deprecated.c */ +#include "tommath_private.h" +#ifdef BN_DEPRECATED_C +/* LibTomMath, multiple-precision integer library -- Tom St Denis */ +/* SPDX-License-Identifier: Unlicense */ + +#ifdef BN_MP_GET_BIT_C +int mp_get_bit(const mp_int *a, int b) +{ + if (b < 0) { + return MP_VAL; + } + return (s_mp_get_bit(a, (unsigned int)b) == MP_YES) ? MP_YES : MP_NO; +} +#endif +#ifdef BN_MP_JACOBI_C +mp_err mp_jacobi(const mp_int *a, const mp_int *n, int *c) +{ + if (a->sign == MP_NEG) { + return MP_VAL; + } + if (mp_cmp_d(n, 0uL) != MP_GT) { + return MP_VAL; + } + return mp_kronecker(a, n, c); +} +#endif +#ifdef BN_MP_PRIME_RANDOM_EX_C +mp_err mp_prime_random_ex(mp_int *a, int t, int size, int flags, private_mp_prime_callback cb, void *dat) +{ + return s_mp_prime_random_ex(a, t, size, flags, cb, dat); +} +#endif +#ifdef BN_MP_RAND_DIGIT_C +mp_err mp_rand_digit(mp_digit *r) +{ + mp_err err = s_mp_rand_source(r, sizeof(mp_digit)); + *r &= MP_MASK; + return err; +} +#endif +#ifdef BN_FAST_MP_INVMOD_C +mp_err fast_mp_invmod(const mp_int *a, const mp_int *b, mp_int *c) +{ + return s_mp_invmod_fast(a, b, c); +} +#endif +#ifdef BN_FAST_MP_MONTGOMERY_REDUCE_C +mp_err fast_mp_montgomery_reduce(mp_int *x, const mp_int *n, mp_digit rho) +{ + return s_mp_montgomery_reduce_fast(x, n, rho); +} +#endif +#ifdef BN_FAST_S_MP_MUL_DIGS_C +mp_err fast_s_mp_mul_digs(const mp_int *a, const mp_int *b, mp_int *c, int digs) +{ + return s_mp_mul_digs_fast(a, b, c, digs); +} +#endif +#ifdef BN_FAST_S_MP_MUL_HIGH_DIGS_C +mp_err fast_s_mp_mul_high_digs(const mp_int *a, const mp_int *b, mp_int *c, int digs) +{ + return s_mp_mul_high_digs_fast(a, b, c, digs); +} +#endif +#ifdef BN_FAST_S_MP_SQR_C +mp_err fast_s_mp_sqr(const mp_int *a, mp_int *b) +{ + return s_mp_sqr_fast(a, b); +} +#endif +#ifdef BN_MP_BALANCE_MUL_C +mp_err mp_balance_mul(const mp_int *a, const mp_int *b, mp_int *c) +{ + return s_mp_balance_mul(a, b, c); +} +#endif +#ifdef BN_MP_EXPTMOD_FAST_C +mp_err mp_exptmod_fast(const mp_int *G, const mp_int *X, const mp_int *P, mp_int *Y, int redmode) +{ + return s_mp_exptmod_fast(G, X, P, Y, redmode); +} +#endif +#ifdef BN_MP_INVMOD_SLOW_C +mp_err mp_invmod_slow(const mp_int *a, const mp_int *b, mp_int *c) +{ + return s_mp_invmod_slow(a, b, c); +} +#endif +#ifdef BN_MP_KARATSUBA_MUL_C +mp_err mp_karatsuba_mul(const mp_int *a, const mp_int *b, mp_int *c) +{ + return s_mp_karatsuba_mul(a, b, c); +} +#endif +#ifdef BN_MP_KARATSUBA_SQR_C +mp_err mp_karatsuba_sqr(const mp_int *a, mp_int *b) +{ + return s_mp_karatsuba_sqr(a, b); +} +#endif +#ifdef BN_MP_TOOM_MUL_C +mp_err mp_toom_mul(const mp_int *a, const mp_int *b, mp_int *c) +{ + return s_mp_toom_mul(a, b, c); +} +#endif +#ifdef BN_MP_TOOM_SQR_C +mp_err mp_toom_sqr(const mp_int *a, mp_int *b) +{ + return s_mp_toom_sqr(a, b); +} +#endif +#ifdef S_MP_REVERSE_C +void bn_reverse(unsigned char *s, int len) +{ + if (len > 0) { + s_mp_reverse(s, (size_t)len); + } +} +#endif +#ifdef BN_MP_TC_AND_C +mp_err mp_tc_and(const mp_int *a, const mp_int *b, mp_int *c) +{ + return mp_and(a, b, c); +} +#endif +#ifdef BN_MP_TC_OR_C +mp_err mp_tc_or(const mp_int *a, const mp_int *b, mp_int *c) +{ + return mp_or(a, b, c); +} +#endif +#ifdef BN_MP_TC_XOR_C +mp_err mp_tc_xor(const mp_int *a, const mp_int *b, mp_int *c) +{ + return mp_xor(a, b, c); +} +#endif +#ifdef BN_MP_TC_DIV_2D_C +mp_err mp_tc_div_2d(const mp_int *a, int b, mp_int *c) +{ + return mp_signed_rsh(a, b, c); +} +#endif +#ifdef BN_MP_INIT_SET_INT_C +mp_err mp_init_set_int(mp_int *a, unsigned long b) +{ + return mp_init_u32(a, (uint32_t)b); +} +#endif +#ifdef BN_MP_SET_INT_C +mp_err mp_set_int(mp_int *a, unsigned long b) +{ + mp_set_u32(a, (uint32_t)b); + return MP_OKAY; +} +#endif +#ifdef BN_MP_SET_LONG_C +mp_err mp_set_long(mp_int *a, unsigned long b) +{ + mp_set_u64(a, b); + return MP_OKAY; +} +#endif +#ifdef BN_MP_SET_LONG_LONG_C +mp_err mp_set_long_long(mp_int *a, unsigned long long b) +{ + mp_set_u64(a, b); + return MP_OKAY; +} +#endif +#ifdef BN_MP_GET_INT_C +unsigned long mp_get_int(const mp_int *a) +{ + return (unsigned long)mp_get_mag_u32(a); +} +#endif +#ifdef BN_MP_GET_LONG_C +unsigned long mp_get_long(const mp_int *a) +{ + return (unsigned long)mp_get_mag_ul(a); +} +#endif +#ifdef BN_MP_GET_LONG_LONG_C +unsigned long long mp_get_long_long(const mp_int *a) +{ + return mp_get_mag_ull(a); +} +#endif +#ifdef BN_MP_PRIME_IS_DIVISIBLE_C +mp_err mp_prime_is_divisible(const mp_int *a, mp_bool *result) +{ + return s_mp_prime_is_divisible(a, result); +} +#endif +#ifdef BN_MP_EXPT_D_EX_C +mp_err mp_expt_d_ex(const mp_int *a, mp_digit b, mp_int *c, int fast) +{ + (void)fast; + if (b > MP_MIN(MP_DIGIT_MAX, UINT32_MAX)) { + return MP_VAL; + } + return mp_expt_u32(a, (uint32_t)b, c); +} +#endif +#ifdef BN_MP_EXPT_D_C +mp_err mp_expt_d(const mp_int *a, mp_digit b, mp_int *c) +{ + if (b > MP_MIN(MP_DIGIT_MAX, UINT32_MAX)) { + return MP_VAL; + } + return mp_expt_u32(a, (uint32_t)b, c); +} +#endif +#ifdef BN_MP_N_ROOT_EX_C +mp_err mp_n_root_ex(const mp_int *a, mp_digit b, mp_int *c, int fast) +{ + (void)fast; + if (b > MP_MIN(MP_DIGIT_MAX, UINT32_MAX)) { + return MP_VAL; + } + return mp_root_u32(a, (uint32_t)b, c); +} +#endif +#ifdef BN_MP_N_ROOT_C +mp_err mp_n_root(const mp_int *a, mp_digit b, mp_int *c) +{ + if (b > MP_MIN(MP_DIGIT_MAX, UINT32_MAX)) { + return MP_VAL; + } + return mp_root_u32(a, (uint32_t)b, c); +} +#endif +#ifdef BN_MP_UNSIGNED_BIN_SIZE_C +int mp_unsigned_bin_size(const mp_int *a) +{ + return (int)mp_ubin_size(a); +} +#endif +#ifdef BN_MP_READ_UNSIGNED_BIN_C +mp_err mp_read_unsigned_bin(mp_int *a, const unsigned char *b, int c) +{ + return mp_from_ubin(a, b, (size_t) c); +} +#endif +#ifdef BN_MP_TO_UNSIGNED_BIN_C +mp_err mp_to_unsigned_bin(const mp_int *a, unsigned char *b) +{ + return mp_to_ubin(a, b, SIZE_MAX, NULL); +} +#endif +#ifdef BN_MP_TO_UNSIGNED_BIN_N_C +mp_err mp_to_unsigned_bin_n(const mp_int *a, unsigned char *b, unsigned long *outlen) +{ + size_t n = mp_ubin_size(a); + if (*outlen < (unsigned long)n) { + return MP_VAL; + } + *outlen = (unsigned long)n; + return mp_to_ubin(a, b, n, NULL); +} +#endif +#ifdef BN_MP_SIGNED_BIN_SIZE_C +int mp_signed_bin_size(const mp_int *a) +{ + return (int)mp_sbin_size(a); +} +#endif +#ifdef BN_MP_READ_SIGNED_BIN_C +mp_err mp_read_signed_bin(mp_int *a, const unsigned char *b, int c) +{ + return mp_from_sbin(a, b, (size_t) c); +} +#endif +#ifdef BN_MP_TO_SIGNED_BIN_C +mp_err mp_to_signed_bin(const mp_int *a, unsigned char *b) +{ + return mp_to_sbin(a, b, SIZE_MAX, NULL); +} +#endif +#ifdef BN_MP_TO_SIGNED_BIN_N_C +mp_err mp_to_signed_bin_n(const mp_int *a, unsigned char *b, unsigned long *outlen) +{ + size_t n = mp_sbin_size(a); + if (*outlen < (unsigned long)n) { + return MP_VAL; + } + *outlen = (unsigned long)n; + return mp_to_sbin(a, b, n, NULL); +} +#endif +#ifdef BN_MP_TORADIX_N_C +mp_err mp_toradix_n(const mp_int *a, char *str, int radix, int maxlen) +{ + if (maxlen < 0) { + return MP_VAL; + } + return mp_to_radix(a, str, (size_t)maxlen, NULL, radix); +} +#endif +#ifdef BN_MP_TORADIX_C +mp_err mp_toradix(const mp_int *a, char *str, int radix) +{ + return mp_to_radix(a, str, SIZE_MAX, NULL, radix); +} +#endif +#ifdef BN_MP_IMPORT_C +mp_err mp_import(mp_int *rop, size_t count, int order, size_t size, int endian, size_t nails, + const void *op) +{ + return mp_unpack(rop, count, order, size, endian, nails, op); +} +#endif +#ifdef BN_MP_EXPORT_C +mp_err mp_export(void *rop, size_t *countp, int order, size_t size, + int endian, size_t nails, const mp_int *op) +{ + return mp_pack(rop, SIZE_MAX, countp, order, size, endian, nails, op); +} +#endif +#endif + +/* End: bn_deprecated.c */ + +/* Start: bn_mp_2expt.c */ +#include "tommath_private.h" +#ifdef BN_MP_2EXPT_C +/* LibTomMath, multiple-precision integer library -- Tom St Denis */ +/* SPDX-License-Identifier: Unlicense */ + +/* computes a = 2**b + * + * Simple algorithm which zeroes the int, grows it then just sets one bit + * as required. + */ +mp_err mp_2expt(mp_int *a, int b) +{ + mp_err err; + + /* zero a as per default */ + mp_zero(a); + + /* grow a to accomodate the single bit */ + if ((err = mp_grow(a, (b / MP_DIGIT_BIT) + 1)) != MP_OKAY) { + return err; + } + + /* set the used count of where the bit will go */ + a->used = (b / MP_DIGIT_BIT) + 1; + + /* put the single bit in its place */ + a->dp[b / MP_DIGIT_BIT] = (mp_digit)1 << (mp_digit)(b % MP_DIGIT_BIT); + + return MP_OKAY; +} +#endif + +/* End: bn_mp_2expt.c */ + +/* Start: bn_mp_abs.c */ +#include "tommath_private.h" +#ifdef BN_MP_ABS_C +/* LibTomMath, multiple-precision integer library -- Tom St Denis */ +/* SPDX-License-Identifier: Unlicense */ + +/* b = |a| + * + * Simple function copies the input and fixes the sign to positive + */ +mp_err mp_abs(const mp_int *a, mp_int *b) +{ + mp_err err; + + /* copy a to b */ + if (a != b) { + if ((err = mp_copy(a, b)) != MP_OKAY) { + return err; + } + } + + /* force the sign of b to positive */ + b->sign = MP_ZPOS; + + return MP_OKAY; +} +#endif + +/* End: bn_mp_abs.c */ + +/* Start: bn_mp_add.c */ +#include "tommath_private.h" +#ifdef BN_MP_ADD_C +/* LibTomMath, multiple-precision integer library -- Tom St Denis */ +/* SPDX-License-Identifier: Unlicense */ + +/* high level addition (handles signs) */ +mp_err mp_add(const mp_int *a, const mp_int *b, mp_int *c) +{ + mp_sign sa, sb; + mp_err err; + + /* get sign of both inputs */ + sa = a->sign; + sb = b->sign; + + /* handle two cases, not four */ + if (sa == sb) { + /* both positive or both negative */ + /* add their magnitudes, copy the sign */ + c->sign = sa; + err = s_mp_add(a, b, c); + } else { + /* one positive, the other negative */ + /* subtract the one with the greater magnitude from */ + /* the one of the lesser magnitude. The result gets */ + /* the sign of the one with the greater magnitude. */ + if (mp_cmp_mag(a, b) == MP_LT) { + c->sign = sb; + err = s_mp_sub(b, a, c); + } else { + c->sign = sa; + err = s_mp_sub(a, b, c); + } + } + return err; +} + +#endif + +/* End: bn_mp_add.c */ + +/* Start: bn_mp_add_d.c */ +#include "tommath_private.h" +#ifdef BN_MP_ADD_D_C +/* LibTomMath, multiple-precision integer library -- Tom St Denis */ +/* SPDX-License-Identifier: Unlicense */ + +/* single digit addition */ +mp_err mp_add_d(const mp_int *a, mp_digit b, mp_int *c) +{ + mp_err err; + int ix, oldused; + mp_digit *tmpa, *tmpc; + + /* grow c as required */ + if (c->alloc < (a->used + 1)) { + if ((err = mp_grow(c, a->used + 1)) != MP_OKAY) { + return err; + } + } + + /* if a is negative and |a| >= b, call c = |a| - b */ + if ((a->sign == MP_NEG) && ((a->used > 1) || (a->dp[0] >= b))) { + mp_int a_ = *a; + /* temporarily fix sign of a */ + a_.sign = MP_ZPOS; + + /* c = |a| - b */ + err = mp_sub_d(&a_, b, c); + + /* fix sign */ + c->sign = MP_NEG; + + /* clamp */ + mp_clamp(c); + + return err; + } + + /* old number of used digits in c */ + oldused = c->used; + + /* source alias */ + tmpa = a->dp; + + /* destination alias */ + tmpc = c->dp; + + /* if a is positive */ + if (a->sign == MP_ZPOS) { + /* add digits, mu is carry */ + mp_digit mu = b; + for (ix = 0; ix < a->used; ix++) { + *tmpc = *tmpa++ + mu; + mu = *tmpc >> MP_DIGIT_BIT; + *tmpc++ &= MP_MASK; + } + /* set final carry */ + ix++; + *tmpc++ = mu; + + /* setup size */ + c->used = a->used + 1; + } else { + /* a was negative and |a| < b */ + c->used = 1; + + /* the result is a single digit */ + if (a->used == 1) { + *tmpc++ = b - a->dp[0]; + } else { + *tmpc++ = b; + } + + /* setup count so the clearing of oldused + * can fall through correctly + */ + ix = 1; + } + + /* sign always positive */ + c->sign = MP_ZPOS; + + /* now zero to oldused */ + MP_ZERO_DIGITS(tmpc, oldused - ix); + mp_clamp(c); + + return MP_OKAY; +} + +#endif + +/* End: bn_mp_add_d.c */ + +/* Start: bn_mp_addmod.c */ +#include "tommath_private.h" +#ifdef BN_MP_ADDMOD_C +/* LibTomMath, multiple-precision integer library -- Tom St Denis */ +/* SPDX-License-Identifier: Unlicense */ + +/* d = a + b (mod c) */ +mp_err mp_addmod(const mp_int *a, const mp_int *b, const mp_int *c, mp_int *d) +{ + mp_err err; + mp_int t; + + if ((err = mp_init(&t)) != MP_OKAY) { + return err; + } + + if ((err = mp_add(a, b, &t)) != MP_OKAY) { + goto LBL_ERR; + } + err = mp_mod(&t, c, d); + +LBL_ERR: + mp_clear(&t); + return err; +} +#endif + +/* End: bn_mp_addmod.c */ + +/* Start: bn_mp_and.c */ +#include "tommath_private.h" +#ifdef BN_MP_AND_C +/* LibTomMath, multiple-precision integer library -- Tom St Denis */ +/* SPDX-License-Identifier: Unlicense */ + +/* two complement and */ +mp_err mp_and(const mp_int *a, const mp_int *b, mp_int *c) +{ + int used = MP_MAX(a->used, b->used) + 1, i; + mp_err err; + mp_digit ac = 1, bc = 1, cc = 1; + mp_sign csign = ((a->sign == MP_NEG) && (b->sign == MP_NEG)) ? MP_NEG : MP_ZPOS; + + if (c->alloc < used) { + if ((err = mp_grow(c, used)) != MP_OKAY) { + return err; + } + } + + for (i = 0; i < used; i++) { + mp_digit x, y; + + /* convert to two complement if negative */ + if (a->sign == MP_NEG) { + ac += (i >= a->used) ? MP_MASK : (~a->dp[i] & MP_MASK); + x = ac & MP_MASK; + ac >>= MP_DIGIT_BIT; + } else { + x = (i >= a->used) ? 0uL : a->dp[i]; + } + + /* convert to two complement if negative */ + if (b->sign == MP_NEG) { + bc += (i >= b->used) ? MP_MASK : (~b->dp[i] & MP_MASK); + y = bc & MP_MASK; + bc >>= MP_DIGIT_BIT; + } else { + y = (i >= b->used) ? 0uL : b->dp[i]; + } + + c->dp[i] = x & y; + + /* convert to to sign-magnitude if negative */ + if (csign == MP_NEG) { + cc += ~c->dp[i] & MP_MASK; + c->dp[i] = cc & MP_MASK; + cc >>= MP_DIGIT_BIT; + } + } + + c->used = used; + c->sign = csign; + mp_clamp(c); + return MP_OKAY; +} +#endif + +/* End: bn_mp_and.c */ + +/* Start: bn_mp_clamp.c */ +#include "tommath_private.h" +#ifdef BN_MP_CLAMP_C +/* LibTomMath, multiple-precision integer library -- Tom St Denis */ +/* SPDX-License-Identifier: Unlicense */ + +/* trim unused digits + * + * This is used to ensure that leading zero digits are + * trimed and the leading "used" digit will be non-zero + * Typically very fast. Also fixes the sign if there + * are no more leading digits + */ +void mp_clamp(mp_int *a) +{ + /* decrease used while the most significant digit is + * zero. + */ + while ((a->used > 0) && (a->dp[a->used - 1] == 0u)) { + --(a->used); + } + + /* reset the sign flag if used == 0 */ + if (a->used == 0) { + a->sign = MP_ZPOS; + } +} +#endif + +/* End: bn_mp_clamp.c */ + +/* Start: bn_mp_clear.c */ +#include "tommath_private.h" +#ifdef BN_MP_CLEAR_C +/* LibTomMath, multiple-precision integer library -- Tom St Denis */ +/* SPDX-License-Identifier: Unlicense */ + +/* clear one (frees) */ +void mp_clear(mp_int *a) +{ + /* only do anything if a hasn't been freed previously */ + if (a->dp != NULL) { + /* free ram */ + MP_FREE_DIGITS(a->dp, a->alloc); + + /* reset members to make debugging easier */ + a->dp = NULL; + a->alloc = a->used = 0; + a->sign = MP_ZPOS; + } +} +#endif + +/* End: bn_mp_clear.c */ + +/* Start: bn_mp_clear_multi.c */ +#include "tommath_private.h" +#ifdef BN_MP_CLEAR_MULTI_C +/* LibTomMath, multiple-precision integer library -- Tom St Denis */ +/* SPDX-License-Identifier: Unlicense */ + +#include <stdarg.h> + +void mp_clear_multi(mp_int *mp, ...) +{ + mp_int *next_mp = mp; + va_list args; + va_start(args, mp); + while (next_mp != NULL) { + mp_clear(next_mp); + next_mp = va_arg(args, mp_int *); + } + va_end(args); +} +#endif + +/* End: bn_mp_clear_multi.c */ + +/* Start: bn_mp_cmp.c */ +#include "tommath_private.h" +#ifdef BN_MP_CMP_C +/* LibTomMath, multiple-precision integer library -- Tom St Denis */ +/* SPDX-License-Identifier: Unlicense */ + +/* compare two ints (signed)*/ +mp_ord mp_cmp(const mp_int *a, const mp_int *b) +{ + /* compare based on sign */ + if (a->sign != b->sign) { + if (a->sign == MP_NEG) { + return MP_LT; + } else { + return MP_GT; + } + } + + /* compare digits */ + if (a->sign == MP_NEG) { + /* if negative compare opposite direction */ + return mp_cmp_mag(b, a); + } else { + return mp_cmp_mag(a, b); + } +} +#endif + +/* End: bn_mp_cmp.c */ + +/* Start: bn_mp_cmp_d.c */ +#include "tommath_private.h" +#ifdef BN_MP_CMP_D_C +/* LibTomMath, multiple-precision integer library -- Tom St Denis */ +/* SPDX-License-Identifier: Unlicense */ + +/* compare a digit */ +mp_ord mp_cmp_d(const mp_int *a, mp_digit b) +{ + /* compare based on sign */ + if (a->sign == MP_NEG) { + return MP_LT; + } + + /* compare based on magnitude */ + if (a->used > 1) { + return MP_GT; + } + + /* compare the only digit of a to b */ + if (a->dp[0] > b) { + return MP_GT; + } else if (a->dp[0] < b) { + return MP_LT; + } else { + return MP_EQ; + } +} +#endif + +/* End: bn_mp_cmp_d.c */ + +/* Start: bn_mp_cmp_mag.c */ +#include "tommath_private.h" +#ifdef BN_MP_CMP_MAG_C +/* LibTomMath, multiple-precision integer library -- Tom St Denis */ +/* SPDX-License-Identifier: Unlicense */ + +/* compare maginitude of two ints (unsigned) */ +mp_ord mp_cmp_mag(const mp_int *a, const mp_int *b) +{ + int n; + const mp_digit *tmpa, *tmpb; + + /* compare based on # of non-zero digits */ + if (a->used > b->used) { + return MP_GT; + } + + if (a->used < b->used) { + return MP_LT; + } + + /* alias for a */ + tmpa = a->dp + (a->used - 1); + + /* alias for b */ + tmpb = b->dp + (a->used - 1); + + /* compare based on digits */ + for (n = 0; n < a->used; ++n, --tmpa, --tmpb) { + if (*tmpa > *tmpb) { + return MP_GT; + } + + if (*tmpa < *tmpb) { + return MP_LT; + } + } + return MP_EQ; +} +#endif + +/* End: bn_mp_cmp_mag.c */ + +/* Start: bn_mp_cnt_lsb.c */ +#include "tommath_private.h" +#ifdef BN_MP_CNT_LSB_C +/* LibTomMath, multiple-precision integer library -- Tom St Denis */ +/* SPDX-License-Identifier: Unlicense */ + +static const int lnz[16] = { + 4, 0, 1, 0, 2, 0, 1, 0, 3, 0, 1, 0, 2, 0, 1, 0 +}; + +/* Counts the number of lsbs which are zero before the first zero bit */ +int mp_cnt_lsb(const mp_int *a) +{ + int x; + mp_digit q, qq; + + /* easy out */ + if (MP_IS_ZERO(a)) { + return 0; + } + + /* scan lower digits until non-zero */ + for (x = 0; (x < a->used) && (a->dp[x] == 0u); x++) {} + q = a->dp[x]; + x *= MP_DIGIT_BIT; + + /* now scan this digit until a 1 is found */ + if ((q & 1u) == 0u) { + do { + qq = q & 15u; + x += lnz[qq]; + q >>= 4; + } while (qq == 0u); + } + return x; +} + +#endif + +/* End: bn_mp_cnt_lsb.c */ + +/* Start: bn_mp_complement.c */ +#include "tommath_private.h" +#ifdef BN_MP_COMPLEMENT_C +/* LibTomMath, multiple-precision integer library -- Tom St Denis */ +/* SPDX-License-Identifier: Unlicense */ + +/* b = ~a */ +mp_err mp_complement(const mp_int *a, mp_int *b) +{ + mp_err err = mp_neg(a, b); + return (err == MP_OKAY) ? mp_sub_d(b, 1uL, b) : err; +} +#endif + +/* End: bn_mp_complement.c */ + +/* Start: bn_mp_copy.c */ +#include "tommath_private.h" +#ifdef BN_MP_COPY_C +/* LibTomMath, multiple-precision integer library -- Tom St Denis */ +/* SPDX-License-Identifier: Unlicense */ + +/* copy, b = a */ +mp_err mp_copy(const mp_int *a, mp_int *b) +{ + int n; + mp_digit *tmpa, *tmpb; + mp_err err; + + /* if dst == src do nothing */ + if (a == b) { + return MP_OKAY; + } + + /* grow dest */ + if (b->alloc < a->used) { + if ((err = mp_grow(b, a->used)) != MP_OKAY) { + return err; + } + } + + /* zero b and copy the parameters over */ + /* pointer aliases */ + + /* source */ + tmpa = a->dp; + + /* destination */ + tmpb = b->dp; + + /* copy all the digits */ + for (n = 0; n < a->used; n++) { + *tmpb++ = *tmpa++; + } + + /* clear high digits */ + MP_ZERO_DIGITS(tmpb, b->used - n); + + /* copy used count and sign */ + b->used = a->used; + b->sign = a->sign; + return MP_OKAY; +} +#endif + +/* End: bn_mp_copy.c */ + +/* Start: bn_mp_count_bits.c */ +#include "tommath_private.h" +#ifdef BN_MP_COUNT_BITS_C +/* LibTomMath, multiple-precision integer library -- Tom St Denis */ +/* SPDX-License-Identifier: Unlicense */ + +/* returns the number of bits in an int */ +int mp_count_bits(const mp_int *a) +{ + int r; + mp_digit q; + + /* shortcut */ + if (MP_IS_ZERO(a)) { + return 0; + } + + /* get number of digits and add that */ + r = (a->used - 1) * MP_DIGIT_BIT; + + /* take the last digit and count the bits in it */ + q = a->dp[a->used - 1]; + while (q > 0u) { + ++r; + q >>= 1u; + } + return r; +} +#endif + +/* End: bn_mp_count_bits.c */ + +/* Start: bn_mp_decr.c */ +#include "tommath_private.h" +#ifdef BN_MP_DECR_C +/* LibTomMath, multiple-precision integer library -- Tom St Denis */ +/* SPDX-License-Identifier: Unlicense */ + +/* Decrement "a" by one like "a--". Changes input! */ +mp_err mp_decr(mp_int *a) +{ + if (MP_IS_ZERO(a)) { + mp_set(a,1uL); + a->sign = MP_NEG; + return MP_OKAY; + } else if (a->sign == MP_NEG) { + mp_err err; + a->sign = MP_ZPOS; + if ((err = mp_incr(a)) != MP_OKAY) { + return err; + } + /* There is no -0 in LTM */ + if (!MP_IS_ZERO(a)) { + a->sign = MP_NEG; + } + return MP_OKAY; + } else if (a->dp[0] > 1uL) { + a->dp[0]--; + if (a->dp[0] == 0u) { + mp_zero(a); + } + return MP_OKAY; + } else { + return mp_sub_d(a, 1uL,a); + } +} +#endif + +/* End: bn_mp_decr.c */ + +/* Start: bn_mp_div.c */ +#include "tommath_private.h" +#ifdef BN_MP_DIV_C +/* LibTomMath, multiple-precision integer library -- Tom St Denis */ +/* SPDX-License-Identifier: Unlicense */ + +#ifdef BN_MP_DIV_SMALL + +/* slower bit-bang division... also smaller */ +mp_err mp_div(const mp_int *a, const mp_int *b, mp_int *c, mp_int *d) +{ + mp_int ta, tb, tq, q; + int n, n2; + mp_err err; + + /* is divisor zero ? */ + if (MP_IS_ZERO(b)) { + return MP_VAL; + } + + /* if a < b then q=0, r = a */ + if (mp_cmp_mag(a, b) == MP_LT) { + if (d != NULL) { + err = mp_copy(a, d); + } else { + err = MP_OKAY; + } + if (c != NULL) { + mp_zero(c); + } + return err; + } + + /* init our temps */ + if ((err = mp_init_multi(&ta, &tb, &tq, &q, NULL)) != MP_OKAY) { + return err; + } + + + mp_set(&tq, 1uL); + n = mp_count_bits(a) - mp_count_bits(b); + if ((err = mp_abs(a, &ta)) != MP_OKAY) goto LBL_ERR; + if ((err = mp_abs(b, &tb)) != MP_OKAY) goto LBL_ERR; + if ((err = mp_mul_2d(&tb, n, &tb)) != MP_OKAY) goto LBL_ERR; + if ((err = mp_mul_2d(&tq, n, &tq)) != MP_OKAY) goto LBL_ERR; + + while (n-- >= 0) { + if (mp_cmp(&tb, &ta) != MP_GT) { + if ((err = mp_sub(&ta, &tb, &ta)) != MP_OKAY) goto LBL_ERR; + if ((err = mp_add(&q, &tq, &q)) != MP_OKAY) goto LBL_ERR; + } + if ((err = mp_div_2d(&tb, 1, &tb, NULL)) != MP_OKAY) goto LBL_ERR; + if ((err = mp_div_2d(&tq, 1, &tq, NULL)) != MP_OKAY) goto LBL_ERR; + } + + /* now q == quotient and ta == remainder */ + n = a->sign; + n2 = (a->sign == b->sign) ? MP_ZPOS : MP_NEG; + if (c != NULL) { + mp_exch(c, &q); + c->sign = MP_IS_ZERO(c) ? MP_ZPOS : n2; + } + if (d != NULL) { + mp_exch(d, &ta); + d->sign = MP_IS_ZERO(d) ? MP_ZPOS : n; + } +LBL_ERR: + mp_clear_multi(&ta, &tb, &tq, &q, NULL); + return err; +} + +#else + +/* integer signed division. + * c*b + d == a [e.g. a/b, c=quotient, d=remainder] + * HAC pp.598 Algorithm 14.20 + * + * Note that the description in HAC is horribly + * incomplete. For example, it doesn't consider + * the case where digits are removed from 'x' in + * the inner loop. It also doesn't consider the + * case that y has fewer than three digits, etc.. + * + * The overall algorithm is as described as + * 14.20 from HAC but fixed to treat these cases. +*/ +mp_err mp_div(const mp_int *a, const mp_int *b, mp_int *c, mp_int *d) +{ + mp_int q, x, y, t1, t2; + int n, t, i, norm; + mp_sign neg; + mp_err err; + + /* is divisor zero ? */ + if (MP_IS_ZERO(b)) { + return MP_VAL; + } + + /* if a < b then q=0, r = a */ + if (mp_cmp_mag(a, b) == MP_LT) { + if (d != NULL) { + err = mp_copy(a, d); + } else { + err = MP_OKAY; + } + if (c != NULL) { + mp_zero(c); + } + return err; + } + + if ((err = mp_init_size(&q, a->used + 2)) != MP_OKAY) { + return err; + } + q.used = a->used + 2; + + if ((err = mp_init(&t1)) != MP_OKAY) goto LBL_Q; + + if ((err = mp_init(&t2)) != MP_OKAY) goto LBL_T1; + + if ((err = mp_init_copy(&x, a)) != MP_OKAY) goto LBL_T2; + + if ((err = mp_init_copy(&y, b)) != MP_OKAY) goto LBL_X; + + /* fix the sign */ + neg = (a->sign == b->sign) ? MP_ZPOS : MP_NEG; + x.sign = y.sign = MP_ZPOS; + + /* normalize both x and y, ensure that y >= b/2, [b == 2**MP_DIGIT_BIT] */ + norm = mp_count_bits(&y) % MP_DIGIT_BIT; + if (norm < (MP_DIGIT_BIT - 1)) { + norm = (MP_DIGIT_BIT - 1) - norm; + if ((err = mp_mul_2d(&x, norm, &x)) != MP_OKAY) goto LBL_Y; + if ((err = mp_mul_2d(&y, norm, &y)) != MP_OKAY) goto LBL_Y; + } else { + norm = 0; + } + + /* note hac does 0 based, so if used==5 then its 0,1,2,3,4, e.g. use 4 */ + n = x.used - 1; + t = y.used - 1; + + /* while (x >= y*b**n-t) do { q[n-t] += 1; x -= y*b**{n-t} } */ + /* y = y*b**{n-t} */ + if ((err = mp_lshd(&y, n - t)) != MP_OKAY) goto LBL_Y; + + while (mp_cmp(&x, &y) != MP_LT) { + ++(q.dp[n - t]); + if ((err = mp_sub(&x, &y, &x)) != MP_OKAY) goto LBL_Y; + } + + /* reset y by shifting it back down */ + mp_rshd(&y, n - t); + + /* step 3. for i from n down to (t + 1) */ + for (i = n; i >= (t + 1); i--) { + if (i > x.used) { + continue; + } + + /* step 3.1 if xi == yt then set q{i-t-1} to b-1, + * otherwise set q{i-t-1} to (xi*b + x{i-1})/yt */ + if (x.dp[i] == y.dp[t]) { + q.dp[(i - t) - 1] = ((mp_digit)1 << (mp_digit)MP_DIGIT_BIT) - (mp_digit)1; + } else { + mp_word tmp; + tmp = (mp_word)x.dp[i] << (mp_word)MP_DIGIT_BIT; + tmp |= (mp_word)x.dp[i - 1]; + tmp /= (mp_word)y.dp[t]; + if (tmp > (mp_word)MP_MASK) { + tmp = MP_MASK; + } + q.dp[(i - t) - 1] = (mp_digit)(tmp & (mp_word)MP_MASK); + } + + /* while (q{i-t-1} * (yt * b + y{t-1})) > + xi * b**2 + xi-1 * b + xi-2 + + do q{i-t-1} -= 1; + */ + q.dp[(i - t) - 1] = (q.dp[(i - t) - 1] + 1uL) & (mp_digit)MP_MASK; + do { + q.dp[(i - t) - 1] = (q.dp[(i - t) - 1] - 1uL) & (mp_digit)MP_MASK; + + /* find left hand */ + mp_zero(&t1); + t1.dp[0] = ((t - 1) < 0) ? 0u : y.dp[t - 1]; + t1.dp[1] = y.dp[t]; + t1.used = 2; + if ((err = mp_mul_d(&t1, q.dp[(i - t) - 1], &t1)) != MP_OKAY) goto LBL_Y; + + /* find right hand */ + t2.dp[0] = ((i - 2) < 0) ? 0u : x.dp[i - 2]; + t2.dp[1] = x.dp[i - 1]; /* i >= 1 always holds */ + t2.dp[2] = x.dp[i]; + t2.used = 3; + } while (mp_cmp_mag(&t1, &t2) == MP_GT); + + /* step 3.3 x = x - q{i-t-1} * y * b**{i-t-1} */ + if ((err = mp_mul_d(&y, q.dp[(i - t) - 1], &t1)) != MP_OKAY) goto LBL_Y; + + if ((err = mp_lshd(&t1, (i - t) - 1)) != MP_OKAY) goto LBL_Y; + + if ((err = mp_sub(&x, &t1, &x)) != MP_OKAY) goto LBL_Y; + + /* if x < 0 then { x = x + y*b**{i-t-1}; q{i-t-1} -= 1; } */ + if (x.sign == MP_NEG) { + if ((err = mp_copy(&y, &t1)) != MP_OKAY) goto LBL_Y; + if ((err = mp_lshd(&t1, (i - t) - 1)) != MP_OKAY) goto LBL_Y; + if ((err = mp_add(&x, &t1, &x)) != MP_OKAY) goto LBL_Y; + + q.dp[(i - t) - 1] = (q.dp[(i - t) - 1] - 1uL) & MP_MASK; + } + } + + /* now q is the quotient and x is the remainder + * [which we have to normalize] + */ + + /* get sign before writing to c */ + x.sign = (x.used == 0) ? MP_ZPOS : a->sign; + + if (c != NULL) { + mp_clamp(&q); + mp_exch(&q, c); + c->sign = neg; + } + + if (d != NULL) { + if ((err = mp_div_2d(&x, norm, &x, NULL)) != MP_OKAY) goto LBL_Y; + mp_exch(&x, d); + } + + err = MP_OKAY; + +LBL_Y: + mp_clear(&y); +LBL_X: + mp_clear(&x); +LBL_T2: + mp_clear(&t2); +LBL_T1: + mp_clear(&t1); +LBL_Q: + mp_clear(&q); + return err; +} + +#endif + +#endif + +/* End: bn_mp_div.c */ + +/* Start: bn_mp_div_2.c */ +#include "tommath_private.h" +#ifdef BN_MP_DIV_2_C +/* LibTomMath, multiple-precision integer library -- Tom St Denis */ +/* SPDX-License-Identifier: Unlicense */ + +/* b = a/2 */ +mp_err mp_div_2(const mp_int *a, mp_int *b) +{ + int x, oldused; + mp_digit r, rr, *tmpa, *tmpb; + mp_err err; + + /* copy */ + if (b->alloc < a->used) { + if ((err = mp_grow(b, a->used)) != MP_OKAY) { + return err; + } + } + + oldused = b->used; + b->used = a->used; + + /* source alias */ + tmpa = a->dp + b->used - 1; + + /* dest alias */ + tmpb = b->dp + b->used - 1; + + /* carry */ + r = 0; + for (x = b->used - 1; x >= 0; x--) { + /* get the carry for the next iteration */ + rr = *tmpa & 1u; + + /* shift the current digit, add in carry and store */ + *tmpb-- = (*tmpa-- >> 1) | (r << (MP_DIGIT_BIT - 1)); + + /* forward carry to next iteration */ + r = rr; + } + + /* zero excess digits */ + MP_ZERO_DIGITS(b->dp + b->used, oldused - b->used); + + b->sign = a->sign; + mp_clamp(b); + return MP_OKAY; +} +#endif + +/* End: bn_mp_div_2.c */ + +/* Start: bn_mp_div_2d.c */ +#include "tommath_private.h" +#ifdef BN_MP_DIV_2D_C +/* LibTomMath, multiple-precision integer library -- Tom St Denis */ +/* SPDX-License-Identifier: Unlicense */ + +/* shift right by a certain bit count (store quotient in c, optional remainder in d) */ +mp_err mp_div_2d(const mp_int *a, int b, mp_int *c, mp_int *d) +{ + mp_digit D, r, rr; + int x; + mp_err err; + + /* if the shift count is <= 0 then we do no work */ + if (b <= 0) { + err = mp_copy(a, c); + if (d != NULL) { + mp_zero(d); + } + return err; + } + + /* copy */ + if ((err = mp_copy(a, c)) != MP_OKAY) { + return err; + } + /* 'a' should not be used after here - it might be the same as d */ + + /* get the remainder */ + if (d != NULL) { + if ((err = mp_mod_2d(a, b, d)) != MP_OKAY) { + return err; + } + } + + /* shift by as many digits in the bit count */ + if (b >= MP_DIGIT_BIT) { + mp_rshd(c, b / MP_DIGIT_BIT); + } + + /* shift any bit count < MP_DIGIT_BIT */ + D = (mp_digit)(b % MP_DIGIT_BIT); + if (D != 0u) { + mp_digit *tmpc, mask, shift; + + /* mask */ + mask = ((mp_digit)1 << D) - 1uL; + + /* shift for lsb */ + shift = (mp_digit)MP_DIGIT_BIT - D; + + /* alias */ + tmpc = c->dp + (c->used - 1); + + /* carry */ + r = 0; + for (x = c->used - 1; x >= 0; x--) { + /* get the lower bits of this word in a temp */ + rr = *tmpc & mask; + + /* shift the current word and mix in the carry bits from the previous word */ + *tmpc = (*tmpc >> D) | (r << shift); + --tmpc; + + /* set the carry to the carry bits of the current word found above */ + r = rr; + } + } + mp_clamp(c); + return MP_OKAY; +} +#endif + +/* End: bn_mp_div_2d.c */ + +/* Start: bn_mp_div_3.c */ +#include "tommath_private.h" +#ifdef BN_MP_DIV_3_C +/* LibTomMath, multiple-precision integer library -- Tom St Denis */ +/* SPDX-License-Identifier: Unlicense */ + +/* divide by three (based on routine from MPI and the GMP manual) */ +mp_err mp_div_3(const mp_int *a, mp_int *c, mp_digit *d) +{ + mp_int q; + mp_word w, t; + mp_digit b; + mp_err err; + int ix; + + /* b = 2**MP_DIGIT_BIT / 3 */ + b = ((mp_word)1 << (mp_word)MP_DIGIT_BIT) / (mp_word)3; + + if ((err = mp_init_size(&q, a->used)) != MP_OKAY) { + return err; + } + + q.used = a->used; + q.sign = a->sign; + w = 0; + for (ix = a->used - 1; ix >= 0; ix--) { + w = (w << (mp_word)MP_DIGIT_BIT) | (mp_word)a->dp[ix]; + + if (w >= 3u) { + /* multiply w by [1/3] */ + t = (w * (mp_word)b) >> (mp_word)MP_DIGIT_BIT; + + /* now subtract 3 * [w/3] from w, to get the remainder */ + w -= t+t+t; + + /* fixup the remainder as required since + * the optimization is not exact. + */ + while (w >= 3u) { + t += 1u; + w -= 3u; + } + } else { + t = 0; + } + q.dp[ix] = (mp_digit)t; + } + + /* [optional] store the remainder */ + if (d != NULL) { + *d = (mp_digit)w; + } + + /* [optional] store the quotient */ + if (c != NULL) { + mp_clamp(&q); + mp_exch(&q, c); + } + mp_clear(&q); + + return err; +} + +#endif + +/* End: bn_mp_div_3.c */ + +/* Start: bn_mp_div_d.c */ +#include "tommath_private.h" +#ifdef BN_MP_DIV_D_C +/* LibTomMath, multiple-precision integer library -- Tom St Denis */ +/* SPDX-License-Identifier: Unlicense */ + +/* single digit division (based on routine from MPI) */ +mp_err mp_div_d(const mp_int *a, mp_digit b, mp_int *c, mp_digit *d) +{ + mp_int q; + mp_word w; + mp_digit t; + mp_err err; + int ix; + + /* cannot divide by zero */ + if (b == 0u) { + return MP_VAL; + } + + /* quick outs */ + if ((b == 1u) || MP_IS_ZERO(a)) { + if (d != NULL) { + *d = 0; + } + if (c != NULL) { + return mp_copy(a, c); + } + return MP_OKAY; + } + + /* power of two ? */ + if ((b & (b - 1u)) == 0u) { + ix = 1; + while ((ix < MP_DIGIT_BIT) && (b != (((mp_digit)1)<<ix))) { + ix++; + } + if (d != NULL) { + *d = a->dp[0] & (((mp_digit)1<<(mp_digit)ix) - 1uL); + } + if (c != NULL) { + return mp_div_2d(a, ix, c, NULL); + } + return MP_OKAY; + } + + /* three? */ + if (MP_HAS(MP_DIV_3) && (b == 3u)) { + return mp_div_3(a, c, d); + } + + /* no easy answer [c'est la vie]. Just division */ + if ((err = mp_init_size(&q, a->used)) != MP_OKAY) { + return err; + } + + q.used = a->used; + q.sign = a->sign; + w = 0; + for (ix = a->used - 1; ix >= 0; ix--) { + w = (w << (mp_word)MP_DIGIT_BIT) | (mp_word)a->dp[ix]; + + if (w >= b) { + t = (mp_digit)(w / b); + w -= (mp_word)t * (mp_word)b; + } else { + t = 0; + } + q.dp[ix] = t; + } + + if (d != NULL) { + *d = (mp_digit)w; + } + + if (c != NULL) { + mp_clamp(&q); + mp_exch(&q, c); + } + mp_clear(&q); + + return err; +} + +#endif + +/* End: bn_mp_div_d.c */ + +/* Start: bn_mp_dr_is_modulus.c */ +#include "tommath_private.h" +#ifdef BN_MP_DR_IS_MODULUS_C +/* LibTomMath, multiple-precision integer library -- Tom St Denis */ +/* SPDX-License-Identifier: Unlicense */ + +/* determines if a number is a valid DR modulus */ +mp_bool mp_dr_is_modulus(const mp_int *a) +{ + int ix; + + /* must be at least two digits */ + if (a->used < 2) { + return MP_NO; + } + + /* must be of the form b**k - a [a <= b] so all + * but the first digit must be equal to -1 (mod b). + */ + for (ix = 1; ix < a->used; ix++) { + if (a->dp[ix] != MP_MASK) { + return MP_NO; + } + } + return MP_YES; +} + +#endif + +/* End: bn_mp_dr_is_modulus.c */ + +/* Start: bn_mp_dr_reduce.c */ +#include "tommath_private.h" +#ifdef BN_MP_DR_REDUCE_C +/* LibTomMath, multiple-precision integer library -- Tom St Denis */ +/* SPDX-License-Identifier: Unlicense */ + +/* reduce "x" in place modulo "n" using the Diminished Radix algorithm. + * + * Based on algorithm from the paper + * + * "Generating Efficient Primes for Discrete Log Cryptosystems" + * Chae Hoon Lim, Pil Joong Lee, + * POSTECH Information Research Laboratories + * + * The modulus must be of a special format [see manual] + * + * Has been modified to use algorithm 7.10 from the LTM book instead + * + * Input x must be in the range 0 <= x <= (n-1)**2 + */ +mp_err mp_dr_reduce(mp_int *x, const mp_int *n, mp_digit k) +{ + mp_err err; + int i, m; + mp_word r; + mp_digit mu, *tmpx1, *tmpx2; + + /* m = digits in modulus */ + m = n->used; + + /* ensure that "x" has at least 2m digits */ + if (x->alloc < (m + m)) { + if ((err = mp_grow(x, m + m)) != MP_OKAY) { + return err; + } + } + + /* top of loop, this is where the code resumes if + * another reduction pass is required. + */ +top: + /* aliases for digits */ + /* alias for lower half of x */ + tmpx1 = x->dp; + + /* alias for upper half of x, or x/B**m */ + tmpx2 = x->dp + m; + + /* set carry to zero */ + mu = 0; + + /* compute (x mod B**m) + k * [x/B**m] inline and inplace */ + for (i = 0; i < m; i++) { + r = ((mp_word)*tmpx2++ * (mp_word)k) + *tmpx1 + mu; + *tmpx1++ = (mp_digit)(r & MP_MASK); + mu = (mp_digit)(r >> ((mp_word)MP_DIGIT_BIT)); + } + + /* set final carry */ + *tmpx1++ = mu; + + /* zero words above m */ + MP_ZERO_DIGITS(tmpx1, (x->used - m) - 1); + + /* clamp, sub and return */ + mp_clamp(x); + + /* if x >= n then subtract and reduce again + * Each successive "recursion" makes the input smaller and smaller. + */ + if (mp_cmp_mag(x, n) != MP_LT) { + if ((err = s_mp_sub(x, n, x)) != MP_OKAY) { + return err; + } + goto top; + } + return MP_OKAY; +} +#endif + +/* End: bn_mp_dr_reduce.c */ + +/* Start: bn_mp_dr_setup.c */ +#include "tommath_private.h" +#ifdef BN_MP_DR_SETUP_C +/* LibTomMath, multiple-precision integer library -- Tom St Denis */ +/* SPDX-License-Identifier: Unlicense */ + +/* determines the setup value */ +void mp_dr_setup(const mp_int *a, mp_digit *d) +{ + /* the casts are required if MP_DIGIT_BIT is one less than + * the number of bits in a mp_digit [e.g. MP_DIGIT_BIT==31] + */ + *d = (mp_digit)(((mp_word)1 << (mp_word)MP_DIGIT_BIT) - (mp_word)a->dp[0]); +} + +#endif + +/* End: bn_mp_dr_setup.c */ + +/* Start: bn_mp_error_to_string.c */ +#include "tommath_private.h" +#ifdef BN_MP_ERROR_TO_STRING_C +/* LibTomMath, multiple-precision integer library -- Tom St Denis */ +/* SPDX-License-Identifier: Unlicense */ + +/* return a char * string for a given code */ +const char *mp_error_to_string(mp_err code) +{ + switch (code) { + case MP_OKAY: + return "Successful"; + case MP_ERR: + return "Unknown error"; + case MP_MEM: + return "Out of heap"; + case MP_VAL: + return "Value out of range"; + case MP_ITER: + return "Max. iterations reached"; + case MP_BUF: + return "Buffer overflow"; + default: + return "Invalid error code"; + } +} + +#endif + +/* End: bn_mp_error_to_string.c */ + +/* Start: bn_mp_exch.c */ +#include "tommath_private.h" +#ifdef BN_MP_EXCH_C +/* LibTomMath, multiple-precision integer library -- Tom St Denis */ +/* SPDX-License-Identifier: Unlicense */ + +/* swap the elements of two integers, for cases where you can't simply swap the + * mp_int pointers around + */ +void mp_exch(mp_int *a, mp_int *b) +{ + mp_int t; + + t = *a; + *a = *b; + *b = t; +} +#endif + +/* End: bn_mp_exch.c */ + +/* Start: bn_mp_expt_u32.c */ +#include "tommath_private.h" +#ifdef BN_MP_EXPT_U32_C +/* LibTomMath, multiple-precision integer library -- Tom St Denis */ +/* SPDX-License-Identifier: Unlicense */ + +/* calculate c = a**b using a square-multiply algorithm */ +mp_err mp_expt_u32(const mp_int *a, uint32_t b, mp_int *c) +{ + mp_err err; + + mp_int g; + + if ((err = mp_init_copy(&g, a)) != MP_OKAY) { + return err; + } + + /* set initial result */ + mp_set(c, 1uL); + + while (b > 0u) { + /* if the bit is set multiply */ + if ((b & 1u) != 0u) { + if ((err = mp_mul(c, &g, c)) != MP_OKAY) { + goto LBL_ERR; + } + } + + /* square */ + if (b > 1u) { + if ((err = mp_sqr(&g, &g)) != MP_OKAY) { + goto LBL_ERR; + } + } + + /* shift to next bit */ + b >>= 1; + } + + err = MP_OKAY; + +LBL_ERR: + mp_clear(&g); + return err; +} + +#endif + +/* End: bn_mp_expt_u32.c */ + +/* Start: bn_mp_exptmod.c */ +#include "tommath_private.h" +#ifdef BN_MP_EXPTMOD_C +/* LibTomMath, multiple-precision integer library -- Tom St Denis */ +/* SPDX-License-Identifier: Unlicense */ + +/* this is a shell function that calls either the normal or Montgomery + * exptmod functions. Originally the call to the montgomery code was + * embedded in the normal function but that wasted alot of stack space + * for nothing (since 99% of the time the Montgomery code would be called) + */ +mp_err mp_exptmod(const mp_int *G, const mp_int *X, const mp_int *P, mp_int *Y) +{ + int dr; + + /* modulus P must be positive */ + if (P->sign == MP_NEG) { + return MP_VAL; + } + + /* if exponent X is negative we have to recurse */ + if (X->sign == MP_NEG) { + mp_int tmpG, tmpX; + mp_err err; + + if (!MP_HAS(MP_INVMOD)) { + return MP_VAL; + } + + if ((err = mp_init_multi(&tmpG, &tmpX, NULL)) != MP_OKAY) { + return err; + } + + /* first compute 1/G mod P */ + if ((err = mp_invmod(G, P, &tmpG)) != MP_OKAY) { + goto LBL_ERR; + } + + /* now get |X| */ + if ((err = mp_abs(X, &tmpX)) != MP_OKAY) { + goto LBL_ERR; + } + + /* and now compute (1/G)**|X| instead of G**X [X < 0] */ + err = mp_exptmod(&tmpG, &tmpX, P, Y); +LBL_ERR: + mp_clear_multi(&tmpG, &tmpX, NULL); + return err; + } + + /* modified diminished radix reduction */ + if (MP_HAS(MP_REDUCE_IS_2K_L) && MP_HAS(MP_REDUCE_2K_L) && MP_HAS(S_MP_EXPTMOD) && + (mp_reduce_is_2k_l(P) == MP_YES)) { + return s_mp_exptmod(G, X, P, Y, 1); + } + + /* is it a DR modulus? default to no */ + dr = (MP_HAS(MP_DR_IS_MODULUS) && (mp_dr_is_modulus(P) == MP_YES)) ? 1 : 0; + + /* if not, is it a unrestricted DR modulus? */ + if (MP_HAS(MP_REDUCE_IS_2K) && (dr == 0)) { + dr = (mp_reduce_is_2k(P) == MP_YES) ? 2 : 0; + } + + /* if the modulus is odd or dr != 0 use the montgomery method */ + if (MP_HAS(S_MP_EXPTMOD_FAST) && (MP_IS_ODD(P) || (dr != 0))) { + return s_mp_exptmod_fast(G, X, P, Y, dr); + } else if (MP_HAS(S_MP_EXPTMOD)) { + /* otherwise use the generic Barrett reduction technique */ + return s_mp_exptmod(G, X, P, Y, 0); + } else { + /* no exptmod for evens */ + return MP_VAL; + } +} + +#endif + +/* End: bn_mp_exptmod.c */ + +/* Start: bn_mp_exteuclid.c */ +#include "tommath_private.h" +#ifdef BN_MP_EXTEUCLID_C +/* LibTomMath, multiple-precision integer library -- Tom St Denis */ +/* SPDX-License-Identifier: Unlicense */ + +/* Extended euclidean algorithm of (a, b) produces + a*u1 + b*u2 = u3 + */ +mp_err mp_exteuclid(const mp_int *a, const mp_int *b, mp_int *U1, mp_int *U2, mp_int *U3) +{ + mp_int u1, u2, u3, v1, v2, v3, t1, t2, t3, q, tmp; + mp_err err; + + if ((err = mp_init_multi(&u1, &u2, &u3, &v1, &v2, &v3, &t1, &t2, &t3, &q, &tmp, NULL)) != MP_OKAY) { + return err; + } + + /* initialize, (u1,u2,u3) = (1,0,a) */ + mp_set(&u1, 1uL); + if ((err = mp_copy(a, &u3)) != MP_OKAY) goto LBL_ERR; + + /* initialize, (v1,v2,v3) = (0,1,b) */ + mp_set(&v2, 1uL); + if ((err = mp_copy(b, &v3)) != MP_OKAY) goto LBL_ERR; + + /* loop while v3 != 0 */ + while (!MP_IS_ZERO(&v3)) { + /* q = u3/v3 */ + if ((err = mp_div(&u3, &v3, &q, NULL)) != MP_OKAY) goto LBL_ERR; + + /* (t1,t2,t3) = (u1,u2,u3) - (v1,v2,v3)q */ + if ((err = mp_mul(&v1, &q, &tmp)) != MP_OKAY) goto LBL_ERR; + if ((err = mp_sub(&u1, &tmp, &t1)) != MP_OKAY) goto LBL_ERR; + if ((err = mp_mul(&v2, &q, &tmp)) != MP_OKAY) goto LBL_ERR; + if ((err = mp_sub(&u2, &tmp, &t2)) != MP_OKAY) goto LBL_ERR; + if ((err = mp_mul(&v3, &q, &tmp)) != MP_OKAY) goto LBL_ERR; + if ((err = mp_sub(&u3, &tmp, &t3)) != MP_OKAY) goto LBL_ERR; + + /* (u1,u2,u3) = (v1,v2,v3) */ + if ((err = mp_copy(&v1, &u1)) != MP_OKAY) goto LBL_ERR; + if ((err = mp_copy(&v2, &u2)) != MP_OKAY) goto LBL_ERR; + if ((err = mp_copy(&v3, &u3)) != MP_OKAY) goto LBL_ERR; + + /* (v1,v2,v3) = (t1,t2,t3) */ + if ((err = mp_copy(&t1, &v1)) != MP_OKAY) goto LBL_ERR; + if ((err = mp_copy(&t2, &v2)) != MP_OKAY) goto LBL_ERR; + if ((err = mp_copy(&t3, &v3)) != MP_OKAY) goto LBL_ERR; + } + + /* make sure U3 >= 0 */ + if (u3.sign == MP_NEG) { + if ((err = mp_neg(&u1, &u1)) != MP_OKAY) goto LBL_ERR; + if ((err = mp_neg(&u2, &u2)) != MP_OKAY) goto LBL_ERR; + if ((err = mp_neg(&u3, &u3)) != MP_OKAY) goto LBL_ERR; + } + + /* copy result out */ + if (U1 != NULL) { + mp_exch(U1, &u1); + } + if (U2 != NULL) { + mp_exch(U2, &u2); + } + if (U3 != NULL) { + mp_exch(U3, &u3); + } + + err = MP_OKAY; +LBL_ERR: + mp_clear_multi(&u1, &u2, &u3, &v1, &v2, &v3, &t1, &t2, &t3, &q, &tmp, NULL); + return err; +} +#endif + +/* End: bn_mp_exteuclid.c */ + +/* Start: bn_mp_fread.c */ +#include "tommath_private.h" +#ifdef BN_MP_FREAD_C +/* LibTomMath, multiple-precision integer library -- Tom St Denis */ +/* SPDX-License-Identifier: Unlicense */ + +#ifndef MP_NO_FILE +/* read a bigint from a file stream in ASCII */ +mp_err mp_fread(mp_int *a, int radix, FILE *stream) +{ + mp_err err; + mp_sign neg; + + /* if first digit is - then set negative */ + int ch = fgetc(stream); + if (ch == (int)'-') { + neg = MP_NEG; + ch = fgetc(stream); + } else { + neg = MP_ZPOS; + } + + /* no digits, return error */ + if (ch == EOF) { + return MP_ERR; + } + + /* clear a */ + mp_zero(a); + + do { + int y; + unsigned pos = (unsigned)(ch - (int)'('); + if (mp_s_rmap_reverse_sz < pos) { + break; + } + + y = (int)mp_s_rmap_reverse[pos]; + + if ((y == 0xff) || (y >= radix)) { + break; + } + + /* shift up and add */ + if ((err = mp_mul_d(a, (mp_digit)radix, a)) != MP_OKAY) { + return err; + } + if ((err = mp_add_d(a, (mp_digit)y, a)) != MP_OKAY) { + return err; + } + } while ((ch = fgetc(stream)) != EOF); + + if (a->used != 0) { + a->sign = neg; + } + + return MP_OKAY; +} +#endif + +#endif + +/* End: bn_mp_fread.c */ + +/* Start: bn_mp_from_sbin.c */ +#include "tommath_private.h" +#ifdef BN_MP_FROM_SBIN_C +/* LibTomMath, multiple-precision integer library -- Tom St Denis */ +/* SPDX-License-Identifier: Unlicense */ + +/* read signed bin, big endian, first byte is 0==positive or 1==negative */ +mp_err mp_from_sbin(mp_int *a, const unsigned char *buf, size_t size) +{ + mp_err err; + + /* read magnitude */ + if ((err = mp_from_ubin(a, buf + 1, size - 1u)) != MP_OKAY) { + return err; + } + + /* first byte is 0 for positive, non-zero for negative */ + if (buf[0] == (unsigned char)0) { + a->sign = MP_ZPOS; + } else { + a->sign = MP_NEG; + } + + return MP_OKAY; +} +#endif + +/* End: bn_mp_from_sbin.c */ + +/* Start: bn_mp_from_ubin.c */ +#include "tommath_private.h" +#ifdef BN_MP_FROM_UBIN_C +/* LibTomMath, multiple-precision integer library -- Tom St Denis */ +/* SPDX-License-Identifier: Unlicense */ + +/* reads a unsigned char array, assumes the msb is stored first [big endian] */ +mp_err mp_from_ubin(mp_int *a, const unsigned char *buf, size_t size) +{ + mp_err err; + + /* make sure there are at least two digits */ + if (a->alloc < 2) { + if ((err = mp_grow(a, 2)) != MP_OKAY) { + return err; + } + } + + /* zero the int */ + mp_zero(a); + + /* read the bytes in */ + while (size-- > 0u) { + if ((err = mp_mul_2d(a, 8, a)) != MP_OKAY) { + return err; + } + +#ifndef MP_8BIT + a->dp[0] |= *buf++; + a->used += 1; +#else + a->dp[0] = (*buf & MP_MASK); + a->dp[1] |= ((*buf++ >> 7) & 1u); + a->used += 2; +#endif + } + mp_clamp(a); + return MP_OKAY; +} +#endif + +/* End: bn_mp_from_ubin.c */ + +/* Start: bn_mp_fwrite.c */ +#include "tommath_private.h" +#ifdef BN_MP_FWRITE_C +/* LibTomMath, multiple-precision integer library -- Tom St Denis */ +/* SPDX-License-Identifier: Unlicense */ + +#ifndef MP_NO_FILE +mp_err mp_fwrite(const mp_int *a, int radix, FILE *stream) +{ + char *buf; + mp_err err; + int len; + size_t written; + + /* TODO: this function is not in this PR */ + if (MP_HAS(MP_RADIX_SIZE_OVERESTIMATE)) { + /* if ((err = mp_radix_size_overestimate(&t, base, &len)) != MP_OKAY) goto LBL_ERR; */ + } else { + if ((err = mp_radix_size(a, radix, &len)) != MP_OKAY) { + return err; + } + } + + buf = (char *) MP_MALLOC((size_t)len); + if (buf == NULL) { + return MP_MEM; + } + + if ((err = mp_to_radix(a, buf, (size_t)len, &written, radix)) != MP_OKAY) { + goto LBL_ERR; + } + + if (fwrite(buf, written, 1uL, stream) != 1uL) { + err = MP_ERR; + goto LBL_ERR; + } + err = MP_OKAY; + + +LBL_ERR: + MP_FREE_BUFFER(buf, (size_t)len); + return err; +} +#endif + +#endif + +/* End: bn_mp_fwrite.c */ + +/* Start: bn_mp_gcd.c */ +#include "tommath_private.h" +#ifdef BN_MP_GCD_C +/* LibTomMath, multiple-precision integer library -- Tom St Denis */ +/* SPDX-License-Identifier: Unlicense */ + +/* Greatest Common Divisor using the binary method */ +mp_err mp_gcd(const mp_int *a, const mp_int *b, mp_int *c) +{ + mp_int u, v; + int k, u_lsb, v_lsb; + mp_err err; + + /* either zero than gcd is the largest */ + if (MP_IS_ZERO(a)) { + return mp_abs(b, c); + } + if (MP_IS_ZERO(b)) { + return mp_abs(a, c); + } + + /* get copies of a and b we can modify */ + if ((err = mp_init_copy(&u, a)) != MP_OKAY) { + return err; + } + + if ((err = mp_init_copy(&v, b)) != MP_OKAY) { + goto LBL_U; + } + + /* must be positive for the remainder of the algorithm */ + u.sign = v.sign = MP_ZPOS; + + /* B1. Find the common power of two for u and v */ + u_lsb = mp_cnt_lsb(&u); + v_lsb = mp_cnt_lsb(&v); + k = MP_MIN(u_lsb, v_lsb); + + if (k > 0) { + /* divide the power of two out */ + if ((err = mp_div_2d(&u, k, &u, NULL)) != MP_OKAY) { + goto LBL_V; + } + + if ((err = mp_div_2d(&v, k, &v, NULL)) != MP_OKAY) { + goto LBL_V; + } + } + + /* divide any remaining factors of two out */ + if (u_lsb != k) { + if ((err = mp_div_2d(&u, u_lsb - k, &u, NULL)) != MP_OKAY) { + goto LBL_V; + } + } + + if (v_lsb != k) { + if ((err = mp_div_2d(&v, v_lsb - k, &v, NULL)) != MP_OKAY) { + goto LBL_V; + } + } + + while (!MP_IS_ZERO(&v)) { + /* make sure v is the largest */ + if (mp_cmp_mag(&u, &v) == MP_GT) { + /* swap u and v to make sure v is >= u */ + mp_exch(&u, &v); + } + + /* subtract smallest from largest */ + if ((err = s_mp_sub(&v, &u, &v)) != MP_OKAY) { + goto LBL_V; + } + + /* Divide out all factors of two */ + if ((err = mp_div_2d(&v, mp_cnt_lsb(&v), &v, NULL)) != MP_OKAY) { + goto LBL_V; + } + } + + /* multiply by 2**k which we divided out at the beginning */ + if ((err = mp_mul_2d(&u, k, c)) != MP_OKAY) { + goto LBL_V; + } + c->sign = MP_ZPOS; + err = MP_OKAY; +LBL_V: + mp_clear(&u); +LBL_U: + mp_clear(&v); + return err; +} +#endif + +/* End: bn_mp_gcd.c */ + +/* Start: bn_mp_get_double.c */ +#include "tommath_private.h" +#ifdef BN_MP_GET_DOUBLE_C +/* LibTomMath, multiple-precision integer library -- Tom St Denis */ +/* SPDX-License-Identifier: Unlicense */ + +double mp_get_double(const mp_int *a) +{ + int i; + double d = 0.0, fac = 1.0; + for (i = 0; i < MP_DIGIT_BIT; ++i) { + fac *= 2.0; + } + for (i = a->used; i --> 0;) { + d = (d * fac) + (double)a->dp[i]; + } + return (a->sign == MP_NEG) ? -d : d; +} +#endif + +/* End: bn_mp_get_double.c */ + +/* Start: bn_mp_get_i32.c */ +#include "tommath_private.h" +#ifdef BN_MP_GET_I32_C +/* LibTomMath, multiple-precision integer library -- Tom St Denis */ +/* SPDX-License-Identifier: Unlicense */ + +MP_GET_SIGNED(mp_get_i32, mp_get_mag_u32, int32_t, uint32_t) +#endif + +/* End: bn_mp_get_i32.c */ + +/* Start: bn_mp_get_i64.c */ +#include "tommath_private.h" +#ifdef BN_MP_GET_I64_C +/* LibTomMath, multiple-precision integer library -- Tom St Denis */ +/* SPDX-License-Identifier: Unlicense */ + +MP_GET_SIGNED(mp_get_i64, mp_get_mag_u64, int64_t, uint64_t) +#endif + +/* End: bn_mp_get_i64.c */ + +/* Start: bn_mp_get_l.c */ +#include "tommath_private.h" +#ifdef BN_MP_GET_L_C +/* LibTomMath, multiple-precision integer library -- Tom St Denis */ +/* SPDX-License-Identifier: Unlicense */ + +MP_GET_SIGNED(mp_get_l, mp_get_mag_ul, long, unsigned long) +#endif + +/* End: bn_mp_get_l.c */ + +/* Start: bn_mp_get_ll.c */ +#include "tommath_private.h" +#ifdef BN_MP_GET_LL_C +/* LibTomMath, multiple-precision integer library -- Tom St Denis */ +/* SPDX-License-Identifier: Unlicense */ + +MP_GET_SIGNED(mp_get_ll, mp_get_mag_ull, long long, unsigned long long) +#endif + +/* End: bn_mp_get_ll.c */ + +/* Start: bn_mp_get_mag_u32.c */ +#include "tommath_private.h" +#ifdef BN_MP_GET_MAG_U32_C +/* LibTomMath, multiple-precision integer library -- Tom St Denis */ +/* SPDX-License-Identifier: Unlicense */ + +MP_GET_MAG(mp_get_mag_u32, uint32_t) +#endif + +/* End: bn_mp_get_mag_u32.c */ + +/* Start: bn_mp_get_mag_u64.c */ +#include "tommath_private.h" +#ifdef BN_MP_GET_MAG_U64_C +/* LibTomMath, multiple-precision integer library -- Tom St Denis */ +/* SPDX-License-Identifier: Unlicense */ + +MP_GET_MAG(mp_get_mag_u64, uint64_t) +#endif + +/* End: bn_mp_get_mag_u64.c */ + +/* Start: bn_mp_get_mag_ul.c */ +#include "tommath_private.h" +#ifdef BN_MP_GET_MAG_UL_C +/* LibTomMath, multiple-precision integer library -- Tom St Denis */ +/* SPDX-License-Identifier: Unlicense */ + +MP_GET_MAG(mp_get_mag_ul, unsigned long) +#endif + +/* End: bn_mp_get_mag_ul.c */ + +/* Start: bn_mp_get_mag_ull.c */ +#include "tommath_private.h" +#ifdef BN_MP_GET_MAG_ULL_C +/* LibTomMath, multiple-precision integer library -- Tom St Denis */ +/* SPDX-License-Identifier: Unlicense */ + +MP_GET_MAG(mp_get_mag_ull, unsigned long long) +#endif + +/* End: bn_mp_get_mag_ull.c */ + +/* Start: bn_mp_grow.c */ +#include "tommath_private.h" +#ifdef BN_MP_GROW_C +/* LibTomMath, multiple-precision integer library -- Tom St Denis */ +/* SPDX-License-Identifier: Unlicense */ + +/* grow as required */ +mp_err mp_grow(mp_int *a, int size) +{ + int i; + mp_digit *tmp; + + /* if the alloc size is smaller alloc more ram */ + if (a->alloc < size) { + /* reallocate the array a->dp + * + * We store the return in a temporary variable + * in case the operation failed we don't want + * to overwrite the dp member of a. + */ + tmp = (mp_digit *) MP_REALLOC(a->dp, + (size_t)a->alloc * sizeof(mp_digit), + (size_t)size * sizeof(mp_digit)); + if (tmp == NULL) { + /* reallocation failed but "a" is still valid [can be freed] */ + return MP_MEM; + } + + /* reallocation succeeded so set a->dp */ + a->dp = tmp; + + /* zero excess digits */ + i = a->alloc; + a->alloc = size; + MP_ZERO_DIGITS(a->dp + i, a->alloc - i); + } + return MP_OKAY; +} +#endif + +/* End: bn_mp_grow.c */ + +/* Start: bn_mp_incr.c */ +#include "tommath_private.h" +#ifdef BN_MP_INCR_C +/* LibTomMath, multiple-precision integer library -- Tom St Denis */ +/* SPDX-License-Identifier: Unlicense */ + +/* Increment "a" by one like "a++". Changes input! */ +mp_err mp_incr(mp_int *a) +{ + if (MP_IS_ZERO(a)) { + mp_set(a,1uL); + return MP_OKAY; + } else if (a->sign == MP_NEG) { + mp_err err; + a->sign = MP_ZPOS; + if ((err = mp_decr(a)) != MP_OKAY) { + return err; + } + /* There is no -0 in LTM */ + if (!MP_IS_ZERO(a)) { + a->sign = MP_NEG; + } + return MP_OKAY; + } else if (a->dp[0] < MP_DIGIT_MAX) { + a->dp[0]++; + return MP_OKAY; + } else { + return mp_add_d(a, 1uL,a); + } +} +#endif + +/* End: bn_mp_incr.c */ + +/* Start: bn_mp_init.c */ +#include "tommath_private.h" +#ifdef BN_MP_INIT_C +/* LibTomMath, multiple-precision integer library -- Tom St Denis */ +/* SPDX-License-Identifier: Unlicense */ + +/* init a new mp_int */ +mp_err mp_init(mp_int *a) +{ + /* allocate memory required and clear it */ + a->dp = (mp_digit *) MP_CALLOC((size_t)MP_PREC, sizeof(mp_digit)); + if (a->dp == NULL) { + return MP_MEM; + } + + /* set the used to zero, allocated digits to the default precision + * and sign to positive */ + a->used = 0; + a->alloc = MP_PREC; + a->sign = MP_ZPOS; + + return MP_OKAY; +} +#endif + +/* End: bn_mp_init.c */ + +/* Start: bn_mp_init_copy.c */ +#include "tommath_private.h" +#ifdef BN_MP_INIT_COPY_C +/* LibTomMath, multiple-precision integer library -- Tom St Denis */ +/* SPDX-License-Identifier: Unlicense */ + +/* creates "a" then copies b into it */ +mp_err mp_init_copy(mp_int *a, const mp_int *b) +{ + mp_err err; + + if ((err = mp_init_size(a, b->used)) != MP_OKAY) { + return err; + } + + if ((err = mp_copy(b, a)) != MP_OKAY) { + mp_clear(a); + } + + return err; +} +#endif + +/* End: bn_mp_init_copy.c */ + +/* Start: bn_mp_init_i32.c */ +#include "tommath_private.h" +#ifdef BN_MP_INIT_I32_C +/* LibTomMath, multiple-precision integer library -- Tom St Denis */ +/* SPDX-License-Identifier: Unlicense */ + +MP_INIT_INT(mp_init_i32, mp_set_i32, int32_t) +#endif + +/* End: bn_mp_init_i32.c */ + +/* Start: bn_mp_init_i64.c */ +#include "tommath_private.h" +#ifdef BN_MP_INIT_I64_C +/* LibTomMath, multiple-precision integer library -- Tom St Denis */ +/* SPDX-License-Identifier: Unlicense */ + +MP_INIT_INT(mp_init_i64, mp_set_i64, int64_t) +#endif + +/* End: bn_mp_init_i64.c */ + +/* Start: bn_mp_init_l.c */ +#include "tommath_private.h" +#ifdef BN_MP_INIT_L_C +/* LibTomMath, multiple-precision integer library -- Tom St Denis */ +/* SPDX-License-Identifier: Unlicense */ + +MP_INIT_INT(mp_init_l, mp_set_l, long) +#endif + +/* End: bn_mp_init_l.c */ + +/* Start: bn_mp_init_ll.c */ +#include "tommath_private.h" +#ifdef BN_MP_INIT_LL_C +/* LibTomMath, multiple-precision integer library -- Tom St Denis */ +/* SPDX-License-Identifier: Unlicense */ + +MP_INIT_INT(mp_init_ll, mp_set_ll, long long) +#endif + +/* End: bn_mp_init_ll.c */ + +/* Start: bn_mp_init_multi.c */ +#include "tommath_private.h" +#ifdef BN_MP_INIT_MULTI_C +/* LibTomMath, multiple-precision integer library -- Tom St Denis */ +/* SPDX-License-Identifier: Unlicense */ + +#include <stdarg.h> + +mp_err mp_init_multi(mp_int *mp, ...) +{ + mp_err err = MP_OKAY; /* Assume ok until proven otherwise */ + int n = 0; /* Number of ok inits */ + mp_int *cur_arg = mp; + va_list args; + + va_start(args, mp); /* init args to next argument from caller */ + while (cur_arg != NULL) { + if (mp_init(cur_arg) != MP_OKAY) { + /* Oops - error! Back-track and mp_clear what we already + succeeded in init-ing, then return error. + */ + va_list clean_args; + + /* now start cleaning up */ + cur_arg = mp; + va_start(clean_args, mp); + while (n-- != 0) { + mp_clear(cur_arg); + cur_arg = va_arg(clean_args, mp_int *); + } + va_end(clean_args); + err = MP_MEM; + break; + } + n++; + cur_arg = va_arg(args, mp_int *); + } + va_end(args); + return err; /* Assumed ok, if error flagged above. */ +} + +#endif + +/* End: bn_mp_init_multi.c */ + +/* Start: bn_mp_init_set.c */ +#include "tommath_private.h" +#ifdef BN_MP_INIT_SET_C +/* LibTomMath, multiple-precision integer library -- Tom St Denis */ +/* SPDX-License-Identifier: Unlicense */ + +/* initialize and set a digit */ +mp_err mp_init_set(mp_int *a, mp_digit b) +{ + mp_err err; + if ((err = mp_init(a)) != MP_OKAY) { + return err; + } + mp_set(a, b); + return err; +} +#endif + +/* End: bn_mp_init_set.c */ + +/* Start: bn_mp_init_size.c */ +#include "tommath_private.h" +#ifdef BN_MP_INIT_SIZE_C +/* LibTomMath, multiple-precision integer library -- Tom St Denis */ +/* SPDX-License-Identifier: Unlicense */ + +/* init an mp_init for a given size */ +mp_err mp_init_size(mp_int *a, int size) +{ + size = MP_MAX(MP_MIN_PREC, size); + + /* alloc mem */ + a->dp = (mp_digit *) MP_CALLOC((size_t)size, sizeof(mp_digit)); + if (a->dp == NULL) { + return MP_MEM; + } + + /* set the members */ + a->used = 0; + a->alloc = size; + a->sign = MP_ZPOS; + + return MP_OKAY; +} +#endif + +/* End: bn_mp_init_size.c */ + +/* Start: bn_mp_init_u32.c */ +#include "tommath_private.h" +#ifdef BN_MP_INIT_U32_C +/* LibTomMath, multiple-precision integer library -- Tom St Denis */ +/* SPDX-License-Identifier: Unlicense */ + +MP_INIT_INT(mp_init_u32, mp_set_u32, uint32_t) +#endif + +/* End: bn_mp_init_u32.c */ + +/* Start: bn_mp_init_u64.c */ +#include "tommath_private.h" +#ifdef BN_MP_INIT_U64_C +/* LibTomMath, multiple-precision integer library -- Tom St Denis */ +/* SPDX-License-Identifier: Unlicense */ + +MP_INIT_INT(mp_init_u64, mp_set_u64, uint64_t) +#endif + +/* End: bn_mp_init_u64.c */ + +/* Start: bn_mp_init_ul.c */ +#include "tommath_private.h" +#ifdef BN_MP_INIT_UL_C +/* LibTomMath, multiple-precision integer library -- Tom St Denis */ +/* SPDX-License-Identifier: Unlicense */ + +MP_INIT_INT(mp_init_ul, mp_set_ul, unsigned long) +#endif + +/* End: bn_mp_init_ul.c */ + +/* Start: bn_mp_init_ull.c */ +#include "tommath_private.h" +#ifdef BN_MP_INIT_ULL_C +/* LibTomMath, multiple-precision integer library -- Tom St Denis */ +/* SPDX-License-Identifier: Unlicense */ + +MP_INIT_INT(mp_init_ull, mp_set_ull, unsigned long long) +#endif + +/* End: bn_mp_init_ull.c */ + +/* Start: bn_mp_invmod.c */ +#include "tommath_private.h" +#ifdef BN_MP_INVMOD_C +/* LibTomMath, multiple-precision integer library -- Tom St Denis */ +/* SPDX-License-Identifier: Unlicense */ + +/* hac 14.61, pp608 */ +mp_err mp_invmod(const mp_int *a, const mp_int *b, mp_int *c) +{ + /* b cannot be negative and has to be >1 */ + if ((b->sign == MP_NEG) || (mp_cmp_d(b, 1uL) != MP_GT)) { + return MP_VAL; + } + + /* if the modulus is odd we can use a faster routine instead */ + if (MP_HAS(S_MP_INVMOD_FAST) && MP_IS_ODD(b)) { + return s_mp_invmod_fast(a, b, c); + } + + return MP_HAS(S_MP_INVMOD_SLOW) + ? s_mp_invmod_slow(a, b, c) + : MP_VAL; +} +#endif + +/* End: bn_mp_invmod.c */ + +/* Start: bn_mp_is_square.c */ +#include "tommath_private.h" +#ifdef BN_MP_IS_SQUARE_C +/* LibTomMath, multiple-precision integer library -- Tom St Denis */ +/* SPDX-License-Identifier: Unlicense */ + +/* Check if remainders are possible squares - fast exclude non-squares */ +static const char rem_128[128] = { + 0, 0, 1, 1, 0, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, + 0, 0, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, + 1, 0, 1, 1, 0, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, + 1, 0, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, + 0, 0, 1, 1, 0, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, + 1, 0, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, + 1, 0, 1, 1, 0, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, + 1, 0, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1 +}; + +static const char rem_105[105] = { + 0, 0, 1, 1, 0, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, + 0, 0, 1, 1, 1, 1, 0, 1, 1, 1, 0, 1, 1, 1, 1, + 0, 1, 1, 1, 1, 1, 0, 1, 1, 0, 1, 1, 1, 1, 1, + 1, 0, 1, 1, 0, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, + 0, 1, 1, 1, 0, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, + 1, 1, 1, 1, 0, 1, 0, 1, 1, 0, 0, 1, 1, 1, 1, + 1, 0, 1, 1, 1, 1, 1, 1, 1, 0, 0, 1, 1, 1, 1 +}; + +/* Store non-zero to ret if arg is square, and zero if not */ +mp_err mp_is_square(const mp_int *arg, mp_bool *ret) +{ + mp_err err; + mp_digit c; + mp_int t; + unsigned long r; + + /* Default to Non-square :) */ + *ret = MP_NO; + + if (arg->sign == MP_NEG) { + return MP_VAL; + } + + if (MP_IS_ZERO(arg)) { + return MP_OKAY; + } + + /* First check mod 128 (suppose that MP_DIGIT_BIT is at least 7) */ + if (rem_128[127u & arg->dp[0]] == (char)1) { + return MP_OKAY; + } + + /* Next check mod 105 (3*5*7) */ + if ((err = mp_mod_d(arg, 105uL, &c)) != MP_OKAY) { + return err; + } + if (rem_105[c] == (char)1) { + return MP_OKAY; + } + + + if ((err = mp_init_u32(&t, 11u*13u*17u*19u*23u*29u*31u)) != MP_OKAY) { + return err; + } + if ((err = mp_mod(arg, &t, &t)) != MP_OKAY) { + goto LBL_ERR; + } + r = mp_get_u32(&t); + /* Check for other prime modules, note it's not an ERROR but we must + * free "t" so the easiest way is to goto LBL_ERR. We know that err + * is already equal to MP_OKAY from the mp_mod call + */ + if (((1uL<<(r%11uL)) & 0x5C4uL) != 0uL) goto LBL_ERR; + if (((1uL<<(r%13uL)) & 0x9E4uL) != 0uL) goto LBL_ERR; + if (((1uL<<(r%17uL)) & 0x5CE8uL) != 0uL) goto LBL_ERR; + if (((1uL<<(r%19uL)) & 0x4F50CuL) != 0uL) goto LBL_ERR; + if (((1uL<<(r%23uL)) & 0x7ACCA0uL) != 0uL) goto LBL_ERR; + if (((1uL<<(r%29uL)) & 0xC2EDD0CuL) != 0uL) goto LBL_ERR; + if (((1uL<<(r%31uL)) & 0x6DE2B848uL) != 0uL) goto LBL_ERR; + + /* Final check - is sqr(sqrt(arg)) == arg ? */ + if ((err = mp_sqrt(arg, &t)) != MP_OKAY) { + goto LBL_ERR; + } + if ((err = mp_sqr(&t, &t)) != MP_OKAY) { + goto LBL_ERR; + } + + *ret = (mp_cmp_mag(&t, arg) == MP_EQ) ? MP_YES : MP_NO; +LBL_ERR: + mp_clear(&t); + return err; +} +#endif + +/* End: bn_mp_is_square.c */ + +/* Start: bn_mp_iseven.c */ +#include "tommath_private.h" +#ifdef BN_MP_ISEVEN_C +/* LibTomMath, multiple-precision integer library -- Tom St Denis */ +/* SPDX-License-Identifier: Unlicense */ + +mp_bool mp_iseven(const mp_int *a) +{ + return MP_IS_EVEN(a) ? MP_YES : MP_NO; +} +#endif + +/* End: bn_mp_iseven.c */ + +/* Start: bn_mp_isodd.c */ +#include "tommath_private.h" +#ifdef BN_MP_ISODD_C +/* LibTomMath, multiple-precision integer library -- Tom St Denis */ +/* SPDX-License-Identifier: Unlicense */ + +mp_bool mp_isodd(const mp_int *a) +{ + return MP_IS_ODD(a) ? MP_YES : MP_NO; +} +#endif + +/* End: bn_mp_isodd.c */ + +/* Start: bn_mp_kronecker.c */ +#include "tommath_private.h" +#ifdef BN_MP_KRONECKER_C + +/* LibTomMath, multiple-precision integer library -- Tom St Denis */ +/* SPDX-License-Identifier: Unlicense */ + +/* + Kronecker symbol (a|p) + Straightforward implementation of algorithm 1.4.10 in + Henri Cohen: "A Course in Computational Algebraic Number Theory" + + @book{cohen2013course, + title={A course in computational algebraic number theory}, + author={Cohen, Henri}, + volume={138}, + year={2013}, + publisher={Springer Science \& Business Media} + } + */ +mp_err mp_kronecker(const mp_int *a, const mp_int *p, int *c) +{ + mp_int a1, p1, r; + mp_err err; + int v, k; + + static const int table[8] = {0, 1, 0, -1, 0, -1, 0, 1}; + + if (MP_IS_ZERO(p)) { + if ((a->used == 1) && (a->dp[0] == 1u)) { + *c = 1; + } else { + *c = 0; + } + return MP_OKAY; + } + + if (MP_IS_EVEN(a) && MP_IS_EVEN(p)) { + *c = 0; + return MP_OKAY; + } + + if ((err = mp_init_copy(&a1, a)) != MP_OKAY) { + return err; + } + if ((err = mp_init_copy(&p1, p)) != MP_OKAY) { + goto LBL_KRON_0; + } + + v = mp_cnt_lsb(&p1); + if ((err = mp_div_2d(&p1, v, &p1, NULL)) != MP_OKAY) { + goto LBL_KRON_1; + } + + if ((v & 1) == 0) { + k = 1; + } else { + k = table[a->dp[0] & 7u]; + } + + if (p1.sign == MP_NEG) { + p1.sign = MP_ZPOS; + if (a1.sign == MP_NEG) { + k = -k; + } + } + + if ((err = mp_init(&r)) != MP_OKAY) { + goto LBL_KRON_1; + } + + for (;;) { + if (MP_IS_ZERO(&a1)) { + if (mp_cmp_d(&p1, 1uL) == MP_EQ) { + *c = k; + goto LBL_KRON; + } else { + *c = 0; + goto LBL_KRON; + } + } + + v = mp_cnt_lsb(&a1); + if ((err = mp_div_2d(&a1, v, &a1, NULL)) != MP_OKAY) { + goto LBL_KRON; + } + + if ((v & 1) == 1) { + k = k * table[p1.dp[0] & 7u]; + } + + if (a1.sign == MP_NEG) { + /* + * Compute k = (-1)^((a1)*(p1-1)/4) * k + * a1.dp[0] + 1 cannot overflow because the MSB + * of the type mp_digit is not set by definition + */ + if (((a1.dp[0] + 1u) & p1.dp[0] & 2u) != 0u) { + k = -k; + } + } else { + /* compute k = (-1)^((a1-1)*(p1-1)/4) * k */ + if ((a1.dp[0] & p1.dp[0] & 2u) != 0u) { + k = -k; + } + } + + if ((err = mp_copy(&a1, &r)) != MP_OKAY) { + goto LBL_KRON; + } + r.sign = MP_ZPOS; + if ((err = mp_mod(&p1, &r, &a1)) != MP_OKAY) { + goto LBL_KRON; + } + if ((err = mp_copy(&r, &p1)) != MP_OKAY) { + goto LBL_KRON; + } + } + +LBL_KRON: + mp_clear(&r); +LBL_KRON_1: + mp_clear(&p1); +LBL_KRON_0: + mp_clear(&a1); + + return err; +} + +#endif + +/* End: bn_mp_kronecker.c */ + +/* Start: bn_mp_lcm.c */ +#include "tommath_private.h" +#ifdef BN_MP_LCM_C +/* LibTomMath, multiple-precision integer library -- Tom St Denis */ +/* SPDX-License-Identifier: Unlicense */ + +/* computes least common multiple as |a*b|/(a, b) */ +mp_err mp_lcm(const mp_int *a, const mp_int *b, mp_int *c) +{ + mp_err err; + mp_int t1, t2; + + + if ((err = mp_init_multi(&t1, &t2, NULL)) != MP_OKAY) { + return err; + } + + /* t1 = get the GCD of the two inputs */ + if ((err = mp_gcd(a, b, &t1)) != MP_OKAY) { + goto LBL_T; + } + + /* divide the smallest by the GCD */ + if (mp_cmp_mag(a, b) == MP_LT) { + /* store quotient in t2 such that t2 * b is the LCM */ + if ((err = mp_div(a, &t1, &t2, NULL)) != MP_OKAY) { + goto LBL_T; + } + err = mp_mul(b, &t2, c); + } else { + /* store quotient in t2 such that t2 * a is the LCM */ + if ((err = mp_div(b, &t1, &t2, NULL)) != MP_OKAY) { + goto LBL_T; + } + err = mp_mul(a, &t2, c); + } + + /* fix the sign to positive */ + c->sign = MP_ZPOS; + +LBL_T: + mp_clear_multi(&t1, &t2, NULL); + return err; +} +#endif + +/* End: bn_mp_lcm.c */ + +/* Start: bn_mp_log_u32.c */ +#include "tommath_private.h" +#ifdef BN_MP_LOG_U32_C +/* LibTomMath, multiple-precision integer library -- Tom St Denis */ +/* SPDX-License-Identifier: Unlicense */ + +/* Compute log_{base}(a) */ +static mp_word s_pow(mp_word base, mp_word exponent) +{ + mp_word result = 1uLL; + while (exponent != 0u) { + if ((exponent & 1u) == 1u) { + result *= base; + } + exponent >>= 1; + base *= base; + } + + return result; +} + +static mp_digit s_digit_ilogb(mp_digit base, mp_digit n) +{ + mp_word bracket_low = 1uLL, bracket_mid, bracket_high, N; + mp_digit ret, high = 1uL, low = 0uL, mid; + + if (n < base) { + return 0uL; + } + if (n == base) { + return 1uL; + } + + bracket_high = (mp_word) base ; + N = (mp_word) n; + + while (bracket_high < N) { + low = high; + bracket_low = bracket_high; + high <<= 1; + bracket_high *= bracket_high; + } + + while (((mp_digit)(high - low)) > 1uL) { + mid = (low + high) >> 1; + bracket_mid = bracket_low * s_pow(base, (mp_word)(mid - low)); + + if (N < bracket_mid) { + high = mid ; + bracket_high = bracket_mid ; + } + if (N > bracket_mid) { + low = mid ; + bracket_low = bracket_mid ; + } + if (N == bracket_mid) { + return (mp_digit) mid; + } + } + + if (bracket_high == N) { + ret = high; + } else { + ret = low; + } + + return ret; +} + +/* TODO: output could be "int" because the output of mp_radix_size is int, too, + as is the output of mp_bitcount. + With the same problem: max size is INT_MAX * MP_DIGIT not INT_MAX only! +*/ +mp_err mp_log_u32(const mp_int *a, uint32_t base, uint32_t *c) +{ + mp_err err; + mp_ord cmp; + uint32_t high, low, mid; + mp_int bracket_low, bracket_high, bracket_mid, t, bi_base; + + err = MP_OKAY; + + if (a->sign == MP_NEG) { + return MP_VAL; + } + + if (MP_IS_ZERO(a)) { + return MP_VAL; + } + + if (base < 2u) { + return MP_VAL; + } + + /* A small shortcut for bases that are powers of two. */ + if ((base & (base - 1u)) == 0u) { + int y, bit_count; + for (y=0; (y < 7) && ((base & 1u) == 0u); y++) { + base >>= 1; + } + bit_count = mp_count_bits(a) - 1; + *c = (uint32_t)(bit_count/y); + return MP_OKAY; + } + + if (a->used == 1) { + *c = (uint32_t)s_digit_ilogb(base, a->dp[0]); + return err; + } + + cmp = mp_cmp_d(a, base); + if ((cmp == MP_LT) || (cmp == MP_EQ)) { + *c = cmp == MP_EQ; + return err; + } + + if ((err = + mp_init_multi(&bracket_low, &bracket_high, + &bracket_mid, &t, &bi_base, NULL)) != MP_OKAY) { + return err; + } + + low = 0u; + mp_set(&bracket_low, 1uL); + high = 1u; + + mp_set(&bracket_high, base); + + /* + A kind of Giant-step/baby-step algorithm. + Idea shamelessly stolen from https://programmingpraxis.com/2010/05/07/integer-logarithms/2/ + The effect is asymptotic, hence needs benchmarks to test if the Giant-step should be skipped + for small n. + */ + while (mp_cmp(&bracket_high, a) == MP_LT) { + low = high; + if ((err = mp_copy(&bracket_high, &bracket_low)) != MP_OKAY) { + goto LBL_ERR; + } + high <<= 1; + if ((err = mp_sqr(&bracket_high, &bracket_high)) != MP_OKAY) { + goto LBL_ERR; + } + } + mp_set(&bi_base, base); + + while ((high - low) > 1u) { + mid = (high + low) >> 1; + + if ((err = mp_expt_u32(&bi_base, (uint32_t)(mid - low), &t)) != MP_OKAY) { + goto LBL_ERR; + } + if ((err = mp_mul(&bracket_low, &t, &bracket_mid)) != MP_OKAY) { + goto LBL_ERR; + } + cmp = mp_cmp(a, &bracket_mid); + if (cmp == MP_LT) { + high = mid; + mp_exch(&bracket_mid, &bracket_high); + } + if (cmp == MP_GT) { + low = mid; + mp_exch(&bracket_mid, &bracket_low); + } + if (cmp == MP_EQ) { + *c = mid; + goto LBL_END; + } + } + + *c = (mp_cmp(&bracket_high, a) == MP_EQ) ? high : low; + +LBL_END: +LBL_ERR: + mp_clear_multi(&bracket_low, &bracket_high, &bracket_mid, + &t, &bi_base, NULL); + return err; +} + + +#endif + +/* End: bn_mp_log_u32.c */ + +/* Start: bn_mp_lshd.c */ +#include "tommath_private.h" +#ifdef BN_MP_LSHD_C +/* LibTomMath, multiple-precision integer library -- Tom St Denis */ +/* SPDX-License-Identifier: Unlicense */ + +/* shift left a certain amount of digits */ +mp_err mp_lshd(mp_int *a, int b) +{ + int x; + mp_err err; + mp_digit *top, *bottom; + + /* if its less than zero return */ + if (b <= 0) { + return MP_OKAY; + } + /* no need to shift 0 around */ + if (MP_IS_ZERO(a)) { + return MP_OKAY; + } + + /* grow to fit the new digits */ + if (a->alloc < (a->used + b)) { + if ((err = mp_grow(a, a->used + b)) != MP_OKAY) { + return err; + } + } + + /* increment the used by the shift amount then copy upwards */ + a->used += b; + + /* top */ + top = a->dp + a->used - 1; + + /* base */ + bottom = (a->dp + a->used - 1) - b; + + /* much like mp_rshd this is implemented using a sliding window + * except the window goes the otherway around. Copying from + * the bottom to the top. see bn_mp_rshd.c for more info. + */ + for (x = a->used - 1; x >= b; x--) { + *top-- = *bottom--; + } + + /* zero the lower digits */ + MP_ZERO_DIGITS(a->dp, b); + + return MP_OKAY; +} +#endif + +/* End: bn_mp_lshd.c */ + +/* Start: bn_mp_mod.c */ +#include "tommath_private.h" +#ifdef BN_MP_MOD_C +/* LibTomMath, multiple-precision integer library -- Tom St Denis */ +/* SPDX-License-Identifier: Unlicense */ + +/* c = a mod b, 0 <= c < b if b > 0, b < c <= 0 if b < 0 */ +mp_err mp_mod(const mp_int *a, const mp_int *b, mp_int *c) +{ + mp_int t; + mp_err err; + + if ((err = mp_init_size(&t, b->used)) != MP_OKAY) { + return err; + } + + if ((err = mp_div(a, b, NULL, &t)) != MP_OKAY) { + goto LBL_ERR; + } + + if (MP_IS_ZERO(&t) || (t.sign == b->sign)) { + err = MP_OKAY; + mp_exch(&t, c); + } else { + err = mp_add(b, &t, c); + } + +LBL_ERR: + mp_clear(&t); + return err; +} +#endif + +/* End: bn_mp_mod.c */ + +/* Start: bn_mp_mod_2d.c */ +#include "tommath_private.h" +#ifdef BN_MP_MOD_2D_C +/* LibTomMath, multiple-precision integer library -- Tom St Denis */ +/* SPDX-License-Identifier: Unlicense */ + +/* calc a value mod 2**b */ +mp_err mp_mod_2d(const mp_int *a, int b, mp_int *c) +{ + int x; + mp_err err; + + /* if b is <= 0 then zero the int */ + if (b <= 0) { + mp_zero(c); + return MP_OKAY; + } + + /* if the modulus is larger than the value than return */ + if (b >= (a->used * MP_DIGIT_BIT)) { + return mp_copy(a, c); + } + + /* copy */ + if ((err = mp_copy(a, c)) != MP_OKAY) { + return err; + } + + /* zero digits above the last digit of the modulus */ + x = (b / MP_DIGIT_BIT) + (((b % MP_DIGIT_BIT) == 0) ? 0 : 1); + MP_ZERO_DIGITS(c->dp + x, c->used - x); + + /* clear the digit that is not completely outside/inside the modulus */ + c->dp[b / MP_DIGIT_BIT] &= + ((mp_digit)1 << (mp_digit)(b % MP_DIGIT_BIT)) - (mp_digit)1; + mp_clamp(c); + return MP_OKAY; +} +#endif + +/* End: bn_mp_mod_2d.c */ + +/* Start: bn_mp_mod_d.c */ +#include "tommath_private.h" +#ifdef BN_MP_MOD_D_C +/* LibTomMath, multiple-precision integer library -- Tom St Denis */ +/* SPDX-License-Identifier: Unlicense */ + +mp_err mp_mod_d(const mp_int *a, mp_digit b, mp_digit *c) +{ + return mp_div_d(a, b, NULL, c); +} +#endif + +/* End: bn_mp_mod_d.c */ + +/* Start: bn_mp_montgomery_calc_normalization.c */ +#include "tommath_private.h" +#ifdef BN_MP_MONTGOMERY_CALC_NORMALIZATION_C +/* LibTomMath, multiple-precision integer library -- Tom St Denis */ +/* SPDX-License-Identifier: Unlicense */ + +/* + * shifts with subtractions when the result is greater than b. + * + * The method is slightly modified to shift B unconditionally upto just under + * the leading bit of b. This saves alot of multiple precision shifting. + */ +mp_err mp_montgomery_calc_normalization(mp_int *a, const mp_int *b) +{ + int x, bits; + mp_err err; + + /* how many bits of last digit does b use */ + bits = mp_count_bits(b) % MP_DIGIT_BIT; + + if (b->used > 1) { + if ((err = mp_2expt(a, ((b->used - 1) * MP_DIGIT_BIT) + bits - 1)) != MP_OKAY) { + return err; + } + } else { + mp_set(a, 1uL); + bits = 1; + } + + + /* now compute C = A * B mod b */ + for (x = bits - 1; x < (int)MP_DIGIT_BIT; x++) { + if ((err = mp_mul_2(a, a)) != MP_OKAY) { + return err; + } + if (mp_cmp_mag(a, b) != MP_LT) { + if ((err = s_mp_sub(a, b, a)) != MP_OKAY) { + return err; + } + } + } + + return MP_OKAY; +} +#endif + +/* End: bn_mp_montgomery_calc_normalization.c */ + +/* Start: bn_mp_montgomery_reduce.c */ +#include "tommath_private.h" +#ifdef BN_MP_MONTGOMERY_REDUCE_C +/* LibTomMath, multiple-precision integer library -- Tom St Denis */ +/* SPDX-License-Identifier: Unlicense */ + +/* computes xR**-1 == x (mod N) via Montgomery Reduction */ +mp_err mp_montgomery_reduce(mp_int *x, const mp_int *n, mp_digit rho) +{ + int ix, digs; + mp_err err; + mp_digit mu; + + /* can the fast reduction [comba] method be used? + * + * Note that unlike in mul you're safely allowed *less* + * than the available columns [255 per default] since carries + * are fixed up in the inner loop. + */ + digs = (n->used * 2) + 1; + if ((digs < MP_WARRAY) && + (x->used <= MP_WARRAY) && + (n->used < MP_MAXFAST)) { + return s_mp_montgomery_reduce_fast(x, n, rho); + } + + /* grow the input as required */ + if (x->alloc < digs) { + if ((err = mp_grow(x, digs)) != MP_OKAY) { + return err; + } + } + x->used = digs; + + for (ix = 0; ix < n->used; ix++) { + /* mu = ai * rho mod b + * + * The value of rho must be precalculated via + * montgomery_setup() such that + * it equals -1/n0 mod b this allows the + * following inner loop to reduce the + * input one digit at a time + */ + mu = (mp_digit)(((mp_word)x->dp[ix] * (mp_word)rho) & MP_MASK); + + /* a = a + mu * m * b**i */ + { + int iy; + mp_digit *tmpn, *tmpx, u; + mp_word r; + + /* alias for digits of the modulus */ + tmpn = n->dp; + + /* alias for the digits of x [the input] */ + tmpx = x->dp + ix; + + /* set the carry to zero */ + u = 0; + + /* Multiply and add in place */ + for (iy = 0; iy < n->used; iy++) { + /* compute product and sum */ + r = ((mp_word)mu * (mp_word)*tmpn++) + + (mp_word)u + (mp_word)*tmpx; + + /* get carry */ + u = (mp_digit)(r >> (mp_word)MP_DIGIT_BIT); + + /* fix digit */ + *tmpx++ = (mp_digit)(r & (mp_word)MP_MASK); + } + /* At this point the ix'th digit of x should be zero */ + + + /* propagate carries upwards as required*/ + while (u != 0u) { + *tmpx += u; + u = *tmpx >> MP_DIGIT_BIT; + *tmpx++ &= MP_MASK; + } + } + } + + /* at this point the n.used'th least + * significant digits of x are all zero + * which means we can shift x to the + * right by n.used digits and the + * residue is unchanged. + */ + + /* x = x/b**n.used */ + mp_clamp(x); + mp_rshd(x, n->used); + + /* if x >= n then x = x - n */ + if (mp_cmp_mag(x, n) != MP_LT) { + return s_mp_sub(x, n, x); + } + + return MP_OKAY; +} +#endif + +/* End: bn_mp_montgomery_reduce.c */ + +/* Start: bn_mp_montgomery_setup.c */ +#include "tommath_private.h" +#ifdef BN_MP_MONTGOMERY_SETUP_C +/* LibTomMath, multiple-precision integer library -- Tom St Denis */ +/* SPDX-License-Identifier: Unlicense */ + +/* setups the montgomery reduction stuff */ +mp_err mp_montgomery_setup(const mp_int *n, mp_digit *rho) +{ + mp_digit x, b; + + /* fast inversion mod 2**k + * + * Based on the fact that + * + * XA = 1 (mod 2**n) => (X(2-XA)) A = 1 (mod 2**2n) + * => 2*X*A - X*X*A*A = 1 + * => 2*(1) - (1) = 1 + */ + b = n->dp[0]; + + if ((b & 1u) == 0u) { + return MP_VAL; + } + + x = (((b + 2u) & 4u) << 1) + b; /* here x*a==1 mod 2**4 */ + x *= 2u - (b * x); /* here x*a==1 mod 2**8 */ +#if !defined(MP_8BIT) + x *= 2u - (b * x); /* here x*a==1 mod 2**16 */ +#endif +#if defined(MP_64BIT) || !(defined(MP_8BIT) || defined(MP_16BIT)) + x *= 2u - (b * x); /* here x*a==1 mod 2**32 */ +#endif +#ifdef MP_64BIT + x *= 2u - (b * x); /* here x*a==1 mod 2**64 */ +#endif + + /* rho = -1/m mod b */ + *rho = (mp_digit)(((mp_word)1 << (mp_word)MP_DIGIT_BIT) - x) & MP_MASK; + + return MP_OKAY; +} +#endif + +/* End: bn_mp_montgomery_setup.c */ + +/* Start: bn_mp_mul.c */ +#include "tommath_private.h" +#ifdef BN_MP_MUL_C +/* LibTomMath, multiple-precision integer library -- Tom St Denis */ +/* SPDX-License-Identifier: Unlicense */ + +/* high level multiplication (handles sign) */ +mp_err mp_mul(const mp_int *a, const mp_int *b, mp_int *c) +{ + mp_err err; + int min_len = MP_MIN(a->used, b->used), + max_len = MP_MAX(a->used, b->used), + digs = a->used + b->used + 1; + mp_sign neg = (a->sign == b->sign) ? MP_ZPOS : MP_NEG; + + if (MP_HAS(S_MP_BALANCE_MUL) && + /* Check sizes. The smaller one needs to be larger than the Karatsuba cut-off. + * The bigger one needs to be at least about one MP_KARATSUBA_MUL_CUTOFF bigger + * to make some sense, but it depends on architecture, OS, position of the + * stars... so YMMV. + * Using it to cut the input into slices small enough for fast_s_mp_mul_digs + * was actually slower on the author's machine, but YMMV. + */ + (min_len >= MP_KARATSUBA_MUL_CUTOFF) && + ((max_len / 2) >= MP_KARATSUBA_MUL_CUTOFF) && + /* Not much effect was observed below a ratio of 1:2, but again: YMMV. */ + (max_len >= (2 * min_len))) { + err = s_mp_balance_mul(a,b,c); + } else if (MP_HAS(S_MP_TOOM_MUL) && + (min_len >= MP_TOOM_MUL_CUTOFF)) { + err = s_mp_toom_mul(a, b, c); + } else if (MP_HAS(S_MP_KARATSUBA_MUL) && + (min_len >= MP_KARATSUBA_MUL_CUTOFF)) { + err = s_mp_karatsuba_mul(a, b, c); + } else if (MP_HAS(S_MP_MUL_DIGS_FAST) && + /* can we use the fast multiplier? + * + * The fast multiplier can be used if the output will + * have less than MP_WARRAY digits and the number of + * digits won't affect carry propagation + */ + (digs < MP_WARRAY) && + (min_len <= MP_MAXFAST)) { + err = s_mp_mul_digs_fast(a, b, c, digs); + } else if (MP_HAS(S_MP_MUL_DIGS)) { + err = s_mp_mul_digs(a, b, c, digs); + } else { + err = MP_VAL; + } + c->sign = (c->used > 0) ? neg : MP_ZPOS; + return err; +} +#endif + +/* End: bn_mp_mul.c */ + +/* Start: bn_mp_mul_2.c */ +#include "tommath_private.h" +#ifdef BN_MP_MUL_2_C +/* LibTomMath, multiple-precision integer library -- Tom St Denis */ +/* SPDX-License-Identifier: Unlicense */ + +/* b = a*2 */ +mp_err mp_mul_2(const mp_int *a, mp_int *b) +{ + int x, oldused; + mp_err err; + + /* grow to accomodate result */ + if (b->alloc < (a->used + 1)) { + if ((err = mp_grow(b, a->used + 1)) != MP_OKAY) { + return err; + } + } + + oldused = b->used; + b->used = a->used; + + { + mp_digit r, rr, *tmpa, *tmpb; + + /* alias for source */ + tmpa = a->dp; + + /* alias for dest */ + tmpb = b->dp; + + /* carry */ + r = 0; + for (x = 0; x < a->used; x++) { + + /* get what will be the *next* carry bit from the + * MSB of the current digit + */ + rr = *tmpa >> (mp_digit)(MP_DIGIT_BIT - 1); + + /* now shift up this digit, add in the carry [from the previous] */ + *tmpb++ = ((*tmpa++ << 1uL) | r) & MP_MASK; + + /* copy the carry that would be from the source + * digit into the next iteration + */ + r = rr; + } + + /* new leading digit? */ + if (r != 0u) { + /* add a MSB which is always 1 at this point */ + *tmpb = 1; + ++(b->used); + } + + /* now zero any excess digits on the destination + * that we didn't write to + */ + MP_ZERO_DIGITS(b->dp + b->used, oldused - b->used); + } + b->sign = a->sign; + return MP_OKAY; +} +#endif + +/* End: bn_mp_mul_2.c */ + +/* Start: bn_mp_mul_2d.c */ +#include "tommath_private.h" +#ifdef BN_MP_MUL_2D_C +/* LibTomMath, multiple-precision integer library -- Tom St Denis */ +/* SPDX-License-Identifier: Unlicense */ + +/* shift left by a certain bit count */ +mp_err mp_mul_2d(const mp_int *a, int b, mp_int *c) +{ + mp_digit d; + mp_err err; + + /* copy */ + if (a != c) { + if ((err = mp_copy(a, c)) != MP_OKAY) { + return err; + } + } + + if (c->alloc < (c->used + (b / MP_DIGIT_BIT) + 1)) { + if ((err = mp_grow(c, c->used + (b / MP_DIGIT_BIT) + 1)) != MP_OKAY) { + return err; + } + } + + /* shift by as many digits in the bit count */ + if (b >= MP_DIGIT_BIT) { + if ((err = mp_lshd(c, b / MP_DIGIT_BIT)) != MP_OKAY) { + return err; + } + } + + /* shift any bit count < MP_DIGIT_BIT */ + d = (mp_digit)(b % MP_DIGIT_BIT); + if (d != 0u) { + mp_digit *tmpc, shift, mask, r, rr; + int x; + + /* bitmask for carries */ + mask = ((mp_digit)1 << d) - (mp_digit)1; + + /* shift for msbs */ + shift = (mp_digit)MP_DIGIT_BIT - d; + + /* alias */ + tmpc = c->dp; + + /* carry */ + r = 0; + for (x = 0; x < c->used; x++) { + /* get the higher bits of the current word */ + rr = (*tmpc >> shift) & mask; + + /* shift the current word and OR in the carry */ + *tmpc = ((*tmpc << d) | r) & MP_MASK; + ++tmpc; + + /* set the carry to the carry bits of the current word */ + r = rr; + } + + /* set final carry */ + if (r != 0u) { + c->dp[(c->used)++] = r; + } + } + mp_clamp(c); + return MP_OKAY; +} +#endif + +/* End: bn_mp_mul_2d.c */ + +/* Start: bn_mp_mul_d.c */ +#include "tommath_private.h" +#ifdef BN_MP_MUL_D_C +/* LibTomMath, multiple-precision integer library -- Tom St Denis */ +/* SPDX-License-Identifier: Unlicense */ + +/* multiply by a digit */ +mp_err mp_mul_d(const mp_int *a, mp_digit b, mp_int *c) +{ + mp_digit u, *tmpa, *tmpc; + mp_word r; + mp_err err; + int ix, olduse; + + /* make sure c is big enough to hold a*b */ + if (c->alloc < (a->used + 1)) { + if ((err = mp_grow(c, a->used + 1)) != MP_OKAY) { + return err; + } + } + + /* get the original destinations used count */ + olduse = c->used; + + /* set the sign */ + c->sign = a->sign; + + /* alias for a->dp [source] */ + tmpa = a->dp; + + /* alias for c->dp [dest] */ + tmpc = c->dp; + + /* zero carry */ + u = 0; + + /* compute columns */ + for (ix = 0; ix < a->used; ix++) { + /* compute product and carry sum for this term */ + r = (mp_word)u + ((mp_word)*tmpa++ * (mp_word)b); + + /* mask off higher bits to get a single digit */ + *tmpc++ = (mp_digit)(r & (mp_word)MP_MASK); + + /* send carry into next iteration */ + u = (mp_digit)(r >> (mp_word)MP_DIGIT_BIT); + } + + /* store final carry [if any] and increment ix offset */ + *tmpc++ = u; + ++ix; + + /* now zero digits above the top */ + MP_ZERO_DIGITS(tmpc, olduse - ix); + + /* set used count */ + c->used = a->used + 1; + mp_clamp(c); + + return MP_OKAY; +} +#endif + +/* End: bn_mp_mul_d.c */ + +/* Start: bn_mp_mulmod.c */ +#include "tommath_private.h" +#ifdef BN_MP_MULMOD_C +/* LibTomMath, multiple-precision integer library -- Tom St Denis */ +/* SPDX-License-Identifier: Unlicense */ + +/* d = a * b (mod c) */ +mp_err mp_mulmod(const mp_int *a, const mp_int *b, const mp_int *c, mp_int *d) +{ + mp_err err; + mp_int t; + + if ((err = mp_init_size(&t, c->used)) != MP_OKAY) { + return err; + } + + if ((err = mp_mul(a, b, &t)) != MP_OKAY) { + goto LBL_ERR; + } + err = mp_mod(&t, c, d); + +LBL_ERR: + mp_clear(&t); + return err; +} +#endif + +/* End: bn_mp_mulmod.c */ + +/* Start: bn_mp_neg.c */ +#include "tommath_private.h" +#ifdef BN_MP_NEG_C +/* LibTomMath, multiple-precision integer library -- Tom St Denis */ +/* SPDX-License-Identifier: Unlicense */ + +/* b = -a */ +mp_err mp_neg(const mp_int *a, mp_int *b) +{ + mp_err err; + if (a != b) { + if ((err = mp_copy(a, b)) != MP_OKAY) { + return err; + } + } + + if (!MP_IS_ZERO(b)) { + b->sign = (a->sign == MP_ZPOS) ? MP_NEG : MP_ZPOS; + } else { + b->sign = MP_ZPOS; + } + + return MP_OKAY; +} +#endif + +/* End: bn_mp_neg.c */ + +/* Start: bn_mp_or.c */ +#include "tommath_private.h" +#ifdef BN_MP_OR_C +/* LibTomMath, multiple-precision integer library -- Tom St Denis */ +/* SPDX-License-Identifier: Unlicense */ + +/* two complement or */ +mp_err mp_or(const mp_int *a, const mp_int *b, mp_int *c) +{ + int used = MP_MAX(a->used, b->used) + 1, i; + mp_err err; + mp_digit ac = 1, bc = 1, cc = 1; + mp_sign csign = ((a->sign == MP_NEG) || (b->sign == MP_NEG)) ? MP_NEG : MP_ZPOS; + + if (c->alloc < used) { + if ((err = mp_grow(c, used)) != MP_OKAY) { + return err; + } + } + + for (i = 0; i < used; i++) { + mp_digit x, y; + + /* convert to two complement if negative */ + if (a->sign == MP_NEG) { + ac += (i >= a->used) ? MP_MASK : (~a->dp[i] & MP_MASK); + x = ac & MP_MASK; + ac >>= MP_DIGIT_BIT; + } else { + x = (i >= a->used) ? 0uL : a->dp[i]; + } + + /* convert to two complement if negative */ + if (b->sign == MP_NEG) { + bc += (i >= b->used) ? MP_MASK : (~b->dp[i] & MP_MASK); + y = bc & MP_MASK; + bc >>= MP_DIGIT_BIT; + } else { + y = (i >= b->used) ? 0uL : b->dp[i]; + } + + c->dp[i] = x | y; + + /* convert to to sign-magnitude if negative */ + if (csign == MP_NEG) { + cc += ~c->dp[i] & MP_MASK; + c->dp[i] = cc & MP_MASK; + cc >>= MP_DIGIT_BIT; + } + } + + c->used = used; + c->sign = csign; + mp_clamp(c); + return MP_OKAY; +} +#endif + +/* End: bn_mp_or.c */ + +/* Start: bn_mp_pack.c */ +#include "tommath_private.h" +#ifdef BN_MP_PACK_C +/* LibTomMath, multiple-precision integer library -- Tom St Denis */ +/* SPDX-License-Identifier: Unlicense */ + +/* based on gmp's mpz_export. + * see http://gmplib.org/manual/Integer-Import-and-Export.html + */ +mp_err mp_pack(void *rop, size_t maxcount, size_t *written, mp_order order, size_t size, + mp_endian endian, size_t nails, const mp_int *op) +{ + mp_err err; + size_t odd_nails, nail_bytes, i, j, count; + unsigned char odd_nail_mask; + + mp_int t; + + count = mp_pack_count(op, nails, size); + + if (count > maxcount) { + return MP_BUF; + } + + if ((err = mp_init_copy(&t, op)) != MP_OKAY) { + return err; + } + + if (endian == MP_NATIVE_ENDIAN) { + MP_GET_ENDIANNESS(endian); + } + + odd_nails = (nails % 8u); + odd_nail_mask = 0xff; + for (i = 0u; i < odd_nails; ++i) { + odd_nail_mask ^= (unsigned char)(1u << (7u - i)); + } + nail_bytes = nails / 8u; + + for (i = 0u; i < count; ++i) { + for (j = 0u; j < size; ++j) { + unsigned char *byte = (unsigned char *)rop + + (((order == MP_LSB_FIRST) ? i : ((count - 1u) - i)) * size) + + ((endian == MP_LITTLE_ENDIAN) ? j : ((size - 1u) - j)); + + if (j >= (size - nail_bytes)) { + *byte = 0; + continue; + } + + *byte = (unsigned char)((j == ((size - nail_bytes) - 1u)) ? (t.dp[0] & odd_nail_mask) : (t.dp[0] & 0xFFuL)); + + if ((err = mp_div_2d(&t, (j == ((size - nail_bytes) - 1u)) ? (int)(8u - odd_nails) : 8, &t, NULL)) != MP_OKAY) { + goto LBL_ERR; + } + + } + } + + if (written != NULL) { + *written = count; + } + err = MP_OKAY; + +LBL_ERR: + mp_clear(&t); + return err; +} + +#endif + +/* End: bn_mp_pack.c */ + +/* Start: bn_mp_pack_count.c */ +#include "tommath_private.h" +#ifdef BN_MP_PACK_COUNT_C +/* LibTomMath, multiple-precision integer library -- Tom St Denis */ +/* SPDX-License-Identifier: Unlicense */ + +size_t mp_pack_count(const mp_int *a, size_t nails, size_t size) +{ + size_t bits = (size_t)mp_count_bits(a); + return ((bits / ((size * 8u) - nails)) + (((bits % ((size * 8u) - nails)) != 0u) ? 1u : 0u)); +} + +#endif + +/* End: bn_mp_pack_count.c */ + +/* Start: bn_mp_prime_fermat.c */ +#include "tommath_private.h" +#ifdef BN_MP_PRIME_FERMAT_C +/* LibTomMath, multiple-precision integer library -- Tom St Denis */ +/* SPDX-License-Identifier: Unlicense */ + +/* performs one Fermat test. + * + * If "a" were prime then b**a == b (mod a) since the order of + * the multiplicative sub-group would be phi(a) = a-1. That means + * it would be the same as b**(a mod (a-1)) == b**1 == b (mod a). + * + * Sets result to 1 if the congruence holds, or zero otherwise. + */ +mp_err mp_prime_fermat(const mp_int *a, const mp_int *b, mp_bool *result) +{ + mp_int t; + mp_err err; + + /* default to composite */ + *result = MP_NO; + + /* ensure b > 1 */ + if (mp_cmp_d(b, 1uL) != MP_GT) { + return MP_VAL; + } + + /* init t */ + if ((err = mp_init(&t)) != MP_OKAY) { + return err; + } + + /* compute t = b**a mod a */ + if ((err = mp_exptmod(b, a, a, &t)) != MP_OKAY) { + goto LBL_T; + } + + /* is it equal to b? */ + if (mp_cmp(&t, b) == MP_EQ) { + *result = MP_YES; + } + + err = MP_OKAY; +LBL_T: + mp_clear(&t); + return err; +} +#endif + +/* End: bn_mp_prime_fermat.c */ + +/* Start: bn_mp_prime_frobenius_underwood.c */ +#include "tommath_private.h" +#ifdef BN_MP_PRIME_FROBENIUS_UNDERWOOD_C + +/* LibTomMath, multiple-precision integer library -- Tom St Denis */ +/* SPDX-License-Identifier: Unlicense */ + +/* + * See file bn_mp_prime_is_prime.c or the documentation in doc/bn.tex for the details + */ +#ifndef LTM_USE_ONLY_MR + +#ifdef MP_8BIT +/* + * floor of positive solution of + * (2^16)-1 = (a+4)*(2*a+5) + * TODO: Both values are smaller than N^(1/4), would have to use a bigint + * for a instead but any a biger than about 120 are already so rare that + * it is possible to ignore them and still get enough pseudoprimes. + * But it is still a restriction of the set of available pseudoprimes + * which makes this implementation less secure if used stand-alone. + */ +#define LTM_FROBENIUS_UNDERWOOD_A 177 +#else +#define LTM_FROBENIUS_UNDERWOOD_A 32764 +#endif +mp_err mp_prime_frobenius_underwood(const mp_int *N, mp_bool *result) +{ + mp_int T1z, T2z, Np1z, sz, tz; + + int a, ap2, length, i, j; + mp_err err; + + *result = MP_NO; + + if ((err = mp_init_multi(&T1z, &T2z, &Np1z, &sz, &tz, NULL)) != MP_OKAY) { + return err; + } + + for (a = 0; a < LTM_FROBENIUS_UNDERWOOD_A; a++) { + /* TODO: That's ugly! No, really, it is! */ + if ((a==2) || (a==4) || (a==7) || (a==8) || (a==10) || + (a==14) || (a==18) || (a==23) || (a==26) || (a==28)) { + continue; + } + /* (32764^2 - 4) < 2^31, no bigint for >MP_8BIT needed) */ + mp_set_u32(&T1z, (uint32_t)a); + + if ((err = mp_sqr(&T1z, &T1z)) != MP_OKAY) goto LBL_FU_ERR; + + if ((err = mp_sub_d(&T1z, 4uL, &T1z)) != MP_OKAY) goto LBL_FU_ERR; + + if ((err = mp_kronecker(&T1z, N, &j)) != MP_OKAY) goto LBL_FU_ERR; + + if (j == -1) { + break; + } + + if (j == 0) { + /* composite */ + goto LBL_FU_ERR; + } + } + /* Tell it a composite and set return value accordingly */ + if (a >= LTM_FROBENIUS_UNDERWOOD_A) { + err = MP_ITER; + goto LBL_FU_ERR; + } + /* Composite if N and (a+4)*(2*a+5) are not coprime */ + mp_set_u32(&T1z, (uint32_t)((a+4)*((2*a)+5))); + + if ((err = mp_gcd(N, &T1z, &T1z)) != MP_OKAY) goto LBL_FU_ERR; + + if (!((T1z.used == 1) && (T1z.dp[0] == 1u))) goto LBL_FU_ERR; + + ap2 = a + 2; + if ((err = mp_add_d(N, 1uL, &Np1z)) != MP_OKAY) goto LBL_FU_ERR; + + mp_set(&sz, 1uL); + mp_set(&tz, 2uL); + length = mp_count_bits(&Np1z); + + for (i = length - 2; i >= 0; i--) { + /* + * temp = (sz*(a*sz+2*tz))%N; + * tz = ((tz-sz)*(tz+sz))%N; + * sz = temp; + */ + if ((err = mp_mul_2(&tz, &T2z)) != MP_OKAY) goto LBL_FU_ERR; + + /* a = 0 at about 50% of the cases (non-square and odd input) */ + if (a != 0) { + if ((err = mp_mul_d(&sz, (mp_digit)a, &T1z)) != MP_OKAY) goto LBL_FU_ERR; + if ((err = mp_add(&T1z, &T2z, &T2z)) != MP_OKAY) goto LBL_FU_ERR; + } + + if ((err = mp_mul(&T2z, &sz, &T1z)) != MP_OKAY) goto LBL_FU_ERR; + if ((err = mp_sub(&tz, &sz, &T2z)) != MP_OKAY) goto LBL_FU_ERR; + if ((err = mp_add(&sz, &tz, &sz)) != MP_OKAY) goto LBL_FU_ERR; + if ((err = mp_mul(&sz, &T2z, &tz)) != MP_OKAY) goto LBL_FU_ERR; + if ((err = mp_mod(&tz, N, &tz)) != MP_OKAY) goto LBL_FU_ERR; + if ((err = mp_mod(&T1z, N, &sz)) != MP_OKAY) goto LBL_FU_ERR; + if (s_mp_get_bit(&Np1z, (unsigned int)i) == MP_YES) { + /* + * temp = (a+2) * sz + tz + * tz = 2 * tz - sz + * sz = temp + */ + if (a == 0) { + if ((err = mp_mul_2(&sz, &T1z)) != MP_OKAY) goto LBL_FU_ERR; + } else { + if ((err = mp_mul_d(&sz, (mp_digit)ap2, &T1z)) != MP_OKAY) goto LBL_FU_ERR; + } + if ((err = mp_add(&T1z, &tz, &T1z)) != MP_OKAY) goto LBL_FU_ERR; + if ((err = mp_mul_2(&tz, &T2z)) != MP_OKAY) goto LBL_FU_ERR; + if ((err = mp_sub(&T2z, &sz, &tz)) != MP_OKAY) goto LBL_FU_ERR; + mp_exch(&sz, &T1z); + } + } + + mp_set_u32(&T1z, (uint32_t)((2 * a) + 5)); + if ((err = mp_mod(&T1z, N, &T1z)) != MP_OKAY) goto LBL_FU_ERR; + if (MP_IS_ZERO(&sz) && (mp_cmp(&tz, &T1z) == MP_EQ)) { + *result = MP_YES; + } + +LBL_FU_ERR: + mp_clear_multi(&tz, &sz, &Np1z, &T2z, &T1z, NULL); + return err; +} + +#endif +#endif + +/* End: bn_mp_prime_frobenius_underwood.c */ + +/* Start: bn_mp_prime_is_prime.c */ +#include "tommath_private.h" +#ifdef BN_MP_PRIME_IS_PRIME_C +/* LibTomMath, multiple-precision integer library -- Tom St Denis */ +/* SPDX-License-Identifier: Unlicense */ + +/* portable integer log of two with small footprint */ +static unsigned int s_floor_ilog2(int value) +{ + unsigned int r = 0; + while ((value >>= 1) != 0) { + r++; + } + return r; +} + + +mp_err mp_prime_is_prime(const mp_int *a, int t, mp_bool *result) +{ + mp_int b; + int ix, p_max = 0, size_a, len; + mp_bool res; + mp_err err; + unsigned int fips_rand, mask; + + /* default to no */ + *result = MP_NO; + + /* Some shortcuts */ + /* N > 3 */ + if (a->used == 1) { + if ((a->dp[0] == 0u) || (a->dp[0] == 1u)) { + *result = MP_NO; + return MP_OKAY; + } + if (a->dp[0] == 2u) { + *result = MP_YES; + return MP_OKAY; + } + } + + /* N must be odd */ + if (MP_IS_EVEN(a)) { + return MP_OKAY; + } + /* N is not a perfect square: floor(sqrt(N))^2 != N */ + if ((err = mp_is_square(a, &res)) != MP_OKAY) { + return err; + } + if (res != MP_NO) { + return MP_OKAY; + } + + /* is the input equal to one of the primes in the table? */ + for (ix = 0; ix < PRIVATE_MP_PRIME_TAB_SIZE; ix++) { + if (mp_cmp_d(a, s_mp_prime_tab[ix]) == MP_EQ) { + *result = MP_YES; + return MP_OKAY; + } + } +#ifdef MP_8BIT + /* The search in the loop above was exhaustive in this case */ + if ((a->used == 1) && (PRIVATE_MP_PRIME_TAB_SIZE >= 31)) { + return MP_OKAY; + } +#endif + + /* first perform trial division */ + if ((err = s_mp_prime_is_divisible(a, &res)) != MP_OKAY) { + return err; + } + + /* return if it was trivially divisible */ + if (res == MP_YES) { + return MP_OKAY; + } + + /* + Run the Miller-Rabin test with base 2 for the BPSW test. + */ + if ((err = mp_init_set(&b, 2uL)) != MP_OKAY) { + return err; + } + + if ((err = mp_prime_miller_rabin(a, &b, &res)) != MP_OKAY) { + goto LBL_B; + } + if (res == MP_NO) { + goto LBL_B; + } + /* + Rumours have it that Mathematica does a second M-R test with base 3. + Other rumours have it that their strong L-S test is slightly different. + It does not hurt, though, beside a bit of extra runtime. + */ + b.dp[0]++; + if ((err = mp_prime_miller_rabin(a, &b, &res)) != MP_OKAY) { + goto LBL_B; + } + if (res == MP_NO) { + goto LBL_B; + } + + /* + * Both, the Frobenius-Underwood test and the the Lucas-Selfridge test are quite + * slow so if speed is an issue, define LTM_USE_ONLY_MR to use M-R tests with + * bases 2, 3 and t random bases. + */ +#ifndef LTM_USE_ONLY_MR + if (t >= 0) { + /* + * Use a Frobenius-Underwood test instead of the Lucas-Selfridge test for + * MP_8BIT (It is unknown if the Lucas-Selfridge test works with 16-bit + * integers but the necesssary analysis is on the todo-list). + */ +#if defined (MP_8BIT) || defined (LTM_USE_FROBENIUS_TEST) + err = mp_prime_frobenius_underwood(a, &res); + if ((err != MP_OKAY) && (err != MP_ITER)) { + goto LBL_B; + } + if (res == MP_NO) { + goto LBL_B; + } +#else + if ((err = mp_prime_strong_lucas_selfridge(a, &res)) != MP_OKAY) { + goto LBL_B; + } + if (res == MP_NO) { + goto LBL_B; + } +#endif + } +#endif + + /* run at least one Miller-Rabin test with a random base */ + if (t == 0) { + t = 1; + } + + /* + Only recommended if the input range is known to be < 3317044064679887385961981 + + It uses the bases necessary for a deterministic M-R test if the input is + smaller than 3317044064679887385961981 + The caller has to check the size. + TODO: can be made a bit finer grained but comparing is not free. + */ + if (t < 0) { + /* + Sorenson, Jonathan; Webster, Jonathan (2015). + "Strong Pseudoprimes to Twelve Prime Bases". + */ + /* 0x437ae92817f9fc85b7e5 = 318665857834031151167461 */ + if ((err = mp_read_radix(&b, "437ae92817f9fc85b7e5", 16)) != MP_OKAY) { + goto LBL_B; + } + + if (mp_cmp(a, &b) == MP_LT) { + p_max = 12; + } else { + /* 0x2be6951adc5b22410a5fd = 3317044064679887385961981 */ + if ((err = mp_read_radix(&b, "2be6951adc5b22410a5fd", 16)) != MP_OKAY) { + goto LBL_B; + } + + if (mp_cmp(a, &b) == MP_LT) { + p_max = 13; + } else { + err = MP_VAL; + goto LBL_B; + } + } + + /* we did bases 2 and 3 already, skip them */ + for (ix = 2; ix < p_max; ix++) { + mp_set(&b, s_mp_prime_tab[ix]); + if ((err = mp_prime_miller_rabin(a, &b, &res)) != MP_OKAY) { + goto LBL_B; + } + if (res == MP_NO) { + goto LBL_B; + } + } + } + /* + Do "t" M-R tests with random bases between 3 and "a". + See Fips 186.4 p. 126ff + */ + else if (t > 0) { + /* + * The mp_digit's have a defined bit-size but the size of the + * array a.dp is a simple 'int' and this library can not assume full + * compliance to the current C-standard (ISO/IEC 9899:2011) because + * it gets used for small embeded processors, too. Some of those MCUs + * have compilers that one cannot call standard compliant by any means. + * Hence the ugly type-fiddling in the following code. + */ + size_a = mp_count_bits(a); + mask = (1u << s_floor_ilog2(size_a)) - 1u; + /* + Assuming the General Rieman hypothesis (never thought to write that in a + comment) the upper bound can be lowered to 2*(log a)^2. + E. Bach, "Explicit bounds for primality testing and related problems," + Math. Comp. 55 (1990), 355-380. + + size_a = (size_a/10) * 7; + len = 2 * (size_a * size_a); + + E.g.: a number of size 2^2048 would be reduced to the upper limit + + floor(2048/10)*7 = 1428 + 2 * 1428^2 = 4078368 + + (would have been ~4030331.9962 with floats and natural log instead) + That number is smaller than 2^28, the default bit-size of mp_digit. + */ + + /* + How many tests, you might ask? Dana Jacobsen of Math::Prime::Util fame + does exactly 1. In words: one. Look at the end of _GMP_is_prime() in + Math-Prime-Util-GMP-0.50/primality.c if you do not believe it. + + The function mp_rand() goes to some length to use a cryptographically + good PRNG. That also means that the chance to always get the same base + in the loop is non-zero, although very low. + If the BPSW test and/or the addtional Frobenious test have been + performed instead of just the Miller-Rabin test with the bases 2 and 3, + a single extra test should suffice, so such a very unlikely event + will not do much harm. + + To preemptivly answer the dangling question: no, a witness does not + need to be prime. + */ + for (ix = 0; ix < t; ix++) { + /* mp_rand() guarantees the first digit to be non-zero */ + if ((err = mp_rand(&b, 1)) != MP_OKAY) { + goto LBL_B; + } + /* + * Reduce digit before casting because mp_digit might be bigger than + * an unsigned int and "mask" on the other side is most probably not. + */ + fips_rand = (unsigned int)(b.dp[0] & (mp_digit) mask); +#ifdef MP_8BIT + /* + * One 8-bit digit is too small, so concatenate two if the size of + * unsigned int allows for it. + */ + if ((MP_SIZEOF_BITS(unsigned int)/2) >= MP_SIZEOF_BITS(mp_digit)) { + if ((err = mp_rand(&b, 1)) != MP_OKAY) { + goto LBL_B; + } + fips_rand <<= MP_SIZEOF_BITS(mp_digit); + fips_rand |= (unsigned int) b.dp[0]; + fips_rand &= mask; + } +#endif + if (fips_rand > (unsigned int)(INT_MAX - MP_DIGIT_BIT)) { + len = INT_MAX / MP_DIGIT_BIT; + } else { + len = (((int)fips_rand + MP_DIGIT_BIT) / MP_DIGIT_BIT); + } + /* Unlikely. */ + if (len < 0) { + ix--; + continue; + } + /* + * As mentioned above, one 8-bit digit is too small and + * although it can only happen in the unlikely case that + * an "unsigned int" is smaller than 16 bit a simple test + * is cheap and the correction even cheaper. + */ +#ifdef MP_8BIT + /* All "a" < 2^8 have been caught before */ + if (len == 1) { + len++; + } +#endif + if ((err = mp_rand(&b, len)) != MP_OKAY) { + goto LBL_B; + } + /* + * That number might got too big and the witness has to be + * smaller than "a" + */ + len = mp_count_bits(&b); + if (len >= size_a) { + len = (len - size_a) + 1; + if ((err = mp_div_2d(&b, len, &b, NULL)) != MP_OKAY) { + goto LBL_B; + } + } + /* Although the chance for b <= 3 is miniscule, try again. */ + if (mp_cmp_d(&b, 3uL) != MP_GT) { + ix--; + continue; + } + if ((err = mp_prime_miller_rabin(a, &b, &res)) != MP_OKAY) { + goto LBL_B; + } + if (res == MP_NO) { + goto LBL_B; + } + } + } + + /* passed the test */ + *result = MP_YES; +LBL_B: + mp_clear(&b); + return err; +} + +#endif + +/* End: bn_mp_prime_is_prime.c */ + +/* Start: bn_mp_prime_miller_rabin.c */ +#include "tommath_private.h" +#ifdef BN_MP_PRIME_MILLER_RABIN_C +/* LibTomMath, multiple-precision integer library -- Tom St Denis */ +/* SPDX-License-Identifier: Unlicense */ + +/* Miller-Rabin test of "a" to the base of "b" as described in + * HAC pp. 139 Algorithm 4.24 + * + * Sets result to 0 if definitely composite or 1 if probably prime. + * Randomly the chance of error is no more than 1/4 and often + * very much lower. + */ +mp_err mp_prime_miller_rabin(const mp_int *a, const mp_int *b, mp_bool *result) +{ + mp_int n1, y, r; + mp_err err; + int s, j; + + /* default */ + *result = MP_NO; + + /* ensure b > 1 */ + if (mp_cmp_d(b, 1uL) != MP_GT) { + return MP_VAL; + } + + /* get n1 = a - 1 */ + if ((err = mp_init_copy(&n1, a)) != MP_OKAY) { + return err; + } + if ((err = mp_sub_d(&n1, 1uL, &n1)) != MP_OKAY) { + goto LBL_N1; + } + + /* set 2**s * r = n1 */ + if ((err = mp_init_copy(&r, &n1)) != MP_OKAY) { + goto LBL_N1; + } + + /* count the number of least significant bits + * which are zero + */ + s = mp_cnt_lsb(&r); + + /* now divide n - 1 by 2**s */ + if ((err = mp_div_2d(&r, s, &r, NULL)) != MP_OKAY) { + goto LBL_R; + } + + /* compute y = b**r mod a */ + if ((err = mp_init(&y)) != MP_OKAY) { + goto LBL_R; + } + if ((err = mp_exptmod(b, &r, a, &y)) != MP_OKAY) { + goto LBL_Y; + } + + /* if y != 1 and y != n1 do */ + if ((mp_cmp_d(&y, 1uL) != MP_EQ) && (mp_cmp(&y, &n1) != MP_EQ)) { + j = 1; + /* while j <= s-1 and y != n1 */ + while ((j <= (s - 1)) && (mp_cmp(&y, &n1) != MP_EQ)) { + if ((err = mp_sqrmod(&y, a, &y)) != MP_OKAY) { + goto LBL_Y; + } + + /* if y == 1 then composite */ + if (mp_cmp_d(&y, 1uL) == MP_EQ) { + goto LBL_Y; + } + + ++j; + } + + /* if y != n1 then composite */ + if (mp_cmp(&y, &n1) != MP_EQ) { + goto LBL_Y; + } + } + + /* probably prime now */ + *result = MP_YES; +LBL_Y: + mp_clear(&y); +LBL_R: + mp_clear(&r); +LBL_N1: + mp_clear(&n1); + return err; +} +#endif + +/* End: bn_mp_prime_miller_rabin.c */ + +/* Start: bn_mp_prime_next_prime.c */ +#include "tommath_private.h" +#ifdef BN_MP_PRIME_NEXT_PRIME_C +/* LibTomMath, multiple-precision integer library -- Tom St Denis */ +/* SPDX-License-Identifier: Unlicense */ + +/* finds the next prime after the number "a" using "t" trials + * of Miller-Rabin. + * + * bbs_style = 1 means the prime must be congruent to 3 mod 4 + */ +mp_err mp_prime_next_prime(mp_int *a, int t, int bbs_style) +{ + int x, y; + mp_ord cmp; + mp_err err; + mp_bool res = MP_NO; + mp_digit res_tab[PRIVATE_MP_PRIME_TAB_SIZE], step, kstep; + mp_int b; + + /* force positive */ + a->sign = MP_ZPOS; + + /* simple algo if a is less than the largest prime in the table */ + if (mp_cmp_d(a, s_mp_prime_tab[PRIVATE_MP_PRIME_TAB_SIZE-1]) == MP_LT) { + /* find which prime it is bigger than "a" */ + for (x = 0; x < PRIVATE_MP_PRIME_TAB_SIZE; x++) { + cmp = mp_cmp_d(a, s_mp_prime_tab[x]); + if (cmp == MP_EQ) { + continue; + } + if (cmp != MP_GT) { + if ((bbs_style == 1) && ((s_mp_prime_tab[x] & 3u) != 3u)) { + /* try again until we get a prime congruent to 3 mod 4 */ + continue; + } else { + mp_set(a, s_mp_prime_tab[x]); + return MP_OKAY; + } + } + } + /* fall through to the sieve */ + } + + /* generate a prime congruent to 3 mod 4 or 1/3 mod 4? */ + if (bbs_style == 1) { + kstep = 4; + } else { + kstep = 2; + } + + /* at this point we will use a combination of a sieve and Miller-Rabin */ + + if (bbs_style == 1) { + /* if a mod 4 != 3 subtract the correct value to make it so */ + if ((a->dp[0] & 3u) != 3u) { + if ((err = mp_sub_d(a, (a->dp[0] & 3u) + 1u, a)) != MP_OKAY) { + return err; + } + } + } else { + if (MP_IS_EVEN(a)) { + /* force odd */ + if ((err = mp_sub_d(a, 1uL, a)) != MP_OKAY) { + return err; + } + } + } + + /* generate the restable */ + for (x = 1; x < PRIVATE_MP_PRIME_TAB_SIZE; x++) { + if ((err = mp_mod_d(a, s_mp_prime_tab[x], res_tab + x)) != MP_OKAY) { + return err; + } + } + + /* init temp used for Miller-Rabin Testing */ + if ((err = mp_init(&b)) != MP_OKAY) { + return err; + } + + for (;;) { + /* skip to the next non-trivially divisible candidate */ + step = 0; + do { + /* y == 1 if any residue was zero [e.g. cannot be prime] */ + y = 0; + + /* increase step to next candidate */ + step += kstep; + + /* compute the new residue without using division */ + for (x = 1; x < PRIVATE_MP_PRIME_TAB_SIZE; x++) { + /* add the step to each residue */ + res_tab[x] += kstep; + + /* subtract the modulus [instead of using division] */ + if (res_tab[x] >= s_mp_prime_tab[x]) { + res_tab[x] -= s_mp_prime_tab[x]; + } + + /* set flag if zero */ + if (res_tab[x] == 0u) { + y = 1; + } + } + } while ((y == 1) && (step < (((mp_digit)1 << MP_DIGIT_BIT) - kstep))); + + /* add the step */ + if ((err = mp_add_d(a, step, a)) != MP_OKAY) { + goto LBL_ERR; + } + + /* if didn't pass sieve and step == MP_MAX then skip test */ + if ((y == 1) && (step >= (((mp_digit)1 << MP_DIGIT_BIT) - kstep))) { + continue; + } + + if ((err = mp_prime_is_prime(a, t, &res)) != MP_OKAY) { + goto LBL_ERR; + } + if (res == MP_YES) { + break; + } + } + + err = MP_OKAY; +LBL_ERR: + mp_clear(&b); + return err; +} + +#endif + +/* End: bn_mp_prime_next_prime.c */ + +/* Start: bn_mp_prime_rabin_miller_trials.c */ +#include "tommath_private.h" +#ifdef BN_MP_PRIME_RABIN_MILLER_TRIALS_C +/* LibTomMath, multiple-precision integer library -- Tom St Denis */ +/* SPDX-License-Identifier: Unlicense */ + +static const struct { + int k, t; +} sizes[] = { + { 80, -1 }, /* Use deterministic algorithm for size <= 80 bits */ + { 81, 37 }, /* max. error = 2^(-96)*/ + { 96, 32 }, /* max. error = 2^(-96)*/ + { 128, 40 }, /* max. error = 2^(-112)*/ + { 160, 35 }, /* max. error = 2^(-112)*/ + { 256, 27 }, /* max. error = 2^(-128)*/ + { 384, 16 }, /* max. error = 2^(-128)*/ + { 512, 18 }, /* max. error = 2^(-160)*/ + { 768, 11 }, /* max. error = 2^(-160)*/ + { 896, 10 }, /* max. error = 2^(-160)*/ + { 1024, 12 }, /* max. error = 2^(-192)*/ + { 1536, 8 }, /* max. error = 2^(-192)*/ + { 2048, 6 }, /* max. error = 2^(-192)*/ + { 3072, 4 }, /* max. error = 2^(-192)*/ + { 4096, 5 }, /* max. error = 2^(-256)*/ + { 5120, 4 }, /* max. error = 2^(-256)*/ + { 6144, 4 }, /* max. error = 2^(-256)*/ + { 8192, 3 }, /* max. error = 2^(-256)*/ + { 9216, 3 }, /* max. error = 2^(-256)*/ + { 10240, 2 } /* For bigger keysizes use always at least 2 Rounds */ +}; + +/* returns # of RM trials required for a given bit size */ +int mp_prime_rabin_miller_trials(int size) +{ + int x; + + for (x = 0; x < (int)(sizeof(sizes)/(sizeof(sizes[0]))); x++) { + if (sizes[x].k == size) { + return sizes[x].t; + } else if (sizes[x].k > size) { + return (x == 0) ? sizes[0].t : sizes[x - 1].t; + } + } + return sizes[x-1].t; +} + + +#endif + +/* End: bn_mp_prime_rabin_miller_trials.c */ + +/* Start: bn_mp_prime_rand.c */ +#include "tommath_private.h" +#ifdef BN_MP_PRIME_RAND_C +/* LibTomMath, multiple-precision integer library -- Tom St Denis */ +/* SPDX-License-Identifier: Unlicense */ + +/* makes a truly random prime of a given size (bits), + * + * Flags are as follows: + * + * MP_PRIME_BBS - make prime congruent to 3 mod 4 + * MP_PRIME_SAFE - make sure (p-1)/2 is prime as well (implies MP_PRIME_BBS) + * MP_PRIME_2MSB_ON - make the 2nd highest bit one + * + * You have to supply a callback which fills in a buffer with random bytes. "dat" is a parameter you can + * have passed to the callback (e.g. a state or something). This function doesn't use "dat" itself + * so it can be NULL + * + */ + +/* This is possibly the mother of all prime generation functions, muahahahahaha! */ +mp_err s_mp_prime_random_ex(mp_int *a, int t, int size, int flags, private_mp_prime_callback cb, void *dat) +{ + unsigned char *tmp, maskAND, maskOR_msb, maskOR_lsb; + int bsize, maskOR_msb_offset; + mp_bool res; + mp_err err; + + /* sanity check the input */ + if ((size <= 1) || (t <= 0)) { + return MP_VAL; + } + + /* MP_PRIME_SAFE implies MP_PRIME_BBS */ + if ((flags & MP_PRIME_SAFE) != 0) { + flags |= MP_PRIME_BBS; + } + + /* calc the byte size */ + bsize = (size>>3) + ((size&7)?1:0); + + /* we need a buffer of bsize bytes */ + tmp = (unsigned char *) MP_MALLOC((size_t)bsize); + if (tmp == NULL) { + return MP_MEM; + } + + /* calc the maskAND value for the MSbyte*/ + maskAND = ((size&7) == 0) ? 0xFFu : (unsigned char)(0xFFu >> (8 - (size & 7))); + + /* calc the maskOR_msb */ + maskOR_msb = 0; + maskOR_msb_offset = ((size & 7) == 1) ? 1 : 0; + if ((flags & MP_PRIME_2MSB_ON) != 0) { + maskOR_msb |= (unsigned char)(0x80 >> ((9 - size) & 7)); + } + + /* get the maskOR_lsb */ + maskOR_lsb = 1u; + if ((flags & MP_PRIME_BBS) != 0) { + maskOR_lsb |= 3u; + } + + do { + /* read the bytes */ + if (cb(tmp, bsize, dat) != bsize) { + err = MP_VAL; + goto error; + } + + /* work over the MSbyte */ + tmp[0] &= maskAND; + tmp[0] |= (unsigned char)(1 << ((size - 1) & 7)); + + /* mix in the maskORs */ + tmp[maskOR_msb_offset] |= maskOR_msb; + tmp[bsize-1] |= maskOR_lsb; + + /* read it in */ + /* TODO: casting only for now until all lengths have been changed to the type "size_t"*/ + if ((err = mp_from_ubin(a, tmp, (size_t)bsize)) != MP_OKAY) { + goto error; + } + + /* is it prime? */ + if ((err = mp_prime_is_prime(a, t, &res)) != MP_OKAY) { + goto error; + } + if (res == MP_NO) { + continue; + } + + if ((flags & MP_PRIME_SAFE) != 0) { + /* see if (a-1)/2 is prime */ + if ((err = mp_sub_d(a, 1uL, a)) != MP_OKAY) { + goto error; + } + if ((err = mp_div_2(a, a)) != MP_OKAY) { + goto error; + } + + /* is it prime? */ + if ((err = mp_prime_is_prime(a, t, &res)) != MP_OKAY) { + goto error; + } + } + } while (res == MP_NO); + + if ((flags & MP_PRIME_SAFE) != 0) { + /* restore a to the original value */ + if ((err = mp_mul_2(a, a)) != MP_OKAY) { + goto error; + } + if ((err = mp_add_d(a, 1uL, a)) != MP_OKAY) { + goto error; + } + } + + err = MP_OKAY; +error: + MP_FREE_BUFFER(tmp, (size_t)bsize); + return err; +} + +static int s_mp_rand_cb(unsigned char *dst, int len, void *dat) +{ + (void)dat; + if (len <= 0) { + return len; + } + if (s_mp_rand_source(dst, (size_t)len) != MP_OKAY) { + return 0; + } + return len; +} + +mp_err mp_prime_rand(mp_int *a, int t, int size, int flags) +{ + return s_mp_prime_random_ex(a, t, size, flags, s_mp_rand_cb, NULL); +} + +#endif + +/* End: bn_mp_prime_rand.c */ + +/* Start: bn_mp_prime_strong_lucas_selfridge.c */ +#include "tommath_private.h" +#ifdef BN_MP_PRIME_STRONG_LUCAS_SELFRIDGE_C + +/* LibTomMath, multiple-precision integer library -- Tom St Denis */ +/* SPDX-License-Identifier: Unlicense */ + +/* + * See file bn_mp_prime_is_prime.c or the documentation in doc/bn.tex for the details + */ +#ifndef LTM_USE_ONLY_MR + +/* + * 8-bit is just too small. You can try the Frobenius test + * but that frobenius test can fail, too, for the same reason. + */ +#ifndef MP_8BIT + +/* + * multiply bigint a with int d and put the result in c + * Like mp_mul_d() but with a signed long as the small input + */ +static mp_err s_mp_mul_si(const mp_int *a, int32_t d, mp_int *c) +{ + mp_int t; + mp_err err; + + if ((err = mp_init(&t)) != MP_OKAY) { + return err; + } + + /* + * mp_digit might be smaller than a long, which excludes + * the use of mp_mul_d() here. + */ + mp_set_i32(&t, d); + err = mp_mul(a, &t, c); + mp_clear(&t); + return err; +} +/* + Strong Lucas-Selfridge test. + returns MP_YES if it is a strong L-S prime, MP_NO if it is composite + + Code ported from Thomas Ray Nicely's implementation of the BPSW test + at http://www.trnicely.net/misc/bpsw.html + + Freeware copyright (C) 2016 Thomas R. Nicely <http://www.trnicely.net>. + Released into the public domain by the author, who disclaims any legal + liability arising from its use + + The multi-line comments are made by Thomas R. Nicely and are copied verbatim. + Additional comments marked "CZ" (without the quotes) are by the code-portist. + + (If that name sounds familiar, he is the guy who found the fdiv bug in the + Pentium (P5x, I think) Intel processor) +*/ +mp_err mp_prime_strong_lucas_selfridge(const mp_int *a, mp_bool *result) +{ + /* CZ TODO: choose better variable names! */ + mp_int Dz, gcd, Np1, Uz, Vz, U2mz, V2mz, Qmz, Q2mz, Qkdz, T1z, T2z, T3z, T4z, Q2kdz; + /* CZ TODO: Some of them need the full 32 bit, hence the (temporary) exclusion of MP_8BIT */ + int32_t D, Ds, J, sign, P, Q, r, s, u, Nbits; + mp_err err; + mp_bool oddness; + + *result = MP_NO; + /* + Find the first element D in the sequence {5, -7, 9, -11, 13, ...} + such that Jacobi(D,N) = -1 (Selfridge's algorithm). Theory + indicates that, if N is not a perfect square, D will "nearly + always" be "small." Just in case, an overflow trap for D is + included. + */ + + if ((err = mp_init_multi(&Dz, &gcd, &Np1, &Uz, &Vz, &U2mz, &V2mz, &Qmz, &Q2mz, &Qkdz, &T1z, &T2z, &T3z, &T4z, &Q2kdz, + NULL)) != MP_OKAY) { + return err; + } + + D = 5; + sign = 1; + + for (;;) { + Ds = sign * D; + sign = -sign; + mp_set_u32(&Dz, (uint32_t)D); + if ((err = mp_gcd(a, &Dz, &gcd)) != MP_OKAY) goto LBL_LS_ERR; + + /* if 1 < GCD < N then N is composite with factor "D", and + Jacobi(D,N) is technically undefined (but often returned + as zero). */ + if ((mp_cmp_d(&gcd, 1uL) == MP_GT) && (mp_cmp(&gcd, a) == MP_LT)) { + goto LBL_LS_ERR; + } + if (Ds < 0) { + Dz.sign = MP_NEG; + } + if ((err = mp_kronecker(&Dz, a, &J)) != MP_OKAY) goto LBL_LS_ERR; + + if (J == -1) { + break; + } + D += 2; + + if (D > (INT_MAX - 2)) { + err = MP_VAL; + goto LBL_LS_ERR; + } + } + + + + P = 1; /* Selfridge's choice */ + Q = (1 - Ds) / 4; /* Required so D = P*P - 4*Q */ + + /* NOTE: The conditions (a) N does not divide Q, and + (b) D is square-free or not a perfect square, are included by + some authors; e.g., "Prime numbers and computer methods for + factorization," Hans Riesel (2nd ed., 1994, Birkhauser, Boston), + p. 130. For this particular application of Lucas sequences, + these conditions were found to be immaterial. */ + + /* Now calculate N - Jacobi(D,N) = N + 1 (even), and calculate the + odd positive integer d and positive integer s for which + N + 1 = 2^s*d (similar to the step for N - 1 in Miller's test). + The strong Lucas-Selfridge test then returns N as a strong + Lucas probable prime (slprp) if any of the following + conditions is met: U_d=0, V_d=0, V_2d=0, V_4d=0, V_8d=0, + V_16d=0, ..., etc., ending with V_{2^(s-1)*d}=V_{(N+1)/2}=0 + (all equalities mod N). Thus d is the highest index of U that + must be computed (since V_2m is independent of U), compared + to U_{N+1} for the standard Lucas-Selfridge test; and no + index of V beyond (N+1)/2 is required, just as in the + standard Lucas-Selfridge test. However, the quantity Q^d must + be computed for use (if necessary) in the latter stages of + the test. The result is that the strong Lucas-Selfridge test + has a running time only slightly greater (order of 10 %) than + that of the standard Lucas-Selfridge test, while producing + only (roughly) 30 % as many pseudoprimes (and every strong + Lucas pseudoprime is also a standard Lucas pseudoprime). Thus + the evidence indicates that the strong Lucas-Selfridge test is + more effective than the standard Lucas-Selfridge test, and a + Baillie-PSW test based on the strong Lucas-Selfridge test + should be more reliable. */ + + if ((err = mp_add_d(a, 1uL, &Np1)) != MP_OKAY) goto LBL_LS_ERR; + s = mp_cnt_lsb(&Np1); + + /* CZ + * This should round towards zero because + * Thomas R. Nicely used GMP's mpz_tdiv_q_2exp() + * and mp_div_2d() is equivalent. Additionally: + * dividing an even number by two does not produce + * any leftovers. + */ + if ((err = mp_div_2d(&Np1, s, &Dz, NULL)) != MP_OKAY) goto LBL_LS_ERR; + /* We must now compute U_d and V_d. Since d is odd, the accumulated + values U and V are initialized to U_1 and V_1 (if the target + index were even, U and V would be initialized instead to U_0=0 + and V_0=2). The values of U_2m and V_2m are also initialized to + U_1 and V_1; the FOR loop calculates in succession U_2 and V_2, + U_4 and V_4, U_8 and V_8, etc. If the corresponding bits + (1, 2, 3, ...) of t are on (the zero bit having been accounted + for in the initialization of U and V), these values are then + combined with the previous totals for U and V, using the + composition formulas for addition of indices. */ + + mp_set(&Uz, 1uL); /* U=U_1 */ + mp_set(&Vz, (mp_digit)P); /* V=V_1 */ + mp_set(&U2mz, 1uL); /* U_1 */ + mp_set(&V2mz, (mp_digit)P); /* V_1 */ + + mp_set_i32(&Qmz, Q); + if ((err = mp_mul_2(&Qmz, &Q2mz)) != MP_OKAY) goto LBL_LS_ERR; + /* Initializes calculation of Q^d */ + mp_set_i32(&Qkdz, Q); + + Nbits = mp_count_bits(&Dz); + + for (u = 1; u < Nbits; u++) { /* zero bit off, already accounted for */ + /* Formulas for doubling of indices (carried out mod N). Note that + * the indices denoted as "2m" are actually powers of 2, specifically + * 2^(ul-1) beginning each loop and 2^ul ending each loop. + * + * U_2m = U_m*V_m + * V_2m = V_m*V_m - 2*Q^m + */ + + if ((err = mp_mul(&U2mz, &V2mz, &U2mz)) != MP_OKAY) goto LBL_LS_ERR; + if ((err = mp_mod(&U2mz, a, &U2mz)) != MP_OKAY) goto LBL_LS_ERR; + if ((err = mp_sqr(&V2mz, &V2mz)) != MP_OKAY) goto LBL_LS_ERR; + if ((err = mp_sub(&V2mz, &Q2mz, &V2mz)) != MP_OKAY) goto LBL_LS_ERR; + if ((err = mp_mod(&V2mz, a, &V2mz)) != MP_OKAY) goto LBL_LS_ERR; + + /* Must calculate powers of Q for use in V_2m, also for Q^d later */ + if ((err = mp_sqr(&Qmz, &Qmz)) != MP_OKAY) goto LBL_LS_ERR; + + /* prevents overflow */ /* CZ still necessary without a fixed prealloc'd mem.? */ + if ((err = mp_mod(&Qmz, a, &Qmz)) != MP_OKAY) goto LBL_LS_ERR; + if ((err = mp_mul_2(&Qmz, &Q2mz)) != MP_OKAY) goto LBL_LS_ERR; + + if (s_mp_get_bit(&Dz, (unsigned int)u) == MP_YES) { + /* Formulas for addition of indices (carried out mod N); + * + * U_(m+n) = (U_m*V_n + U_n*V_m)/2 + * V_(m+n) = (V_m*V_n + D*U_m*U_n)/2 + * + * Be careful with division by 2 (mod N)! + */ + if ((err = mp_mul(&U2mz, &Vz, &T1z)) != MP_OKAY) goto LBL_LS_ERR; + if ((err = mp_mul(&Uz, &V2mz, &T2z)) != MP_OKAY) goto LBL_LS_ERR; + if ((err = mp_mul(&V2mz, &Vz, &T3z)) != MP_OKAY) goto LBL_LS_ERR; + if ((err = mp_mul(&U2mz, &Uz, &T4z)) != MP_OKAY) goto LBL_LS_ERR; + if ((err = s_mp_mul_si(&T4z, Ds, &T4z)) != MP_OKAY) goto LBL_LS_ERR; + if ((err = mp_add(&T1z, &T2z, &Uz)) != MP_OKAY) goto LBL_LS_ERR; + if (MP_IS_ODD(&Uz)) { + if ((err = mp_add(&Uz, a, &Uz)) != MP_OKAY) goto LBL_LS_ERR; + } + /* CZ + * This should round towards negative infinity because + * Thomas R. Nicely used GMP's mpz_fdiv_q_2exp(). + * But mp_div_2() does not do so, it is truncating instead. + */ + oddness = MP_IS_ODD(&Uz) ? MP_YES : MP_NO; + if ((err = mp_div_2(&Uz, &Uz)) != MP_OKAY) goto LBL_LS_ERR; + if ((Uz.sign == MP_NEG) && (oddness != MP_NO)) { + if ((err = mp_sub_d(&Uz, 1uL, &Uz)) != MP_OKAY) goto LBL_LS_ERR; + } + if ((err = mp_add(&T3z, &T4z, &Vz)) != MP_OKAY) goto LBL_LS_ERR; + if (MP_IS_ODD(&Vz)) { + if ((err = mp_add(&Vz, a, &Vz)) != MP_OKAY) goto LBL_LS_ERR; + } + oddness = MP_IS_ODD(&Vz) ? MP_YES : MP_NO; + if ((err = mp_div_2(&Vz, &Vz)) != MP_OKAY) goto LBL_LS_ERR; + if ((Vz.sign == MP_NEG) && (oddness != MP_NO)) { + if ((err = mp_sub_d(&Vz, 1uL, &Vz)) != MP_OKAY) goto LBL_LS_ERR; + } + if ((err = mp_mod(&Uz, a, &Uz)) != MP_OKAY) goto LBL_LS_ERR; + if ((err = mp_mod(&Vz, a, &Vz)) != MP_OKAY) goto LBL_LS_ERR; + + /* Calculating Q^d for later use */ + if ((err = mp_mul(&Qkdz, &Qmz, &Qkdz)) != MP_OKAY) goto LBL_LS_ERR; + if ((err = mp_mod(&Qkdz, a, &Qkdz)) != MP_OKAY) goto LBL_LS_ERR; + } + } + + /* If U_d or V_d is congruent to 0 mod N, then N is a prime or a + strong Lucas pseudoprime. */ + if (MP_IS_ZERO(&Uz) || MP_IS_ZERO(&Vz)) { + *result = MP_YES; + goto LBL_LS_ERR; + } + + /* NOTE: Ribenboim ("The new book of prime number records," 3rd ed., + 1995/6) omits the condition V0 on p.142, but includes it on + p. 130. The condition is NECESSARY; otherwise the test will + return false negatives---e.g., the primes 29 and 2000029 will be + returned as composite. */ + + /* Otherwise, we must compute V_2d, V_4d, V_8d, ..., V_{2^(s-1)*d} + by repeated use of the formula V_2m = V_m*V_m - 2*Q^m. If any of + these are congruent to 0 mod N, then N is a prime or a strong + Lucas pseudoprime. */ + + /* Initialize 2*Q^(d*2^r) for V_2m */ + if ((err = mp_mul_2(&Qkdz, &Q2kdz)) != MP_OKAY) goto LBL_LS_ERR; + + for (r = 1; r < s; r++) { + if ((err = mp_sqr(&Vz, &Vz)) != MP_OKAY) goto LBL_LS_ERR; + if ((err = mp_sub(&Vz, &Q2kdz, &Vz)) != MP_OKAY) goto LBL_LS_ERR; + if ((err = mp_mod(&Vz, a, &Vz)) != MP_OKAY) goto LBL_LS_ERR; + if (MP_IS_ZERO(&Vz)) { + *result = MP_YES; + goto LBL_LS_ERR; + } + /* Calculate Q^{d*2^r} for next r (final iteration irrelevant). */ + if (r < (s - 1)) { + if ((err = mp_sqr(&Qkdz, &Qkdz)) != MP_OKAY) goto LBL_LS_ERR; + if ((err = mp_mod(&Qkdz, a, &Qkdz)) != MP_OKAY) goto LBL_LS_ERR; + if ((err = mp_mul_2(&Qkdz, &Q2kdz)) != MP_OKAY) goto LBL_LS_ERR; + } + } +LBL_LS_ERR: + mp_clear_multi(&Q2kdz, &T4z, &T3z, &T2z, &T1z, &Qkdz, &Q2mz, &Qmz, &V2mz, &U2mz, &Vz, &Uz, &Np1, &gcd, &Dz, NULL); + return err; +} +#endif +#endif +#endif + +/* End: bn_mp_prime_strong_lucas_selfridge.c */ + +/* Start: bn_mp_radix_size.c */ +#include "tommath_private.h" +#ifdef BN_MP_RADIX_SIZE_C +/* LibTomMath, multiple-precision integer library -- Tom St Denis */ +/* SPDX-License-Identifier: Unlicense */ + +/* returns size of ASCII representation */ +mp_err mp_radix_size(const mp_int *a, int radix, int *size) +{ + mp_err err; + int digs; + mp_int t; + mp_digit d; + + *size = 0; + + /* make sure the radix is in range */ + if ((radix < 2) || (radix > 64)) { + return MP_VAL; + } + + if (MP_IS_ZERO(a)) { + *size = 2; + return MP_OKAY; + } + + /* special case for binary */ + if (radix == 2) { + *size = (mp_count_bits(a) + ((a->sign == MP_NEG) ? 1 : 0) + 1); + return MP_OKAY; + } + + /* digs is the digit count */ + digs = 0; + + /* if it's negative add one for the sign */ + if (a->sign == MP_NEG) { + ++digs; + } + + /* init a copy of the input */ + if ((err = mp_init_copy(&t, a)) != MP_OKAY) { + return err; + } + + /* force temp to positive */ + t.sign = MP_ZPOS; + + /* fetch out all of the digits */ + while (!MP_IS_ZERO(&t)) { + if ((err = mp_div_d(&t, (mp_digit)radix, &t, &d)) != MP_OKAY) { + goto LBL_ERR; + } + ++digs; + } + + /* return digs + 1, the 1 is for the NULL byte that would be required. */ + *size = digs + 1; + err = MP_OKAY; + +LBL_ERR: + mp_clear(&t); + return err; +} + +#endif + +/* End: bn_mp_radix_size.c */ + +/* Start: bn_mp_radix_smap.c */ +#include "tommath_private.h" +#ifdef BN_MP_RADIX_SMAP_C +/* LibTomMath, multiple-precision integer library -- Tom St Denis */ +/* SPDX-License-Identifier: Unlicense */ + +/* chars used in radix conversions */ +const char *const mp_s_rmap = "0123456789ABCDEFGHIJKLMNOPQRSTUVWXYZabcdefghijklmnopqrstuvwxyz+/"; +const uint8_t mp_s_rmap_reverse[] = { + 0xff, 0xff, 0xff, 0x3e, 0xff, 0xff, 0xff, 0x3f, /* ()*+,-./ */ + 0x00, 0x01, 0x02, 0x03, 0x04, 0x05, 0x06, 0x07, /* 01234567 */ + 0x08, 0x09, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, /* 89:;<=>? */ + 0xff, 0x0a, 0x0b, 0x0c, 0x0d, 0x0e, 0x0f, 0x10, /* @ABCDEFG */ + 0x11, 0x12, 0x13, 0x14, 0x15, 0x16, 0x17, 0x18, /* HIJKLMNO */ + 0x19, 0x1a, 0x1b, 0x1c, 0x1d, 0x1e, 0x1f, 0x20, /* PQRSTUVW */ + 0x21, 0x22, 0x23, 0xff, 0xff, 0xff, 0xff, 0xff, /* XYZ[\]^_ */ + 0xff, 0x24, 0x25, 0x26, 0x27, 0x28, 0x29, 0x2a, /* `abcdefg */ + 0x2b, 0x2c, 0x2d, 0x2e, 0x2f, 0x30, 0x31, 0x32, /* hijklmno */ + 0x33, 0x34, 0x35, 0x36, 0x37, 0x38, 0x39, 0x3a, /* pqrstuvw */ + 0x3b, 0x3c, 0x3d, 0xff, 0xff, 0xff, 0xff, 0xff, /* xyz{|}~. */ +}; +const size_t mp_s_rmap_reverse_sz = sizeof(mp_s_rmap_reverse); +#endif + +/* End: bn_mp_radix_smap.c */ + +/* Start: bn_mp_rand.c */ +#include "tommath_private.h" +#ifdef BN_MP_RAND_C +/* LibTomMath, multiple-precision integer library -- Tom St Denis */ +/* SPDX-License-Identifier: Unlicense */ + +mp_err(*s_mp_rand_source)(void *out, size_t size) = s_mp_rand_platform; + +void mp_rand_source(mp_err(*source)(void *out, size_t size)) +{ + s_mp_rand_source = (source == NULL) ? s_mp_rand_platform : source; +} + +mp_err mp_rand(mp_int *a, int digits) +{ + int i; + mp_err err; + + mp_zero(a); + + if (digits <= 0) { + return MP_OKAY; + } + + if ((err = mp_grow(a, digits)) != MP_OKAY) { + return err; + } + + if ((err = s_mp_rand_source(a->dp, (size_t)digits * sizeof(mp_digit))) != MP_OKAY) { + return err; + } + + /* TODO: We ensure that the highest digit is nonzero. Should this be removed? */ + while ((a->dp[digits - 1] & MP_MASK) == 0u) { + if ((err = s_mp_rand_source(a->dp + digits - 1, sizeof(mp_digit))) != MP_OKAY) { + return err; + } + } + + a->used = digits; + for (i = 0; i < digits; ++i) { + a->dp[i] &= MP_MASK; + } + + return MP_OKAY; +} +#endif + +/* End: bn_mp_rand.c */ + +/* Start: bn_mp_read_radix.c */ +#include "tommath_private.h" +#ifdef BN_MP_READ_RADIX_C +/* LibTomMath, multiple-precision integer library -- Tom St Denis */ +/* SPDX-License-Identifier: Unlicense */ + +#define MP_TOUPPER(c) ((((c) >= 'a') && ((c) <= 'z')) ? (((c) + 'A') - 'a') : (c)) + +/* read a string [ASCII] in a given radix */ +mp_err mp_read_radix(mp_int *a, const char *str, int radix) +{ + mp_err err; + int y; + mp_sign neg; + unsigned pos; + char ch; + + /* zero the digit bignum */ + mp_zero(a); + + /* make sure the radix is ok */ + if ((radix < 2) || (radix > 64)) { + return MP_VAL; + } + + /* if the leading digit is a + * minus set the sign to negative. + */ + if (*str == '-') { + ++str; + neg = MP_NEG; + } else { + neg = MP_ZPOS; + } + + /* set the integer to the default of zero */ + mp_zero(a); + + /* process each digit of the string */ + while (*str != '\0') { + /* if the radix <= 36 the conversion is case insensitive + * this allows numbers like 1AB and 1ab to represent the same value + * [e.g. in hex] + */ + ch = (radix <= 36) ? (char)MP_TOUPPER((int)*str) : *str; + pos = (unsigned)(ch - '('); + if (mp_s_rmap_reverse_sz < pos) { + break; + } + y = (int)mp_s_rmap_reverse[pos]; + + /* if the char was found in the map + * and is less than the given radix add it + * to the number, otherwise exit the loop. + */ + if ((y == 0xff) || (y >= radix)) { + break; + } + if ((err = mp_mul_d(a, (mp_digit)radix, a)) != MP_OKAY) { + return err; + } + if ((err = mp_add_d(a, (mp_digit)y, a)) != MP_OKAY) { + return err; + } + ++str; + } + + /* if an illegal character was found, fail. */ + if (!((*str == '\0') || (*str == '\r') || (*str == '\n'))) { + mp_zero(a); + return MP_VAL; + } + + /* set the sign only if a != 0 */ + if (!MP_IS_ZERO(a)) { + a->sign = neg; + } + return MP_OKAY; +} +#endif + +/* End: bn_mp_read_radix.c */ + +/* Start: bn_mp_reduce.c */ +#include "tommath_private.h" +#ifdef BN_MP_REDUCE_C +/* LibTomMath, multiple-precision integer library -- Tom St Denis */ +/* SPDX-License-Identifier: Unlicense */ + +/* reduces x mod m, assumes 0 < x < m**2, mu is + * precomputed via mp_reduce_setup. + * From HAC pp.604 Algorithm 14.42 + */ +mp_err mp_reduce(mp_int *x, const mp_int *m, const mp_int *mu) +{ + mp_int q; + mp_err err; + int um = m->used; + + /* q = x */ + if ((err = mp_init_copy(&q, x)) != MP_OKAY) { + return err; + } + + /* q1 = x / b**(k-1) */ + mp_rshd(&q, um - 1); + + /* according to HAC this optimization is ok */ + if ((mp_digit)um > ((mp_digit)1 << (MP_DIGIT_BIT - 1))) { + if ((err = mp_mul(&q, mu, &q)) != MP_OKAY) { + goto CLEANUP; + } + } else if (MP_HAS(S_MP_MUL_HIGH_DIGS)) { + if ((err = s_mp_mul_high_digs(&q, mu, &q, um)) != MP_OKAY) { + goto CLEANUP; + } + } else if (MP_HAS(S_MP_MUL_HIGH_DIGS_FAST)) { + if ((err = s_mp_mul_high_digs_fast(&q, mu, &q, um)) != MP_OKAY) { + goto CLEANUP; + } + } else { + err = MP_VAL; + goto CLEANUP; + } + + /* q3 = q2 / b**(k+1) */ + mp_rshd(&q, um + 1); + + /* x = x mod b**(k+1), quick (no division) */ + if ((err = mp_mod_2d(x, MP_DIGIT_BIT * (um + 1), x)) != MP_OKAY) { + goto CLEANUP; + } + + /* q = q * m mod b**(k+1), quick (no division) */ + if ((err = s_mp_mul_digs(&q, m, &q, um + 1)) != MP_OKAY) { + goto CLEANUP; + } + + /* x = x - q */ + if ((err = mp_sub(x, &q, x)) != MP_OKAY) { + goto CLEANUP; + } + + /* If x < 0, add b**(k+1) to it */ + if (mp_cmp_d(x, 0uL) == MP_LT) { + mp_set(&q, 1uL); + if ((err = mp_lshd(&q, um + 1)) != MP_OKAY) { + goto CLEANUP; + } + if ((err = mp_add(x, &q, x)) != MP_OKAY) { + goto CLEANUP; + } + } + + /* Back off if it's too big */ + while (mp_cmp(x, m) != MP_LT) { + if ((err = s_mp_sub(x, m, x)) != MP_OKAY) { + goto CLEANUP; + } + } + +CLEANUP: + mp_clear(&q); + + return err; +} +#endif + +/* End: bn_mp_reduce.c */ + +/* Start: bn_mp_reduce_2k.c */ +#include "tommath_private.h" +#ifdef BN_MP_REDUCE_2K_C +/* LibTomMath, multiple-precision integer library -- Tom St Denis */ +/* SPDX-License-Identifier: Unlicense */ + +/* reduces a modulo n where n is of the form 2**p - d */ +mp_err mp_reduce_2k(mp_int *a, const mp_int *n, mp_digit d) +{ + mp_int q; + mp_err err; + int p; + + if ((err = mp_init(&q)) != MP_OKAY) { + return err; + } + + p = mp_count_bits(n); +top: + /* q = a/2**p, a = a mod 2**p */ + if ((err = mp_div_2d(a, p, &q, a)) != MP_OKAY) { + goto LBL_ERR; + } + + if (d != 1u) { + /* q = q * d */ + if ((err = mp_mul_d(&q, d, &q)) != MP_OKAY) { + goto LBL_ERR; + } + } + + /* a = a + q */ + if ((err = s_mp_add(a, &q, a)) != MP_OKAY) { + goto LBL_ERR; + } + + if (mp_cmp_mag(a, n) != MP_LT) { + if ((err = s_mp_sub(a, n, a)) != MP_OKAY) { + goto LBL_ERR; + } + goto top; + } + +LBL_ERR: + mp_clear(&q); + return err; +} + +#endif + +/* End: bn_mp_reduce_2k.c */ + +/* Start: bn_mp_reduce_2k_l.c */ +#include "tommath_private.h" +#ifdef BN_MP_REDUCE_2K_L_C +/* LibTomMath, multiple-precision integer library -- Tom St Denis */ +/* SPDX-License-Identifier: Unlicense */ + +/* reduces a modulo n where n is of the form 2**p - d + This differs from reduce_2k since "d" can be larger + than a single digit. +*/ +mp_err mp_reduce_2k_l(mp_int *a, const mp_int *n, const mp_int *d) +{ + mp_int q; + mp_err err; + int p; + + if ((err = mp_init(&q)) != MP_OKAY) { + return err; + } + + p = mp_count_bits(n); +top: + /* q = a/2**p, a = a mod 2**p */ + if ((err = mp_div_2d(a, p, &q, a)) != MP_OKAY) { + goto LBL_ERR; + } + + /* q = q * d */ + if ((err = mp_mul(&q, d, &q)) != MP_OKAY) { + goto LBL_ERR; + } + + /* a = a + q */ + if ((err = s_mp_add(a, &q, a)) != MP_OKAY) { + goto LBL_ERR; + } + + if (mp_cmp_mag(a, n) != MP_LT) { + if ((err = s_mp_sub(a, n, a)) != MP_OKAY) { + goto LBL_ERR; + } + goto top; + } + +LBL_ERR: + mp_clear(&q); + return err; +} + +#endif + +/* End: bn_mp_reduce_2k_l.c */ + +/* Start: bn_mp_reduce_2k_setup.c */ +#include "tommath_private.h" +#ifdef BN_MP_REDUCE_2K_SETUP_C +/* LibTomMath, multiple-precision integer library -- Tom St Denis */ +/* SPDX-License-Identifier: Unlicense */ + +/* determines the setup value */ +mp_err mp_reduce_2k_setup(const mp_int *a, mp_digit *d) +{ + mp_err err; + mp_int tmp; + int p; + + if ((err = mp_init(&tmp)) != MP_OKAY) { + return err; + } + + p = mp_count_bits(a); + if ((err = mp_2expt(&tmp, p)) != MP_OKAY) { + mp_clear(&tmp); + return err; + } + + if ((err = s_mp_sub(&tmp, a, &tmp)) != MP_OKAY) { + mp_clear(&tmp); + return err; + } + + *d = tmp.dp[0]; + mp_clear(&tmp); + return MP_OKAY; +} +#endif + +/* End: bn_mp_reduce_2k_setup.c */ + +/* Start: bn_mp_reduce_2k_setup_l.c */ +#include "tommath_private.h" +#ifdef BN_MP_REDUCE_2K_SETUP_L_C +/* LibTomMath, multiple-precision integer library -- Tom St Denis */ +/* SPDX-License-Identifier: Unlicense */ + +/* determines the setup value */ +mp_err mp_reduce_2k_setup_l(const mp_int *a, mp_int *d) +{ + mp_err err; + mp_int tmp; + + if ((err = mp_init(&tmp)) != MP_OKAY) { + return err; + } + + if ((err = mp_2expt(&tmp, mp_count_bits(a))) != MP_OKAY) { + goto LBL_ERR; + } + + if ((err = s_mp_sub(&tmp, a, d)) != MP_OKAY) { + goto LBL_ERR; + } + +LBL_ERR: + mp_clear(&tmp); + return err; +} +#endif + +/* End: bn_mp_reduce_2k_setup_l.c */ + +/* Start: bn_mp_reduce_is_2k.c */ +#include "tommath_private.h" +#ifdef BN_MP_REDUCE_IS_2K_C +/* LibTomMath, multiple-precision integer library -- Tom St Denis */ +/* SPDX-License-Identifier: Unlicense */ + +/* determines if mp_reduce_2k can be used */ +mp_bool mp_reduce_is_2k(const mp_int *a) +{ + int ix, iy, iw; + mp_digit iz; + + if (a->used == 0) { + return MP_NO; + } else if (a->used == 1) { + return MP_YES; + } else if (a->used > 1) { + iy = mp_count_bits(a); + iz = 1; + iw = 1; + + /* Test every bit from the second digit up, must be 1 */ + for (ix = MP_DIGIT_BIT; ix < iy; ix++) { + if ((a->dp[iw] & iz) == 0u) { + return MP_NO; + } + iz <<= 1; + if (iz > MP_DIGIT_MAX) { + ++iw; + iz = 1; + } + } + return MP_YES; + } else { + return MP_YES; + } +} + +#endif + +/* End: bn_mp_reduce_is_2k.c */ + +/* Start: bn_mp_reduce_is_2k_l.c */ +#include "tommath_private.h" +#ifdef BN_MP_REDUCE_IS_2K_L_C +/* LibTomMath, multiple-precision integer library -- Tom St Denis */ +/* SPDX-License-Identifier: Unlicense */ + +/* determines if reduce_2k_l can be used */ +mp_bool mp_reduce_is_2k_l(const mp_int *a) +{ + int ix, iy; + + if (a->used == 0) { + return MP_NO; + } else if (a->used == 1) { + return MP_YES; + } else if (a->used > 1) { + /* if more than half of the digits are -1 we're sold */ + for (iy = ix = 0; ix < a->used; ix++) { + if (a->dp[ix] == MP_DIGIT_MAX) { + ++iy; + } + } + return (iy >= (a->used/2)) ? MP_YES : MP_NO; + } else { + return MP_NO; + } +} + +#endif + +/* End: bn_mp_reduce_is_2k_l.c */ + +/* Start: bn_mp_reduce_setup.c */ +#include "tommath_private.h" +#ifdef BN_MP_REDUCE_SETUP_C +/* LibTomMath, multiple-precision integer library -- Tom St Denis */ +/* SPDX-License-Identifier: Unlicense */ + +/* pre-calculate the value required for Barrett reduction + * For a given modulus "b" it calulates the value required in "a" + */ +mp_err mp_reduce_setup(mp_int *a, const mp_int *b) +{ + mp_err err; + if ((err = mp_2expt(a, b->used * 2 * MP_DIGIT_BIT)) != MP_OKAY) { + return err; + } + return mp_div(a, b, a, NULL); +} +#endif + +/* End: bn_mp_reduce_setup.c */ + +/* Start: bn_mp_root_u32.c */ +#include "tommath_private.h" +#ifdef BN_MP_ROOT_U32_C +/* LibTomMath, multiple-precision integer library -- Tom St Denis */ +/* SPDX-License-Identifier: Unlicense */ + +/* find the n'th root of an integer + * + * Result found such that (c)**b <= a and (c+1)**b > a + * + * This algorithm uses Newton's approximation + * x[i+1] = x[i] - f(x[i])/f'(x[i]) + * which will find the root in log(N) time where + * each step involves a fair bit. + */ +mp_err mp_root_u32(const mp_int *a, uint32_t b, mp_int *c) +{ + mp_int t1, t2, t3, a_; + mp_ord cmp; + int ilog2; + mp_err err; + + /* input must be positive if b is even */ + if (((b & 1u) == 0u) && (a->sign == MP_NEG)) { + return MP_VAL; + } + + if ((err = mp_init_multi(&t1, &t2, &t3, NULL)) != MP_OKAY) { + return err; + } + + /* if a is negative fudge the sign but keep track */ + a_ = *a; + a_.sign = MP_ZPOS; + + /* Compute seed: 2^(log_2(n)/b + 2)*/ + ilog2 = mp_count_bits(a); + + /* + If "b" is larger than INT_MAX it is also larger than + log_2(n) because the bit-length of the "n" is measured + with an int and hence the root is always < 2 (two). + */ + if (b > (uint32_t)(INT_MAX/2)) { + mp_set(c, 1uL); + c->sign = a->sign; + err = MP_OKAY; + goto LBL_ERR; + } + + /* "b" is smaller than INT_MAX, we can cast safely */ + if (ilog2 < (int)b) { + mp_set(c, 1uL); + c->sign = a->sign; + err = MP_OKAY; + goto LBL_ERR; + } + ilog2 = ilog2 / ((int)b); + if (ilog2 == 0) { + mp_set(c, 1uL); + c->sign = a->sign; + err = MP_OKAY; + goto LBL_ERR; + } + /* Start value must be larger than root */ + ilog2 += 2; + if ((err = mp_2expt(&t2,ilog2)) != MP_OKAY) goto LBL_ERR; + do { + /* t1 = t2 */ + if ((err = mp_copy(&t2, &t1)) != MP_OKAY) goto LBL_ERR; + + /* t2 = t1 - ((t1**b - a) / (b * t1**(b-1))) */ + + /* t3 = t1**(b-1) */ + if ((err = mp_expt_u32(&t1, b - 1u, &t3)) != MP_OKAY) goto LBL_ERR; + + /* numerator */ + /* t2 = t1**b */ + if ((err = mp_mul(&t3, &t1, &t2)) != MP_OKAY) goto LBL_ERR; + + /* t2 = t1**b - a */ + if ((err = mp_sub(&t2, &a_, &t2)) != MP_OKAY) goto LBL_ERR; + + /* denominator */ + /* t3 = t1**(b-1) * b */ + if ((err = mp_mul_d(&t3, b, &t3)) != MP_OKAY) goto LBL_ERR; + + /* t3 = (t1**b - a)/(b * t1**(b-1)) */ + if ((err = mp_div(&t2, &t3, &t3, NULL)) != MP_OKAY) goto LBL_ERR; + + if ((err = mp_sub(&t1, &t3, &t2)) != MP_OKAY) goto LBL_ERR; + + /* + Number of rounds is at most log_2(root). If it is more it + got stuck, so break out of the loop and do the rest manually. + */ + if (ilog2-- == 0) { + break; + } + } while (mp_cmp(&t1, &t2) != MP_EQ); + + /* result can be off by a few so check */ + /* Loop beneath can overshoot by one if found root is smaller than actual root */ + for (;;) { + if ((err = mp_expt_u32(&t1, b, &t2)) != MP_OKAY) goto LBL_ERR; + cmp = mp_cmp(&t2, &a_); + if (cmp == MP_EQ) { + err = MP_OKAY; + goto LBL_ERR; + } + if (cmp == MP_LT) { + if ((err = mp_add_d(&t1, 1uL, &t1)) != MP_OKAY) goto LBL_ERR; + } else { + break; + } + } + /* correct overshoot from above or from recurrence */ + for (;;) { + if ((err = mp_expt_u32(&t1, b, &t2)) != MP_OKAY) goto LBL_ERR; + if (mp_cmp(&t2, &a_) == MP_GT) { + if ((err = mp_sub_d(&t1, 1uL, &t1)) != MP_OKAY) goto LBL_ERR; + } else { + break; + } + } + + /* set the result */ + mp_exch(&t1, c); + + /* set the sign of the result */ + c->sign = a->sign; + + err = MP_OKAY; + +LBL_ERR: + mp_clear_multi(&t1, &t2, &t3, NULL); + return err; +} + +#endif + +/* End: bn_mp_root_u32.c */ + +/* Start: bn_mp_rshd.c */ +#include "tommath_private.h" +#ifdef BN_MP_RSHD_C +/* LibTomMath, multiple-precision integer library -- Tom St Denis */ +/* SPDX-License-Identifier: Unlicense */ + +/* shift right a certain amount of digits */ +void mp_rshd(mp_int *a, int b) +{ + int x; + mp_digit *bottom, *top; + + /* if b <= 0 then ignore it */ + if (b <= 0) { + return; + } + + /* if b > used then simply zero it and return */ + if (a->used <= b) { + mp_zero(a); + return; + } + + /* shift the digits down */ + + /* bottom */ + bottom = a->dp; + + /* top [offset into digits] */ + top = a->dp + b; + + /* this is implemented as a sliding window where + * the window is b-digits long and digits from + * the top of the window are copied to the bottom + * + * e.g. + + b-2 | b-1 | b0 | b1 | b2 | ... | bb | ----> + /\ | ----> + \-------------------/ ----> + */ + for (x = 0; x < (a->used - b); x++) { + *bottom++ = *top++; + } + + /* zero the top digits */ + MP_ZERO_DIGITS(bottom, a->used - x); + + /* remove excess digits */ + a->used -= b; +} +#endif + +/* End: bn_mp_rshd.c */ + +/* Start: bn_mp_sbin_size.c */ +#include "tommath_private.h" +#ifdef BN_MP_SBIN_SIZE_C +/* LibTomMath, multiple-precision integer library -- Tom St Denis */ +/* SPDX-License-Identifier: Unlicense */ + +/* get the size for an signed equivalent */ +size_t mp_sbin_size(const mp_int *a) +{ + return 1u + mp_ubin_size(a); +} +#endif + +/* End: bn_mp_sbin_size.c */ + +/* Start: bn_mp_set.c */ +#include "tommath_private.h" +#ifdef BN_MP_SET_C +/* LibTomMath, multiple-precision integer library -- Tom St Denis */ +/* SPDX-License-Identifier: Unlicense */ + +/* set to a digit */ +void mp_set(mp_int *a, mp_digit b) +{ + a->dp[0] = b & MP_MASK; + a->sign = MP_ZPOS; + a->used = (a->dp[0] != 0u) ? 1 : 0; + MP_ZERO_DIGITS(a->dp + a->used, a->alloc - a->used); +} +#endif + +/* End: bn_mp_set.c */ + +/* Start: bn_mp_set_double.c */ +#include "tommath_private.h" +#ifdef BN_MP_SET_DOUBLE_C +/* LibTomMath, multiple-precision integer library -- Tom St Denis */ +/* SPDX-License-Identifier: Unlicense */ + +#if defined(__STDC_IEC_559__) || defined(__GCC_IEC_559) +mp_err mp_set_double(mp_int *a, double b) +{ + uint64_t frac; + int exp; + mp_err err; + union { + double dbl; + uint64_t bits; + } cast; + cast.dbl = b; + + exp = (int)((unsigned)(cast.bits >> 52) & 0x7FFu); + frac = (cast.bits & ((1uLL << 52) - 1uLL)) | (1uLL << 52); + + if (exp == 0x7FF) { /* +-inf, NaN */ + return MP_VAL; + } + exp -= 1023 + 52; + + mp_set_u64(a, frac); + + err = (exp < 0) ? mp_div_2d(a, -exp, a, NULL) : mp_mul_2d(a, exp, a); + if (err != MP_OKAY) { + return err; + } + + if (((cast.bits >> 63) != 0uLL) && !MP_IS_ZERO(a)) { + a->sign = MP_NEG; + } + + return MP_OKAY; +} +#else +/* pragma message() not supported by several compilers (in mostly older but still used versions) */ +# ifdef _MSC_VER +# pragma message("mp_set_double implementation is only available on platforms with IEEE754 floating point format") +# else +# warning "mp_set_double implementation is only available on platforms with IEEE754 floating point format" +# endif +#endif +#endif + +/* End: bn_mp_set_double.c */ + +/* Start: bn_mp_set_i32.c */ +#include "tommath_private.h" +#ifdef BN_MP_SET_I32_C +/* LibTomMath, multiple-precision integer library -- Tom St Denis */ +/* SPDX-License-Identifier: Unlicense */ + +MP_SET_SIGNED(mp_set_i32, mp_set_u32, int32_t, uint32_t) +#endif + +/* End: bn_mp_set_i32.c */ + +/* Start: bn_mp_set_i64.c */ +#include "tommath_private.h" +#ifdef BN_MP_SET_I64_C +/* LibTomMath, multiple-precision integer library -- Tom St Denis */ +/* SPDX-License-Identifier: Unlicense */ + +MP_SET_SIGNED(mp_set_i64, mp_set_u64, int64_t, uint64_t) +#endif + +/* End: bn_mp_set_i64.c */ + +/* Start: bn_mp_set_l.c */ +#include "tommath_private.h" +#ifdef BN_MP_SET_L_C +/* LibTomMath, multiple-precision integer library -- Tom St Denis */ +/* SPDX-License-Identifier: Unlicense */ + +MP_SET_SIGNED(mp_set_l, mp_set_ul, long, unsigned long) +#endif + +/* End: bn_mp_set_l.c */ + +/* Start: bn_mp_set_ll.c */ +#include "tommath_private.h" +#ifdef BN_MP_SET_LL_C +/* LibTomMath, multiple-precision integer library -- Tom St Denis */ +/* SPDX-License-Identifier: Unlicense */ + +MP_SET_SIGNED(mp_set_ll, mp_set_ull, long long, unsigned long long) +#endif + +/* End: bn_mp_set_ll.c */ + +/* Start: bn_mp_set_u32.c */ +#include "tommath_private.h" +#ifdef BN_MP_SET_U32_C +/* LibTomMath, multiple-precision integer library -- Tom St Denis */ +/* SPDX-License-Identifier: Unlicense */ + +MP_SET_UNSIGNED(mp_set_u32, uint32_t) +#endif + +/* End: bn_mp_set_u32.c */ + +/* Start: bn_mp_set_u64.c */ +#include "tommath_private.h" +#ifdef BN_MP_SET_U64_C +/* LibTomMath, multiple-precision integer library -- Tom St Denis */ +/* SPDX-License-Identifier: Unlicense */ + +MP_SET_UNSIGNED(mp_set_u64, uint64_t) +#endif + +/* End: bn_mp_set_u64.c */ + +/* Start: bn_mp_set_ul.c */ +#include "tommath_private.h" +#ifdef BN_MP_SET_UL_C +/* LibTomMath, multiple-precision integer library -- Tom St Denis */ +/* SPDX-License-Identifier: Unlicense */ + +MP_SET_UNSIGNED(mp_set_ul, unsigned long) +#endif + +/* End: bn_mp_set_ul.c */ + +/* Start: bn_mp_set_ull.c */ +#include "tommath_private.h" +#ifdef BN_MP_SET_ULL_C +/* LibTomMath, multiple-precision integer library -- Tom St Denis */ +/* SPDX-License-Identifier: Unlicense */ + +MP_SET_UNSIGNED(mp_set_ull, unsigned long long) +#endif + +/* End: bn_mp_set_ull.c */ + +/* Start: bn_mp_shrink.c */ +#include "tommath_private.h" +#ifdef BN_MP_SHRINK_C +/* LibTomMath, multiple-precision integer library -- Tom St Denis */ +/* SPDX-License-Identifier: Unlicense */ + +/* shrink a bignum */ +mp_err mp_shrink(mp_int *a) +{ + mp_digit *tmp; + int alloc = MP_MAX(MP_MIN_PREC, a->used); + if (a->alloc != alloc) { + if ((tmp = (mp_digit *) MP_REALLOC(a->dp, + (size_t)a->alloc * sizeof(mp_digit), + (size_t)alloc * sizeof(mp_digit))) == NULL) { + return MP_MEM; + } + a->dp = tmp; + a->alloc = alloc; + } + return MP_OKAY; +} +#endif + +/* End: bn_mp_shrink.c */ + +/* Start: bn_mp_signed_rsh.c */ +#include "tommath_private.h" +#ifdef BN_MP_SIGNED_RSH_C +/* LibTomMath, multiple-precision integer library -- Tom St Denis */ +/* SPDX-License-Identifier: Unlicense */ + +/* shift right by a certain bit count with sign extension */ +mp_err mp_signed_rsh(const mp_int *a, int b, mp_int *c) +{ + mp_err res; + if (a->sign == MP_ZPOS) { + return mp_div_2d(a, b, c, NULL); + } + + res = mp_add_d(a, 1uL, c); + if (res != MP_OKAY) { + return res; + } + + res = mp_div_2d(c, b, c, NULL); + return (res == MP_OKAY) ? mp_sub_d(c, 1uL, c) : res; +} +#endif + +/* End: bn_mp_signed_rsh.c */ + +/* Start: bn_mp_sqr.c */ +#include "tommath_private.h" +#ifdef BN_MP_SQR_C +/* LibTomMath, multiple-precision integer library -- Tom St Denis */ +/* SPDX-License-Identifier: Unlicense */ + +/* computes b = a*a */ +mp_err mp_sqr(const mp_int *a, mp_int *b) +{ + mp_err err; + if (MP_HAS(S_MP_TOOM_SQR) && /* use Toom-Cook? */ + (a->used >= MP_TOOM_SQR_CUTOFF)) { + err = s_mp_toom_sqr(a, b); + } else if (MP_HAS(S_MP_KARATSUBA_SQR) && /* Karatsuba? */ + (a->used >= MP_KARATSUBA_SQR_CUTOFF)) { + err = s_mp_karatsuba_sqr(a, b); + } else if (MP_HAS(S_MP_SQR_FAST) && /* can we use the fast comba multiplier? */ + (((a->used * 2) + 1) < MP_WARRAY) && + (a->used < (MP_MAXFAST / 2))) { + err = s_mp_sqr_fast(a, b); + } else if (MP_HAS(S_MP_SQR)) { + err = s_mp_sqr(a, b); + } else { + err = MP_VAL; + } + b->sign = MP_ZPOS; + return err; +} +#endif + +/* End: bn_mp_sqr.c */ + +/* Start: bn_mp_sqrmod.c */ +#include "tommath_private.h" +#ifdef BN_MP_SQRMOD_C +/* LibTomMath, multiple-precision integer library -- Tom St Denis */ +/* SPDX-License-Identifier: Unlicense */ + +/* c = a * a (mod b) */ +mp_err mp_sqrmod(const mp_int *a, const mp_int *b, mp_int *c) +{ + mp_err err; + mp_int t; + + if ((err = mp_init(&t)) != MP_OKAY) { + return err; + } + + if ((err = mp_sqr(a, &t)) != MP_OKAY) { + goto LBL_ERR; + } + err = mp_mod(&t, b, c); + +LBL_ERR: + mp_clear(&t); + return err; +} +#endif + +/* End: bn_mp_sqrmod.c */ + +/* Start: bn_mp_sqrt.c */ +#include "tommath_private.h" +#ifdef BN_MP_SQRT_C +/* LibTomMath, multiple-precision integer library -- Tom St Denis */ +/* SPDX-License-Identifier: Unlicense */ + +/* this function is less generic than mp_n_root, simpler and faster */ +mp_err mp_sqrt(const mp_int *arg, mp_int *ret) +{ + mp_err err; + mp_int t1, t2; + + /* must be positive */ + if (arg->sign == MP_NEG) { + return MP_VAL; + } + + /* easy out */ + if (MP_IS_ZERO(arg)) { + mp_zero(ret); + return MP_OKAY; + } + + if ((err = mp_init_copy(&t1, arg)) != MP_OKAY) { + return err; + } + + if ((err = mp_init(&t2)) != MP_OKAY) { + goto E2; + } + + /* First approx. (not very bad for large arg) */ + mp_rshd(&t1, t1.used/2); + + /* t1 > 0 */ + if ((err = mp_div(arg, &t1, &t2, NULL)) != MP_OKAY) { + goto E1; + } + if ((err = mp_add(&t1, &t2, &t1)) != MP_OKAY) { + goto E1; + } + if ((err = mp_div_2(&t1, &t1)) != MP_OKAY) { + goto E1; + } + /* And now t1 > sqrt(arg) */ + do { + if ((err = mp_div(arg, &t1, &t2, NULL)) != MP_OKAY) { + goto E1; + } + if ((err = mp_add(&t1, &t2, &t1)) != MP_OKAY) { + goto E1; + } + if ((err = mp_div_2(&t1, &t1)) != MP_OKAY) { + goto E1; + } + /* t1 >= sqrt(arg) >= t2 at this point */ + } while (mp_cmp_mag(&t1, &t2) == MP_GT); + + mp_exch(&t1, ret); + +E1: + mp_clear(&t2); +E2: + mp_clear(&t1); + return err; +} + +#endif + +/* End: bn_mp_sqrt.c */ + +/* Start: bn_mp_sqrtmod_prime.c */ +#include "tommath_private.h" +#ifdef BN_MP_SQRTMOD_PRIME_C +/* LibTomMath, multiple-precision integer library -- Tom St Denis */ +/* SPDX-License-Identifier: Unlicense */ + +/* Tonelli-Shanks algorithm + * https://en.wikipedia.org/wiki/Tonelli%E2%80%93Shanks_algorithm + * https://gmplib.org/list-archives/gmp-discuss/2013-April/005300.html + * + */ + +mp_err mp_sqrtmod_prime(const mp_int *n, const mp_int *prime, mp_int *ret) +{ + mp_err err; + int legendre; + mp_int t1, C, Q, S, Z, M, T, R, two; + mp_digit i; + + /* first handle the simple cases */ + if (mp_cmp_d(n, 0uL) == MP_EQ) { + mp_zero(ret); + return MP_OKAY; + } + if (mp_cmp_d(prime, 2uL) == MP_EQ) return MP_VAL; /* prime must be odd */ + if ((err = mp_kronecker(n, prime, &legendre)) != MP_OKAY) return err; + if (legendre == -1) return MP_VAL; /* quadratic non-residue mod prime */ + + if ((err = mp_init_multi(&t1, &C, &Q, &S, &Z, &M, &T, &R, &two, NULL)) != MP_OKAY) { + return err; + } + + /* SPECIAL CASE: if prime mod 4 == 3 + * compute directly: err = n^(prime+1)/4 mod prime + * Handbook of Applied Cryptography algorithm 3.36 + */ + if ((err = mp_mod_d(prime, 4uL, &i)) != MP_OKAY) goto cleanup; + if (i == 3u) { + if ((err = mp_add_d(prime, 1uL, &t1)) != MP_OKAY) goto cleanup; + if ((err = mp_div_2(&t1, &t1)) != MP_OKAY) goto cleanup; + if ((err = mp_div_2(&t1, &t1)) != MP_OKAY) goto cleanup; + if ((err = mp_exptmod(n, &t1, prime, ret)) != MP_OKAY) goto cleanup; + err = MP_OKAY; + goto cleanup; + } + + /* NOW: Tonelli-Shanks algorithm */ + + /* factor out powers of 2 from prime-1, defining Q and S as: prime-1 = Q*2^S */ + if ((err = mp_copy(prime, &Q)) != MP_OKAY) goto cleanup; + if ((err = mp_sub_d(&Q, 1uL, &Q)) != MP_OKAY) goto cleanup; + /* Q = prime - 1 */ + mp_zero(&S); + /* S = 0 */ + while (MP_IS_EVEN(&Q)) { + if ((err = mp_div_2(&Q, &Q)) != MP_OKAY) goto cleanup; + /* Q = Q / 2 */ + if ((err = mp_add_d(&S, 1uL, &S)) != MP_OKAY) goto cleanup; + /* S = S + 1 */ + } + + /* find a Z such that the Legendre symbol (Z|prime) == -1 */ + mp_set_u32(&Z, 2u); + /* Z = 2 */ + for (;;) { + if ((err = mp_kronecker(&Z, prime, &legendre)) != MP_OKAY) goto cleanup; + if (legendre == -1) break; + if ((err = mp_add_d(&Z, 1uL, &Z)) != MP_OKAY) goto cleanup; + /* Z = Z + 1 */ + } + + if ((err = mp_exptmod(&Z, &Q, prime, &C)) != MP_OKAY) goto cleanup; + /* C = Z ^ Q mod prime */ + if ((err = mp_add_d(&Q, 1uL, &t1)) != MP_OKAY) goto cleanup; + if ((err = mp_div_2(&t1, &t1)) != MP_OKAY) goto cleanup; + /* t1 = (Q + 1) / 2 */ + if ((err = mp_exptmod(n, &t1, prime, &R)) != MP_OKAY) goto cleanup; + /* R = n ^ ((Q + 1) / 2) mod prime */ + if ((err = mp_exptmod(n, &Q, prime, &T)) != MP_OKAY) goto cleanup; + /* T = n ^ Q mod prime */ + if ((err = mp_copy(&S, &M)) != MP_OKAY) goto cleanup; + /* M = S */ + mp_set_u32(&two, 2u); + + for (;;) { + if ((err = mp_copy(&T, &t1)) != MP_OKAY) goto cleanup; + i = 0; + for (;;) { + if (mp_cmp_d(&t1, 1uL) == MP_EQ) break; + if ((err = mp_exptmod(&t1, &two, prime, &t1)) != MP_OKAY) goto cleanup; + i++; + } + if (i == 0u) { + if ((err = mp_copy(&R, ret)) != MP_OKAY) goto cleanup; + err = MP_OKAY; + goto cleanup; + } + if ((err = mp_sub_d(&M, i, &t1)) != MP_OKAY) goto cleanup; + if ((err = mp_sub_d(&t1, 1uL, &t1)) != MP_OKAY) goto cleanup; + if ((err = mp_exptmod(&two, &t1, prime, &t1)) != MP_OKAY) goto cleanup; + /* t1 = 2 ^ (M - i - 1) */ + if ((err = mp_exptmod(&C, &t1, prime, &t1)) != MP_OKAY) goto cleanup; + /* t1 = C ^ (2 ^ (M - i - 1)) mod prime */ + if ((err = mp_sqrmod(&t1, prime, &C)) != MP_OKAY) goto cleanup; + /* C = (t1 * t1) mod prime */ + if ((err = mp_mulmod(&R, &t1, prime, &R)) != MP_OKAY) goto cleanup; + /* R = (R * t1) mod prime */ + if ((err = mp_mulmod(&T, &C, prime, &T)) != MP_OKAY) goto cleanup; + /* T = (T * C) mod prime */ + mp_set(&M, i); + /* M = i */ + } + +cleanup: + mp_clear_multi(&t1, &C, &Q, &S, &Z, &M, &T, &R, &two, NULL); + return err; +} + +#endif + +/* End: bn_mp_sqrtmod_prime.c */ + +/* Start: bn_mp_sub.c */ +#include "tommath_private.h" +#ifdef BN_MP_SUB_C +/* LibTomMath, multiple-precision integer library -- Tom St Denis */ +/* SPDX-License-Identifier: Unlicense */ + +/* high level subtraction (handles signs) */ +mp_err mp_sub(const mp_int *a, const mp_int *b, mp_int *c) +{ + mp_sign sa = a->sign, sb = b->sign; + mp_err err; + + if (sa != sb) { + /* subtract a negative from a positive, OR */ + /* subtract a positive from a negative. */ + /* In either case, ADD their magnitudes, */ + /* and use the sign of the first number. */ + c->sign = sa; + err = s_mp_add(a, b, c); + } else { + /* subtract a positive from a positive, OR */ + /* subtract a negative from a negative. */ + /* First, take the difference between their */ + /* magnitudes, then... */ + if (mp_cmp_mag(a, b) != MP_LT) { + /* Copy the sign from the first */ + c->sign = sa; + /* The first has a larger or equal magnitude */ + err = s_mp_sub(a, b, c); + } else { + /* The result has the *opposite* sign from */ + /* the first number. */ + c->sign = (sa == MP_ZPOS) ? MP_NEG : MP_ZPOS; + /* The second has a larger magnitude */ + err = s_mp_sub(b, a, c); + } + } + return err; +} + +#endif + +/* End: bn_mp_sub.c */ + +/* Start: bn_mp_sub_d.c */ +#include "tommath_private.h" +#ifdef BN_MP_SUB_D_C +/* LibTomMath, multiple-precision integer library -- Tom St Denis */ +/* SPDX-License-Identifier: Unlicense */ + +/* single digit subtraction */ +mp_err mp_sub_d(const mp_int *a, mp_digit b, mp_int *c) +{ + mp_digit *tmpa, *tmpc; + mp_err err; + int ix, oldused; + + /* grow c as required */ + if (c->alloc < (a->used + 1)) { + if ((err = mp_grow(c, a->used + 1)) != MP_OKAY) { + return err; + } + } + + /* if a is negative just do an unsigned + * addition [with fudged signs] + */ + if (a->sign == MP_NEG) { + mp_int a_ = *a; + a_.sign = MP_ZPOS; + err = mp_add_d(&a_, b, c); + c->sign = MP_NEG; + + /* clamp */ + mp_clamp(c); + + return err; + } + + /* setup regs */ + oldused = c->used; + tmpa = a->dp; + tmpc = c->dp; + + /* if a <= b simply fix the single digit */ + if (((a->used == 1) && (a->dp[0] <= b)) || (a->used == 0)) { + if (a->used == 1) { + *tmpc++ = b - *tmpa; + } else { + *tmpc++ = b; + } + ix = 1; + + /* negative/1digit */ + c->sign = MP_NEG; + c->used = 1; + } else { + mp_digit mu = b; + + /* positive/size */ + c->sign = MP_ZPOS; + c->used = a->used; + + /* subtract digits, mu is carry */ + for (ix = 0; ix < a->used; ix++) { + *tmpc = *tmpa++ - mu; + mu = *tmpc >> (MP_SIZEOF_BITS(mp_digit) - 1u); + *tmpc++ &= MP_MASK; + } + } + + /* zero excess digits */ + MP_ZERO_DIGITS(tmpc, oldused - ix); + + mp_clamp(c); + return MP_OKAY; +} + +#endif + +/* End: bn_mp_sub_d.c */ + +/* Start: bn_mp_submod.c */ +#include "tommath_private.h" +#ifdef BN_MP_SUBMOD_C +/* LibTomMath, multiple-precision integer library -- Tom St Denis */ +/* SPDX-License-Identifier: Unlicense */ + +/* d = a - b (mod c) */ +mp_err mp_submod(const mp_int *a, const mp_int *b, const mp_int *c, mp_int *d) +{ + mp_err err; + mp_int t; + + if ((err = mp_init(&t)) != MP_OKAY) { + return err; + } + + if ((err = mp_sub(a, b, &t)) != MP_OKAY) { + goto LBL_ERR; + } + err = mp_mod(&t, c, d); + +LBL_ERR: + mp_clear(&t); + return err; +} +#endif + +/* End: bn_mp_submod.c */ + +/* Start: bn_mp_to_radix.c */ +#include "tommath_private.h" +#ifdef BN_MP_TO_RADIX_C +/* LibTomMath, multiple-precision integer library -- Tom St Denis */ +/* SPDX-License-Identifier: Unlicense */ + +/* stores a bignum as a ASCII string in a given radix (2..64) + * + * Stores upto "size - 1" chars and always a NULL byte, puts the number of characters + * written, including the '\0', in "written". + */ +mp_err mp_to_radix(const mp_int *a, char *str, size_t maxlen, size_t *written, int radix) +{ + size_t digs; + mp_err err; + mp_int t; + mp_digit d; + char *_s = str; + + /* check range of radix and size*/ + if (maxlen < 2u) { + return MP_BUF; + } + if ((radix < 2) || (radix > 64)) { + return MP_VAL; + } + + /* quick out if its zero */ + if (MP_IS_ZERO(a)) { + *str++ = '0'; + *str = '\0'; + if (written != NULL) { + *written = 2u; + } + return MP_OKAY; + } + + if ((err = mp_init_copy(&t, a)) != MP_OKAY) { + return err; + } + + /* if it is negative output a - */ + if (t.sign == MP_NEG) { + /* we have to reverse our digits later... but not the - sign!! */ + ++_s; + + /* store the flag and mark the number as positive */ + *str++ = '-'; + t.sign = MP_ZPOS; + + /* subtract a char */ + --maxlen; + } + digs = 0u; + while (!MP_IS_ZERO(&t)) { + if (--maxlen < 1u) { + /* no more room */ + err = MP_BUF; + goto LBL_ERR; + } + if ((err = mp_div_d(&t, (mp_digit)radix, &t, &d)) != MP_OKAY) { + goto LBL_ERR; + } + *str++ = mp_s_rmap[d]; + ++digs; + } + /* reverse the digits of the string. In this case _s points + * to the first digit [exluding the sign] of the number + */ + s_mp_reverse((unsigned char *)_s, digs); + + /* append a NULL so the string is properly terminated */ + *str = '\0'; + digs++; + + if (written != NULL) { + *written = (a->sign == MP_NEG) ? (digs + 1u): digs; + } + +LBL_ERR: + mp_clear(&t); + return err; +} + +#endif + +/* End: bn_mp_to_radix.c */ + +/* Start: bn_mp_to_sbin.c */ +#include "tommath_private.h" +#ifdef BN_MP_TO_SBIN_C +/* LibTomMath, multiple-precision integer library -- Tom St Denis */ +/* SPDX-License-Identifier: Unlicense */ + +/* store in signed [big endian] format */ +mp_err mp_to_sbin(const mp_int *a, unsigned char *buf, size_t maxlen, size_t *written) +{ + mp_err err; + if (maxlen == 0u) { + return MP_BUF; + } + if ((err = mp_to_ubin(a, buf + 1, maxlen - 1u, written)) != MP_OKAY) { + return err; + } + if (written != NULL) { + (*written)++; + } + buf[0] = (a->sign == MP_ZPOS) ? (unsigned char)0 : (unsigned char)1; + return MP_OKAY; +} +#endif + +/* End: bn_mp_to_sbin.c */ + +/* Start: bn_mp_to_ubin.c */ +#include "tommath_private.h" +#ifdef BN_MP_TO_UBIN_C +/* LibTomMath, multiple-precision integer library -- Tom St Denis */ +/* SPDX-License-Identifier: Unlicense */ + +/* store in unsigned [big endian] format */ +mp_err mp_to_ubin(const mp_int *a, unsigned char *buf, size_t maxlen, size_t *written) +{ + size_t x, count; + mp_err err; + mp_int t; + + count = mp_ubin_size(a); + if (count > maxlen) { + return MP_BUF; + } + + if ((err = mp_init_copy(&t, a)) != MP_OKAY) { + return err; + } + + for (x = count; x --> 0u;) { +#ifndef MP_8BIT + buf[x] = (unsigned char)(t.dp[0] & 255u); +#else + buf[x] = (unsigned char)(t.dp[0] | ((t.dp[1] & 1u) << 7)); +#endif + if ((err = mp_div_2d(&t, 8, &t, NULL)) != MP_OKAY) { + goto LBL_ERR; + } + } + + if (written != NULL) { + *written = count; + } + +LBL_ERR: + mp_clear(&t); + return err; +} +#endif + +/* End: bn_mp_to_ubin.c */ + +/* Start: bn_mp_ubin_size.c */ +#include "tommath_private.h" +#ifdef BN_MP_UBIN_SIZE_C +/* LibTomMath, multiple-precision integer library -- Tom St Denis */ +/* SPDX-License-Identifier: Unlicense */ + +/* get the size for an unsigned equivalent */ +size_t mp_ubin_size(const mp_int *a) +{ + size_t size = (size_t)mp_count_bits(a); + return (size / 8u) + (((size & 7u) != 0u) ? 1u : 0u); +} +#endif + +/* End: bn_mp_ubin_size.c */ + +/* Start: bn_mp_unpack.c */ +#include "tommath_private.h" +#ifdef BN_MP_UNPACK_C +/* LibTomMath, multiple-precision integer library -- Tom St Denis */ +/* SPDX-License-Identifier: Unlicense */ + +/* based on gmp's mpz_import. + * see http://gmplib.org/manual/Integer-Import-and-Export.html + */ +mp_err mp_unpack(mp_int *rop, size_t count, mp_order order, size_t size, + mp_endian endian, size_t nails, const void *op) +{ + mp_err err; + size_t odd_nails, nail_bytes, i, j; + unsigned char odd_nail_mask; + + mp_zero(rop); + + if (endian == MP_NATIVE_ENDIAN) { + MP_GET_ENDIANNESS(endian); + } + + odd_nails = (nails % 8u); + odd_nail_mask = 0xff; + for (i = 0; i < odd_nails; ++i) { + odd_nail_mask ^= (unsigned char)(1u << (7u - i)); + } + nail_bytes = nails / 8u; + + for (i = 0; i < count; ++i) { + for (j = 0; j < (size - nail_bytes); ++j) { + unsigned char byte = *((const unsigned char *)op + + (((order == MP_MSB_FIRST) ? i : ((count - 1u) - i)) * size) + + ((endian == MP_BIG_ENDIAN) ? (j + nail_bytes) : (((size - 1u) - j) - nail_bytes))); + + if ((err = mp_mul_2d(rop, (j == 0u) ? (int)(8u - odd_nails) : 8, rop)) != MP_OKAY) { + return err; + } + + rop->dp[0] |= (j == 0u) ? (mp_digit)(byte & odd_nail_mask) : (mp_digit)byte; + rop->used += 1; + } + } + + mp_clamp(rop); + + return MP_OKAY; +} + +#endif + +/* End: bn_mp_unpack.c */ + +/* Start: bn_mp_xor.c */ +#include "tommath_private.h" +#ifdef BN_MP_XOR_C +/* LibTomMath, multiple-precision integer library -- Tom St Denis */ +/* SPDX-License-Identifier: Unlicense */ + +/* two complement xor */ +mp_err mp_xor(const mp_int *a, const mp_int *b, mp_int *c) +{ + int used = MP_MAX(a->used, b->used) + 1, i; + mp_err err; + mp_digit ac = 1, bc = 1, cc = 1; + mp_sign csign = (a->sign != b->sign) ? MP_NEG : MP_ZPOS; + + if (c->alloc < used) { + if ((err = mp_grow(c, used)) != MP_OKAY) { + return err; + } + } + + for (i = 0; i < used; i++) { + mp_digit x, y; + + /* convert to two complement if negative */ + if (a->sign == MP_NEG) { + ac += (i >= a->used) ? MP_MASK : (~a->dp[i] & MP_MASK); + x = ac & MP_MASK; + ac >>= MP_DIGIT_BIT; + } else { + x = (i >= a->used) ? 0uL : a->dp[i]; + } + + /* convert to two complement if negative */ + if (b->sign == MP_NEG) { + bc += (i >= b->used) ? MP_MASK : (~b->dp[i] & MP_MASK); + y = bc & MP_MASK; + bc >>= MP_DIGIT_BIT; + } else { + y = (i >= b->used) ? 0uL : b->dp[i]; + } + + c->dp[i] = x ^ y; + + /* convert to to sign-magnitude if negative */ + if (csign == MP_NEG) { + cc += ~c->dp[i] & MP_MASK; + c->dp[i] = cc & MP_MASK; + cc >>= MP_DIGIT_BIT; + } + } + + c->used = used; + c->sign = csign; + mp_clamp(c); + return MP_OKAY; +} +#endif + +/* End: bn_mp_xor.c */ + +/* Start: bn_mp_zero.c */ +#include "tommath_private.h" +#ifdef BN_MP_ZERO_C +/* LibTomMath, multiple-precision integer library -- Tom St Denis */ +/* SPDX-License-Identifier: Unlicense */ + +/* set to zero */ +void mp_zero(mp_int *a) +{ + a->sign = MP_ZPOS; + a->used = 0; + MP_ZERO_DIGITS(a->dp, a->alloc); +} +#endif + +/* End: bn_mp_zero.c */ + +/* Start: bn_prime_tab.c */ +#include "tommath_private.h" +#ifdef BN_PRIME_TAB_C +/* LibTomMath, multiple-precision integer library -- Tom St Denis */ +/* SPDX-License-Identifier: Unlicense */ + +const mp_digit ltm_prime_tab[] = { + 0x0002, 0x0003, 0x0005, 0x0007, 0x000B, 0x000D, 0x0011, 0x0013, + 0x0017, 0x001D, 0x001F, 0x0025, 0x0029, 0x002B, 0x002F, 0x0035, + 0x003B, 0x003D, 0x0043, 0x0047, 0x0049, 0x004F, 0x0053, 0x0059, + 0x0061, 0x0065, 0x0067, 0x006B, 0x006D, 0x0071, 0x007F, +#ifndef MP_8BIT + 0x0083, + 0x0089, 0x008B, 0x0095, 0x0097, 0x009D, 0x00A3, 0x00A7, 0x00AD, + 0x00B3, 0x00B5, 0x00BF, 0x00C1, 0x00C5, 0x00C7, 0x00D3, 0x00DF, + 0x00E3, 0x00E5, 0x00E9, 0x00EF, 0x00F1, 0x00FB, 0x0101, 0x0107, + 0x010D, 0x010F, 0x0115, 0x0119, 0x011B, 0x0125, 0x0133, 0x0137, + + 0x0139, 0x013D, 0x014B, 0x0151, 0x015B, 0x015D, 0x0161, 0x0167, + 0x016F, 0x0175, 0x017B, 0x017F, 0x0185, 0x018D, 0x0191, 0x0199, + 0x01A3, 0x01A5, 0x01AF, 0x01B1, 0x01B7, 0x01BB, 0x01C1, 0x01C9, + 0x01CD, 0x01CF, 0x01D3, 0x01DF, 0x01E7, 0x01EB, 0x01F3, 0x01F7, + 0x01FD, 0x0209, 0x020B, 0x021D, 0x0223, 0x022D, 0x0233, 0x0239, + 0x023B, 0x0241, 0x024B, 0x0251, 0x0257, 0x0259, 0x025F, 0x0265, + 0x0269, 0x026B, 0x0277, 0x0281, 0x0283, 0x0287, 0x028D, 0x0293, + 0x0295, 0x02A1, 0x02A5, 0x02AB, 0x02B3, 0x02BD, 0x02C5, 0x02CF, + + 0x02D7, 0x02DD, 0x02E3, 0x02E7, 0x02EF, 0x02F5, 0x02F9, 0x0301, + 0x0305, 0x0313, 0x031D, 0x0329, 0x032B, 0x0335, 0x0337, 0x033B, + 0x033D, 0x0347, 0x0355, 0x0359, 0x035B, 0x035F, 0x036D, 0x0371, + 0x0373, 0x0377, 0x038B, 0x038F, 0x0397, 0x03A1, 0x03A9, 0x03AD, + 0x03B3, 0x03B9, 0x03C7, 0x03CB, 0x03D1, 0x03D7, 0x03DF, 0x03E5, + 0x03F1, 0x03F5, 0x03FB, 0x03FD, 0x0407, 0x0409, 0x040F, 0x0419, + 0x041B, 0x0425, 0x0427, 0x042D, 0x043F, 0x0443, 0x0445, 0x0449, + 0x044F, 0x0455, 0x045D, 0x0463, 0x0469, 0x047F, 0x0481, 0x048B, + + 0x0493, 0x049D, 0x04A3, 0x04A9, 0x04B1, 0x04BD, 0x04C1, 0x04C7, + 0x04CD, 0x04CF, 0x04D5, 0x04E1, 0x04EB, 0x04FD, 0x04FF, 0x0503, + 0x0509, 0x050B, 0x0511, 0x0515, 0x0517, 0x051B, 0x0527, 0x0529, + 0x052F, 0x0551, 0x0557, 0x055D, 0x0565, 0x0577, 0x0581, 0x058F, + 0x0593, 0x0595, 0x0599, 0x059F, 0x05A7, 0x05AB, 0x05AD, 0x05B3, + 0x05BF, 0x05C9, 0x05CB, 0x05CF, 0x05D1, 0x05D5, 0x05DB, 0x05E7, + 0x05F3, 0x05FB, 0x0607, 0x060D, 0x0611, 0x0617, 0x061F, 0x0623, + 0x062B, 0x062F, 0x063D, 0x0641, 0x0647, 0x0649, 0x064D, 0x0653 +#endif +}; + +#if defined(__GNUC__) && __GNUC__ >= 4 +#pragma GCC diagnostic push +#pragma GCC diagnostic ignored "-Wdeprecated-declarations" +const mp_digit *s_mp_prime_tab = ltm_prime_tab; +#pragma GCC diagnostic pop +#elif defined(_MSC_VER) && _MSC_VER >= 1500 +#pragma warning(push) +#pragma warning(disable: 4996) +const mp_digit *s_mp_prime_tab = ltm_prime_tab; +#pragma warning(pop) +#else +const mp_digit *s_mp_prime_tab = ltm_prime_tab; +#endif + +#endif + +/* End: bn_prime_tab.c */ + +/* Start: bn_s_mp_add.c */ +#include "tommath_private.h" +#ifdef BN_S_MP_ADD_C +/* LibTomMath, multiple-precision integer library -- Tom St Denis */ +/* SPDX-License-Identifier: Unlicense */ + +/* low level addition, based on HAC pp.594, Algorithm 14.7 */ +mp_err s_mp_add(const mp_int *a, const mp_int *b, mp_int *c) +{ + const mp_int *x; + mp_err err; + int olduse, min, max; + + /* find sizes, we let |a| <= |b| which means we have to sort + * them. "x" will point to the input with the most digits + */ + if (a->used > b->used) { + min = b->used; + max = a->used; + x = a; + } else { + min = a->used; + max = b->used; + x = b; + } + + /* init result */ + if (c->alloc < (max + 1)) { + if ((err = mp_grow(c, max + 1)) != MP_OKAY) { + return err; + } + } + + /* get old used digit count and set new one */ + olduse = c->used; + c->used = max + 1; + + { + mp_digit u, *tmpa, *tmpb, *tmpc; + int i; + + /* alias for digit pointers */ + + /* first input */ + tmpa = a->dp; + + /* second input */ + tmpb = b->dp; + + /* destination */ + tmpc = c->dp; + + /* zero the carry */ + u = 0; + for (i = 0; i < min; i++) { + /* Compute the sum at one digit, T[i] = A[i] + B[i] + U */ + *tmpc = *tmpa++ + *tmpb++ + u; + + /* U = carry bit of T[i] */ + u = *tmpc >> (mp_digit)MP_DIGIT_BIT; + + /* take away carry bit from T[i] */ + *tmpc++ &= MP_MASK; + } + + /* now copy higher words if any, that is in A+B + * if A or B has more digits add those in + */ + if (min != max) { + for (; i < max; i++) { + /* T[i] = X[i] + U */ + *tmpc = x->dp[i] + u; + + /* U = carry bit of T[i] */ + u = *tmpc >> (mp_digit)MP_DIGIT_BIT; + + /* take away carry bit from T[i] */ + *tmpc++ &= MP_MASK; + } + } + + /* add carry */ + *tmpc++ = u; + + /* clear digits above oldused */ + MP_ZERO_DIGITS(tmpc, olduse - c->used); + } + + mp_clamp(c); + return MP_OKAY; +} +#endif + +/* End: bn_s_mp_add.c */ + +/* Start: bn_s_mp_balance_mul.c */ +#include "tommath_private.h" +#ifdef BN_S_MP_BALANCE_MUL_C +/* LibTomMath, multiple-precision integer library -- Tom St Denis */ +/* SPDX-License-Identifier: Unlicense */ + +/* single-digit multiplication with the smaller number as the single-digit */ +mp_err s_mp_balance_mul(const mp_int *a, const mp_int *b, mp_int *c) +{ + int count, len_a, len_b, nblocks, i, j, bsize; + mp_int a0, tmp, A, B, r; + mp_err err; + + len_a = a->used; + len_b = b->used; + + nblocks = MP_MAX(a->used, b->used) / MP_MIN(a->used, b->used); + bsize = MP_MIN(a->used, b->used) ; + + if ((err = mp_init_size(&a0, bsize + 2)) != MP_OKAY) { + return err; + } + if ((err = mp_init_multi(&tmp, &r, NULL)) != MP_OKAY) { + mp_clear(&a0); + return err; + } + + /* Make sure that A is the larger one*/ + if (len_a < len_b) { + B = *a; + A = *b; + } else { + A = *a; + B = *b; + } + + for (i = 0, j=0; i < nblocks; i++) { + /* Cut a slice off of a */ + a0.used = 0; + for (count = 0; count < bsize; count++) { + a0.dp[count] = A.dp[ j++ ]; + a0.used++; + } + mp_clamp(&a0); + /* Multiply with b */ + if ((err = mp_mul(&a0, &B, &tmp)) != MP_OKAY) { + goto LBL_ERR; + } + /* Shift tmp to the correct position */ + if ((err = mp_lshd(&tmp, bsize * i)) != MP_OKAY) { + goto LBL_ERR; + } + /* Add to output. No carry needed */ + if ((err = mp_add(&r, &tmp, &r)) != MP_OKAY) { + goto LBL_ERR; + } + } + /* The left-overs; there are always left-overs */ + if (j < A.used) { + a0.used = 0; + for (count = 0; j < A.used; count++) { + a0.dp[count] = A.dp[ j++ ]; + a0.used++; + } + mp_clamp(&a0); + if ((err = mp_mul(&a0, &B, &tmp)) != MP_OKAY) { + goto LBL_ERR; + } + if ((err = mp_lshd(&tmp, bsize * i)) != MP_OKAY) { + goto LBL_ERR; + } + if ((err = mp_add(&r, &tmp, &r)) != MP_OKAY) { + goto LBL_ERR; + } + } + + mp_exch(&r,c); +LBL_ERR: + mp_clear_multi(&a0, &tmp, &r,NULL); + return err; +} +#endif + +/* End: bn_s_mp_balance_mul.c */ + +/* Start: bn_s_mp_exptmod.c */ +#include "tommath_private.h" +#ifdef BN_S_MP_EXPTMOD_C +/* LibTomMath, multiple-precision integer library -- Tom St Denis */ +/* SPDX-License-Identifier: Unlicense */ + +#ifdef MP_LOW_MEM +# define TAB_SIZE 32 +# define MAX_WINSIZE 5 +#else +# define TAB_SIZE 256 +# define MAX_WINSIZE 0 +#endif + +mp_err s_mp_exptmod(const mp_int *G, const mp_int *X, const mp_int *P, mp_int *Y, int redmode) +{ + mp_int M[TAB_SIZE], res, mu; + mp_digit buf; + mp_err err; + int bitbuf, bitcpy, bitcnt, mode, digidx, x, y, winsize; + mp_err(*redux)(mp_int *x, const mp_int *m, const mp_int *mu); + + /* find window size */ + x = mp_count_bits(X); + if (x <= 7) { + winsize = 2; + } else if (x <= 36) { + winsize = 3; + } else if (x <= 140) { + winsize = 4; + } else if (x <= 450) { + winsize = 5; + } else if (x <= 1303) { + winsize = 6; + } else if (x <= 3529) { + winsize = 7; + } else { + winsize = 8; + } + + winsize = MAX_WINSIZE ? MP_MIN(MAX_WINSIZE, winsize) : winsize; + + /* init M array */ + /* init first cell */ + if ((err = mp_init(&M[1])) != MP_OKAY) { + return err; + } + + /* now init the second half of the array */ + for (x = 1<<(winsize-1); x < (1 << winsize); x++) { + if ((err = mp_init(&M[x])) != MP_OKAY) { + for (y = 1<<(winsize-1); y < x; y++) { + mp_clear(&M[y]); + } + mp_clear(&M[1]); + return err; + } + } + + /* create mu, used for Barrett reduction */ + if ((err = mp_init(&mu)) != MP_OKAY) goto LBL_M; + + if (redmode == 0) { + if ((err = mp_reduce_setup(&mu, P)) != MP_OKAY) goto LBL_MU; + redux = mp_reduce; + } else { + if ((err = mp_reduce_2k_setup_l(P, &mu)) != MP_OKAY) goto LBL_MU; + redux = mp_reduce_2k_l; + } + + /* create M table + * + * The M table contains powers of the base, + * e.g. M[x] = G**x mod P + * + * The first half of the table is not + * computed though accept for M[0] and M[1] + */ + if ((err = mp_mod(G, P, &M[1])) != MP_OKAY) goto LBL_MU; + + /* compute the value at M[1<<(winsize-1)] by squaring + * M[1] (winsize-1) times + */ + if ((err = mp_copy(&M[1], &M[(size_t)1 << (winsize - 1)])) != MP_OKAY) goto LBL_MU; + + for (x = 0; x < (winsize - 1); x++) { + /* square it */ + if ((err = mp_sqr(&M[(size_t)1 << (winsize - 1)], + &M[(size_t)1 << (winsize - 1)])) != MP_OKAY) goto LBL_MU; + + /* reduce modulo P */ + if ((err = redux(&M[(size_t)1 << (winsize - 1)], P, &mu)) != MP_OKAY) goto LBL_MU; + } + + /* create upper table, that is M[x] = M[x-1] * M[1] (mod P) + * for x = (2**(winsize - 1) + 1) to (2**winsize - 1) + */ + for (x = (1 << (winsize - 1)) + 1; x < (1 << winsize); x++) { + if ((err = mp_mul(&M[x - 1], &M[1], &M[x])) != MP_OKAY) goto LBL_MU; + if ((err = redux(&M[x], P, &mu)) != MP_OKAY) goto LBL_MU; + } + + /* setup result */ + if ((err = mp_init(&res)) != MP_OKAY) goto LBL_MU; + mp_set(&res, 1uL); + + /* set initial mode and bit cnt */ + mode = 0; + bitcnt = 1; + buf = 0; + digidx = X->used - 1; + bitcpy = 0; + bitbuf = 0; + + for (;;) { + /* grab next digit as required */ + if (--bitcnt == 0) { + /* if digidx == -1 we are out of digits */ + if (digidx == -1) { + break; + } + /* read next digit and reset the bitcnt */ + buf = X->dp[digidx--]; + bitcnt = (int)MP_DIGIT_BIT; + } + + /* grab the next msb from the exponent */ + y = (buf >> (mp_digit)(MP_DIGIT_BIT - 1)) & 1uL; + buf <<= (mp_digit)1; + + /* if the bit is zero and mode == 0 then we ignore it + * These represent the leading zero bits before the first 1 bit + * in the exponent. Technically this opt is not required but it + * does lower the # of trivial squaring/reductions used + */ + if ((mode == 0) && (y == 0)) { + continue; + } + + /* if the bit is zero and mode == 1 then we square */ + if ((mode == 1) && (y == 0)) { + if ((err = mp_sqr(&res, &res)) != MP_OKAY) goto LBL_RES; + if ((err = redux(&res, P, &mu)) != MP_OKAY) goto LBL_RES; + continue; + } + + /* else we add it to the window */ + bitbuf |= (y << (winsize - ++bitcpy)); + mode = 2; + + if (bitcpy == winsize) { + /* ok window is filled so square as required and multiply */ + /* square first */ + for (x = 0; x < winsize; x++) { + if ((err = mp_sqr(&res, &res)) != MP_OKAY) goto LBL_RES; + if ((err = redux(&res, P, &mu)) != MP_OKAY) goto LBL_RES; + } + + /* then multiply */ + if ((err = mp_mul(&res, &M[bitbuf], &res)) != MP_OKAY) goto LBL_RES; + if ((err = redux(&res, P, &mu)) != MP_OKAY) goto LBL_RES; + + /* empty window and reset */ + bitcpy = 0; + bitbuf = 0; + mode = 1; + } + } + + /* if bits remain then square/multiply */ + if ((mode == 2) && (bitcpy > 0)) { + /* square then multiply if the bit is set */ + for (x = 0; x < bitcpy; x++) { + if ((err = mp_sqr(&res, &res)) != MP_OKAY) goto LBL_RES; + if ((err = redux(&res, P, &mu)) != MP_OKAY) goto LBL_RES; + + bitbuf <<= 1; + if ((bitbuf & (1 << winsize)) != 0) { + /* then multiply */ + if ((err = mp_mul(&res, &M[1], &res)) != MP_OKAY) goto LBL_RES; + if ((err = redux(&res, P, &mu)) != MP_OKAY) goto LBL_RES; + } + } + } + + mp_exch(&res, Y); + err = MP_OKAY; +LBL_RES: + mp_clear(&res); +LBL_MU: + mp_clear(&mu); +LBL_M: + mp_clear(&M[1]); + for (x = 1<<(winsize-1); x < (1 << winsize); x++) { + mp_clear(&M[x]); + } + return err; +} +#endif + +/* End: bn_s_mp_exptmod.c */ + +/* Start: bn_s_mp_exptmod_fast.c */ +#include "tommath_private.h" +#ifdef BN_S_MP_EXPTMOD_FAST_C +/* LibTomMath, multiple-precision integer library -- Tom St Denis */ +/* SPDX-License-Identifier: Unlicense */ + +/* computes Y == G**X mod P, HAC pp.616, Algorithm 14.85 + * + * Uses a left-to-right k-ary sliding window to compute the modular exponentiation. + * The value of k changes based on the size of the exponent. + * + * Uses Montgomery or Diminished Radix reduction [whichever appropriate] + */ + +#ifdef MP_LOW_MEM +# define TAB_SIZE 32 +# define MAX_WINSIZE 5 +#else +# define TAB_SIZE 256 +# define MAX_WINSIZE 0 +#endif + +mp_err s_mp_exptmod_fast(const mp_int *G, const mp_int *X, const mp_int *P, mp_int *Y, int redmode) +{ + mp_int M[TAB_SIZE], res; + mp_digit buf, mp; + int bitbuf, bitcpy, bitcnt, mode, digidx, x, y, winsize; + mp_err err; + + /* use a pointer to the reduction algorithm. This allows us to use + * one of many reduction algorithms without modding the guts of + * the code with if statements everywhere. + */ + mp_err(*redux)(mp_int *x, const mp_int *n, mp_digit rho); + + /* find window size */ + x = mp_count_bits(X); + if (x <= 7) { + winsize = 2; + } else if (x <= 36) { + winsize = 3; + } else if (x <= 140) { + winsize = 4; + } else if (x <= 450) { + winsize = 5; + } else if (x <= 1303) { + winsize = 6; + } else if (x <= 3529) { + winsize = 7; + } else { + winsize = 8; + } + + winsize = MAX_WINSIZE ? MP_MIN(MAX_WINSIZE, winsize) : winsize; + + /* init M array */ + /* init first cell */ + if ((err = mp_init_size(&M[1], P->alloc)) != MP_OKAY) { + return err; + } + + /* now init the second half of the array */ + for (x = 1<<(winsize-1); x < (1 << winsize); x++) { + if ((err = mp_init_size(&M[x], P->alloc)) != MP_OKAY) { + for (y = 1<<(winsize-1); y < x; y++) { + mp_clear(&M[y]); + } + mp_clear(&M[1]); + return err; + } + } + + /* determine and setup reduction code */ + if (redmode == 0) { + if (MP_HAS(MP_MONTGOMERY_SETUP)) { + /* now setup montgomery */ + if ((err = mp_montgomery_setup(P, &mp)) != MP_OKAY) goto LBL_M; + } else { + err = MP_VAL; + goto LBL_M; + } + + /* automatically pick the comba one if available (saves quite a few calls/ifs) */ + if (MP_HAS(S_MP_MONTGOMERY_REDUCE_FAST) && + (((P->used * 2) + 1) < MP_WARRAY) && + (P->used < MP_MAXFAST)) { + redux = s_mp_montgomery_reduce_fast; + } else if (MP_HAS(MP_MONTGOMERY_REDUCE)) { + /* use slower baseline Montgomery method */ + redux = mp_montgomery_reduce; + } else { + err = MP_VAL; + goto LBL_M; + } + } else if (redmode == 1) { + if (MP_HAS(MP_DR_SETUP) && MP_HAS(MP_DR_REDUCE)) { + /* setup DR reduction for moduli of the form B**k - b */ + mp_dr_setup(P, &mp); + redux = mp_dr_reduce; + } else { + err = MP_VAL; + goto LBL_M; + } + } else if (MP_HAS(MP_REDUCE_2K_SETUP) && MP_HAS(MP_REDUCE_2K)) { + /* setup DR reduction for moduli of the form 2**k - b */ + if ((err = mp_reduce_2k_setup(P, &mp)) != MP_OKAY) goto LBL_M; + redux = mp_reduce_2k; + } else { + err = MP_VAL; + goto LBL_M; + } + + /* setup result */ + if ((err = mp_init_size(&res, P->alloc)) != MP_OKAY) goto LBL_M; + + /* create M table + * + + * + * The first half of the table is not computed though accept for M[0] and M[1] + */ + + if (redmode == 0) { + if (MP_HAS(MP_MONTGOMERY_CALC_NORMALIZATION)) { + /* now we need R mod m */ + if ((err = mp_montgomery_calc_normalization(&res, P)) != MP_OKAY) goto LBL_RES; + + /* now set M[1] to G * R mod m */ + if ((err = mp_mulmod(G, &res, P, &M[1])) != MP_OKAY) goto LBL_RES; + } else { + err = MP_VAL; + goto LBL_RES; + } + } else { + mp_set(&res, 1uL); + if ((err = mp_mod(G, P, &M[1])) != MP_OKAY) goto LBL_RES; + } + + /* compute the value at M[1<<(winsize-1)] by squaring M[1] (winsize-1) times */ + if ((err = mp_copy(&M[1], &M[(size_t)1 << (winsize - 1)])) != MP_OKAY) goto LBL_RES; + + for (x = 0; x < (winsize - 1); x++) { + if ((err = mp_sqr(&M[(size_t)1 << (winsize - 1)], &M[(size_t)1 << (winsize - 1)])) != MP_OKAY) goto LBL_RES; + if ((err = redux(&M[(size_t)1 << (winsize - 1)], P, mp)) != MP_OKAY) goto LBL_RES; + } + + /* create upper table */ + for (x = (1 << (winsize - 1)) + 1; x < (1 << winsize); x++) { + if ((err = mp_mul(&M[x - 1], &M[1], &M[x])) != MP_OKAY) goto LBL_RES; + if ((err = redux(&M[x], P, mp)) != MP_OKAY) goto LBL_RES; + } + + /* set initial mode and bit cnt */ + mode = 0; + bitcnt = 1; + buf = 0; + digidx = X->used - 1; + bitcpy = 0; + bitbuf = 0; + + for (;;) { + /* grab next digit as required */ + if (--bitcnt == 0) { + /* if digidx == -1 we are out of digits so break */ + if (digidx == -1) { + break; + } + /* read next digit and reset bitcnt */ + buf = X->dp[digidx--]; + bitcnt = (int)MP_DIGIT_BIT; + } + + /* grab the next msb from the exponent */ + y = (mp_digit)(buf >> (MP_DIGIT_BIT - 1)) & 1uL; + buf <<= (mp_digit)1; + + /* if the bit is zero and mode == 0 then we ignore it + * These represent the leading zero bits before the first 1 bit + * in the exponent. Technically this opt is not required but it + * does lower the # of trivial squaring/reductions used + */ + if ((mode == 0) && (y == 0)) { + continue; + } + + /* if the bit is zero and mode == 1 then we square */ + if ((mode == 1) && (y == 0)) { + if ((err = mp_sqr(&res, &res)) != MP_OKAY) goto LBL_RES; + if ((err = redux(&res, P, mp)) != MP_OKAY) goto LBL_RES; + continue; + } + + /* else we add it to the window */ + bitbuf |= (y << (winsize - ++bitcpy)); + mode = 2; + + if (bitcpy == winsize) { + /* ok window is filled so square as required and multiply */ + /* square first */ + for (x = 0; x < winsize; x++) { + if ((err = mp_sqr(&res, &res)) != MP_OKAY) goto LBL_RES; + if ((err = redux(&res, P, mp)) != MP_OKAY) goto LBL_RES; + } + + /* then multiply */ + if ((err = mp_mul(&res, &M[bitbuf], &res)) != MP_OKAY) goto LBL_RES; + if ((err = redux(&res, P, mp)) != MP_OKAY) goto LBL_RES; + + /* empty window and reset */ + bitcpy = 0; + bitbuf = 0; + mode = 1; + } + } + + /* if bits remain then square/multiply */ + if ((mode == 2) && (bitcpy > 0)) { + /* square then multiply if the bit is set */ + for (x = 0; x < bitcpy; x++) { + if ((err = mp_sqr(&res, &res)) != MP_OKAY) goto LBL_RES; + if ((err = redux(&res, P, mp)) != MP_OKAY) goto LBL_RES; + + /* get next bit of the window */ + bitbuf <<= 1; + if ((bitbuf & (1 << winsize)) != 0) { + /* then multiply */ + if ((err = mp_mul(&res, &M[1], &res)) != MP_OKAY) goto LBL_RES; + if ((err = redux(&res, P, mp)) != MP_OKAY) goto LBL_RES; + } + } + } + + if (redmode == 0) { + /* fixup result if Montgomery reduction is used + * recall that any value in a Montgomery system is + * actually multiplied by R mod n. So we have + * to reduce one more time to cancel out the factor + * of R. + */ + if ((err = redux(&res, P, mp)) != MP_OKAY) goto LBL_RES; + } + + /* swap res with Y */ + mp_exch(&res, Y); + err = MP_OKAY; +LBL_RES: + mp_clear(&res); +LBL_M: + mp_clear(&M[1]); + for (x = 1<<(winsize-1); x < (1 << winsize); x++) { + mp_clear(&M[x]); + } + return err; +} +#endif + +/* End: bn_s_mp_exptmod_fast.c */ + +/* Start: bn_s_mp_get_bit.c */ +#include "tommath_private.h" +#ifdef BN_S_MP_GET_BIT_C + +/* LibTomMath, multiple-precision integer library -- Tom St Denis */ +/* SPDX-License-Identifier: Unlicense */ + +/* Get bit at position b and return MP_YES if the bit is 1, MP_NO if it is 0 */ +mp_bool s_mp_get_bit(const mp_int *a, unsigned int b) +{ + mp_digit bit; + int limb = (int)(b / MP_DIGIT_BIT); + + if (limb >= a->used) { + return MP_NO; + } + + bit = (mp_digit)1 << (b % MP_DIGIT_BIT); + return ((a->dp[limb] & bit) != 0u) ? MP_YES : MP_NO; +} + +#endif + +/* End: bn_s_mp_get_bit.c */ + +/* Start: bn_s_mp_invmod_fast.c */ +#include "tommath_private.h" +#ifdef BN_S_MP_INVMOD_FAST_C +/* LibTomMath, multiple-precision integer library -- Tom St Denis */ +/* SPDX-License-Identifier: Unlicense */ + +/* computes the modular inverse via binary extended euclidean algorithm, + * that is c = 1/a mod b + * + * Based on slow invmod except this is optimized for the case where b is + * odd as per HAC Note 14.64 on pp. 610 + */ +mp_err s_mp_invmod_fast(const mp_int *a, const mp_int *b, mp_int *c) +{ + mp_int x, y, u, v, B, D; + mp_sign neg; + mp_err err; + + /* 2. [modified] b must be odd */ + if (MP_IS_EVEN(b)) { + return MP_VAL; + } + + /* init all our temps */ + if ((err = mp_init_multi(&x, &y, &u, &v, &B, &D, NULL)) != MP_OKAY) { + return err; + } + + /* x == modulus, y == value to invert */ + if ((err = mp_copy(b, &x)) != MP_OKAY) goto LBL_ERR; + + /* we need y = |a| */ + if ((err = mp_mod(a, b, &y)) != MP_OKAY) goto LBL_ERR; + + /* if one of x,y is zero return an error! */ + if (MP_IS_ZERO(&x) || MP_IS_ZERO(&y)) { + err = MP_VAL; + goto LBL_ERR; + } + + /* 3. u=x, v=y, A=1, B=0, C=0,D=1 */ + if ((err = mp_copy(&x, &u)) != MP_OKAY) goto LBL_ERR; + if ((err = mp_copy(&y, &v)) != MP_OKAY) goto LBL_ERR; + mp_set(&D, 1uL); + +top: + /* 4. while u is even do */ + while (MP_IS_EVEN(&u)) { + /* 4.1 u = u/2 */ + if ((err = mp_div_2(&u, &u)) != MP_OKAY) goto LBL_ERR; + + /* 4.2 if B is odd then */ + if (MP_IS_ODD(&B)) { + if ((err = mp_sub(&B, &x, &B)) != MP_OKAY) goto LBL_ERR; + } + /* B = B/2 */ + if ((err = mp_div_2(&B, &B)) != MP_OKAY) goto LBL_ERR; + } + + /* 5. while v is even do */ + while (MP_IS_EVEN(&v)) { + /* 5.1 v = v/2 */ + if ((err = mp_div_2(&v, &v)) != MP_OKAY) goto LBL_ERR; + + /* 5.2 if D is odd then */ + if (MP_IS_ODD(&D)) { + /* D = (D-x)/2 */ + if ((err = mp_sub(&D, &x, &D)) != MP_OKAY) goto LBL_ERR; + } + /* D = D/2 */ + if ((err = mp_div_2(&D, &D)) != MP_OKAY) goto LBL_ERR; + } + + /* 6. if u >= v then */ + if (mp_cmp(&u, &v) != MP_LT) { + /* u = u - v, B = B - D */ + if ((err = mp_sub(&u, &v, &u)) != MP_OKAY) goto LBL_ERR; + + if ((err = mp_sub(&B, &D, &B)) != MP_OKAY) goto LBL_ERR; + } else { + /* v - v - u, D = D - B */ + if ((err = mp_sub(&v, &u, &v)) != MP_OKAY) goto LBL_ERR; + + if ((err = mp_sub(&D, &B, &D)) != MP_OKAY) goto LBL_ERR; + } + + /* if not zero goto step 4 */ + if (!MP_IS_ZERO(&u)) { + goto top; + } + + /* now a = C, b = D, gcd == g*v */ + + /* if v != 1 then there is no inverse */ + if (mp_cmp_d(&v, 1uL) != MP_EQ) { + err = MP_VAL; + goto LBL_ERR; + } + + /* b is now the inverse */ + neg = a->sign; + while (D.sign == MP_NEG) { + if ((err = mp_add(&D, b, &D)) != MP_OKAY) goto LBL_ERR; + } + + /* too big */ + while (mp_cmp_mag(&D, b) != MP_LT) { + if ((err = mp_sub(&D, b, &D)) != MP_OKAY) goto LBL_ERR; + } + + mp_exch(&D, c); + c->sign = neg; + err = MP_OKAY; + +LBL_ERR: + mp_clear_multi(&x, &y, &u, &v, &B, &D, NULL); + return err; +} +#endif + +/* End: bn_s_mp_invmod_fast.c */ + +/* Start: bn_s_mp_invmod_slow.c */ +#include "tommath_private.h" +#ifdef BN_S_MP_INVMOD_SLOW_C +/* LibTomMath, multiple-precision integer library -- Tom St Denis */ +/* SPDX-License-Identifier: Unlicense */ + +/* hac 14.61, pp608 */ +mp_err s_mp_invmod_slow(const mp_int *a, const mp_int *b, mp_int *c) +{ + mp_int x, y, u, v, A, B, C, D; + mp_err err; + + /* b cannot be negative */ + if ((b->sign == MP_NEG) || MP_IS_ZERO(b)) { + return MP_VAL; + } + + /* init temps */ + if ((err = mp_init_multi(&x, &y, &u, &v, + &A, &B, &C, &D, NULL)) != MP_OKAY) { + return err; + } + + /* x = a, y = b */ + if ((err = mp_mod(a, b, &x)) != MP_OKAY) goto LBL_ERR; + if ((err = mp_copy(b, &y)) != MP_OKAY) goto LBL_ERR; + + /* 2. [modified] if x,y are both even then return an error! */ + if (MP_IS_EVEN(&x) && MP_IS_EVEN(&y)) { + err = MP_VAL; + goto LBL_ERR; + } + + /* 3. u=x, v=y, A=1, B=0, C=0,D=1 */ + if ((err = mp_copy(&x, &u)) != MP_OKAY) goto LBL_ERR; + if ((err = mp_copy(&y, &v)) != MP_OKAY) goto LBL_ERR; + mp_set(&A, 1uL); + mp_set(&D, 1uL); + +top: + /* 4. while u is even do */ + while (MP_IS_EVEN(&u)) { + /* 4.1 u = u/2 */ + if ((err = mp_div_2(&u, &u)) != MP_OKAY) goto LBL_ERR; + + /* 4.2 if A or B is odd then */ + if (MP_IS_ODD(&A) || MP_IS_ODD(&B)) { + /* A = (A+y)/2, B = (B-x)/2 */ + if ((err = mp_add(&A, &y, &A)) != MP_OKAY) goto LBL_ERR; + if ((err = mp_sub(&B, &x, &B)) != MP_OKAY) goto LBL_ERR; + } + /* A = A/2, B = B/2 */ + if ((err = mp_div_2(&A, &A)) != MP_OKAY) goto LBL_ERR; + if ((err = mp_div_2(&B, &B)) != MP_OKAY) goto LBL_ERR; + } + + /* 5. while v is even do */ + while (MP_IS_EVEN(&v)) { + /* 5.1 v = v/2 */ + if ((err = mp_div_2(&v, &v)) != MP_OKAY) goto LBL_ERR; + + /* 5.2 if C or D is odd then */ + if (MP_IS_ODD(&C) || MP_IS_ODD(&D)) { + /* C = (C+y)/2, D = (D-x)/2 */ + if ((err = mp_add(&C, &y, &C)) != MP_OKAY) goto LBL_ERR; + if ((err = mp_sub(&D, &x, &D)) != MP_OKAY) goto LBL_ERR; + } + /* C = C/2, D = D/2 */ + if ((err = mp_div_2(&C, &C)) != MP_OKAY) goto LBL_ERR; + if ((err = mp_div_2(&D, &D)) != MP_OKAY) goto LBL_ERR; + } + + /* 6. if u >= v then */ + if (mp_cmp(&u, &v) != MP_LT) { + /* u = u - v, A = A - C, B = B - D */ + if ((err = mp_sub(&u, &v, &u)) != MP_OKAY) goto LBL_ERR; + + if ((err = mp_sub(&A, &C, &A)) != MP_OKAY) goto LBL_ERR; + + if ((err = mp_sub(&B, &D, &B)) != MP_OKAY) goto LBL_ERR; + } else { + /* v - v - u, C = C - A, D = D - B */ + if ((err = mp_sub(&v, &u, &v)) != MP_OKAY) goto LBL_ERR; + + if ((err = mp_sub(&C, &A, &C)) != MP_OKAY) goto LBL_ERR; + + if ((err = mp_sub(&D, &B, &D)) != MP_OKAY) goto LBL_ERR; + } + + /* if not zero goto step 4 */ + if (!MP_IS_ZERO(&u)) { + goto top; + } + + /* now a = C, b = D, gcd == g*v */ + + /* if v != 1 then there is no inverse */ + if (mp_cmp_d(&v, 1uL) != MP_EQ) { + err = MP_VAL; + goto LBL_ERR; + } + + /* if its too low */ + while (mp_cmp_d(&C, 0uL) == MP_LT) { + if ((err = mp_add(&C, b, &C)) != MP_OKAY) goto LBL_ERR; + } + + /* too big */ + while (mp_cmp_mag(&C, b) != MP_LT) { + if ((err = mp_sub(&C, b, &C)) != MP_OKAY) goto LBL_ERR; + } + + /* C is now the inverse */ + mp_exch(&C, c); + err = MP_OKAY; +LBL_ERR: + mp_clear_multi(&x, &y, &u, &v, &A, &B, &C, &D, NULL); + return err; +} +#endif + +/* End: bn_s_mp_invmod_slow.c */ + +/* Start: bn_s_mp_karatsuba_mul.c */ +#include "tommath_private.h" +#ifdef BN_S_MP_KARATSUBA_MUL_C +/* LibTomMath, multiple-precision integer library -- Tom St Denis */ +/* SPDX-License-Identifier: Unlicense */ + +/* c = |a| * |b| using Karatsuba Multiplication using + * three half size multiplications + * + * Let B represent the radix [e.g. 2**MP_DIGIT_BIT] and + * let n represent half of the number of digits in + * the min(a,b) + * + * a = a1 * B**n + a0 + * b = b1 * B**n + b0 + * + * Then, a * b => + a1b1 * B**2n + ((a1 + a0)(b1 + b0) - (a0b0 + a1b1)) * B + a0b0 + * + * Note that a1b1 and a0b0 are used twice and only need to be + * computed once. So in total three half size (half # of + * digit) multiplications are performed, a0b0, a1b1 and + * (a1+b1)(a0+b0) + * + * Note that a multiplication of half the digits requires + * 1/4th the number of single precision multiplications so in + * total after one call 25% of the single precision multiplications + * are saved. Note also that the call to mp_mul can end up back + * in this function if the a0, a1, b0, or b1 are above the threshold. + * This is known as divide-and-conquer and leads to the famous + * O(N**lg(3)) or O(N**1.584) work which is asymptopically lower than + * the standard O(N**2) that the baseline/comba methods use. + * Generally though the overhead of this method doesn't pay off + * until a certain size (N ~ 80) is reached. + */ +mp_err s_mp_karatsuba_mul(const mp_int *a, const mp_int *b, mp_int *c) +{ + mp_int x0, x1, y0, y1, t1, x0y0, x1y1; + int B; + mp_err err = MP_MEM; /* default the return code to an error */ + + /* min # of digits */ + B = MP_MIN(a->used, b->used); + + /* now divide in two */ + B = B >> 1; + + /* init copy all the temps */ + if (mp_init_size(&x0, B) != MP_OKAY) { + goto LBL_ERR; + } + if (mp_init_size(&x1, a->used - B) != MP_OKAY) { + goto X0; + } + if (mp_init_size(&y0, B) != MP_OKAY) { + goto X1; + } + if (mp_init_size(&y1, b->used - B) != MP_OKAY) { + goto Y0; + } + + /* init temps */ + if (mp_init_size(&t1, B * 2) != MP_OKAY) { + goto Y1; + } + if (mp_init_size(&x0y0, B * 2) != MP_OKAY) { + goto T1; + } + if (mp_init_size(&x1y1, B * 2) != MP_OKAY) { + goto X0Y0; + } + + /* now shift the digits */ + x0.used = y0.used = B; + x1.used = a->used - B; + y1.used = b->used - B; + + { + int x; + mp_digit *tmpa, *tmpb, *tmpx, *tmpy; + + /* we copy the digits directly instead of using higher level functions + * since we also need to shift the digits + */ + tmpa = a->dp; + tmpb = b->dp; + + tmpx = x0.dp; + tmpy = y0.dp; + for (x = 0; x < B; x++) { + *tmpx++ = *tmpa++; + *tmpy++ = *tmpb++; + } + + tmpx = x1.dp; + for (x = B; x < a->used; x++) { + *tmpx++ = *tmpa++; + } + + tmpy = y1.dp; + for (x = B; x < b->used; x++) { + *tmpy++ = *tmpb++; + } + } + + /* only need to clamp the lower words since by definition the + * upper words x1/y1 must have a known number of digits + */ + mp_clamp(&x0); + mp_clamp(&y0); + + /* now calc the products x0y0 and x1y1 */ + /* after this x0 is no longer required, free temp [x0==t2]! */ + if (mp_mul(&x0, &y0, &x0y0) != MP_OKAY) { + goto X1Y1; /* x0y0 = x0*y0 */ + } + if (mp_mul(&x1, &y1, &x1y1) != MP_OKAY) { + goto X1Y1; /* x1y1 = x1*y1 */ + } + + /* now calc x1+x0 and y1+y0 */ + if (s_mp_add(&x1, &x0, &t1) != MP_OKAY) { + goto X1Y1; /* t1 = x1 - x0 */ + } + if (s_mp_add(&y1, &y0, &x0) != MP_OKAY) { + goto X1Y1; /* t2 = y1 - y0 */ + } + if (mp_mul(&t1, &x0, &t1) != MP_OKAY) { + goto X1Y1; /* t1 = (x1 + x0) * (y1 + y0) */ + } + + /* add x0y0 */ + if (mp_add(&x0y0, &x1y1, &x0) != MP_OKAY) { + goto X1Y1; /* t2 = x0y0 + x1y1 */ + } + if (s_mp_sub(&t1, &x0, &t1) != MP_OKAY) { + goto X1Y1; /* t1 = (x1+x0)*(y1+y0) - (x1y1 + x0y0) */ + } + + /* shift by B */ + if (mp_lshd(&t1, B) != MP_OKAY) { + goto X1Y1; /* t1 = (x0y0 + x1y1 - (x1-x0)*(y1-y0))<<B */ + } + if (mp_lshd(&x1y1, B * 2) != MP_OKAY) { + goto X1Y1; /* x1y1 = x1y1 << 2*B */ + } + + if (mp_add(&x0y0, &t1, &t1) != MP_OKAY) { + goto X1Y1; /* t1 = x0y0 + t1 */ + } + if (mp_add(&t1, &x1y1, c) != MP_OKAY) { + goto X1Y1; /* t1 = x0y0 + t1 + x1y1 */ + } + + /* Algorithm succeeded set the return code to MP_OKAY */ + err = MP_OKAY; + +X1Y1: + mp_clear(&x1y1); +X0Y0: + mp_clear(&x0y0); +T1: + mp_clear(&t1); +Y1: + mp_clear(&y1); +Y0: + mp_clear(&y0); +X1: + mp_clear(&x1); +X0: + mp_clear(&x0); +LBL_ERR: + return err; +} +#endif + +/* End: bn_s_mp_karatsuba_mul.c */ + +/* Start: bn_s_mp_karatsuba_sqr.c */ +#include "tommath_private.h" +#ifdef BN_S_MP_KARATSUBA_SQR_C +/* LibTomMath, multiple-precision integer library -- Tom St Denis */ +/* SPDX-License-Identifier: Unlicense */ + +/* Karatsuba squaring, computes b = a*a using three + * half size squarings + * + * See comments of karatsuba_mul for details. It + * is essentially the same algorithm but merely + * tuned to perform recursive squarings. + */ +mp_err s_mp_karatsuba_sqr(const mp_int *a, mp_int *b) +{ + mp_int x0, x1, t1, t2, x0x0, x1x1; + int B; + mp_err err = MP_MEM; + + /* min # of digits */ + B = a->used; + + /* now divide in two */ + B = B >> 1; + + /* init copy all the temps */ + if (mp_init_size(&x0, B) != MP_OKAY) + goto LBL_ERR; + if (mp_init_size(&x1, a->used - B) != MP_OKAY) + goto X0; + + /* init temps */ + if (mp_init_size(&t1, a->used * 2) != MP_OKAY) + goto X1; + if (mp_init_size(&t2, a->used * 2) != MP_OKAY) + goto T1; + if (mp_init_size(&x0x0, B * 2) != MP_OKAY) + goto T2; + if (mp_init_size(&x1x1, (a->used - B) * 2) != MP_OKAY) + goto X0X0; + + { + int x; + mp_digit *dst, *src; + + src = a->dp; + + /* now shift the digits */ + dst = x0.dp; + for (x = 0; x < B; x++) { + *dst++ = *src++; + } + + dst = x1.dp; + for (x = B; x < a->used; x++) { + *dst++ = *src++; + } + } + + x0.used = B; + x1.used = a->used - B; + + mp_clamp(&x0); + + /* now calc the products x0*x0 and x1*x1 */ + if (mp_sqr(&x0, &x0x0) != MP_OKAY) + goto X1X1; /* x0x0 = x0*x0 */ + if (mp_sqr(&x1, &x1x1) != MP_OKAY) + goto X1X1; /* x1x1 = x1*x1 */ + + /* now calc (x1+x0)**2 */ + if (s_mp_add(&x1, &x0, &t1) != MP_OKAY) + goto X1X1; /* t1 = x1 - x0 */ + if (mp_sqr(&t1, &t1) != MP_OKAY) + goto X1X1; /* t1 = (x1 - x0) * (x1 - x0) */ + + /* add x0y0 */ + if (s_mp_add(&x0x0, &x1x1, &t2) != MP_OKAY) + goto X1X1; /* t2 = x0x0 + x1x1 */ + if (s_mp_sub(&t1, &t2, &t1) != MP_OKAY) + goto X1X1; /* t1 = (x1+x0)**2 - (x0x0 + x1x1) */ + + /* shift by B */ + if (mp_lshd(&t1, B) != MP_OKAY) + goto X1X1; /* t1 = (x0x0 + x1x1 - (x1-x0)*(x1-x0))<<B */ + if (mp_lshd(&x1x1, B * 2) != MP_OKAY) + goto X1X1; /* x1x1 = x1x1 << 2*B */ + + if (mp_add(&x0x0, &t1, &t1) != MP_OKAY) + goto X1X1; /* t1 = x0x0 + t1 */ + if (mp_add(&t1, &x1x1, b) != MP_OKAY) + goto X1X1; /* t1 = x0x0 + t1 + x1x1 */ + + err = MP_OKAY; + +X1X1: + mp_clear(&x1x1); +X0X0: + mp_clear(&x0x0); +T2: + mp_clear(&t2); +T1: + mp_clear(&t1); +X1: + mp_clear(&x1); +X0: + mp_clear(&x0); +LBL_ERR: + return err; +} +#endif + +/* End: bn_s_mp_karatsuba_sqr.c */ + +/* Start: bn_s_mp_montgomery_reduce_fast.c */ +#include "tommath_private.h" +#ifdef BN_S_MP_MONTGOMERY_REDUCE_FAST_C +/* LibTomMath, multiple-precision integer library -- Tom St Denis */ +/* SPDX-License-Identifier: Unlicense */ + +/* computes xR**-1 == x (mod N) via Montgomery Reduction + * + * This is an optimized implementation of montgomery_reduce + * which uses the comba method to quickly calculate the columns of the + * reduction. + * + * Based on Algorithm 14.32 on pp.601 of HAC. +*/ +mp_err s_mp_montgomery_reduce_fast(mp_int *x, const mp_int *n, mp_digit rho) +{ + int ix, olduse; + mp_err err; + mp_word W[MP_WARRAY]; + + if (x->used > MP_WARRAY) { + return MP_VAL; + } + + /* get old used count */ + olduse = x->used; + + /* grow a as required */ + if (x->alloc < (n->used + 1)) { + if ((err = mp_grow(x, n->used + 1)) != MP_OKAY) { + return err; + } + } + + /* first we have to get the digits of the input into + * an array of double precision words W[...] + */ + { + mp_word *_W; + mp_digit *tmpx; + + /* alias for the W[] array */ + _W = W; + + /* alias for the digits of x*/ + tmpx = x->dp; + + /* copy the digits of a into W[0..a->used-1] */ + for (ix = 0; ix < x->used; ix++) { + *_W++ = *tmpx++; + } + + /* zero the high words of W[a->used..m->used*2] */ + if (ix < ((n->used * 2) + 1)) { + MP_ZERO_BUFFER(_W, sizeof(mp_word) * (size_t)(((n->used * 2) + 1) - ix)); + } + } + + /* now we proceed to zero successive digits + * from the least significant upwards + */ + for (ix = 0; ix < n->used; ix++) { + /* mu = ai * m' mod b + * + * We avoid a double precision multiplication (which isn't required) + * by casting the value down to a mp_digit. Note this requires + * that W[ix-1] have the carry cleared (see after the inner loop) + */ + mp_digit mu; + mu = ((W[ix] & MP_MASK) * rho) & MP_MASK; + + /* a = a + mu * m * b**i + * + * This is computed in place and on the fly. The multiplication + * by b**i is handled by offseting which columns the results + * are added to. + * + * Note the comba method normally doesn't handle carries in the + * inner loop In this case we fix the carry from the previous + * column since the Montgomery reduction requires digits of the + * result (so far) [see above] to work. This is + * handled by fixing up one carry after the inner loop. The + * carry fixups are done in order so after these loops the + * first m->used words of W[] have the carries fixed + */ + { + int iy; + mp_digit *tmpn; + mp_word *_W; + + /* alias for the digits of the modulus */ + tmpn = n->dp; + + /* Alias for the columns set by an offset of ix */ + _W = W + ix; + + /* inner loop */ + for (iy = 0; iy < n->used; iy++) { + *_W++ += (mp_word)mu * (mp_word)*tmpn++; + } + } + + /* now fix carry for next digit, W[ix+1] */ + W[ix + 1] += W[ix] >> (mp_word)MP_DIGIT_BIT; + } + + /* now we have to propagate the carries and + * shift the words downward [all those least + * significant digits we zeroed]. + */ + { + mp_digit *tmpx; + mp_word *_W, *_W1; + + /* nox fix rest of carries */ + + /* alias for current word */ + _W1 = W + ix; + + /* alias for next word, where the carry goes */ + _W = W + ++ix; + + for (; ix < ((n->used * 2) + 1); ix++) { + *_W++ += *_W1++ >> (mp_word)MP_DIGIT_BIT; + } + + /* copy out, A = A/b**n + * + * The result is A/b**n but instead of converting from an + * array of mp_word to mp_digit than calling mp_rshd + * we just copy them in the right order + */ + + /* alias for destination word */ + tmpx = x->dp; + + /* alias for shifted double precision result */ + _W = W + n->used; + + for (ix = 0; ix < (n->used + 1); ix++) { + *tmpx++ = *_W++ & (mp_word)MP_MASK; + } + + /* zero oldused digits, if the input a was larger than + * m->used+1 we'll have to clear the digits + */ + MP_ZERO_DIGITS(tmpx, olduse - ix); + } + + /* set the max used and clamp */ + x->used = n->used + 1; + mp_clamp(x); + + /* if A >= m then A = A - m */ + if (mp_cmp_mag(x, n) != MP_LT) { + return s_mp_sub(x, n, x); + } + return MP_OKAY; +} +#endif + +/* End: bn_s_mp_montgomery_reduce_fast.c */ + +/* Start: bn_s_mp_mul_digs.c */ +#include "tommath_private.h" +#ifdef BN_S_MP_MUL_DIGS_C +/* LibTomMath, multiple-precision integer library -- Tom St Denis */ +/* SPDX-License-Identifier: Unlicense */ + +/* multiplies |a| * |b| and only computes upto digs digits of result + * HAC pp. 595, Algorithm 14.12 Modified so you can control how + * many digits of output are created. + */ +mp_err s_mp_mul_digs(const mp_int *a, const mp_int *b, mp_int *c, int digs) +{ + mp_int t; + mp_err err; + int pa, pb, ix, iy; + mp_digit u; + mp_word r; + mp_digit tmpx, *tmpt, *tmpy; + + /* can we use the fast multiplier? */ + if ((digs < MP_WARRAY) && + (MP_MIN(a->used, b->used) < MP_MAXFAST)) { + return s_mp_mul_digs_fast(a, b, c, digs); + } + + if ((err = mp_init_size(&t, digs)) != MP_OKAY) { + return err; + } + t.used = digs; + + /* compute the digits of the product directly */ + pa = a->used; + for (ix = 0; ix < pa; ix++) { + /* set the carry to zero */ + u = 0; + + /* limit ourselves to making digs digits of output */ + pb = MP_MIN(b->used, digs - ix); + + /* setup some aliases */ + /* copy of the digit from a used within the nested loop */ + tmpx = a->dp[ix]; + + /* an alias for the destination shifted ix places */ + tmpt = t.dp + ix; + + /* an alias for the digits of b */ + tmpy = b->dp; + + /* compute the columns of the output and propagate the carry */ + for (iy = 0; iy < pb; iy++) { + /* compute the column as a mp_word */ + r = (mp_word)*tmpt + + ((mp_word)tmpx * (mp_word)*tmpy++) + + (mp_word)u; + + /* the new column is the lower part of the result */ + *tmpt++ = (mp_digit)(r & (mp_word)MP_MASK); + + /* get the carry word from the result */ + u = (mp_digit)(r >> (mp_word)MP_DIGIT_BIT); + } + /* set carry if it is placed below digs */ + if ((ix + iy) < digs) { + *tmpt = u; + } + } + + mp_clamp(&t); + mp_exch(&t, c); + + mp_clear(&t); + return MP_OKAY; +} +#endif + +/* End: bn_s_mp_mul_digs.c */ + +/* Start: bn_s_mp_mul_digs_fast.c */ +#include "tommath_private.h" +#ifdef BN_S_MP_MUL_DIGS_FAST_C +/* LibTomMath, multiple-precision integer library -- Tom St Denis */ +/* SPDX-License-Identifier: Unlicense */ + +/* Fast (comba) multiplier + * + * This is the fast column-array [comba] multiplier. It is + * designed to compute the columns of the product first + * then handle the carries afterwards. This has the effect + * of making the nested loops that compute the columns very + * simple and schedulable on super-scalar processors. + * + * This has been modified to produce a variable number of + * digits of output so if say only a half-product is required + * you don't have to compute the upper half (a feature + * required for fast Barrett reduction). + * + * Based on Algorithm 14.12 on pp.595 of HAC. + * + */ +mp_err s_mp_mul_digs_fast(const mp_int *a, const mp_int *b, mp_int *c, int digs) +{ + int olduse, pa, ix, iz; + mp_err err; + mp_digit W[MP_WARRAY]; + mp_word _W; + + /* grow the destination as required */ + if (c->alloc < digs) { + if ((err = mp_grow(c, digs)) != MP_OKAY) { + return err; + } + } + + /* number of output digits to produce */ + pa = MP_MIN(digs, a->used + b->used); + + /* clear the carry */ + _W = 0; + for (ix = 0; ix < pa; ix++) { + int tx, ty; + int iy; + mp_digit *tmpx, *tmpy; + + /* get offsets into the two bignums */ + ty = MP_MIN(b->used-1, ix); + tx = ix - ty; + + /* setup temp aliases */ + tmpx = a->dp + tx; + tmpy = b->dp + ty; + + /* this is the number of times the loop will iterrate, essentially + while (tx++ < a->used && ty-- >= 0) { ... } + */ + iy = MP_MIN(a->used-tx, ty+1); + + /* execute loop */ + for (iz = 0; iz < iy; ++iz) { + _W += (mp_word)*tmpx++ * (mp_word)*tmpy--; + + } + + /* store term */ + W[ix] = (mp_digit)_W & MP_MASK; + + /* make next carry */ + _W = _W >> (mp_word)MP_DIGIT_BIT; + } + + /* setup dest */ + olduse = c->used; + c->used = pa; + + { + mp_digit *tmpc; + tmpc = c->dp; + for (ix = 0; ix < pa; ix++) { + /* now extract the previous digit [below the carry] */ + *tmpc++ = W[ix]; + } + + /* clear unused digits [that existed in the old copy of c] */ + MP_ZERO_DIGITS(tmpc, olduse - ix); + } + mp_clamp(c); + return MP_OKAY; +} +#endif + +/* End: bn_s_mp_mul_digs_fast.c */ + +/* Start: bn_s_mp_mul_high_digs.c */ +#include "tommath_private.h" +#ifdef BN_S_MP_MUL_HIGH_DIGS_C +/* LibTomMath, multiple-precision integer library -- Tom St Denis */ +/* SPDX-License-Identifier: Unlicense */ + +/* multiplies |a| * |b| and does not compute the lower digs digits + * [meant to get the higher part of the product] + */ +mp_err s_mp_mul_high_digs(const mp_int *a, const mp_int *b, mp_int *c, int digs) +{ + mp_int t; + int pa, pb, ix, iy; + mp_err err; + mp_digit u; + mp_word r; + mp_digit tmpx, *tmpt, *tmpy; + + /* can we use the fast multiplier? */ + if (MP_HAS(S_MP_MUL_HIGH_DIGS_FAST) + && ((a->used + b->used + 1) < MP_WARRAY) + && (MP_MIN(a->used, b->used) < MP_MAXFAST)) { + return s_mp_mul_high_digs_fast(a, b, c, digs); + } + + if ((err = mp_init_size(&t, a->used + b->used + 1)) != MP_OKAY) { + return err; + } + t.used = a->used + b->used + 1; + + pa = a->used; + pb = b->used; + for (ix = 0; ix < pa; ix++) { + /* clear the carry */ + u = 0; + + /* left hand side of A[ix] * B[iy] */ + tmpx = a->dp[ix]; + + /* alias to the address of where the digits will be stored */ + tmpt = &(t.dp[digs]); + + /* alias for where to read the right hand side from */ + tmpy = b->dp + (digs - ix); + + for (iy = digs - ix; iy < pb; iy++) { + /* calculate the double precision result */ + r = (mp_word)*tmpt + + ((mp_word)tmpx * (mp_word)*tmpy++) + + (mp_word)u; + + /* get the lower part */ + *tmpt++ = (mp_digit)(r & (mp_word)MP_MASK); + + /* carry the carry */ + u = (mp_digit)(r >> (mp_word)MP_DIGIT_BIT); + } + *tmpt = u; + } + mp_clamp(&t); + mp_exch(&t, c); + mp_clear(&t); + return MP_OKAY; +} +#endif + +/* End: bn_s_mp_mul_high_digs.c */ + +/* Start: bn_s_mp_mul_high_digs_fast.c */ +#include "tommath_private.h" +#ifdef BN_S_MP_MUL_HIGH_DIGS_FAST_C +/* LibTomMath, multiple-precision integer library -- Tom St Denis */ +/* SPDX-License-Identifier: Unlicense */ + +/* this is a modified version of fast_s_mul_digs that only produces + * output digits *above* digs. See the comments for fast_s_mul_digs + * to see how it works. + * + * This is used in the Barrett reduction since for one of the multiplications + * only the higher digits were needed. This essentially halves the work. + * + * Based on Algorithm 14.12 on pp.595 of HAC. + */ +mp_err s_mp_mul_high_digs_fast(const mp_int *a, const mp_int *b, mp_int *c, int digs) +{ + int olduse, pa, ix, iz; + mp_err err; + mp_digit W[MP_WARRAY]; + mp_word _W; + + /* grow the destination as required */ + pa = a->used + b->used; + if (c->alloc < pa) { + if ((err = mp_grow(c, pa)) != MP_OKAY) { + return err; + } + } + + /* number of output digits to produce */ + pa = a->used + b->used; + _W = 0; + for (ix = digs; ix < pa; ix++) { + int tx, ty, iy; + mp_digit *tmpx, *tmpy; + + /* get offsets into the two bignums */ + ty = MP_MIN(b->used-1, ix); + tx = ix - ty; + + /* setup temp aliases */ + tmpx = a->dp + tx; + tmpy = b->dp + ty; + + /* this is the number of times the loop will iterrate, essentially its + while (tx++ < a->used && ty-- >= 0) { ... } + */ + iy = MP_MIN(a->used-tx, ty+1); + + /* execute loop */ + for (iz = 0; iz < iy; iz++) { + _W += (mp_word)*tmpx++ * (mp_word)*tmpy--; + } + + /* store term */ + W[ix] = (mp_digit)_W & MP_MASK; + + /* make next carry */ + _W = _W >> (mp_word)MP_DIGIT_BIT; + } + + /* setup dest */ + olduse = c->used; + c->used = pa; + + { + mp_digit *tmpc; + + tmpc = c->dp + digs; + for (ix = digs; ix < pa; ix++) { + /* now extract the previous digit [below the carry] */ + *tmpc++ = W[ix]; + } + + /* clear unused digits [that existed in the old copy of c] */ + MP_ZERO_DIGITS(tmpc, olduse - ix); + } + mp_clamp(c); + return MP_OKAY; +} +#endif + +/* End: bn_s_mp_mul_high_digs_fast.c */ + +/* Start: bn_s_mp_prime_is_divisible.c */ +#include "tommath_private.h" +#ifdef BN_S_MP_PRIME_IS_DIVISIBLE_C +/* LibTomMath, multiple-precision integer library -- Tom St Denis */ +/* SPDX-License-Identifier: Unlicense */ + +/* determines if an integers is divisible by one + * of the first PRIME_SIZE primes or not + * + * sets result to 0 if not, 1 if yes + */ +mp_err s_mp_prime_is_divisible(const mp_int *a, mp_bool *result) +{ + int ix; + mp_err err; + mp_digit res; + + /* default to not */ + *result = MP_NO; + + for (ix = 0; ix < PRIVATE_MP_PRIME_TAB_SIZE; ix++) { + /* what is a mod LBL_prime_tab[ix] */ + if ((err = mp_mod_d(a, s_mp_prime_tab[ix], &res)) != MP_OKAY) { + return err; + } + + /* is the residue zero? */ + if (res == 0u) { + *result = MP_YES; + return MP_OKAY; + } + } + + return MP_OKAY; +} +#endif + +/* End: bn_s_mp_prime_is_divisible.c */ + +/* Start: bn_s_mp_rand_jenkins.c */ +#include "tommath_private.h" +#ifdef BN_S_MP_RAND_JENKINS_C +/* LibTomMath, multiple-precision integer library -- Tom St Denis */ +/* SPDX-License-Identifier: Unlicense */ + +/* Bob Jenkins' http://burtleburtle.net/bob/rand/smallprng.html */ +/* Chosen for speed and a good "mix" */ +typedef struct { + uint64_t a; + uint64_t b; + uint64_t c; + uint64_t d; +} ranctx; + +static ranctx jenkins_x; + +#define rot(x,k) (((x)<<(k))|((x)>>(64-(k)))) +static uint64_t s_rand_jenkins_val(void) +{ + uint64_t e = jenkins_x.a - rot(jenkins_x.b, 7); + jenkins_x.a = jenkins_x.b ^ rot(jenkins_x.c, 13); + jenkins_x.b = jenkins_x.c + rot(jenkins_x.d, 37); + jenkins_x.c = jenkins_x.d + e; + jenkins_x.d = e + jenkins_x.a; + return jenkins_x.d; +} + +void s_mp_rand_jenkins_init(uint64_t seed) +{ + uint64_t i; + jenkins_x.a = 0xf1ea5eedULL; + jenkins_x.b = jenkins_x.c = jenkins_x.d = seed; + for (i = 0uLL; i < 20uLL; ++i) { + (void)s_rand_jenkins_val(); + } +} + +mp_err s_mp_rand_jenkins(void *p, size_t n) +{ + char *q = (char *)p; + while (n > 0u) { + int i; + uint64_t x = s_rand_jenkins_val(); + for (i = 0; (i < 8) && (n > 0u); ++i, --n) { + *q++ = (char)(x & 0xFFuLL); + x >>= 8; + } + } + return MP_OKAY; +} + +#endif + +/* End: bn_s_mp_rand_jenkins.c */ + +/* Start: bn_s_mp_rand_platform.c */ +#include "tommath_private.h" +#ifdef BN_S_MP_RAND_PLATFORM_C +/* LibTomMath, multiple-precision integer library -- Tom St Denis */ +/* SPDX-License-Identifier: Unlicense */ + +/* First the OS-specific special cases + * - *BSD + * - Windows + */ +#if defined(__FreeBSD__) || defined(__OpenBSD__) || defined(__NetBSD__) || defined(__DragonFly__) +#define BN_S_READ_ARC4RANDOM_C +static mp_err s_read_arc4random(void *p, size_t n) +{ + arc4random_buf(p, n); + return MP_OKAY; +} +#endif + +#if defined(_WIN32) || defined(_WIN32_WCE) +#define BN_S_READ_WINCSP_C + +#ifndef _WIN32_WINNT +#define _WIN32_WINNT 0x0400 +#endif +#ifdef _WIN32_WCE +#define UNDER_CE +#define ARM +#endif + +#define WIN32_LEAN_AND_MEAN +#include <windows.h> +#include <wincrypt.h> + +static mp_err s_read_wincsp(void *p, size_t n) +{ + static HCRYPTPROV hProv = 0; + if (hProv == 0) { + HCRYPTPROV h = 0; + if (!CryptAcquireContext(&h, NULL, MS_DEF_PROV, PROV_RSA_FULL, + (CRYPT_VERIFYCONTEXT | CRYPT_MACHINE_KEYSET)) && + !CryptAcquireContext(&h, NULL, MS_DEF_PROV, PROV_RSA_FULL, + CRYPT_VERIFYCONTEXT | CRYPT_MACHINE_KEYSET | CRYPT_NEWKEYSET)) { + return MP_ERR; + } + hProv = h; + } + return CryptGenRandom(hProv, (DWORD)n, (BYTE *)p) == TRUE ? MP_OKAY : MP_ERR; +} +#endif /* WIN32 */ + +#if !defined(BN_S_READ_WINCSP_C) && defined(__linux__) && defined(__GLIBC_PREREQ) +#if __GLIBC_PREREQ(2, 25) +#define BN_S_READ_GETRANDOM_C +#include <sys/random.h> +#include <errno.h> + +static mp_err s_read_getrandom(void *p, size_t n) +{ + char *q = (char *)p; + while (n > 0u) { + ssize_t ret = getrandom(q, n, 0); + if (ret < 0) { + if (errno == EINTR) { + continue; + } + return MP_ERR; + } + q += ret; + n -= (size_t)ret; + } + return MP_OKAY; +} +#endif +#endif + +/* We assume all platforms besides windows provide "/dev/urandom". + * In case yours doesn't, define MP_NO_DEV_URANDOM at compile-time. + */ +#if !defined(BN_S_READ_WINCSP_C) && !defined(MP_NO_DEV_URANDOM) +#define BN_S_READ_URANDOM_C +#ifndef MP_DEV_URANDOM +#define MP_DEV_URANDOM "/dev/urandom" +#endif +#include <fcntl.h> +#include <errno.h> +#include <unistd.h> + +static mp_err s_read_urandom(void *p, size_t n) +{ + int fd; + char *q = (char *)p; + + do { + fd = open(MP_DEV_URANDOM, O_RDONLY); + } while ((fd == -1) && (errno == EINTR)); + if (fd == -1) return MP_ERR; + + while (n > 0u) { + ssize_t ret = read(fd, p, n); + if (ret < 0) { + if (errno == EINTR) { + continue; + } + close(fd); + return MP_ERR; + } + q += ret; + n -= (size_t)ret; + } + + close(fd); + return MP_OKAY; +} +#endif + +#if defined(MP_PRNG_ENABLE_LTM_RNG) +#define BN_S_READ_LTM_RNG +unsigned long (*ltm_rng)(unsigned char *out, unsigned long outlen, void (*callback)(void)); +void (*ltm_rng_callback)(void); + +static mp_err s_read_ltm_rng(void *p, size_t n) +{ + unsigned long res; + if (ltm_rng == NULL) return MP_ERR; + res = ltm_rng(p, n, ltm_rng_callback); + if (res != n) return MP_ERR; + return MP_OKAY; +} +#endif + +mp_err s_read_arc4random(void *p, size_t n); +mp_err s_read_wincsp(void *p, size_t n); +mp_err s_read_getrandom(void *p, size_t n); +mp_err s_read_urandom(void *p, size_t n); +mp_err s_read_ltm_rng(void *p, size_t n); + +mp_err s_mp_rand_platform(void *p, size_t n) +{ + mp_err err = MP_ERR; + if ((err != MP_OKAY) && MP_HAS(S_READ_ARC4RANDOM)) err = s_read_arc4random(p, n); + if ((err != MP_OKAY) && MP_HAS(S_READ_WINCSP)) err = s_read_wincsp(p, n); + if ((err != MP_OKAY) && MP_HAS(S_READ_GETRANDOM)) err = s_read_getrandom(p, n); + if ((err != MP_OKAY) && MP_HAS(S_READ_URANDOM)) err = s_read_urandom(p, n); + if ((err != MP_OKAY) && MP_HAS(S_READ_LTM_RNG)) err = s_read_ltm_rng(p, n); + return err; +} + +#endif + +/* End: bn_s_mp_rand_platform.c */ + +/* Start: bn_s_mp_reverse.c */ +#include "tommath_private.h" +#ifdef BN_S_MP_REVERSE_C +/* LibTomMath, multiple-precision integer library -- Tom St Denis */ +/* SPDX-License-Identifier: Unlicense */ + +/* reverse an array, used for radix code */ +void s_mp_reverse(unsigned char *s, size_t len) +{ + size_t ix, iy; + unsigned char t; + + ix = 0u; + iy = len - 1u; + while (ix < iy) { + t = s[ix]; + s[ix] = s[iy]; + s[iy] = t; + ++ix; + --iy; + } +} +#endif + +/* End: bn_s_mp_reverse.c */ + +/* Start: bn_s_mp_sqr.c */ +#include "tommath_private.h" +#ifdef BN_S_MP_SQR_C +/* LibTomMath, multiple-precision integer library -- Tom St Denis */ +/* SPDX-License-Identifier: Unlicense */ + +/* low level squaring, b = a*a, HAC pp.596-597, Algorithm 14.16 */ +mp_err s_mp_sqr(const mp_int *a, mp_int *b) +{ + mp_int t; + int ix, iy, pa; + mp_err err; + mp_word r; + mp_digit u, tmpx, *tmpt; + + pa = a->used; + if ((err = mp_init_size(&t, (2 * pa) + 1)) != MP_OKAY) { + return err; + } + + /* default used is maximum possible size */ + t.used = (2 * pa) + 1; + + for (ix = 0; ix < pa; ix++) { + /* first calculate the digit at 2*ix */ + /* calculate double precision result */ + r = (mp_word)t.dp[2*ix] + + ((mp_word)a->dp[ix] * (mp_word)a->dp[ix]); + + /* store lower part in result */ + t.dp[ix+ix] = (mp_digit)(r & (mp_word)MP_MASK); + + /* get the carry */ + u = (mp_digit)(r >> (mp_word)MP_DIGIT_BIT); + + /* left hand side of A[ix] * A[iy] */ + tmpx = a->dp[ix]; + + /* alias for where to store the results */ + tmpt = t.dp + ((2 * ix) + 1); + + for (iy = ix + 1; iy < pa; iy++) { + /* first calculate the product */ + r = (mp_word)tmpx * (mp_word)a->dp[iy]; + + /* now calculate the double precision result, note we use + * addition instead of *2 since it's easier to optimize + */ + r = (mp_word)*tmpt + r + r + (mp_word)u; + + /* store lower part */ + *tmpt++ = (mp_digit)(r & (mp_word)MP_MASK); + + /* get carry */ + u = (mp_digit)(r >> (mp_word)MP_DIGIT_BIT); + } + /* propagate upwards */ + while (u != 0uL) { + r = (mp_word)*tmpt + (mp_word)u; + *tmpt++ = (mp_digit)(r & (mp_word)MP_MASK); + u = (mp_digit)(r >> (mp_word)MP_DIGIT_BIT); + } + } + + mp_clamp(&t); + mp_exch(&t, b); + mp_clear(&t); + return MP_OKAY; +} +#endif + +/* End: bn_s_mp_sqr.c */ + +/* Start: bn_s_mp_sqr_fast.c */ +#include "tommath_private.h" +#ifdef BN_S_MP_SQR_FAST_C +/* LibTomMath, multiple-precision integer library -- Tom St Denis */ +/* SPDX-License-Identifier: Unlicense */ + +/* the jist of squaring... + * you do like mult except the offset of the tmpx [one that + * starts closer to zero] can't equal the offset of tmpy. + * So basically you set up iy like before then you min it with + * (ty-tx) so that it never happens. You double all those + * you add in the inner loop + +After that loop you do the squares and add them in. +*/ + +mp_err s_mp_sqr_fast(const mp_int *a, mp_int *b) +{ + int olduse, pa, ix, iz; + mp_digit W[MP_WARRAY], *tmpx; + mp_word W1; + mp_err err; + + /* grow the destination as required */ + pa = a->used + a->used; + if (b->alloc < pa) { + if ((err = mp_grow(b, pa)) != MP_OKAY) { + return err; + } + } + + /* number of output digits to produce */ + W1 = 0; + for (ix = 0; ix < pa; ix++) { + int tx, ty, iy; + mp_word _W; + mp_digit *tmpy; + + /* clear counter */ + _W = 0; + + /* get offsets into the two bignums */ + ty = MP_MIN(a->used-1, ix); + tx = ix - ty; + + /* setup temp aliases */ + tmpx = a->dp + tx; + tmpy = a->dp + ty; + + /* this is the number of times the loop will iterrate, essentially + while (tx++ < a->used && ty-- >= 0) { ... } + */ + iy = MP_MIN(a->used-tx, ty+1); + + /* now for squaring tx can never equal ty + * we halve the distance since they approach at a rate of 2x + * and we have to round because odd cases need to be executed + */ + iy = MP_MIN(iy, ((ty-tx)+1)>>1); + + /* execute loop */ + for (iz = 0; iz < iy; iz++) { + _W += (mp_word)*tmpx++ * (mp_word)*tmpy--; + } + + /* double the inner product and add carry */ + _W = _W + _W + W1; + + /* even columns have the square term in them */ + if (((unsigned)ix & 1u) == 0u) { + _W += (mp_word)a->dp[ix>>1] * (mp_word)a->dp[ix>>1]; + } + + /* store it */ + W[ix] = (mp_digit)_W & MP_MASK; + + /* make next carry */ + W1 = _W >> (mp_word)MP_DIGIT_BIT; + } + + /* setup dest */ + olduse = b->used; + b->used = a->used+a->used; + + { + mp_digit *tmpb; + tmpb = b->dp; + for (ix = 0; ix < pa; ix++) { + *tmpb++ = W[ix] & MP_MASK; + } + + /* clear unused digits [that existed in the old copy of c] */ + MP_ZERO_DIGITS(tmpb, olduse - ix); + } + mp_clamp(b); + return MP_OKAY; +} +#endif + +/* End: bn_s_mp_sqr_fast.c */ + +/* Start: bn_s_mp_sub.c */ +#include "tommath_private.h" +#ifdef BN_S_MP_SUB_C +/* LibTomMath, multiple-precision integer library -- Tom St Denis */ +/* SPDX-License-Identifier: Unlicense */ + +/* low level subtraction (assumes |a| > |b|), HAC pp.595 Algorithm 14.9 */ +mp_err s_mp_sub(const mp_int *a, const mp_int *b, mp_int *c) +{ + int olduse, min, max; + mp_err err; + + /* find sizes */ + min = b->used; + max = a->used; + + /* init result */ + if (c->alloc < max) { + if ((err = mp_grow(c, max)) != MP_OKAY) { + return err; + } + } + olduse = c->used; + c->used = max; + + { + mp_digit u, *tmpa, *tmpb, *tmpc; + int i; + + /* alias for digit pointers */ + tmpa = a->dp; + tmpb = b->dp; + tmpc = c->dp; + + /* set carry to zero */ + u = 0; + for (i = 0; i < min; i++) { + /* T[i] = A[i] - B[i] - U */ + *tmpc = (*tmpa++ - *tmpb++) - u; + + /* U = carry bit of T[i] + * Note this saves performing an AND operation since + * if a carry does occur it will propagate all the way to the + * MSB. As a result a single shift is enough to get the carry + */ + u = *tmpc >> (MP_SIZEOF_BITS(mp_digit) - 1u); + + /* Clear carry from T[i] */ + *tmpc++ &= MP_MASK; + } + + /* now copy higher words if any, e.g. if A has more digits than B */ + for (; i < max; i++) { + /* T[i] = A[i] - U */ + *tmpc = *tmpa++ - u; + + /* U = carry bit of T[i] */ + u = *tmpc >> (MP_SIZEOF_BITS(mp_digit) - 1u); + + /* Clear carry from T[i] */ + *tmpc++ &= MP_MASK; + } + + /* clear digits above used (since we may not have grown result above) */ + MP_ZERO_DIGITS(tmpc, olduse - c->used); + } + + mp_clamp(c); + return MP_OKAY; +} + +#endif + +/* End: bn_s_mp_sub.c */ + +/* Start: bn_s_mp_toom_mul.c */ +#include "tommath_private.h" +#ifdef BN_S_MP_TOOM_MUL_C +/* LibTomMath, multiple-precision integer library -- Tom St Denis */ +/* SPDX-License-Identifier: Unlicense */ + +/* multiplication using the Toom-Cook 3-way algorithm + * + * Much more complicated than Karatsuba but has a lower + * asymptotic running time of O(N**1.464). This algorithm is + * only particularly useful on VERY large inputs + * (we're talking 1000s of digits here...). +*/ + +/* + This file contains code from J. Arndt's book "Matters Computational" + and the accompanying FXT-library with permission of the author. +*/ + +/* + Setup from + + Chung, Jaewook, and M. Anwar Hasan. "Asymmetric squaring formulae." + 18th IEEE Symposium on Computer Arithmetic (ARITH'07). IEEE, 2007. + + The interpolation from above needed one temporary variable more + than the interpolation here: + + Bodrato, Marco, and Alberto Zanoni. "What about Toom-Cook matrices optimality." + Centro Vito Volterra Universita di Roma Tor Vergata (2006) +*/ + +mp_err s_mp_toom_mul(const mp_int *a, const mp_int *b, mp_int *c) +{ + mp_int S1, S2, T1, a0, a1, a2, b0, b1, b2; + int B, count; + mp_err err; + + /* init temps */ + if ((err = mp_init_multi(&S1, &S2, &T1, NULL)) != MP_OKAY) { + return err; + } + + /* B */ + B = MP_MIN(a->used, b->used) / 3; + + /** a = a2 * x^2 + a1 * x + a0; */ + if ((err = mp_init_size(&a0, B)) != MP_OKAY) goto LBL_ERRa0; + + for (count = 0; count < B; count++) { + a0.dp[count] = a->dp[count]; + a0.used++; + } + mp_clamp(&a0); + if ((err = mp_init_size(&a1, B)) != MP_OKAY) goto LBL_ERRa1; + for (; count < (2 * B); count++) { + a1.dp[count - B] = a->dp[count]; + a1.used++; + } + mp_clamp(&a1); + if ((err = mp_init_size(&a2, B + (a->used - (3 * B)))) != MP_OKAY) goto LBL_ERRa2; + for (; count < a->used; count++) { + a2.dp[count - (2 * B)] = a->dp[count]; + a2.used++; + } + mp_clamp(&a2); + + /** b = b2 * x^2 + b1 * x + b0; */ + if ((err = mp_init_size(&b0, B)) != MP_OKAY) goto LBL_ERRb0; + for (count = 0; count < B; count++) { + b0.dp[count] = b->dp[count]; + b0.used++; + } + mp_clamp(&b0); + if ((err = mp_init_size(&b1, B)) != MP_OKAY) goto LBL_ERRb1; + for (; count < (2 * B); count++) { + b1.dp[count - B] = b->dp[count]; + b1.used++; + } + mp_clamp(&b1); + if ((err = mp_init_size(&b2, B + (b->used - (3 * B)))) != MP_OKAY) goto LBL_ERRb2; + for (; count < b->used; count++) { + b2.dp[count - (2 * B)] = b->dp[count]; + b2.used++; + } + mp_clamp(&b2); + + /** \\ S1 = (a2+a1+a0) * (b2+b1+b0); */ + /** T1 = a2 + a1; */ + if ((err = mp_add(&a2, &a1, &T1)) != MP_OKAY) goto LBL_ERR; + + /** S2 = T1 + a0; */ + if ((err = mp_add(&T1, &a0, &S2)) != MP_OKAY) goto LBL_ERR; + + /** c = b2 + b1; */ + if ((err = mp_add(&b2, &b1, c)) != MP_OKAY) goto LBL_ERR; + + /** S1 = c + b0; */ + if ((err = mp_add(c, &b0, &S1)) != MP_OKAY) goto LBL_ERR; + + /** S1 = S1 * S2; */ + if ((err = mp_mul(&S1, &S2, &S1)) != MP_OKAY) goto LBL_ERR; + + /** \\S2 = (4*a2+2*a1+a0) * (4*b2+2*b1+b0); */ + /** T1 = T1 + a2; */ + if ((err = mp_add(&T1, &a2, &T1)) != MP_OKAY) goto LBL_ERR; + + /** T1 = T1 << 1; */ + if ((err = mp_mul_2(&T1, &T1)) != MP_OKAY) goto LBL_ERR; + + /** T1 = T1 + a0; */ + if ((err = mp_add(&T1, &a0, &T1)) != MP_OKAY) goto LBL_ERR; + + /** c = c + b2; */ + if ((err = mp_add(c, &b2, c)) != MP_OKAY) goto LBL_ERR; + + /** c = c << 1; */ + if ((err = mp_mul_2(c, c)) != MP_OKAY) goto LBL_ERR; + + /** c = c + b0; */ + if ((err = mp_add(c, &b0, c)) != MP_OKAY) goto LBL_ERR; + + /** S2 = T1 * c; */ + if ((err = mp_mul(&T1, c, &S2)) != MP_OKAY) goto LBL_ERR; + + /** \\S3 = (a2-a1+a0) * (b2-b1+b0); */ + /** a1 = a2 - a1; */ + if ((err = mp_sub(&a2, &a1, &a1)) != MP_OKAY) goto LBL_ERR; + + /** a1 = a1 + a0; */ + if ((err = mp_add(&a1, &a0, &a1)) != MP_OKAY) goto LBL_ERR; + + /** b1 = b2 - b1; */ + if ((err = mp_sub(&b2, &b1, &b1)) != MP_OKAY) goto LBL_ERR; + + /** b1 = b1 + b0; */ + if ((err = mp_add(&b1, &b0, &b1)) != MP_OKAY) goto LBL_ERR; + + /** a1 = a1 * b1; */ + if ((err = mp_mul(&a1, &b1, &a1)) != MP_OKAY) goto LBL_ERR; + + /** b1 = a2 * b2; */ + if ((err = mp_mul(&a2, &b2, &b1)) != MP_OKAY) goto LBL_ERR; + + /** \\S2 = (S2 - S3)/3; */ + /** S2 = S2 - a1; */ + if ((err = mp_sub(&S2, &a1, &S2)) != MP_OKAY) goto LBL_ERR; + + /** S2 = S2 / 3; \\ this is an exact division */ + if ((err = mp_div_3(&S2, &S2, NULL)) != MP_OKAY) goto LBL_ERR; + + /** a1 = S1 - a1; */ + if ((err = mp_sub(&S1, &a1, &a1)) != MP_OKAY) goto LBL_ERR; + + /** a1 = a1 >> 1; */ + if ((err = mp_div_2(&a1, &a1)) != MP_OKAY) goto LBL_ERR; + + /** a0 = a0 * b0; */ + if ((err = mp_mul(&a0, &b0, &a0)) != MP_OKAY) goto LBL_ERR; + + /** S1 = S1 - a0; */ + if ((err = mp_sub(&S1, &a0, &S1)) != MP_OKAY) goto LBL_ERR; + + /** S2 = S2 - S1; */ + if ((err = mp_sub(&S2, &S1, &S2)) != MP_OKAY) goto LBL_ERR; + + /** S2 = S2 >> 1; */ + if ((err = mp_div_2(&S2, &S2)) != MP_OKAY) goto LBL_ERR; + + /** S1 = S1 - a1; */ + if ((err = mp_sub(&S1, &a1, &S1)) != MP_OKAY) goto LBL_ERR; + + /** S1 = S1 - b1; */ + if ((err = mp_sub(&S1, &b1, &S1)) != MP_OKAY) goto LBL_ERR; + + /** T1 = b1 << 1; */ + if ((err = mp_mul_2(&b1, &T1)) != MP_OKAY) goto LBL_ERR; + + /** S2 = S2 - T1; */ + if ((err = mp_sub(&S2, &T1, &S2)) != MP_OKAY) goto LBL_ERR; + + /** a1 = a1 - S2; */ + if ((err = mp_sub(&a1, &S2, &a1)) != MP_OKAY) goto LBL_ERR; + + + /** P = b1*x^4+ S2*x^3+ S1*x^2+ a1*x + a0; */ + if ((err = mp_lshd(&b1, 4 * B)) != MP_OKAY) goto LBL_ERR; + if ((err = mp_lshd(&S2, 3 * B)) != MP_OKAY) goto LBL_ERR; + if ((err = mp_add(&b1, &S2, &b1)) != MP_OKAY) goto LBL_ERR; + if ((err = mp_lshd(&S1, 2 * B)) != MP_OKAY) goto LBL_ERR; + if ((err = mp_add(&b1, &S1, &b1)) != MP_OKAY) goto LBL_ERR; + if ((err = mp_lshd(&a1, 1 * B)) != MP_OKAY) goto LBL_ERR; + if ((err = mp_add(&b1, &a1, &b1)) != MP_OKAY) goto LBL_ERR; + if ((err = mp_add(&b1, &a0, c)) != MP_OKAY) goto LBL_ERR; + + /** a * b - P */ + + +LBL_ERR: + mp_clear(&b2); +LBL_ERRb2: + mp_clear(&b1); +LBL_ERRb1: + mp_clear(&b0); +LBL_ERRb0: + mp_clear(&a2); +LBL_ERRa2: + mp_clear(&a1); +LBL_ERRa1: + mp_clear(&a0); +LBL_ERRa0: + mp_clear_multi(&S1, &S2, &T1, NULL); + return err; +} + +#endif + +/* End: bn_s_mp_toom_mul.c */ + +/* Start: bn_s_mp_toom_sqr.c */ +#include "tommath_private.h" +#ifdef BN_S_MP_TOOM_SQR_C +/* LibTomMath, multiple-precision integer library -- Tom St Denis */ +/* SPDX-License-Identifier: Unlicense */ + +/* squaring using Toom-Cook 3-way algorithm */ + +/* + This file contains code from J. Arndt's book "Matters Computational" + and the accompanying FXT-library with permission of the author. +*/ + +/* squaring using Toom-Cook 3-way algorithm */ +/* + Setup and interpolation from algorithm SQR_3 in + + Chung, Jaewook, and M. Anwar Hasan. "Asymmetric squaring formulae." + 18th IEEE Symposium on Computer Arithmetic (ARITH'07). IEEE, 2007. + +*/ +mp_err s_mp_toom_sqr(const mp_int *a, mp_int *b) +{ + mp_int S0, a0, a1, a2; + mp_digit *tmpa, *tmpc; + int B, count; + mp_err err; + + + /* init temps */ + if ((err = mp_init(&S0)) != MP_OKAY) { + return err; + } + + /* B */ + B = a->used / 3; + + /** a = a2 * x^2 + a1 * x + a0; */ + if ((err = mp_init_size(&a0, B)) != MP_OKAY) goto LBL_ERRa0; + + a0.used = B; + if ((err = mp_init_size(&a1, B)) != MP_OKAY) goto LBL_ERRa1; + a1.used = B; + if ((err = mp_init_size(&a2, B + (a->used - (3 * B)))) != MP_OKAY) goto LBL_ERRa2; + + tmpa = a->dp; + tmpc = a0.dp; + for (count = 0; count < B; count++) { + *tmpc++ = *tmpa++; + } + tmpc = a1.dp; + for (; count < (2 * B); count++) { + *tmpc++ = *tmpa++; + } + tmpc = a2.dp; + for (; count < a->used; count++) { + *tmpc++ = *tmpa++; + a2.used++; + } + mp_clamp(&a0); + mp_clamp(&a1); + mp_clamp(&a2); + + /** S0 = a0^2; */ + if ((err = mp_sqr(&a0, &S0)) != MP_OKAY) goto LBL_ERR; + + /** \\S1 = (a2 + a1 + a0)^2 */ + /** \\S2 = (a2 - a1 + a0)^2 */ + /** \\S1 = a0 + a2; */ + /** a0 = a0 + a2; */ + if ((err = mp_add(&a0, &a2, &a0)) != MP_OKAY) goto LBL_ERR; + /** \\S2 = S1 - a1; */ + /** b = a0 - a1; */ + if ((err = mp_sub(&a0, &a1, b)) != MP_OKAY) goto LBL_ERR; + /** \\S1 = S1 + a1; */ + /** a0 = a0 + a1; */ + if ((err = mp_add(&a0, &a1, &a0)) != MP_OKAY) goto LBL_ERR; + /** \\S1 = S1^2; */ + /** a0 = a0^2; */ + if ((err = mp_sqr(&a0, &a0)) != MP_OKAY) goto LBL_ERR; + /** \\S2 = S2^2; */ + /** b = b^2; */ + if ((err = mp_sqr(b, b)) != MP_OKAY) goto LBL_ERR; + + /** \\ S3 = 2 * a1 * a2 */ + /** \\S3 = a1 * a2; */ + /** a1 = a1 * a2; */ + if ((err = mp_mul(&a1, &a2, &a1)) != MP_OKAY) goto LBL_ERR; + /** \\S3 = S3 << 1; */ + /** a1 = a1 << 1; */ + if ((err = mp_mul_2(&a1, &a1)) != MP_OKAY) goto LBL_ERR; + + /** \\S4 = a2^2; */ + /** a2 = a2^2; */ + if ((err = mp_sqr(&a2, &a2)) != MP_OKAY) goto LBL_ERR; + + /** \\ tmp = (S1 + S2)/2 */ + /** \\tmp = S1 + S2; */ + /** b = a0 + b; */ + if ((err = mp_add(&a0, b, b)) != MP_OKAY) goto LBL_ERR; + /** \\tmp = tmp >> 1; */ + /** b = b >> 1; */ + if ((err = mp_div_2(b, b)) != MP_OKAY) goto LBL_ERR; + + /** \\ S1 = S1 - tmp - S3 */ + /** \\S1 = S1 - tmp; */ + /** a0 = a0 - b; */ + if ((err = mp_sub(&a0, b, &a0)) != MP_OKAY) goto LBL_ERR; + /** \\S1 = S1 - S3; */ + /** a0 = a0 - a1; */ + if ((err = mp_sub(&a0, &a1, &a0)) != MP_OKAY) goto LBL_ERR; + + /** \\S2 = tmp - S4 -S0 */ + /** \\S2 = tmp - S4; */ + /** b = b - a2; */ + if ((err = mp_sub(b, &a2, b)) != MP_OKAY) goto LBL_ERR; + /** \\S2 = S2 - S0; */ + /** b = b - S0; */ + if ((err = mp_sub(b, &S0, b)) != MP_OKAY) goto LBL_ERR; + + + /** \\P = S4*x^4 + S3*x^3 + S2*x^2 + S1*x + S0; */ + /** P = a2*x^4 + a1*x^3 + b*x^2 + a0*x + S0; */ + + if ((err = mp_lshd(&a2, 4 * B)) != MP_OKAY) goto LBL_ERR; + if ((err = mp_lshd(&a1, 3 * B)) != MP_OKAY) goto LBL_ERR; + if ((err = mp_lshd(b, 2 * B)) != MP_OKAY) goto LBL_ERR; + if ((err = mp_lshd(&a0, 1 * B)) != MP_OKAY) goto LBL_ERR; + if ((err = mp_add(&a2, &a1, &a2)) != MP_OKAY) goto LBL_ERR; + if ((err = mp_add(&a2, b, b)) != MP_OKAY) goto LBL_ERR; + if ((err = mp_add(b, &a0, b)) != MP_OKAY) goto LBL_ERR; + if ((err = mp_add(b, &S0, b)) != MP_OKAY) goto LBL_ERR; + /** a^2 - P */ + + +LBL_ERR: + mp_clear(&a2); +LBL_ERRa2: + mp_clear(&a1); +LBL_ERRa1: + mp_clear(&a0); +LBL_ERRa0: + mp_clear(&S0); + + return err; +} + +#endif + +/* End: bn_s_mp_toom_sqr.c */ + + +/* EOF */ diff --git a/lib/hcrypto/libtommath/testme.sh b/lib/hcrypto/libtommath/testme.sh new file mode 100755 index 000000000000..40fa32d500d7 --- /dev/null +++ b/lib/hcrypto/libtommath/testme.sh @@ -0,0 +1,394 @@ +#!/bin/bash +# +# return values of this script are: +# 0 success +# 128 a test failed +# >0 the number of timed-out tests +# 255 parsing of parameters failed + +set -e + +if [ -f /proc/cpuinfo ] +then + MAKE_JOBS=$(( ($(cat /proc/cpuinfo | grep -E '^processor[[:space:]]*:' | tail -n -1 | cut -d':' -f2) + 1) * 2 + 1 )) +else + MAKE_JOBS=8 +fi + +ret=0 +TEST_CFLAGS="" + +_help() +{ + echo "Usage options for $(basename $0) [--with-cc=arg [other options]]" + echo + echo "Executing this script without any parameter will only run the default" + echo "configuration that has automatically been determined for the" + echo "architecture you're running." + echo + echo " --with-cc=* The compiler(s) to use for the tests" + echo " This is an option that will be iterated." + echo + echo " --test-vs-mtest=* Run test vs. mtest for '*' operations." + echo " Only the first of each options will be" + echo " taken into account." + echo + echo "To be able to specify options a compiler has to be given with" + echo "the option --with-cc=compilername" + echo "All other options will be tested with all MP_xBIT configurations." + echo + echo " --with-{m64,m32,mx32} The architecture(s) to build and test" + echo " for, e.g. --with-mx32." + echo " This is an option that will be iterated," + echo " multiple selections are possible." + echo " The mx32 architecture is not supported" + echo " by clang and will not be executed." + echo + echo " --cflags=* Give an option to the compiler," + echo " e.g. --cflags=-g" + echo " This is an option that will always be" + echo " passed as parameter to CC." + echo + echo " --make-option=* Give an option to make," + echo " e.g. --make-option=\"-f makefile.shared\"" + echo " This is an option that will always be" + echo " passed as parameter to make." + echo + echo " --with-low-mp Also build&run tests with -DMP_{8,16,32}BIT." + echo + echo " --mtest-real-rand Use real random data when running mtest." + echo + echo " --with-valgrind" + echo " --with-valgrind=* Run in valgrind (slow!)." + echo + echo " --with-travis-valgrind Run with valgrind on Travis on specific branches." + echo + echo " --valgrind-options Additional Valgrind options" + echo " Some of the options like e.g.:" + echo " --track-origins=yes add a lot of extra" + echo " runtime and may trigger the 30 minutes" + echo " timeout." + echo + echo "Godmode:" + echo + echo " --all Choose all architectures and gcc and clang" + echo " as compilers but does not run valgrind." + echo + echo " --format Runs the various source-code formatters" + echo " and generators and checks if the sources" + echo " are clean." + echo + echo " -h" + echo " --help This message" + echo + echo " -v" + echo " --version Prints the version. It is just the number" + echo " of git commits to this file, no deeper" + echo " meaning attached" + exit 0 +} + +_die() +{ + echo "error $2 while $1" + if [ "$2" != "124" ] + then + exit 128 + else + echo "assuming timeout while running test - continue" + local _tail="" + which tail >/dev/null && _tail="tail -n 1 test_${suffix}.log" && \ + echo "last line of test_"${suffix}".log was:" && $_tail && echo "" + ret=$(( $ret + 1 )) + fi +} + +_make() +{ + echo -ne " Compile $1 $2" + suffix=$(echo ${1}${2} | tr ' ' '_') + CC="$1" CFLAGS="$2 $TEST_CFLAGS" make -j$MAKE_JOBS $3 $MAKE_OPTIONS > /dev/null 2>gcc_errors_${suffix}.log + errcnt=$(wc -l < gcc_errors_${suffix}.log) + if [[ ${errcnt} -gt 1 ]]; then + echo " failed" + cat gcc_errors_${suffix}.log + exit 128 + fi +} + + +_runtest() +{ + make clean > /dev/null + local _timeout="" + which timeout >/dev/null && _timeout="timeout --foreground 90" + if [[ "$MAKE_OPTIONS" =~ "tune" ]] + then + # "make tune" will run "tune_it.sh" automatically, hence "autotune", but it cannot + # get switched off without some effort, so we just let it run twice for testing purposes + echo -e "\rRun autotune $1 $2" + _make "$1" "$2" "" + $_timeout $TUNE_CMD > test_${suffix}.log || _die "running autotune" $? + else + _make "$1" "$2" "test" + echo -e "\rRun test $1 $2" + $_timeout ./test > test_${suffix}.log || _die "running tests" $? + fi +} + +# This is not much more of a C&P of _runtest with a different timeout +# and the additional valgrind call. +# TODO: merge +_runvalgrind() +{ + make clean > /dev/null + local _timeout="" + # 30 minutes? Yes. Had it at 20 minutes and the Valgrind run needed over 25 minutes. + # A bit too close for comfort. + which timeout >/dev/null && _timeout="timeout --foreground 1800" +echo "MAKE_OPTIONS = \"$MAKE_OPTIONS\"" + if [[ "$MAKE_OPTIONS" =~ "tune" ]] + then +echo "autotune branch" + _make "$1" "$2" "" + # The shell used for /bin/sh is DASH 0.5.7-4ubuntu1 on the author's machine which fails valgrind, so + # we just run on instance of etc/tune with the same options as in etc/tune_it.sh + echo -e "\rRun etc/tune $1 $2 once inside valgrind" + $_timeout $VALGRIND_BIN $VALGRIND_OPTS $TUNE_CMD > test_${suffix}.log || _die "running etc/tune" $? + else + _make "$1" "$2" "test" + echo -e "\rRun test $1 $2 inside valgrind" + $_timeout $VALGRIND_BIN $VALGRIND_OPTS ./test > test_${suffix}.log || _die "running tests" $? + fi +} + + +_banner() +{ + echo "uname="$(uname -a) + [[ "$#" != "0" ]] && (echo $1=$($1 -dumpversion)) || true +} + +_exit() +{ + if [ "$ret" == "0" ] + then + echo "Tests successful" + else + echo "$ret tests timed out" + fi + + exit $ret +} + +ARCHFLAGS="" +COMPILERS="" +CFLAGS="" +WITH_LOW_MP="" +TEST_VS_MTEST="" +MTEST_RAND="" +# timed with an AMD A8-6600K +# 25 minutes +#VALGRIND_OPTS=" --track-origins=yes --leak-check=full --show-leak-kinds=all --error-exitcode=1 " +# 9 minutes (14 minutes with --test-vs-mtest=333333 --mtest-real-rand) +VALGRIND_OPTS=" --leak-check=full --show-leak-kinds=all --error-exitcode=1 " +#VALGRIND_OPTS="" +VALGRIND_BIN="" +CHECK_FORMAT="" +TUNE_CMD="./etc/tune -t -r 10 -L 3" + +alive_pid=0 + +function kill_alive() { + disown $alive_pid || true + kill $alive_pid 2>/dev/null +} + +function start_alive_printing() { + [ "$alive_pid" == "0" ] || return 0; + for i in `seq 1 10` ; do sleep 300 && echo "Tests still in Progress..."; done & + alive_pid=$! + trap kill_alive EXIT +} + +while [ $# -gt 0 ]; +do + case $1 in + "--with-m64" | "--with-m32" | "--with-mx32") + ARCHFLAGS="$ARCHFLAGS ${1:6}" + ;; + --with-cc=*) + COMPILERS="$COMPILERS ${1#*=}" + ;; + --cflags=*) + CFLAGS="$CFLAGS ${1#*=}" + ;; + --valgrind-options=*) + VALGRIND_OPTS="$VALGRIND_OPTS ${1#*=}" + ;; + --with-valgrind*) + if [[ ${1#*d} != "" ]] + then + VALGRIND_BIN="${1#*=}" + else + VALGRIND_BIN="valgrind" + fi + start_alive_printing + ;; + --with-travis-valgrind*) + if [[ ("$TRAVIS_BRANCH" == "develop" && "$TRAVIS_PULL_REQUEST" == "false") || "$TRAVIS_BRANCH" == *"valgrind"* || "$TRAVIS_COMMIT_MESSAGE" == *"valgrind"* ]] + then + if [[ ${1#*d} != "" ]] + then + VALGRIND_BIN="${1#*=}" + else + VALGRIND_BIN="valgrind" + fi + start_alive_printing + fi + ;; + --make-option=*) + MAKE_OPTIONS="$MAKE_OPTIONS ${1#*=}" + ;; + --with-low-mp) + WITH_LOW_MP="1" + ;; + --test-vs-mtest=*) + TEST_VS_MTEST="${1#*=}" + if ! [ "$TEST_VS_MTEST" -eq "$TEST_VS_MTEST" ] 2> /dev/null + then + echo "--test-vs-mtest Parameter has to be int" + exit 255 + fi + start_alive_printing + ;; + --mtest-real-rand) + MTEST_RAND="-DLTM_MTEST_REAL_RAND" + ;; + --format) + CHECK_FORMAT="1" + ;; + --all) + COMPILERS="gcc clang" + ARCHFLAGS="-m64 -m32 -mx32" + ;; + --help | -h) + _help + ;; + --version | -v) + echo $(git rev-list HEAD --count -- testme.sh) || echo "Unknown. Please run in original libtommath git repository." + exit 0 + ;; + *) + echo "Ignoring option ${1}" + ;; + esac + shift +done + +function _check_git() { + git update-index --refresh >/dev/null || true + git diff-index --quiet HEAD -- . || ( echo "FAILURE: $*" && exit 1 ) +} + +if [[ "$CHECK_FORMAT" == "1" ]] +then + make astyle + _check_git "make astyle" + perl helper.pl --update-files + _check_git "helper.pl --update-files" + perl helper.pl --check-all + _check_git "helper.pl --check-all" + exit $? +fi + +[[ "$VALGRIND_BIN" == "" ]] && VALGRIND_OPTS="" + +# default to CC environment variable if no compiler is defined but some other options +if [[ "$COMPILERS" == "" ]] && [[ "$ARCHFLAGS$MAKE_OPTIONS$CFLAGS" != "" ]] +then + COMPILERS="$CC" +# default to CC environment variable and run only default config if no option is given +elif [[ "$COMPILERS" == "" ]] +then + _banner "$CC" + if [[ "$VALGRIND_BIN" != "" ]] + then + _runvalgrind "$CC" "" + else + _runtest "$CC" "" + fi + _exit +fi + + +archflags=( $ARCHFLAGS ) +compilers=( $COMPILERS ) + +# choosing a compiler without specifying an architecture will use the default architecture +if [ "${#archflags[@]}" == "0" ] +then + archflags[0]=" " +fi + +_banner + +if [[ "$TEST_VS_MTEST" != "" ]] +then + make clean > /dev/null + _make "${compilers[0]} ${archflags[0]}" "$CFLAGS" "mtest_opponent" + echo + _make "gcc" "$MTEST_RAND" "mtest" + echo + echo "Run test vs. mtest for $TEST_VS_MTEST iterations" + _timeout="" + which timeout >/dev/null && _timeout="timeout --foreground 1800" + $_timeout ./mtest/mtest $TEST_VS_MTEST | $VALGRIND_BIN $VALGRIND_OPTS ./mtest_opponent > valgrind_test.log 2> test_vs_mtest_err.log + retval=$? + head -n 5 valgrind_test.log + tail -n 2 valgrind_test.log + exit $retval +fi + +for i in "${compilers[@]}" +do + if [ -z "$(which $i)" ] + then + echo "Skipped compiler $i, file not found" + continue + fi + compiler_version=$(echo "$i="$($i -dumpversion)) + if [ "$compiler_version" == "clang=4.2.1" ] + then + # one of my versions of clang complains about some stuff in stdio.h and stdarg.h ... + TEST_CFLAGS="-Wno-typedef-redefinition" + else + TEST_CFLAGS="" + fi + echo $compiler_version + + for a in "${archflags[@]}" + do + if [[ $(expr "$i" : "clang") -ne 0 && "$a" == "-mx32" ]] + then + echo "clang -mx32 tests skipped" + continue + fi + if [[ "$VALGRIND_BIN" != "" ]] + then + _runvalgrind "$i $a" "$CFLAGS" + [ "$WITH_LOW_MP" != "1" ] && continue + _runvalgrind "$i $a" "-DMP_8BIT $CFLAGS" + _runvalgrind "$i $a" "-DMP_16BIT $CFLAGS" + _runvalgrind "$i $a" "-DMP_32BIT $CFLAGS" + else + _runtest "$i $a" "$CFLAGS" + [ "$WITH_LOW_MP" != "1" ] && continue + _runtest "$i $a" "-DMP_8BIT $CFLAGS" + _runtest "$i $a" "-DMP_16BIT $CFLAGS" + _runtest "$i $a" "-DMP_32BIT $CFLAGS" + fi + done +done + +_exit diff --git a/lib/hcrypto/libtommath/tommath.def b/lib/hcrypto/libtommath/tommath.def new file mode 100644 index 000000000000..229fae49ad8c --- /dev/null +++ b/lib/hcrypto/libtommath/tommath.def @@ -0,0 +1,145 @@ +; libtommath +; +; Use this command to produce a 32-bit .lib file, for use in any MSVC version +; lib -machine:X86 -name:libtommath.dll -def:tommath.def -out:tommath.lib +; Use this command to produce a 64-bit .lib file, for use in any MSVC version +; lib -machine:X64 -name:libtommath.dll -def:tommath.def -out:tommath.lib +; +EXPORTS + mp_2expt + mp_abs + mp_add + mp_add_d + mp_addmod + mp_and + mp_clamp + mp_clear + mp_clear_multi + mp_cmp + mp_cmp_d + mp_cmp_mag + mp_cnt_lsb + mp_complement + mp_copy + mp_count_bits + mp_decr + mp_div + mp_div_2 + mp_div_2d + mp_div_3 + mp_div_d + mp_dr_is_modulus + mp_dr_reduce + mp_dr_setup + mp_error_to_string + mp_exch + mp_expt_u32 + mp_exptmod + mp_exteuclid + mp_fread + mp_from_sbin + mp_from_ubin + mp_fwrite + mp_gcd + mp_get_double + mp_get_i32 + mp_get_i64 + mp_get_int + mp_get_l + mp_get_ll + mp_get_long + mp_get_long_long + mp_get_mag_u32 + mp_get_mag_u64 + mp_get_mag_ul + mp_get_mag_ull + mp_grow + mp_incr + mp_init + mp_init_copy + mp_init_i32 + mp_init_i64 + mp_init_l + mp_init_ll + mp_init_multi + mp_init_set + mp_init_set_int + mp_init_size + mp_init_u32 + mp_init_u64 + mp_init_ul + mp_init_ull + mp_invmod + mp_is_square + mp_iseven + mp_isodd + mp_kronecker + mp_lcm + mp_log_u32 + mp_lshd + mp_mod + mp_mod_2d + mp_mod_d + mp_montgomery_calc_normalization + mp_montgomery_reduce + mp_montgomery_setup + mp_mul + mp_mul_2 + mp_mul_2d + mp_mul_d + mp_mulmod + mp_neg + mp_or + mp_pack + mp_pack_count + mp_prime_fermat + mp_prime_frobenius_underwood + mp_prime_is_prime + mp_prime_miller_rabin + mp_prime_next_prime + mp_prime_rabin_miller_trials + mp_prime_rand + mp_prime_strong_lucas_selfridge + mp_radix_size + mp_rand + mp_read_radix + mp_reduce + mp_reduce_2k + mp_reduce_2k_l + mp_reduce_2k_setup + mp_reduce_2k_setup_l + mp_reduce_is_2k + mp_reduce_is_2k_l + mp_reduce_setup + mp_root_u32 + mp_rshd + mp_sbin_size + mp_set + mp_set_double + mp_set_i32 + mp_set_i64 + mp_set_int + mp_set_l + mp_set_ll + mp_set_long + mp_set_long_long + mp_set_u32 + mp_set_u64 + mp_set_ul + mp_set_ull + mp_shrink + mp_signed_rsh + mp_sqr + mp_sqrmod + mp_sqrt + mp_sqrtmod_prime + mp_sub + mp_sub_d + mp_submod + mp_to_radix + mp_to_sbin + mp_to_ubin + mp_ubin_size + mp_unpack + mp_xor + mp_zero diff --git a/lib/hcrypto/libtommath/tommath.h b/lib/hcrypto/libtommath/tommath.h index e5d8d5367a82..e87bb086cbbe 100644 --- a/lib/hcrypto/libtommath/tommath.h +++ b/lib/hcrypto/libtommath/tommath.h @@ -1,497 +1,692 @@ -/* LibTomMath, multiple-precision integer library -- Tom St Denis - * - * LibTomMath is a library that provides multiple-precision - * integer arithmetic as well as number theoretic functionality. - * - * The library was designed directly after the MPI library by - * Michael Fromberger but has been written from scratch with - * additional optimizations in place. - * - * The library is free for all purposes without any express - * guarantee it works. - * - * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com - */ +/* LibTomMath, multiple-precision integer library -- Tom St Denis */ +/* SPDX-License-Identifier: Unlicense */ + #ifndef BN_H_ #define BN_H_ -#include <stdio.h> -#include <string.h> -#include <stdlib.h> -#include <ctype.h> +#include <stdint.h> +#include <stddef.h> #include <limits.h> -#include <tommath_class.h> +#ifdef LTM_NO_FILE +# warning LTM_NO_FILE has been deprecated, use MP_NO_FILE. +# define MP_NO_FILE +#endif -#ifndef MIN - #define MIN(x,y) ((x)<(y)?(x):(y)) +#ifndef MP_NO_FILE +# include <stdio.h> #endif -#ifndef MAX - #define MAX(x,y) ((x)>(y)?(x):(y)) +#ifdef MP_8BIT +# ifdef _MSC_VER +# pragma message("8-bit (MP_8BIT) support is deprecated and will be dropped completely in the next version.") +# else +# warning "8-bit (MP_8BIT) support is deprecated and will be dropped completely in the next version." +# endif #endif #ifdef __cplusplus extern "C" { - -/* C++ compilers don't like assigning void * to mp_digit * */ -#define OPT_CAST(x) (x *) - -#else - -/* C on the other hand doesn't care */ -#define OPT_CAST(x) - #endif +/* MS Visual C++ doesn't have a 128bit type for words, so fall back to 32bit MPI's (where words are 64bit) */ +#if (defined(_MSC_VER) || defined(__LLP64__) || defined(__e2k__) || defined(__LCC__)) && !defined(MP_64BIT) +# define MP_32BIT +#endif /* detect 64-bit mode if possible */ -#if defined(__x86_64__) && !defined(__ILP32__) - #if !(defined(MP_64BIT) && defined(MP_16BIT) && defined(MP_8BIT)) - #define MP_64BIT - #endif +#if defined(__x86_64__) || defined(_M_X64) || defined(_M_AMD64) || \ + defined(__powerpc64__) || defined(__ppc64__) || defined(__PPC64__) || \ + defined(__s390x__) || defined(__arch64__) || defined(__aarch64__) || \ + defined(__sparcv9) || defined(__sparc_v9__) || defined(__sparc64__) || \ + defined(__ia64) || defined(__ia64__) || defined(__itanium__) || defined(_M_IA64) || \ + defined(__LP64__) || defined(_LP64) || defined(__64BIT__) +# if !(defined(MP_64BIT) || defined(MP_32BIT) || defined(MP_16BIT) || defined(MP_8BIT)) +# if defined(__GNUC__) && !defined(__hppa) +/* we support 128bit integers only via: __attribute__((mode(TI))) */ +# define MP_64BIT +# else +/* otherwise we fall back to MP_32BIT even on 64bit platforms */ +# define MP_32BIT +# endif +# endif +#endif + +#ifdef MP_DIGIT_BIT +# error Defining MP_DIGIT_BIT is disallowed, use MP_8/16/31/32/64BIT #endif /* some default configurations. * - * A "mp_digit" must be able to hold DIGIT_BIT + 1 bits - * A "mp_word" must be able to hold 2*DIGIT_BIT + 1 bits + * A "mp_digit" must be able to hold MP_DIGIT_BIT + 1 bits + * A "mp_word" must be able to hold 2*MP_DIGIT_BIT + 1 bits * * At the very least a mp_digit must be able to hold 7 bits * [any size beyond that is ok provided it doesn't overflow the data type] */ + #ifdef MP_8BIT - typedef unsigned char mp_digit; - typedef unsigned short mp_word; +typedef uint8_t mp_digit; +typedef uint16_t private_mp_word; +# define MP_DIGIT_BIT 7 #elif defined(MP_16BIT) - typedef unsigned short mp_digit; - typedef unsigned long mp_word; +typedef uint16_t mp_digit; +typedef uint32_t private_mp_word; +# define MP_DIGIT_BIT 15 #elif defined(MP_64BIT) - /* for GCC only on supported platforms */ -#ifndef CRYPT - typedef unsigned long long ulong64; - typedef signed long long long64; +/* for GCC only on supported platforms */ +typedef uint64_t mp_digit; +#if defined(__GNUC__) +typedef unsigned long private_mp_word __attribute__((mode(TI))); #endif - - typedef unsigned long mp_digit; - typedef unsigned long mp_word __attribute__ ((mode(TI))); - - #define DIGIT_BIT 60 +# define MP_DIGIT_BIT 60 #else - /* this is the default case, 28-bit digits */ - - /* this is to make porting into LibTomCrypt easier :-) */ -#ifndef CRYPT - #if defined(_MSC_VER) || defined(__BORLANDC__) - typedef unsigned __int64 ulong64; - typedef signed __int64 long64; - #else - typedef unsigned long long ulong64; - typedef signed long long long64; - #endif -#endif - - typedef unsigned long mp_digit; - typedef ulong64 mp_word; - -#ifdef MP_31BIT - /* this is an extension that uses 31-bit digits */ - #define DIGIT_BIT 31 -#else - /* default case is 28-bit digits, defines MP_28BIT as a handy macro to test */ - #define DIGIT_BIT 28 - #define MP_28BIT -#endif -#endif - -/* define heap macros */ -#ifndef CRYPT - /* default to libc stuff */ - #ifndef XMALLOC - #define XMALLOC malloc - #define XFREE free - #define XREALLOC realloc - #define XCALLOC calloc - #else - /* prototypes for our heap functions */ - extern void *XMALLOC(size_t n); - extern void *XREALLOC(void *p, size_t n); - extern void *XCALLOC(size_t n, size_t s); - extern void XFREE(void *p); - #endif +typedef uint32_t mp_digit; +typedef uint64_t private_mp_word; +# ifdef MP_31BIT +/* + * This is an extension that uses 31-bit digits. + * Please be aware that not all functions support this size, especially s_mp_mul_digs_fast + * will be reduced to work on small numbers only: + * Up to 8 limbs, 248 bits instead of up to 512 limbs, 15872 bits with MP_28BIT. + */ +# define MP_DIGIT_BIT 31 +# else +/* default case is 28-bit digits, defines MP_28BIT as a handy macro to test */ +# define MP_DIGIT_BIT 28 +# define MP_28BIT +# endif #endif +/* mp_word is a private type */ +#define mp_word MP_DEPRECATED_PRAGMA("mp_word has been made private") private_mp_word -/* otherwise the bits per digit is calculated automatically from the size of a mp_digit */ -#ifndef DIGIT_BIT - #define DIGIT_BIT ((int)((CHAR_BIT * sizeof(mp_digit) - 1))) /* bits per digit */ -#endif +#define MP_SIZEOF_MP_DIGIT (MP_DEPRECATED_PRAGMA("MP_SIZEOF_MP_DIGIT has been deprecated, use sizeof (mp_digit)") sizeof (mp_digit)) -#define MP_DIGIT_BIT DIGIT_BIT -#define MP_MASK ((((mp_digit)1)<<((mp_digit)DIGIT_BIT))-((mp_digit)1)) +#define MP_MASK ((((mp_digit)1)<<((mp_digit)MP_DIGIT_BIT))-((mp_digit)1)) #define MP_DIGIT_MAX MP_MASK -/* equalities */ +/* Primality generation flags */ +#define MP_PRIME_BBS 0x0001 /* BBS style prime */ +#define MP_PRIME_SAFE 0x0002 /* Safe prime (p-1)/2 == prime */ +#define MP_PRIME_2MSB_ON 0x0008 /* force 2nd MSB to 1 */ + +#define LTM_PRIME_BBS (MP_DEPRECATED_PRAGMA("LTM_PRIME_BBS has been deprecated, use MP_PRIME_BBS") MP_PRIME_BBS) +#define LTM_PRIME_SAFE (MP_DEPRECATED_PRAGMA("LTM_PRIME_SAFE has been deprecated, use MP_PRIME_SAFE") MP_PRIME_SAFE) +#define LTM_PRIME_2MSB_ON (MP_DEPRECATED_PRAGMA("LTM_PRIME_2MSB_ON has been deprecated, use MP_PRIME_2MSB_ON") MP_PRIME_2MSB_ON) + +#ifdef MP_USE_ENUMS +typedef enum { + MP_ZPOS = 0, /* positive */ + MP_NEG = 1 /* negative */ +} mp_sign; +typedef enum { + MP_LT = -1, /* less than */ + MP_EQ = 0, /* equal */ + MP_GT = 1 /* greater than */ +} mp_ord; +typedef enum { + MP_NO = 0, + MP_YES = 1 +} mp_bool; +typedef enum { + MP_OKAY = 0, /* no error */ + MP_ERR = -1, /* unknown error */ + MP_MEM = -2, /* out of mem */ + MP_VAL = -3, /* invalid input */ + MP_ITER = -4, /* maximum iterations reached */ + MP_BUF = -5 /* buffer overflow, supplied buffer too small */ +} mp_err; +typedef enum { + MP_LSB_FIRST = -1, + MP_MSB_FIRST = 1 +} mp_order; +typedef enum { + MP_LITTLE_ENDIAN = -1, + MP_NATIVE_ENDIAN = 0, + MP_BIG_ENDIAN = 1 +} mp_endian; +#else +typedef int mp_sign; +#define MP_ZPOS 0 /* positive integer */ +#define MP_NEG 1 /* negative */ +typedef int mp_ord; #define MP_LT -1 /* less than */ #define MP_EQ 0 /* equal to */ #define MP_GT 1 /* greater than */ - -#define MP_ZPOS 0 /* positive integer */ -#define MP_NEG 1 /* negative */ - -#define MP_OKAY 0 /* ok result */ +typedef int mp_bool; +#define MP_YES 1 +#define MP_NO 0 +typedef int mp_err; +#define MP_OKAY 0 /* no error */ +#define MP_ERR -1 /* unknown error */ #define MP_MEM -2 /* out of mem */ #define MP_VAL -3 /* invalid input */ -#define MP_RANGE MP_VAL - -#define MP_YES 1 /* yes response */ -#define MP_NO 0 /* no response */ - -/* Primality generation flags */ -#define LTM_PRIME_BBS 0x0001 /* BBS style prime */ -#define LTM_PRIME_SAFE 0x0002 /* Safe prime (p-1)/2 == prime */ -#define LTM_PRIME_2MSB_ON 0x0008 /* force 2nd MSB to 1 */ +#define MP_RANGE (MP_DEPRECATED_PRAGMA("MP_RANGE has been deprecated in favor of MP_VAL") MP_VAL) +#define MP_ITER -4 /* maximum iterations reached */ +#define MP_BUF -5 /* buffer overflow, supplied buffer too small */ +typedef int mp_order; +#define MP_LSB_FIRST -1 +#define MP_MSB_FIRST 1 +typedef int mp_endian; +#define MP_LITTLE_ENDIAN -1 +#define MP_NATIVE_ENDIAN 0 +#define MP_BIG_ENDIAN 1 +#endif -typedef int mp_err; +/* tunable cutoffs */ -/* you'll have to tune these... */ -extern int KARATSUBA_MUL_CUTOFF, - KARATSUBA_SQR_CUTOFF, - TOOM_MUL_CUTOFF, - TOOM_SQR_CUTOFF; +#ifndef MP_FIXED_CUTOFFS +extern int +KARATSUBA_MUL_CUTOFF, +KARATSUBA_SQR_CUTOFF, +TOOM_MUL_CUTOFF, +TOOM_SQR_CUTOFF; +#endif /* define this to use lower memory usage routines (exptmods mostly) */ /* #define MP_LOW_MEM */ /* default precision */ #ifndef MP_PREC - #ifndef MP_LOW_MEM - #define MP_PREC 32 /* default digits of precision */ - #else - #define MP_PREC 8 /* default digits of precision */ - #endif +# ifndef MP_LOW_MEM +# define PRIVATE_MP_PREC 32 /* default digits of precision */ +# elif defined(MP_8BIT) +# define PRIVATE_MP_PREC 16 /* default digits of precision */ +# else +# define PRIVATE_MP_PREC 8 /* default digits of precision */ +# endif +# define MP_PREC (MP_DEPRECATED_PRAGMA("MP_PREC is an internal macro") PRIVATE_MP_PREC) #endif /* size of comba arrays, should be at least 2 * 2**(BITS_PER_WORD - BITS_PER_DIGIT*2) */ -#define MP_WARRAY (1 << (sizeof(mp_word) * CHAR_BIT - 2 * DIGIT_BIT + 1)) +#define PRIVATE_MP_WARRAY (int)(1uLL << (((CHAR_BIT * sizeof(private_mp_word)) - (2 * MP_DIGIT_BIT)) + 1)) +#define MP_WARRAY (MP_DEPRECATED_PRAGMA("MP_WARRAY is an internal macro") PRIVATE_MP_WARRAY) + +#if defined(__GNUC__) && __GNUC__ >= 4 +# define MP_NULL_TERMINATED __attribute__((sentinel)) +#else +# define MP_NULL_TERMINATED +#endif + +/* + * MP_WUR - warn unused result + * --------------------------- + * + * The result of functions annotated with MP_WUR must be + * checked and cannot be ignored. + * + * Most functions in libtommath return an error code. + * This error code must be checked in order to prevent crashes or invalid + * results. + * + * If you still want to avoid the error checks for quick and dirty programs + * without robustness guarantees, you can `#define MP_WUR` before including + * tommath.h, disabling the warnings. + */ +#ifndef MP_WUR +# if defined(__GNUC__) && __GNUC__ >= 4 +# define MP_WUR __attribute__((warn_unused_result)) +# else +# define MP_WUR +# endif +#endif + +#if defined(__GNUC__) && (__GNUC__ * 100 + __GNUC_MINOR__ >= 405) +# define MP_DEPRECATED(x) __attribute__((deprecated("replaced by " #x))) +# define PRIVATE_MP_DEPRECATED_PRAGMA(s) _Pragma(#s) +# define MP_DEPRECATED_PRAGMA(s) PRIVATE_MP_DEPRECATED_PRAGMA(GCC warning s) +#elif defined(_MSC_VER) && _MSC_VER >= 1500 +# define MP_DEPRECATED(x) __declspec(deprecated("replaced by " #x)) +# define MP_DEPRECATED_PRAGMA(s) __pragma(message(s)) +#else +# define MP_DEPRECATED(s) +# define MP_DEPRECATED_PRAGMA(s) +#endif + +#define DIGIT_BIT (MP_DEPRECATED_PRAGMA("DIGIT_BIT macro is deprecated, MP_DIGIT_BIT instead") MP_DIGIT_BIT) +#define USED(m) (MP_DEPRECATED_PRAGMA("USED macro is deprecated, use z->used instead") (m)->used) +#define DIGIT(m, k) (MP_DEPRECATED_PRAGMA("DIGIT macro is deprecated, use z->dp instead") (m)->dp[(k)]) +#define SIGN(m) (MP_DEPRECATED_PRAGMA("SIGN macro is deprecated, use z->sign instead") (m)->sign) /* the infamous mp_int structure */ typedef struct { - int used, alloc, sign; - mp_digit *dp; + int used, alloc; + mp_sign sign; + mp_digit *dp; } mp_int; /* callback for mp_prime_random, should fill dst with random bytes and return how many read [upto len] */ -typedef int ltm_prime_callback(unsigned char *dst, int len, void *dat); - +typedef int private_mp_prime_callback(unsigned char *dst, int len, void *dat); +typedef private_mp_prime_callback MP_DEPRECATED(mp_rand_source) ltm_prime_callback; -#define USED(m) ((m)->used) -#define DIGIT(m,k) ((m)->dp[(k)]) -#define SIGN(m) ((m)->sign) - -/* error code to const char* string */ -const char *mp_error_to_string(int code); +/* error code to char* string */ +const char *mp_error_to_string(mp_err code) MP_WUR; /* ---> init and deinit bignum functions <--- */ /* init a bignum */ -int mp_init(mp_int *a); +mp_err mp_init(mp_int *a) MP_WUR; /* free a bignum */ void mp_clear(mp_int *a); /* init a null terminated series of arguments */ -int mp_init_multi(mp_int *mp, ...); +mp_err mp_init_multi(mp_int *mp, ...) MP_NULL_TERMINATED MP_WUR; /* clear a null terminated series of arguments */ -void mp_clear_multi(mp_int *mp, ...); +void mp_clear_multi(mp_int *mp, ...) MP_NULL_TERMINATED; /* exchange two ints */ void mp_exch(mp_int *a, mp_int *b); /* shrink ram required for a bignum */ -int mp_shrink(mp_int *a); +mp_err mp_shrink(mp_int *a) MP_WUR; /* grow an int to a given size */ -int mp_grow(mp_int *a, int size); +mp_err mp_grow(mp_int *a, int size) MP_WUR; /* init to a given number of digits */ -int mp_init_size(mp_int *a, int size); +mp_err mp_init_size(mp_int *a, int size) MP_WUR; /* ---> Basic Manipulations <--- */ #define mp_iszero(a) (((a)->used == 0) ? MP_YES : MP_NO) -#define mp_iseven(a) (((a)->used > 0 && (((a)->dp[0] & 1) == 0)) ? MP_YES : MP_NO) -#define mp_isodd(a) (((a)->used > 0 && (((a)->dp[0] & 1) == 1)) ? MP_YES : MP_NO) -#define mp_isneg(a) (((a)->sign) ? MP_YES : MP_NO) +mp_bool mp_iseven(const mp_int *a) MP_WUR; +mp_bool mp_isodd(const mp_int *a) MP_WUR; +#define mp_isneg(a) (((a)->sign != MP_ZPOS) ? MP_YES : MP_NO) /* set to zero */ void mp_zero(mp_int *a); -/* set to zero, multi */ -void mp_zero_multi(mp_int *a, ...); - -/* set to a digit */ +/* get and set doubles */ +double mp_get_double(const mp_int *a) MP_WUR; +mp_err mp_set_double(mp_int *a, double b) MP_WUR; + +/* get integer, set integer and init with integer (int32_t) */ +int32_t mp_get_i32(const mp_int *a) MP_WUR; +void mp_set_i32(mp_int *a, int32_t b); +mp_err mp_init_i32(mp_int *a, int32_t b) MP_WUR; + +/* get integer, set integer and init with integer, behaves like two complement for negative numbers (uint32_t) */ +#define mp_get_u32(a) ((uint32_t)mp_get_i32(a)) +void mp_set_u32(mp_int *a, uint32_t b); +mp_err mp_init_u32(mp_int *a, uint32_t b) MP_WUR; + +/* get integer, set integer and init with integer (int64_t) */ +int64_t mp_get_i64(const mp_int *a) MP_WUR; +void mp_set_i64(mp_int *a, int64_t b); +mp_err mp_init_i64(mp_int *a, int64_t b) MP_WUR; + +/* get integer, set integer and init with integer, behaves like two complement for negative numbers (uint64_t) */ +#define mp_get_u64(a) ((uint64_t)mp_get_i64(a)) +void mp_set_u64(mp_int *a, uint64_t b); +mp_err mp_init_u64(mp_int *a, uint64_t b) MP_WUR; + +/* get magnitude */ +uint32_t mp_get_mag_u32(const mp_int *a) MP_WUR; +uint64_t mp_get_mag_u64(const mp_int *a) MP_WUR; +unsigned long mp_get_mag_ul(const mp_int *a) MP_WUR; +unsigned long long mp_get_mag_ull(const mp_int *a) MP_WUR; + +/* get integer, set integer (long) */ +long mp_get_l(const mp_int *a) MP_WUR; +void mp_set_l(mp_int *a, long b); +mp_err mp_init_l(mp_int *a, long b) MP_WUR; + +/* get integer, set integer (unsigned long) */ +#define mp_get_ul(a) ((unsigned long)mp_get_l(a)) +void mp_set_ul(mp_int *a, unsigned long b); +mp_err mp_init_ul(mp_int *a, unsigned long b) MP_WUR; + +/* get integer, set integer (long long) */ +long long mp_get_ll(const mp_int *a) MP_WUR; +void mp_set_ll(mp_int *a, long long b); +mp_err mp_init_ll(mp_int *a, long long b) MP_WUR; + +/* get integer, set integer (unsigned long long) */ +#define mp_get_ull(a) ((unsigned long long)mp_get_ll(a)) +void mp_set_ull(mp_int *a, unsigned long long b); +mp_err mp_init_ull(mp_int *a, unsigned long long b) MP_WUR; + +/* set to single unsigned digit, up to MP_DIGIT_MAX */ void mp_set(mp_int *a, mp_digit b); +mp_err mp_init_set(mp_int *a, mp_digit b) MP_WUR; -/* set a 32-bit const */ -int mp_set_int(mp_int *a, unsigned long b); - -/* get a 32-bit value */ -unsigned long mp_get_int(mp_int * a); - -/* initialize and set a digit */ -int mp_init_set (mp_int * a, mp_digit b); - -/* initialize and set 32-bit value */ -int mp_init_set_int (mp_int * a, unsigned long b); +/* get integer, set integer and init with integer (deprecated) */ +MP_DEPRECATED(mp_get_mag_u32/mp_get_u32) unsigned long mp_get_int(const mp_int *a) MP_WUR; +MP_DEPRECATED(mp_get_mag_ul/mp_get_ul) unsigned long mp_get_long(const mp_int *a) MP_WUR; +MP_DEPRECATED(mp_get_mag_ull/mp_get_ull) unsigned long long mp_get_long_long(const mp_int *a) MP_WUR; +MP_DEPRECATED(mp_set_ul) mp_err mp_set_int(mp_int *a, unsigned long b); +MP_DEPRECATED(mp_set_ul) mp_err mp_set_long(mp_int *a, unsigned long b); +MP_DEPRECATED(mp_set_ull) mp_err mp_set_long_long(mp_int *a, unsigned long long b); +MP_DEPRECATED(mp_init_ul) mp_err mp_init_set_int(mp_int *a, unsigned long b) MP_WUR; /* copy, b = a */ -int mp_copy(mp_int *a, mp_int *b); +mp_err mp_copy(const mp_int *a, mp_int *b) MP_WUR; /* inits and copies, a = b */ -int mp_init_copy(mp_int *a, mp_int *b); +mp_err mp_init_copy(mp_int *a, const mp_int *b) MP_WUR; /* trim unused digits */ void mp_clamp(mp_int *a); + +/* export binary data */ +MP_DEPRECATED(mp_pack) mp_err mp_export(void *rop, size_t *countp, int order, size_t size, + int endian, size_t nails, const mp_int *op) MP_WUR; + +/* import binary data */ +MP_DEPRECATED(mp_unpack) mp_err mp_import(mp_int *rop, size_t count, int order, + size_t size, int endian, size_t nails, + const void *op) MP_WUR; + +/* unpack binary data */ +mp_err mp_unpack(mp_int *rop, size_t count, mp_order order, size_t size, mp_endian endian, + size_t nails, const void *op) MP_WUR; + +/* pack binary data */ +size_t mp_pack_count(const mp_int *a, size_t nails, size_t size) MP_WUR; +mp_err mp_pack(void *rop, size_t maxcount, size_t *written, mp_order order, size_t size, + mp_endian endian, size_t nails, const mp_int *op) MP_WUR; + /* ---> digit manipulation <--- */ /* right shift by "b" digits */ void mp_rshd(mp_int *a, int b); /* left shift by "b" digits */ -int mp_lshd(mp_int *a, int b); +mp_err mp_lshd(mp_int *a, int b) MP_WUR; -/* c = a / 2**b */ -int mp_div_2d(mp_int *a, int b, mp_int *c, mp_int *d); +/* c = a / 2**b, implemented as c = a >> b */ +mp_err mp_div_2d(const mp_int *a, int b, mp_int *c, mp_int *d) MP_WUR; /* b = a/2 */ -int mp_div_2(mp_int *a, mp_int *b); +mp_err mp_div_2(const mp_int *a, mp_int *b) MP_WUR; + +/* a/3 => 3c + d == a */ +mp_err mp_div_3(const mp_int *a, mp_int *c, mp_digit *d) MP_WUR; -/* c = a * 2**b */ -int mp_mul_2d(mp_int *a, int b, mp_int *c); +/* c = a * 2**b, implemented as c = a << b */ +mp_err mp_mul_2d(const mp_int *a, int b, mp_int *c) MP_WUR; /* b = a*2 */ -int mp_mul_2(mp_int *a, mp_int *b); +mp_err mp_mul_2(const mp_int *a, mp_int *b) MP_WUR; -/* c = a mod 2**d */ -int mp_mod_2d(mp_int *a, int b, mp_int *c); +/* c = a mod 2**b */ +mp_err mp_mod_2d(const mp_int *a, int b, mp_int *c) MP_WUR; /* computes a = 2**b */ -int mp_2expt(mp_int *a, int b); +mp_err mp_2expt(mp_int *a, int b) MP_WUR; /* Counts the number of lsbs which are zero before the first zero bit */ -int mp_cnt_lsb(mp_int *a); +int mp_cnt_lsb(const mp_int *a) MP_WUR; /* I Love Earth! */ -/* makes a pseudo-random int of a given size */ -int mp_rand(mp_int *a, int digits); +/* makes a pseudo-random mp_int of a given size */ +mp_err mp_rand(mp_int *a, int digits) MP_WUR; +/* makes a pseudo-random small int of a given size */ +MP_DEPRECATED(mp_rand) mp_err mp_rand_digit(mp_digit *r) MP_WUR; +/* use custom random data source instead of source provided the platform */ +void mp_rand_source(mp_err(*source)(void *out, size_t size)); + +#ifdef MP_PRNG_ENABLE_LTM_RNG +# warning MP_PRNG_ENABLE_LTM_RNG has been deprecated, use mp_rand_source instead. +/* A last resort to provide random data on systems without any of the other + * implemented ways to gather entropy. + * It is compatible with `rng_get_bytes()` from libtomcrypt so you could + * provide that one and then set `ltm_rng = rng_get_bytes;` */ +extern unsigned long (*ltm_rng)(unsigned char *out, unsigned long outlen, void (*callback)(void)); +extern void (*ltm_rng_callback)(void); +#endif /* ---> binary operations <--- */ -/* c = a XOR b */ -int mp_xor(mp_int *a, mp_int *b, mp_int *c); -/* c = a OR b */ -int mp_or(mp_int *a, mp_int *b, mp_int *c); +/* Checks the bit at position b and returns MP_YES + * if the bit is 1, MP_NO if it is 0 and MP_VAL + * in case of error + */ +MP_DEPRECATED(s_mp_get_bit) int mp_get_bit(const mp_int *a, int b) MP_WUR; + +/* c = a XOR b (two complement) */ +MP_DEPRECATED(mp_xor) mp_err mp_tc_xor(const mp_int *a, const mp_int *b, mp_int *c) MP_WUR; +mp_err mp_xor(const mp_int *a, const mp_int *b, mp_int *c) MP_WUR; + +/* c = a OR b (two complement) */ +MP_DEPRECATED(mp_or) mp_err mp_tc_or(const mp_int *a, const mp_int *b, mp_int *c) MP_WUR; +mp_err mp_or(const mp_int *a, const mp_int *b, mp_int *c) MP_WUR; -/* c = a AND b */ -int mp_and(mp_int *a, mp_int *b, mp_int *c); +/* c = a AND b (two complement) */ +MP_DEPRECATED(mp_and) mp_err mp_tc_and(const mp_int *a, const mp_int *b, mp_int *c) MP_WUR; +mp_err mp_and(const mp_int *a, const mp_int *b, mp_int *c) MP_WUR; + +/* b = ~a (bitwise not, two complement) */ +mp_err mp_complement(const mp_int *a, mp_int *b) MP_WUR; + +/* right shift with sign extension */ +MP_DEPRECATED(mp_signed_rsh) mp_err mp_tc_div_2d(const mp_int *a, int b, mp_int *c) MP_WUR; +mp_err mp_signed_rsh(const mp_int *a, int b, mp_int *c) MP_WUR; /* ---> Basic arithmetic <--- */ /* b = -a */ -int mp_neg(mp_int *a, mp_int *b); +mp_err mp_neg(const mp_int *a, mp_int *b) MP_WUR; /* b = |a| */ -int mp_abs(mp_int *a, mp_int *b); +mp_err mp_abs(const mp_int *a, mp_int *b) MP_WUR; /* compare a to b */ -int mp_cmp(mp_int *a, mp_int *b); +mp_ord mp_cmp(const mp_int *a, const mp_int *b) MP_WUR; /* compare |a| to |b| */ -int mp_cmp_mag(mp_int *a, mp_int *b); +mp_ord mp_cmp_mag(const mp_int *a, const mp_int *b) MP_WUR; /* c = a + b */ -int mp_add(mp_int *a, mp_int *b, mp_int *c); +mp_err mp_add(const mp_int *a, const mp_int *b, mp_int *c) MP_WUR; /* c = a - b */ -int mp_sub(mp_int *a, mp_int *b, mp_int *c); +mp_err mp_sub(const mp_int *a, const mp_int *b, mp_int *c) MP_WUR; /* c = a * b */ -int mp_mul(mp_int *a, mp_int *b, mp_int *c); +mp_err mp_mul(const mp_int *a, const mp_int *b, mp_int *c) MP_WUR; /* b = a*a */ -int mp_sqr(mp_int *a, mp_int *b); +mp_err mp_sqr(const mp_int *a, mp_int *b) MP_WUR; /* a/b => cb + d == a */ -int mp_div(mp_int *a, mp_int *b, mp_int *c, mp_int *d); +mp_err mp_div(const mp_int *a, const mp_int *b, mp_int *c, mp_int *d) MP_WUR; /* c = a mod b, 0 <= c < b */ -int mp_mod(mp_int *a, mp_int *b, mp_int *c); +mp_err mp_mod(const mp_int *a, const mp_int *b, mp_int *c) MP_WUR; + +/* Increment "a" by one like "a++". Changes input! */ +mp_err mp_incr(mp_int *a) MP_WUR; + +/* Decrement "a" by one like "a--". Changes input! */ +mp_err mp_decr(mp_int *a) MP_WUR; /* ---> single digit functions <--- */ /* compare against a single digit */ -int mp_cmp_d(mp_int *a, mp_digit b); +mp_ord mp_cmp_d(const mp_int *a, mp_digit b) MP_WUR; /* c = a + b */ -int mp_add_d(mp_int *a, mp_digit b, mp_int *c); +mp_err mp_add_d(const mp_int *a, mp_digit b, mp_int *c) MP_WUR; /* c = a - b */ -int mp_sub_d(mp_int *a, mp_digit b, mp_int *c); +mp_err mp_sub_d(const mp_int *a, mp_digit b, mp_int *c) MP_WUR; /* c = a * b */ -int mp_mul_d(mp_int *a, mp_digit b, mp_int *c); +mp_err mp_mul_d(const mp_int *a, mp_digit b, mp_int *c) MP_WUR; /* a/b => cb + d == a */ -int mp_div_d(mp_int *a, mp_digit b, mp_int *c, mp_digit *d); - -/* a/3 => 3c + d == a */ -int mp_div_3(mp_int *a, mp_int *c, mp_digit *d); - -/* c = a**b */ -int mp_expt_d(mp_int *a, mp_digit b, mp_int *c); +mp_err mp_div_d(const mp_int *a, mp_digit b, mp_int *c, mp_digit *d) MP_WUR; /* c = a mod b, 0 <= c < b */ -int mp_mod_d(mp_int *a, mp_digit b, mp_digit *c); +mp_err mp_mod_d(const mp_int *a, mp_digit b, mp_digit *c) MP_WUR; /* ---> number theory <--- */ /* d = a + b (mod c) */ -int mp_addmod(mp_int *a, mp_int *b, mp_int *c, mp_int *d); +mp_err mp_addmod(const mp_int *a, const mp_int *b, const mp_int *c, mp_int *d) MP_WUR; /* d = a - b (mod c) */ -int mp_submod(mp_int *a, mp_int *b, mp_int *c, mp_int *d); +mp_err mp_submod(const mp_int *a, const mp_int *b, const mp_int *c, mp_int *d) MP_WUR; /* d = a * b (mod c) */ -int mp_mulmod(mp_int *a, mp_int *b, mp_int *c, mp_int *d); +mp_err mp_mulmod(const mp_int *a, const mp_int *b, const mp_int *c, mp_int *d) MP_WUR; /* c = a * a (mod b) */ -int mp_sqrmod(mp_int *a, mp_int *b, mp_int *c); +mp_err mp_sqrmod(const mp_int *a, const mp_int *b, mp_int *c) MP_WUR; /* c = 1/a (mod b) */ -int mp_invmod(mp_int *a, mp_int *b, mp_int *c); +mp_err mp_invmod(const mp_int *a, const mp_int *b, mp_int *c) MP_WUR; /* c = (a, b) */ -int mp_gcd(mp_int *a, mp_int *b, mp_int *c); +mp_err mp_gcd(const mp_int *a, const mp_int *b, mp_int *c) MP_WUR; /* produces value such that U1*a + U2*b = U3 */ -int mp_exteuclid(mp_int *a, mp_int *b, mp_int *U1, mp_int *U2, mp_int *U3); +mp_err mp_exteuclid(const mp_int *a, const mp_int *b, mp_int *U1, mp_int *U2, mp_int *U3) MP_WUR; /* c = [a, b] or (a*b)/(a, b) */ -int mp_lcm(mp_int *a, mp_int *b, mp_int *c); +mp_err mp_lcm(const mp_int *a, const mp_int *b, mp_int *c) MP_WUR; /* finds one of the b'th root of a, such that |c|**b <= |a| * * returns error if a < 0 and b is even */ -int mp_n_root(mp_int *a, mp_digit b, mp_int *c); +mp_err mp_root_u32(const mp_int *a, uint32_t b, mp_int *c) MP_WUR; +MP_DEPRECATED(mp_root_u32) mp_err mp_n_root(const mp_int *a, mp_digit b, mp_int *c) MP_WUR; +MP_DEPRECATED(mp_root_u32) mp_err mp_n_root_ex(const mp_int *a, mp_digit b, mp_int *c, int fast) MP_WUR; /* special sqrt algo */ -int mp_sqrt(mp_int *arg, mp_int *ret); +mp_err mp_sqrt(const mp_int *arg, mp_int *ret) MP_WUR; + +/* special sqrt (mod prime) */ +mp_err mp_sqrtmod_prime(const mp_int *n, const mp_int *prime, mp_int *ret) MP_WUR; /* is number a square? */ -int mp_is_square(mp_int *arg, int *ret); +mp_err mp_is_square(const mp_int *arg, mp_bool *ret) MP_WUR; /* computes the jacobi c = (a | n) (or Legendre if b is prime) */ -int mp_jacobi(mp_int *a, mp_int *n, int *c); +MP_DEPRECATED(mp_kronecker) mp_err mp_jacobi(const mp_int *a, const mp_int *n, int *c) MP_WUR; + +/* computes the Kronecker symbol c = (a | p) (like jacobi() but with {a,p} in Z */ +mp_err mp_kronecker(const mp_int *a, const mp_int *p, int *c) MP_WUR; /* used to setup the Barrett reduction for a given modulus b */ -int mp_reduce_setup(mp_int *a, mp_int *b); +mp_err mp_reduce_setup(mp_int *a, const mp_int *b) MP_WUR; /* Barrett Reduction, computes a (mod b) with a precomputed value c * - * Assumes that 0 < a <= b*b, note if 0 > a > -(b*b) then you can merely - * compute the reduction as -1 * mp_reduce(mp_abs(a)) [pseudo code]. + * Assumes that 0 < x <= m*m, note if 0 > x > -(m*m) then you can merely + * compute the reduction as -1 * mp_reduce(mp_abs(x)) [pseudo code]. */ -int mp_reduce(mp_int *a, mp_int *b, mp_int *c); +mp_err mp_reduce(mp_int *x, const mp_int *m, const mp_int *mu) MP_WUR; /* setups the montgomery reduction */ -int mp_montgomery_setup(mp_int *a, mp_digit *mp); +mp_err mp_montgomery_setup(const mp_int *n, mp_digit *rho) MP_WUR; /* computes a = B**n mod b without division or multiplication useful for * normalizing numbers in a Montgomery system. */ -int mp_montgomery_calc_normalization(mp_int *a, mp_int *b); +mp_err mp_montgomery_calc_normalization(mp_int *a, const mp_int *b) MP_WUR; /* computes x/R == x (mod N) via Montgomery Reduction */ -int mp_montgomery_reduce(mp_int *a, mp_int *m, mp_digit mp); +mp_err mp_montgomery_reduce(mp_int *x, const mp_int *n, mp_digit rho) MP_WUR; /* returns 1 if a is a valid DR modulus */ -int mp_dr_is_modulus(mp_int *a); +mp_bool mp_dr_is_modulus(const mp_int *a) MP_WUR; /* sets the value of "d" required for mp_dr_reduce */ -void mp_dr_setup(mp_int *a, mp_digit *d); +void mp_dr_setup(const mp_int *a, mp_digit *d); -/* reduces a modulo b using the Diminished Radix method */ -int mp_dr_reduce(mp_int *a, mp_int *b, mp_digit mp); +/* reduces a modulo n using the Diminished Radix method */ +mp_err mp_dr_reduce(mp_int *x, const mp_int *n, mp_digit k) MP_WUR; /* returns true if a can be reduced with mp_reduce_2k */ -int mp_reduce_is_2k(mp_int *a); +mp_bool mp_reduce_is_2k(const mp_int *a) MP_WUR; /* determines k value for 2k reduction */ -int mp_reduce_2k_setup(mp_int *a, mp_digit *d); +mp_err mp_reduce_2k_setup(const mp_int *a, mp_digit *d) MP_WUR; /* reduces a modulo b where b is of the form 2**p - k [0 <= a] */ -int mp_reduce_2k(mp_int *a, mp_int *n, mp_digit d); +mp_err mp_reduce_2k(mp_int *a, const mp_int *n, mp_digit d) MP_WUR; /* returns true if a can be reduced with mp_reduce_2k_l */ -int mp_reduce_is_2k_l(mp_int *a); +mp_bool mp_reduce_is_2k_l(const mp_int *a) MP_WUR; /* determines k value for 2k reduction */ -int mp_reduce_2k_setup_l(mp_int *a, mp_int *d); +mp_err mp_reduce_2k_setup_l(const mp_int *a, mp_int *d) MP_WUR; /* reduces a modulo b where b is of the form 2**p - k [0 <= a] */ -int mp_reduce_2k_l(mp_int *a, mp_int *n, mp_int *d); +mp_err mp_reduce_2k_l(mp_int *a, const mp_int *n, const mp_int *d) MP_WUR; -/* d = a**b (mod c) */ -int mp_exptmod(mp_int *a, mp_int *b, mp_int *c, mp_int *d); +/* Y = G**X (mod P) */ +mp_err mp_exptmod(const mp_int *G, const mp_int *X, const mp_int *P, mp_int *Y) MP_WUR; /* ---> Primes <--- */ /* number of primes */ #ifdef MP_8BIT - #define PRIME_SIZE 31 +# define PRIVATE_MP_PRIME_TAB_SIZE 31 #else - #define PRIME_SIZE 256 +# define PRIVATE_MP_PRIME_TAB_SIZE 256 #endif +#define PRIME_SIZE (MP_DEPRECATED_PRAGMA("PRIME_SIZE has been made internal") PRIVATE_MP_PRIME_TAB_SIZE) /* table of first PRIME_SIZE primes */ -extern const mp_digit ltm_prime_tab[]; +MP_DEPRECATED(internal) extern const mp_digit ltm_prime_tab[PRIVATE_MP_PRIME_TAB_SIZE]; /* result=1 if a is divisible by one of the first PRIME_SIZE primes */ -int mp_prime_is_divisible(mp_int *a, int *result); +MP_DEPRECATED(mp_prime_is_prime) mp_err mp_prime_is_divisible(const mp_int *a, mp_bool *result) MP_WUR; /* performs one Fermat test of "a" using base "b". * Sets result to 0 if composite or 1 if probable prime */ -int mp_prime_fermat(mp_int *a, mp_int *b, int *result); +mp_err mp_prime_fermat(const mp_int *a, const mp_int *b, mp_bool *result) MP_WUR; /* performs one Miller-Rabin test of "a" using base "b". * Sets result to 0 if composite or 1 if probable prime */ -int mp_prime_miller_rabin(mp_int *a, mp_int *b, int *result); +mp_err mp_prime_miller_rabin(const mp_int *a, const mp_int *b, mp_bool *result) MP_WUR; /* This gives [for a given bit size] the number of trials required * such that Miller-Rabin gives a prob of failure lower than 2^-96 */ -int mp_prime_rabin_miller_trials(int size); +int mp_prime_rabin_miller_trials(int size) MP_WUR; + +/* performs one strong Lucas-Selfridge test of "a". + * Sets result to 0 if composite or 1 if probable prime + */ +mp_err mp_prime_strong_lucas_selfridge(const mp_int *a, mp_bool *result) MP_WUR; -/* performs t rounds of Miller-Rabin on "a" using the first - * t prime bases. Also performs an initial sieve of trial +/* performs one Frobenius test of "a" as described by Paul Underwood. + * Sets result to 0 if composite or 1 if probable prime + */ +mp_err mp_prime_frobenius_underwood(const mp_int *N, mp_bool *result) MP_WUR; + +/* performs t random rounds of Miller-Rabin on "a" additional to + * bases 2 and 3. Also performs an initial sieve of trial * division. Determines if "a" is prime with probability * of error no more than (1/4)**t. + * Both a strong Lucas-Selfridge to complete the BPSW test + * and a separate Frobenius test are available at compile time. + * With t<0 a deterministic test is run for primes up to + * 318665857834031151167461. With t<13 (abs(t)-13) additional + * tests with sequential small primes are run starting at 43. + * Is Fips 186.4 compliant if called with t as computed by + * mp_prime_rabin_miller_trials(); * * Sets result to 1 if probably prime, 0 otherwise */ -int mp_prime_is_prime(mp_int *a, int t, int *result); +mp_err mp_prime_is_prime(const mp_int *a, int t, mp_bool *result) MP_WUR; /* finds the next prime after the number "a" using "t" trials * of Miller-Rabin. * * bbs_style = 1 means the prime must be congruent to 3 mod 4 */ -int mp_prime_next_prime(mp_int *a, int t, int bbs_style); +mp_err mp_prime_next_prime(mp_int *a, int t, int bbs_style) MP_WUR; /* makes a truly random prime of a given size (bytes), * call with bbs = 1 if you want it to be congruent to 3 mod 4 @@ -502,89 +697,85 @@ int mp_prime_next_prime(mp_int *a, int t, int bbs_style); * * The prime generated will be larger than 2^(8*size). */ -#define mp_prime_random(a, t, size, bbs, cb, dat) mp_prime_random_ex(a, t, ((size) * 8) + 1, (bbs==1)?LTM_PRIME_BBS:0, cb, dat) +#define mp_prime_random(a, t, size, bbs, cb, dat) (MP_DEPRECATED_PRAGMA("mp_prime_random has been deprecated, use mp_prime_rand instead") mp_prime_random_ex(a, t, ((size) * 8) + 1, (bbs==1)?MP_PRIME_BBS:0, cb, dat)) /* makes a truly random prime of a given size (bits), * * Flags are as follows: * - * LTM_PRIME_BBS - make prime congruent to 3 mod 4 - * LTM_PRIME_SAFE - make sure (p-1)/2 is prime as well (implies LTM_PRIME_BBS) - * LTM_PRIME_2MSB_OFF - make the 2nd highest bit zero - * LTM_PRIME_2MSB_ON - make the 2nd highest bit one + * MP_PRIME_BBS - make prime congruent to 3 mod 4 + * MP_PRIME_SAFE - make sure (p-1)/2 is prime as well (implies MP_PRIME_BBS) + * MP_PRIME_2MSB_ON - make the 2nd highest bit one * * You have to supply a callback which fills in a buffer with random bytes. "dat" is a parameter you can * have passed to the callback (e.g. a state or something). This function doesn't use "dat" itself * so it can be NULL * */ -int mp_prime_random_ex(mp_int *a, int t, int size, int flags, ltm_prime_callback cb, void *dat); +MP_DEPRECATED(mp_prime_rand) mp_err mp_prime_random_ex(mp_int *a, int t, int size, int flags, + private_mp_prime_callback cb, void *dat) MP_WUR; +mp_err mp_prime_rand(mp_int *a, int t, int size, int flags) MP_WUR; -int mp_find_prime(mp_int *a, int t); +/* Integer logarithm to integer base */ +mp_err mp_log_u32(const mp_int *a, uint32_t base, uint32_t *c) MP_WUR; + +/* c = a**b */ +mp_err mp_expt_u32(const mp_int *a, uint32_t b, mp_int *c) MP_WUR; +MP_DEPRECATED(mp_expt_u32) mp_err mp_expt_d(const mp_int *a, mp_digit b, mp_int *c) MP_WUR; +MP_DEPRECATED(mp_expt_u32) mp_err mp_expt_d_ex(const mp_int *a, mp_digit b, mp_int *c, int fast) MP_WUR; /* ---> radix conversion <--- */ -int mp_count_bits(mp_int *a); - -int mp_unsigned_bin_size(mp_int *a); -int mp_read_unsigned_bin(mp_int *a, const unsigned char *b, int c); -int mp_to_unsigned_bin(mp_int *a, unsigned char *b); -int mp_to_unsigned_bin_n (mp_int * a, unsigned char *b, unsigned long *outlen); - -int mp_signed_bin_size(mp_int *a); -int mp_read_signed_bin(mp_int *a, const unsigned char *b, int c); -int mp_to_signed_bin(mp_int *a, unsigned char *b); -int mp_to_signed_bin_n (mp_int * a, unsigned char *b, unsigned long *outlen); - -int mp_read_radix(mp_int *a, const char *str, int radix); -int mp_toradix(mp_int *a, char *str, int radix); -int mp_toradix_n(mp_int * a, char *str, int radix, int maxlen); -int mp_radix_size(mp_int *a, int radix, int *size); - -int mp_fread(mp_int *a, int radix, FILE *stream); -int mp_fwrite(mp_int *a, int radix, FILE *stream); - -#define mp_read_raw(mp, str, len) mp_read_signed_bin((mp), (str), (len)) -#define mp_raw_size(mp) mp_signed_bin_size(mp) -#define mp_toraw(mp, str) mp_to_signed_bin((mp), (str)) -#define mp_read_mag(mp, str, len) mp_read_unsigned_bin((mp), (str), (len)) -#define mp_mag_size(mp) mp_unsigned_bin_size(mp) -#define mp_tomag(mp, str) mp_to_unsigned_bin((mp), (str)) - -#define mp_tobinary(M, S) mp_toradix((M), (S), 2) -#define mp_tooctal(M, S) mp_toradix((M), (S), 8) -#define mp_todecimal(M, S) mp_toradix((M), (S), 10) -#define mp_tohex(M, S) mp_toradix((M), (S), 16) - -/* lowlevel functions, do not call! */ -int s_mp_add(mp_int *a, mp_int *b, mp_int *c); -int s_mp_sub(mp_int *a, mp_int *b, mp_int *c); -#define s_mp_mul(a, b, c) s_mp_mul_digs(a, b, c, (a)->used + (b)->used + 1) -int fast_s_mp_mul_digs(mp_int *a, mp_int *b, mp_int *c, int digs); -int s_mp_mul_digs(mp_int *a, mp_int *b, mp_int *c, int digs); -int fast_s_mp_mul_high_digs(mp_int *a, mp_int *b, mp_int *c, int digs); -int s_mp_mul_high_digs(mp_int *a, mp_int *b, mp_int *c, int digs); -int fast_s_mp_sqr(mp_int *a, mp_int *b); -int s_mp_sqr(mp_int *a, mp_int *b); -int mp_karatsuba_mul(mp_int *a, mp_int *b, mp_int *c); -int mp_toom_mul(mp_int *a, mp_int *b, mp_int *c); -int mp_karatsuba_sqr(mp_int *a, mp_int *b); -int mp_toom_sqr(mp_int *a, mp_int *b); -int fast_mp_invmod(mp_int *a, mp_int *b, mp_int *c); -int mp_invmod_slow (mp_int * a, mp_int * b, mp_int * c); -int fast_mp_montgomery_reduce(mp_int *a, mp_int *m, mp_digit mp); -int mp_exptmod_fast(mp_int *G, mp_int *X, mp_int *P, mp_int *Y, int mode); -int s_mp_exptmod (mp_int * G, mp_int * X, mp_int * P, mp_int * Y, int mode); -void bn_reverse(unsigned char *s, int len); - -extern const char *mp_s_rmap; +int mp_count_bits(const mp_int *a) MP_WUR; -#ifdef __cplusplus - } -#endif +MP_DEPRECATED(mp_ubin_size) int mp_unsigned_bin_size(const mp_int *a) MP_WUR; +MP_DEPRECATED(mp_from_ubin) mp_err mp_read_unsigned_bin(mp_int *a, const unsigned char *b, int c) MP_WUR; +MP_DEPRECATED(mp_to_ubin) mp_err mp_to_unsigned_bin(const mp_int *a, unsigned char *b) MP_WUR; +MP_DEPRECATED(mp_to_ubin) mp_err mp_to_unsigned_bin_n(const mp_int *a, unsigned char *b, unsigned long *outlen) MP_WUR; + +MP_DEPRECATED(mp_sbin_size) int mp_signed_bin_size(const mp_int *a) MP_WUR; +MP_DEPRECATED(mp_from_sbin) mp_err mp_read_signed_bin(mp_int *a, const unsigned char *b, int c) MP_WUR; +MP_DEPRECATED(mp_to_sbin) mp_err mp_to_signed_bin(const mp_int *a, unsigned char *b) MP_WUR; +MP_DEPRECATED(mp_to_sbin) mp_err mp_to_signed_bin_n(const mp_int *a, unsigned char *b, unsigned long *outlen) MP_WUR; + +size_t mp_ubin_size(const mp_int *a) MP_WUR; +mp_err mp_from_ubin(mp_int *a, const unsigned char *buf, size_t size) MP_WUR; +mp_err mp_to_ubin(const mp_int *a, unsigned char *buf, size_t maxlen, size_t *written) MP_WUR; + +size_t mp_sbin_size(const mp_int *a) MP_WUR; +mp_err mp_from_sbin(mp_int *a, const unsigned char *buf, size_t size) MP_WUR; +mp_err mp_to_sbin(const mp_int *a, unsigned char *buf, size_t maxlen, size_t *written) MP_WUR; + +mp_err mp_read_radix(mp_int *a, const char *str, int radix) MP_WUR; +MP_DEPRECATED(mp_to_radix) mp_err mp_toradix(const mp_int *a, char *str, int radix) MP_WUR; +MP_DEPRECATED(mp_to_radix) mp_err mp_toradix_n(const mp_int *a, char *str, int radix, int maxlen) MP_WUR; +mp_err mp_to_radix(const mp_int *a, char *str, size_t maxlen, size_t *written, int radix) MP_WUR; +mp_err mp_radix_size(const mp_int *a, int radix, int *size) MP_WUR; + +#ifndef MP_NO_FILE +mp_err mp_fread(mp_int *a, int radix, FILE *stream) MP_WUR; +mp_err mp_fwrite(const mp_int *a, int radix, FILE *stream) MP_WUR; #endif +#define mp_read_raw(mp, str, len) (MP_DEPRECATED_PRAGMA("replaced by mp_read_signed_bin") mp_read_signed_bin((mp), (str), (len))) +#define mp_raw_size(mp) (MP_DEPRECATED_PRAGMA("replaced by mp_signed_bin_size") mp_signed_bin_size(mp)) +#define mp_toraw(mp, str) (MP_DEPRECATED_PRAGMA("replaced by mp_to_signed_bin") mp_to_signed_bin((mp), (str))) +#define mp_read_mag(mp, str, len) (MP_DEPRECATED_PRAGMA("replaced by mp_read_unsigned_bin") mp_read_unsigned_bin((mp), (str), (len)) +#define mp_mag_size(mp) (MP_DEPRECATED_PRAGMA("replaced by mp_unsigned_bin_size") mp_unsigned_bin_size(mp)) +#define mp_tomag(mp, str) (MP_DEPRECATED_PRAGMA("replaced by mp_to_unsigned_bin") mp_to_unsigned_bin((mp), (str))) -/* $Source: /cvs/libtom/libtommath/tommath.h,v $ */ -/* $Revision: 1.8 $ */ -/* $Date: 2006/03/31 14:18:44 $ */ +#define mp_tobinary(M, S) (MP_DEPRECATED_PRAGMA("replaced by mp_to_binary") mp_toradix((M), (S), 2)) +#define mp_tooctal(M, S) (MP_DEPRECATED_PRAGMA("replaced by mp_to_octal") mp_toradix((M), (S), 8)) +#define mp_todecimal(M, S) (MP_DEPRECATED_PRAGMA("replaced by mp_to_decimal") mp_toradix((M), (S), 10)) +#define mp_tohex(M, S) (MP_DEPRECATED_PRAGMA("replaced by mp_to_hex") mp_toradix((M), (S), 16)) + +#define mp_to_binary(M, S, N) mp_to_radix((M), (S), (N), NULL, 2) +#define mp_to_octal(M, S, N) mp_to_radix((M), (S), (N), NULL, 8) +#define mp_to_decimal(M, S, N) mp_to_radix((M), (S), (N), NULL, 10) +#define mp_to_hex(M, S, N) mp_to_radix((M), (S), (N), NULL, 16) + +#ifdef __cplusplus +} +#endif + +#endif diff --git a/lib/hcrypto/libtommath/tommath_class.h b/lib/hcrypto/libtommath/tommath_class.h index 8fd0f52f49bb..52ba585ecf1c 100644 --- a/lib/hcrypto/libtommath/tommath_class.h +++ b/lib/hcrypto/libtommath/tommath_class.h @@ -1,214 +1,296 @@ +/* LibTomMath, multiple-precision integer library -- Tom St Denis */ +/* SPDX-License-Identifier: Unlicense */ + #if !(defined(LTM1) && defined(LTM2) && defined(LTM3)) +#define LTM_INSIDE #if defined(LTM2) -#define LTM3 +# define LTM3 #endif #if defined(LTM1) -#define LTM2 +# define LTM2 #endif #define LTM1 - #if defined(LTM_ALL) -#define BN_ERROR_C -#define BN_FAST_MP_INVMOD_C -#define BN_FAST_MP_MONTGOMERY_REDUCE_C -#define BN_FAST_S_MP_MUL_DIGS_C -#define BN_FAST_S_MP_MUL_HIGH_DIGS_C -#define BN_FAST_S_MP_SQR_C -#define BN_MP_2EXPT_C -#define BN_MP_ABS_C -#define BN_MP_ADD_C -#define BN_MP_ADD_D_C -#define BN_MP_ADDMOD_C -#define BN_MP_AND_C -#define BN_MP_CLAMP_C -#define BN_MP_CLEAR_C -#define BN_MP_CLEAR_MULTI_C -#define BN_MP_CMP_C -#define BN_MP_CMP_D_C -#define BN_MP_CMP_MAG_C -#define BN_MP_CNT_LSB_C -#define BN_MP_COPY_C -#define BN_MP_COUNT_BITS_C -#define BN_MP_DIV_C -#define BN_MP_DIV_2_C -#define BN_MP_DIV_2D_C -#define BN_MP_DIV_3_C -#define BN_MP_DIV_D_C -#define BN_MP_DR_IS_MODULUS_C -#define BN_MP_DR_REDUCE_C -#define BN_MP_DR_SETUP_C -#define BN_MP_EXCH_C -#define BN_MP_EXPT_D_C -#define BN_MP_EXPTMOD_C -#define BN_MP_EXPTMOD_FAST_C -#define BN_MP_EXTEUCLID_C -#define BN_MP_FIND_PRIME_C -#define BN_MP_FREAD_C -#define BN_MP_FWRITE_C -#define BN_MP_GCD_C -#define BN_MP_GET_INT_C -#define BN_MP_GROW_C -#define BN_MP_INIT_C -#define BN_MP_INIT_COPY_C -#define BN_MP_INIT_MULTI_C -#define BN_MP_INIT_SET_C -#define BN_MP_INIT_SET_INT_C -#define BN_MP_INIT_SIZE_C -#define BN_MP_INVMOD_C -#define BN_MP_INVMOD_SLOW_C -#define BN_MP_ISPRIME_C -#define BN_MP_IS_SQUARE_C -#define BN_MP_JACOBI_C -#define BN_MP_KARATSUBA_MUL_C -#define BN_MP_KARATSUBA_SQR_C -#define BN_MP_LCM_C -#define BN_MP_LSHD_C -#define BN_MP_MOD_C -#define BN_MP_MOD_2D_C -#define BN_MP_MOD_D_C -#define BN_MP_MONTGOMERY_CALC_NORMALIZATION_C -#define BN_MP_MONTGOMERY_REDUCE_C -#define BN_MP_MONTGOMERY_SETUP_C -#define BN_MP_MUL_C -#define BN_MP_MUL_2_C -#define BN_MP_MUL_2D_C -#define BN_MP_MUL_D_C -#define BN_MP_MULMOD_C -#define BN_MP_N_ROOT_C -#define BN_MP_NEG_C -#define BN_MP_OR_C -#define BN_MP_PRIME_FERMAT_C -#define BN_MP_PRIME_IS_DIVISIBLE_C -#define BN_MP_PRIME_IS_PRIME_C -#define BN_MP_PRIME_MILLER_RABIN_C -#define BN_MP_PRIME_NEXT_PRIME_C -#define BN_MP_PRIME_RABIN_MILLER_TRIALS_C -#define BN_MP_PRIME_RANDOM_EX_C -#define BN_MP_RADIX_SIZE_C -#define BN_MP_RADIX_SMAP_C -#define BN_MP_RAND_C -#define BN_MP_READ_RADIX_C -#define BN_MP_READ_SIGNED_BIN_C -#define BN_MP_READ_UNSIGNED_BIN_C -#define BN_MP_REDUCE_C -#define BN_MP_REDUCE_2K_C -#define BN_MP_REDUCE_2K_L_C -#define BN_MP_REDUCE_2K_SETUP_C -#define BN_MP_REDUCE_2K_SETUP_L_C -#define BN_MP_REDUCE_IS_2K_C -#define BN_MP_REDUCE_IS_2K_L_C -#define BN_MP_REDUCE_SETUP_C -#define BN_MP_RSHD_C -#define BN_MP_SET_C -#define BN_MP_SET_INT_C -#define BN_MP_SHRINK_C -#define BN_MP_SIGNED_BIN_SIZE_C -#define BN_MP_SQR_C -#define BN_MP_SQRMOD_C -#define BN_MP_SQRT_C -#define BN_MP_SUB_C -#define BN_MP_SUB_D_C -#define BN_MP_SUBMOD_C -#define BN_MP_TO_SIGNED_BIN_C -#define BN_MP_TO_SIGNED_BIN_N_C -#define BN_MP_TO_UNSIGNED_BIN_C -#define BN_MP_TO_UNSIGNED_BIN_N_C -#define BN_MP_TOOM_MUL_C -#define BN_MP_TOOM_SQR_C -#define BN_MP_TORADIX_C -#define BN_MP_TORADIX_N_C -#define BN_MP_UNSIGNED_BIN_SIZE_C -#define BN_MP_XOR_C -#define BN_MP_ZERO_C -#define BN_MP_ZERO_MULTI_C -#define BN_PRIME_TAB_C -#define BN_REVERSE_C -#define BN_S_MP_ADD_C -#define BN_S_MP_EXPTMOD_C -#define BN_S_MP_MUL_DIGS_C -#define BN_S_MP_MUL_HIGH_DIGS_C -#define BN_S_MP_SQR_C -#define BN_S_MP_SUB_C -#define BNCORE_C -#endif - -#if defined(BN_ERROR_C) - #define BN_MP_ERROR_TO_STRING_C -#endif - -#if defined(BN_FAST_MP_INVMOD_C) - #define BN_MP_ISEVEN_C - #define BN_MP_INIT_MULTI_C - #define BN_MP_COPY_C - #define BN_MP_MOD_C - #define BN_MP_SET_C - #define BN_MP_DIV_2_C - #define BN_MP_ISODD_C - #define BN_MP_SUB_C - #define BN_MP_CMP_C - #define BN_MP_ISZERO_C - #define BN_MP_CMP_D_C - #define BN_MP_ADD_C - #define BN_MP_EXCH_C - #define BN_MP_CLEAR_MULTI_C -#endif - -#if defined(BN_FAST_MP_MONTGOMERY_REDUCE_C) - #define BN_MP_GROW_C - #define BN_MP_RSHD_C - #define BN_MP_CLAMP_C - #define BN_MP_CMP_MAG_C - #define BN_S_MP_SUB_C -#endif - -#if defined(BN_FAST_S_MP_MUL_DIGS_C) - #define BN_MP_GROW_C - #define BN_MP_CLAMP_C -#endif - -#if defined(BN_FAST_S_MP_MUL_HIGH_DIGS_C) - #define BN_MP_GROW_C - #define BN_MP_CLAMP_C -#endif - -#if defined(BN_FAST_S_MP_SQR_C) - #define BN_MP_GROW_C - #define BN_MP_CLAMP_C +# define BN_CUTOFFS_C +# define BN_DEPRECATED_C +# define BN_MP_2EXPT_C +# define BN_MP_ABS_C +# define BN_MP_ADD_C +# define BN_MP_ADD_D_C +# define BN_MP_ADDMOD_C +# define BN_MP_AND_C +# define BN_MP_CLAMP_C +# define BN_MP_CLEAR_C +# define BN_MP_CLEAR_MULTI_C +# define BN_MP_CMP_C +# define BN_MP_CMP_D_C +# define BN_MP_CMP_MAG_C +# define BN_MP_CNT_LSB_C +# define BN_MP_COMPLEMENT_C +# define BN_MP_COPY_C +# define BN_MP_COUNT_BITS_C +# define BN_MP_DECR_C +# define BN_MP_DIV_C +# define BN_MP_DIV_2_C +# define BN_MP_DIV_2D_C +# define BN_MP_DIV_3_C +# define BN_MP_DIV_D_C +# define BN_MP_DR_IS_MODULUS_C +# define BN_MP_DR_REDUCE_C +# define BN_MP_DR_SETUP_C +# define BN_MP_ERROR_TO_STRING_C +# define BN_MP_EXCH_C +# define BN_MP_EXPT_U32_C +# define BN_MP_EXPTMOD_C +# define BN_MP_EXTEUCLID_C +# define BN_MP_FREAD_C +# define BN_MP_FROM_SBIN_C +# define BN_MP_FROM_UBIN_C +# define BN_MP_FWRITE_C +# define BN_MP_GCD_C +# define BN_MP_GET_DOUBLE_C +# define BN_MP_GET_I32_C +# define BN_MP_GET_I64_C +# define BN_MP_GET_L_C +# define BN_MP_GET_LL_C +# define BN_MP_GET_MAG_U32_C +# define BN_MP_GET_MAG_U64_C +# define BN_MP_GET_MAG_UL_C +# define BN_MP_GET_MAG_ULL_C +# define BN_MP_GROW_C +# define BN_MP_INCR_C +# define BN_MP_INIT_C +# define BN_MP_INIT_COPY_C +# define BN_MP_INIT_I32_C +# define BN_MP_INIT_I64_C +# define BN_MP_INIT_L_C +# define BN_MP_INIT_LL_C +# define BN_MP_INIT_MULTI_C +# define BN_MP_INIT_SET_C +# define BN_MP_INIT_SIZE_C +# define BN_MP_INIT_U32_C +# define BN_MP_INIT_U64_C +# define BN_MP_INIT_UL_C +# define BN_MP_INIT_ULL_C +# define BN_MP_INVMOD_C +# define BN_MP_IS_SQUARE_C +# define BN_MP_ISEVEN_C +# define BN_MP_ISODD_C +# define BN_MP_KRONECKER_C +# define BN_MP_LCM_C +# define BN_MP_LOG_U32_C +# define BN_MP_LSHD_C +# define BN_MP_MOD_C +# define BN_MP_MOD_2D_C +# define BN_MP_MOD_D_C +# define BN_MP_MONTGOMERY_CALC_NORMALIZATION_C +# define BN_MP_MONTGOMERY_REDUCE_C +# define BN_MP_MONTGOMERY_SETUP_C +# define BN_MP_MUL_C +# define BN_MP_MUL_2_C +# define BN_MP_MUL_2D_C +# define BN_MP_MUL_D_C +# define BN_MP_MULMOD_C +# define BN_MP_NEG_C +# define BN_MP_OR_C +# define BN_MP_PACK_C +# define BN_MP_PACK_COUNT_C +# define BN_MP_PRIME_FERMAT_C +# define BN_MP_PRIME_FROBENIUS_UNDERWOOD_C +# define BN_MP_PRIME_IS_PRIME_C +# define BN_MP_PRIME_MILLER_RABIN_C +# define BN_MP_PRIME_NEXT_PRIME_C +# define BN_MP_PRIME_RABIN_MILLER_TRIALS_C +# define BN_MP_PRIME_RAND_C +# define BN_MP_PRIME_STRONG_LUCAS_SELFRIDGE_C +# define BN_MP_RADIX_SIZE_C +# define BN_MP_RADIX_SMAP_C +# define BN_MP_RAND_C +# define BN_MP_READ_RADIX_C +# define BN_MP_REDUCE_C +# define BN_MP_REDUCE_2K_C +# define BN_MP_REDUCE_2K_L_C +# define BN_MP_REDUCE_2K_SETUP_C +# define BN_MP_REDUCE_2K_SETUP_L_C +# define BN_MP_REDUCE_IS_2K_C +# define BN_MP_REDUCE_IS_2K_L_C +# define BN_MP_REDUCE_SETUP_C +# define BN_MP_ROOT_U32_C +# define BN_MP_RSHD_C +# define BN_MP_SBIN_SIZE_C +# define BN_MP_SET_C +# define BN_MP_SET_DOUBLE_C +# define BN_MP_SET_I32_C +# define BN_MP_SET_I64_C +# define BN_MP_SET_L_C +# define BN_MP_SET_LL_C +# define BN_MP_SET_U32_C +# define BN_MP_SET_U64_C +# define BN_MP_SET_UL_C +# define BN_MP_SET_ULL_C +# define BN_MP_SHRINK_C +# define BN_MP_SIGNED_RSH_C +# define BN_MP_SQR_C +# define BN_MP_SQRMOD_C +# define BN_MP_SQRT_C +# define BN_MP_SQRTMOD_PRIME_C +# define BN_MP_SUB_C +# define BN_MP_SUB_D_C +# define BN_MP_SUBMOD_C +# define BN_MP_TO_RADIX_C +# define BN_MP_TO_SBIN_C +# define BN_MP_TO_UBIN_C +# define BN_MP_UBIN_SIZE_C +# define BN_MP_UNPACK_C +# define BN_MP_XOR_C +# define BN_MP_ZERO_C +# define BN_PRIME_TAB_C +# define BN_S_MP_ADD_C +# define BN_S_MP_BALANCE_MUL_C +# define BN_S_MP_EXPTMOD_C +# define BN_S_MP_EXPTMOD_FAST_C +# define BN_S_MP_GET_BIT_C +# define BN_S_MP_INVMOD_FAST_C +# define BN_S_MP_INVMOD_SLOW_C +# define BN_S_MP_KARATSUBA_MUL_C +# define BN_S_MP_KARATSUBA_SQR_C +# define BN_S_MP_MONTGOMERY_REDUCE_FAST_C +# define BN_S_MP_MUL_DIGS_C +# define BN_S_MP_MUL_DIGS_FAST_C +# define BN_S_MP_MUL_HIGH_DIGS_C +# define BN_S_MP_MUL_HIGH_DIGS_FAST_C +# define BN_S_MP_PRIME_IS_DIVISIBLE_C +# define BN_S_MP_RAND_JENKINS_C +# define BN_S_MP_RAND_PLATFORM_C +# define BN_S_MP_REVERSE_C +# define BN_S_MP_SQR_C +# define BN_S_MP_SQR_FAST_C +# define BN_S_MP_SUB_C +# define BN_S_MP_TOOM_MUL_C +# define BN_S_MP_TOOM_SQR_C +#endif +#endif +#if defined(BN_CUTOFFS_C) +#endif + +#if defined(BN_DEPRECATED_C) +# define BN_FAST_MP_INVMOD_C +# define BN_FAST_MP_MONTGOMERY_REDUCE_C +# define BN_FAST_S_MP_MUL_DIGS_C +# define BN_FAST_S_MP_MUL_HIGH_DIGS_C +# define BN_FAST_S_MP_SQR_C +# define BN_MP_AND_C +# define BN_MP_BALANCE_MUL_C +# define BN_MP_CMP_D_C +# define BN_MP_EXPORT_C +# define BN_MP_EXPTMOD_FAST_C +# define BN_MP_EXPT_D_C +# define BN_MP_EXPT_D_EX_C +# define BN_MP_EXPT_U32_C +# define BN_MP_FROM_SBIN_C +# define BN_MP_FROM_UBIN_C +# define BN_MP_GET_BIT_C +# define BN_MP_GET_INT_C +# define BN_MP_GET_LONG_C +# define BN_MP_GET_LONG_LONG_C +# define BN_MP_GET_MAG_U32_C +# define BN_MP_GET_MAG_ULL_C +# define BN_MP_GET_MAG_UL_C +# define BN_MP_IMPORT_C +# define BN_MP_INIT_SET_INT_C +# define BN_MP_INIT_U32_C +# define BN_MP_INVMOD_SLOW_C +# define BN_MP_JACOBI_C +# define BN_MP_KARATSUBA_MUL_C +# define BN_MP_KARATSUBA_SQR_C +# define BN_MP_KRONECKER_C +# define BN_MP_N_ROOT_C +# define BN_MP_N_ROOT_EX_C +# define BN_MP_OR_C +# define BN_MP_PACK_C +# define BN_MP_PRIME_IS_DIVISIBLE_C +# define BN_MP_PRIME_RANDOM_EX_C +# define BN_MP_RAND_DIGIT_C +# define BN_MP_READ_SIGNED_BIN_C +# define BN_MP_READ_UNSIGNED_BIN_C +# define BN_MP_ROOT_U32_C +# define BN_MP_SBIN_SIZE_C +# define BN_MP_SET_INT_C +# define BN_MP_SET_LONG_C +# define BN_MP_SET_LONG_LONG_C +# define BN_MP_SET_U32_C +# define BN_MP_SET_U64_C +# define BN_MP_SIGNED_BIN_SIZE_C +# define BN_MP_SIGNED_RSH_C +# define BN_MP_TC_AND_C +# define BN_MP_TC_DIV_2D_C +# define BN_MP_TC_OR_C +# define BN_MP_TC_XOR_C +# define BN_MP_TOOM_MUL_C +# define BN_MP_TOOM_SQR_C +# define BN_MP_TORADIX_C +# define BN_MP_TORADIX_N_C +# define BN_MP_TO_RADIX_C +# define BN_MP_TO_SBIN_C +# define BN_MP_TO_SIGNED_BIN_C +# define BN_MP_TO_SIGNED_BIN_N_C +# define BN_MP_TO_UBIN_C +# define BN_MP_TO_UNSIGNED_BIN_C +# define BN_MP_TO_UNSIGNED_BIN_N_C +# define BN_MP_UBIN_SIZE_C +# define BN_MP_UNPACK_C +# define BN_MP_UNSIGNED_BIN_SIZE_C +# define BN_MP_XOR_C +# define BN_S_MP_BALANCE_MUL_C +# define BN_S_MP_EXPTMOD_FAST_C +# define BN_S_MP_GET_BIT_C +# define BN_S_MP_INVMOD_FAST_C +# define BN_S_MP_INVMOD_SLOW_C +# define BN_S_MP_KARATSUBA_MUL_C +# define BN_S_MP_KARATSUBA_SQR_C +# define BN_S_MP_MONTGOMERY_REDUCE_FAST_C +# define BN_S_MP_MUL_DIGS_FAST_C +# define BN_S_MP_MUL_HIGH_DIGS_FAST_C +# define BN_S_MP_PRIME_IS_DIVISIBLE_C +# define BN_S_MP_PRIME_RANDOM_EX_C +# define BN_S_MP_RAND_SOURCE_C +# define BN_S_MP_REVERSE_C +# define BN_S_MP_SQR_FAST_C +# define BN_S_MP_TOOM_MUL_C +# define BN_S_MP_TOOM_SQR_C #endif #if defined(BN_MP_2EXPT_C) - #define BN_MP_ZERO_C - #define BN_MP_GROW_C +# define BN_MP_GROW_C +# define BN_MP_ZERO_C #endif #if defined(BN_MP_ABS_C) - #define BN_MP_COPY_C +# define BN_MP_COPY_C #endif #if defined(BN_MP_ADD_C) - #define BN_S_MP_ADD_C - #define BN_MP_CMP_MAG_C - #define BN_S_MP_SUB_C +# define BN_MP_CMP_MAG_C +# define BN_S_MP_ADD_C +# define BN_S_MP_SUB_C #endif #if defined(BN_MP_ADD_D_C) - #define BN_MP_GROW_C - #define BN_MP_SUB_D_C - #define BN_MP_CLAMP_C +# define BN_MP_CLAMP_C +# define BN_MP_GROW_C +# define BN_MP_SUB_D_C #endif #if defined(BN_MP_ADDMOD_C) - #define BN_MP_INIT_C - #define BN_MP_ADD_C - #define BN_MP_CLEAR_C - #define BN_MP_MOD_C +# define BN_MP_ADD_C +# define BN_MP_CLEAR_C +# define BN_MP_INIT_C +# define BN_MP_MOD_C #endif #if defined(BN_MP_AND_C) - #define BN_MP_INIT_COPY_C - #define BN_MP_CLAMP_C - #define BN_MP_EXCH_C - #define BN_MP_CLEAR_C +# define BN_MP_CLAMP_C +# define BN_MP_GROW_C #endif #if defined(BN_MP_CLAMP_C) @@ -218,11 +300,11 @@ #endif #if defined(BN_MP_CLEAR_MULTI_C) - #define BN_MP_CLEAR_C +# define BN_MP_CLEAR_C #endif #if defined(BN_MP_CMP_C) - #define BN_MP_CMP_MAG_C +# define BN_MP_CMP_MAG_C #endif #if defined(BN_MP_CMP_D_C) @@ -232,771 +314,1006 @@ #endif #if defined(BN_MP_CNT_LSB_C) - #define BN_MP_ISZERO_C +#endif + +#if defined(BN_MP_COMPLEMENT_C) +# define BN_MP_NEG_C +# define BN_MP_SUB_D_C #endif #if defined(BN_MP_COPY_C) - #define BN_MP_GROW_C +# define BN_MP_GROW_C #endif #if defined(BN_MP_COUNT_BITS_C) #endif +#if defined(BN_MP_DECR_C) +# define BN_MP_INCR_C +# define BN_MP_SET_C +# define BN_MP_SUB_D_C +# define BN_MP_ZERO_C +#endif + #if defined(BN_MP_DIV_C) - #define BN_MP_ISZERO_C - #define BN_MP_CMP_MAG_C - #define BN_MP_COPY_C - #define BN_MP_ZERO_C - #define BN_MP_INIT_MULTI_C - #define BN_MP_SET_C - #define BN_MP_COUNT_BITS_C - #define BN_MP_ABS_C - #define BN_MP_MUL_2D_C - #define BN_MP_CMP_C - #define BN_MP_SUB_C - #define BN_MP_ADD_C - #define BN_MP_DIV_2D_C - #define BN_MP_EXCH_C - #define BN_MP_CLEAR_MULTI_C - #define BN_MP_INIT_SIZE_C - #define BN_MP_INIT_C - #define BN_MP_INIT_COPY_C - #define BN_MP_LSHD_C - #define BN_MP_RSHD_C - #define BN_MP_MUL_D_C - #define BN_MP_CLAMP_C - #define BN_MP_CLEAR_C +# define BN_MP_ADD_C +# define BN_MP_CLAMP_C +# define BN_MP_CLEAR_C +# define BN_MP_CMP_C +# define BN_MP_CMP_MAG_C +# define BN_MP_COPY_C +# define BN_MP_COUNT_BITS_C +# define BN_MP_DIV_2D_C +# define BN_MP_EXCH_C +# define BN_MP_INIT_C +# define BN_MP_INIT_COPY_C +# define BN_MP_INIT_SIZE_C +# define BN_MP_LSHD_C +# define BN_MP_MUL_2D_C +# define BN_MP_MUL_D_C +# define BN_MP_RSHD_C +# define BN_MP_SUB_C +# define BN_MP_ZERO_C #endif #if defined(BN_MP_DIV_2_C) - #define BN_MP_GROW_C - #define BN_MP_CLAMP_C +# define BN_MP_CLAMP_C +# define BN_MP_GROW_C #endif #if defined(BN_MP_DIV_2D_C) - #define BN_MP_COPY_C - #define BN_MP_ZERO_C - #define BN_MP_INIT_C - #define BN_MP_MOD_2D_C - #define BN_MP_CLEAR_C - #define BN_MP_RSHD_C - #define BN_MP_CLAMP_C - #define BN_MP_EXCH_C +# define BN_MP_CLAMP_C +# define BN_MP_COPY_C +# define BN_MP_MOD_2D_C +# define BN_MP_RSHD_C +# define BN_MP_ZERO_C #endif #if defined(BN_MP_DIV_3_C) - #define BN_MP_INIT_SIZE_C - #define BN_MP_CLAMP_C - #define BN_MP_EXCH_C - #define BN_MP_CLEAR_C +# define BN_MP_CLAMP_C +# define BN_MP_CLEAR_C +# define BN_MP_EXCH_C +# define BN_MP_INIT_SIZE_C #endif #if defined(BN_MP_DIV_D_C) - #define BN_MP_ISZERO_C - #define BN_MP_COPY_C - #define BN_MP_DIV_2D_C - #define BN_MP_DIV_3_C - #define BN_MP_INIT_SIZE_C - #define BN_MP_CLAMP_C - #define BN_MP_EXCH_C - #define BN_MP_CLEAR_C +# define BN_MP_CLAMP_C +# define BN_MP_CLEAR_C +# define BN_MP_COPY_C +# define BN_MP_DIV_2D_C +# define BN_MP_DIV_3_C +# define BN_MP_EXCH_C +# define BN_MP_INIT_SIZE_C #endif #if defined(BN_MP_DR_IS_MODULUS_C) #endif #if defined(BN_MP_DR_REDUCE_C) - #define BN_MP_GROW_C - #define BN_MP_CLAMP_C - #define BN_MP_CMP_MAG_C - #define BN_S_MP_SUB_C +# define BN_MP_CLAMP_C +# define BN_MP_CMP_MAG_C +# define BN_MP_GROW_C +# define BN_S_MP_SUB_C #endif #if defined(BN_MP_DR_SETUP_C) #endif +#if defined(BN_MP_ERROR_TO_STRING_C) +#endif + #if defined(BN_MP_EXCH_C) #endif -#if defined(BN_MP_EXPT_D_C) - #define BN_MP_INIT_COPY_C - #define BN_MP_SET_C - #define BN_MP_SQR_C - #define BN_MP_CLEAR_C - #define BN_MP_MUL_C +#if defined(BN_MP_EXPT_U32_C) +# define BN_MP_CLEAR_C +# define BN_MP_INIT_COPY_C +# define BN_MP_MUL_C +# define BN_MP_SET_C +# define BN_MP_SQR_C #endif #if defined(BN_MP_EXPTMOD_C) - #define BN_MP_INIT_C - #define BN_MP_INVMOD_C - #define BN_MP_CLEAR_C - #define BN_MP_ABS_C - #define BN_MP_CLEAR_MULTI_C - #define BN_MP_REDUCE_IS_2K_L_C - #define BN_S_MP_EXPTMOD_C - #define BN_MP_DR_IS_MODULUS_C - #define BN_MP_REDUCE_IS_2K_C - #define BN_MP_ISODD_C - #define BN_MP_EXPTMOD_FAST_C -#endif - -#if defined(BN_MP_EXPTMOD_FAST_C) - #define BN_MP_COUNT_BITS_C - #define BN_MP_INIT_C - #define BN_MP_CLEAR_C - #define BN_MP_MONTGOMERY_SETUP_C - #define BN_FAST_MP_MONTGOMERY_REDUCE_C - #define BN_MP_MONTGOMERY_REDUCE_C - #define BN_MP_DR_SETUP_C - #define BN_MP_DR_REDUCE_C - #define BN_MP_REDUCE_2K_SETUP_C - #define BN_MP_REDUCE_2K_C - #define BN_MP_MONTGOMERY_CALC_NORMALIZATION_C - #define BN_MP_MULMOD_C - #define BN_MP_SET_C - #define BN_MP_MOD_C - #define BN_MP_COPY_C - #define BN_MP_SQR_C - #define BN_MP_MUL_C - #define BN_MP_EXCH_C +# define BN_MP_ABS_C +# define BN_MP_CLEAR_MULTI_C +# define BN_MP_DR_IS_MODULUS_C +# define BN_MP_INIT_MULTI_C +# define BN_MP_INVMOD_C +# define BN_MP_REDUCE_IS_2K_C +# define BN_MP_REDUCE_IS_2K_L_C +# define BN_S_MP_EXPTMOD_C +# define BN_S_MP_EXPTMOD_FAST_C #endif #if defined(BN_MP_EXTEUCLID_C) - #define BN_MP_INIT_MULTI_C - #define BN_MP_SET_C - #define BN_MP_COPY_C - #define BN_MP_ISZERO_C - #define BN_MP_DIV_C - #define BN_MP_MUL_C - #define BN_MP_SUB_C - #define BN_MP_NEG_C - #define BN_MP_EXCH_C - #define BN_MP_CLEAR_MULTI_C +# define BN_MP_CLEAR_MULTI_C +# define BN_MP_COPY_C +# define BN_MP_DIV_C +# define BN_MP_EXCH_C +# define BN_MP_INIT_MULTI_C +# define BN_MP_MUL_C +# define BN_MP_NEG_C +# define BN_MP_SET_C +# define BN_MP_SUB_C #endif #if defined(BN_MP_FREAD_C) - #define BN_MP_ZERO_C - #define BN_MP_S_RMAP_C - #define BN_MP_MUL_D_C - #define BN_MP_ADD_D_C - #define BN_MP_CMP_D_C +# define BN_MP_ADD_D_C +# define BN_MP_MUL_D_C +# define BN_MP_ZERO_C +#endif + +#if defined(BN_MP_FROM_SBIN_C) +# define BN_MP_FROM_UBIN_C +#endif + +#if defined(BN_MP_FROM_UBIN_C) +# define BN_MP_CLAMP_C +# define BN_MP_GROW_C +# define BN_MP_MUL_2D_C +# define BN_MP_ZERO_C #endif #if defined(BN_MP_FWRITE_C) - #define BN_MP_RADIX_SIZE_C - #define BN_MP_TORADIX_C +# define BN_MP_RADIX_SIZE_C +# define BN_MP_TO_RADIX_C #endif #if defined(BN_MP_GCD_C) - #define BN_MP_ISZERO_C - #define BN_MP_ABS_C - #define BN_MP_ZERO_C - #define BN_MP_INIT_COPY_C - #define BN_MP_CNT_LSB_C - #define BN_MP_DIV_2D_C - #define BN_MP_CMP_MAG_C - #define BN_MP_EXCH_C - #define BN_S_MP_SUB_C - #define BN_MP_MUL_2D_C - #define BN_MP_CLEAR_C +# define BN_MP_ABS_C +# define BN_MP_CLEAR_C +# define BN_MP_CMP_MAG_C +# define BN_MP_CNT_LSB_C +# define BN_MP_DIV_2D_C +# define BN_MP_EXCH_C +# define BN_MP_INIT_COPY_C +# define BN_MP_MUL_2D_C +# define BN_S_MP_SUB_C +#endif + +#if defined(BN_MP_GET_DOUBLE_C) +#endif + +#if defined(BN_MP_GET_I32_C) +# define BN_MP_GET_MAG_U32_C +#endif + +#if defined(BN_MP_GET_I64_C) +# define BN_MP_GET_MAG_U64_C +#endif + +#if defined(BN_MP_GET_L_C) +# define BN_MP_GET_MAG_UL_C +#endif + +#if defined(BN_MP_GET_LL_C) +# define BN_MP_GET_MAG_ULL_C +#endif + +#if defined(BN_MP_GET_MAG_U32_C) +#endif + +#if defined(BN_MP_GET_MAG_U64_C) +#endif + +#if defined(BN_MP_GET_MAG_UL_C) #endif -#if defined(BN_MP_GET_INT_C) +#if defined(BN_MP_GET_MAG_ULL_C) #endif #if defined(BN_MP_GROW_C) #endif +#if defined(BN_MP_INCR_C) +# define BN_MP_ADD_D_C +# define BN_MP_DECR_C +# define BN_MP_SET_C +#endif + #if defined(BN_MP_INIT_C) #endif #if defined(BN_MP_INIT_COPY_C) - #define BN_MP_COPY_C +# define BN_MP_CLEAR_C +# define BN_MP_COPY_C +# define BN_MP_INIT_SIZE_C +#endif + +#if defined(BN_MP_INIT_I32_C) +# define BN_MP_INIT_C +# define BN_MP_SET_I32_C +#endif + +#if defined(BN_MP_INIT_I64_C) +# define BN_MP_INIT_C +# define BN_MP_SET_I64_C +#endif + +#if defined(BN_MP_INIT_L_C) +# define BN_MP_INIT_C +# define BN_MP_SET_L_C +#endif + +#if defined(BN_MP_INIT_LL_C) +# define BN_MP_INIT_C +# define BN_MP_SET_LL_C #endif #if defined(BN_MP_INIT_MULTI_C) - #define BN_MP_ERR_C - #define BN_MP_INIT_C - #define BN_MP_CLEAR_C +# define BN_MP_CLEAR_C +# define BN_MP_INIT_C #endif #if defined(BN_MP_INIT_SET_C) - #define BN_MP_INIT_C - #define BN_MP_SET_C +# define BN_MP_INIT_C +# define BN_MP_SET_C #endif -#if defined(BN_MP_INIT_SET_INT_C) - #define BN_MP_INIT_C - #define BN_MP_SET_INT_C +#if defined(BN_MP_INIT_SIZE_C) #endif -#if defined(BN_MP_INIT_SIZE_C) - #define BN_MP_INIT_C +#if defined(BN_MP_INIT_U32_C) +# define BN_MP_INIT_C +# define BN_MP_SET_U32_C +#endif + +#if defined(BN_MP_INIT_U64_C) +# define BN_MP_INIT_C +# define BN_MP_SET_U64_C +#endif + +#if defined(BN_MP_INIT_UL_C) +# define BN_MP_INIT_C +# define BN_MP_SET_UL_C +#endif + +#if defined(BN_MP_INIT_ULL_C) +# define BN_MP_INIT_C +# define BN_MP_SET_ULL_C #endif #if defined(BN_MP_INVMOD_C) - #define BN_MP_ISZERO_C - #define BN_MP_ISODD_C - #define BN_FAST_MP_INVMOD_C - #define BN_MP_INVMOD_SLOW_C -#endif - -#if defined(BN_MP_INVMOD_SLOW_C) - #define BN_MP_ISZERO_C - #define BN_MP_INIT_MULTI_C - #define BN_MP_MOD_C - #define BN_MP_COPY_C - #define BN_MP_ISEVEN_C - #define BN_MP_SET_C - #define BN_MP_DIV_2_C - #define BN_MP_ISODD_C - #define BN_MP_ADD_C - #define BN_MP_SUB_C - #define BN_MP_CMP_C - #define BN_MP_CMP_D_C - #define BN_MP_CMP_MAG_C - #define BN_MP_EXCH_C - #define BN_MP_CLEAR_MULTI_C +# define BN_MP_CMP_D_C +# define BN_S_MP_INVMOD_FAST_C +# define BN_S_MP_INVMOD_SLOW_C #endif #if defined(BN_MP_IS_SQUARE_C) - #define BN_MP_MOD_D_C - #define BN_MP_INIT_SET_INT_C - #define BN_MP_MOD_C - #define BN_MP_GET_INT_C - #define BN_MP_SQRT_C - #define BN_MP_SQR_C - #define BN_MP_CMP_MAG_C - #define BN_MP_CLEAR_C -#endif - -#if defined(BN_MP_JACOBI_C) - #define BN_MP_CMP_D_C - #define BN_MP_ISZERO_C - #define BN_MP_INIT_COPY_C - #define BN_MP_CNT_LSB_C - #define BN_MP_DIV_2D_C - #define BN_MP_MOD_C - #define BN_MP_CLEAR_C -#endif - -#if defined(BN_MP_KARATSUBA_MUL_C) - #define BN_MP_MUL_C - #define BN_MP_INIT_SIZE_C - #define BN_MP_CLAMP_C - #define BN_MP_SUB_C - #define BN_MP_ADD_C - #define BN_MP_LSHD_C - #define BN_MP_CLEAR_C -#endif - -#if defined(BN_MP_KARATSUBA_SQR_C) - #define BN_MP_INIT_SIZE_C - #define BN_MP_CLAMP_C - #define BN_MP_SQR_C - #define BN_MP_SUB_C - #define BN_S_MP_ADD_C - #define BN_MP_LSHD_C - #define BN_MP_ADD_C - #define BN_MP_CLEAR_C +# define BN_MP_CLEAR_C +# define BN_MP_CMP_MAG_C +# define BN_MP_GET_I32_C +# define BN_MP_INIT_U32_C +# define BN_MP_MOD_C +# define BN_MP_MOD_D_C +# define BN_MP_SQRT_C +# define BN_MP_SQR_C +#endif + +#if defined(BN_MP_ISEVEN_C) +#endif + +#if defined(BN_MP_ISODD_C) +#endif + +#if defined(BN_MP_KRONECKER_C) +# define BN_MP_CLEAR_C +# define BN_MP_CMP_D_C +# define BN_MP_CNT_LSB_C +# define BN_MP_COPY_C +# define BN_MP_DIV_2D_C +# define BN_MP_INIT_C +# define BN_MP_INIT_COPY_C +# define BN_MP_MOD_C #endif #if defined(BN_MP_LCM_C) - #define BN_MP_INIT_MULTI_C - #define BN_MP_GCD_C - #define BN_MP_CMP_MAG_C - #define BN_MP_DIV_C - #define BN_MP_MUL_C - #define BN_MP_CLEAR_MULTI_C +# define BN_MP_CLEAR_MULTI_C +# define BN_MP_CMP_MAG_C +# define BN_MP_DIV_C +# define BN_MP_GCD_C +# define BN_MP_INIT_MULTI_C +# define BN_MP_MUL_C +#endif + +#if defined(BN_MP_LOG_U32_C) +# define BN_MP_CLEAR_MULTI_C +# define BN_MP_CMP_C +# define BN_MP_CMP_D_C +# define BN_MP_COPY_C +# define BN_MP_COUNT_BITS_C +# define BN_MP_EXCH_C +# define BN_MP_EXPT_U32_C +# define BN_MP_INIT_MULTI_C +# define BN_MP_MUL_C +# define BN_MP_SET_C +# define BN_MP_SQR_C #endif #if defined(BN_MP_LSHD_C) - #define BN_MP_GROW_C - #define BN_MP_RSHD_C +# define BN_MP_GROW_C #endif #if defined(BN_MP_MOD_C) - #define BN_MP_INIT_C - #define BN_MP_DIV_C - #define BN_MP_CLEAR_C - #define BN_MP_ADD_C - #define BN_MP_EXCH_C +# define BN_MP_ADD_C +# define BN_MP_CLEAR_C +# define BN_MP_DIV_C +# define BN_MP_EXCH_C +# define BN_MP_INIT_SIZE_C #endif #if defined(BN_MP_MOD_2D_C) - #define BN_MP_ZERO_C - #define BN_MP_COPY_C - #define BN_MP_CLAMP_C +# define BN_MP_CLAMP_C +# define BN_MP_COPY_C +# define BN_MP_ZERO_C #endif #if defined(BN_MP_MOD_D_C) - #define BN_MP_DIV_D_C +# define BN_MP_DIV_D_C #endif #if defined(BN_MP_MONTGOMERY_CALC_NORMALIZATION_C) - #define BN_MP_COUNT_BITS_C - #define BN_MP_2EXPT_C - #define BN_MP_SET_C - #define BN_MP_MUL_2_C - #define BN_MP_CMP_MAG_C - #define BN_S_MP_SUB_C +# define BN_MP_2EXPT_C +# define BN_MP_CMP_MAG_C +# define BN_MP_COUNT_BITS_C +# define BN_MP_MUL_2_C +# define BN_MP_SET_C +# define BN_S_MP_SUB_C #endif #if defined(BN_MP_MONTGOMERY_REDUCE_C) - #define BN_FAST_MP_MONTGOMERY_REDUCE_C - #define BN_MP_GROW_C - #define BN_MP_CLAMP_C - #define BN_MP_RSHD_C - #define BN_MP_CMP_MAG_C - #define BN_S_MP_SUB_C +# define BN_MP_CLAMP_C +# define BN_MP_CMP_MAG_C +# define BN_MP_GROW_C +# define BN_MP_RSHD_C +# define BN_S_MP_MONTGOMERY_REDUCE_FAST_C +# define BN_S_MP_SUB_C #endif #if defined(BN_MP_MONTGOMERY_SETUP_C) #endif #if defined(BN_MP_MUL_C) - #define BN_MP_TOOM_MUL_C - #define BN_MP_KARATSUBA_MUL_C - #define BN_FAST_S_MP_MUL_DIGS_C - #define BN_S_MP_MUL_C - #define BN_S_MP_MUL_DIGS_C +# define BN_S_MP_BALANCE_MUL_C +# define BN_S_MP_KARATSUBA_MUL_C +# define BN_S_MP_MUL_DIGS_C +# define BN_S_MP_MUL_DIGS_FAST_C +# define BN_S_MP_TOOM_MUL_C #endif #if defined(BN_MP_MUL_2_C) - #define BN_MP_GROW_C +# define BN_MP_GROW_C #endif #if defined(BN_MP_MUL_2D_C) - #define BN_MP_COPY_C - #define BN_MP_GROW_C - #define BN_MP_LSHD_C - #define BN_MP_CLAMP_C +# define BN_MP_CLAMP_C +# define BN_MP_COPY_C +# define BN_MP_GROW_C +# define BN_MP_LSHD_C #endif #if defined(BN_MP_MUL_D_C) - #define BN_MP_GROW_C - #define BN_MP_CLAMP_C +# define BN_MP_CLAMP_C +# define BN_MP_GROW_C #endif #if defined(BN_MP_MULMOD_C) - #define BN_MP_INIT_C - #define BN_MP_MUL_C - #define BN_MP_CLEAR_C - #define BN_MP_MOD_C -#endif - -#if defined(BN_MP_N_ROOT_C) - #define BN_MP_INIT_C - #define BN_MP_SET_C - #define BN_MP_COPY_C - #define BN_MP_EXPT_D_C - #define BN_MP_MUL_C - #define BN_MP_SUB_C - #define BN_MP_MUL_D_C - #define BN_MP_DIV_C - #define BN_MP_CMP_C - #define BN_MP_SUB_D_C - #define BN_MP_EXCH_C - #define BN_MP_CLEAR_C +# define BN_MP_CLEAR_C +# define BN_MP_INIT_SIZE_C +# define BN_MP_MOD_C +# define BN_MP_MUL_C #endif #if defined(BN_MP_NEG_C) - #define BN_MP_COPY_C - #define BN_MP_ISZERO_C +# define BN_MP_COPY_C #endif #if defined(BN_MP_OR_C) - #define BN_MP_INIT_COPY_C - #define BN_MP_CLAMP_C - #define BN_MP_EXCH_C - #define BN_MP_CLEAR_C +# define BN_MP_CLAMP_C +# define BN_MP_GROW_C #endif -#if defined(BN_MP_PRIME_FERMAT_C) - #define BN_MP_CMP_D_C - #define BN_MP_INIT_C - #define BN_MP_EXPTMOD_C - #define BN_MP_CMP_C - #define BN_MP_CLEAR_C +#if defined(BN_MP_PACK_C) +# define BN_MP_CLEAR_C +# define BN_MP_DIV_2D_C +# define BN_MP_INIT_COPY_C +# define BN_MP_PACK_COUNT_C #endif -#if defined(BN_MP_PRIME_IS_DIVISIBLE_C) - #define BN_MP_MOD_D_C +#if defined(BN_MP_PACK_COUNT_C) +# define BN_MP_COUNT_BITS_C +#endif + +#if defined(BN_MP_PRIME_FERMAT_C) +# define BN_MP_CLEAR_C +# define BN_MP_CMP_C +# define BN_MP_CMP_D_C +# define BN_MP_EXPTMOD_C +# define BN_MP_INIT_C +#endif + +#if defined(BN_MP_PRIME_FROBENIUS_UNDERWOOD_C) +# define BN_MP_ADD_C +# define BN_MP_ADD_D_C +# define BN_MP_CLEAR_MULTI_C +# define BN_MP_CMP_C +# define BN_MP_COUNT_BITS_C +# define BN_MP_EXCH_C +# define BN_MP_GCD_C +# define BN_MP_INIT_MULTI_C +# define BN_MP_KRONECKER_C +# define BN_MP_MOD_C +# define BN_MP_MUL_2_C +# define BN_MP_MUL_C +# define BN_MP_MUL_D_C +# define BN_MP_SET_C +# define BN_MP_SET_U32_C +# define BN_MP_SQR_C +# define BN_MP_SUB_C +# define BN_MP_SUB_D_C +# define BN_S_MP_GET_BIT_C #endif #if defined(BN_MP_PRIME_IS_PRIME_C) - #define BN_MP_CMP_D_C - #define BN_MP_PRIME_IS_DIVISIBLE_C - #define BN_MP_INIT_C - #define BN_MP_SET_C - #define BN_MP_PRIME_MILLER_RABIN_C - #define BN_MP_CLEAR_C +# define BN_MP_CLEAR_C +# define BN_MP_CMP_C +# define BN_MP_CMP_D_C +# define BN_MP_COUNT_BITS_C +# define BN_MP_DIV_2D_C +# define BN_MP_INIT_SET_C +# define BN_MP_IS_SQUARE_C +# define BN_MP_PRIME_MILLER_RABIN_C +# define BN_MP_PRIME_STRONG_LUCAS_SELFRIDGE_C +# define BN_MP_RAND_C +# define BN_MP_READ_RADIX_C +# define BN_MP_SET_C +# define BN_S_MP_PRIME_IS_DIVISIBLE_C #endif #if defined(BN_MP_PRIME_MILLER_RABIN_C) - #define BN_MP_CMP_D_C - #define BN_MP_INIT_COPY_C - #define BN_MP_SUB_D_C - #define BN_MP_CNT_LSB_C - #define BN_MP_DIV_2D_C - #define BN_MP_EXPTMOD_C - #define BN_MP_CMP_C - #define BN_MP_SQRMOD_C - #define BN_MP_CLEAR_C +# define BN_MP_CLEAR_C +# define BN_MP_CMP_C +# define BN_MP_CMP_D_C +# define BN_MP_CNT_LSB_C +# define BN_MP_DIV_2D_C +# define BN_MP_EXPTMOD_C +# define BN_MP_INIT_C +# define BN_MP_INIT_COPY_C +# define BN_MP_SQRMOD_C +# define BN_MP_SUB_D_C #endif #if defined(BN_MP_PRIME_NEXT_PRIME_C) - #define BN_MP_CMP_D_C - #define BN_MP_SET_C - #define BN_MP_SUB_D_C - #define BN_MP_ISEVEN_C - #define BN_MP_MOD_D_C - #define BN_MP_INIT_C - #define BN_MP_ADD_D_C - #define BN_MP_PRIME_MILLER_RABIN_C - #define BN_MP_CLEAR_C +# define BN_MP_ADD_D_C +# define BN_MP_CLEAR_C +# define BN_MP_CMP_D_C +# define BN_MP_INIT_C +# define BN_MP_MOD_D_C +# define BN_MP_PRIME_IS_PRIME_C +# define BN_MP_SET_C +# define BN_MP_SUB_D_C #endif #if defined(BN_MP_PRIME_RABIN_MILLER_TRIALS_C) #endif -#if defined(BN_MP_PRIME_RANDOM_EX_C) - #define BN_MP_READ_UNSIGNED_BIN_C - #define BN_MP_PRIME_IS_PRIME_C - #define BN_MP_SUB_D_C - #define BN_MP_DIV_2_C - #define BN_MP_MUL_2_C - #define BN_MP_ADD_D_C +#if defined(BN_MP_PRIME_RAND_C) +# define BN_MP_ADD_D_C +# define BN_MP_DIV_2_C +# define BN_MP_FROM_UBIN_C +# define BN_MP_MUL_2_C +# define BN_MP_PRIME_IS_PRIME_C +# define BN_MP_SUB_D_C +# define BN_S_MP_PRIME_RANDOM_EX_C +# define BN_S_MP_RAND_CB_C +# define BN_S_MP_RAND_SOURCE_C +#endif + +#if defined(BN_MP_PRIME_STRONG_LUCAS_SELFRIDGE_C) +# define BN_MP_ADD_C +# define BN_MP_ADD_D_C +# define BN_MP_CLEAR_C +# define BN_MP_CLEAR_MULTI_C +# define BN_MP_CMP_C +# define BN_MP_CMP_D_C +# define BN_MP_CNT_LSB_C +# define BN_MP_COUNT_BITS_C +# define BN_MP_DIV_2D_C +# define BN_MP_DIV_2_C +# define BN_MP_GCD_C +# define BN_MP_INIT_C +# define BN_MP_INIT_MULTI_C +# define BN_MP_KRONECKER_C +# define BN_MP_MOD_C +# define BN_MP_MUL_2_C +# define BN_MP_MUL_C +# define BN_MP_SET_C +# define BN_MP_SET_I32_C +# define BN_MP_SET_U32_C +# define BN_MP_SQR_C +# define BN_MP_SUB_C +# define BN_MP_SUB_D_C +# define BN_S_MP_GET_BIT_C +# define BN_S_MP_MUL_SI_C #endif #if defined(BN_MP_RADIX_SIZE_C) - #define BN_MP_COUNT_BITS_C - #define BN_MP_INIT_COPY_C - #define BN_MP_ISZERO_C - #define BN_MP_DIV_D_C - #define BN_MP_CLEAR_C +# define BN_MP_CLEAR_C +# define BN_MP_COUNT_BITS_C +# define BN_MP_DIV_D_C +# define BN_MP_INIT_COPY_C #endif #if defined(BN_MP_RADIX_SMAP_C) - #define BN_MP_S_RMAP_C #endif #if defined(BN_MP_RAND_C) - #define BN_MP_ZERO_C - #define BN_MP_ADD_D_C - #define BN_MP_LSHD_C +# define BN_MP_GROW_C +# define BN_MP_RAND_SOURCE_C +# define BN_MP_ZERO_C +# define BN_S_MP_RAND_PLATFORM_C +# define BN_S_MP_RAND_SOURCE_C #endif #if defined(BN_MP_READ_RADIX_C) - #define BN_MP_ZERO_C - #define BN_MP_S_RMAP_C - #define BN_MP_RADIX_SMAP_C - #define BN_MP_MUL_D_C - #define BN_MP_ADD_D_C - #define BN_MP_ISZERO_C -#endif - -#if defined(BN_MP_READ_SIGNED_BIN_C) - #define BN_MP_READ_UNSIGNED_BIN_C -#endif - -#if defined(BN_MP_READ_UNSIGNED_BIN_C) - #define BN_MP_GROW_C - #define BN_MP_ZERO_C - #define BN_MP_MUL_2D_C - #define BN_MP_CLAMP_C +# define BN_MP_ADD_D_C +# define BN_MP_MUL_D_C +# define BN_MP_ZERO_C #endif #if defined(BN_MP_REDUCE_C) - #define BN_MP_REDUCE_SETUP_C - #define BN_MP_INIT_COPY_C - #define BN_MP_RSHD_C - #define BN_MP_MUL_C - #define BN_S_MP_MUL_HIGH_DIGS_C - #define BN_FAST_S_MP_MUL_HIGH_DIGS_C - #define BN_MP_MOD_2D_C - #define BN_S_MP_MUL_DIGS_C - #define BN_MP_SUB_C - #define BN_MP_CMP_D_C - #define BN_MP_SET_C - #define BN_MP_LSHD_C - #define BN_MP_ADD_C - #define BN_MP_CMP_C - #define BN_S_MP_SUB_C - #define BN_MP_CLEAR_C +# define BN_MP_ADD_C +# define BN_MP_CLEAR_C +# define BN_MP_CMP_C +# define BN_MP_CMP_D_C +# define BN_MP_INIT_COPY_C +# define BN_MP_LSHD_C +# define BN_MP_MOD_2D_C +# define BN_MP_MUL_C +# define BN_MP_RSHD_C +# define BN_MP_SET_C +# define BN_MP_SUB_C +# define BN_S_MP_MUL_DIGS_C +# define BN_S_MP_MUL_HIGH_DIGS_C +# define BN_S_MP_MUL_HIGH_DIGS_FAST_C +# define BN_S_MP_SUB_C #endif #if defined(BN_MP_REDUCE_2K_C) - #define BN_MP_INIT_C - #define BN_MP_COUNT_BITS_C - #define BN_MP_DIV_2D_C - #define BN_MP_MUL_D_C - #define BN_S_MP_ADD_C - #define BN_MP_CMP_MAG_C - #define BN_S_MP_SUB_C - #define BN_MP_CLEAR_C +# define BN_MP_CLEAR_C +# define BN_MP_CMP_MAG_C +# define BN_MP_COUNT_BITS_C +# define BN_MP_DIV_2D_C +# define BN_MP_INIT_C +# define BN_MP_MUL_D_C +# define BN_S_MP_ADD_C +# define BN_S_MP_SUB_C #endif #if defined(BN_MP_REDUCE_2K_L_C) - #define BN_MP_INIT_C - #define BN_MP_COUNT_BITS_C - #define BN_MP_DIV_2D_C - #define BN_MP_MUL_C - #define BN_S_MP_ADD_C - #define BN_MP_CMP_MAG_C - #define BN_S_MP_SUB_C - #define BN_MP_CLEAR_C +# define BN_MP_CLEAR_C +# define BN_MP_CMP_MAG_C +# define BN_MP_COUNT_BITS_C +# define BN_MP_DIV_2D_C +# define BN_MP_INIT_C +# define BN_MP_MUL_C +# define BN_S_MP_ADD_C +# define BN_S_MP_SUB_C #endif #if defined(BN_MP_REDUCE_2K_SETUP_C) - #define BN_MP_INIT_C - #define BN_MP_COUNT_BITS_C - #define BN_MP_2EXPT_C - #define BN_MP_CLEAR_C - #define BN_S_MP_SUB_C +# define BN_MP_2EXPT_C +# define BN_MP_CLEAR_C +# define BN_MP_COUNT_BITS_C +# define BN_MP_INIT_C +# define BN_S_MP_SUB_C #endif #if defined(BN_MP_REDUCE_2K_SETUP_L_C) - #define BN_MP_INIT_C - #define BN_MP_2EXPT_C - #define BN_MP_COUNT_BITS_C - #define BN_S_MP_SUB_C - #define BN_MP_CLEAR_C +# define BN_MP_2EXPT_C +# define BN_MP_CLEAR_C +# define BN_MP_COUNT_BITS_C +# define BN_MP_INIT_C +# define BN_S_MP_SUB_C #endif #if defined(BN_MP_REDUCE_IS_2K_C) - #define BN_MP_REDUCE_2K_C - #define BN_MP_COUNT_BITS_C +# define BN_MP_COUNT_BITS_C #endif #if defined(BN_MP_REDUCE_IS_2K_L_C) #endif #if defined(BN_MP_REDUCE_SETUP_C) - #define BN_MP_2EXPT_C - #define BN_MP_DIV_C +# define BN_MP_2EXPT_C +# define BN_MP_DIV_C +#endif + +#if defined(BN_MP_ROOT_U32_C) +# define BN_MP_2EXPT_C +# define BN_MP_ADD_D_C +# define BN_MP_CLEAR_MULTI_C +# define BN_MP_CMP_C +# define BN_MP_COPY_C +# define BN_MP_COUNT_BITS_C +# define BN_MP_DIV_C +# define BN_MP_EXCH_C +# define BN_MP_EXPT_U32_C +# define BN_MP_INIT_MULTI_C +# define BN_MP_MUL_C +# define BN_MP_MUL_D_C +# define BN_MP_SET_C +# define BN_MP_SUB_C +# define BN_MP_SUB_D_C #endif #if defined(BN_MP_RSHD_C) - #define BN_MP_ZERO_C +# define BN_MP_ZERO_C +#endif + +#if defined(BN_MP_SBIN_SIZE_C) +# define BN_MP_UBIN_SIZE_C #endif #if defined(BN_MP_SET_C) - #define BN_MP_ZERO_C #endif -#if defined(BN_MP_SET_INT_C) - #define BN_MP_ZERO_C - #define BN_MP_MUL_2D_C - #define BN_MP_CLAMP_C +#if defined(BN_MP_SET_DOUBLE_C) +# define BN_MP_DIV_2D_C +# define BN_MP_MUL_2D_C +# define BN_MP_SET_U64_C +#endif + +#if defined(BN_MP_SET_I32_C) +# define BN_MP_SET_U32_C +#endif + +#if defined(BN_MP_SET_I64_C) +# define BN_MP_SET_U64_C +#endif + +#if defined(BN_MP_SET_L_C) +# define BN_MP_SET_UL_C +#endif + +#if defined(BN_MP_SET_LL_C) +# define BN_MP_SET_ULL_C +#endif + +#if defined(BN_MP_SET_U32_C) +#endif + +#if defined(BN_MP_SET_U64_C) +#endif + +#if defined(BN_MP_SET_UL_C) +#endif + +#if defined(BN_MP_SET_ULL_C) #endif #if defined(BN_MP_SHRINK_C) #endif -#if defined(BN_MP_SIGNED_BIN_SIZE_C) - #define BN_MP_UNSIGNED_BIN_SIZE_C +#if defined(BN_MP_SIGNED_RSH_C) +# define BN_MP_ADD_D_C +# define BN_MP_DIV_2D_C +# define BN_MP_SUB_D_C #endif #if defined(BN_MP_SQR_C) - #define BN_MP_TOOM_SQR_C - #define BN_MP_KARATSUBA_SQR_C - #define BN_FAST_S_MP_SQR_C - #define BN_S_MP_SQR_C +# define BN_S_MP_KARATSUBA_SQR_C +# define BN_S_MP_SQR_C +# define BN_S_MP_SQR_FAST_C +# define BN_S_MP_TOOM_SQR_C #endif #if defined(BN_MP_SQRMOD_C) - #define BN_MP_INIT_C - #define BN_MP_SQR_C - #define BN_MP_CLEAR_C - #define BN_MP_MOD_C +# define BN_MP_CLEAR_C +# define BN_MP_INIT_C +# define BN_MP_MOD_C +# define BN_MP_SQR_C #endif #if defined(BN_MP_SQRT_C) - #define BN_MP_N_ROOT_C - #define BN_MP_ISZERO_C - #define BN_MP_ZERO_C - #define BN_MP_INIT_COPY_C - #define BN_MP_RSHD_C - #define BN_MP_DIV_C - #define BN_MP_ADD_C - #define BN_MP_DIV_2_C - #define BN_MP_CMP_MAG_C - #define BN_MP_EXCH_C - #define BN_MP_CLEAR_C +# define BN_MP_ADD_C +# define BN_MP_CLEAR_C +# define BN_MP_CMP_MAG_C +# define BN_MP_DIV_2_C +# define BN_MP_DIV_C +# define BN_MP_EXCH_C +# define BN_MP_INIT_C +# define BN_MP_INIT_COPY_C +# define BN_MP_RSHD_C +# define BN_MP_ZERO_C +#endif + +#if defined(BN_MP_SQRTMOD_PRIME_C) +# define BN_MP_ADD_D_C +# define BN_MP_CLEAR_MULTI_C +# define BN_MP_CMP_D_C +# define BN_MP_COPY_C +# define BN_MP_DIV_2_C +# define BN_MP_EXPTMOD_C +# define BN_MP_INIT_MULTI_C +# define BN_MP_KRONECKER_C +# define BN_MP_MOD_D_C +# define BN_MP_MULMOD_C +# define BN_MP_SET_C +# define BN_MP_SET_U32_C +# define BN_MP_SQRMOD_C +# define BN_MP_SUB_D_C +# define BN_MP_ZERO_C #endif #if defined(BN_MP_SUB_C) - #define BN_S_MP_ADD_C - #define BN_MP_CMP_MAG_C - #define BN_S_MP_SUB_C +# define BN_MP_CMP_MAG_C +# define BN_S_MP_ADD_C +# define BN_S_MP_SUB_C #endif #if defined(BN_MP_SUB_D_C) - #define BN_MP_GROW_C - #define BN_MP_ADD_D_C - #define BN_MP_CLAMP_C +# define BN_MP_ADD_D_C +# define BN_MP_CLAMP_C +# define BN_MP_GROW_C #endif #if defined(BN_MP_SUBMOD_C) - #define BN_MP_INIT_C - #define BN_MP_SUB_C - #define BN_MP_CLEAR_C - #define BN_MP_MOD_C +# define BN_MP_CLEAR_C +# define BN_MP_INIT_C +# define BN_MP_MOD_C +# define BN_MP_SUB_C #endif -#if defined(BN_MP_TO_SIGNED_BIN_C) - #define BN_MP_TO_UNSIGNED_BIN_C +#if defined(BN_MP_TO_RADIX_C) +# define BN_MP_CLEAR_C +# define BN_MP_DIV_D_C +# define BN_MP_INIT_COPY_C +# define BN_S_MP_REVERSE_C #endif -#if defined(BN_MP_TO_SIGNED_BIN_N_C) - #define BN_MP_SIGNED_BIN_SIZE_C - #define BN_MP_TO_SIGNED_BIN_C +#if defined(BN_MP_TO_SBIN_C) +# define BN_MP_TO_UBIN_C #endif -#if defined(BN_MP_TO_UNSIGNED_BIN_C) - #define BN_MP_INIT_COPY_C - #define BN_MP_ISZERO_C - #define BN_MP_DIV_2D_C - #define BN_MP_CLEAR_C +#if defined(BN_MP_TO_UBIN_C) +# define BN_MP_CLEAR_C +# define BN_MP_DIV_2D_C +# define BN_MP_INIT_COPY_C +# define BN_MP_UBIN_SIZE_C #endif -#if defined(BN_MP_TO_UNSIGNED_BIN_N_C) - #define BN_MP_UNSIGNED_BIN_SIZE_C - #define BN_MP_TO_UNSIGNED_BIN_C +#if defined(BN_MP_UBIN_SIZE_C) +# define BN_MP_COUNT_BITS_C #endif -#if defined(BN_MP_TOOM_MUL_C) - #define BN_MP_INIT_MULTI_C - #define BN_MP_MOD_2D_C - #define BN_MP_COPY_C - #define BN_MP_RSHD_C - #define BN_MP_MUL_C - #define BN_MP_MUL_2_C - #define BN_MP_ADD_C - #define BN_MP_SUB_C - #define BN_MP_DIV_2_C - #define BN_MP_MUL_2D_C - #define BN_MP_MUL_D_C - #define BN_MP_DIV_3_C - #define BN_MP_LSHD_C - #define BN_MP_CLEAR_MULTI_C +#if defined(BN_MP_UNPACK_C) +# define BN_MP_CLAMP_C +# define BN_MP_MUL_2D_C +# define BN_MP_ZERO_C #endif -#if defined(BN_MP_TOOM_SQR_C) - #define BN_MP_INIT_MULTI_C - #define BN_MP_MOD_2D_C - #define BN_MP_COPY_C - #define BN_MP_RSHD_C - #define BN_MP_SQR_C - #define BN_MP_MUL_2_C - #define BN_MP_ADD_C - #define BN_MP_SUB_C - #define BN_MP_DIV_2_C - #define BN_MP_MUL_2D_C - #define BN_MP_MUL_D_C - #define BN_MP_DIV_3_C - #define BN_MP_LSHD_C - #define BN_MP_CLEAR_MULTI_C +#if defined(BN_MP_XOR_C) +# define BN_MP_CLAMP_C +# define BN_MP_GROW_C #endif -#if defined(BN_MP_TORADIX_C) - #define BN_MP_ISZERO_C - #define BN_MP_INIT_COPY_C - #define BN_MP_DIV_D_C - #define BN_MP_CLEAR_C - #define BN_MP_S_RMAP_C +#if defined(BN_MP_ZERO_C) #endif -#if defined(BN_MP_TORADIX_N_C) - #define BN_MP_ISZERO_C - #define BN_MP_INIT_COPY_C - #define BN_MP_DIV_D_C - #define BN_MP_CLEAR_C - #define BN_MP_S_RMAP_C +#if defined(BN_PRIME_TAB_C) #endif -#if defined(BN_MP_UNSIGNED_BIN_SIZE_C) - #define BN_MP_COUNT_BITS_C +#if defined(BN_S_MP_ADD_C) +# define BN_MP_CLAMP_C +# define BN_MP_GROW_C #endif -#if defined(BN_MP_XOR_C) - #define BN_MP_INIT_COPY_C - #define BN_MP_CLAMP_C - #define BN_MP_EXCH_C - #define BN_MP_CLEAR_C +#if defined(BN_S_MP_BALANCE_MUL_C) +# define BN_MP_ADD_C +# define BN_MP_CLAMP_C +# define BN_MP_CLEAR_C +# define BN_MP_CLEAR_MULTI_C +# define BN_MP_EXCH_C +# define BN_MP_INIT_MULTI_C +# define BN_MP_INIT_SIZE_C +# define BN_MP_LSHD_C +# define BN_MP_MUL_C #endif -#if defined(BN_MP_ZERO_C) +#if defined(BN_S_MP_EXPTMOD_C) +# define BN_MP_CLEAR_C +# define BN_MP_COPY_C +# define BN_MP_COUNT_BITS_C +# define BN_MP_EXCH_C +# define BN_MP_INIT_C +# define BN_MP_MOD_C +# define BN_MP_MUL_C +# define BN_MP_REDUCE_2K_L_C +# define BN_MP_REDUCE_2K_SETUP_L_C +# define BN_MP_REDUCE_C +# define BN_MP_REDUCE_SETUP_C +# define BN_MP_SET_C +# define BN_MP_SQR_C +#endif + +#if defined(BN_S_MP_EXPTMOD_FAST_C) +# define BN_MP_CLEAR_C +# define BN_MP_COPY_C +# define BN_MP_COUNT_BITS_C +# define BN_MP_DR_REDUCE_C +# define BN_MP_DR_SETUP_C +# define BN_MP_EXCH_C +# define BN_MP_INIT_SIZE_C +# define BN_MP_MOD_C +# define BN_MP_MONTGOMERY_CALC_NORMALIZATION_C +# define BN_MP_MONTGOMERY_REDUCE_C +# define BN_MP_MONTGOMERY_SETUP_C +# define BN_MP_MULMOD_C +# define BN_MP_MUL_C +# define BN_MP_REDUCE_2K_C +# define BN_MP_REDUCE_2K_SETUP_C +# define BN_MP_SET_C +# define BN_MP_SQR_C +# define BN_S_MP_MONTGOMERY_REDUCE_FAST_C +#endif + +#if defined(BN_S_MP_GET_BIT_C) +#endif + +#if defined(BN_S_MP_INVMOD_FAST_C) +# define BN_MP_ADD_C +# define BN_MP_CLEAR_MULTI_C +# define BN_MP_CMP_C +# define BN_MP_CMP_D_C +# define BN_MP_CMP_MAG_C +# define BN_MP_COPY_C +# define BN_MP_DIV_2_C +# define BN_MP_EXCH_C +# define BN_MP_INIT_MULTI_C +# define BN_MP_MOD_C +# define BN_MP_SET_C +# define BN_MP_SUB_C +#endif + +#if defined(BN_S_MP_INVMOD_SLOW_C) +# define BN_MP_ADD_C +# define BN_MP_CLEAR_MULTI_C +# define BN_MP_CMP_C +# define BN_MP_CMP_D_C +# define BN_MP_CMP_MAG_C +# define BN_MP_COPY_C +# define BN_MP_DIV_2_C +# define BN_MP_EXCH_C +# define BN_MP_INIT_MULTI_C +# define BN_MP_MOD_C +# define BN_MP_SET_C +# define BN_MP_SUB_C +#endif + +#if defined(BN_S_MP_KARATSUBA_MUL_C) +# define BN_MP_ADD_C +# define BN_MP_CLAMP_C +# define BN_MP_CLEAR_C +# define BN_MP_INIT_SIZE_C +# define BN_MP_LSHD_C +# define BN_MP_MUL_C +# define BN_S_MP_ADD_C +# define BN_S_MP_SUB_C +#endif + +#if defined(BN_S_MP_KARATSUBA_SQR_C) +# define BN_MP_ADD_C +# define BN_MP_CLAMP_C +# define BN_MP_CLEAR_C +# define BN_MP_INIT_SIZE_C +# define BN_MP_LSHD_C +# define BN_MP_SQR_C +# define BN_S_MP_ADD_C +# define BN_S_MP_SUB_C +#endif + +#if defined(BN_S_MP_MONTGOMERY_REDUCE_FAST_C) +# define BN_MP_CLAMP_C +# define BN_MP_CMP_MAG_C +# define BN_MP_GROW_C +# define BN_S_MP_SUB_C #endif -#if defined(BN_PRIME_TAB_C) +#if defined(BN_S_MP_MUL_DIGS_C) +# define BN_MP_CLAMP_C +# define BN_MP_CLEAR_C +# define BN_MP_EXCH_C +# define BN_MP_INIT_SIZE_C +# define BN_S_MP_MUL_DIGS_FAST_C #endif -#if defined(BN_REVERSE_C) +#if defined(BN_S_MP_MUL_DIGS_FAST_C) +# define BN_MP_CLAMP_C +# define BN_MP_GROW_C #endif -#if defined(BN_S_MP_ADD_C) - #define BN_MP_GROW_C - #define BN_MP_CLAMP_C +#if defined(BN_S_MP_MUL_HIGH_DIGS_C) +# define BN_MP_CLAMP_C +# define BN_MP_CLEAR_C +# define BN_MP_EXCH_C +# define BN_MP_INIT_SIZE_C +# define BN_S_MP_MUL_HIGH_DIGS_FAST_C #endif -#if defined(BN_S_MP_EXPTMOD_C) - #define BN_MP_COUNT_BITS_C - #define BN_MP_INIT_C - #define BN_MP_CLEAR_C - #define BN_MP_REDUCE_SETUP_C - #define BN_MP_REDUCE_C - #define BN_MP_REDUCE_2K_SETUP_L_C - #define BN_MP_REDUCE_2K_L_C - #define BN_MP_MOD_C - #define BN_MP_COPY_C - #define BN_MP_SQR_C - #define BN_MP_MUL_C - #define BN_MP_SET_C - #define BN_MP_EXCH_C +#if defined(BN_S_MP_MUL_HIGH_DIGS_FAST_C) +# define BN_MP_CLAMP_C +# define BN_MP_GROW_C #endif -#if defined(BN_S_MP_MUL_DIGS_C) - #define BN_FAST_S_MP_MUL_DIGS_C - #define BN_MP_INIT_SIZE_C - #define BN_MP_CLAMP_C - #define BN_MP_EXCH_C - #define BN_MP_CLEAR_C +#if defined(BN_S_MP_PRIME_IS_DIVISIBLE_C) +# define BN_MP_MOD_D_C #endif -#if defined(BN_S_MP_MUL_HIGH_DIGS_C) - #define BN_FAST_S_MP_MUL_HIGH_DIGS_C - #define BN_MP_INIT_SIZE_C - #define BN_MP_CLAMP_C - #define BN_MP_EXCH_C - #define BN_MP_CLEAR_C +#if defined(BN_S_MP_RAND_JENKINS_C) +# define BN_S_MP_RAND_JENKINS_INIT_C #endif -#if defined(BN_S_MP_SQR_C) - #define BN_MP_INIT_SIZE_C - #define BN_MP_CLAMP_C - #define BN_MP_EXCH_C - #define BN_MP_CLEAR_C +#if defined(BN_S_MP_RAND_PLATFORM_C) #endif -#if defined(BN_S_MP_SUB_C) - #define BN_MP_GROW_C - #define BN_MP_CLAMP_C +#if defined(BN_S_MP_REVERSE_C) #endif -#if defined(BNCORE_C) +#if defined(BN_S_MP_SQR_C) +# define BN_MP_CLAMP_C +# define BN_MP_CLEAR_C +# define BN_MP_EXCH_C +# define BN_MP_INIT_SIZE_C +#endif + +#if defined(BN_S_MP_SQR_FAST_C) +# define BN_MP_CLAMP_C +# define BN_MP_GROW_C #endif +#if defined(BN_S_MP_SUB_C) +# define BN_MP_CLAMP_C +# define BN_MP_GROW_C +#endif + +#if defined(BN_S_MP_TOOM_MUL_C) +# define BN_MP_ADD_C +# define BN_MP_CLAMP_C +# define BN_MP_CLEAR_C +# define BN_MP_CLEAR_MULTI_C +# define BN_MP_DIV_2_C +# define BN_MP_DIV_3_C +# define BN_MP_INIT_MULTI_C +# define BN_MP_INIT_SIZE_C +# define BN_MP_LSHD_C +# define BN_MP_MUL_2_C +# define BN_MP_MUL_C +# define BN_MP_SUB_C +#endif + +#if defined(BN_S_MP_TOOM_SQR_C) +# define BN_MP_ADD_C +# define BN_MP_CLAMP_C +# define BN_MP_CLEAR_C +# define BN_MP_DIV_2_C +# define BN_MP_INIT_C +# define BN_MP_INIT_SIZE_C +# define BN_MP_LSHD_C +# define BN_MP_MUL_2_C +# define BN_MP_MUL_C +# define BN_MP_SQR_C +# define BN_MP_SUB_C +#endif + +#ifdef LTM_INSIDE +#undef LTM_INSIDE #ifdef LTM3 -#define LTM_LAST +# define LTM_LAST #endif -#include <tommath_superclass.h> -#include <tommath_class.h> + +#include "tommath_superclass.h" +#include "tommath_class.h" #else -#define LTM_LAST +# define LTM_LAST #endif - -/* $Source: /cvs/libtom/libtommath/tommath_class.h,v $ */ -/* $Revision: 1.3 $ */ -/* $Date: 2005/07/28 11:59:32 $ */ diff --git a/lib/hcrypto/libtommath/tommath_cutoffs.h b/lib/hcrypto/libtommath/tommath_cutoffs.h new file mode 100644 index 000000000000..a65a9b3e32be --- /dev/null +++ b/lib/hcrypto/libtommath/tommath_cutoffs.h @@ -0,0 +1,13 @@ +/* LibTomMath, multiple-precision integer library -- Tom St Denis */ +/* SPDX-License-Identifier: Unlicense */ +/* + Current values evaluated on an AMD A8-6600K (64-bit). + Type "make tune" to optimize them for your machine but + be aware that it may take a long time. It took 2:30 minutes + on the aforementioned machine for example. + */ + +#define MP_DEFAULT_KARATSUBA_MUL_CUTOFF 80 +#define MP_DEFAULT_KARATSUBA_SQR_CUTOFF 120 +#define MP_DEFAULT_TOOM_MUL_CUTOFF 350 +#define MP_DEFAULT_TOOM_SQR_CUTOFF 400 diff --git a/lib/hcrypto/libtommath/tommath_private.h b/lib/hcrypto/libtommath/tommath_private.h new file mode 100644 index 000000000000..1a0096f85505 --- /dev/null +++ b/lib/hcrypto/libtommath/tommath_private.h @@ -0,0 +1,303 @@ +/* LibTomMath, multiple-precision integer library -- Tom St Denis */ +/* SPDX-License-Identifier: Unlicense */ + +#ifndef TOMMATH_PRIV_H_ +#define TOMMATH_PRIV_H_ + +#include "tommath.h" +#include "tommath_class.h" + +/* + * Private symbols + * --------------- + * + * On Unix symbols can be marked as hidden if libtommath is compiled + * as a shared object. By default, symbols are visible. + * As of now, this feature is opt-in via the MP_PRIVATE_SYMBOLS define. + * + * On Win32 a .def file must be used to specify the exported symbols. + */ +#if defined (MP_PRIVATE_SYMBOLS) && defined(__GNUC__) && __GNUC__ >= 4 +# define MP_PRIVATE __attribute__ ((visibility ("hidden"))) +#else +# define MP_PRIVATE +#endif + +/* Hardening libtommath + * -------------------- + * + * By default memory is zeroed before calling + * MP_FREE to avoid leaking data. This is good + * practice in cryptographical applications. + * + * Note however that memory allocators used + * in cryptographical applications can often + * be configured by itself to clear memory, + * rendering the clearing in tommath unnecessary. + * See for example https://github.com/GrapheneOS/hardened_malloc + * and the option CONFIG_ZERO_ON_FREE. + * + * Furthermore there are applications which + * value performance more and want this + * feature to be disabled. For such applications + * define MP_NO_ZERO_ON_FREE during compilation. + */ +#ifdef MP_NO_ZERO_ON_FREE +# define MP_FREE_BUFFER(mem, size) MP_FREE((mem), (size)) +# define MP_FREE_DIGITS(mem, digits) MP_FREE((mem), sizeof (mp_digit) * (size_t)(digits)) +#else +# define MP_FREE_BUFFER(mem, size) \ +do { \ + size_t fs_ = (size); \ + void* fm_ = (mem); \ + if (fm_ != NULL) { \ + MP_ZERO_BUFFER(fm_, fs_); \ + MP_FREE(fm_, fs_); \ + } \ +} while (0) +# define MP_FREE_DIGITS(mem, digits) \ +do { \ + int fd_ = (digits); \ + void* fm_ = (mem); \ + if (fm_ != NULL) { \ + size_t fs_ = sizeof (mp_digit) * (size_t)fd_; \ + MP_ZERO_BUFFER(fm_, fs_); \ + MP_FREE(fm_, fs_); \ + } \ +} while (0) +#endif + +#ifdef MP_USE_MEMSET +# include <string.h> +# define MP_ZERO_BUFFER(mem, size) memset((mem), 0, (size)) +# define MP_ZERO_DIGITS(mem, digits) \ +do { \ + int zd_ = (digits); \ + if (zd_ > 0) { \ + memset((mem), 0, sizeof(mp_digit) * (size_t)zd_); \ + } \ +} while (0) +#else +# define MP_ZERO_BUFFER(mem, size) \ +do { \ + size_t zs_ = (size); \ + char* zm_ = (char*)(mem); \ + while (zs_-- > 0u) { \ + *zm_++ = '\0'; \ + } \ +} while (0) +# define MP_ZERO_DIGITS(mem, digits) \ +do { \ + int zd_ = (digits); \ + mp_digit* zm_ = (mem); \ + while (zd_-- > 0) { \ + *zm_++ = 0; \ + } \ +} while (0) +#endif + +/* Tunable cutoffs + * --------------- + * + * - In the default settings, a cutoff X can be modified at runtime + * by adjusting the corresponding X_CUTOFF variable. + * + * - Tunability of the library can be disabled at compile time + * by defining the MP_FIXED_CUTOFFS macro. + * + * - There is an additional file tommath_cutoffs.h, which defines + * the default cutoffs. These can be adjusted manually or by the + * autotuner. + * + */ + +#ifdef MP_FIXED_CUTOFFS +# include "tommath_cutoffs.h" +# define MP_KARATSUBA_MUL_CUTOFF MP_DEFAULT_KARATSUBA_MUL_CUTOFF +# define MP_KARATSUBA_SQR_CUTOFF MP_DEFAULT_KARATSUBA_SQR_CUTOFF +# define MP_TOOM_MUL_CUTOFF MP_DEFAULT_TOOM_MUL_CUTOFF +# define MP_TOOM_SQR_CUTOFF MP_DEFAULT_TOOM_SQR_CUTOFF +#else +# define MP_KARATSUBA_MUL_CUTOFF KARATSUBA_MUL_CUTOFF +# define MP_KARATSUBA_SQR_CUTOFF KARATSUBA_SQR_CUTOFF +# define MP_TOOM_MUL_CUTOFF TOOM_MUL_CUTOFF +# define MP_TOOM_SQR_CUTOFF TOOM_SQR_CUTOFF +#endif + +/* define heap macros */ +#ifndef MP_MALLOC +/* default to libc stuff */ +# include <stdlib.h> +# define MP_MALLOC(size) malloc(size) +# define MP_REALLOC(mem, oldsize, newsize) realloc((mem), (newsize)) +# define MP_CALLOC(nmemb, size) calloc((nmemb), (size)) +# define MP_FREE(mem, size) free(mem) +#else +/* prototypes for our heap functions */ +extern void *MP_MALLOC(size_t size); +extern void *MP_REALLOC(void *mem, size_t oldsize, size_t newsize); +extern void *MP_CALLOC(size_t nmemb, size_t size); +extern void MP_FREE(void *mem, size_t size); +#endif + +/* feature detection macro */ +#ifdef _MSC_VER +/* Prevent false positive: not enough arguments for function-like macro invocation */ +#pragma warning(disable: 4003) +#endif +#define MP_STRINGIZE(x) MP__STRINGIZE(x) +#define MP__STRINGIZE(x) ""#x"" +#define MP_HAS(x) (sizeof(MP_STRINGIZE(BN_##x##_C)) == 1u) + +/* TODO: Remove private_mp_word as soon as deprecated mp_word is removed from tommath. */ +#undef mp_word +typedef private_mp_word mp_word; + +#define MP_MIN(x, y) (((x) < (y)) ? (x) : (y)) +#define MP_MAX(x, y) (((x) > (y)) ? (x) : (y)) + +/* Static assertion */ +#define MP_STATIC_ASSERT(msg, cond) typedef char mp_static_assert_##msg[(cond) ? 1 : -1]; + +/* ---> Basic Manipulations <--- */ +#define MP_IS_ZERO(a) ((a)->used == 0) +#define MP_IS_EVEN(a) (((a)->used == 0) || (((a)->dp[0] & 1u) == 0u)) +#define MP_IS_ODD(a) (((a)->used > 0) && (((a)->dp[0] & 1u) == 1u)) + +#define MP_SIZEOF_BITS(type) ((size_t)CHAR_BIT * sizeof(type)) +#define MP_MAXFAST (int)(1uL << (MP_SIZEOF_BITS(mp_word) - (2u * (size_t)MP_DIGIT_BIT))) + +/* TODO: Remove PRIVATE_MP_WARRAY as soon as deprecated MP_WARRAY is removed from tommath.h */ +#undef MP_WARRAY +#define MP_WARRAY PRIVATE_MP_WARRAY + +/* TODO: Remove PRIVATE_MP_PREC as soon as deprecated MP_PREC is removed from tommath.h */ +#ifdef PRIVATE_MP_PREC +# undef MP_PREC +# define MP_PREC PRIVATE_MP_PREC +#endif + +/* Minimum number of available digits in mp_int, MP_PREC >= MP_MIN_PREC */ +#define MP_MIN_PREC ((((int)MP_SIZEOF_BITS(long long) + MP_DIGIT_BIT) - 1) / MP_DIGIT_BIT) + +MP_STATIC_ASSERT(prec_geq_min_prec, MP_PREC >= MP_MIN_PREC) + +/* random number source */ +extern MP_PRIVATE mp_err(*s_mp_rand_source)(void *out, size_t size); + +/* lowlevel functions, do not call! */ +MP_PRIVATE mp_bool s_mp_get_bit(const mp_int *a, unsigned int b); +MP_PRIVATE mp_err s_mp_add(const mp_int *a, const mp_int *b, mp_int *c) MP_WUR; +MP_PRIVATE mp_err s_mp_sub(const mp_int *a, const mp_int *b, mp_int *c) MP_WUR; +MP_PRIVATE mp_err s_mp_mul_digs_fast(const mp_int *a, const mp_int *b, mp_int *c, int digs) MP_WUR; +MP_PRIVATE mp_err s_mp_mul_digs(const mp_int *a, const mp_int *b, mp_int *c, int digs) MP_WUR; +MP_PRIVATE mp_err s_mp_mul_high_digs_fast(const mp_int *a, const mp_int *b, mp_int *c, int digs) MP_WUR; +MP_PRIVATE mp_err s_mp_mul_high_digs(const mp_int *a, const mp_int *b, mp_int *c, int digs) MP_WUR; +MP_PRIVATE mp_err s_mp_sqr_fast(const mp_int *a, mp_int *b) MP_WUR; +MP_PRIVATE mp_err s_mp_sqr(const mp_int *a, mp_int *b) MP_WUR; +MP_PRIVATE mp_err s_mp_balance_mul(const mp_int *a, const mp_int *b, mp_int *c) MP_WUR; +MP_PRIVATE mp_err s_mp_karatsuba_mul(const mp_int *a, const mp_int *b, mp_int *c) MP_WUR; +MP_PRIVATE mp_err s_mp_toom_mul(const mp_int *a, const mp_int *b, mp_int *c) MP_WUR; +MP_PRIVATE mp_err s_mp_karatsuba_sqr(const mp_int *a, mp_int *b) MP_WUR; +MP_PRIVATE mp_err s_mp_toom_sqr(const mp_int *a, mp_int *b) MP_WUR; +MP_PRIVATE mp_err s_mp_invmod_fast(const mp_int *a, const mp_int *b, mp_int *c) MP_WUR; +MP_PRIVATE mp_err s_mp_invmod_slow(const mp_int *a, const mp_int *b, mp_int *c) MP_WUR; +MP_PRIVATE mp_err s_mp_montgomery_reduce_fast(mp_int *x, const mp_int *n, mp_digit rho) MP_WUR; +MP_PRIVATE mp_err s_mp_exptmod_fast(const mp_int *G, const mp_int *X, const mp_int *P, mp_int *Y, int redmode) MP_WUR; +MP_PRIVATE mp_err s_mp_exptmod(const mp_int *G, const mp_int *X, const mp_int *P, mp_int *Y, int redmode) MP_WUR; +MP_PRIVATE mp_err s_mp_rand_platform(void *p, size_t n) MP_WUR; +MP_PRIVATE mp_err s_mp_prime_random_ex(mp_int *a, int t, int size, int flags, private_mp_prime_callback cb, void *dat); +MP_PRIVATE void s_mp_reverse(unsigned char *s, size_t len); +MP_PRIVATE mp_err s_mp_prime_is_divisible(const mp_int *a, mp_bool *result); + +/* TODO: jenkins prng is not thread safe as of now */ +MP_PRIVATE mp_err s_mp_rand_jenkins(void *p, size_t n) MP_WUR; +MP_PRIVATE void s_mp_rand_jenkins_init(uint64_t seed); + +extern MP_PRIVATE const char *const mp_s_rmap; +extern MP_PRIVATE const uint8_t mp_s_rmap_reverse[]; +extern MP_PRIVATE const size_t mp_s_rmap_reverse_sz; +extern MP_PRIVATE const mp_digit *s_mp_prime_tab; + +/* deprecated functions */ +MP_DEPRECATED(s_mp_invmod_fast) mp_err fast_mp_invmod(const mp_int *a, const mp_int *b, mp_int *c); +MP_DEPRECATED(s_mp_montgomery_reduce_fast) mp_err fast_mp_montgomery_reduce(mp_int *x, const mp_int *n, + mp_digit rho); +MP_DEPRECATED(s_mp_mul_digs_fast) mp_err fast_s_mp_mul_digs(const mp_int *a, const mp_int *b, mp_int *c, + int digs); +MP_DEPRECATED(s_mp_mul_high_digs_fast) mp_err fast_s_mp_mul_high_digs(const mp_int *a, const mp_int *b, + mp_int *c, + int digs); +MP_DEPRECATED(s_mp_sqr_fast) mp_err fast_s_mp_sqr(const mp_int *a, mp_int *b); +MP_DEPRECATED(s_mp_balance_mul) mp_err mp_balance_mul(const mp_int *a, const mp_int *b, mp_int *c); +MP_DEPRECATED(s_mp_exptmod_fast) mp_err mp_exptmod_fast(const mp_int *G, const mp_int *X, const mp_int *P, + mp_int *Y, + int redmode); +MP_DEPRECATED(s_mp_invmod_slow) mp_err mp_invmod_slow(const mp_int *a, const mp_int *b, mp_int *c); +MP_DEPRECATED(s_mp_karatsuba_mul) mp_err mp_karatsuba_mul(const mp_int *a, const mp_int *b, mp_int *c); +MP_DEPRECATED(s_mp_karatsuba_sqr) mp_err mp_karatsuba_sqr(const mp_int *a, mp_int *b); +MP_DEPRECATED(s_mp_toom_mul) mp_err mp_toom_mul(const mp_int *a, const mp_int *b, mp_int *c); +MP_DEPRECATED(s_mp_toom_sqr) mp_err mp_toom_sqr(const mp_int *a, mp_int *b); +MP_DEPRECATED(s_mp_reverse) void bn_reverse(unsigned char *s, int len); + +#define MP_GET_ENDIANNESS(x) \ + do{\ + int16_t n = 0x1; \ + char *p = (char *)&n; \ + x = (p[0] == '\x01') ? MP_LITTLE_ENDIAN : MP_BIG_ENDIAN; \ + } while (0) + +/* code-generating macros */ +#define MP_SET_UNSIGNED(name, type) \ + void name(mp_int * a, type b) \ + { \ + int i = 0; \ + while (b != 0u) { \ + a->dp[i++] = ((mp_digit)b & MP_MASK); \ + if (MP_SIZEOF_BITS(type) <= MP_DIGIT_BIT) { break; } \ + b >>= ((MP_SIZEOF_BITS(type) <= MP_DIGIT_BIT) ? 0 : MP_DIGIT_BIT); \ + } \ + a->used = i; \ + a->sign = MP_ZPOS; \ + MP_ZERO_DIGITS(a->dp + a->used, a->alloc - a->used); \ + } + +#define MP_SET_SIGNED(name, uname, type, utype) \ + void name(mp_int * a, type b) \ + { \ + uname(a, (b < 0) ? -(utype)b : (utype)b); \ + if (b < 0) { a->sign = MP_NEG; } \ + } + +#define MP_INIT_INT(name , set, type) \ + mp_err name(mp_int * a, type b) \ + { \ + mp_err err; \ + if ((err = mp_init(a)) != MP_OKAY) { \ + return err; \ + } \ + set(a, b); \ + return MP_OKAY; \ + } + +#define MP_GET_MAG(name, type) \ + type name(const mp_int* a) \ + { \ + unsigned i = MP_MIN((unsigned)a->used, (unsigned)((MP_SIZEOF_BITS(type) + MP_DIGIT_BIT - 1) / MP_DIGIT_BIT)); \ + type res = 0u; \ + while (i --> 0u) { \ + res <<= ((MP_SIZEOF_BITS(type) <= MP_DIGIT_BIT) ? 0 : MP_DIGIT_BIT); \ + res |= (type)a->dp[i]; \ + if (MP_SIZEOF_BITS(type) <= MP_DIGIT_BIT) { break; } \ + } \ + return res; \ + } + +#define MP_GET_SIGNED(name, mag, type, utype) \ + type name(const mp_int* a) \ + { \ + utype res = mag(a); \ + return (a->sign == MP_NEG) ? (type)-res : (type)res; \ + } + +#endif diff --git a/lib/hcrypto/libtommath/tommath_superclass.h b/lib/hcrypto/libtommath/tommath_superclass.h index a96c36feb82b..d88bce9c7b4f 100644 --- a/lib/hcrypto/libtommath/tommath_superclass.h +++ b/lib/hcrypto/libtommath/tommath_superclass.h @@ -1,10 +1,16 @@ +/* LibTomMath, multiple-precision integer library -- Tom St Denis */ +/* SPDX-License-Identifier: Unlicense */ + /* super class file for PK algos */ /* default ... include all MPI */ +#ifndef LTM_NOTHING #define LTM_ALL +#endif /* RSA only (does not support DH/DSA/ECC) */ /* #define SC_RSA_1 */ +/* #define SC_RSA_1_WITH_TESTS */ /* For reference.... On an Athlon64 optimizing for speed... @@ -12,65 +18,93 @@ */ +#ifdef SC_RSA_1_WITH_TESTS +# define BN_MP_ERROR_TO_STRING_C +# define BN_MP_FREAD_C +# define BN_MP_FWRITE_C +# define BN_MP_INCR_C +# define BN_MP_ISEVEN_C +# define BN_MP_ISODD_C +# define BN_MP_NEG_C +# define BN_MP_PRIME_FROBENIUS_UNDERWOOD_C +# define BN_MP_RADIX_SIZE_C +# define BN_MP_RAND_C +# define BN_MP_REDUCE_C +# define BN_MP_REDUCE_2K_L_C +# define BN_MP_FROM_SBIN_C +# define BN_MP_ROOT_U32_C +# define BN_MP_SET_L_C +# define BN_MP_SET_UL_C +# define BN_MP_SBIN_SIZE_C +# define BN_MP_TO_RADIX_C +# define BN_MP_TO_SBIN_C +# define BN_S_MP_RAND_JENKINS_C +# define BN_S_MP_RAND_PLATFORM_C +#endif + /* Works for RSA only, mpi.o is 68KiB */ -#ifdef SC_RSA_1 - #define BN_MP_SHRINK_C - #define BN_MP_LCM_C - #define BN_MP_PRIME_RANDOM_EX_C - #define BN_MP_INVMOD_C - #define BN_MP_GCD_C - #define BN_MP_MOD_C - #define BN_MP_MULMOD_C - #define BN_MP_ADDMOD_C - #define BN_MP_EXPTMOD_C - #define BN_MP_SET_INT_C - #define BN_MP_INIT_MULTI_C - #define BN_MP_CLEAR_MULTI_C - #define BN_MP_UNSIGNED_BIN_SIZE_C - #define BN_MP_TO_UNSIGNED_BIN_C - #define BN_MP_MOD_D_C - #define BN_MP_PRIME_RABIN_MILLER_TRIALS_C - #define BN_REVERSE_C - #define BN_PRIME_TAB_C +#if defined(SC_RSA_1) || defined (SC_RSA_1_WITH_TESTS) +# define BN_CUTOFFS_C +# define BN_MP_ADDMOD_C +# define BN_MP_CLEAR_MULTI_C +# define BN_MP_EXPTMOD_C +# define BN_MP_GCD_C +# define BN_MP_INIT_MULTI_C +# define BN_MP_INVMOD_C +# define BN_MP_LCM_C +# define BN_MP_MOD_C +# define BN_MP_MOD_D_C +# define BN_MP_MULMOD_C +# define BN_MP_PRIME_IS_PRIME_C +# define BN_MP_PRIME_RABIN_MILLER_TRIALS_C +# define BN_MP_PRIME_RAND_C +# define BN_MP_RADIX_SMAP_C +# define BN_MP_SET_INT_C +# define BN_MP_SHRINK_C +# define BN_MP_TO_UNSIGNED_BIN_C +# define BN_MP_UNSIGNED_BIN_SIZE_C +# define BN_PRIME_TAB_C +# define BN_S_MP_REVERSE_C - /* other modifiers */ - #define BN_MP_DIV_SMALL /* Slower division, not critical */ +/* other modifiers */ +# define BN_MP_DIV_SMALL /* Slower division, not critical */ - /* here we are on the last pass so we turn things off. The functions classes are still there - * but we remove them specifically from the build. This also invokes tweaks in functions - * like removing support for even moduli, etc... - */ -#ifdef LTM_LAST - #undef BN_MP_TOOM_MUL_C - #undef BN_MP_TOOM_SQR_C - #undef BN_MP_KARATSUBA_MUL_C - #undef BN_MP_KARATSUBA_SQR_C - #undef BN_MP_REDUCE_C - #undef BN_MP_REDUCE_SETUP_C - #undef BN_MP_DR_IS_MODULUS_C - #undef BN_MP_DR_SETUP_C - #undef BN_MP_DR_REDUCE_C - #undef BN_MP_REDUCE_IS_2K_C - #undef BN_MP_REDUCE_2K_SETUP_C - #undef BN_MP_REDUCE_2K_C - #undef BN_S_MP_EXPTMOD_C - #undef BN_MP_DIV_3_C - #undef BN_S_MP_MUL_HIGH_DIGS_C - #undef BN_FAST_S_MP_MUL_HIGH_DIGS_C - #undef BN_FAST_MP_INVMOD_C - /* To safely undefine these you have to make sure your RSA key won't exceed the Comba threshold - * which is roughly 255 digits [7140 bits for 32-bit machines, 15300 bits for 64-bit machines] - * which means roughly speaking you can handle upto 2536-bit RSA keys with these defined without - * trouble. - */ - #undef BN_S_MP_MUL_DIGS_C - #undef BN_S_MP_SQR_C - #undef BN_MP_MONTGOMERY_REDUCE_C -#endif +/* here we are on the last pass so we turn things off. The functions classes are still there + * but we remove them specifically from the build. This also invokes tweaks in functions + * like removing support for even moduli, etc... + */ +# ifdef LTM_LAST +# undef BN_MP_DR_IS_MODULUS_C +# undef BN_MP_DR_SETUP_C +# undef BN_MP_DR_REDUCE_C +# undef BN_MP_DIV_3_C +# undef BN_MP_REDUCE_2K_SETUP_C +# undef BN_MP_REDUCE_2K_C +# undef BN_MP_REDUCE_IS_2K_C +# undef BN_MP_REDUCE_SETUP_C +# undef BN_S_MP_BALANCE_MUL_C +# undef BN_S_MP_EXPTMOD_C +# undef BN_S_MP_INVMOD_FAST_C +# undef BN_S_MP_KARATSUBA_MUL_C +# undef BN_S_MP_KARATSUBA_SQR_C +# undef BN_S_MP_MUL_HIGH_DIGS_C +# undef BN_S_MP_MUL_HIGH_DIGS_FAST_C +# undef BN_S_MP_TOOM_MUL_C +# undef BN_S_MP_TOOM_SQR_C -#endif +# ifndef SC_RSA_1_WITH_TESTS +# undef BN_MP_REDUCE_C +# endif -/* $Source: /cvs/libtom/libtommath/tommath_superclass.h,v $ */ -/* $Revision: 1.3 $ */ -/* $Date: 2005/05/14 13:29:17 $ */ +/* To safely undefine these you have to make sure your RSA key won't exceed the Comba threshold + * which is roughly 255 digits [7140 bits for 32-bit machines, 15300 bits for 64-bit machines] + * which means roughly speaking you can handle upto 2536-bit RSA keys with these defined without + * trouble. + */ +# undef BN_MP_MONTGOMERY_REDUCE_C +# undef BN_S_MP_MUL_DIGS_C +# undef BN_S_MP_SQR_C +# endif + +#endif diff --git a/lib/hcrypto/passwd_dlg.c b/lib/hcrypto/passwd_dlg.c index 037fa7436a43..30721160a2ae 100644 --- a/lib/hcrypto/passwd_dlg.c +++ b/lib/hcrypto/passwd_dlg.c @@ -77,11 +77,11 @@ pwd_dialog(char *buf, int size) { case IDOK: strlcpy(buf, passwd, size); - memset (passwd, 0, sizeof(passwd)); + memset_s (passwd, sizeof(passwd), 0, sizeof(passwd)); return 0; case IDCANCEL: default: - memset (passwd, 0, sizeof(passwd)); + memset_s (passwd, sizeof(passwd), 0, sizeof(passwd)); return 1; } } diff --git a/lib/hcrypto/rand-fortuna.c b/lib/hcrypto/rand-fortuna.c index 2082f35ec72d..31f72330245b 100644 --- a/lib/hcrypto/rand-fortuna.c +++ b/lib/hcrypto/rand-fortuna.c @@ -336,7 +336,7 @@ add_entropy(FState * st, const unsigned char *data, unsigned len) st->pool0_bytes += len; memset_s(hash, sizeof(hash), 0, sizeof(hash)); - memset_s(&md, sizeof(hash), 0, sizeof(md)); + memset_s(&md, sizeof(md), 0, sizeof(md)); } /* @@ -446,7 +446,7 @@ static unsigned resend_bytes; static HEIMDAL_MUTEX fortuna_mutex = HEIMDAL_MUTEX_INITIALIZER; /* - * Try our best to do an inital seed + * Try our best to do an initial seed */ #define INIT_BYTES 128 @@ -501,10 +501,9 @@ fortuna_reseed(void) /* add /etc/shadow */ fd = open("/etc/shadow", O_RDONLY, 0); if (fd >= 0) { - ssize_t n; rk_cloexec(fd); /* add_entropy will hash the buf */ - while ((n = read(fd, (char *)u.shad, sizeof(u.shad))) > 0) + while (read(fd, (char *)u.shad, sizeof(u.shad)) > 0) add_entropy(&main_state, u.shad, sizeof(u.shad)); close(fd); } diff --git a/lib/hcrypto/rand-w32.c b/lib/hcrypto/rand-w32.c index f36903ae3b08..d7d91a367244 100644 --- a/lib/hcrypto/rand-w32.c +++ b/lib/hcrypto/rand-w32.c @@ -41,15 +41,15 @@ #include "randi.h" -volatile static HCRYPTPROV g_cryptprovider = NULL; +volatile static HCRYPTPROV g_cryptprovider; static HCRYPTPROV _hc_CryptProvider(void) { BOOL rv; - HCRYPTPROV cryptprovider = NULL; + HCRYPTPROV cryptprovider = (HCRYPTPROV)0; - if (g_cryptprovider != NULL) + if (g_cryptprovider) goto out; rv = CryptAcquireContext(&cryptprovider, NULL, diff --git a/lib/hcrypto/rand.c b/lib/hcrypto/rand.c index 98432e75ed89..893d5c6ac1ae 100644 --- a/lib/hcrypto/rand.c +++ b/lib/hcrypto/rand.c @@ -350,13 +350,11 @@ RAND_file_name(char *filename, size_t size) const char *e = NULL; int pathp = 0, ret; - if (!issuid()) { - e = getenv("RANDFILE"); - if (e == NULL) - e = getenv("HOME"); - if (e) - pathp = 1; - } + e = secure_getenv("RANDFILE"); + if (e == NULL) + e = secure_getenv("HOME"); + if (e) + pathp = 1; #ifndef _WIN32 /* diff --git a/lib/hcrypto/rand.h b/lib/hcrypto/rand.h index 7b5553803fc9..1955c44874c8 100644 --- a/lib/hcrypto/rand.h +++ b/lib/hcrypto/rand.h @@ -59,6 +59,7 @@ typedef struct RAND_METHOD RAND_METHOD; #define RAND_write_file hc_RAND_write_file #define RAND_status hc_RAND_status #define RAND_fortuna_method hc_RAND_fortuna_method +#define RAND_timer_method hc_RAND_timer_method #define RAND_unix_method hc_RAND_unix_method #define RAND_w32crypto_method hc_RAND_w32crypto_method diff --git a/lib/hcrypto/rc2.c b/lib/hcrypto/rc2.c index 02b684cbd4b0..53d32cf0417e 100644 --- a/lib/hcrypto/rc2.c +++ b/lib/hcrypto/rc2.c @@ -105,7 +105,7 @@ RC2_set_key(RC2_KEY *key, int len, const unsigned char *data, int bits) for (j = 0; j < 64; j++) key->data[j] = k[(j * 2) + 0] | (k[(j * 2) + 1] << 8); - memset(k, 0, sizeof(k)); + memset_s(k, sizeof(k), 0, sizeof(k)); } #define ROT16L(w,n) ((w<<n)|(w>>(16-n))) diff --git a/lib/hcrypto/rsa-ltm.c b/lib/hcrypto/rsa-ltm.c index 4ac5617cb6ba..49e35f5a38a9 100644 --- a/lib/hcrypto/rsa-ltm.c +++ b/lib/hcrypto/rsa-ltm.c @@ -40,96 +40,122 @@ #include "tommath.h" -static int +#define CHECK(f) \ + do { where = __LINE__ + 1; if (ret == MP_OKAY && ((ret = f)) != MP_OKAY) { goto out; } } while (0) +#define FIRST(e) do { ret = (e); } while (0) +#define FIRST_ALLOC(e) \ + do { where = __LINE__; ret = ((e)) ? MP_OKAY : MP_MEM; } while (0) +#define THEN_MP(e) \ + do { where = __LINE__ + 1; if (ret == MP_OKAY) ret = (e); } while (0) +#define THEN_IF_MP(cond, e) \ + do { where = __LINE__ + 1; if (ret == MP_OKAY && (cond)) ret = (e); } while (0) +#define THEN_IF_VOID(cond, e) \ + do { where = __LINE__ + 1; if (ret == MP_OKAY && (cond)) e; } while (0) +#define THEN_VOID(e) \ + do { where = __LINE__ + 1; if (ret == MP_OKAY) e; } while (0) +#define THEN_ALLOC(e) \ + do { where = __LINE__ + 1; if (ret == MP_OKAY) ret = ((e)) ? MP_OKAY : MP_MEM; } while (0) + +static mp_err random_num(mp_int *num, size_t len) { unsigned char *p; + mp_err ret = MP_MEM; - len = (len + 7) / 8; - p = malloc(len); - if (p == NULL) - return 1; - if (RAND_bytes(p, len) != 1) { - free(p); - return 1; - } - mp_read_unsigned_bin(num, p, len); + len = (len + 7) / 8; /* bits to bytes */ + if ((p = malloc(len)) && RAND_bytes(p, len) != 1) + ret = MP_ERR; + if (p) + ret = mp_from_ubin(num, p, len); free(p); - return 0; + return ret; } -static void +static mp_err BN2mpz(mp_int *s, const BIGNUM *bn) { size_t len; + mp_err ret = MP_MEM; void *p; len = BN_num_bytes(bn); p = malloc(len); - BN_bn2bin(bn, p); - mp_read_unsigned_bin(s, p, len); + if (p) { + BN_bn2bin(bn, p); + ret = mp_from_ubin(s, p, len); + } free(p); + return ret; } -static void +static mp_err setup_blind(mp_int *n, mp_int *b, mp_int *bi) { - random_num(b, mp_count_bits(n)); - mp_mod(b, n, b); - mp_invmod(b, n, bi); + mp_err ret; + + ret = random_num(b, mp_count_bits(n)); + if (ret == MP_OKAY) ret = mp_mod(b, n, b); + if (ret == MP_OKAY) ret = mp_invmod(b, n, bi); + return ret; } -static void +static mp_err blind(mp_int *in, mp_int *b, mp_int *e, mp_int *n) { + mp_err ret; mp_int t1; - mp_init(&t1); + + ret = mp_init(&t1); /* in' = (in * b^e) mod n */ - mp_exptmod(b, e, n, &t1); - mp_mul(&t1, in, in); - mp_mod(in, n, in); + if (ret == MP_OKAY) ret = mp_exptmod(b, e, n, &t1); + if (ret == MP_OKAY) ret = mp_mul(&t1, in, in); + if (ret == MP_OKAY) ret = mp_mod(in, n, in); mp_clear(&t1); + return ret; } -static void +static mp_err unblind(mp_int *out, mp_int *bi, mp_int *n) { + mp_err ret; + /* out' = (out * 1/b) mod n */ - mp_mul(out, bi, out); - mp_mod(out, n, out); + ret = mp_mul(out, bi, out); + if (ret == MP_OKAY) ret = mp_mod(out, n, out); + return ret; } -static int +static mp_err ltm_rsa_private_calculate(mp_int * in, mp_int * p, mp_int * q, mp_int * dmp1, mp_int * dmq1, mp_int * iqmp, mp_int * out) { + mp_err ret; mp_int vp, vq, u; + int where HEIMDAL_UNUSED_ATTRIBUTE = 0; - mp_init_multi(&vp, &vq, &u, NULL); + FIRST(mp_init_multi(&vp, &vq, &u, NULL)); /* vq = c ^ (d mod (q - 1)) mod q */ /* vp = c ^ (d mod (p - 1)) mod p */ - mp_mod(in, p, &u); - mp_exptmod(&u, dmp1, p, &vp); - mp_mod(in, q, &u); - mp_exptmod(&u, dmq1, q, &vq); + THEN_MP(mp_mod(in, p, &u)); + THEN_MP(mp_exptmod(&u, dmp1, p, &vp)); + THEN_MP(mp_mod(in, q, &u)); + THEN_MP(mp_exptmod(&u, dmq1, q, &vq)); /* C2 = 1/q mod p (iqmp) */ /* u = (vp - vq)C2 mod p. */ - mp_sub(&vp, &vq, &u); - if (mp_isneg(&u)) - mp_add(&u, p, &u); - mp_mul(&u, iqmp, &u); - mp_mod(&u, p, &u); + THEN_MP(mp_sub(&vp, &vq, &u)); + THEN_IF_MP(mp_isneg(&u), mp_add(&u, p, &u)); + THEN_MP(mp_mul(&u, iqmp, &u)); + THEN_MP(mp_mod(&u, p, &u)); /* c ^ d mod n = vq + u q */ - mp_mul(&u, q, &u); - mp_add(&u, &vq, out); + THEN_MP(mp_mul(&u, q, &u)); + THEN_MP(mp_add(&u, &vq, out)); mp_clear_multi(&vp, &vq, &u, NULL); - - return 0; + return ret; } /* @@ -140,78 +166,56 @@ static int ltm_rsa_public_encrypt(int flen, const unsigned char* from, unsigned char* to, RSA* rsa, int padding) { - unsigned char *p, *p0; - int res; - size_t size, padlen; + unsigned char *p = NULL, *p0 = NULL; + size_t size, ssize, padlen; mp_int enc, dec, n, e; + mp_err ret; + int where = __LINE__; if (padding != RSA_PKCS1_PADDING) return -1; - mp_init_multi(&n, &e, &enc, &dec, NULL); + FIRST(mp_init_multi(&n, &e, &enc, &dec, NULL)); size = RSA_size(rsa); - - if (size < RSA_PKCS1_PADDING_SIZE || size - RSA_PKCS1_PADDING_SIZE < flen) { - mp_clear_multi(&n, &e, &enc, &dec, NULL); - return -2; - } - - BN2mpz(&n, rsa->n); - BN2mpz(&e, rsa->e); - - if (mp_cmp_d(&e, 3) == MP_LT) { - mp_clear_multi(&e, &n, &enc, &dec, NULL); - return -2; - } - - p = p0 = malloc(size - 1); - if (p0 == NULL) { - mp_clear_multi(&e, &n, &enc, &dec, NULL); - return -3; - } - - padlen = size - flen - 3; - - *p++ = 2; - if (RAND_bytes(p, padlen) != 1) { - mp_clear_multi(&e, &n, &enc, &dec, NULL); - free(p0); - return -4; + THEN_IF_MP((size < RSA_PKCS1_PADDING_SIZE || + size - RSA_PKCS1_PADDING_SIZE < flen), + MP_ERR); + THEN_MP(BN2mpz(&n, rsa->n)); + THEN_MP(BN2mpz(&e, rsa->e)); + THEN_IF_MP((mp_cmp_d(&e, 3) == MP_LT), MP_ERR); + THEN_ALLOC((p = p0 = malloc(size - 1))); + + if (ret == MP_OKAY) { + padlen = size - flen - 3; + *p++ = 2; } - while(padlen) { - if (*p == 0) - *p = 1; - padlen--; - p++; + THEN_IF_MP((RAND_bytes(p, padlen) != 1), MP_ERR); + + if (ret == MP_OKAY) { + while (padlen) { + if (*p == 0) + *p = 1; + padlen--; + p++; + } + *p++ = 0; + memcpy(p, from, flen); + p += flen; + assert((p - p0) == size - 1); } - *p++ = 0; - memcpy(p, from, flen); - p += flen; - assert((p - p0) == size - 1); - mp_read_unsigned_bin(&dec, p0, size - 1); - free(p0); - - res = mp_exptmod(&dec, &e, &n, &enc); + THEN_MP(mp_from_ubin(&dec, p0, size - 1)); + THEN_MP(mp_exptmod(&dec, &e, &n, &enc)); + THEN_VOID(ssize = mp_ubin_size(&enc)); + THEN_VOID(assert(size >= ssize)); + THEN_MP(mp_to_ubin(&enc, to, SIZE_MAX, NULL)); + THEN_VOID(size = ssize); mp_clear_multi(&dec, &e, &n, NULL); - - if (res != 0) { - mp_clear(&enc); - return -4; - } - - { - size_t ssize; - ssize = mp_unsigned_bin_size(&enc); - assert(size >= ssize); - mp_to_unsigned_bin(&enc, to); - size = ssize; - } mp_clear(&enc); - - return size; + free(p0); + return ret == MP_OKAY ? size : -where; } static int @@ -219,9 +223,10 @@ ltm_rsa_public_decrypt(int flen, const unsigned char* from, unsigned char* to, RSA* rsa, int padding) { unsigned char *p; - int res; + mp_err ret; size_t size; mp_int s, us, n, e; + int where = __LINE__; if (padding != RSA_PKCS1_PADDING) return -1; @@ -229,55 +234,38 @@ ltm_rsa_public_decrypt(int flen, const unsigned char* from, if (flen > RSA_size(rsa)) return -2; - mp_init_multi(&e, &n, &s, &us, NULL); - - BN2mpz(&n, rsa->n); - BN2mpz(&e, rsa->e); + FIRST(mp_init_multi(&e, &n, &s, &us, NULL)); + THEN_MP(BN2mpz(&n, rsa->n)); + THEN_MP(BN2mpz(&e, rsa->e)); + THEN_MP((mp_cmp_d(&e, 3) == MP_LT) ? MP_ERR : MP_OKAY); + THEN_MP(mp_from_ubin(&s, rk_UNCONST(from), (size_t)flen)); + THEN_MP((mp_cmp(&s, &n) >= 0) ? MP_ERR : MP_OKAY); + THEN_MP(mp_exptmod(&s, &e, &n, &us)); - if (mp_cmp_d(&e, 3) == MP_LT) { - mp_clear_multi(&e, &n, &s, &us, NULL); - return -3; - } - - mp_read_unsigned_bin(&s, rk_UNCONST(from), flen); - - if (mp_cmp(&s, &n) >= 0) { - mp_clear_multi(&e, &n, &s, &us, NULL); - return -4; - } - - res = mp_exptmod(&s, &e, &n, &us); + THEN_VOID(p = to); + THEN_VOID(size = mp_ubin_size(&us)); + THEN_VOID(assert(size <= RSA_size(rsa))); + THEN_MP(mp_to_ubin(&us, p, SIZE_MAX, NULL)); mp_clear_multi(&e, &n, &s, NULL); - - if (res != 0) { - mp_clear(&us); - return -5; - } - p = to; - - - size = mp_unsigned_bin_size(&us); - assert(size <= RSA_size(rsa)); - mp_to_unsigned_bin(&us, p); - mp_clear(&us); + if (ret != MP_OKAY || size == 0) + return -where; + /* head zero was skipped by mp_to_unsigned_bin */ if (*p == 0) - return -6; + return -where; if (*p != 1) - return -7; + return -(where + 1); size--; p++; while (size && *p == 0xff) { - size--; p++; + size--; p++; } if (size == 0 || *p != 0) - return -8; + return -(where + 2); size--; p++; - memmove(to, p, size); - return size; } @@ -285,102 +273,88 @@ static int ltm_rsa_private_encrypt(int flen, const unsigned char* from, unsigned char* to, RSA* rsa, int padding) { - unsigned char *ptr, *ptr0; - int res; - int size; + unsigned char *ptr, *ptr0 = NULL; + mp_err ret; mp_int in, out, n, e; mp_int bi, b; + size_t size; int blinding = (rsa->flags & RSA_FLAG_NO_BLINDING) == 0; int do_unblind = 0; + int where = __LINE__; if (padding != RSA_PKCS1_PADDING) return -1; - mp_init_multi(&e, &n, &in, &out, &b, &bi, NULL); + FIRST(mp_init_multi(&e, &n, &in, &out, &b, &bi, NULL)); size = RSA_size(rsa); - if (size < RSA_PKCS1_PADDING_SIZE || size - RSA_PKCS1_PADDING_SIZE < flen) return -2; - ptr0 = ptr = malloc(size); - *ptr++ = 0; - *ptr++ = 1; - memset(ptr, 0xff, size - flen - 3); - ptr += size - flen - 3; - *ptr++ = 0; - memcpy(ptr, from, flen); - ptr += flen; - assert((ptr - ptr0) == size); - - BN2mpz(&n, rsa->n); - BN2mpz(&e, rsa->e); - - if (mp_cmp_d(&e, 3) == MP_LT) { - size = -3; - goto out; + THEN_ALLOC((ptr0 = ptr = malloc(size))); + if (ret == MP_OKAY) { + *ptr++ = 0; + *ptr++ = 1; + memset(ptr, 0xff, size - flen - 3); + ptr += size - flen - 3; + *ptr++ = 0; + memcpy(ptr, from, flen); + ptr += flen; + assert((ptr - ptr0) == size); } - mp_read_unsigned_bin(&in, ptr0, size); + THEN_MP(BN2mpz(&n, rsa->n)); + THEN_MP(BN2mpz(&e, rsa->e)); + THEN_IF_MP((mp_cmp_d(&e, 3) == MP_LT), MP_ERR); + THEN_MP(mp_from_ubin(&in, ptr0, size)); free(ptr0); - if(mp_isneg(&in) || mp_cmp(&in, &n) >= 0) { - size = -3; - goto out; - } + THEN_IF_MP((mp_isneg(&in) || mp_cmp(&in, &n) >= 0), MP_ERR); if (blinding) { - setup_blind(&n, &b, &bi); - blind(&in, &b, &e, &n); + THEN_MP(setup_blind(&n, &b, &bi)); + THEN_MP(blind(&in, &b, &e, &n)); do_unblind = 1; } - if (rsa->p && rsa->q && rsa->dmp1 && rsa->dmq1 && rsa->iqmp) { + if (ret == MP_OKAY && rsa->p && rsa->q && rsa->dmp1 && rsa->dmq1 && + rsa->iqmp) { mp_int p, q, dmp1, dmq1, iqmp; - mp_init_multi(&p, &q, &dmp1, &dmq1, &iqmp, NULL); - - BN2mpz(&p, rsa->p); - BN2mpz(&q, rsa->q); - BN2mpz(&dmp1, rsa->dmp1); - BN2mpz(&dmq1, rsa->dmq1); - BN2mpz(&iqmp, rsa->iqmp); - - res = ltm_rsa_private_calculate(&in, &p, &q, &dmp1, &dmq1, &iqmp, &out); - + FIRST(mp_init_multi(&p, &q, &dmp1, &dmq1, &iqmp, NULL)); + THEN_MP(BN2mpz(&p, rsa->p)); + THEN_MP(BN2mpz(&q, rsa->q)); + THEN_MP(BN2mpz(&dmp1, rsa->dmp1)); + THEN_MP(BN2mpz(&dmq1, rsa->dmq1)); + THEN_MP(BN2mpz(&iqmp, rsa->iqmp)); + THEN_MP(ltm_rsa_private_calculate(&in, &p, &q, &dmp1, &dmq1, &iqmp, + &out)); mp_clear_multi(&p, &q, &dmp1, &dmq1, &iqmp, NULL); - - if (res != 0) { - size = -4; - goto out; - } - } else { + if (ret != MP_OKAY) goto out; + } else if (ret == MP_OKAY) { mp_int d; - BN2mpz(&d, rsa->d); - res = mp_exptmod(&in, &d, &n, &out); + THEN_MP(BN2mpz(&d, rsa->d)); + THEN_MP(mp_exptmod(&in, &d, &n, &out)); mp_clear(&d); - if (res != 0) { - size = -5; - goto out; - } + if (ret != MP_OKAY) goto out; } if (do_unblind) - unblind(&out, &bi, &n); + THEN_MP(unblind(&out, &bi, &n)); - if (size > 0) { + if (ret == MP_OKAY && size > 0) { size_t ssize; - ssize = mp_unsigned_bin_size(&out); + + ssize = mp_ubin_size(&out); assert(size >= ssize); - mp_to_unsigned_bin(&out, to); + THEN_MP(mp_to_ubin(&out, to, SIZE_MAX, NULL)); size = ssize; } out: mp_clear_multi(&e, &n, &in, &out, &b, &bi, NULL); - - return size; + return ret == MP_OKAY ? size : -where; } static int @@ -388,10 +362,12 @@ ltm_rsa_private_decrypt(int flen, const unsigned char* from, unsigned char* to, RSA* rsa, int padding) { unsigned char *ptr; - int res, size; + size_t size; + mp_err ret; mp_int in, out, n, e, b, bi; int blinding = (rsa->flags & RSA_FLAG_NO_BLINDING) == 0; int do_unblind = 0; + int where = __LINE__; if (padding != RSA_PKCS1_PADDING) return -1; @@ -400,95 +376,75 @@ ltm_rsa_private_decrypt(int flen, const unsigned char* from, if (flen > size) return -2; - mp_init_multi(&in, &n, &e, &out, &b, &bi, NULL); - - BN2mpz(&n, rsa->n); - BN2mpz(&e, rsa->e); - - if (mp_cmp_d(&e, 3) == MP_LT) { - size = -2; - goto out; - } - - mp_read_unsigned_bin(&in, rk_UNCONST(from), flen); - - if(mp_isneg(&in) || mp_cmp(&in, &n) >= 0) { - size = -2; - goto out; - } + FIRST(mp_init_multi(&in, &n, &e, &out, &b, &bi, NULL)); + THEN_MP(BN2mpz(&n, rsa->n)); + THEN_MP(BN2mpz(&e, rsa->e)); + THEN_IF_MP((mp_cmp_d(&e, 3) == MP_LT), MP_ERR); + THEN_MP(mp_from_ubin(&in, rk_UNCONST(from), flen)); + THEN_IF_MP((mp_isneg(&in) || mp_cmp(&in, &n) >= 0), MP_ERR); if (blinding) { - setup_blind(&n, &b, &bi); - blind(&in, &b, &e, &n); + THEN_MP(setup_blind(&n, &b, &bi)); + THEN_MP(blind(&in, &b, &e, &n)); do_unblind = 1; } - if (rsa->p && rsa->q && rsa->dmp1 && rsa->dmq1 && rsa->iqmp) { + if (ret == MP_OKAY && rsa->p && rsa->q && rsa->dmp1 && rsa->dmq1 && + rsa->iqmp) { mp_int p, q, dmp1, dmq1, iqmp; - mp_init_multi(&p, &q, &dmp1, &dmq1, &iqmp, NULL); - - BN2mpz(&p, rsa->p); - BN2mpz(&q, rsa->q); - BN2mpz(&dmp1, rsa->dmp1); - BN2mpz(&dmq1, rsa->dmq1); - BN2mpz(&iqmp, rsa->iqmp); - - res = ltm_rsa_private_calculate(&in, &p, &q, &dmp1, &dmq1, &iqmp, &out); - + THEN_MP(mp_init_multi(&p, &q, &dmp1, &dmq1, &iqmp, NULL)); + THEN_MP(BN2mpz(&p, rsa->p)); + THEN_MP(BN2mpz(&q, rsa->q)); + THEN_MP(BN2mpz(&dmp1, rsa->dmp1)); + THEN_MP(BN2mpz(&dmq1, rsa->dmq1)); + THEN_MP(BN2mpz(&iqmp, rsa->iqmp)); + THEN_MP(ltm_rsa_private_calculate(&in, &p, &q, &dmp1, &dmq1, &iqmp, &out)); mp_clear_multi(&p, &q, &dmp1, &dmq1, &iqmp, NULL); - - if (res != 0) { - size = -3; - goto out; - } - - } else { + if (ret != MP_OKAY) goto out; + } else if (ret == MP_OKAY) { mp_int d; - if(mp_isneg(&in) || mp_cmp(&in, &n) >= 0) - return -4; - - BN2mpz(&d, rsa->d); - res = mp_exptmod(&in, &d, &n, &out); + THEN_IF_MP((mp_isneg(&in) || mp_cmp(&in, &n) >= 0), MP_ERR); + THEN_MP(BN2mpz(&d, rsa->d)); + THEN_MP(mp_exptmod(&in, &d, &n, &out)); mp_clear(&d); - if (res != 0) { - size = -5; - goto out; - } + if (ret != MP_OKAY) goto out; } if (do_unblind) - unblind(&out, &bi, &n); + THEN_MP(unblind(&out, &bi, &n)); - ptr = to; - { - size_t ssize; - ssize = mp_unsigned_bin_size(&out); - assert(size >= ssize); - mp_to_unsigned_bin(&out, ptr); + if (ret == MP_OKAY) { + size_t ssize; + + ptr = to; + ssize = mp_ubin_size(&out); + assert(size >= ssize); + ret = mp_to_ubin(&out, ptr, SIZE_MAX, NULL); + if (ret != MP_OKAY) goto out; size = ssize; - } - /* head zero was skipped by mp_int_to_unsigned */ - if (*ptr != 2) { - size = -6; - goto out; - } - size--; ptr++; - while (size && *ptr != 0) { - size--; ptr++; + /* head zero was skipped by mp_int_to_unsigned */ + if (*ptr != 2) { + where = __LINE__; + goto out; + } + size--; ptr++; + while (size && *ptr != 0) { + size--; ptr++; + } + if (size == 0) { + where = __LINE__; + goto out; + } + size--; ptr++; + memmove(to, ptr, size); } - if (size == 0) - return -7; - size--; ptr++; - - memmove(to, ptr, size); out: mp_clear_multi(&e, &n, &in, &out, &b, &bi, NULL); - - return size; + return (ret == MP_OKAY) ? size : -where; } static BIGNUM * @@ -496,66 +452,109 @@ mpz2BN(mp_int *s) { size_t size; BIGNUM *bn; + mp_err ret; void *p; - size = mp_unsigned_bin_size(s); - p = malloc(size); - if (p == NULL && size != 0) + size = mp_ubin_size(s); + if (size == 0) return NULL; - mp_to_unsigned_bin(s, p); + p = malloc(size); + if (p == NULL) + return NULL; - bn = BN_bin2bn(p, size, NULL); + ret = mp_to_ubin(s, p, SIZE_MAX, NULL); + if (ret == MP_OKAY) + bn = BN_bin2bn(p, size, NULL); free(p); - return bn; + return (ret == MP_OKAY) ? bn : NULL; +} + +enum gen_pq_type { GEN_P, GEN_Q }; + +static int +gen_p(int bits, enum gen_pq_type pq_type, uint8_t nibble_pair, mp_int *p, mp_int *e, BN_GENCB *cb) +{ + unsigned char *buf = NULL; + mp_bool res; + mp_err ret = MP_MEM; + mp_int t1, t2; + size_t len = (bits + 7) / 8; + int trials = mp_prime_rabin_miller_trials(bits); + int counter = 0; + int where HEIMDAL_UNUSED_ATTRIBUTE = 0; + + + FIRST(mp_init_multi(&t1, &t2, NULL)); + if (ret == MP_OKAY && (buf = malloc(len))) do { + BN_GENCB_call(cb, 2, counter++); + /* random bytes */ + ret = (RAND_bytes(buf, len) == 1) ? MP_OKAY : MP_ERR; + + /* make it odd */ + buf[len - 1] |= 1; + + /* ensure the high nibble of the product is at least 128 */ + if (pq_type == GEN_P) + buf[0] = (nibble_pair & 0xf0) | (buf[0] & 0x0f); + else + buf[0] = ((nibble_pair & 0x0f) << 4) | (buf[0] & 0x0f); + + /* load number */ + THEN_MP(mp_from_ubin(p, buf, len)); + + /* test primality; repeat if not */ + THEN_MP(mp_prime_is_prime(p, trials, &res)); + if (ret == MP_OKAY && res == MP_NO) continue; + + /* check gcd(p - 1, e) == 1 */ + THEN_MP(mp_sub_d(p, 1, &t1)); + THEN_MP(mp_gcd(&t1, e, &t2)); + } while (ret == MP_OKAY && mp_cmp_d(&t2, 1) != MP_EQ); + + mp_clear_multi(&t1, &t2, NULL); + free(buf); + return ret; } -#define CHECK(f, v) if ((f) != (v)) { goto out; } +static uint8_t pq_high_nibble_pairs[] = { +0x9f, 0xad, 0xae, 0xaf, 0xbc, 0xbd, 0xbe, 0xbf, 0xcb, 0xcc, 0xcd, 0xce, 0xcf, +0xda, 0xdb, 0xdc, 0xdd, 0xde, 0xdf, 0xea, 0xeb, 0xec, 0xed, 0xee, 0xef, 0xf9, +0xfa, 0xfb, 0xfc, 0xfd, 0xfe, 0xff +}; static int ltm_rsa_generate_key(RSA *rsa, int bits, BIGNUM *e, BN_GENCB *cb) { mp_int el, p, q, n, d, dmp1, dmq1, iqmp, t1, t2, t3; - int counter, ret, bitsp; + mp_err ret; + uint8_t high_nibbles = 0; + int bitsp; + int where = __LINE__; if (bits < 789) return -1; bitsp = (bits + 1) / 2; - ret = -1; - - mp_init_multi(&el, &p, &q, &n, &d, - &dmp1, &dmq1, &iqmp, - &t1, &t2, &t3, NULL); + FIRST(mp_init_multi(&el, &p, &q, &n, &d, + &dmp1, &dmq1, &iqmp, + &t1, &t2, &t3, NULL)); + THEN_MP(BN2mpz(&el, e)); - BN2mpz(&el, e); + /* + * randomly pick a pair of high nibbles for p and q to ensure the product's + * high nibble is at least 128 + */ + if (ret == MP_OKAY) + ret = (RAND_bytes(&high_nibbles, 1) == 1) ? MP_OKAY : MP_ERR; + high_nibbles %= sizeof(pq_high_nibble_pairs); + high_nibbles = pq_high_nibble_pairs[high_nibbles]; /* generate p and q so that p != q and bits(pq) ~ bits */ - counter = 0; - do { - BN_GENCB_call(cb, 2, counter++); - CHECK(random_num(&p, bitsp), 0); - CHECK(mp_find_prime(&p,128), MP_YES); - - mp_sub_d(&p, 1, &t1); - mp_gcd(&t1, &el, &t2); - } while(mp_cmp_d(&t2, 1) != 0); - + THEN_MP(gen_p(bitsp, GEN_P, high_nibbles, &p, &el, cb)); BN_GENCB_call(cb, 3, 0); - - counter = 0; - do { - BN_GENCB_call(cb, 2, counter++); - CHECK(random_num(&q, bits - bitsp), 0); - CHECK(mp_find_prime(&q,128), MP_YES); - - if (mp_cmp(&p, &q) == 0) /* don't let p and q be the same */ - continue; - - mp_sub_d(&q, 1, &t1); - mp_gcd(&t1, &el, &t2); - } while(mp_cmp_d(&t2, 1) != 0); + THEN_MP(gen_p(bitsp, GEN_Q, high_nibbles, &q, &el, cb)); /* make p > q */ if (mp_cmp(&p, &q) < 0) { @@ -568,40 +567,38 @@ ltm_rsa_generate_key(RSA *rsa, int bits, BIGNUM *e, BN_GENCB *cb) BN_GENCB_call(cb, 3, 1); /* calculate n, n = p * q */ - mp_mul(&p, &q, &n); + THEN_MP(mp_mul(&p, &q, &n)); /* calculate d, d = 1/e mod (p - 1)(q - 1) */ - mp_sub_d(&p, 1, &t1); - mp_sub_d(&q, 1, &t2); - mp_mul(&t1, &t2, &t3); - mp_invmod(&el, &t3, &d); + THEN_MP(mp_sub_d(&p, 1, &t1)); + THEN_MP(mp_sub_d(&q, 1, &t2)); + THEN_MP(mp_mul(&t1, &t2, &t3)); + THEN_MP(mp_invmod(&el, &t3, &d)); /* calculate dmp1 dmp1 = d mod (p-1) */ - mp_mod(&d, &t1, &dmp1); + THEN_MP(mp_mod(&d, &t1, &dmp1)); /* calculate dmq1 dmq1 = d mod (q-1) */ - mp_mod(&d, &t2, &dmq1); + THEN_MP(mp_mod(&d, &t2, &dmq1)); /* calculate iqmp iqmp = 1/q mod p */ - mp_invmod(&q, &p, &iqmp); + THEN_MP(mp_invmod(&q, &p, &iqmp)); /* fill in RSA key */ - rsa->e = mpz2BN(&el); - rsa->p = mpz2BN(&p); - rsa->q = mpz2BN(&q); - rsa->n = mpz2BN(&n); - rsa->d = mpz2BN(&d); - rsa->dmp1 = mpz2BN(&dmp1); - rsa->dmq1 = mpz2BN(&dmq1); - rsa->iqmp = mpz2BN(&iqmp); - - ret = 1; + if (ret == MP_OKAY) { + rsa->e = mpz2BN(&el); + rsa->p = mpz2BN(&p); + rsa->q = mpz2BN(&q); + rsa->n = mpz2BN(&n); + rsa->d = mpz2BN(&d); + rsa->dmp1 = mpz2BN(&dmp1); + rsa->dmq1 = mpz2BN(&dmq1); + rsa->iqmp = mpz2BN(&iqmp); + } -out: mp_clear_multi(&el, &p, &q, &n, &d, &dmp1, &dmq1, &iqmp, &t1, &t2, &t3, NULL); - - return ret; + return (ret == MP_OKAY) ? 1 : -where; } static int diff --git a/lib/hcrypto/rsa.c b/lib/hcrypto/rsa.c index c99b2b6cbe95..31470d0069a3 100644 --- a/lib/hcrypto/rsa.c +++ b/lib/hcrypto/rsa.c @@ -114,7 +114,7 @@ RSA_new_method(ENGINE *engine) if (rsa->engine) { rsa->meth = ENGINE_get_RSA(rsa->engine); if (rsa->meth == NULL) { - ENGINE_finish(engine); + ENGINE_finish(rsa->engine); free(rsa); return 0; } @@ -160,7 +160,7 @@ RSA_free(RSA *rsa) free_if(rsa->iqmp); #undef free_if - memset(rsa, 0, sizeof(*rsa)); + memset_s(rsa, sizeof(*rsa), 0, sizeof(*rsa)); free(rsa); } @@ -272,7 +272,10 @@ RSA_check_key(const RSA *key) * and then decrypt/verify. */ - if ((rsa->d == NULL || rsa->n == NULL) && + if (rsa->n == NULL) + return 0; + + if (rsa->d == NULL && (rsa->p == NULL || rsa->q || rsa->dmp1 == NULL || rsa->dmq1 == NULL || rsa->iqmp == NULL)) return 0; @@ -423,7 +426,7 @@ RSA_verify(int type, const unsigned char *from, unsigned int flen, return -4; } - if (flen != di.digest.length || memcmp(di.digest.data, from, flen) != 0) { + if (flen != di.digest.length || ct_memcmp(di.digest.data, from, flen) != 0) { free_DigestInfo(&di); return -5; } diff --git a/lib/hcrypto/test_cipher.c b/lib/hcrypto/test_cipher.c index 26bf42c1b09d..9be65dd16e5d 100644 --- a/lib/hcrypto/test_cipher.c +++ b/lib/hcrypto/test_cipher.c @@ -295,10 +295,11 @@ test_cipher(int i, const EVP_CIPHER *c, struct tests *t) hex_encode(d, t->datasize, &s); errx(1, "%s: %d decrypt not the same: %s", t->name, i, s); } - if (t->outiv) { - /* XXXX check */ - ; - } + +#if 0 /* TODO */ + if (t->outiv) + /* XXXX check */; +#endif EVP_CIPHER_CTX_cleanup(&ectx); EVP_CIPHER_CTX_cleanup(&dctx); @@ -421,14 +422,8 @@ main(int argc, char **argv) ret += test_cipher(i, EVP_ossl_aes_256_cbc(), &aes_tests[i]); for (i = 0; i < sizeof(aes_cfb_tests)/sizeof(aes_cfb_tests[0]); i++) ret += test_cipher(i, EVP_ossl_aes_128_cfb8(), &aes_cfb_tests[i]); - for (i = 0; i < sizeof(rc2_tests)/sizeof(rc2_tests[0]); i++) - ret += test_cipher(i, EVP_ossl_rc2_cbc(), &rc2_tests[i]); - for (i = 0; i < sizeof(rc2_40_tests)/sizeof(rc2_40_tests[0]); i++) - ret += test_cipher(i, EVP_ossl_rc2_40_cbc(), &rc2_40_tests[i]); for (i = 0; i < sizeof(des_ede3_tests)/sizeof(des_ede3_tests[0]); i++) ret += test_cipher(i, EVP_ossl_des_ede3_cbc(), &des_ede3_tests[i]); - for (i = 0; i < sizeof(rc4_tests)/sizeof(rc4_tests[0]); i++) - ret += test_cipher(i, EVP_ossl_rc4(), &rc4_tests[i]); #endif /* PKCS11_MODULE_PATH */ return ret; diff --git a/lib/hcrypto/test_crypto.in b/lib/hcrypto/test_crypto.in index d5b3893164ab..91c4d8f1093e 100644 --- a/lib/hcrypto/test_crypto.in +++ b/lib/hcrypto/test_crypto.in @@ -82,11 +82,11 @@ for a in unix fortuna egd w32crypto ;do { echo "rand output same!" ; exit 1; } done -./example_evp_cipher 1 ${srcdir}/test_crypto.in test-out-1 || \ - { echo "1 failed" ; exit 1; } - -for a in 7 15 16 17 31 32 33 ; do - ./example_evp_cipher $a ${srcdir}/test_crypto.in test-out-$a +for a in 1 7 15 16 17 31 32 33 ; do + ./example_evp_cipher $a ${srcdir}/test_crypto.in test-out-$a || + { echo "$s failed" ; exit 1; } +done +for a in 7 15 16 17 31 32 33 ; do cmp test-out-1 test-out-$a || { echo "cmp $a failed" ; exit 1; } done diff --git a/lib/hcrypto/test_dh.c b/lib/hcrypto/test_dh.c index 638d25f706db..2ee947727246 100644 --- a/lib/hcrypto/test_dh.c +++ b/lib/hcrypto/test_dh.c @@ -260,9 +260,9 @@ str2val(const char *str, int base, size_t *len) i = 0; for (p = str; *p != '\0'; p++) { - if (isxdigit((int)*p)) + if (isxdigit((unsigned char)*p)) i++; - else if (isspace((int)*p)) + else if (isspace((unsigned char)*p)) ; else return NULL; @@ -277,7 +277,7 @@ str2val(const char *str, int base, size_t *len) i = 0; f = 0; for (rp = dst, p = str; *p != '\0'; p++) { - if (isxdigit((int)*p)) { + if (isxdigit((unsigned char)*p)) { if (!f) { b[0] = *p; f = 1; @@ -466,8 +466,6 @@ main(int argc, char **argv) printf("%s: shared secret OK\n", p->name); else printf("%s: shared secret FAILURE\n", p->name); - - return 0; } return 0; diff --git a/lib/hcrypto/test_hmac.c b/lib/hcrypto/test_hmac.c index 063a461cc161..36a5626a7086 100644 --- a/lib/hcrypto/test_hmac.c +++ b/lib/hcrypto/test_hmac.c @@ -51,7 +51,11 @@ main(int argc, char **argv) "\x6f\xd1\x52\x4d\x54\x58\x73\x0f\xf3\x24"; HMAC_CTX_init(&c); - HMAC_Init_ex(&c, hmackey, hmackey_size, EVP_sha1(), NULL); + if (HMAC_Init_ex(&c, hmackey, hmackey_size, EVP_sha1(), NULL) == 0) { + HMAC_CTX_cleanup(&c); + printf("out of memory\n"); + return 1; + } HMAC_Update(&c, buf, sizeof(buf)); HMAC_Final(&c, hmac, &hmaclen); HMAC_CTX_cleanup(&c); diff --git a/lib/hcrypto/test_rsa.c b/lib/hcrypto/test_rsa.c index 54b7a66c5ba1..c9766b8b3727 100644 --- a/lib/hcrypto/test_rsa.c +++ b/lib/hcrypto/test_rsa.c @@ -292,6 +292,7 @@ main(int argc, char **argv) if (RSA_generate_key_ex(rsa, 1024, e, NULL) != 1) errx(1, "RSA_generate_key_ex"); + BN_free(e); } else { rsa = read_key(engine, time_key); } @@ -314,6 +315,7 @@ main(int argc, char **argv) RSA_free(rsa); ENGINE_finish(engine); + free(p); return 0; } diff --git a/lib/hcrypto/validate.c b/lib/hcrypto/validate.c index 562e5aa4dd02..4b655f262c87 100644 --- a/lib/hcrypto/validate.c +++ b/lib/hcrypto/validate.c @@ -276,7 +276,8 @@ check_hmac(void) "\x6f\xd1\x52\x4d\x54\x58\x73\x0f\xf3\x24"; HMAC_CTX_init(&c); - HMAC_Init_ex(&c, hmackey, hmackey_size, EVP_sha1(), NULL); + if (HMAC_Init_ex(&c, hmackey, hmackey_size, EVP_sha1(), NULL) == 0) + errx(1, "HMAC_Init_ex() out of memory"); HMAC_Update(&c, buf, sizeof(buf)); HMAC_Final(&c, hmac, &hmaclen); HMAC_CTX_cleanup(&c); diff --git a/lib/hcrypto/version-script.map b/lib/hcrypto/version-script.map index 03583c5be4d7..b51d4bb607f1 100644 --- a/lib/hcrypto/version-script.map +++ b/lib/hcrypto/version-script.map @@ -238,7 +238,9 @@ HEIMDAL_CRYPTO_1.0 { hc_EVP_hcrypto_aes_256_cts; hc_HMAC; hc_HMAC_CTX_cleanup; + hc_HMAC_CTX_free; hc_HMAC_CTX_init; + hc_HMAC_CTX_new; hc_HMAC_Final; hc_HMAC_Init_ex; hc_HMAC_Update; @@ -324,6 +326,8 @@ HEIMDAL_CRYPTO_1.0 { hc_EVP_CipherUpdate; hc_EVP_CipherFinal_ex; hc_hcrypto_validate; + hc_hcrypto_scalarmult_curve25519; + hc_hcrypto_scalarmult_curve25519_base; local: *; }; diff --git a/lib/hcrypto/x25519/NTMakefile b/lib/hcrypto/x25519/NTMakefile new file mode 100644 index 000000000000..408f2402bf2c --- /dev/null +++ b/lib/hcrypto/x25519/NTMakefile @@ -0,0 +1,46 @@ +######################################################################## +# +# Copyright (c) 2009, Secure Endpoints Inc. +# All rights reserved. +# +# Redistribution and use in source and binary forms, with or without +# modification, are permitted provided that the following conditions +# are met: +# +# - Redistributions of source code must retain the above copyright +# notice, this list of conditions and the following disclaimer. +# +# - Redistributions in binary form must reproduce the above copyright +# notice, this list of conditions and the following disclaimer in +# the documentation and/or other materials provided with the +# distribution. +# +# THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS +# "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT +# LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS +# FOR A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE +# COPYRIGHT HOLDER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, +# INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, +# BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; +# LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER +# CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT +# LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN +# ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE +# POSSIBILITY OF SUCH DAMAGE. +# + +RELDIR=lib\hcrypto\x25519 + +!include ../../../windows/NTMakefile.w32 + +intcflags=-I$(SRC)\lib\hcrypto + +LIBX25519_OBJS= \ + $(OBJ)\ed25519_ref10.obj \ + $(OBJ)\x25519_ref10.obj + +$(LIBX25519): $(LIBX25519_OBJS) + $(LIBCON) + +all:: $(LIBX25519) + diff --git a/lib/hcrypto/x25519/align.h b/lib/hcrypto/x25519/align.h new file mode 100644 index 000000000000..57c90ecce690 --- /dev/null +++ b/lib/hcrypto/x25519/align.h @@ -0,0 +1,7 @@ +#ifndef CRYPTO_ALIGN +# if defined(__INTEL_COMPILER) || defined(_MSC_VER) +# define CRYPTO_ALIGN(x) __declspec(align(x)) +# else +# define CRYPTO_ALIGN(x) __attribute__ ((aligned(x))) +# endif +#endif diff --git a/lib/hcrypto/x25519/ed25519_ref10.c b/lib/hcrypto/x25519/ed25519_ref10.c new file mode 100644 index 000000000000..6533404ce2e4 --- /dev/null +++ b/lib/hcrypto/x25519/ed25519_ref10.c @@ -0,0 +1,2886 @@ +/* + * ISC License + * + * Copyright (c) 2013-2019 + * Frank Denis <j at pureftpd dot org> + * + * Permission to use, copy, modify, and/or distribute this software for any + * purpose with or without fee is hereby granted, provided that the above + * copyright notice and this permission notice appear in all copies. + * + * THE SOFTWARE IS PROVIDED "AS IS" AND THE AUTHOR DISCLAIMS ALL WARRANTIES + * WITH REGARD TO THIS SOFTWARE INCLUDING ALL IMPLIED WARRANTIES OF + * MERCHANTABILITY AND FITNESS. IN NO EVENT SHALL THE AUTHOR BE LIABLE FOR + * ANY SPECIAL, DIRECT, INDIRECT, OR CONSEQUENTIAL DAMAGES OR ANY DAMAGES + * WHATSOEVER RESULTING FROM LOSS OF USE, DATA OR PROFITS, WHETHER IN AN + * ACTION OF CONTRACT, NEGLIGENCE OR OTHER TORTIOUS ACTION, ARISING OUT OF + * OR IN CONNECTION WITH THE USE OR PERFORMANCE OF THIS SOFTWARE. + */ + +#include <roken.h> +#include <stddef.h> +#include <stdint.h> +#include <stdlib.h> +#include <string.h> + +#include "ed25519_ref10.h" +#include "align.h" + +static inline uint64_t +load_3(const unsigned char *in) +{ + uint64_t result; + + result = (uint64_t) in[0]; + result |= ((uint64_t) in[1]) << 8; + result |= ((uint64_t) in[2]) << 16; + + return result; +} + +static inline uint64_t +load_4(const unsigned char *in) +{ + uint64_t result; + + result = (uint64_t) in[0]; + result |= ((uint64_t) in[1]) << 8; + result |= ((uint64_t) in[2]) << 16; + result |= ((uint64_t) in[3]) << 24; + + return result; +} + +/* + * Field arithmetic: + * Use 5*51 bit limbs on 64-bit systems with support for 128 bit arithmetic, + * and 10*25.5 bit limbs elsewhere. + * + * Functions used elsewhere that are candidates for inlining are defined + * via "private/curve25519_ref10.h". + */ + +#ifdef HAVE_TI_MODE +# include "fe_51/constants.h" +# include "fe_51/fe.h" +#else +# include "fe_25_5/constants.h" +# include "fe_25_5/fe.h" +#endif + +void +fe25519_invert(fe25519 out, const fe25519 z) +{ + fe25519 t0; + fe25519 t1; + fe25519 t2; + fe25519 t3; + int i; + + fe25519_sq(t0, z); + fe25519_sq(t1, t0); + fe25519_sq(t1, t1); + fe25519_mul(t1, z, t1); + fe25519_mul(t0, t0, t1); + fe25519_sq(t2, t0); + fe25519_mul(t1, t1, t2); + fe25519_sq(t2, t1); + for (i = 1; i < 5; ++i) { + fe25519_sq(t2, t2); + } + fe25519_mul(t1, t2, t1); + fe25519_sq(t2, t1); + for (i = 1; i < 10; ++i) { + fe25519_sq(t2, t2); + } + fe25519_mul(t2, t2, t1); + fe25519_sq(t3, t2); + for (i = 1; i < 20; ++i) { + fe25519_sq(t3, t3); + } + fe25519_mul(t2, t3, t2); + fe25519_sq(t2, t2); + for (i = 1; i < 10; ++i) { + fe25519_sq(t2, t2); + } + fe25519_mul(t1, t2, t1); + fe25519_sq(t2, t1); + for (i = 1; i < 50; ++i) { + fe25519_sq(t2, t2); + } + fe25519_mul(t2, t2, t1); + fe25519_sq(t3, t2); + for (i = 1; i < 100; ++i) { + fe25519_sq(t3, t3); + } + fe25519_mul(t2, t3, t2); + fe25519_sq(t2, t2); + for (i = 1; i < 50; ++i) { + fe25519_sq(t2, t2); + } + fe25519_mul(t1, t2, t1); + fe25519_sq(t1, t1); + for (i = 1; i < 5; ++i) { + fe25519_sq(t1, t1); + } + fe25519_mul(out, t1, t0); +} + +static void +fe25519_pow22523(fe25519 out, const fe25519 z) +{ + fe25519 t0; + fe25519 t1; + fe25519 t2; + int i; + + fe25519_sq(t0, z); + fe25519_sq(t1, t0); + fe25519_sq(t1, t1); + fe25519_mul(t1, z, t1); + fe25519_mul(t0, t0, t1); + fe25519_sq(t0, t0); + fe25519_mul(t0, t1, t0); + fe25519_sq(t1, t0); + for (i = 1; i < 5; ++i) { + fe25519_sq(t1, t1); + } + fe25519_mul(t0, t1, t0); + fe25519_sq(t1, t0); + for (i = 1; i < 10; ++i) { + fe25519_sq(t1, t1); + } + fe25519_mul(t1, t1, t0); + fe25519_sq(t2, t1); + for (i = 1; i < 20; ++i) { + fe25519_sq(t2, t2); + } + fe25519_mul(t1, t2, t1); + fe25519_sq(t1, t1); + for (i = 1; i < 10; ++i) { + fe25519_sq(t1, t1); + } + fe25519_mul(t0, t1, t0); + fe25519_sq(t1, t0); + for (i = 1; i < 50; ++i) { + fe25519_sq(t1, t1); + } + fe25519_mul(t1, t1, t0); + fe25519_sq(t2, t1); + for (i = 1; i < 100; ++i) { + fe25519_sq(t2, t2); + } + fe25519_mul(t1, t2, t1); + fe25519_sq(t1, t1); + for (i = 1; i < 50; ++i) { + fe25519_sq(t1, t1); + } + fe25519_mul(t0, t1, t0); + fe25519_sq(t0, t0); + fe25519_sq(t0, t0); + fe25519_mul(out, t0, z); +} + +static inline void +fe25519_cneg(fe25519 h, const fe25519 f, unsigned int b) +{ + fe25519 negf; + + fe25519_neg(negf, f); + fe25519_copy(h, f); + fe25519_cmov(h, negf, b); +} + +static inline void +fe25519_abs(fe25519 h, const fe25519 f) +{ + fe25519_cneg(h, f, fe25519_isnegative(f)); +} + +/* + r = p + q + */ + +void +ge25519_add(ge25519_p1p1 *r, const ge25519_p3 *p, const ge25519_cached *q) +{ + fe25519 t0; + + fe25519_add(r->X, p->Y, p->X); + fe25519_sub(r->Y, p->Y, p->X); + fe25519_mul(r->Z, r->X, q->YplusX); + fe25519_mul(r->Y, r->Y, q->YminusX); + fe25519_mul(r->T, q->T2d, p->T); + fe25519_mul(r->X, p->Z, q->Z); + fe25519_add(t0, r->X, r->X); + fe25519_sub(r->X, r->Z, r->Y); + fe25519_add(r->Y, r->Z, r->Y); + fe25519_add(r->Z, t0, r->T); + fe25519_sub(r->T, t0, r->T); +} + +static void +slide_vartime(signed char *r, const unsigned char *a) +{ + int i; + int b; + int k; + int ribs; + int cmp; + + for (i = 0; i < 256; ++i) { + r[i] = 1 & (a[i >> 3] >> (i & 7)); + } + for (i = 0; i < 256; ++i) { + if (! r[i]) { + continue; + } + for (b = 1; b <= 6 && i + b < 256; ++b) { + if (! r[i + b]) { + continue; + } + ribs = r[i + b] << b; + cmp = r[i] + ribs; + if (cmp <= 15) { + r[i] = cmp; + r[i + b] = 0; + } else { + cmp = r[i] - ribs; + if (cmp < -15) { + break; + } + r[i] = cmp; + for (k = i + b; k < 256; ++k) { + if (! r[k]) { + r[k] = 1; + break; + } + r[k] = 0; + } + } + } + } +} + +int +ge25519_frombytes(ge25519_p3 *h, const unsigned char *s) +{ + fe25519 u; + fe25519 v; + fe25519 v3; + fe25519 vxx; + fe25519 m_root_check, p_root_check; + fe25519 negx; + fe25519 x_sqrtm1; + int has_m_root, has_p_root; + + fe25519_frombytes(h->Y, s); + fe25519_1(h->Z); + fe25519_sq(u, h->Y); + fe25519_mul(v, u, d); + fe25519_sub(u, u, h->Z); /* u = y^2-1 */ + fe25519_add(v, v, h->Z); /* v = dy^2+1 */ + + fe25519_sq(v3, v); + fe25519_mul(v3, v3, v); /* v3 = v^3 */ + fe25519_sq(h->X, v3); + fe25519_mul(h->X, h->X, v); + fe25519_mul(h->X, h->X, u); /* x = uv^7 */ + + fe25519_pow22523(h->X, h->X); /* x = (uv^7)^((q-5)/8) */ + fe25519_mul(h->X, h->X, v3); + fe25519_mul(h->X, h->X, u); /* x = uv^3(uv^7)^((q-5)/8) */ + + fe25519_sq(vxx, h->X); + fe25519_mul(vxx, vxx, v); + fe25519_sub(m_root_check, vxx, u); /* vx^2-u */ + fe25519_add(p_root_check, vxx, u); /* vx^2+u */ + has_m_root = fe25519_iszero(m_root_check); + has_p_root = fe25519_iszero(p_root_check); + fe25519_mul(x_sqrtm1, h->X, sqrtm1); /* x*sqrt(-1) */ + fe25519_cmov(h->X, x_sqrtm1, 1 - has_m_root); + + fe25519_neg(negx, h->X); + fe25519_cmov(h->X, negx, fe25519_isnegative(h->X) ^ (s[31] >> 7)); + fe25519_mul(h->T, h->X, h->Y); + + return (has_m_root | has_p_root) - 1; +} + +int +ge25519_frombytes_negate_vartime(ge25519_p3 *h, const unsigned char *s) +{ + fe25519 u; + fe25519 v; + fe25519 v3; + fe25519 vxx; + fe25519 m_root_check, p_root_check; + + fe25519_frombytes(h->Y, s); + fe25519_1(h->Z); + fe25519_sq(u, h->Y); + fe25519_mul(v, u, d); + fe25519_sub(u, u, h->Z); /* u = y^2-1 */ + fe25519_add(v, v, h->Z); /* v = dy^2+1 */ + + fe25519_sq(v3, v); + fe25519_mul(v3, v3, v); /* v3 = v^3 */ + fe25519_sq(h->X, v3); + fe25519_mul(h->X, h->X, v); + fe25519_mul(h->X, h->X, u); /* x = uv^7 */ + + fe25519_pow22523(h->X, h->X); /* x = (uv^7)^((q-5)/8) */ + fe25519_mul(h->X, h->X, v3); + fe25519_mul(h->X, h->X, u); /* x = uv^3(uv^7)^((q-5)/8) */ + + fe25519_sq(vxx, h->X); + fe25519_mul(vxx, vxx, v); + fe25519_sub(m_root_check, vxx, u); /* vx^2-u */ + if (fe25519_iszero(m_root_check) == 0) { + fe25519_add(p_root_check, vxx, u); /* vx^2+u */ + if (fe25519_iszero(p_root_check) == 0) { + return -1; + } + fe25519_mul(h->X, h->X, sqrtm1); + } + + if (fe25519_isnegative(h->X) == (s[31] >> 7)) { + fe25519_neg(h->X, h->X); + } + fe25519_mul(h->T, h->X, h->Y); + + return 0; +} + +/* + r = p + q + */ + +static void +ge25519_madd(ge25519_p1p1 *r, const ge25519_p3 *p, const ge25519_precomp *q) +{ + fe25519 t0; + + fe25519_add(r->X, p->Y, p->X); + fe25519_sub(r->Y, p->Y, p->X); + fe25519_mul(r->Z, r->X, q->yplusx); + fe25519_mul(r->Y, r->Y, q->yminusx); + fe25519_mul(r->T, q->xy2d, p->T); + fe25519_add(t0, p->Z, p->Z); + fe25519_sub(r->X, r->Z, r->Y); + fe25519_add(r->Y, r->Z, r->Y); + fe25519_add(r->Z, t0, r->T); + fe25519_sub(r->T, t0, r->T); +} + +/* + r = p - q + */ + +static void +ge25519_msub(ge25519_p1p1 *r, const ge25519_p3 *p, const ge25519_precomp *q) +{ + fe25519 t0; + + fe25519_add(r->X, p->Y, p->X); + fe25519_sub(r->Y, p->Y, p->X); + fe25519_mul(r->Z, r->X, q->yminusx); + fe25519_mul(r->Y, r->Y, q->yplusx); + fe25519_mul(r->T, q->xy2d, p->T); + fe25519_add(t0, p->Z, p->Z); + fe25519_sub(r->X, r->Z, r->Y); + fe25519_add(r->Y, r->Z, r->Y); + fe25519_sub(r->Z, t0, r->T); + fe25519_add(r->T, t0, r->T); +} + +/* + r = p + */ + +void +ge25519_p1p1_to_p2(ge25519_p2 *r, const ge25519_p1p1 *p) +{ + fe25519_mul(r->X, p->X, p->T); + fe25519_mul(r->Y, p->Y, p->Z); + fe25519_mul(r->Z, p->Z, p->T); +} + +/* + r = p + */ + +void +ge25519_p1p1_to_p3(ge25519_p3 *r, const ge25519_p1p1 *p) +{ + fe25519_mul(r->X, p->X, p->T); + fe25519_mul(r->Y, p->Y, p->Z); + fe25519_mul(r->Z, p->Z, p->T); + fe25519_mul(r->T, p->X, p->Y); +} + +static void +ge25519_p2_0(ge25519_p2 *h) +{ + fe25519_0(h->X); + fe25519_1(h->Y); + fe25519_1(h->Z); +} + +/* + r = 2 * p + */ + +static void +ge25519_p2_dbl(ge25519_p1p1 *r, const ge25519_p2 *p) +{ + fe25519 t0; + + fe25519_sq(r->X, p->X); + fe25519_sq(r->Z, p->Y); + fe25519_sq2(r->T, p->Z); + fe25519_add(r->Y, p->X, p->Y); + fe25519_sq(t0, r->Y); + fe25519_add(r->Y, r->Z, r->X); + fe25519_sub(r->Z, r->Z, r->X); + fe25519_sub(r->X, t0, r->Y); + fe25519_sub(r->T, r->T, r->Z); +} + +static void +ge25519_p3_0(ge25519_p3 *h) +{ + fe25519_0(h->X); + fe25519_1(h->Y); + fe25519_1(h->Z); + fe25519_0(h->T); +} + +static void +ge25519_cached_0(ge25519_cached *h) +{ + fe25519_1(h->YplusX); + fe25519_1(h->YminusX); + fe25519_1(h->Z); + fe25519_0(h->T2d); +} + +/* + r = p + */ + +void +ge25519_p3_to_cached(ge25519_cached *r, const ge25519_p3 *p) +{ + fe25519_add(r->YplusX, p->Y, p->X); + fe25519_sub(r->YminusX, p->Y, p->X); + fe25519_copy(r->Z, p->Z); + fe25519_mul(r->T2d, p->T, d2); +} + +static void +ge25519_p3_to_precomp(ge25519_precomp *pi, const ge25519_p3 *p) +{ + fe25519 recip; + fe25519 x; + fe25519 y; + fe25519 xy; + + fe25519_invert(recip, p->Z); + fe25519_mul(x, p->X, recip); + fe25519_mul(y, p->Y, recip); + fe25519_add(pi->yplusx, y, x); + fe25519_sub(pi->yminusx, y, x); + fe25519_mul(xy, x, y); + fe25519_mul(pi->xy2d, xy, d2); +} + +/* + r = p + */ + +static void +ge25519_p3_to_p2(ge25519_p2 *r, const ge25519_p3 *p) +{ + fe25519_copy(r->X, p->X); + fe25519_copy(r->Y, p->Y); + fe25519_copy(r->Z, p->Z); +} + +void +ge25519_p3_tobytes(unsigned char *s, const ge25519_p3 *h) +{ + fe25519 recip; + fe25519 x; + fe25519 y; + + fe25519_invert(recip, h->Z); + fe25519_mul(x, h->X, recip); + fe25519_mul(y, h->Y, recip); + fe25519_tobytes(s, y); + s[31] ^= fe25519_isnegative(x) << 7; +} + +/* + r = 2 * p + */ + +static void +ge25519_p3_dbl(ge25519_p1p1 *r, const ge25519_p3 *p) +{ + ge25519_p2 q; + ge25519_p3_to_p2(&q, p); + ge25519_p2_dbl(r, &q); +} + +static void +ge25519_precomp_0(ge25519_precomp *h) +{ + fe25519_1(h->yplusx); + fe25519_1(h->yminusx); + fe25519_0(h->xy2d); +} + +static unsigned char +equal(signed char b, signed char c) +{ + unsigned char ub = b; + unsigned char uc = c; + unsigned char x = ub ^ uc; /* 0: yes; 1..255: no */ + uint32_t y = (uint32_t) x; /* 0: yes; 1..255: no */ + + y -= 1; /* 4294967295: yes; 0..254: no */ + y >>= 31; /* 1: yes; 0: no */ + + return y; +} + +static unsigned char +negative(signed char b) +{ + /* 18446744073709551361..18446744073709551615: yes; 0..255: no */ + uint64_t x = b; + + x >>= 63; /* 1: yes; 0: no */ + + return x; +} + +static void +ge25519_cmov(ge25519_precomp *t, const ge25519_precomp *u, unsigned char b) +{ + fe25519_cmov(t->yplusx, u->yplusx, b); + fe25519_cmov(t->yminusx, u->yminusx, b); + fe25519_cmov(t->xy2d, u->xy2d, b); +} + +static void +ge25519_cmov_cached(ge25519_cached *t, const ge25519_cached *u, unsigned char b) +{ + fe25519_cmov(t->YplusX, u->YplusX, b); + fe25519_cmov(t->YminusX, u->YminusX, b); + fe25519_cmov(t->Z, u->Z, b); + fe25519_cmov(t->T2d, u->T2d, b); +} + +static void +ge25519_cmov8(ge25519_precomp *t, const ge25519_precomp precomp[8], const signed char b) +{ + ge25519_precomp minust; + const unsigned char bnegative = negative(b); + const unsigned char babs = b - (((-bnegative) & b) * ((signed char) 1 << 1)); + + ge25519_precomp_0(t); + ge25519_cmov(t, &precomp[0], equal(babs, 1)); + ge25519_cmov(t, &precomp[1], equal(babs, 2)); + ge25519_cmov(t, &precomp[2], equal(babs, 3)); + ge25519_cmov(t, &precomp[3], equal(babs, 4)); + ge25519_cmov(t, &precomp[4], equal(babs, 5)); + ge25519_cmov(t, &precomp[5], equal(babs, 6)); + ge25519_cmov(t, &precomp[6], equal(babs, 7)); + ge25519_cmov(t, &precomp[7], equal(babs, 8)); + fe25519_copy(minust.yplusx, t->yminusx); + fe25519_copy(minust.yminusx, t->yplusx); + fe25519_neg(minust.xy2d, t->xy2d); + ge25519_cmov(t, &minust, bnegative); +} + +static void +ge25519_cmov8_base(ge25519_precomp *t, const int pos, const signed char b) +{ + static const ge25519_precomp base[32][8] = { /* base[i][j] = (j+1)*256^i*B */ +#ifdef HAVE_TI_MODE +# include "fe_51/base.h" +#else +# include "fe_25_5/base.h" +#endif + }; + ge25519_cmov8(t, base[pos], b); +} + +static void +ge25519_cmov8_cached(ge25519_cached *t, const ge25519_cached cached[8], const signed char b) +{ + ge25519_cached minust; + const unsigned char bnegative = negative(b); + const unsigned char babs = b - (((-bnegative) & b) * ((signed char) 1 << 1)); + + ge25519_cached_0(t); + ge25519_cmov_cached(t, &cached[0], equal(babs, 1)); + ge25519_cmov_cached(t, &cached[1], equal(babs, 2)); + ge25519_cmov_cached(t, &cached[2], equal(babs, 3)); + ge25519_cmov_cached(t, &cached[3], equal(babs, 4)); + ge25519_cmov_cached(t, &cached[4], equal(babs, 5)); + ge25519_cmov_cached(t, &cached[5], equal(babs, 6)); + ge25519_cmov_cached(t, &cached[6], equal(babs, 7)); + ge25519_cmov_cached(t, &cached[7], equal(babs, 8)); + fe25519_copy(minust.YplusX, t->YminusX); + fe25519_copy(minust.YminusX, t->YplusX); + fe25519_copy(minust.Z, t->Z); + fe25519_neg(minust.T2d, t->T2d); + ge25519_cmov_cached(t, &minust, bnegative); +} + +/* + r = p - q + */ + +void +ge25519_sub(ge25519_p1p1 *r, const ge25519_p3 *p, const ge25519_cached *q) +{ + fe25519 t0; + + fe25519_add(r->X, p->Y, p->X); + fe25519_sub(r->Y, p->Y, p->X); + fe25519_mul(r->Z, r->X, q->YminusX); + fe25519_mul(r->Y, r->Y, q->YplusX); + fe25519_mul(r->T, q->T2d, p->T); + fe25519_mul(r->X, p->Z, q->Z); + fe25519_add(t0, r->X, r->X); + fe25519_sub(r->X, r->Z, r->Y); + fe25519_add(r->Y, r->Z, r->Y); + fe25519_sub(r->Z, t0, r->T); + fe25519_add(r->T, t0, r->T); +} + +void +ge25519_tobytes(unsigned char *s, const ge25519_p2 *h) +{ + fe25519 recip; + fe25519 x; + fe25519 y; + + fe25519_invert(recip, h->Z); + fe25519_mul(x, h->X, recip); + fe25519_mul(y, h->Y, recip); + fe25519_tobytes(s, y); + s[31] ^= fe25519_isnegative(x) << 7; +} + +/* + r = a * A + b * B + where a = a[0]+256*a[1]+...+256^31 a[31]. + and b = b[0]+256*b[1]+...+256^31 b[31]. + B is the Ed25519 base point (x,4/5) with x positive. + + Only used for signatures verification. + */ + +void +ge25519_double_scalarmult_vartime(ge25519_p2 *r, const unsigned char *a, + const ge25519_p3 *A, const unsigned char *b) +{ + static const ge25519_precomp Bi[8] = { +#ifdef HAVE_TI_MODE +# include "fe_51/base2.h" +#else +# include "fe_25_5/base2.h" +#endif + }; + signed char aslide[256]; + signed char bslide[256]; + ge25519_cached Ai[8]; /* A,3A,5A,7A,9A,11A,13A,15A */ + ge25519_p1p1 t; + ge25519_p3 u; + ge25519_p3 A2; + int i; + + slide_vartime(aslide, a); + slide_vartime(bslide, b); + + ge25519_p3_to_cached(&Ai[0], A); + + ge25519_p3_dbl(&t, A); + ge25519_p1p1_to_p3(&A2, &t); + + ge25519_add(&t, &A2, &Ai[0]); + ge25519_p1p1_to_p3(&u, &t); + ge25519_p3_to_cached(&Ai[1], &u); + + ge25519_add(&t, &A2, &Ai[1]); + ge25519_p1p1_to_p3(&u, &t); + ge25519_p3_to_cached(&Ai[2], &u); + + ge25519_add(&t, &A2, &Ai[2]); + ge25519_p1p1_to_p3(&u, &t); + ge25519_p3_to_cached(&Ai[3], &u); + + ge25519_add(&t, &A2, &Ai[3]); + ge25519_p1p1_to_p3(&u, &t); + ge25519_p3_to_cached(&Ai[4], &u); + + ge25519_add(&t, &A2, &Ai[4]); + ge25519_p1p1_to_p3(&u, &t); + ge25519_p3_to_cached(&Ai[5], &u); + + ge25519_add(&t, &A2, &Ai[5]); + ge25519_p1p1_to_p3(&u, &t); + ge25519_p3_to_cached(&Ai[6], &u); + + ge25519_add(&t, &A2, &Ai[6]); + ge25519_p1p1_to_p3(&u, &t); + ge25519_p3_to_cached(&Ai[7], &u); + + ge25519_p2_0(r); + + for (i = 255; i >= 0; --i) { + if (aslide[i] || bslide[i]) { + break; + } + } + + for (; i >= 0; --i) { + ge25519_p2_dbl(&t, r); + + if (aslide[i] > 0) { + ge25519_p1p1_to_p3(&u, &t); + ge25519_add(&t, &u, &Ai[aslide[i] / 2]); + } else if (aslide[i] < 0) { + ge25519_p1p1_to_p3(&u, &t); + ge25519_sub(&t, &u, &Ai[(-aslide[i]) / 2]); + } + + if (bslide[i] > 0) { + ge25519_p1p1_to_p3(&u, &t); + ge25519_madd(&t, &u, &Bi[bslide[i] / 2]); + } else if (bslide[i] < 0) { + ge25519_p1p1_to_p3(&u, &t); + ge25519_msub(&t, &u, &Bi[(-bslide[i]) / 2]); + } + + ge25519_p1p1_to_p2(r, &t); + } +} + +/* + h = a * p + where a = a[0]+256*a[1]+...+256^31 a[31] + + Preconditions: + a[31] <= 127 + + p is public + */ + +void +ge25519_scalarmult(ge25519_p3 *h, const unsigned char *a, const ge25519_p3 *p) +{ + signed char e[64]; + signed char carry; + ge25519_p1p1 r; + ge25519_p2 s; + ge25519_p1p1 t2, t3, t4, t5, t6, t7, t8; + ge25519_p3 p2, p3, p4, p5, p6, p7, p8; + ge25519_cached pi[8]; + ge25519_cached t; + int i; + + ge25519_p3_to_cached(&pi[1 - 1], p); /* p */ + + ge25519_p3_dbl(&t2, p); + ge25519_p1p1_to_p3(&p2, &t2); + ge25519_p3_to_cached(&pi[2 - 1], &p2); /* 2p = 2*p */ + + ge25519_add(&t3, p, &pi[2 - 1]); + ge25519_p1p1_to_p3(&p3, &t3); + ge25519_p3_to_cached(&pi[3 - 1], &p3); /* 3p = 2p+p */ + + ge25519_p3_dbl(&t4, &p2); + ge25519_p1p1_to_p3(&p4, &t4); + ge25519_p3_to_cached(&pi[4 - 1], &p4); /* 4p = 2*2p */ + + ge25519_add(&t5, p, &pi[4 - 1]); + ge25519_p1p1_to_p3(&p5, &t5); + ge25519_p3_to_cached(&pi[5 - 1], &p5); /* 5p = 4p+p */ + + ge25519_p3_dbl(&t6, &p3); + ge25519_p1p1_to_p3(&p6, &t6); + ge25519_p3_to_cached(&pi[6 - 1], &p6); /* 6p = 2*3p */ + + ge25519_add(&t7, p, &pi[6 - 1]); + ge25519_p1p1_to_p3(&p7, &t7); + ge25519_p3_to_cached(&pi[7 - 1], &p7); /* 7p = 6p+p */ + + ge25519_p3_dbl(&t8, &p4); + ge25519_p1p1_to_p3(&p8, &t8); + ge25519_p3_to_cached(&pi[8 - 1], &p8); /* 8p = 2*4p */ + + for (i = 0; i < 32; ++i) { + e[2 * i + 0] = (a[i] >> 0) & 15; + e[2 * i + 1] = (a[i] >> 4) & 15; + } + /* each e[i] is between 0 and 15 */ + /* e[63] is between 0 and 7 */ + + carry = 0; + for (i = 0; i < 63; ++i) { + e[i] += carry; + carry = e[i] + 8; + carry >>= 4; + e[i] -= carry * ((signed char) 1 << 4); + } + e[63] += carry; + /* each e[i] is between -8 and 8 */ + + ge25519_p3_0(h); + + for (i = 63; i != 0; i--) { + ge25519_cmov8_cached(&t, pi, e[i]); + ge25519_add(&r, h, &t); + + ge25519_p1p1_to_p2(&s, &r); + ge25519_p2_dbl(&r, &s); + ge25519_p1p1_to_p2(&s, &r); + ge25519_p2_dbl(&r, &s); + ge25519_p1p1_to_p2(&s, &r); + ge25519_p2_dbl(&r, &s); + ge25519_p1p1_to_p2(&s, &r); + ge25519_p2_dbl(&r, &s); + + ge25519_p1p1_to_p3(h, &r); /* *16 */ + } + ge25519_cmov8_cached(&t, pi, e[i]); + ge25519_add(&r, h, &t); + + ge25519_p1p1_to_p3(h, &r); +} + +/* + h = a * B (with precomputation) + where a = a[0]+256*a[1]+...+256^31 a[31] + B is the Ed25519 base point (x,4/5) with x positive + (as bytes: 0x5866666666666666666666666666666666666666666666666666666666666666) + + Preconditions: + a[31] <= 127 + */ + +void +ge25519_scalarmult_base(ge25519_p3 *h, const unsigned char *a) +{ + signed char e[64]; + signed char carry; + ge25519_p1p1 r; + ge25519_p2 s; + ge25519_precomp t; + int i; + + for (i = 0; i < 32; ++i) { + e[2 * i + 0] = (a[i] >> 0) & 15; + e[2 * i + 1] = (a[i] >> 4) & 15; + } + /* each e[i] is between 0 and 15 */ + /* e[63] is between 0 and 7 */ + + carry = 0; + for (i = 0; i < 63; ++i) { + e[i] += carry; + carry = e[i] + 8; + carry >>= 4; + e[i] -= carry * ((signed char) 1 << 4); + } + e[63] += carry; + /* each e[i] is between -8 and 8 */ + + ge25519_p3_0(h); + + for (i = 1; i < 64; i += 2) { + ge25519_cmov8_base(&t, i / 2, e[i]); + ge25519_madd(&r, h, &t); + ge25519_p1p1_to_p3(h, &r); + } + + ge25519_p3_dbl(&r, h); + ge25519_p1p1_to_p2(&s, &r); + ge25519_p2_dbl(&r, &s); + ge25519_p1p1_to_p2(&s, &r); + ge25519_p2_dbl(&r, &s); + ge25519_p1p1_to_p2(&s, &r); + ge25519_p2_dbl(&r, &s); + ge25519_p1p1_to_p3(h, &r); + + for (i = 0; i < 64; i += 2) { + ge25519_cmov8_base(&t, i / 2, e[i]); + ge25519_madd(&r, h, &t); + ge25519_p1p1_to_p3(h, &r); + } +} + +/* multiply by the order of the main subgroup l = 2^252+27742317777372353535851937790883648493 */ +static void +ge25519_mul_l(ge25519_p3 *r, const ge25519_p3 *A) +{ + static const signed char aslide[253] = { + 13, 0, 0, 0, 0, -1, 0, 0, 0, 0, -11, 0, 0, 0, 0, 0, 0, -5, 0, 0, 0, 0, 0, 0, -3, 0, 0, 0, 0, -13, 0, 0, 0, 0, 7, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, -13, 0, 0, 0, 0, 5, 0, 0, 0, 0, 0, 0, 0, 0, 11, 0, 0, 0, 0, 0, 11, 0, 0, 0, 0, -13, 0, 0, 0, 0, 0, 0, -3, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 3, 0, 0, 0, 0, -11, 0, 0, 0, 0, 0, 0, 0, 15, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, -1, 0, 0, 0, 0, 7, 0, 0, 0, 0, 5, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1 + }; + ge25519_cached Ai[8]; + ge25519_p1p1 t; + ge25519_p3 u; + ge25519_p3 A2; + int i; + + ge25519_p3_to_cached(&Ai[0], A); + ge25519_p3_dbl(&t, A); + ge25519_p1p1_to_p3(&A2, &t); + ge25519_add(&t, &A2, &Ai[0]); + ge25519_p1p1_to_p3(&u, &t); + ge25519_p3_to_cached(&Ai[1], &u); + ge25519_add(&t, &A2, &Ai[1]); + ge25519_p1p1_to_p3(&u, &t); + ge25519_p3_to_cached(&Ai[2], &u); + ge25519_add(&t, &A2, &Ai[2]); + ge25519_p1p1_to_p3(&u, &t); + ge25519_p3_to_cached(&Ai[3], &u); + ge25519_add(&t, &A2, &Ai[3]); + ge25519_p1p1_to_p3(&u, &t); + ge25519_p3_to_cached(&Ai[4], &u); + ge25519_add(&t, &A2, &Ai[4]); + ge25519_p1p1_to_p3(&u, &t); + ge25519_p3_to_cached(&Ai[5], &u); + ge25519_add(&t, &A2, &Ai[5]); + ge25519_p1p1_to_p3(&u, &t); + ge25519_p3_to_cached(&Ai[6], &u); + ge25519_add(&t, &A2, &Ai[6]); + ge25519_p1p1_to_p3(&u, &t); + ge25519_p3_to_cached(&Ai[7], &u); + + ge25519_p3_0(r); + + for (i = 252; i >= 0; --i) { + ge25519_p3_dbl(&t, r); + + if (aslide[i] > 0) { + ge25519_p1p1_to_p3(&u, &t); + ge25519_add(&t, &u, &Ai[aslide[i] / 2]); + } else if (aslide[i] < 0) { + ge25519_p1p1_to_p3(&u, &t); + ge25519_sub(&t, &u, &Ai[(-aslide[i]) / 2]); + } + + ge25519_p1p1_to_p3(r, &t); + } +} + +int +ge25519_is_on_curve(const ge25519_p3 *p) +{ + fe25519 x2; + fe25519 y2; + fe25519 z2; + fe25519 z4; + fe25519 t0; + fe25519 t1; + + fe25519_sq(x2, p->X); + fe25519_sq(y2, p->Y); + fe25519_sq(z2, p->Z); + fe25519_sub(t0, y2, x2); + fe25519_mul(t0, t0, z2); + + fe25519_mul(t1, x2, y2); + fe25519_mul(t1, t1, d); + fe25519_sq(z4, z2); + fe25519_add(t1, t1, z4); + fe25519_sub(t0, t0, t1); + + return fe25519_iszero(t0); +} + +int +ge25519_is_on_main_subgroup(const ge25519_p3 *p) +{ + ge25519_p3 pl; + + ge25519_mul_l(&pl, p); + + return fe25519_iszero(pl.X); +} + +int +ge25519_is_canonical(const unsigned char *s) +{ + unsigned char c; + unsigned char d; + unsigned int i; + + c = (s[31] & 0x7f) ^ 0x7f; + for (i = 30; i > 0; i--) { + c |= s[i] ^ 0xff; + } + c = (((unsigned int) c) - 1U) >> 8; + d = (0xed - 1U - (unsigned int) s[0]) >> 8; + + return 1 - (c & d & 1); +} + +int +ge25519_has_small_order(const unsigned char s[32]) +{ + CRYPTO_ALIGN(16) + static const unsigned char blacklist[][32] = { + /* 0 (order 4) */ + { 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00 }, + /* 1 (order 1) */ + { 0x01, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00 }, + /* 2707385501144840649318225287225658788936804267575313519463743609750303402022 + (order 8) */ + { 0x26, 0xe8, 0x95, 0x8f, 0xc2, 0xb2, 0x27, 0xb0, 0x45, 0xc3, 0xf4, + 0x89, 0xf2, 0xef, 0x98, 0xf0, 0xd5, 0xdf, 0xac, 0x05, 0xd3, 0xc6, + 0x33, 0x39, 0xb1, 0x38, 0x02, 0x88, 0x6d, 0x53, 0xfc, 0x05 }, + /* 55188659117513257062467267217118295137698188065244968500265048394206261417927 + (order 8) */ + { 0xc7, 0x17, 0x6a, 0x70, 0x3d, 0x4d, 0xd8, 0x4f, 0xba, 0x3c, 0x0b, + 0x76, 0x0d, 0x10, 0x67, 0x0f, 0x2a, 0x20, 0x53, 0xfa, 0x2c, 0x39, + 0xcc, 0xc6, 0x4e, 0xc7, 0xfd, 0x77, 0x92, 0xac, 0x03, 0x7a }, + /* p-1 (order 2) */ + { 0xec, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, + 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, + 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0x7f }, + /* p (=0, order 4) */ + { 0xed, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, + 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, + 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0x7f }, + /* p+1 (=1, order 1) */ + { 0xee, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, + 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, + 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0x7f } + }; + unsigned char c[7] = { 0 }; + unsigned int k; + size_t i, j; + +#define COMPILER_ASSERT(X) (void) sizeof(char[(X) ? 1 : -1]) + + COMPILER_ASSERT(7 == sizeof blacklist / sizeof blacklist[0]); + for (j = 0; j < 31; j++) { + for (i = 0; i < sizeof blacklist / sizeof blacklist[0]; i++) { + c[i] |= s[j] ^ blacklist[i][j]; + } + } + for (i = 0; i < sizeof blacklist / sizeof blacklist[0]; i++) { + c[i] |= (s[j] & 0x7f) ^ blacklist[i][j]; + } + k = 0; + for (i = 0; i < sizeof blacklist / sizeof blacklist[0]; i++) { + k |= (c[i] - 1); + } + return (int) ((k >> 8) & 1); +} + +/* + Input: + a[0]+256*a[1]+...+256^31*a[31] = a + b[0]+256*b[1]+...+256^31*b[31] = b + * + Output: + s[0]+256*s[1]+...+256^31*s[31] = (ab) mod l + where l = 2^252 + 27742317777372353535851937790883648493. + */ + +void +sc25519_mul(unsigned char s[32], const unsigned char a[32], const unsigned char b[32]) +{ + int64_t a0 = 2097151 & load_3(a); + int64_t a1 = 2097151 & (load_4(a + 2) >> 5); + int64_t a2 = 2097151 & (load_3(a + 5) >> 2); + int64_t a3 = 2097151 & (load_4(a + 7) >> 7); + int64_t a4 = 2097151 & (load_4(a + 10) >> 4); + int64_t a5 = 2097151 & (load_3(a + 13) >> 1); + int64_t a6 = 2097151 & (load_4(a + 15) >> 6); + int64_t a7 = 2097151 & (load_3(a + 18) >> 3); + int64_t a8 = 2097151 & load_3(a + 21); + int64_t a9 = 2097151 & (load_4(a + 23) >> 5); + int64_t a10 = 2097151 & (load_3(a + 26) >> 2); + int64_t a11 = (load_4(a + 28) >> 7); + + int64_t b0 = 2097151 & load_3(b); + int64_t b1 = 2097151 & (load_4(b + 2) >> 5); + int64_t b2 = 2097151 & (load_3(b + 5) >> 2); + int64_t b3 = 2097151 & (load_4(b + 7) >> 7); + int64_t b4 = 2097151 & (load_4(b + 10) >> 4); + int64_t b5 = 2097151 & (load_3(b + 13) >> 1); + int64_t b6 = 2097151 & (load_4(b + 15) >> 6); + int64_t b7 = 2097151 & (load_3(b + 18) >> 3); + int64_t b8 = 2097151 & load_3(b + 21); + int64_t b9 = 2097151 & (load_4(b + 23) >> 5); + int64_t b10 = 2097151 & (load_3(b + 26) >> 2); + int64_t b11 = (load_4(b + 28) >> 7); + + int64_t s0; + int64_t s1; + int64_t s2; + int64_t s3; + int64_t s4; + int64_t s5; + int64_t s6; + int64_t s7; + int64_t s8; + int64_t s9; + int64_t s10; + int64_t s11; + int64_t s12; + int64_t s13; + int64_t s14; + int64_t s15; + int64_t s16; + int64_t s17; + int64_t s18; + int64_t s19; + int64_t s20; + int64_t s21; + int64_t s22; + int64_t s23; + + int64_t carry0; + int64_t carry1; + int64_t carry2; + int64_t carry3; + int64_t carry4; + int64_t carry5; + int64_t carry6; + int64_t carry7; + int64_t carry8; + int64_t carry9; + int64_t carry10; + int64_t carry11; + int64_t carry12; + int64_t carry13; + int64_t carry14; + int64_t carry15; + int64_t carry16; + int64_t carry17; + int64_t carry18; + int64_t carry19; + int64_t carry20; + int64_t carry21; + int64_t carry22; + + s0 = a0 * b0; + s1 = a0 * b1 + a1 * b0; + s2 = a0 * b2 + a1 * b1 + a2 * b0; + s3 = a0 * b3 + a1 * b2 + a2 * b1 + a3 * b0; + s4 = a0 * b4 + a1 * b3 + a2 * b2 + a3 * b1 + a4 * b0; + s5 = a0 * b5 + a1 * b4 + a2 * b3 + a3 * b2 + a4 * b1 + a5 * b0; + s6 = a0 * b6 + a1 * b5 + a2 * b4 + a3 * b3 + a4 * b2 + a5 * b1 + a6 * b0; + s7 = a0 * b7 + a1 * b6 + a2 * b5 + a3 * b4 + a4 * b3 + a5 * b2 + + a6 * b1 + a7 * b0; + s8 = a0 * b8 + a1 * b7 + a2 * b6 + a3 * b5 + a4 * b4 + a5 * b3 + + a6 * b2 + a7 * b1 + a8 * b0; + s9 = a0 * b9 + a1 * b8 + a2 * b7 + a3 * b6 + a4 * b5 + a5 * b4 + + a6 * b3 + a7 * b2 + a8 * b1 + a9 * b0; + s10 = a0 * b10 + a1 * b9 + a2 * b8 + a3 * b7 + a4 * b6 + a5 * b5 + + a6 * b4 + a7 * b3 + a8 * b2 + a9 * b1 + a10 * b0; + s11 = a0 * b11 + a1 * b10 + a2 * b9 + a3 * b8 + a4 * b7 + a5 * b6 + + a6 * b5 + a7 * b4 + a8 * b3 + a9 * b2 + a10 * b1 + a11 * b0; + s12 = a1 * b11 + a2 * b10 + a3 * b9 + a4 * b8 + a5 * b7 + a6 * b6 + + a7 * b5 + a8 * b4 + a9 * b3 + a10 * b2 + a11 * b1; + s13 = a2 * b11 + a3 * b10 + a4 * b9 + a5 * b8 + a6 * b7 + a7 * b6 + + a8 * b5 + a9 * b4 + a10 * b3 + a11 * b2; + s14 = a3 * b11 + a4 * b10 + a5 * b9 + a6 * b8 + a7 * b7 + a8 * b6 + + a9 * b5 + a10 * b4 + a11 * b3; + s15 = a4 * b11 + a5 * b10 + a6 * b9 + a7 * b8 + a8 * b7 + a9 * b6 + + a10 * b5 + a11 * b4; + s16 = + a5 * b11 + a6 * b10 + a7 * b9 + a8 * b8 + a9 * b7 + a10 * b6 + a11 * b5; + s17 = a6 * b11 + a7 * b10 + a8 * b9 + a9 * b8 + a10 * b7 + a11 * b6; + s18 = a7 * b11 + a8 * b10 + a9 * b9 + a10 * b8 + a11 * b7; + s19 = a8 * b11 + a9 * b10 + a10 * b9 + a11 * b8; + s20 = a9 * b11 + a10 * b10 + a11 * b9; + s21 = a10 * b11 + a11 * b10; + s22 = a11 * b11; + s23 = 0; + + carry0 = (s0 + (int64_t) (1L << 20)) >> 21; + s1 += carry0; + s0 -= carry0 * ((uint64_t) 1L << 21); + carry2 = (s2 + (int64_t) (1L << 20)) >> 21; + s3 += carry2; + s2 -= carry2 * ((uint64_t) 1L << 21); + carry4 = (s4 + (int64_t) (1L << 20)) >> 21; + s5 += carry4; + s4 -= carry4 * ((uint64_t) 1L << 21); + carry6 = (s6 + (int64_t) (1L << 20)) >> 21; + s7 += carry6; + s6 -= carry6 * ((uint64_t) 1L << 21); + carry8 = (s8 + (int64_t) (1L << 20)) >> 21; + s9 += carry8; + s8 -= carry8 * ((uint64_t) 1L << 21); + carry10 = (s10 + (int64_t) (1L << 20)) >> 21; + s11 += carry10; + s10 -= carry10 * ((uint64_t) 1L << 21); + carry12 = (s12 + (int64_t) (1L << 20)) >> 21; + s13 += carry12; + s12 -= carry12 * ((uint64_t) 1L << 21); + carry14 = (s14 + (int64_t) (1L << 20)) >> 21; + s15 += carry14; + s14 -= carry14 * ((uint64_t) 1L << 21); + carry16 = (s16 + (int64_t) (1L << 20)) >> 21; + s17 += carry16; + s16 -= carry16 * ((uint64_t) 1L << 21); + carry18 = (s18 + (int64_t) (1L << 20)) >> 21; + s19 += carry18; + s18 -= carry18 * ((uint64_t) 1L << 21); + carry20 = (s20 + (int64_t) (1L << 20)) >> 21; + s21 += carry20; + s20 -= carry20 * ((uint64_t) 1L << 21); + carry22 = (s22 + (int64_t) (1L << 20)) >> 21; + s23 += carry22; + s22 -= carry22 * ((uint64_t) 1L << 21); + + carry1 = (s1 + (int64_t) (1L << 20)) >> 21; + s2 += carry1; + s1 -= carry1 * ((uint64_t) 1L << 21); + carry3 = (s3 + (int64_t) (1L << 20)) >> 21; + s4 += carry3; + s3 -= carry3 * ((uint64_t) 1L << 21); + carry5 = (s5 + (int64_t) (1L << 20)) >> 21; + s6 += carry5; + s5 -= carry5 * ((uint64_t) 1L << 21); + carry7 = (s7 + (int64_t) (1L << 20)) >> 21; + s8 += carry7; + s7 -= carry7 * ((uint64_t) 1L << 21); + carry9 = (s9 + (int64_t) (1L << 20)) >> 21; + s10 += carry9; + s9 -= carry9 * ((uint64_t) 1L << 21); + carry11 = (s11 + (int64_t) (1L << 20)) >> 21; + s12 += carry11; + s11 -= carry11 * ((uint64_t) 1L << 21); + carry13 = (s13 + (int64_t) (1L << 20)) >> 21; + s14 += carry13; + s13 -= carry13 * ((uint64_t) 1L << 21); + carry15 = (s15 + (int64_t) (1L << 20)) >> 21; + s16 += carry15; + s15 -= carry15 * ((uint64_t) 1L << 21); + carry17 = (s17 + (int64_t) (1L << 20)) >> 21; + s18 += carry17; + s17 -= carry17 * ((uint64_t) 1L << 21); + carry19 = (s19 + (int64_t) (1L << 20)) >> 21; + s20 += carry19; + s19 -= carry19 * ((uint64_t) 1L << 21); + carry21 = (s21 + (int64_t) (1L << 20)) >> 21; + s22 += carry21; + s21 -= carry21 * ((uint64_t) 1L << 21); + + s11 += s23 * 666643; + s12 += s23 * 470296; + s13 += s23 * 654183; + s14 -= s23 * 997805; + s15 += s23 * 136657; + s16 -= s23 * 683901; + + s10 += s22 * 666643; + s11 += s22 * 470296; + s12 += s22 * 654183; + s13 -= s22 * 997805; + s14 += s22 * 136657; + s15 -= s22 * 683901; + + s9 += s21 * 666643; + s10 += s21 * 470296; + s11 += s21 * 654183; + s12 -= s21 * 997805; + s13 += s21 * 136657; + s14 -= s21 * 683901; + + s8 += s20 * 666643; + s9 += s20 * 470296; + s10 += s20 * 654183; + s11 -= s20 * 997805; + s12 += s20 * 136657; + s13 -= s20 * 683901; + + s7 += s19 * 666643; + s8 += s19 * 470296; + s9 += s19 * 654183; + s10 -= s19 * 997805; + s11 += s19 * 136657; + s12 -= s19 * 683901; + + s6 += s18 * 666643; + s7 += s18 * 470296; + s8 += s18 * 654183; + s9 -= s18 * 997805; + s10 += s18 * 136657; + s11 -= s18 * 683901; + + carry6 = (s6 + (int64_t) (1L << 20)) >> 21; + s7 += carry6; + s6 -= carry6 * ((uint64_t) 1L << 21); + carry8 = (s8 + (int64_t) (1L << 20)) >> 21; + s9 += carry8; + s8 -= carry8 * ((uint64_t) 1L << 21); + carry10 = (s10 + (int64_t) (1L << 20)) >> 21; + s11 += carry10; + s10 -= carry10 * ((uint64_t) 1L << 21); + carry12 = (s12 + (int64_t) (1L << 20)) >> 21; + s13 += carry12; + s12 -= carry12 * ((uint64_t) 1L << 21); + carry14 = (s14 + (int64_t) (1L << 20)) >> 21; + s15 += carry14; + s14 -= carry14 * ((uint64_t) 1L << 21); + carry16 = (s16 + (int64_t) (1L << 20)) >> 21; + s17 += carry16; + s16 -= carry16 * ((uint64_t) 1L << 21); + + carry7 = (s7 + (int64_t) (1L << 20)) >> 21; + s8 += carry7; + s7 -= carry7 * ((uint64_t) 1L << 21); + carry9 = (s9 + (int64_t) (1L << 20)) >> 21; + s10 += carry9; + s9 -= carry9 * ((uint64_t) 1L << 21); + carry11 = (s11 + (int64_t) (1L << 20)) >> 21; + s12 += carry11; + s11 -= carry11 * ((uint64_t) 1L << 21); + carry13 = (s13 + (int64_t) (1L << 20)) >> 21; + s14 += carry13; + s13 -= carry13 * ((uint64_t) 1L << 21); + carry15 = (s15 + (int64_t) (1L << 20)) >> 21; + s16 += carry15; + s15 -= carry15 * ((uint64_t) 1L << 21); + + s5 += s17 * 666643; + s6 += s17 * 470296; + s7 += s17 * 654183; + s8 -= s17 * 997805; + s9 += s17 * 136657; + s10 -= s17 * 683901; + + s4 += s16 * 666643; + s5 += s16 * 470296; + s6 += s16 * 654183; + s7 -= s16 * 997805; + s8 += s16 * 136657; + s9 -= s16 * 683901; + + s3 += s15 * 666643; + s4 += s15 * 470296; + s5 += s15 * 654183; + s6 -= s15 * 997805; + s7 += s15 * 136657; + s8 -= s15 * 683901; + + s2 += s14 * 666643; + s3 += s14 * 470296; + s4 += s14 * 654183; + s5 -= s14 * 997805; + s6 += s14 * 136657; + s7 -= s14 * 683901; + + s1 += s13 * 666643; + s2 += s13 * 470296; + s3 += s13 * 654183; + s4 -= s13 * 997805; + s5 += s13 * 136657; + s6 -= s13 * 683901; + + s0 += s12 * 666643; + s1 += s12 * 470296; + s2 += s12 * 654183; + s3 -= s12 * 997805; + s4 += s12 * 136657; + s5 -= s12 * 683901; + s12 = 0; + + carry0 = (s0 + (int64_t) (1L << 20)) >> 21; + s1 += carry0; + s0 -= carry0 * ((uint64_t) 1L << 21); + carry2 = (s2 + (int64_t) (1L << 20)) >> 21; + s3 += carry2; + s2 -= carry2 * ((uint64_t) 1L << 21); + carry4 = (s4 + (int64_t) (1L << 20)) >> 21; + s5 += carry4; + s4 -= carry4 * ((uint64_t) 1L << 21); + carry6 = (s6 + (int64_t) (1L << 20)) >> 21; + s7 += carry6; + s6 -= carry6 * ((uint64_t) 1L << 21); + carry8 = (s8 + (int64_t) (1L << 20)) >> 21; + s9 += carry8; + s8 -= carry8 * ((uint64_t) 1L << 21); + carry10 = (s10 + (int64_t) (1L << 20)) >> 21; + s11 += carry10; + s10 -= carry10 * ((uint64_t) 1L << 21); + + carry1 = (s1 + (int64_t) (1L << 20)) >> 21; + s2 += carry1; + s1 -= carry1 * ((uint64_t) 1L << 21); + carry3 = (s3 + (int64_t) (1L << 20)) >> 21; + s4 += carry3; + s3 -= carry3 * ((uint64_t) 1L << 21); + carry5 = (s5 + (int64_t) (1L << 20)) >> 21; + s6 += carry5; + s5 -= carry5 * ((uint64_t) 1L << 21); + carry7 = (s7 + (int64_t) (1L << 20)) >> 21; + s8 += carry7; + s7 -= carry7 * ((uint64_t) 1L << 21); + carry9 = (s9 + (int64_t) (1L << 20)) >> 21; + s10 += carry9; + s9 -= carry9 * ((uint64_t) 1L << 21); + carry11 = (s11 + (int64_t) (1L << 20)) >> 21; + s12 += carry11; + s11 -= carry11 * ((uint64_t) 1L << 21); + + s0 += s12 * 666643; + s1 += s12 * 470296; + s2 += s12 * 654183; + s3 -= s12 * 997805; + s4 += s12 * 136657; + s5 -= s12 * 683901; + s12 = 0; + + carry0 = s0 >> 21; + s1 += carry0; + s0 -= carry0 * ((uint64_t) 1L << 21); + carry1 = s1 >> 21; + s2 += carry1; + s1 -= carry1 * ((uint64_t) 1L << 21); + carry2 = s2 >> 21; + s3 += carry2; + s2 -= carry2 * ((uint64_t) 1L << 21); + carry3 = s3 >> 21; + s4 += carry3; + s3 -= carry3 * ((uint64_t) 1L << 21); + carry4 = s4 >> 21; + s5 += carry4; + s4 -= carry4 * ((uint64_t) 1L << 21); + carry5 = s5 >> 21; + s6 += carry5; + s5 -= carry5 * ((uint64_t) 1L << 21); + carry6 = s6 >> 21; + s7 += carry6; + s6 -= carry6 * ((uint64_t) 1L << 21); + carry7 = s7 >> 21; + s8 += carry7; + s7 -= carry7 * ((uint64_t) 1L << 21); + carry8 = s8 >> 21; + s9 += carry8; + s8 -= carry8 * ((uint64_t) 1L << 21); + carry9 = s9 >> 21; + s10 += carry9; + s9 -= carry9 * ((uint64_t) 1L << 21); + carry10 = s10 >> 21; + s11 += carry10; + s10 -= carry10 * ((uint64_t) 1L << 21); + carry11 = s11 >> 21; + s12 += carry11; + s11 -= carry11 * ((uint64_t) 1L << 21); + + s0 += s12 * 666643; + s1 += s12 * 470296; + s2 += s12 * 654183; + s3 -= s12 * 997805; + s4 += s12 * 136657; + s5 -= s12 * 683901; + + carry0 = s0 >> 21; + s1 += carry0; + s0 -= carry0 * ((uint64_t) 1L << 21); + carry1 = s1 >> 21; + s2 += carry1; + s1 -= carry1 * ((uint64_t) 1L << 21); + carry2 = s2 >> 21; + s3 += carry2; + s2 -= carry2 * ((uint64_t) 1L << 21); + carry3 = s3 >> 21; + s4 += carry3; + s3 -= carry3 * ((uint64_t) 1L << 21); + carry4 = s4 >> 21; + s5 += carry4; + s4 -= carry4 * ((uint64_t) 1L << 21); + carry5 = s5 >> 21; + s6 += carry5; + s5 -= carry5 * ((uint64_t) 1L << 21); + carry6 = s6 >> 21; + s7 += carry6; + s6 -= carry6 * ((uint64_t) 1L << 21); + carry7 = s7 >> 21; + s8 += carry7; + s7 -= carry7 * ((uint64_t) 1L << 21); + carry8 = s8 >> 21; + s9 += carry8; + s8 -= carry8 * ((uint64_t) 1L << 21); + carry9 = s9 >> 21; + s10 += carry9; + s9 -= carry9 * ((uint64_t) 1L << 21); + carry10 = s10 >> 21; + s11 += carry10; + s10 -= carry10 * ((uint64_t) 1L << 21); + + s[0] = s0 >> 0; + s[1] = s0 >> 8; + s[2] = (s0 >> 16) | (s1 * ((uint64_t) 1 << 5)); + s[3] = s1 >> 3; + s[4] = s1 >> 11; + s[5] = (s1 >> 19) | (s2 * ((uint64_t) 1 << 2)); + s[6] = s2 >> 6; + s[7] = (s2 >> 14) | (s3 * ((uint64_t) 1 << 7)); + s[8] = s3 >> 1; + s[9] = s3 >> 9; + s[10] = (s3 >> 17) | (s4 * ((uint64_t) 1 << 4)); + s[11] = s4 >> 4; + s[12] = s4 >> 12; + s[13] = (s4 >> 20) | (s5 * ((uint64_t) 1 << 1)); + s[14] = s5 >> 7; + s[15] = (s5 >> 15) | (s6 * ((uint64_t) 1 << 6)); + s[16] = s6 >> 2; + s[17] = s6 >> 10; + s[18] = (s6 >> 18) | (s7 * ((uint64_t) 1 << 3)); + s[19] = s7 >> 5; + s[20] = s7 >> 13; + s[21] = s8 >> 0; + s[22] = s8 >> 8; + s[23] = (s8 >> 16) | (s9 * ((uint64_t) 1 << 5)); + s[24] = s9 >> 3; + s[25] = s9 >> 11; + s[26] = (s9 >> 19) | (s10 * ((uint64_t) 1 << 2)); + s[27] = s10 >> 6; + s[28] = (s10 >> 14) | (s11 * ((uint64_t) 1 << 7)); + s[29] = s11 >> 1; + s[30] = s11 >> 9; + s[31] = s11 >> 17; +} + +/* + Input: + a[0]+256*a[1]+...+256^31*a[31] = a + b[0]+256*b[1]+...+256^31*b[31] = b + c[0]+256*c[1]+...+256^31*c[31] = c + * + Output: + s[0]+256*s[1]+...+256^31*s[31] = (ab+c) mod l + where l = 2^252 + 27742317777372353535851937790883648493. + */ + +void +sc25519_muladd(unsigned char s[32], const unsigned char a[32], + const unsigned char b[32], const unsigned char c[32]) +{ + int64_t a0 = 2097151 & load_3(a); + int64_t a1 = 2097151 & (load_4(a + 2) >> 5); + int64_t a2 = 2097151 & (load_3(a + 5) >> 2); + int64_t a3 = 2097151 & (load_4(a + 7) >> 7); + int64_t a4 = 2097151 & (load_4(a + 10) >> 4); + int64_t a5 = 2097151 & (load_3(a + 13) >> 1); + int64_t a6 = 2097151 & (load_4(a + 15) >> 6); + int64_t a7 = 2097151 & (load_3(a + 18) >> 3); + int64_t a8 = 2097151 & load_3(a + 21); + int64_t a9 = 2097151 & (load_4(a + 23) >> 5); + int64_t a10 = 2097151 & (load_3(a + 26) >> 2); + int64_t a11 = (load_4(a + 28) >> 7); + + int64_t b0 = 2097151 & load_3(b); + int64_t b1 = 2097151 & (load_4(b + 2) >> 5); + int64_t b2 = 2097151 & (load_3(b + 5) >> 2); + int64_t b3 = 2097151 & (load_4(b + 7) >> 7); + int64_t b4 = 2097151 & (load_4(b + 10) >> 4); + int64_t b5 = 2097151 & (load_3(b + 13) >> 1); + int64_t b6 = 2097151 & (load_4(b + 15) >> 6); + int64_t b7 = 2097151 & (load_3(b + 18) >> 3); + int64_t b8 = 2097151 & load_3(b + 21); + int64_t b9 = 2097151 & (load_4(b + 23) >> 5); + int64_t b10 = 2097151 & (load_3(b + 26) >> 2); + int64_t b11 = (load_4(b + 28) >> 7); + + int64_t c0 = 2097151 & load_3(c); + int64_t c1 = 2097151 & (load_4(c + 2) >> 5); + int64_t c2 = 2097151 & (load_3(c + 5) >> 2); + int64_t c3 = 2097151 & (load_4(c + 7) >> 7); + int64_t c4 = 2097151 & (load_4(c + 10) >> 4); + int64_t c5 = 2097151 & (load_3(c + 13) >> 1); + int64_t c6 = 2097151 & (load_4(c + 15) >> 6); + int64_t c7 = 2097151 & (load_3(c + 18) >> 3); + int64_t c8 = 2097151 & load_3(c + 21); + int64_t c9 = 2097151 & (load_4(c + 23) >> 5); + int64_t c10 = 2097151 & (load_3(c + 26) >> 2); + int64_t c11 = (load_4(c + 28) >> 7); + + int64_t s0; + int64_t s1; + int64_t s2; + int64_t s3; + int64_t s4; + int64_t s5; + int64_t s6; + int64_t s7; + int64_t s8; + int64_t s9; + int64_t s10; + int64_t s11; + int64_t s12; + int64_t s13; + int64_t s14; + int64_t s15; + int64_t s16; + int64_t s17; + int64_t s18; + int64_t s19; + int64_t s20; + int64_t s21; + int64_t s22; + int64_t s23; + + int64_t carry0; + int64_t carry1; + int64_t carry2; + int64_t carry3; + int64_t carry4; + int64_t carry5; + int64_t carry6; + int64_t carry7; + int64_t carry8; + int64_t carry9; + int64_t carry10; + int64_t carry11; + int64_t carry12; + int64_t carry13; + int64_t carry14; + int64_t carry15; + int64_t carry16; + int64_t carry17; + int64_t carry18; + int64_t carry19; + int64_t carry20; + int64_t carry21; + int64_t carry22; + + s0 = c0 + a0 * b0; + s1 = c1 + a0 * b1 + a1 * b0; + s2 = c2 + a0 * b2 + a1 * b1 + a2 * b0; + s3 = c3 + a0 * b3 + a1 * b2 + a2 * b1 + a3 * b0; + s4 = c4 + a0 * b4 + a1 * b3 + a2 * b2 + a3 * b1 + a4 * b0; + s5 = c5 + a0 * b5 + a1 * b4 + a2 * b3 + a3 * b2 + a4 * b1 + a5 * b0; + s6 = c6 + a0 * b6 + a1 * b5 + a2 * b4 + a3 * b3 + a4 * b2 + a5 * b1 + + a6 * b0; + s7 = c7 + a0 * b7 + a1 * b6 + a2 * b5 + a3 * b4 + a4 * b3 + a5 * b2 + + a6 * b1 + a7 * b0; + s8 = c8 + a0 * b8 + a1 * b7 + a2 * b6 + a3 * b5 + a4 * b4 + a5 * b3 + + a6 * b2 + a7 * b1 + a8 * b0; + s9 = c9 + a0 * b9 + a1 * b8 + a2 * b7 + a3 * b6 + a4 * b5 + a5 * b4 + + a6 * b3 + a7 * b2 + a8 * b1 + a9 * b0; + s10 = c10 + a0 * b10 + a1 * b9 + a2 * b8 + a3 * b7 + a4 * b6 + a5 * b5 + + a6 * b4 + a7 * b3 + a8 * b2 + a9 * b1 + a10 * b0; + s11 = c11 + a0 * b11 + a1 * b10 + a2 * b9 + a3 * b8 + a4 * b7 + a5 * b6 + + a6 * b5 + a7 * b4 + a8 * b3 + a9 * b2 + a10 * b1 + a11 * b0; + s12 = a1 * b11 + a2 * b10 + a3 * b9 + a4 * b8 + a5 * b7 + a6 * b6 + + a7 * b5 + a8 * b4 + a9 * b3 + a10 * b2 + a11 * b1; + s13 = a2 * b11 + a3 * b10 + a4 * b9 + a5 * b8 + a6 * b7 + a7 * b6 + + a8 * b5 + a9 * b4 + a10 * b3 + a11 * b2; + s14 = a3 * b11 + a4 * b10 + a5 * b9 + a6 * b8 + a7 * b7 + a8 * b6 + + a9 * b5 + a10 * b4 + a11 * b3; + s15 = a4 * b11 + a5 * b10 + a6 * b9 + a7 * b8 + a8 * b7 + a9 * b6 + + a10 * b5 + a11 * b4; + s16 = + a5 * b11 + a6 * b10 + a7 * b9 + a8 * b8 + a9 * b7 + a10 * b6 + a11 * b5; + s17 = a6 * b11 + a7 * b10 + a8 * b9 + a9 * b8 + a10 * b7 + a11 * b6; + s18 = a7 * b11 + a8 * b10 + a9 * b9 + a10 * b8 + a11 * b7; + s19 = a8 * b11 + a9 * b10 + a10 * b9 + a11 * b8; + s20 = a9 * b11 + a10 * b10 + a11 * b9; + s21 = a10 * b11 + a11 * b10; + s22 = a11 * b11; + s23 = 0; + + carry0 = (s0 + (int64_t) (1L << 20)) >> 21; + s1 += carry0; + s0 -= carry0 * ((uint64_t) 1L << 21); + carry2 = (s2 + (int64_t) (1L << 20)) >> 21; + s3 += carry2; + s2 -= carry2 * ((uint64_t) 1L << 21); + carry4 = (s4 + (int64_t) (1L << 20)) >> 21; + s5 += carry4; + s4 -= carry4 * ((uint64_t) 1L << 21); + carry6 = (s6 + (int64_t) (1L << 20)) >> 21; + s7 += carry6; + s6 -= carry6 * ((uint64_t) 1L << 21); + carry8 = (s8 + (int64_t) (1L << 20)) >> 21; + s9 += carry8; + s8 -= carry8 * ((uint64_t) 1L << 21); + carry10 = (s10 + (int64_t) (1L << 20)) >> 21; + s11 += carry10; + s10 -= carry10 * ((uint64_t) 1L << 21); + carry12 = (s12 + (int64_t) (1L << 20)) >> 21; + s13 += carry12; + s12 -= carry12 * ((uint64_t) 1L << 21); + carry14 = (s14 + (int64_t) (1L << 20)) >> 21; + s15 += carry14; + s14 -= carry14 * ((uint64_t) 1L << 21); + carry16 = (s16 + (int64_t) (1L << 20)) >> 21; + s17 += carry16; + s16 -= carry16 * ((uint64_t) 1L << 21); + carry18 = (s18 + (int64_t) (1L << 20)) >> 21; + s19 += carry18; + s18 -= carry18 * ((uint64_t) 1L << 21); + carry20 = (s20 + (int64_t) (1L << 20)) >> 21; + s21 += carry20; + s20 -= carry20 * ((uint64_t) 1L << 21); + carry22 = (s22 + (int64_t) (1L << 20)) >> 21; + s23 += carry22; + s22 -= carry22 * ((uint64_t) 1L << 21); + + carry1 = (s1 + (int64_t) (1L << 20)) >> 21; + s2 += carry1; + s1 -= carry1 * ((uint64_t) 1L << 21); + carry3 = (s3 + (int64_t) (1L << 20)) >> 21; + s4 += carry3; + s3 -= carry3 * ((uint64_t) 1L << 21); + carry5 = (s5 + (int64_t) (1L << 20)) >> 21; + s6 += carry5; + s5 -= carry5 * ((uint64_t) 1L << 21); + carry7 = (s7 + (int64_t) (1L << 20)) >> 21; + s8 += carry7; + s7 -= carry7 * ((uint64_t) 1L << 21); + carry9 = (s9 + (int64_t) (1L << 20)) >> 21; + s10 += carry9; + s9 -= carry9 * ((uint64_t) 1L << 21); + carry11 = (s11 + (int64_t) (1L << 20)) >> 21; + s12 += carry11; + s11 -= carry11 * ((uint64_t) 1L << 21); + carry13 = (s13 + (int64_t) (1L << 20)) >> 21; + s14 += carry13; + s13 -= carry13 * ((uint64_t) 1L << 21); + carry15 = (s15 + (int64_t) (1L << 20)) >> 21; + s16 += carry15; + s15 -= carry15 * ((uint64_t) 1L << 21); + carry17 = (s17 + (int64_t) (1L << 20)) >> 21; + s18 += carry17; + s17 -= carry17 * ((uint64_t) 1L << 21); + carry19 = (s19 + (int64_t) (1L << 20)) >> 21; + s20 += carry19; + s19 -= carry19 * ((uint64_t) 1L << 21); + carry21 = (s21 + (int64_t) (1L << 20)) >> 21; + s22 += carry21; + s21 -= carry21 * ((uint64_t) 1L << 21); + + s11 += s23 * 666643; + s12 += s23 * 470296; + s13 += s23 * 654183; + s14 -= s23 * 997805; + s15 += s23 * 136657; + s16 -= s23 * 683901; + + s10 += s22 * 666643; + s11 += s22 * 470296; + s12 += s22 * 654183; + s13 -= s22 * 997805; + s14 += s22 * 136657; + s15 -= s22 * 683901; + + s9 += s21 * 666643; + s10 += s21 * 470296; + s11 += s21 * 654183; + s12 -= s21 * 997805; + s13 += s21 * 136657; + s14 -= s21 * 683901; + + s8 += s20 * 666643; + s9 += s20 * 470296; + s10 += s20 * 654183; + s11 -= s20 * 997805; + s12 += s20 * 136657; + s13 -= s20 * 683901; + + s7 += s19 * 666643; + s8 += s19 * 470296; + s9 += s19 * 654183; + s10 -= s19 * 997805; + s11 += s19 * 136657; + s12 -= s19 * 683901; + + s6 += s18 * 666643; + s7 += s18 * 470296; + s8 += s18 * 654183; + s9 -= s18 * 997805; + s10 += s18 * 136657; + s11 -= s18 * 683901; + + carry6 = (s6 + (int64_t) (1L << 20)) >> 21; + s7 += carry6; + s6 -= carry6 * ((uint64_t) 1L << 21); + carry8 = (s8 + (int64_t) (1L << 20)) >> 21; + s9 += carry8; + s8 -= carry8 * ((uint64_t) 1L << 21); + carry10 = (s10 + (int64_t) (1L << 20)) >> 21; + s11 += carry10; + s10 -= carry10 * ((uint64_t) 1L << 21); + carry12 = (s12 + (int64_t) (1L << 20)) >> 21; + s13 += carry12; + s12 -= carry12 * ((uint64_t) 1L << 21); + carry14 = (s14 + (int64_t) (1L << 20)) >> 21; + s15 += carry14; + s14 -= carry14 * ((uint64_t) 1L << 21); + carry16 = (s16 + (int64_t) (1L << 20)) >> 21; + s17 += carry16; + s16 -= carry16 * ((uint64_t) 1L << 21); + + carry7 = (s7 + (int64_t) (1L << 20)) >> 21; + s8 += carry7; + s7 -= carry7 * ((uint64_t) 1L << 21); + carry9 = (s9 + (int64_t) (1L << 20)) >> 21; + s10 += carry9; + s9 -= carry9 * ((uint64_t) 1L << 21); + carry11 = (s11 + (int64_t) (1L << 20)) >> 21; + s12 += carry11; + s11 -= carry11 * ((uint64_t) 1L << 21); + carry13 = (s13 + (int64_t) (1L << 20)) >> 21; + s14 += carry13; + s13 -= carry13 * ((uint64_t) 1L << 21); + carry15 = (s15 + (int64_t) (1L << 20)) >> 21; + s16 += carry15; + s15 -= carry15 * ((uint64_t) 1L << 21); + + s5 += s17 * 666643; + s6 += s17 * 470296; + s7 += s17 * 654183; + s8 -= s17 * 997805; + s9 += s17 * 136657; + s10 -= s17 * 683901; + + s4 += s16 * 666643; + s5 += s16 * 470296; + s6 += s16 * 654183; + s7 -= s16 * 997805; + s8 += s16 * 136657; + s9 -= s16 * 683901; + + s3 += s15 * 666643; + s4 += s15 * 470296; + s5 += s15 * 654183; + s6 -= s15 * 997805; + s7 += s15 * 136657; + s8 -= s15 * 683901; + + s2 += s14 * 666643; + s3 += s14 * 470296; + s4 += s14 * 654183; + s5 -= s14 * 997805; + s6 += s14 * 136657; + s7 -= s14 * 683901; + + s1 += s13 * 666643; + s2 += s13 * 470296; + s3 += s13 * 654183; + s4 -= s13 * 997805; + s5 += s13 * 136657; + s6 -= s13 * 683901; + + s0 += s12 * 666643; + s1 += s12 * 470296; + s2 += s12 * 654183; + s3 -= s12 * 997805; + s4 += s12 * 136657; + s5 -= s12 * 683901; + s12 = 0; + + carry0 = (s0 + (int64_t) (1L << 20)) >> 21; + s1 += carry0; + s0 -= carry0 * ((uint64_t) 1L << 21); + carry2 = (s2 + (int64_t) (1L << 20)) >> 21; + s3 += carry2; + s2 -= carry2 * ((uint64_t) 1L << 21); + carry4 = (s4 + (int64_t) (1L << 20)) >> 21; + s5 += carry4; + s4 -= carry4 * ((uint64_t) 1L << 21); + carry6 = (s6 + (int64_t) (1L << 20)) >> 21; + s7 += carry6; + s6 -= carry6 * ((uint64_t) 1L << 21); + carry8 = (s8 + (int64_t) (1L << 20)) >> 21; + s9 += carry8; + s8 -= carry8 * ((uint64_t) 1L << 21); + carry10 = (s10 + (int64_t) (1L << 20)) >> 21; + s11 += carry10; + s10 -= carry10 * ((uint64_t) 1L << 21); + + carry1 = (s1 + (int64_t) (1L << 20)) >> 21; + s2 += carry1; + s1 -= carry1 * ((uint64_t) 1L << 21); + carry3 = (s3 + (int64_t) (1L << 20)) >> 21; + s4 += carry3; + s3 -= carry3 * ((uint64_t) 1L << 21); + carry5 = (s5 + (int64_t) (1L << 20)) >> 21; + s6 += carry5; + s5 -= carry5 * ((uint64_t) 1L << 21); + carry7 = (s7 + (int64_t) (1L << 20)) >> 21; + s8 += carry7; + s7 -= carry7 * ((uint64_t) 1L << 21); + carry9 = (s9 + (int64_t) (1L << 20)) >> 21; + s10 += carry9; + s9 -= carry9 * ((uint64_t) 1L << 21); + carry11 = (s11 + (int64_t) (1L << 20)) >> 21; + s12 += carry11; + s11 -= carry11 * ((uint64_t) 1L << 21); + + s0 += s12 * 666643; + s1 += s12 * 470296; + s2 += s12 * 654183; + s3 -= s12 * 997805; + s4 += s12 * 136657; + s5 -= s12 * 683901; + s12 = 0; + + carry0 = s0 >> 21; + s1 += carry0; + s0 -= carry0 * ((uint64_t) 1L << 21); + carry1 = s1 >> 21; + s2 += carry1; + s1 -= carry1 * ((uint64_t) 1L << 21); + carry2 = s2 >> 21; + s3 += carry2; + s2 -= carry2 * ((uint64_t) 1L << 21); + carry3 = s3 >> 21; + s4 += carry3; + s3 -= carry3 * ((uint64_t) 1L << 21); + carry4 = s4 >> 21; + s5 += carry4; + s4 -= carry4 * ((uint64_t) 1L << 21); + carry5 = s5 >> 21; + s6 += carry5; + s5 -= carry5 * ((uint64_t) 1L << 21); + carry6 = s6 >> 21; + s7 += carry6; + s6 -= carry6 * ((uint64_t) 1L << 21); + carry7 = s7 >> 21; + s8 += carry7; + s7 -= carry7 * ((uint64_t) 1L << 21); + carry8 = s8 >> 21; + s9 += carry8; + s8 -= carry8 * ((uint64_t) 1L << 21); + carry9 = s9 >> 21; + s10 += carry9; + s9 -= carry9 * ((uint64_t) 1L << 21); + carry10 = s10 >> 21; + s11 += carry10; + s10 -= carry10 * ((uint64_t) 1L << 21); + carry11 = s11 >> 21; + s12 += carry11; + s11 -= carry11 * ((uint64_t) 1L << 21); + + s0 += s12 * 666643; + s1 += s12 * 470296; + s2 += s12 * 654183; + s3 -= s12 * 997805; + s4 += s12 * 136657; + s5 -= s12 * 683901; + + carry0 = s0 >> 21; + s1 += carry0; + s0 -= carry0 * ((uint64_t) 1L << 21); + carry1 = s1 >> 21; + s2 += carry1; + s1 -= carry1 * ((uint64_t) 1L << 21); + carry2 = s2 >> 21; + s3 += carry2; + s2 -= carry2 * ((uint64_t) 1L << 21); + carry3 = s3 >> 21; + s4 += carry3; + s3 -= carry3 * ((uint64_t) 1L << 21); + carry4 = s4 >> 21; + s5 += carry4; + s4 -= carry4 * ((uint64_t) 1L << 21); + carry5 = s5 >> 21; + s6 += carry5; + s5 -= carry5 * ((uint64_t) 1L << 21); + carry6 = s6 >> 21; + s7 += carry6; + s6 -= carry6 * ((uint64_t) 1L << 21); + carry7 = s7 >> 21; + s8 += carry7; + s7 -= carry7 * ((uint64_t) 1L << 21); + carry8 = s8 >> 21; + s9 += carry8; + s8 -= carry8 * ((uint64_t) 1L << 21); + carry9 = s9 >> 21; + s10 += carry9; + s9 -= carry9 * ((uint64_t) 1L << 21); + carry10 = s10 >> 21; + s11 += carry10; + s10 -= carry10 * ((uint64_t) 1L << 21); + + s[0] = s0 >> 0; + s[1] = s0 >> 8; + s[2] = (s0 >> 16) | (s1 * ((uint64_t) 1 << 5)); + s[3] = s1 >> 3; + s[4] = s1 >> 11; + s[5] = (s1 >> 19) | (s2 * ((uint64_t) 1 << 2)); + s[6] = s2 >> 6; + s[7] = (s2 >> 14) | (s3 * ((uint64_t) 1 << 7)); + s[8] = s3 >> 1; + s[9] = s3 >> 9; + s[10] = (s3 >> 17) | (s4 * ((uint64_t) 1 << 4)); + s[11] = s4 >> 4; + s[12] = s4 >> 12; + s[13] = (s4 >> 20) | (s5 * ((uint64_t) 1 << 1)); + s[14] = s5 >> 7; + s[15] = (s5 >> 15) | (s6 * ((uint64_t) 1 << 6)); + s[16] = s6 >> 2; + s[17] = s6 >> 10; + s[18] = (s6 >> 18) | (s7 * ((uint64_t) 1 << 3)); + s[19] = s7 >> 5; + s[20] = s7 >> 13; + s[21] = s8 >> 0; + s[22] = s8 >> 8; + s[23] = (s8 >> 16) | (s9 * ((uint64_t) 1 << 5)); + s[24] = s9 >> 3; + s[25] = s9 >> 11; + s[26] = (s9 >> 19) | (s10 * ((uint64_t) 1 << 2)); + s[27] = s10 >> 6; + s[28] = (s10 >> 14) | (s11 * ((uint64_t) 1 << 7)); + s[29] = s11 >> 1; + s[30] = s11 >> 9; + s[31] = s11 >> 17; +} + +/* + Input: + a[0]+256*a[1]+...+256^31*a[31] = a + * + Output: + s[0]+256*s[1]+...+256^31*s[31] = a^2 mod l + where l = 2^252 + 27742317777372353535851937790883648493. + */ + +static inline void +sc25519_sq(unsigned char *s, const unsigned char *a) +{ + sc25519_mul(s, a, a); +} + +/* + Input: + s[0]+256*a[1]+...+256^31*a[31] = a + n + * + Output: + s[0]+256*s[1]+...+256^31*s[31] = x * s^(s^n) mod l + where l = 2^252 + 27742317777372353535851937790883648493. + Overwrites s in place. + */ + +static inline void +sc25519_sqmul(unsigned char s[32], const int n, const unsigned char a[32]) +{ + int i; + + for (i = 0; i < n; i++) { + sc25519_sq(s, s); + } + sc25519_mul(s, s, a); +} + +void +sc25519_invert(unsigned char recip[32], const unsigned char s[32]) +{ + unsigned char _10[32], _100[32], _11[32], _101[32], _111[32], + _1001[32], _1011[32], _1111[32]; + + sc25519_sq(_10, s); + sc25519_sq(_100, _10); + sc25519_mul(_11, _10, s); + sc25519_mul(_101, _10, _11); + sc25519_mul(_111, _10, _101); + sc25519_mul(_1001, _10, _111); + sc25519_mul(_1011, _10, _1001); + sc25519_mul(_1111, _100, _1011); + sc25519_mul(recip, _1111, s); + + sc25519_sqmul(recip, 123 + 3, _101); + sc25519_sqmul(recip, 2 + 2, _11); + sc25519_sqmul(recip, 1 + 4, _1111); + sc25519_sqmul(recip, 1 + 4, _1111); + sc25519_sqmul(recip, 4, _1001); + sc25519_sqmul(recip, 2, _11); + sc25519_sqmul(recip, 1 + 4, _1111); + sc25519_sqmul(recip, 1 + 3, _101); + sc25519_sqmul(recip, 3 + 3, _101); + sc25519_sqmul(recip, 3, _111); + sc25519_sqmul(recip, 1 + 4, _1111); + sc25519_sqmul(recip, 2 + 3, _111); + sc25519_sqmul(recip, 2 + 2, _11); + sc25519_sqmul(recip, 1 + 4, _1011); + sc25519_sqmul(recip, 2 + 4, _1011); + sc25519_sqmul(recip, 6 + 4, _1001); + sc25519_sqmul(recip, 2 + 2, _11); + sc25519_sqmul(recip, 3 + 2, _11); + sc25519_sqmul(recip, 3 + 2, _11); + sc25519_sqmul(recip, 1 + 4, _1001); + sc25519_sqmul(recip, 1 + 3, _111); + sc25519_sqmul(recip, 2 + 4, _1111); + sc25519_sqmul(recip, 1 + 4, _1011); + sc25519_sqmul(recip, 3, _101); + sc25519_sqmul(recip, 2 + 4, _1111); + sc25519_sqmul(recip, 3, _101); + sc25519_sqmul(recip, 1 + 2, _11); +} + +/* + Input: + s[0]+256*s[1]+...+256^63*s[63] = s + * + Output: + s[0]+256*s[1]+...+256^31*s[31] = s mod l + where l = 2^252 + 27742317777372353535851937790883648493. + Overwrites s in place. + */ + +void +sc25519_reduce(unsigned char s[64]) +{ + int64_t s0 = 2097151 & load_3(s); + int64_t s1 = 2097151 & (load_4(s + 2) >> 5); + int64_t s2 = 2097151 & (load_3(s + 5) >> 2); + int64_t s3 = 2097151 & (load_4(s + 7) >> 7); + int64_t s4 = 2097151 & (load_4(s + 10) >> 4); + int64_t s5 = 2097151 & (load_3(s + 13) >> 1); + int64_t s6 = 2097151 & (load_4(s + 15) >> 6); + int64_t s7 = 2097151 & (load_3(s + 18) >> 3); + int64_t s8 = 2097151 & load_3(s + 21); + int64_t s9 = 2097151 & (load_4(s + 23) >> 5); + int64_t s10 = 2097151 & (load_3(s + 26) >> 2); + int64_t s11 = 2097151 & (load_4(s + 28) >> 7); + int64_t s12 = 2097151 & (load_4(s + 31) >> 4); + int64_t s13 = 2097151 & (load_3(s + 34) >> 1); + int64_t s14 = 2097151 & (load_4(s + 36) >> 6); + int64_t s15 = 2097151 & (load_3(s + 39) >> 3); + int64_t s16 = 2097151 & load_3(s + 42); + int64_t s17 = 2097151 & (load_4(s + 44) >> 5); + int64_t s18 = 2097151 & (load_3(s + 47) >> 2); + int64_t s19 = 2097151 & (load_4(s + 49) >> 7); + int64_t s20 = 2097151 & (load_4(s + 52) >> 4); + int64_t s21 = 2097151 & (load_3(s + 55) >> 1); + int64_t s22 = 2097151 & (load_4(s + 57) >> 6); + int64_t s23 = (load_4(s + 60) >> 3); + + int64_t carry0; + int64_t carry1; + int64_t carry2; + int64_t carry3; + int64_t carry4; + int64_t carry5; + int64_t carry6; + int64_t carry7; + int64_t carry8; + int64_t carry9; + int64_t carry10; + int64_t carry11; + int64_t carry12; + int64_t carry13; + int64_t carry14; + int64_t carry15; + int64_t carry16; + + s11 += s23 * 666643; + s12 += s23 * 470296; + s13 += s23 * 654183; + s14 -= s23 * 997805; + s15 += s23 * 136657; + s16 -= s23 * 683901; + + s10 += s22 * 666643; + s11 += s22 * 470296; + s12 += s22 * 654183; + s13 -= s22 * 997805; + s14 += s22 * 136657; + s15 -= s22 * 683901; + + s9 += s21 * 666643; + s10 += s21 * 470296; + s11 += s21 * 654183; + s12 -= s21 * 997805; + s13 += s21 * 136657; + s14 -= s21 * 683901; + + s8 += s20 * 666643; + s9 += s20 * 470296; + s10 += s20 * 654183; + s11 -= s20 * 997805; + s12 += s20 * 136657; + s13 -= s20 * 683901; + + s7 += s19 * 666643; + s8 += s19 * 470296; + s9 += s19 * 654183; + s10 -= s19 * 997805; + s11 += s19 * 136657; + s12 -= s19 * 683901; + + s6 += s18 * 666643; + s7 += s18 * 470296; + s8 += s18 * 654183; + s9 -= s18 * 997805; + s10 += s18 * 136657; + s11 -= s18 * 683901; + + carry6 = (s6 + (int64_t) (1L << 20)) >> 21; + s7 += carry6; + s6 -= carry6 * ((uint64_t) 1L << 21); + carry8 = (s8 + (int64_t) (1L << 20)) >> 21; + s9 += carry8; + s8 -= carry8 * ((uint64_t) 1L << 21); + carry10 = (s10 + (int64_t) (1L << 20)) >> 21; + s11 += carry10; + s10 -= carry10 * ((uint64_t) 1L << 21); + carry12 = (s12 + (int64_t) (1L << 20)) >> 21; + s13 += carry12; + s12 -= carry12 * ((uint64_t) 1L << 21); + carry14 = (s14 + (int64_t) (1L << 20)) >> 21; + s15 += carry14; + s14 -= carry14 * ((uint64_t) 1L << 21); + carry16 = (s16 + (int64_t) (1L << 20)) >> 21; + s17 += carry16; + s16 -= carry16 * ((uint64_t) 1L << 21); + + carry7 = (s7 + (int64_t) (1L << 20)) >> 21; + s8 += carry7; + s7 -= carry7 * ((uint64_t) 1L << 21); + carry9 = (s9 + (int64_t) (1L << 20)) >> 21; + s10 += carry9; + s9 -= carry9 * ((uint64_t) 1L << 21); + carry11 = (s11 + (int64_t) (1L << 20)) >> 21; + s12 += carry11; + s11 -= carry11 * ((uint64_t) 1L << 21); + carry13 = (s13 + (int64_t) (1L << 20)) >> 21; + s14 += carry13; + s13 -= carry13 * ((uint64_t) 1L << 21); + carry15 = (s15 + (int64_t) (1L << 20)) >> 21; + s16 += carry15; + s15 -= carry15 * ((uint64_t) 1L << 21); + + s5 += s17 * 666643; + s6 += s17 * 470296; + s7 += s17 * 654183; + s8 -= s17 * 997805; + s9 += s17 * 136657; + s10 -= s17 * 683901; + + s4 += s16 * 666643; + s5 += s16 * 470296; + s6 += s16 * 654183; + s7 -= s16 * 997805; + s8 += s16 * 136657; + s9 -= s16 * 683901; + + s3 += s15 * 666643; + s4 += s15 * 470296; + s5 += s15 * 654183; + s6 -= s15 * 997805; + s7 += s15 * 136657; + s8 -= s15 * 683901; + + s2 += s14 * 666643; + s3 += s14 * 470296; + s4 += s14 * 654183; + s5 -= s14 * 997805; + s6 += s14 * 136657; + s7 -= s14 * 683901; + + s1 += s13 * 666643; + s2 += s13 * 470296; + s3 += s13 * 654183; + s4 -= s13 * 997805; + s5 += s13 * 136657; + s6 -= s13 * 683901; + + s0 += s12 * 666643; + s1 += s12 * 470296; + s2 += s12 * 654183; + s3 -= s12 * 997805; + s4 += s12 * 136657; + s5 -= s12 * 683901; + s12 = 0; + + carry0 = (s0 + (int64_t) (1L << 20)) >> 21; + s1 += carry0; + s0 -= carry0 * ((uint64_t) 1L << 21); + carry2 = (s2 + (int64_t) (1L << 20)) >> 21; + s3 += carry2; + s2 -= carry2 * ((uint64_t) 1L << 21); + carry4 = (s4 + (int64_t) (1L << 20)) >> 21; + s5 += carry4; + s4 -= carry4 * ((uint64_t) 1L << 21); + carry6 = (s6 + (int64_t) (1L << 20)) >> 21; + s7 += carry6; + s6 -= carry6 * ((uint64_t) 1L << 21); + carry8 = (s8 + (int64_t) (1L << 20)) >> 21; + s9 += carry8; + s8 -= carry8 * ((uint64_t) 1L << 21); + carry10 = (s10 + (int64_t) (1L << 20)) >> 21; + s11 += carry10; + s10 -= carry10 * ((uint64_t) 1L << 21); + + carry1 = (s1 + (int64_t) (1L << 20)) >> 21; + s2 += carry1; + s1 -= carry1 * ((uint64_t) 1L << 21); + carry3 = (s3 + (int64_t) (1L << 20)) >> 21; + s4 += carry3; + s3 -= carry3 * ((uint64_t) 1L << 21); + carry5 = (s5 + (int64_t) (1L << 20)) >> 21; + s6 += carry5; + s5 -= carry5 * ((uint64_t) 1L << 21); + carry7 = (s7 + (int64_t) (1L << 20)) >> 21; + s8 += carry7; + s7 -= carry7 * ((uint64_t) 1L << 21); + carry9 = (s9 + (int64_t) (1L << 20)) >> 21; + s10 += carry9; + s9 -= carry9 * ((uint64_t) 1L << 21); + carry11 = (s11 + (int64_t) (1L << 20)) >> 21; + s12 += carry11; + s11 -= carry11 * ((uint64_t) 1L << 21); + + s0 += s12 * 666643; + s1 += s12 * 470296; + s2 += s12 * 654183; + s3 -= s12 * 997805; + s4 += s12 * 136657; + s5 -= s12 * 683901; + s12 = 0; + + carry0 = s0 >> 21; + s1 += carry0; + s0 -= carry0 * ((uint64_t) 1L << 21); + carry1 = s1 >> 21; + s2 += carry1; + s1 -= carry1 * ((uint64_t) 1L << 21); + carry2 = s2 >> 21; + s3 += carry2; + s2 -= carry2 * ((uint64_t) 1L << 21); + carry3 = s3 >> 21; + s4 += carry3; + s3 -= carry3 * ((uint64_t) 1L << 21); + carry4 = s4 >> 21; + s5 += carry4; + s4 -= carry4 * ((uint64_t) 1L << 21); + carry5 = s5 >> 21; + s6 += carry5; + s5 -= carry5 * ((uint64_t) 1L << 21); + carry6 = s6 >> 21; + s7 += carry6; + s6 -= carry6 * ((uint64_t) 1L << 21); + carry7 = s7 >> 21; + s8 += carry7; + s7 -= carry7 * ((uint64_t) 1L << 21); + carry8 = s8 >> 21; + s9 += carry8; + s8 -= carry8 * ((uint64_t) 1L << 21); + carry9 = s9 >> 21; + s10 += carry9; + s9 -= carry9 * ((uint64_t) 1L << 21); + carry10 = s10 >> 21; + s11 += carry10; + s10 -= carry10 * ((uint64_t) 1L << 21); + carry11 = s11 >> 21; + s12 += carry11; + s11 -= carry11 * ((uint64_t) 1L << 21); + + s0 += s12 * 666643; + s1 += s12 * 470296; + s2 += s12 * 654183; + s3 -= s12 * 997805; + s4 += s12 * 136657; + s5 -= s12 * 683901; + + carry0 = s0 >> 21; + s1 += carry0; + s0 -= carry0 * ((uint64_t) 1L << 21); + carry1 = s1 >> 21; + s2 += carry1; + s1 -= carry1 * ((uint64_t) 1L << 21); + carry2 = s2 >> 21; + s3 += carry2; + s2 -= carry2 * ((uint64_t) 1L << 21); + carry3 = s3 >> 21; + s4 += carry3; + s3 -= carry3 * ((uint64_t) 1L << 21); + carry4 = s4 >> 21; + s5 += carry4; + s4 -= carry4 * ((uint64_t) 1L << 21); + carry5 = s5 >> 21; + s6 += carry5; + s5 -= carry5 * ((uint64_t) 1L << 21); + carry6 = s6 >> 21; + s7 += carry6; + s6 -= carry6 * ((uint64_t) 1L << 21); + carry7 = s7 >> 21; + s8 += carry7; + s7 -= carry7 * ((uint64_t) 1L << 21); + carry8 = s8 >> 21; + s9 += carry8; + s8 -= carry8 * ((uint64_t) 1L << 21); + carry9 = s9 >> 21; + s10 += carry9; + s9 -= carry9 * ((uint64_t) 1L << 21); + carry10 = s10 >> 21; + s11 += carry10; + s10 -= carry10 * ((uint64_t) 1L << 21); + + s[0] = s0 >> 0; + s[1] = s0 >> 8; + s[2] = (s0 >> 16) | (s1 * ((uint64_t) 1 << 5)); + s[3] = s1 >> 3; + s[4] = s1 >> 11; + s[5] = (s1 >> 19) | (s2 * ((uint64_t) 1 << 2)); + s[6] = s2 >> 6; + s[7] = (s2 >> 14) | (s3 * ((uint64_t) 1 << 7)); + s[8] = s3 >> 1; + s[9] = s3 >> 9; + s[10] = (s3 >> 17) | (s4 * ((uint64_t) 1 << 4)); + s[11] = s4 >> 4; + s[12] = s4 >> 12; + s[13] = (s4 >> 20) | (s5 * ((uint64_t) 1 << 1)); + s[14] = s5 >> 7; + s[15] = (s5 >> 15) | (s6 * ((uint64_t) 1 << 6)); + s[16] = s6 >> 2; + s[17] = s6 >> 10; + s[18] = (s6 >> 18) | (s7 * ((uint64_t) 1 << 3)); + s[19] = s7 >> 5; + s[20] = s7 >> 13; + s[21] = s8 >> 0; + s[22] = s8 >> 8; + s[23] = (s8 >> 16) | (s9 * ((uint64_t) 1 << 5)); + s[24] = s9 >> 3; + s[25] = s9 >> 11; + s[26] = (s9 >> 19) | (s10 * ((uint64_t) 1 << 2)); + s[27] = s10 >> 6; + s[28] = (s10 >> 14) | (s11 * ((uint64_t) 1 << 7)); + s[29] = s11 >> 1; + s[30] = s11 >> 9; + s[31] = s11 >> 17; +} + +int +sc25519_is_canonical(const unsigned char s[32]) +{ + /* 2^252+27742317777372353535851937790883648493 */ + static const unsigned char L[32] = { + 0xed, 0xd3, 0xf5, 0x5c, 0x1a, 0x63, 0x12, 0x58, 0xd6, 0x9c, 0xf7, + 0xa2, 0xde, 0xf9, 0xde, 0x14, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x10 + }; + unsigned char c = 0; + unsigned char n = 1; + unsigned int i = 32; + + do { + i--; + c |= ((s[i] - L[i]) >> 8) & n; + n &= ((s[i] ^ L[i]) - 1) >> 8; + } while (i != 0); + + return (c != 0); +} + +static void +chi25519(fe25519 out, const fe25519 z) +{ + fe25519 t0, t1, t2, t3; + int i; + + fe25519_sq(t0, z); + fe25519_mul(t1, t0, z); + fe25519_sq(t0, t1); + fe25519_sq(t2, t0); + fe25519_sq(t2, t2); + fe25519_mul(t2, t2, t0); + fe25519_mul(t1, t2, z); + fe25519_sq(t2, t1); + + for (i = 1; i < 5; i++) { + fe25519_sq(t2, t2); + } + fe25519_mul(t1, t2, t1); + fe25519_sq(t2, t1); + for (i = 1; i < 10; i++) { + fe25519_sq(t2, t2); + } + fe25519_mul(t2, t2, t1); + fe25519_sq(t3, t2); + for (i = 1; i < 20; i++) { + fe25519_sq(t3, t3); + } + fe25519_mul(t2, t3, t2); + fe25519_sq(t2, t2); + for (i = 1; i < 10; i++) { + fe25519_sq(t2, t2); + } + fe25519_mul(t1, t2, t1); + fe25519_sq(t2, t1); + for (i = 1; i < 50; i++) { + fe25519_sq(t2, t2); + } + fe25519_mul(t2, t2, t1); + fe25519_sq(t3, t2); + for (i = 1; i < 100; i++) { + fe25519_sq(t3, t3); + } + fe25519_mul(t2, t3, t2); + fe25519_sq(t2, t2); + for (i = 1; i < 50; i++) { + fe25519_sq(t2, t2); + } + fe25519_mul(t1, t2, t1); + fe25519_sq(t1, t1); + for (i = 1; i < 4; i++) { + fe25519_sq(t1, t1); + } + fe25519_mul(out, t1, t0); +} + +static void +ge25519_elligator2(unsigned char s[32], const fe25519 r, const unsigned char x_sign) +{ + fe25519 e; + fe25519 negx; + fe25519 rr2; + fe25519 x, x2, x3; + ge25519_p3 p3; + ge25519_p1p1 p1; + ge25519_p2 p2; + unsigned int e_is_minus_1; + + fe25519_sq2(rr2, r); + rr2[0]++; + fe25519_invert(rr2, rr2); + fe25519_mul(x, curve25519_A, rr2); + fe25519_neg(x, x); + + fe25519_sq(x2, x); + fe25519_mul(x3, x, x2); + fe25519_add(e, x3, x); + fe25519_mul(x2, x2, curve25519_A); + fe25519_add(e, x2, e); + + chi25519(e, e); + + fe25519_tobytes(s, e); + e_is_minus_1 = s[1] & 1; + fe25519_neg(negx, x); + fe25519_cmov(x, negx, e_is_minus_1); + fe25519_0(x2); + fe25519_cmov(x2, curve25519_A, e_is_minus_1); + fe25519_sub(x, x, x2); + + /* yed = (x-1)/(x+1) */ + { + fe25519 one; + fe25519 x_plus_one; + fe25519 x_plus_one_inv; + fe25519 x_minus_one; + fe25519 yed; + + fe25519_1(one); + fe25519_add(x_plus_one, x, one); + fe25519_sub(x_minus_one, x, one); + fe25519_invert(x_plus_one_inv, x_plus_one); + fe25519_mul(yed, x_minus_one, x_plus_one_inv); + fe25519_tobytes(s, yed); + } + + /* recover x */ + s[31] |= x_sign; + if (ge25519_frombytes(&p3, s) != 0) { + abort(); /* LCOV_EXCL_LINE */ + } + + /* multiply by the cofactor */ + ge25519_p3_dbl(&p1, &p3); + ge25519_p1p1_to_p2(&p2, &p1); + ge25519_p2_dbl(&p1, &p2); + ge25519_p1p1_to_p2(&p2, &p1); + ge25519_p2_dbl(&p1, &p2); + ge25519_p1p1_to_p3(&p3, &p1); + + ge25519_p3_tobytes(s, &p3); +} + +void +ge25519_from_uniform(unsigned char s[32], const unsigned char r[32]) +{ + fe25519 r_fe; + unsigned char x_sign; + + memcpy(s, r, 32); + x_sign = s[31] & 0x80; + s[31] &= 0x7f; + fe25519_frombytes(r_fe, s); + ge25519_elligator2(s, r_fe, x_sign); +} + +void +ge25519_from_hash(unsigned char s[32], const unsigned char h[64]) +{ + unsigned char fl[32]; + unsigned char gl[32]; + fe25519 fe_f; + fe25519 fe_g; + size_t i; + unsigned char x_sign; + + x_sign = h[0] & 0x80; + for (i = 0; i < 32; i++) { + fl[i] = h[63 - i]; + gl[i] = h[31 - i]; + } + fl[31] &= 0x7f; + gl[31] &= 0x7f; + fe25519_frombytes(fe_f, fl); + fe25519_frombytes(fe_g, gl); + fe_f[0] += (h[32] >> 7) * 19; + for (i = 0; i < sizeof (fe25519) / sizeof fe_f[0]; i++) { + fe_f[i] += 38 * fe_g[i]; + } + fe25519_reduce(fe_f, fe_f); + ge25519_elligator2(s, fe_f, x_sign); +} + +/* Ristretto group */ + +static int +ristretto255_sqrt_ratio_m1(fe25519 x, const fe25519 u, const fe25519 v) +{ + fe25519 v3; + fe25519 vxx; + fe25519 m_root_check, p_root_check, f_root_check; + fe25519 x_sqrtm1; + int has_m_root, has_p_root, has_f_root; + + fe25519_sq(v3, v); + fe25519_mul(v3, v3, v); /* v3 = v^3 */ + fe25519_sq(x, v3); + fe25519_mul(x, x, v); + fe25519_mul(x, x, u); /* x = uv^7 */ + + fe25519_pow22523(x, x); /* x = (uv^7)^((q-5)/8) */ + fe25519_mul(x, x, v3); + fe25519_mul(x, x, u); /* x = uv^3(uv^7)^((q-5)/8) */ + + fe25519_sq(vxx, x); + fe25519_mul(vxx, vxx, v); /* vx^2 */ + fe25519_sub(m_root_check, vxx, u); /* vx^2-u */ + fe25519_add(p_root_check, vxx, u); /* vx^2+u */ + fe25519_mul(f_root_check, u, sqrtm1); /* u*sqrt(-1) */ + fe25519_add(f_root_check, vxx, f_root_check); /* vx^2+u*sqrt(-1) */ + has_m_root = fe25519_iszero(m_root_check); + has_p_root = fe25519_iszero(p_root_check); + has_f_root = fe25519_iszero(f_root_check); + fe25519_mul(x_sqrtm1, x, sqrtm1); /* x*sqrt(-1) */ + + fe25519_cmov(x, x_sqrtm1, has_p_root | has_f_root); + fe25519_abs(x, x); + + return has_m_root | has_p_root; +} + +static int +ristretto255_is_canonical(const unsigned char *s) +{ + unsigned char c; + unsigned char d; + unsigned int i; + + c = (s[31] & 0x7f) ^ 0x7f; + for (i = 30; i > 0; i--) { + c |= s[i] ^ 0xff; + } + c = (((unsigned int) c) - 1U) >> 8; + d = (0xed - 1U - (unsigned int) s[0]) >> 8; + + return 1 - (((c & d) | s[0]) & 1); +} + +int +ristretto255_frombytes(ge25519_p3 *h, const unsigned char *s) +{ + fe25519 inv_sqrt; + fe25519 one; + fe25519 s_; + fe25519 ss; + fe25519 u1, u2; + fe25519 u1u1, u2u2; + fe25519 v; + fe25519 v_u2u2; + int was_square; + + if (ristretto255_is_canonical(s) == 0) { + return -1; + } + fe25519_frombytes(s_, s); + fe25519_sq(ss, s_); /* ss = s^2 */ + + fe25519_1(u1); + fe25519_sub(u1, u1, ss); /* u1 = 1-ss */ + fe25519_sq(u1u1, u1); /* u1u1 = u1^2 */ + + fe25519_1(u2); + fe25519_add(u2, u2, ss); /* u2 = 1+ss */ + fe25519_sq(u2u2, u2); /* u2u2 = u2^2 */ + + fe25519_mul(v, d, u1u1); /* v = d*u1^2 */ + fe25519_neg(v, v); /* v = -d*u1^2 */ + fe25519_sub(v, v, u2u2); /* v = -(d*u1^2)-u2^2 */ + + fe25519_mul(v_u2u2, v, u2u2); /* v_u2u2 = v*u2^2 */ + + fe25519_1(one); + was_square = ristretto255_sqrt_ratio_m1(inv_sqrt, one, v_u2u2); + fe25519_mul(h->X, inv_sqrt, u2); + fe25519_mul(h->Y, inv_sqrt, h->X); + fe25519_mul(h->Y, h->Y, v); + + fe25519_mul(h->X, h->X, s_); + fe25519_add(h->X, h->X, h->X); + fe25519_abs(h->X, h->X); + fe25519_mul(h->Y, u1, h->Y); + fe25519_1(h->Z); + fe25519_mul(h->T, h->X, h->Y); + + return - ((1 - was_square) | + fe25519_isnegative(h->T) | fe25519_iszero(h->Y)); +} + +void +ristretto255_p3_tobytes(unsigned char *s, const ge25519_p3 *h) +{ + fe25519 den1, den2; + fe25519 den_inv; + fe25519 eden; + fe25519 inv_sqrt; + fe25519 ix, iy; + fe25519 one; + fe25519 s_; + fe25519 t_z_inv; + fe25519 u1, u2; + fe25519 u1_u2u2; + fe25519 x_, y_; + fe25519 x_z_inv; + fe25519 z_inv; + fe25519 zmy; + int rotate; + + fe25519_add(u1, h->Z, h->Y); /* u1 = Z+Y */ + fe25519_sub(zmy, h->Z, h->Y); /* zmy = Z-Y */ + fe25519_mul(u1, u1, zmy); /* u1 = (Z+Y)*(Z-Y) */ + fe25519_mul(u2, h->X, h->Y); /* u2 = X*Y */ + + fe25519_sq(u1_u2u2, u2); /* u1_u2u2 = u2^2 */ + fe25519_mul(u1_u2u2, u1, u1_u2u2); /* u1_u2u2 = u1*u2^2 */ + + fe25519_1(one); + (void) ristretto255_sqrt_ratio_m1(inv_sqrt, one, u1_u2u2); + fe25519_mul(den1, inv_sqrt, u1); /* den1 = inv_sqrt*u1 */ + fe25519_mul(den2, inv_sqrt, u2); /* den2 = inv_sqrt*u2 */ + fe25519_mul(z_inv, den1, den2); /* z_inv = den1*den2 */ + fe25519_mul(z_inv, z_inv, h->T); /* z_inv = den1*den2*T */ + + fe25519_mul(ix, h->X, sqrtm1); /* ix = X*sqrt(-1) */ + fe25519_mul(iy, h->Y, sqrtm1); /* iy = Y*sqrt(-1) */ + fe25519_mul(eden, den1, invsqrtamd); /* eden = den1*sqrt(a-d) */ + + fe25519_mul(t_z_inv, h->T, z_inv); /* t_z_inv = T*z_inv */ + rotate = fe25519_isnegative(t_z_inv); + + fe25519_copy(x_, h->X); + fe25519_copy(y_, h->Y); + fe25519_copy(den_inv, den2); + + fe25519_cmov(x_, iy, rotate); + fe25519_cmov(y_, ix, rotate); + fe25519_cmov(den_inv, eden, rotate); + + fe25519_mul(x_z_inv, x_, z_inv); + fe25519_cneg(y_, y_, fe25519_isnegative(x_z_inv)); + + fe25519_sub(s_, h->Z, y_); + fe25519_mul(s_, den_inv, s_); + fe25519_abs(s_, s_); + fe25519_tobytes(s, s_); +} + +static void +ristretto255_elligator(ge25519_p3 *p, const fe25519 t) +{ + fe25519 c; + fe25519 n; + fe25519 one; + fe25519 r; + fe25519 rpd; + fe25519 s, s_prime; + fe25519 ss; + fe25519 u, v; + fe25519 w0, w1, w2, w3; + int wasnt_square; + + fe25519_1(one); + fe25519_sq(r, t); /* r = t^2 */ + fe25519_mul(r, sqrtm1, r); /* r = sqrt(-1)*t^2 */ + fe25519_add(u, r, one); /* u = r+1 */ + fe25519_mul(u, u, onemsqd); /* u = (r+1)*(1-d^2) */ + fe25519_1(c); + fe25519_neg(c, c); /* c = -1 */ + fe25519_add(rpd, r, d); /* rpd = r*d */ + fe25519_mul(v, r, d); /* v = r*d */ + fe25519_sub(v, c, v); /* v = c-r*d */ + fe25519_mul(v, v, rpd); /* v = (c-r*d)*(r+d) */ + + wasnt_square = 1 - ristretto255_sqrt_ratio_m1(s, u, v); + fe25519_mul(s_prime, s, t); + fe25519_abs(s_prime, s_prime); + fe25519_neg(s_prime, s_prime); /* s_prime = -|s*t| */ + fe25519_cmov(s, s_prime, wasnt_square); + fe25519_cmov(c, r, wasnt_square); + + fe25519_sub(n, r, one); /* n = r-1 */ + fe25519_mul(n, n, c); /* n = c*(r-1) */ + fe25519_mul(n, n, sqdmone); /* n = c*(r-1)*(d-1)^2 */ + fe25519_sub(n, n, v); /* n = c*(r-1)*(d-1)^2-v */ + + fe25519_add(w0, s, s); /* w0 = 2s */ + fe25519_mul(w0, w0, v); /* w0 = 2s*v */ + fe25519_mul(w1, n, sqrtadm1); /* w1 = n*sqrt(ad-1) */ + fe25519_sq(ss, s); /* ss = s^2 */ + fe25519_sub(w2, one, ss); /* w2 = 1-s^2 */ + fe25519_add(w3, one, ss); /* w3 = 1+s^2 */ + + fe25519_mul(p->X, w0, w3); + fe25519_mul(p->Y, w2, w1); + fe25519_mul(p->Z, w1, w3); + fe25519_mul(p->T, w0, w2); +} + +void +ristretto255_from_hash(unsigned char s[32], const unsigned char h[64]) +{ + fe25519 r0, r1; + ge25519_cached p1_cached; + ge25519_p1p1 p_p1p1; + ge25519_p3 p0, p1; + ge25519_p3 p; + + fe25519_frombytes(r0, h); + fe25519_frombytes(r1, h + 32); + ristretto255_elligator(&p0, r0); + ristretto255_elligator(&p1, r1); + ge25519_p3_to_cached(&p1_cached, &p1); + ge25519_add(&p_p1p1, &p0, &p1_cached); + ge25519_p1p1_to_p3(&p, &p_p1p1); + ristretto255_p3_tobytes(s, &p); +} diff --git a/lib/hcrypto/x25519/ed25519_ref10.h b/lib/hcrypto/x25519/ed25519_ref10.h new file mode 100644 index 000000000000..634dd2ba0fe6 --- /dev/null +++ b/lib/hcrypto/x25519/ed25519_ref10.h @@ -0,0 +1,174 @@ +/* + * ISC License + * + * Copyright (c) 2013-2019 + * Frank Denis <j at pureftpd dot org> + * + * Permission to use, copy, modify, and/or distribute this software for any + * purpose with or without fee is hereby granted, provided that the above + * copyright notice and this permission notice appear in all copies. + * + * THE SOFTWARE IS PROVIDED "AS IS" AND THE AUTHOR DISCLAIMS ALL WARRANTIES + * WITH REGARD TO THIS SOFTWARE INCLUDING ALL IMPLIED WARRANTIES OF + * MERCHANTABILITY AND FITNESS. IN NO EVENT SHALL THE AUTHOR BE LIABLE FOR + * ANY SPECIAL, DIRECT, INDIRECT, OR CONSEQUENTIAL DAMAGES OR ANY DAMAGES + * WHATSOEVER RESULTING FROM LOSS OF USE, DATA OR PROFITS, WHETHER IN AN + * ACTION OF CONTRACT, NEGLIGENCE OR OTHER TORTIOUS ACTION, ARISING OUT OF + * OR IN CONNECTION WITH THE USE OR PERFORMANCE OF THIS SOFTWARE. + */ + +#ifndef ed25519_ref10_H +#define ed25519_ref10_H + +#include <roken.h> +#include <stddef.h> +#include <stdint.h> + +/* + fe means field element. + Here the field is \Z/(2^255-19). + */ + +#ifdef HAVE_TI_MODE +typedef uint64_t fe25519[5]; +#else +typedef int32_t fe25519[10]; +#endif + +void fe25519_invert(fe25519 out, const fe25519 z); +void fe25519_frombytes(fe25519 h, const unsigned char *s); +void fe25519_tobytes(unsigned char *s, const fe25519 h); + +static inline int +sodium_is_zero(const unsigned char *n, const size_t nlen) +{ + size_t i; + volatile unsigned char d = 0U; + + for (i = 0U; i < nlen; i++) { + d |= n[i]; + } + return 1 & ((d - 1) >> 8); +} + +#ifdef HAVE_TI_MODE +# include "ed25519_ref10_fe_51.h" +#else +# include "ed25519_ref10_fe_25_5.h" +#endif + + +/* + ge means group element. + + Here the group is the set of pairs (x,y) of field elements + satisfying -x^2 + y^2 = 1 + d x^2y^2 + where d = -121665/121666. + + Representations: + ge25519_p2 (projective): (X:Y:Z) satisfying x=X/Z, y=Y/Z + ge25519_p3 (extended): (X:Y:Z:T) satisfying x=X/Z, y=Y/Z, XY=ZT + ge25519_p1p1 (completed): ((X:Z),(Y:T)) satisfying x=X/Z, y=Y/T + ge25519_precomp (Duif): (y+x,y-x,2dxy) + */ + +typedef struct { + fe25519 X; + fe25519 Y; + fe25519 Z; +} ge25519_p2; + +typedef struct { + fe25519 X; + fe25519 Y; + fe25519 Z; + fe25519 T; +} ge25519_p3; + +typedef struct { + fe25519 X; + fe25519 Y; + fe25519 Z; + fe25519 T; +} ge25519_p1p1; + +typedef struct { + fe25519 yplusx; + fe25519 yminusx; + fe25519 xy2d; +} ge25519_precomp; + +typedef struct { + fe25519 YplusX; + fe25519 YminusX; + fe25519 Z; + fe25519 T2d; +} ge25519_cached; + +void ge25519_tobytes(unsigned char *s, const ge25519_p2 *h); + +void ge25519_p3_tobytes(unsigned char *s, const ge25519_p3 *h); + +int ge25519_frombytes(ge25519_p3 *h, const unsigned char *s); + +int ge25519_frombytes_negate_vartime(ge25519_p3 *h, const unsigned char *s); + +void ge25519_p3_to_cached(ge25519_cached *r, const ge25519_p3 *p); + +void ge25519_p1p1_to_p2(ge25519_p2 *r, const ge25519_p1p1 *p); + +void ge25519_p1p1_to_p3(ge25519_p3 *r, const ge25519_p1p1 *p); + +void ge25519_add(ge25519_p1p1 *r, const ge25519_p3 *p, const ge25519_cached *q); + +void ge25519_sub(ge25519_p1p1 *r, const ge25519_p3 *p, const ge25519_cached *q); + +void ge25519_scalarmult_base(ge25519_p3 *h, const unsigned char *a); + +void ge25519_double_scalarmult_vartime(ge25519_p2 *r, const unsigned char *a, + const ge25519_p3 *A, + const unsigned char *b); + +void ge25519_scalarmult(ge25519_p3 *h, const unsigned char *a, + const ge25519_p3 *p); + +int ge25519_is_canonical(const unsigned char *s); + +int ge25519_is_on_curve(const ge25519_p3 *p); + +int ge25519_is_on_main_subgroup(const ge25519_p3 *p); + +int ge25519_has_small_order(const unsigned char s[32]); + +void ge25519_from_uniform(unsigned char s[32], const unsigned char r[32]); + +void ge25519_from_hash(unsigned char s[32], const unsigned char h[64]); + +/* + Ristretto group + */ + +int ristretto255_frombytes(ge25519_p3 *h, const unsigned char *s); + +void ristretto255_p3_tobytes(unsigned char *s, const ge25519_p3 *h); + +void ristretto255_from_hash(unsigned char s[32], const unsigned char h[64]); + +/* + The set of scalars is \Z/l + where l = 2^252 + 27742317777372353535851937790883648493. + */ + +void sc25519_invert(unsigned char recip[32], const unsigned char s[32]); + +void sc25519_reduce(unsigned char s[64]); + +void sc25519_mul(unsigned char s[32], const unsigned char a[32], + const unsigned char b[32]); + +void sc25519_muladd(unsigned char s[32], const unsigned char a[32], + const unsigned char b[32], const unsigned char c[32]); + +int sc25519_is_canonical(const unsigned char s[32]); + +#endif diff --git a/lib/hcrypto/x25519/ed25519_ref10_fe_25_5.h b/lib/hcrypto/x25519/ed25519_ref10_fe_25_5.h new file mode 100644 index 000000000000..169b581a71d1 --- /dev/null +++ b/lib/hcrypto/x25519/ed25519_ref10_fe_25_5.h @@ -0,0 +1,1067 @@ +/* + * ISC License + * + * Copyright (c) 2013-2019 + * Frank Denis <j at pureftpd dot org> + * + * Permission to use, copy, modify, and/or distribute this software for any + * purpose with or without fee is hereby granted, provided that the above + * copyright notice and this permission notice appear in all copies. + * + * THE SOFTWARE IS PROVIDED "AS IS" AND THE AUTHOR DISCLAIMS ALL WARRANTIES + * WITH REGARD TO THIS SOFTWARE INCLUDING ALL IMPLIED WARRANTIES OF + * MERCHANTABILITY AND FITNESS. IN NO EVENT SHALL THE AUTHOR BE LIABLE FOR + * ANY SPECIAL, DIRECT, INDIRECT, OR CONSEQUENTIAL DAMAGES OR ANY DAMAGES + * WHATSOEVER RESULTING FROM LOSS OF USE, DATA OR PROFITS, WHETHER IN AN + * ACTION OF CONTRACT, NEGLIGENCE OR OTHER TORTIOUS ACTION, ARISING OUT OF + * OR IN CONNECTION WITH THE USE OR PERFORMANCE OF THIS SOFTWARE. + */ + +#include <roken.h> +#include <string.h> + +/* + h = 0 + */ + +static inline void +fe25519_0(fe25519 h) +{ + memset(&h[0], 0, 10 * sizeof h[0]); +} + +/* + h = 1 + */ + +static inline void +fe25519_1(fe25519 h) +{ + h[0] = 1; + h[1] = 0; + memset(&h[2], 0, 8 * sizeof h[0]); +} + +/* + h = f + g + Can overlap h with f or g. + * + Preconditions: + |f| bounded by 1.1*2^25,1.1*2^24,1.1*2^25,1.1*2^24,etc. + |g| bounded by 1.1*2^25,1.1*2^24,1.1*2^25,1.1*2^24,etc. + * + Postconditions: + |h| bounded by 1.1*2^26,1.1*2^25,1.1*2^26,1.1*2^25,etc. + */ + +static inline void +fe25519_add(fe25519 h, const fe25519 f, const fe25519 g) +{ + int32_t h0 = f[0] + g[0]; + int32_t h1 = f[1] + g[1]; + int32_t h2 = f[2] + g[2]; + int32_t h3 = f[3] + g[3]; + int32_t h4 = f[4] + g[4]; + int32_t h5 = f[5] + g[5]; + int32_t h6 = f[6] + g[6]; + int32_t h7 = f[7] + g[7]; + int32_t h8 = f[8] + g[8]; + int32_t h9 = f[9] + g[9]; + + h[0] = h0; + h[1] = h1; + h[2] = h2; + h[3] = h3; + h[4] = h4; + h[5] = h5; + h[6] = h6; + h[7] = h7; + h[8] = h8; + h[9] = h9; +} + +/* + h = f - g + Can overlap h with f or g. + * + Preconditions: + |f| bounded by 1.1*2^25,1.1*2^24,1.1*2^25,1.1*2^24,etc. + |g| bounded by 1.1*2^25,1.1*2^24,1.1*2^25,1.1*2^24,etc. + * + Postconditions: + |h| bounded by 1.1*2^26,1.1*2^25,1.1*2^26,1.1*2^25,etc. + */ + +static void +fe25519_sub(fe25519 h, const fe25519 f, const fe25519 g) +{ + int32_t h0 = f[0] - g[0]; + int32_t h1 = f[1] - g[1]; + int32_t h2 = f[2] - g[2]; + int32_t h3 = f[3] - g[3]; + int32_t h4 = f[4] - g[4]; + int32_t h5 = f[5] - g[5]; + int32_t h6 = f[6] - g[6]; + int32_t h7 = f[7] - g[7]; + int32_t h8 = f[8] - g[8]; + int32_t h9 = f[9] - g[9]; + + h[0] = h0; + h[1] = h1; + h[2] = h2; + h[3] = h3; + h[4] = h4; + h[5] = h5; + h[6] = h6; + h[7] = h7; + h[8] = h8; + h[9] = h9; +} + +/* + h = -f + * + Preconditions: + |f| bounded by 1.1*2^25,1.1*2^24,1.1*2^25,1.1*2^24,etc. + * + Postconditions: + |h| bounded by 1.1*2^25,1.1*2^24,1.1*2^25,1.1*2^24,etc. + */ + +static inline void +fe25519_neg(fe25519 h, const fe25519 f) +{ + int32_t h0 = -f[0]; + int32_t h1 = -f[1]; + int32_t h2 = -f[2]; + int32_t h3 = -f[3]; + int32_t h4 = -f[4]; + int32_t h5 = -f[5]; + int32_t h6 = -f[6]; + int32_t h7 = -f[7]; + int32_t h8 = -f[8]; + int32_t h9 = -f[9]; + + h[0] = h0; + h[1] = h1; + h[2] = h2; + h[3] = h3; + h[4] = h4; + h[5] = h5; + h[6] = h6; + h[7] = h7; + h[8] = h8; + h[9] = h9; +} + +/* + Replace (f,g) with (g,g) if b == 1; + replace (f,g) with (f,g) if b == 0. + * + Preconditions: b in {0,1}. + */ + +static void +fe25519_cmov(fe25519 f, const fe25519 g, unsigned int b) +{ + const uint32_t mask = (uint32_t) (-(int32_t) b); + + int32_t f0 = f[0]; + int32_t f1 = f[1]; + int32_t f2 = f[2]; + int32_t f3 = f[3]; + int32_t f4 = f[4]; + int32_t f5 = f[5]; + int32_t f6 = f[6]; + int32_t f7 = f[7]; + int32_t f8 = f[8]; + int32_t f9 = f[9]; + + int32_t x0 = f0 ^ g[0]; + int32_t x1 = f1 ^ g[1]; + int32_t x2 = f2 ^ g[2]; + int32_t x3 = f3 ^ g[3]; + int32_t x4 = f4 ^ g[4]; + int32_t x5 = f5 ^ g[5]; + int32_t x6 = f6 ^ g[6]; + int32_t x7 = f7 ^ g[7]; + int32_t x8 = f8 ^ g[8]; + int32_t x9 = f9 ^ g[9]; + + x0 &= mask; + x1 &= mask; + x2 &= mask; + x3 &= mask; + x4 &= mask; + x5 &= mask; + x6 &= mask; + x7 &= mask; + x8 &= mask; + x9 &= mask; + + f[0] = f0 ^ x0; + f[1] = f1 ^ x1; + f[2] = f2 ^ x2; + f[3] = f3 ^ x3; + f[4] = f4 ^ x4; + f[5] = f5 ^ x5; + f[6] = f6 ^ x6; + f[7] = f7 ^ x7; + f[8] = f8 ^ x8; + f[9] = f9 ^ x9; +} + +static void +fe25519_cswap(fe25519 f, fe25519 g, unsigned int b) +{ + const uint32_t mask = (uint32_t) (-(int64_t) b); + + int32_t f0 = f[0]; + int32_t f1 = f[1]; + int32_t f2 = f[2]; + int32_t f3 = f[3]; + int32_t f4 = f[4]; + int32_t f5 = f[5]; + int32_t f6 = f[6]; + int32_t f7 = f[7]; + int32_t f8 = f[8]; + int32_t f9 = f[9]; + + int32_t g0 = g[0]; + int32_t g1 = g[1]; + int32_t g2 = g[2]; + int32_t g3 = g[3]; + int32_t g4 = g[4]; + int32_t g5 = g[5]; + int32_t g6 = g[6]; + int32_t g7 = g[7]; + int32_t g8 = g[8]; + int32_t g9 = g[9]; + + int32_t x0 = f0 ^ g0; + int32_t x1 = f1 ^ g1; + int32_t x2 = f2 ^ g2; + int32_t x3 = f3 ^ g3; + int32_t x4 = f4 ^ g4; + int32_t x5 = f5 ^ g5; + int32_t x6 = f6 ^ g6; + int32_t x7 = f7 ^ g7; + int32_t x8 = f8 ^ g8; + int32_t x9 = f9 ^ g9; + + x0 &= mask; + x1 &= mask; + x2 &= mask; + x3 &= mask; + x4 &= mask; + x5 &= mask; + x6 &= mask; + x7 &= mask; + x8 &= mask; + x9 &= mask; + + f[0] = f0 ^ x0; + f[1] = f1 ^ x1; + f[2] = f2 ^ x2; + f[3] = f3 ^ x3; + f[4] = f4 ^ x4; + f[5] = f5 ^ x5; + f[6] = f6 ^ x6; + f[7] = f7 ^ x7; + f[8] = f8 ^ x8; + f[9] = f9 ^ x9; + + g[0] = g0 ^ x0; + g[1] = g1 ^ x1; + g[2] = g2 ^ x2; + g[3] = g3 ^ x3; + g[4] = g4 ^ x4; + g[5] = g5 ^ x5; + g[6] = g6 ^ x6; + g[7] = g7 ^ x7; + g[8] = g8 ^ x8; + g[9] = g9 ^ x9; +} + +/* + h = f + */ + +static inline void +fe25519_copy(fe25519 h, const fe25519 f) +{ + int32_t f0 = f[0]; + int32_t f1 = f[1]; + int32_t f2 = f[2]; + int32_t f3 = f[3]; + int32_t f4 = f[4]; + int32_t f5 = f[5]; + int32_t f6 = f[6]; + int32_t f7 = f[7]; + int32_t f8 = f[8]; + int32_t f9 = f[9]; + + h[0] = f0; + h[1] = f1; + h[2] = f2; + h[3] = f3; + h[4] = f4; + h[5] = f5; + h[6] = f6; + h[7] = f7; + h[8] = f8; + h[9] = f9; +} + +/* + return 1 if f is in {1,3,5,...,q-2} + return 0 if f is in {0,2,4,...,q-1} + + Preconditions: + |f| bounded by 1.1*2^26,1.1*2^25,1.1*2^26,1.1*2^25,etc. + */ + +static inline int +fe25519_isnegative(const fe25519 f) +{ + unsigned char s[32]; + + fe25519_tobytes(s, f); + + return s[0] & 1; +} + +/* + return 1 if f == 0 + return 0 if f != 0 + + Preconditions: + |f| bounded by 1.1*2^26,1.1*2^25,1.1*2^26,1.1*2^25,etc. + */ + +static inline int +fe25519_iszero(const fe25519 f) +{ + unsigned char s[32]; + + fe25519_tobytes(s, f); + + return sodium_is_zero(s, 32); +} + +/* + h = f * g + Can overlap h with f or g. + * + Preconditions: + |f| bounded by 1.65*2^26,1.65*2^25,1.65*2^26,1.65*2^25,etc. + |g| bounded by 1.65*2^26,1.65*2^25,1.65*2^26,1.65*2^25,etc. + * + Postconditions: + |h| bounded by 1.01*2^25,1.01*2^24,1.01*2^25,1.01*2^24,etc. + */ + +/* + Notes on implementation strategy: + * + Using schoolbook multiplication. + Karatsuba would save a little in some cost models. + * + Most multiplications by 2 and 19 are 32-bit precomputations; + cheaper than 64-bit postcomputations. + * + There is one remaining multiplication by 19 in the carry chain; + one *19 precomputation can be merged into this, + but the resulting data flow is considerably less clean. + * + There are 12 carries below. + 10 of them are 2-way parallelizable and vectorizable. + Can get away with 11 carries, but then data flow is much deeper. + * + With tighter constraints on inputs can squeeze carries into int32. + */ + +static void +fe25519_mul(fe25519 h, const fe25519 f, const fe25519 g) +{ + int32_t f0 = f[0]; + int32_t f1 = f[1]; + int32_t f2 = f[2]; + int32_t f3 = f[3]; + int32_t f4 = f[4]; + int32_t f5 = f[5]; + int32_t f6 = f[6]; + int32_t f7 = f[7]; + int32_t f8 = f[8]; + int32_t f9 = f[9]; + + int32_t g0 = g[0]; + int32_t g1 = g[1]; + int32_t g2 = g[2]; + int32_t g3 = g[3]; + int32_t g4 = g[4]; + int32_t g5 = g[5]; + int32_t g6 = g[6]; + int32_t g7 = g[7]; + int32_t g8 = g[8]; + int32_t g9 = g[9]; + + int32_t g1_19 = 19 * g1; /* 1.959375*2^29 */ + int32_t g2_19 = 19 * g2; /* 1.959375*2^30; still ok */ + int32_t g3_19 = 19 * g3; + int32_t g4_19 = 19 * g4; + int32_t g5_19 = 19 * g5; + int32_t g6_19 = 19 * g6; + int32_t g7_19 = 19 * g7; + int32_t g8_19 = 19 * g8; + int32_t g9_19 = 19 * g9; + int32_t f1_2 = 2 * f1; + int32_t f3_2 = 2 * f3; + int32_t f5_2 = 2 * f5; + int32_t f7_2 = 2 * f7; + int32_t f9_2 = 2 * f9; + + int64_t f0g0 = f0 * (int64_t) g0; + int64_t f0g1 = f0 * (int64_t) g1; + int64_t f0g2 = f0 * (int64_t) g2; + int64_t f0g3 = f0 * (int64_t) g3; + int64_t f0g4 = f0 * (int64_t) g4; + int64_t f0g5 = f0 * (int64_t) g5; + int64_t f0g6 = f0 * (int64_t) g6; + int64_t f0g7 = f0 * (int64_t) g7; + int64_t f0g8 = f0 * (int64_t) g8; + int64_t f0g9 = f0 * (int64_t) g9; + int64_t f1g0 = f1 * (int64_t) g0; + int64_t f1g1_2 = f1_2 * (int64_t) g1; + int64_t f1g2 = f1 * (int64_t) g2; + int64_t f1g3_2 = f1_2 * (int64_t) g3; + int64_t f1g4 = f1 * (int64_t) g4; + int64_t f1g5_2 = f1_2 * (int64_t) g5; + int64_t f1g6 = f1 * (int64_t) g6; + int64_t f1g7_2 = f1_2 * (int64_t) g7; + int64_t f1g8 = f1 * (int64_t) g8; + int64_t f1g9_38 = f1_2 * (int64_t) g9_19; + int64_t f2g0 = f2 * (int64_t) g0; + int64_t f2g1 = f2 * (int64_t) g1; + int64_t f2g2 = f2 * (int64_t) g2; + int64_t f2g3 = f2 * (int64_t) g3; + int64_t f2g4 = f2 * (int64_t) g4; + int64_t f2g5 = f2 * (int64_t) g5; + int64_t f2g6 = f2 * (int64_t) g6; + int64_t f2g7 = f2 * (int64_t) g7; + int64_t f2g8_19 = f2 * (int64_t) g8_19; + int64_t f2g9_19 = f2 * (int64_t) g9_19; + int64_t f3g0 = f3 * (int64_t) g0; + int64_t f3g1_2 = f3_2 * (int64_t) g1; + int64_t f3g2 = f3 * (int64_t) g2; + int64_t f3g3_2 = f3_2 * (int64_t) g3; + int64_t f3g4 = f3 * (int64_t) g4; + int64_t f3g5_2 = f3_2 * (int64_t) g5; + int64_t f3g6 = f3 * (int64_t) g6; + int64_t f3g7_38 = f3_2 * (int64_t) g7_19; + int64_t f3g8_19 = f3 * (int64_t) g8_19; + int64_t f3g9_38 = f3_2 * (int64_t) g9_19; + int64_t f4g0 = f4 * (int64_t) g0; + int64_t f4g1 = f4 * (int64_t) g1; + int64_t f4g2 = f4 * (int64_t) g2; + int64_t f4g3 = f4 * (int64_t) g3; + int64_t f4g4 = f4 * (int64_t) g4; + int64_t f4g5 = f4 * (int64_t) g5; + int64_t f4g6_19 = f4 * (int64_t) g6_19; + int64_t f4g7_19 = f4 * (int64_t) g7_19; + int64_t f4g8_19 = f4 * (int64_t) g8_19; + int64_t f4g9_19 = f4 * (int64_t) g9_19; + int64_t f5g0 = f5 * (int64_t) g0; + int64_t f5g1_2 = f5_2 * (int64_t) g1; + int64_t f5g2 = f5 * (int64_t) g2; + int64_t f5g3_2 = f5_2 * (int64_t) g3; + int64_t f5g4 = f5 * (int64_t) g4; + int64_t f5g5_38 = f5_2 * (int64_t) g5_19; + int64_t f5g6_19 = f5 * (int64_t) g6_19; + int64_t f5g7_38 = f5_2 * (int64_t) g7_19; + int64_t f5g8_19 = f5 * (int64_t) g8_19; + int64_t f5g9_38 = f5_2 * (int64_t) g9_19; + int64_t f6g0 = f6 * (int64_t) g0; + int64_t f6g1 = f6 * (int64_t) g1; + int64_t f6g2 = f6 * (int64_t) g2; + int64_t f6g3 = f6 * (int64_t) g3; + int64_t f6g4_19 = f6 * (int64_t) g4_19; + int64_t f6g5_19 = f6 * (int64_t) g5_19; + int64_t f6g6_19 = f6 * (int64_t) g6_19; + int64_t f6g7_19 = f6 * (int64_t) g7_19; + int64_t f6g8_19 = f6 * (int64_t) g8_19; + int64_t f6g9_19 = f6 * (int64_t) g9_19; + int64_t f7g0 = f7 * (int64_t) g0; + int64_t f7g1_2 = f7_2 * (int64_t) g1; + int64_t f7g2 = f7 * (int64_t) g2; + int64_t f7g3_38 = f7_2 * (int64_t) g3_19; + int64_t f7g4_19 = f7 * (int64_t) g4_19; + int64_t f7g5_38 = f7_2 * (int64_t) g5_19; + int64_t f7g6_19 = f7 * (int64_t) g6_19; + int64_t f7g7_38 = f7_2 * (int64_t) g7_19; + int64_t f7g8_19 = f7 * (int64_t) g8_19; + int64_t f7g9_38 = f7_2 * (int64_t) g9_19; + int64_t f8g0 = f8 * (int64_t) g0; + int64_t f8g1 = f8 * (int64_t) g1; + int64_t f8g2_19 = f8 * (int64_t) g2_19; + int64_t f8g3_19 = f8 * (int64_t) g3_19; + int64_t f8g4_19 = f8 * (int64_t) g4_19; + int64_t f8g5_19 = f8 * (int64_t) g5_19; + int64_t f8g6_19 = f8 * (int64_t) g6_19; + int64_t f8g7_19 = f8 * (int64_t) g7_19; + int64_t f8g8_19 = f8 * (int64_t) g8_19; + int64_t f8g9_19 = f8 * (int64_t) g9_19; + int64_t f9g0 = f9 * (int64_t) g0; + int64_t f9g1_38 = f9_2 * (int64_t) g1_19; + int64_t f9g2_19 = f9 * (int64_t) g2_19; + int64_t f9g3_38 = f9_2 * (int64_t) g3_19; + int64_t f9g4_19 = f9 * (int64_t) g4_19; + int64_t f9g5_38 = f9_2 * (int64_t) g5_19; + int64_t f9g6_19 = f9 * (int64_t) g6_19; + int64_t f9g7_38 = f9_2 * (int64_t) g7_19; + int64_t f9g8_19 = f9 * (int64_t) g8_19; + int64_t f9g9_38 = f9_2 * (int64_t) g9_19; + + int64_t h0 = f0g0 + f1g9_38 + f2g8_19 + f3g7_38 + f4g6_19 + f5g5_38 + + f6g4_19 + f7g3_38 + f8g2_19 + f9g1_38; + int64_t h1 = f0g1 + f1g0 + f2g9_19 + f3g8_19 + f4g7_19 + f5g6_19 + f6g5_19 + + f7g4_19 + f8g3_19 + f9g2_19; + int64_t h2 = f0g2 + f1g1_2 + f2g0 + f3g9_38 + f4g8_19 + f5g7_38 + f6g6_19 + + f7g5_38 + f8g4_19 + f9g3_38; + int64_t h3 = f0g3 + f1g2 + f2g1 + f3g0 + f4g9_19 + f5g8_19 + f6g7_19 + + f7g6_19 + f8g5_19 + f9g4_19; + int64_t h4 = f0g4 + f1g3_2 + f2g2 + f3g1_2 + f4g0 + f5g9_38 + f6g8_19 + + f7g7_38 + f8g6_19 + f9g5_38; + int64_t h5 = f0g5 + f1g4 + f2g3 + f3g2 + f4g1 + f5g0 + f6g9_19 + f7g8_19 + + f8g7_19 + f9g6_19; + int64_t h6 = f0g6 + f1g5_2 + f2g4 + f3g3_2 + f4g2 + f5g1_2 + f6g0 + + f7g9_38 + f8g8_19 + f9g7_38; + int64_t h7 = f0g7 + f1g6 + f2g5 + f3g4 + f4g3 + f5g2 + f6g1 + f7g0 + + f8g9_19 + f9g8_19; + int64_t h8 = f0g8 + f1g7_2 + f2g6 + f3g5_2 + f4g4 + f5g3_2 + f6g2 + f7g1_2 + + f8g0 + f9g9_38; + int64_t h9 = + f0g9 + f1g8 + f2g7 + f3g6 + f4g5 + f5g4 + f6g3 + f7g2 + f8g1 + f9g0; + + int64_t carry0; + int64_t carry1; + int64_t carry2; + int64_t carry3; + int64_t carry4; + int64_t carry5; + int64_t carry6; + int64_t carry7; + int64_t carry8; + int64_t carry9; + + /* + |h0| <= (1.65*1.65*2^52*(1+19+19+19+19)+1.65*1.65*2^50*(38+38+38+38+38)) + i.e. |h0| <= 1.4*2^60; narrower ranges for h2, h4, h6, h8 + |h1| <= (1.65*1.65*2^51*(1+1+19+19+19+19+19+19+19+19)) + i.e. |h1| <= 1.7*2^59; narrower ranges for h3, h5, h7, h9 + */ + + carry0 = (h0 + (int64_t)(1L << 25)) >> 26; + h1 += carry0; + h0 -= carry0 * ((uint64_t) 1L << 26); + carry4 = (h4 + (int64_t)(1L << 25)) >> 26; + h5 += carry4; + h4 -= carry4 * ((uint64_t) 1L << 26); + /* |h0| <= 2^25 */ + /* |h4| <= 2^25 */ + /* |h1| <= 1.71*2^59 */ + /* |h5| <= 1.71*2^59 */ + + carry1 = (h1 + (int64_t)(1L << 24)) >> 25; + h2 += carry1; + h1 -= carry1 * ((uint64_t) 1L << 25); + carry5 = (h5 + (int64_t)(1L << 24)) >> 25; + h6 += carry5; + h5 -= carry5 * ((uint64_t) 1L << 25); + /* |h1| <= 2^24; from now on fits into int32 */ + /* |h5| <= 2^24; from now on fits into int32 */ + /* |h2| <= 1.41*2^60 */ + /* |h6| <= 1.41*2^60 */ + + carry2 = (h2 + (int64_t)(1L << 25)) >> 26; + h3 += carry2; + h2 -= carry2 * ((uint64_t) 1L << 26); + carry6 = (h6 + (int64_t)(1L << 25)) >> 26; + h7 += carry6; + h6 -= carry6 * ((uint64_t) 1L << 26); + /* |h2| <= 2^25; from now on fits into int32 unchanged */ + /* |h6| <= 2^25; from now on fits into int32 unchanged */ + /* |h3| <= 1.71*2^59 */ + /* |h7| <= 1.71*2^59 */ + + carry3 = (h3 + (int64_t)(1L << 24)) >> 25; + h4 += carry3; + h3 -= carry3 * ((uint64_t) 1L << 25); + carry7 = (h7 + (int64_t)(1L << 24)) >> 25; + h8 += carry7; + h7 -= carry7 * ((uint64_t) 1L << 25); + /* |h3| <= 2^24; from now on fits into int32 unchanged */ + /* |h7| <= 2^24; from now on fits into int32 unchanged */ + /* |h4| <= 1.72*2^34 */ + /* |h8| <= 1.41*2^60 */ + + carry4 = (h4 + (int64_t)(1L << 25)) >> 26; + h5 += carry4; + h4 -= carry4 * ((uint64_t) 1L << 26); + carry8 = (h8 + (int64_t)(1L << 25)) >> 26; + h9 += carry8; + h8 -= carry8 * ((uint64_t) 1L << 26); + /* |h4| <= 2^25; from now on fits into int32 unchanged */ + /* |h8| <= 2^25; from now on fits into int32 unchanged */ + /* |h5| <= 1.01*2^24 */ + /* |h9| <= 1.71*2^59 */ + + carry9 = (h9 + (int64_t)(1L << 24)) >> 25; + h0 += carry9 * 19; + h9 -= carry9 * ((uint64_t) 1L << 25); + /* |h9| <= 2^24; from now on fits into int32 unchanged */ + /* |h0| <= 1.1*2^39 */ + + carry0 = (h0 + (int64_t)(1L << 25)) >> 26; + h1 += carry0; + h0 -= carry0 * ((uint64_t) 1L << 26); + /* |h0| <= 2^25; from now on fits into int32 unchanged */ + /* |h1| <= 1.01*2^24 */ + + h[0] = (int32_t) h0; + h[1] = (int32_t) h1; + h[2] = (int32_t) h2; + h[3] = (int32_t) h3; + h[4] = (int32_t) h4; + h[5] = (int32_t) h5; + h[6] = (int32_t) h6; + h[7] = (int32_t) h7; + h[8] = (int32_t) h8; + h[9] = (int32_t) h9; +} + +/* + h = f * f + Can overlap h with f. + * + Preconditions: + |f| bounded by 1.65*2^26,1.65*2^25,1.65*2^26,1.65*2^25,etc. + * + Postconditions: + |h| bounded by 1.01*2^25,1.01*2^24,1.01*2^25,1.01*2^24,etc. + */ + +static void +fe25519_sq(fe25519 h, const fe25519 f) +{ + int32_t f0 = f[0]; + int32_t f1 = f[1]; + int32_t f2 = f[2]; + int32_t f3 = f[3]; + int32_t f4 = f[4]; + int32_t f5 = f[5]; + int32_t f6 = f[6]; + int32_t f7 = f[7]; + int32_t f8 = f[8]; + int32_t f9 = f[9]; + + int32_t f0_2 = 2 * f0; + int32_t f1_2 = 2 * f1; + int32_t f2_2 = 2 * f2; + int32_t f3_2 = 2 * f3; + int32_t f4_2 = 2 * f4; + int32_t f5_2 = 2 * f5; + int32_t f6_2 = 2 * f6; + int32_t f7_2 = 2 * f7; + int32_t f5_38 = 38 * f5; /* 1.959375*2^30 */ + int32_t f6_19 = 19 * f6; /* 1.959375*2^30 */ + int32_t f7_38 = 38 * f7; /* 1.959375*2^30 */ + int32_t f8_19 = 19 * f8; /* 1.959375*2^30 */ + int32_t f9_38 = 38 * f9; /* 1.959375*2^30 */ + + int64_t f0f0 = f0 * (int64_t) f0; + int64_t f0f1_2 = f0_2 * (int64_t) f1; + int64_t f0f2_2 = f0_2 * (int64_t) f2; + int64_t f0f3_2 = f0_2 * (int64_t) f3; + int64_t f0f4_2 = f0_2 * (int64_t) f4; + int64_t f0f5_2 = f0_2 * (int64_t) f5; + int64_t f0f6_2 = f0_2 * (int64_t) f6; + int64_t f0f7_2 = f0_2 * (int64_t) f7; + int64_t f0f8_2 = f0_2 * (int64_t) f8; + int64_t f0f9_2 = f0_2 * (int64_t) f9; + int64_t f1f1_2 = f1_2 * (int64_t) f1; + int64_t f1f2_2 = f1_2 * (int64_t) f2; + int64_t f1f3_4 = f1_2 * (int64_t) f3_2; + int64_t f1f4_2 = f1_2 * (int64_t) f4; + int64_t f1f5_4 = f1_2 * (int64_t) f5_2; + int64_t f1f6_2 = f1_2 * (int64_t) f6; + int64_t f1f7_4 = f1_2 * (int64_t) f7_2; + int64_t f1f8_2 = f1_2 * (int64_t) f8; + int64_t f1f9_76 = f1_2 * (int64_t) f9_38; + int64_t f2f2 = f2 * (int64_t) f2; + int64_t f2f3_2 = f2_2 * (int64_t) f3; + int64_t f2f4_2 = f2_2 * (int64_t) f4; + int64_t f2f5_2 = f2_2 * (int64_t) f5; + int64_t f2f6_2 = f2_2 * (int64_t) f6; + int64_t f2f7_2 = f2_2 * (int64_t) f7; + int64_t f2f8_38 = f2_2 * (int64_t) f8_19; + int64_t f2f9_38 = f2 * (int64_t) f9_38; + int64_t f3f3_2 = f3_2 * (int64_t) f3; + int64_t f3f4_2 = f3_2 * (int64_t) f4; + int64_t f3f5_4 = f3_2 * (int64_t) f5_2; + int64_t f3f6_2 = f3_2 * (int64_t) f6; + int64_t f3f7_76 = f3_2 * (int64_t) f7_38; + int64_t f3f8_38 = f3_2 * (int64_t) f8_19; + int64_t f3f9_76 = f3_2 * (int64_t) f9_38; + int64_t f4f4 = f4 * (int64_t) f4; + int64_t f4f5_2 = f4_2 * (int64_t) f5; + int64_t f4f6_38 = f4_2 * (int64_t) f6_19; + int64_t f4f7_38 = f4 * (int64_t) f7_38; + int64_t f4f8_38 = f4_2 * (int64_t) f8_19; + int64_t f4f9_38 = f4 * (int64_t) f9_38; + int64_t f5f5_38 = f5 * (int64_t) f5_38; + int64_t f5f6_38 = f5_2 * (int64_t) f6_19; + int64_t f5f7_76 = f5_2 * (int64_t) f7_38; + int64_t f5f8_38 = f5_2 * (int64_t) f8_19; + int64_t f5f9_76 = f5_2 * (int64_t) f9_38; + int64_t f6f6_19 = f6 * (int64_t) f6_19; + int64_t f6f7_38 = f6 * (int64_t) f7_38; + int64_t f6f8_38 = f6_2 * (int64_t) f8_19; + int64_t f6f9_38 = f6 * (int64_t) f9_38; + int64_t f7f7_38 = f7 * (int64_t) f7_38; + int64_t f7f8_38 = f7_2 * (int64_t) f8_19; + int64_t f7f9_76 = f7_2 * (int64_t) f9_38; + int64_t f8f8_19 = f8 * (int64_t) f8_19; + int64_t f8f9_38 = f8 * (int64_t) f9_38; + int64_t f9f9_38 = f9 * (int64_t) f9_38; + + int64_t h0 = f0f0 + f1f9_76 + f2f8_38 + f3f7_76 + f4f6_38 + f5f5_38; + int64_t h1 = f0f1_2 + f2f9_38 + f3f8_38 + f4f7_38 + f5f6_38; + int64_t h2 = f0f2_2 + f1f1_2 + f3f9_76 + f4f8_38 + f5f7_76 + f6f6_19; + int64_t h3 = f0f3_2 + f1f2_2 + f4f9_38 + f5f8_38 + f6f7_38; + int64_t h4 = f0f4_2 + f1f3_4 + f2f2 + f5f9_76 + f6f8_38 + f7f7_38; + int64_t h5 = f0f5_2 + f1f4_2 + f2f3_2 + f6f9_38 + f7f8_38; + int64_t h6 = f0f6_2 + f1f5_4 + f2f4_2 + f3f3_2 + f7f9_76 + f8f8_19; + int64_t h7 = f0f7_2 + f1f6_2 + f2f5_2 + f3f4_2 + f8f9_38; + int64_t h8 = f0f8_2 + f1f7_4 + f2f6_2 + f3f5_4 + f4f4 + f9f9_38; + int64_t h9 = f0f9_2 + f1f8_2 + f2f7_2 + f3f6_2 + f4f5_2; + + int64_t carry0; + int64_t carry1; + int64_t carry2; + int64_t carry3; + int64_t carry4; + int64_t carry5; + int64_t carry6; + int64_t carry7; + int64_t carry8; + int64_t carry9; + + carry0 = (h0 + (int64_t)(1L << 25)) >> 26; + h1 += carry0; + h0 -= carry0 * ((uint64_t) 1L << 26); + carry4 = (h4 + (int64_t)(1L << 25)) >> 26; + h5 += carry4; + h4 -= carry4 * ((uint64_t) 1L << 26); + + carry1 = (h1 + (int64_t)(1L << 24)) >> 25; + h2 += carry1; + h1 -= carry1 * ((uint64_t) 1L << 25); + carry5 = (h5 + (int64_t)(1L << 24)) >> 25; + h6 += carry5; + h5 -= carry5 * ((uint64_t) 1L << 25); + + carry2 = (h2 + (int64_t)(1L << 25)) >> 26; + h3 += carry2; + h2 -= carry2 * ((uint64_t) 1L << 26); + carry6 = (h6 + (int64_t)(1L << 25)) >> 26; + h7 += carry6; + h6 -= carry6 * ((uint64_t) 1L << 26); + + carry3 = (h3 + (int64_t)(1L << 24)) >> 25; + h4 += carry3; + h3 -= carry3 * ((uint64_t) 1L << 25); + carry7 = (h7 + (int64_t)(1L << 24)) >> 25; + h8 += carry7; + h7 -= carry7 * ((uint64_t) 1L << 25); + + carry4 = (h4 + (int64_t)(1L << 25)) >> 26; + h5 += carry4; + h4 -= carry4 * ((uint64_t) 1L << 26); + carry8 = (h8 + (int64_t)(1L << 25)) >> 26; + h9 += carry8; + h8 -= carry8 * ((uint64_t) 1L << 26); + + carry9 = (h9 + (int64_t)(1L << 24)) >> 25; + h0 += carry9 * 19; + h9 -= carry9 * ((uint64_t) 1L << 25); + + carry0 = (h0 + (int64_t)(1L << 25)) >> 26; + h1 += carry0; + h0 -= carry0 * ((uint64_t) 1L << 26); + + h[0] = (int32_t) h0; + h[1] = (int32_t) h1; + h[2] = (int32_t) h2; + h[3] = (int32_t) h3; + h[4] = (int32_t) h4; + h[5] = (int32_t) h5; + h[6] = (int32_t) h6; + h[7] = (int32_t) h7; + h[8] = (int32_t) h8; + h[9] = (int32_t) h9; +} + +/* + h = 2 * f * f + Can overlap h with f. + * + Preconditions: + |f| bounded by 1.65*2^26,1.65*2^25,1.65*2^26,1.65*2^25,etc. + * + Postconditions: + |h| bounded by 1.01*2^25,1.01*2^24,1.01*2^25,1.01*2^24,etc. + */ + +static void +fe25519_sq2(fe25519 h, const fe25519 f) +{ + int32_t f0 = f[0]; + int32_t f1 = f[1]; + int32_t f2 = f[2]; + int32_t f3 = f[3]; + int32_t f4 = f[4]; + int32_t f5 = f[5]; + int32_t f6 = f[6]; + int32_t f7 = f[7]; + int32_t f8 = f[8]; + int32_t f9 = f[9]; + + int32_t f0_2 = 2 * f0; + int32_t f1_2 = 2 * f1; + int32_t f2_2 = 2 * f2; + int32_t f3_2 = 2 * f3; + int32_t f4_2 = 2 * f4; + int32_t f5_2 = 2 * f5; + int32_t f6_2 = 2 * f6; + int32_t f7_2 = 2 * f7; + int32_t f5_38 = 38 * f5; /* 1.959375*2^30 */ + int32_t f6_19 = 19 * f6; /* 1.959375*2^30 */ + int32_t f7_38 = 38 * f7; /* 1.959375*2^30 */ + int32_t f8_19 = 19 * f8; /* 1.959375*2^30 */ + int32_t f9_38 = 38 * f9; /* 1.959375*2^30 */ + + int64_t f0f0 = f0 * (int64_t) f0; + int64_t f0f1_2 = f0_2 * (int64_t) f1; + int64_t f0f2_2 = f0_2 * (int64_t) f2; + int64_t f0f3_2 = f0_2 * (int64_t) f3; + int64_t f0f4_2 = f0_2 * (int64_t) f4; + int64_t f0f5_2 = f0_2 * (int64_t) f5; + int64_t f0f6_2 = f0_2 * (int64_t) f6; + int64_t f0f7_2 = f0_2 * (int64_t) f7; + int64_t f0f8_2 = f0_2 * (int64_t) f8; + int64_t f0f9_2 = f0_2 * (int64_t) f9; + int64_t f1f1_2 = f1_2 * (int64_t) f1; + int64_t f1f2_2 = f1_2 * (int64_t) f2; + int64_t f1f3_4 = f1_2 * (int64_t) f3_2; + int64_t f1f4_2 = f1_2 * (int64_t) f4; + int64_t f1f5_4 = f1_2 * (int64_t) f5_2; + int64_t f1f6_2 = f1_2 * (int64_t) f6; + int64_t f1f7_4 = f1_2 * (int64_t) f7_2; + int64_t f1f8_2 = f1_2 * (int64_t) f8; + int64_t f1f9_76 = f1_2 * (int64_t) f9_38; + int64_t f2f2 = f2 * (int64_t) f2; + int64_t f2f3_2 = f2_2 * (int64_t) f3; + int64_t f2f4_2 = f2_2 * (int64_t) f4; + int64_t f2f5_2 = f2_2 * (int64_t) f5; + int64_t f2f6_2 = f2_2 * (int64_t) f6; + int64_t f2f7_2 = f2_2 * (int64_t) f7; + int64_t f2f8_38 = f2_2 * (int64_t) f8_19; + int64_t f2f9_38 = f2 * (int64_t) f9_38; + int64_t f3f3_2 = f3_2 * (int64_t) f3; + int64_t f3f4_2 = f3_2 * (int64_t) f4; + int64_t f3f5_4 = f3_2 * (int64_t) f5_2; + int64_t f3f6_2 = f3_2 * (int64_t) f6; + int64_t f3f7_76 = f3_2 * (int64_t) f7_38; + int64_t f3f8_38 = f3_2 * (int64_t) f8_19; + int64_t f3f9_76 = f3_2 * (int64_t) f9_38; + int64_t f4f4 = f4 * (int64_t) f4; + int64_t f4f5_2 = f4_2 * (int64_t) f5; + int64_t f4f6_38 = f4_2 * (int64_t) f6_19; + int64_t f4f7_38 = f4 * (int64_t) f7_38; + int64_t f4f8_38 = f4_2 * (int64_t) f8_19; + int64_t f4f9_38 = f4 * (int64_t) f9_38; + int64_t f5f5_38 = f5 * (int64_t) f5_38; + int64_t f5f6_38 = f5_2 * (int64_t) f6_19; + int64_t f5f7_76 = f5_2 * (int64_t) f7_38; + int64_t f5f8_38 = f5_2 * (int64_t) f8_19; + int64_t f5f9_76 = f5_2 * (int64_t) f9_38; + int64_t f6f6_19 = f6 * (int64_t) f6_19; + int64_t f6f7_38 = f6 * (int64_t) f7_38; + int64_t f6f8_38 = f6_2 * (int64_t) f8_19; + int64_t f6f9_38 = f6 * (int64_t) f9_38; + int64_t f7f7_38 = f7 * (int64_t) f7_38; + int64_t f7f8_38 = f7_2 * (int64_t) f8_19; + int64_t f7f9_76 = f7_2 * (int64_t) f9_38; + int64_t f8f8_19 = f8 * (int64_t) f8_19; + int64_t f8f9_38 = f8 * (int64_t) f9_38; + int64_t f9f9_38 = f9 * (int64_t) f9_38; + + int64_t h0 = f0f0 + f1f9_76 + f2f8_38 + f3f7_76 + f4f6_38 + f5f5_38; + int64_t h1 = f0f1_2 + f2f9_38 + f3f8_38 + f4f7_38 + f5f6_38; + int64_t h2 = f0f2_2 + f1f1_2 + f3f9_76 + f4f8_38 + f5f7_76 + f6f6_19; + int64_t h3 = f0f3_2 + f1f2_2 + f4f9_38 + f5f8_38 + f6f7_38; + int64_t h4 = f0f4_2 + f1f3_4 + f2f2 + f5f9_76 + f6f8_38 + f7f7_38; + int64_t h5 = f0f5_2 + f1f4_2 + f2f3_2 + f6f9_38 + f7f8_38; + int64_t h6 = f0f6_2 + f1f5_4 + f2f4_2 + f3f3_2 + f7f9_76 + f8f8_19; + int64_t h7 = f0f7_2 + f1f6_2 + f2f5_2 + f3f4_2 + f8f9_38; + int64_t h8 = f0f8_2 + f1f7_4 + f2f6_2 + f3f5_4 + f4f4 + f9f9_38; + int64_t h9 = f0f9_2 + f1f8_2 + f2f7_2 + f3f6_2 + f4f5_2; + + int64_t carry0; + int64_t carry1; + int64_t carry2; + int64_t carry3; + int64_t carry4; + int64_t carry5; + int64_t carry6; + int64_t carry7; + int64_t carry8; + int64_t carry9; + + h0 += h0; + h1 += h1; + h2 += h2; + h3 += h3; + h4 += h4; + h5 += h5; + h6 += h6; + h7 += h7; + h8 += h8; + h9 += h9; + + carry0 = (h0 + (int64_t)(1L << 25)) >> 26; + h1 += carry0; + h0 -= carry0 * ((uint64_t) 1L << 26); + carry4 = (h4 + (int64_t)(1L << 25)) >> 26; + h5 += carry4; + h4 -= carry4 * ((uint64_t) 1L << 26); + + carry1 = (h1 + (int64_t)(1L << 24)) >> 25; + h2 += carry1; + h1 -= carry1 * ((uint64_t) 1L << 25); + carry5 = (h5 + (int64_t)(1L << 24)) >> 25; + h6 += carry5; + h5 -= carry5 * ((uint64_t) 1L << 25); + + carry2 = (h2 + (int64_t)(1L << 25)) >> 26; + h3 += carry2; + h2 -= carry2 * ((uint64_t) 1L << 26); + carry6 = (h6 + (int64_t)(1L << 25)) >> 26; + h7 += carry6; + h6 -= carry6 * ((uint64_t) 1L << 26); + + carry3 = (h3 + (int64_t)(1L << 24)) >> 25; + h4 += carry3; + h3 -= carry3 * ((uint64_t) 1L << 25); + carry7 = (h7 + (int64_t)(1L << 24)) >> 25; + h8 += carry7; + h7 -= carry7 * ((uint64_t) 1L << 25); + + carry4 = (h4 + (int64_t)(1L << 25)) >> 26; + h5 += carry4; + h4 -= carry4 * ((uint64_t) 1L << 26); + carry8 = (h8 + (int64_t)(1L << 25)) >> 26; + h9 += carry8; + h8 -= carry8 * ((uint64_t) 1L << 26); + + carry9 = (h9 + (int64_t)(1L << 24)) >> 25; + h0 += carry9 * 19; + h9 -= carry9 * ((uint64_t) 1L << 25); + + carry0 = (h0 + (int64_t)(1L << 25)) >> 26; + h1 += carry0; + h0 -= carry0 * ((uint64_t) 1L << 26); + + h[0] = (int32_t) h0; + h[1] = (int32_t) h1; + h[2] = (int32_t) h2; + h[3] = (int32_t) h3; + h[4] = (int32_t) h4; + h[5] = (int32_t) h5; + h[6] = (int32_t) h6; + h[7] = (int32_t) h7; + h[8] = (int32_t) h8; + h[9] = (int32_t) h9; +} + +static void +fe25519_scalar_product(fe25519 h, const fe25519 f, uint32_t n) +{ + int64_t sn = (int64_t) n; + int32_t f0 = f[0]; + int32_t f1 = f[1]; + int32_t f2 = f[2]; + int32_t f3 = f[3]; + int32_t f4 = f[4]; + int32_t f5 = f[5]; + int32_t f6 = f[6]; + int32_t f7 = f[7]; + int32_t f8 = f[8]; + int32_t f9 = f[9]; + int64_t h0 = f0 * sn; + int64_t h1 = f1 * sn; + int64_t h2 = f2 * sn; + int64_t h3 = f3 * sn; + int64_t h4 = f4 * sn; + int64_t h5 = f5 * sn; + int64_t h6 = f6 * sn; + int64_t h7 = f7 * sn; + int64_t h8 = f8 * sn; + int64_t h9 = f9 * sn; + int64_t carry0, carry1, carry2, carry3, carry4, carry5, carry6, carry7, + carry8, carry9; + + carry9 = (h9 + ((int64_t) 1 << 24)) >> 25; + h0 += carry9 * 19; + h9 -= carry9 * ((int64_t) 1 << 25); + carry1 = (h1 + ((int64_t) 1 << 24)) >> 25; + h2 += carry1; + h1 -= carry1 * ((int64_t) 1 << 25); + carry3 = (h3 + ((int64_t) 1 << 24)) >> 25; + h4 += carry3; + h3 -= carry3 * ((int64_t) 1 << 25); + carry5 = (h5 + ((int64_t) 1 << 24)) >> 25; + h6 += carry5; + h5 -= carry5 * ((int64_t) 1 << 25); + carry7 = (h7 + ((int64_t) 1 << 24)) >> 25; + h8 += carry7; + h7 -= carry7 * ((int64_t) 1 << 25); + + carry0 = (h0 + ((int64_t) 1 << 25)) >> 26; + h1 += carry0; + h0 -= carry0 * ((int64_t) 1 << 26); + carry2 = (h2 + ((int64_t) 1 << 25)) >> 26; + h3 += carry2; + h2 -= carry2 * ((int64_t) 1 << 26); + carry4 = (h4 + ((int64_t) 1 << 25)) >> 26; + h5 += carry4; + h4 -= carry4 * ((int64_t) 1 << 26); + carry6 = (h6 + ((int64_t) 1 << 25)) >> 26; + h7 += carry6; + h6 -= carry6 * ((int64_t) 1 << 26); + carry8 = (h8 + ((int64_t) 1 << 25)) >> 26; + h9 += carry8; + h8 -= carry8 * ((int64_t) 1 << 26); + + h[0] = (int32_t) h0; + h[1] = (int32_t) h1; + h[2] = (int32_t) h2; + h[3] = (int32_t) h3; + h[4] = (int32_t) h4; + h[5] = (int32_t) h5; + h[6] = (int32_t) h6; + h[7] = (int32_t) h7; + h[8] = (int32_t) h8; + h[9] = (int32_t) h9; +} diff --git a/lib/hcrypto/x25519/ed25519_ref10_fe_51.h b/lib/hcrypto/x25519/ed25519_ref10_fe_51.h new file mode 100644 index 000000000000..cd8776dd68aa --- /dev/null +++ b/lib/hcrypto/x25519/ed25519_ref10_fe_51.h @@ -0,0 +1,539 @@ +/* + * ISC License + * + * Copyright (c) 2013-2019 + * Frank Denis <j at pureftpd dot org> + * + * Permission to use, copy, modify, and/or distribute this software for any + * purpose with or without fee is hereby granted, provided that the above + * copyright notice and this permission notice appear in all copies. + * + * THE SOFTWARE IS PROVIDED "AS IS" AND THE AUTHOR DISCLAIMS ALL WARRANTIES + * WITH REGARD TO THIS SOFTWARE INCLUDING ALL IMPLIED WARRANTIES OF + * MERCHANTABILITY AND FITNESS. IN NO EVENT SHALL THE AUTHOR BE LIABLE FOR + * ANY SPECIAL, DIRECT, INDIRECT, OR CONSEQUENTIAL DAMAGES OR ANY DAMAGES + * WHATSOEVER RESULTING FROM LOSS OF USE, DATA OR PROFITS, WHETHER IN AN + * ACTION OF CONTRACT, NEGLIGENCE OR OTHER TORTIOUS ACTION, ARISING OUT OF + * OR IN CONNECTION WITH THE USE OR PERFORMANCE OF THIS SOFTWARE. + */ + +#include <roken.h> +#include <string.h> + +#include "private/common.h" +#include "private/quirks.h" +#include "utils.h" + +/* + h = 0 + */ + +static inline void +fe25519_0(fe25519 h) +{ + memset(&h[0], 0, 5 * sizeof h[0]); +} + +/* + h = 1 + */ + +static inline void +fe25519_1(fe25519 h) +{ + h[0] = 1; + memset(&h[1], 0, 4 * sizeof h[0]); +} + +/* + h = f + g + Can overlap h with f or g. + */ + +static inline void +fe25519_add(fe25519 h, const fe25519 f, const fe25519 g) +{ + uint64_t h0 = f[0] + g[0]; + uint64_t h1 = f[1] + g[1]; + uint64_t h2 = f[2] + g[2]; + uint64_t h3 = f[3] + g[3]; + uint64_t h4 = f[4] + g[4]; + + h[0] = h0; + h[1] = h1; + h[2] = h2; + h[3] = h3; + h[4] = h4; +} + +/* + h = f - g + */ + +static void +fe25519_sub(fe25519 h, const fe25519 f, const fe25519 g) +{ + const uint64_t mask = 0x7ffffffffffffULL; + uint64_t h0, h1, h2, h3, h4; + + h0 = g[0]; + h1 = g[1]; + h2 = g[2]; + h3 = g[3]; + h4 = g[4]; + + h1 += h0 >> 51; + h0 &= mask; + h2 += h1 >> 51; + h1 &= mask; + h3 += h2 >> 51; + h2 &= mask; + h4 += h3 >> 51; + h3 &= mask; + h0 += 19ULL * (h4 >> 51); + h4 &= mask; + + h0 = (f[0] + 0xfffffffffffdaULL) - h0; + h1 = (f[1] + 0xffffffffffffeULL) - h1; + h2 = (f[2] + 0xffffffffffffeULL) - h2; + h3 = (f[3] + 0xffffffffffffeULL) - h3; + h4 = (f[4] + 0xffffffffffffeULL) - h4; + + h[0] = h0; + h[1] = h1; + h[2] = h2; + h[3] = h3; + h[4] = h4; +} + +/* + h = -f + */ + +static inline void +fe25519_neg(fe25519 h, const fe25519 f) +{ + fe25519 zero; + + fe25519_0(zero); + fe25519_sub(h, zero, f); +} + +/* + Replace (f,g) with (g,g) if b == 1; + replace (f,g) with (f,g) if b == 0. + * + Preconditions: b in {0,1}. + */ + +static void +fe25519_cmov(fe25519 f, const fe25519 g, unsigned int b) +{ + const uint64_t mask = (uint64_t) (-(int64_t) b); + + uint64_t f0 = f[0]; + uint64_t f1 = f[1]; + uint64_t f2 = f[2]; + uint64_t f3 = f[3]; + uint64_t f4 = f[4]; + + uint64_t x0 = f0 ^ g[0]; + uint64_t x1 = f1 ^ g[1]; + uint64_t x2 = f2 ^ g[2]; + uint64_t x3 = f3 ^ g[3]; + uint64_t x4 = f4 ^ g[4]; + + x0 &= mask; + x1 &= mask; + x2 &= mask; + x3 &= mask; + x4 &= mask; + + f[0] = f0 ^ x0; + f[1] = f1 ^ x1; + f[2] = f2 ^ x2; + f[3] = f3 ^ x3; + f[4] = f4 ^ x4; +} + +/* +Replace (f,g) with (g,f) if b == 1; +replace (f,g) with (f,g) if b == 0. + +Preconditions: b in {0,1}. +*/ + +static void +fe25519_cswap(fe25519 f, fe25519 g, unsigned int b) +{ + const uint64_t mask = (uint64_t) (-(int64_t) b); + + uint64_t f0 = f[0]; + uint64_t f1 = f[1]; + uint64_t f2 = f[2]; + uint64_t f3 = f[3]; + uint64_t f4 = f[4]; + + uint64_t g0 = g[0]; + uint64_t g1 = g[1]; + uint64_t g2 = g[2]; + uint64_t g3 = g[3]; + uint64_t g4 = g[4]; + + uint64_t x0 = f0 ^ g0; + uint64_t x1 = f1 ^ g1; + uint64_t x2 = f2 ^ g2; + uint64_t x3 = f3 ^ g3; + uint64_t x4 = f4 ^ g4; + + x0 &= mask; + x1 &= mask; + x2 &= mask; + x3 &= mask; + x4 &= mask; + + f[0] = f0 ^ x0; + f[1] = f1 ^ x1; + f[2] = f2 ^ x2; + f[3] = f3 ^ x3; + f[4] = f4 ^ x4; + + g[0] = g0 ^ x0; + g[1] = g1 ^ x1; + g[2] = g2 ^ x2; + g[3] = g3 ^ x3; + g[4] = g4 ^ x4; +} + +/* + h = f + */ + +static inline void +fe25519_copy(fe25519 h, const fe25519 f) +{ + uint64_t f0 = f[0]; + uint64_t f1 = f[1]; + uint64_t f2 = f[2]; + uint64_t f3 = f[3]; + uint64_t f4 = f[4]; + + h[0] = f0; + h[1] = f1; + h[2] = f2; + h[3] = f3; + h[4] = f4; +} + +/* + return 1 if f is in {1,3,5,...,q-2} + return 0 if f is in {0,2,4,...,q-1} + */ + +static inline int +fe25519_isnegative(const fe25519 f) +{ + unsigned char s[32]; + + fe25519_tobytes(s, f); + + return s[0] & 1; +} + +/* + return 1 if f == 0 + return 0 if f != 0 + */ + +static inline int +fe25519_iszero(const fe25519 f) +{ + unsigned char s[32]; + + fe25519_tobytes(s, f); + + return sodium_is_zero(s, 32); +} + +/* + h = f * g + Can overlap h with f or g. + */ + +static void +fe25519_mul(fe25519 h, const fe25519 f, const fe25519 g) +{ + const uint64_t mask = 0x7ffffffffffffULL; + uint128_t r0, r1, r2, r3, r4, carry; + uint64_t f0, f1, f2, f3, f4; + uint64_t f1_19, f2_19, f3_19, f4_19; + uint64_t g0, g1, g2, g3, g4; + uint64_t r00, r01, r02, r03, r04; + + f0 = f[0]; + f1 = f[1]; + f2 = f[2]; + f3 = f[3]; + f4 = f[4]; + + g0 = g[0]; + g1 = g[1]; + g2 = g[2]; + g3 = g[3]; + g4 = g[4]; + + f1_19 = 19ULL * f1; + f2_19 = 19ULL * f2; + f3_19 = 19ULL * f3; + f4_19 = 19ULL * f4; + + r0 = ((uint128_t) f0 ) * ((uint128_t) g0); + r0 += ((uint128_t) f1_19) * ((uint128_t) g4); + r0 += ((uint128_t) f2_19) * ((uint128_t) g3); + r0 += ((uint128_t) f3_19) * ((uint128_t) g2); + r0 += ((uint128_t) f4_19) * ((uint128_t) g1); + + r1 = ((uint128_t) f0 ) * ((uint128_t) g1); + r1 += ((uint128_t) f1 ) * ((uint128_t) g0); + r1 += ((uint128_t) f2_19) * ((uint128_t) g4); + r1 += ((uint128_t) f3_19) * ((uint128_t) g3); + r1 += ((uint128_t) f4_19) * ((uint128_t) g2); + + r2 = ((uint128_t) f0 ) * ((uint128_t) g2); + r2 += ((uint128_t) f1 ) * ((uint128_t) g1); + r2 += ((uint128_t) f2 ) * ((uint128_t) g0); + r2 += ((uint128_t) f3_19) * ((uint128_t) g4); + r2 += ((uint128_t) f4_19) * ((uint128_t) g3); + + r3 = ((uint128_t) f0 ) * ((uint128_t) g3); + r3 += ((uint128_t) f1 ) * ((uint128_t) g2); + r3 += ((uint128_t) f2 ) * ((uint128_t) g1); + r3 += ((uint128_t) f3 ) * ((uint128_t) g0); + r3 += ((uint128_t) f4_19) * ((uint128_t) g4); + + r4 = ((uint128_t) f0 ) * ((uint128_t) g4); + r4 += ((uint128_t) f1 ) * ((uint128_t) g3); + r4 += ((uint128_t) f2 ) * ((uint128_t) g2); + r4 += ((uint128_t) f3 ) * ((uint128_t) g1); + r4 += ((uint128_t) f4 ) * ((uint128_t) g0); + + r00 = ((uint64_t) r0) & mask; + carry = r0 >> 51; + r1 += carry; + r01 = ((uint64_t) r1) & mask; + carry = r1 >> 51; + r2 += carry; + r02 = ((uint64_t) r2) & mask; + carry = r2 >> 51; + r3 += carry; + r03 = ((uint64_t) r3) & mask; + carry = r3 >> 51; + r4 += carry; + r04 = ((uint64_t) r4) & mask; + carry = r4 >> 51; + r00 += 19ULL * (uint64_t) carry; + carry = r00 >> 51; + r00 &= mask; + r01 += (uint64_t) carry; + carry = r01 >> 51; + r01 &= mask; + r02 += (uint64_t) carry; + + h[0] = r00; + h[1] = r01; + h[2] = r02; + h[3] = r03; + h[4] = r04; +} + +/* + h = f * f + Can overlap h with f. + */ + +static void +fe25519_sq(fe25519 h, const fe25519 f) +{ + const uint64_t mask = 0x7ffffffffffffULL; + uint128_t r0, r1, r2, r3, r4, carry; + uint64_t f0, f1, f2, f3, f4; + uint64_t f0_2, f1_2, f1_38, f2_38, f3_38, f3_19, f4_19; + uint64_t r00, r01, r02, r03, r04; + + f0 = f[0]; + f1 = f[1]; + f2 = f[2]; + f3 = f[3]; + f4 = f[4]; + + f0_2 = f0 << 1; + f1_2 = f1 << 1; + + f1_38 = 38ULL * f1; + f2_38 = 38ULL * f2; + f3_38 = 38ULL * f3; + + f3_19 = 19ULL * f3; + f4_19 = 19ULL * f4; + + r0 = ((uint128_t) f0 ) * ((uint128_t) f0); + r0 += ((uint128_t) f1_38) * ((uint128_t) f4); + r0 += ((uint128_t) f2_38) * ((uint128_t) f3); + + r1 = ((uint128_t) f0_2 ) * ((uint128_t) f1); + r1 += ((uint128_t) f2_38) * ((uint128_t) f4); + r1 += ((uint128_t) f3_19) * ((uint128_t) f3); + + r2 = ((uint128_t) f0_2 ) * ((uint128_t) f2); + r2 += ((uint128_t) f1 ) * ((uint128_t) f1); + r2 += ((uint128_t) f3_38) * ((uint128_t) f4); + + r3 = ((uint128_t) f0_2 ) * ((uint128_t) f3); + r3 += ((uint128_t) f1_2 ) * ((uint128_t) f2); + r3 += ((uint128_t) f4_19) * ((uint128_t) f4); + + r4 = ((uint128_t) f0_2 ) * ((uint128_t) f4); + r4 += ((uint128_t) f1_2 ) * ((uint128_t) f3); + r4 += ((uint128_t) f2 ) * ((uint128_t) f2); + + r00 = ((uint64_t) r0) & mask; + carry = r0 >> 51; + r1 += carry; + r01 = ((uint64_t) r1) & mask; + carry = r1 >> 51; + r2 += carry; + r02 = ((uint64_t) r2) & mask; + carry = r2 >> 51; + r3 += carry; + r03 = ((uint64_t) r3) & mask; + carry = r3 >> 51; + r4 += carry; + r04 = ((uint64_t) r4) & mask; + carry = r4 >> 51; + r00 += 19ULL * (uint64_t) carry; + carry = r00 >> 51; + r00 &= mask; + r01 += (uint64_t) carry; + carry = r01 >> 51; + r01 &= mask; + r02 += (uint64_t) carry; + + h[0] = r00; + h[1] = r01; + h[2] = r02; + h[3] = r03; + h[4] = r04; +} + +/* + h = 2 * f * f + Can overlap h with f. +*/ + +static void +fe25519_sq2(fe25519 h, const fe25519 f) +{ + const uint64_t mask = 0x7ffffffffffffULL; + uint128_t r0, r1, r2, r3, r4, carry; + uint64_t f0, f1, f2, f3, f4; + uint64_t f0_2, f1_2, f1_38, f2_38, f3_38, f3_19, f4_19; + uint64_t r00, r01, r02, r03, r04; + + f0 = f[0]; + f1 = f[1]; + f2 = f[2]; + f3 = f[3]; + f4 = f[4]; + + f0_2 = f0 << 1; + f1_2 = f1 << 1; + + f1_38 = 38ULL * f1; + f2_38 = 38ULL * f2; + f3_38 = 38ULL * f3; + + f3_19 = 19ULL * f3; + f4_19 = 19ULL * f4; + + r0 = ((uint128_t) f0 ) * ((uint128_t) f0); + r0 += ((uint128_t) f1_38) * ((uint128_t) f4); + r0 += ((uint128_t) f2_38) * ((uint128_t) f3); + + r1 = ((uint128_t) f0_2 ) * ((uint128_t) f1); + r1 += ((uint128_t) f2_38) * ((uint128_t) f4); + r1 += ((uint128_t) f3_19) * ((uint128_t) f3); + + r2 = ((uint128_t) f0_2 ) * ((uint128_t) f2); + r2 += ((uint128_t) f1 ) * ((uint128_t) f1); + r2 += ((uint128_t) f3_38) * ((uint128_t) f4); + + r3 = ((uint128_t) f0_2 ) * ((uint128_t) f3); + r3 += ((uint128_t) f1_2 ) * ((uint128_t) f2); + r3 += ((uint128_t) f4_19) * ((uint128_t) f4); + + r4 = ((uint128_t) f0_2 ) * ((uint128_t) f4); + r4 += ((uint128_t) f1_2 ) * ((uint128_t) f3); + r4 += ((uint128_t) f2 ) * ((uint128_t) f2); + + r0 <<= 1; + r1 <<= 1; + r2 <<= 1; + r3 <<= 1; + r4 <<= 1; + + r00 = ((uint64_t) r0) & mask; + carry = r0 >> 51; + r1 += carry; + r01 = ((uint64_t) r1) & mask; + carry = r1 >> 51; + r2 += carry; + r02 = ((uint64_t) r2) & mask; + carry = r2 >> 51; + r3 += carry; + r03 = ((uint64_t) r3) & mask; + carry = r3 >> 51; + r4 += carry; + r04 = ((uint64_t) r4) & mask; + carry = r4 >> 51; + r00 += 19ULL * (uint64_t) carry; + carry = r00 >> 51; + r00 &= mask; + r01 += (uint64_t) carry; + carry = r01 >> 51; + r01 &= mask; + r02 += (uint64_t) carry; + + h[0] = r00; + h[1] = r01; + h[2] = r02; + h[3] = r03; + h[4] = r04; +} + +static void +fe25519_scalar_product(fe25519 h, const fe25519 f, uint32_t n) +{ + const uint64_t mask = 0x7ffffffffffffULL; + uint128_t a; + uint128_t sn = (uint128_t) n; + uint64_t h0, h1, h2, h3, h4; + + a = f[0] * sn; + h0 = ((uint64_t) a) & mask; + a = f[1] * sn + ((uint64_t) (a >> 51)); + h1 = ((uint64_t) a) & mask; + a = f[2] * sn + ((uint64_t) (a >> 51)); + h2 = ((uint64_t) a) & mask; + a = f[3] * sn + ((uint64_t) (a >> 51)); + h3 = ((uint64_t) a) & mask; + a = f[4] * sn + ((uint64_t) (a >> 51)); + h4 = ((uint64_t) a) & mask; + + h0 += (a >> 51) * 19ULL; + + h[0] = h0; + h[1] = h1; + h[2] = h2; + h[3] = h3; + h[4] = h4; +} diff --git a/lib/hcrypto/x25519/fe_25_5/base.h b/lib/hcrypto/x25519/fe_25_5/base.h new file mode 100644 index 000000000000..e18530bbb174 --- /dev/null +++ b/lib/hcrypto/x25519/fe_25_5/base.h @@ -0,0 +1,1344 @@ +{ /* 0/31 */ + { + { 25967493, -14356035, 29566456, 3660896, -12694345, 4014787, 27544626, -11754271, -6079156, 2047605 }, + { -12545711, 934262, -2722910, 3049990, -727428, 9406986, 12720692, 5043384, 19500929, -15469378 }, + { -8738181, 4489570, 9688441, -14785194, 10184609, -12363380, 29287919, 11864899, -24514362, -4438546 } + }, + { + { -12815894, -12976347, -21581243, 11784320, -25355658, -2750717, -11717903, -3814571, -358445, -10211303 }, + { -21703237, 6903825, 27185491, 6451973, -29577724, -9554005, -15616551, 11189268, -26829678, -5319081 }, + { 26966642, 11152617, 32442495, 15396054, 14353839, -12752335, -3128826, -9541118, -15472047, -4166697 } + }, + { + { 15636291, -9688557, 24204773, -7912398, 616977, -16685262, 27787600, -14772189, 28944400, -1550024 }, + { 16568933, 4717097, -11556148, -1102322, 15682896, -11807043, 16354577, -11775962, 7689662, 11199574 }, + { 30464156, -5976125, -11779434, -15670865, 23220365, 15915852, 7512774, 10017326, -17749093, -9920357 } + }, + { + { -17036878, 13921892, 10945806, -6033431, 27105052, -16084379, -28926210, 15006023, 3284568, -6276540 }, + { 23599295, -8306047, -11193664, -7687416, 13236774, 10506355, 7464579, 9656445, 13059162, 10374397 }, + { 7798556, 16710257, 3033922, 2874086, 28997861, 2835604, 32406664, -3839045, -641708, -101325 } + }, + { + { 10861363, 11473154, 27284546, 1981175, -30064349, 12577861, 32867885, 14515107, -15438304, 10819380 }, + { 4708026, 6336745, 20377586, 9066809, -11272109, 6594696, -25653668, 12483688, -12668491, 5581306 }, + { 19563160, 16186464, -29386857, 4097519, 10237984, -4348115, 28542350, 13850243, -23678021, -15815942 } + }, + { + { -15371964, -12862754, 32573250, 4720197, -26436522, 5875511, -19188627, -15224819, -9818940, -12085777 }, + { -8549212, 109983, 15149363, 2178705, 22900618, 4543417, 3044240, -15689887, 1762328, 14866737 }, + { -18199695, -15951423, -10473290, 1707278, -17185920, 3916101, -28236412, 3959421, 27914454, 4383652 } + }, + { + { 5153746, 9909285, 1723747, -2777874, 30523605, 5516873, 19480852, 5230134, -23952439, -15175766 }, + { -30269007, -3463509, 7665486, 10083793, 28475525, 1649722, 20654025, 16520125, 30598449, 7715701 }, + { 28881845, 14381568, 9657904, 3680757, -20181635, 7843316, -31400660, 1370708, 29794553, -1409300 } + }, + { + { 14499471, -2729599, -33191113, -4254652, 28494862, 14271267, 30290735, 10876454, -33154098, 2381726 }, + { -7195431, -2655363, -14730155, 462251, -27724326, 3941372, -6236617, 3696005, -32300832, 15351955 }, + { 27431194, 8222322, 16448760, -3907995, -18707002, 11938355, -32961401, -2970515, 29551813, 10109425 } + } +}, +{ /* 1/31 */ + { + { -13657040, -13155431, -31283750, 11777098, 21447386, 6519384, -2378284, -1627556, 10092783, -4764171 }, + { 27939166, 14210322, 4677035, 16277044, -22964462, -12398139, -32508754, 12005538, -17810127, 12803510 }, + { 17228999, -15661624, -1233527, 300140, -1224870, -11714777, 30364213, -9038194, 18016357, 4397660 } + }, + { + { -10958843, -7690207, 4776341, -14954238, 27850028, -15602212, -26619106, 14544525, -17477504, 982639 }, + { 29253598, 15796703, -2863982, -9908884, 10057023, 3163536, 7332899, -4120128, -21047696, 9934963 }, + { 5793303, 16271923, -24131614, -10116404, 29188560, 1206517, -14747930, 4559895, -30123922, -10897950 } + }, + { + { -27643952, -11493006, 16282657, -11036493, 28414021, -15012264, 24191034, 4541697, -13338309, 5500568 }, + { 12650548, -1497113, 9052871, 11355358, -17680037, -8400164, -17430592, 12264343, 10874051, 13524335 }, + { 25556948, -3045990, 714651, 2510400, 23394682, -10415330, 33119038, 5080568, -22528059, 5376628 } + }, + { + { -26088264, -4011052, -17013699, -3537628, -6726793, 1920897, -22321305, -9447443, 4535768, 1569007 }, + { -2255422, 14606630, -21692440, -8039818, 28430649, 8775819, -30494562, 3044290, 31848280, 12543772 }, + { -22028579, 2943893, -31857513, 6777306, 13784462, -4292203, -27377195, -2062731, 7718482, 14474653 } + }, + { + { 2385315, 2454213, -22631320, 46603, -4437935, -15680415, 656965, -7236665, 24316168, -5253567 }, + { 13741529, 10911568, -33233417, -8603737, -20177830, -1033297, 33040651, -13424532, -20729456, 8321686 }, + { 21060490, -2212744, 15712757, -4336099, 1639040, 10656336, 23845965, -11874838, -9984458, 608372 } + }, + { + { -13672732, -15087586, -10889693, -7557059, -6036909, 11305547, 1123968, -6780577, 27229399, 23887 }, + { -23244140, -294205, -11744728, 14712571, -29465699, -2029617, 12797024, -6440308, -1633405, 16678954 }, + { -29500620, 4770662, -16054387, 14001338, 7830047, 9564805, -1508144, -4795045, -17169265, 4904953 } + }, + { + { 24059557, 14617003, 19037157, -15039908, 19766093, -14906429, 5169211, 16191880, 2128236, -4326833 }, + { -16981152, 4124966, -8540610, -10653797, 30336522, -14105247, -29806336, 916033, -6882542, -2986532 }, + { -22630907, 12419372, -7134229, -7473371, -16478904, 16739175, 285431, 2763829, 15736322, 4143876 } + }, + { + { 2379352, 11839345, -4110402, -5988665, 11274298, 794957, 212801, -14594663, 23527084, -16458268 }, + { 33431127, -11130478, -17838966, -15626900, 8909499, 8376530, -32625340, 4087881, -15188911, -14416214 }, + { 1767683, 7197987, -13205226, -2022635, -13091350, 448826, 5799055, 4357868, -4774191, -16323038 } + } +}, +{ /* 2/31 */ + { + { 6721966, 13833823, -23523388, -1551314, 26354293, -11863321, 23365147, -3949732, 7390890, 2759800 }, + { 4409041, 2052381, 23373853, 10530217, 7676779, -12885954, 21302353, -4264057, 1244380, -12919645 }, + { -4421239, 7169619, 4982368, -2957590, 30256825, -2777540, 14086413, 9208236, 15886429, 16489664 } + }, + { + { 1996075, 10375649, 14346367, 13311202, -6874135, -16438411, -13693198, 398369, -30606455, -712933 }, + { -25307465, 9795880, -2777414, 14878809, -33531835, 14780363, 13348553, 12076947, -30836462, 5113182 }, + { -17770784, 11797796, 31950843, 13929123, -25888302, 12288344, -30341101, -7336386, 13847711, 5387222 } + }, + { + { -18582163, -3416217, 17824843, -2340966, 22744343, -10442611, 8763061, 3617786, -19600662, 10370991 }, + { 20246567, -14369378, 22358229, -543712, 18507283, -10413996, 14554437, -8746092, 32232924, 16763880 }, + { 9648505, 10094563, 26416693, 14745928, -30374318, -6472621, 11094161, 15689506, 3140038, -16510092 } + }, + { + { -16160072, 5472695, 31895588, 4744994, 8823515, 10365685, -27224800, 9448613, -28774454, 366295 }, + { 19153450, 11523972, -11096490, -6503142, -24647631, 5420647, 28344573, 8041113, 719605, 11671788 }, + { 8678025, 2694440, -6808014, 2517372, 4964326, 11152271, -15432916, -15266516, 27000813, -10195553 } + }, + { + { -15157904, 7134312, 8639287, -2814877, -7235688, 10421742, 564065, 5336097, 6750977, -14521026 }, + { 11836410, -3979488, 26297894, 16080799, 23455045, 15735944, 1695823, -8819122, 8169720, 16220347 }, + { -18115838, 8653647, 17578566, -6092619, -8025777, -16012763, -11144307, -2627664, -5990708, -14166033 } + }, + { + { -23308498, -10968312, 15213228, -10081214, -30853605, -11050004, 27884329, 2847284, 2655861, 1738395 }, + { -27537433, -14253021, -25336301, -8002780, -9370762, 8129821, 21651608, -3239336, -19087449, -11005278 }, + { 1533110, 3437855, 23735889, 459276, 29970501, 11335377, 26030092, 5821408, 10478196, 8544890 } + }, + { + { 32173121, -16129311, 24896207, 3921497, 22579056, -3410854, 19270449, 12217473, 17789017, -3395995 }, + { -30552961, -2228401, -15578829, -10147201, 13243889, 517024, 15479401, -3853233, 30460520, 1052596 }, + { -11614875, 13323618, 32618793, 8175907, -15230173, 12596687, 27491595, -4612359, 3179268, -9478891 } + }, + { + { 31947069, -14366651, -4640583, -15339921, -15125977, -6039709, -14756777, -16411740, 19072640, -9511060 }, + { 11685058, 11822410, 3158003, -13952594, 33402194, -4165066, 5977896, -5215017, 473099, 5040608 }, + { -20290863, 8198642, -27410132, 11602123, 1290375, -2799760, 28326862, 1721092, -19558642, -3131606 } + } +}, +{ /* 3/31 */ + { + { 7881532, 10687937, 7578723, 7738378, -18951012, -2553952, 21820786, 8076149, -27868496, 11538389 }, + { -19935666, 3899861, 18283497, -6801568, -15728660, -11249211, 8754525, 7446702, -5676054, 5797016 }, + { -11295600, -3793569, -15782110, -7964573, 12708869, -8456199, 2014099, -9050574, -2369172, -5877341 } + }, + { + { -22472376, -11568741, -27682020, 1146375, 18956691, 16640559, 1192730, -3714199, 15123619, 10811505 }, + { 14352098, -3419715, -18942044, 10822655, 32750596, 4699007, -70363, 15776356, -28886779, -11974553 }, + { -28241164, -8072475, -4978962, -5315317, 29416931, 1847569, -20654173, -16484855, 4714547, -9600655 } + }, + { + { 15200332, 8368572, 19679101, 15970074, -31872674, 1959451, 24611599, -4543832, -11745876, 12340220 }, + { 12876937, -10480056, 33134381, 6590940, -6307776, 14872440, 9613953, 8241152, 15370987, 9608631 }, + { -4143277, -12014408, 8446281, -391603, 4407738, 13629032, -7724868, 15866074, -28210621, -8814099 } + }, + { + { 26660628, -15677655, 8393734, 358047, -7401291, 992988, -23904233, 858697, 20571223, 8420556 }, + { 14620715, 13067227, -15447274, 8264467, 14106269, 15080814, 33531827, 12516406, -21574435, -12476749 }, + { 236881, 10476226, 57258, -14677024, 6472998, 2466984, 17258519, 7256740, 8791136, 15069930 } + }, + { + { 1276410, -9371918, 22949635, -16322807, -23493039, -5702186, 14711875, 4874229, -30663140, -2331391 }, + { 5855666, 4990204, -13711848, 7294284, -7804282, 1924647, -1423175, -7912378, -33069337, 9234253 }, + { 20590503, -9018988, 31529744, -7352666, -2706834, 10650548, 31559055, -11609587, 18979186, 13396066 } + }, + { + { 24474287, 4968103, 22267082, 4407354, 24063882, -8325180, -18816887, 13594782, 33514650, 7021958 }, + { -11566906, -6565505, -21365085, 15928892, -26158305, 4315421, -25948728, -3916677, -21480480, 12868082 }, + { -28635013, 13504661, 19988037, -2132761, 21078225, 6443208, -21446107, 2244500, -12455797, -8089383 } + }, + { + { -30595528, 13793479, -5852820, 319136, -25723172, -6263899, 33086546, 8957937, -15233648, 5540521 }, + { -11630176, -11503902, -8119500, -7643073, 2620056, 1022908, -23710744, -1568984, -16128528, -14962807 }, + { 23152971, 775386, 27395463, 14006635, -9701118, 4649512, 1689819, 892185, -11513277, -15205948 } + }, + { + { 9770129, 9586738, 26496094, 4324120, 1556511, -3550024, 27453819, 4763127, -19179614, 5867134 }, + { -32765025, 1927590, 31726409, -4753295, 23962434, -16019500, 27846559, 5931263, -29749703, -16108455 }, + { 27461885, -2977536, 22380810, 1815854, -23033753, -3031938, 7283490, -15148073, -19526700, 7734629 } + } +}, +{ /* 4/31 */ + { + { -8010264, -9590817, -11120403, 6196038, 29344158, -13430885, 7585295, -3176626, 18549497, 15302069 }, + { -32658337, -6171222, -7672793, -11051681, 6258878, 13504381, 10458790, -6418461, -8872242, 8424746 }, + { 24687205, 8613276, -30667046, -3233545, 1863892, -1830544, 19206234, 7134917, -11284482, -828919 } + }, + { + { 11334899, -9218022, 8025293, 12707519, 17523892, -10476071, 10243738, -14685461, -5066034, 16498837 }, + { 8911542, 6887158, -9584260, -6958590, 11145641, -9543680, 17303925, -14124238, 6536641, 10543906 }, + { -28946384, 15479763, -17466835, 568876, -1497683, 11223454, -2669190, -16625574, -27235709, 8876771 } + }, + { + { -25742899, -12566864, -15649966, -846607, -33026686, -796288, -33481822, 15824474, -604426, -9039817 }, + { 10330056, 70051, 7957388, -9002667, 9764902, 15609756, 27698697, -4890037, 1657394, 3084098 }, + { 10477963, -7470260, 12119566, -13250805, 29016247, -5365589, 31280319, 14396151, -30233575, 15272409 } + }, + { + { -12288309, 3169463, 28813183, 16658753, 25116432, -5630466, -25173957, -12636138, -25014757, 1950504 }, + { -26180358, 9489187, 11053416, -14746161, -31053720, 5825630, -8384306, -8767532, 15341279, 8373727 }, + { 28685821, 7759505, -14378516, -12002860, -31971820, 4079242, 298136, -10232602, -2878207, 15190420 } + }, + { + { -32932876, 13806336, -14337485, -15794431, -24004620, 10940928, 8669718, 2742393, -26033313, -6875003 }, + { -1580388, -11729417, -25979658, -11445023, -17411874, -10912854, 9291594, -16247779, -12154742, 6048605 }, + { -30305315, 14843444, 1539301, 11864366, 20201677, 1900163, 13934231, 5128323, 11213262, 9168384 } + }, + { + { -26280513, 11007847, 19408960, -940758, -18592965, -4328580, -5088060, -11105150, 20470157, -16398701 }, + { -23136053, 9282192, 14855179, -15390078, -7362815, -14408560, -22783952, 14461608, 14042978, 5230683 }, + { 29969567, -2741594, -16711867, -8552442, 9175486, -2468974, 21556951, 3506042, -5933891, -12449708 } + }, + { + { -3144746, 8744661, 19704003, 4581278, -20430686, 6830683, -21284170, 8971513, -28539189, 15326563 }, + { -19464629, 10110288, -17262528, -3503892, -23500387, 1355669, -15523050, 15300988, -20514118, 9168260 }, + { -5353335, 4488613, -23803248, 16314347, 7780487, -15638939, -28948358, 9601605, 33087103, -9011387 } + }, + { + { -19443170, -15512900, -20797467, -12445323, -29824447, 10229461, -27444329, -15000531, -5996870, 15664672 }, + { 23294591, -16632613, -22650781, -8470978, 27844204, 11461195, 13099750, -2460356, 18151676, 13417686 }, + { -24722913, -4176517, -31150679, 5988919, -26858785, 6685065, 1661597, -12551441, 15271676, -15452665 } + } +}, +{ /* 5/31 */ + { + { 11433042, -13228665, 8239631, -5279517, -1985436, -725718, -18698764, 2167544, -6921301, -13440182 }, + { -31436171, 15575146, 30436815, 12192228, -22463353, 9395379, -9917708, -8638997, 12215110, 12028277 }, + { 14098400, 6555944, 23007258, 5757252, -15427832, -12950502, 30123440, 4617780, -16900089, -655628 } + }, + { + { -4026201, -15240835, 11893168, 13718664, -14809462, 1847385, -15819999, 10154009, 23973261, -12684474 }, + { -26531820, -3695990, -1908898, 2534301, -31870557, -16550355, 18341390, -11419951, 32013174, -10103539 }, + { -25479301, 10876443, -11771086, -14625140, -12369567, 1838104, 21911214, 6354752, 4425632, -837822 } + }, + { + { -10433389, -14612966, 22229858, -3091047, -13191166, 776729, -17415375, -12020462, 4725005, 14044970 }, + { 19268650, -7304421, 1555349, 8692754, -21474059, -9910664, 6347390, -1411784, -19522291, -16109756 }, + { -24864089, 12986008, -10898878, -5558584, -11312371, -148526, 19541418, 8180106, 9282262, 10282508 } + }, + { + { -26205082, 4428547, -8661196, -13194263, 4098402, -14165257, 15522535, 8372215, 5542595, -10702683 }, + { -10562541, 14895633, 26814552, -16673850, -17480754, -2489360, -2781891, 6993761, -18093885, 10114655 }, + { -20107055, -929418, 31422704, 10427861, -7110749, 6150669, -29091755, -11529146, 25953725, -106158 } + }, + { + { -4234397, -8039292, -9119125, 3046000, 2101609, -12607294, 19390020, 6094296, -3315279, 12831125 }, + { -15998678, 7578152, 5310217, 14408357, -33548620, -224739, 31575954, 6326196, 7381791, -2421839 }, + { -20902779, 3296811, 24736065, -16328389, 18374254, 7318640, 6295303, 8082724, -15362489, 12339664 } + }, + { + { 27724736, 2291157, 6088201, -14184798, 1792727, 5857634, 13848414, 15768922, 25091167, 14856294 }, + { -18866652, 8331043, 24373479, 8541013, -701998, -9269457, 12927300, -12695493, -22182473, -9012899 }, + { -11423429, -5421590, 11632845, 3405020, 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9192020, -1802462, 17271490, 12349094, 26939669, -3752294 } + }, + { + { -12889898, 9373458, 31595848, 16374215, 21471720, 13221525, -27283495, -12348559, -3698806, 117887 }, + { 22263325, -6560050, 3984570, -11174646, -15114008, -566785, 28311253, 5358056, -23319780, 541964 }, + { 16259219, 3261970, 2309254, -15534474, -16885711, -4581916, 24134070, -16705829, -13337066, -13552195 } + }, + { + { 9378160, -13140186, -22845982, -12745264, 28198281, -7244098, -2399684, -717351, 690426, 14876244 }, + { 24977353, -314384, -8223969, -13465086, 28432343, -1176353, -13068804, -12297348, -22380984, 6618999 }, + { -1538174, 11685646, 12944378, 13682314, -24389511, -14413193, 8044829, -13817328, 32239829, -5652762 } + }, + { + { -18603066, 4762990, -926250, 8885304, -28412480, -3187315, 9781647, -10350059, 32779359, 5095274 }, + { -33008130, -5214506, -32264887, -3685216, 9460461, -9327423, -24601656, 14506724, 21639561, -2630236 }, + { -16400943, -13112215, 25239338, 15531969, 3987758, -4499318, -1289502, -6863535, 17874574, 558605 } + }, + { + { -13600129, 10240081, 9171883, 16131053, -20869254, 9599700, 33499487, 5080151, 2085892, 5119761 }, + { -22205145, -2519528, -16381601, 414691, -25019550, 2170430, 30634760, -8363614, -31999993, -5759884 }, + { -6845704, 15791202, 8550074, -1312654, 29928809, -12092256, 27534430, -7192145, -22351378, 12961482 } + }, + { + { -24492060, -9570771, 10368194, 11582341, -23397293, -2245287, 16533930, 8206996, -30194652, -5159638 }, + { -11121496, -3382234, 2307366, 6362031, -135455, 8868177, -16835630, 7031275, 7589640, 8945490 }, + { -32152748, 8917967, 6661220, -11677616, -1192060, -15793393, 7251489, -11182180, 24099109, -14456170 } + }, + { + { 5019558, -7907470, 4244127, -14714356, -26933272, 6453165, -19118182, -13289025, -6231896, -10280736 }, + { 10853594, 10721687, 26480089, 5861829, -22995819, 1972175, -1866647, -10557898, -3363451, -6441124 }, + { -17002408, 5906790, 221599, -6563147, 7828208, -13248918, 24362661, -2008168, -13866408, 7421392 } + }, + { + { 8139927, -6546497, 32257646, -5890546, 30375719, 1886181, -21175108, 15441252, 28826358, -4123029 }, + { 6267086, 9695052, 7709135, -16603597, -32869068, -1886135, 14795160, -7840124, 13746021, -1742048 }, + { 28584902, 7787108, -6732942, -15050729, 22846041, -7571236, -3181936, -363524, 4771362, -8419958 } + } +}, +{ /* 7/31 */ + { + { 24949256, 6376279, -27466481, -8174608, -18646154, -9930606, 33543569, -12141695, 3569627, 11342593 }, + { 26514989, 4740088, 27912651, 3697550, 19331575, -11472339, 6809886, 4608608, 7325975, -14801071 }, + { -11618399, -14554430, -24321212, 7655128, -1369274, 5214312, -27400540, 10258390, -17646694, -8186692 } + }, + { + { 11431204, 15823007, 26570245, 14329124, 18029990, 4796082, -31446179, 15580664, 9280358, -3973687 }, + { -160783, -10326257, -22855316, -4304997, -20861367, -13621002, -32810901, -11181622, -15545091, 4387441 }, + { -20799378, 12194512, 3937617, -5805892, -27154820, 9340370, -24513992, 8548137, 20617071, -7482001 } + }, + { + { -938825, -3930586, -8714311, 16124718, 24603125, -6225393, -13775352, -11875822, 24345683, 10325460 }, + { -19855277, -1568885, -22202708, 8714034, 14007766, 6928528, 16318175, -1010689, 4766743, 3552007 }, + { -21751364, -16730916, 1351763, -803421, -4009670, 3950935, 3217514, 14481909, 10988822, -3994762 } + }, + { + { 15564307, -14311570, 3101243, 5684148, 30446780, -8051356, 12677127, -6505343, -8295852, 13296005 }, + { -9442290, 6624296, -30298964, -11913677, -4670981, -2057379, 31521204, 9614054, -30000824, 12074674 }, + { 4771191, -135239, 14290749, -13089852, 27992298, 14998318, -1413936, -1556716, 29832613, -16391035 } + }, + { + { 7064884, -7541174, -19161962, -5067537, -18891269, -2912736, 25825242, 5293297, -27122660, 13101590 }, + { -2298563, 2439670, -7466610, 1719965, -27267541, -16328445, 32512469, -5317593, -30356070, -4190957 }, + { -30006540, 10162316, -33180176, 3981723, -16482138, -13070044, 14413974, 9515896, 19568978, 9628812 } + }, + { + { 33053803, 199357, 15894591, 1583059, 27380243, -4580435, -17838894, -6106839, -6291786, 3437740 }, + { -18978877, 3884493, 19469877, 12726490, 15913552, 13614290, -22961733, 70104, 7463304, 4176122 }, + { -27124001, 10659917, 11482427, -16070381, 12771467, -6635117, -32719404, -5322751, 24216882, 5944158 } + }, + { + { 8894125, 7450974, -2664149, -9765752, -28080517, -12389115, 19345746, 14680796, 11632993, 5847885 }, + { 26942781, -2315317, 9129564, -4906607, 26024105, 11769399, -11518837, 6367194, -9727230, 4782140 }, + { 19916461, -4828410, -22910704, -11414391, 25606324, -5972441, 33253853, 8220911, 6358847, -1873857 } + }, + { + { 801428, -2081702, 16569428, 11065167, 29875704, 96627, 7908388, -4480480, -13538503, 1387155 }, + { 19646058, 5720633, -11416706, 12814209, 11607948, 12749789, 14147075, 15156355, -21866831, 11835260 }, + { 19299512, 1155910, 28703737, 14890794, 2925026, 7269399, 26121523, 15467869, -26560550, 5052483 } + } +}, +{ /* 8/31 */ + { + 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-9702530, -8876562, -1410617, -12907383, -8659932, -29576300, 1903856 }, + { 23134274, -14279132, -10681997, -1611936, 20684485, 15770816, -12989750, 3190296, 26955097, 14109738 }, + { 15308788, 5320727, -30113809, -14318877, 22902008, 7767164, 29425325, -11277562, 31960942, 11934971 } + }, + { + { -27395711, 8435796, 4109644, 12222639, -24627868, 14818669, 20638173, 4875028, 10491392, 1379718 }, + { -13159415, 9197841, 3875503, -8936108, -1383712, -5879801, 33518459, 16176658, 21432314, 12180697 }, + { -11787308, 11500838, 13787581, -13832590, -22430679, 10140205, 1465425, 12689540, -10301319, -13872883 } + } +}, +{ /* 9/31 */ + { + { 5414091, -15386041, -21007664, 9643570, 12834970, 1186149, -2622916, -1342231, 26128231, 6032912 }, + { -26337395, -13766162, 32496025, -13653919, 17847801, -12669156, 3604025, 8316894, -25875034, -10437358 }, + { 3296484, 6223048, 24680646, -12246460, -23052020, 5903205, -8862297, -4639164, 12376617, 3188849 } + }, + { + { 29190488, -14659046, 27549113, 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15826977, 17693930, 544696, -11985298, 12422646 }, + { 31117226, -12215734, -13502838, 6561947, -9876867, -12757670, -5118685, -4096706, 29120153, 13924425 }, + { -17400879, -14233209, 19675799, -2734756, -11006962, -5858820, -9383939, -11317700, 7240931, -237388 } + }, + { + { -31361739, -11346780, -15007447, -5856218, -22453340, -12152771, 1222336, 4389483, 3293637, -15551743 }, + { -16684801, -14444245, 11038544, 11054958, -13801175, -3338533, -24319580, 7733547, 12796905, -6335822 }, + { -8759414, -10817836, -25418864, 10783769, -30615557, -9746811, -28253339, 3647836, 3222231, -11160462 } + }, + { + { 18606113, 1693100, -25448386, -15170272, 4112353, 10045021, 23603893, -2048234, -7550776, 2484985 }, + { 9255317, -3131197, -12156162, -1004256, 13098013, -9214866, 16377220, -2102812, -19802075, -3034702 }, + { -22729289, 7496160, -5742199, 11329249, 19991973, -3347502, -31718148, 9936966, -30097688, -10618797 } + }, + { + { 21878590, -5001297, 4338336, 13643897, -3036865, 13160960, 19708896, 5415497, -7360503, -4109293 }, + { 27736861, 10103576, 12500508, 8502413, -3413016, -9633558, 10436918, -1550276, -23659143, -8132100 }, + { 19492550, -12104365, -29681976, -852630, -3208171, 12403437, 30066266, 8367329, 13243957, 8709688 } + } +}, +{ /* 10/31 */ + { + { 12015105, 2801261, 28198131, 10151021, 24818120, -4743133, -11194191, -5645734, 5150968, 7274186 }, + { 2831366, -12492146, 1478975, 6122054, 23825128, -12733586, 31097299, 6083058, 31021603, -9793610 }, + { -2529932, -2229646, 445613, 10720828, -13849527, -11505937, -23507731, 16354465, 15067285, -14147707 } + }, + { + { 7840942, 14037873, -33364863, 15934016, -728213, -3642706, 21403988, 1057586, -19379462, -12403220 }, + { 915865, -16469274, 15608285, -8789130, -24357026, 6060030, -17371319, 8410997, -7220461, 16527025 }, + { 32922597, -556987, 20336074, -16184568, 10903705, -5384487, 16957574, 52992, 23834301, 6588044 } + }, + { + { 32752030, 11232950, 3381995, -8714866, 22652988, -10744103, 17159699, 16689107, -20314580, -1305992 }, + { -4689649, 9166776, -25710296, -10847306, 11576752, 12733943, 7924251, -2752281, 1976123, -7249027 }, + { 21251222, 16309901, -2983015, -6783122, 30810597, 12967303, 156041, -3371252, 12331345, -8237197 } + }, + { + { 8651614, -4477032, -16085636, -4996994, 13002507, 2950805, 29054427, -5106970, 10008136, -4667901 }, + { 31486080, 15114593, -14261250, 12951354, 14369431, -7387845, 16347321, -13662089, 8684155, -10532952 }, + { 19443825, 11385320, 24468943, -9659068, -23919258, 2187569, -26263207, -6086921, 31316348, 14219878 } + }, + { + { -28594490, 1193785, 32245219, 11392485, 31092169, 15722801, 27146014, 6992409, 29126555, 9207390 }, + { 32382935, 1110093, 18477781, 11028262, -27411763, -7548111, -4980517, 10843782, -7957600, -14435730 }, + { 2814918, 7836403, 27519878, -7868156, -20894015, -11553689, -21494559, 8550130, 28346258, 1994730 } + }, + { + { -19578299, 8085545, -14000519, -3948622, 2785838, -16231307, -19516951, 7174894, 22628102, 8115180 }, + { -30405132, 955511, -11133838, -15078069, -32447087, -13278079, -25651578, 3317160, -9943017, 930272 }, + { -15303681, -6833769, 28856490, 1357446, 23421993, 1057177, 24091212, -1388970, -22765376, -10650715 } + }, + { + { -22751231, -5303997, -12907607, -12768866, -15811511, -7797053, -14839018, -16554220, -1867018, 8398970 }, + { -31969310, 2106403, -4736360, 1362501, 12813763, 16200670, 22981545, -6291273, 18009408, -15772772 }, + { -17220923, -9545221, -27784654, 14166835, 29815394, 7444469, 29551787, -3727419, 19288549, 1325865 } + }, + { + { 15100157, -15835752, -23923978, -1005098, -26450192, 15509408, 12376730, -3479146, 33166107, -8042750 }, + { 20909231, 13023121, -9209752, 16251778, -5778415, -8094914, 12412151, 10018715, 2213263, -13878373 }, + { 32529814, -11074689, 30361439, -16689753, -9135940, 1513226, 22922121, 6382134, -5766928, 8371348 } + } +}, +{ /* 11/31 */ + { + { 9923462, 11271500, 12616794, 3544722, -29998368, -1721626, 12891687, -8193132, -26442943, 10486144 }, + { -22597207, -7012665, 8587003, -8257861, 4084309, -12970062, 361726, 2610596, -23921530, -11455195 }, + { 5408411, -1136691, -4969122, 10561668, 24145918, 14240566, 31319731, -4235541, 19985175, -3436086 } + }, + { + { -13994457, 16616821, 14549246, 3341099, 32155958, 13648976, -17577068, 8849297, 65030, 8370684 }, + { -8320926, -12049626, 31204563, 5839400, -20627288, -1057277, -19442942, 6922164, 12743482, -9800518 }, + { -2361371, 12678785, 28815050, 4759974, -23893047, 4884717, 23783145, 11038569, 18800704, 255233 } + }, + { + { -5269658, -1773886, 13957886, 7990715, 23132995, 728773, 13393847, 9066957, 19258688, -14753793 }, + { -2936654, -10827535, -10432089, 14516793, -3640786, 4372541, -31934921, 2209390, -1524053, 2055794 }, + { 580882, 16705327, 5468415, -2683018, -30926419, -14696000, -7203346, -8994389, -30021019, 7394435 } + }, + { + { 23838809, 1822728, -15738443, 15242727, 8318092, -3733104, -21672180, -3492205, -4821741, 14799921 }, + { 13345610, 9759151, 3371034, -16137791, 16353039, 8577942, 31129804, 13496856, -9056018, 7402518 }, + { 2286874, -4435931, -20042458, -2008336, -13696227, 5038122, 11006906, -15760352, 8205061, 1607563 } + }, + { + { 14414086, -8002132, 3331830, -3208217, 22249151, -5594188, 18364661, -2906958, 30019587, -9029278 }, + { -27688051, 1585953, -10775053, 931069, -29120221, -11002319, -14410829, 12029093, 9944378, 8024 }, + { 4368715, -3709630, 29874200, -15022983, -20230386, -11410704, -16114594, -999085, -8142388, 5640030 } + }, + { + { 10299610, 13746483, 11661824, 16234854, 7630238, 5998374, 9809887, -16694564, 15219798, -14327783 }, + { 27425505, -5719081, 3055006, 10660664, 23458024, 595578, -15398605, -1173195, -18342183, 9742717 }, + { 6744077, 2427284, 26042789, 2720740, -847906, 1118974, 32324614, 7406442, 12420155, 1994844 } + }, + { + { 14012521, -5024720, -18384453, -9578469, -26485342, -3936439, -13033478, -10909803, 24319929, -6446333 }, + { 16412690, -4507367, 10772641, 15929391, -17068788, -4658621, 10555945, -10484049, -30102368, -4739048 }, + { 22397382, -7767684, -9293161, -12792868, 17166287, -9755136, -27333065, 6199366, 21880021, -12250760 } + }, + { + { -4283307, 5368523, -31117018, 8163389, -30323063, 3209128, 16557151, 8890729, 8840445, 4957760 }, + { -15447727, 709327, -6919446, -10870178, -29777922, 6522332, -21720181, 12130072, -14796503, 5005757 }, + { -2114751, -14308128, 23019042, 15765735, -25269683, 6002752, 10183197, -13239326, -16395286, -2176112 } + } +}, +{ /* 12/31 */ + { + { -19025756, 1632005, 13466291, -7995100, -23640451, 16573537, -32013908, -3057104, 22208662, 2000468 }, + { 3065073, -1412761, -25598674, -361432, -17683065, -5703415, -8164212, 11248527, -3691214, -7414184 }, + { 10379208, -6045554, 8877319, 1473647, -29291284, -12507580, 16690915, 2553332, -3132688, 16400289 } + }, + { + { 15716668, 1254266, -18472690, 7446274, -8448918, 6344164, -22097271, -7285580, 26894937, 9132066 }, + { 24158887, 12938817, 11085297, -8177598, -28063478, -4457083, -30576463, 64452, -6817084, -2692882 }, + { 13488534, 7794716, 22236231, 5989356, 25426474, -12578208, 2350710, -3418511, -4688006, 2364226 } + }, + { + { 16335052, 9132434, 25640582, 6678888, 1725628, 8517937, -11807024, -11697457, 15445875, -7798101 }, + { 29004207, -7867081, 28661402, -640412, -12794003, -7943086, 31863255, -4135540, -278050, -15759279 }, + { -6122061, -14866665, -28614905, 14569919, -10857999, -3591829, 10343412, -6976290, -29828287, -10815811 } + }, + { + { 27081650, 3463984, 14099042, -4517604, 1616303, -6205604, 29542636, 15372179, 17293797, 960709 }, + { 20263915, 11434237, -5765435, 11236810, 13505955, -10857102, -16111345, 6493122, -19384511, 7639714 }, + { -2830798, -14839232, 25403038, -8215196, -8317012, -16173699, 18006287, -16043750, 29994677, -15808121 } + }, + { + { 9769828, 5202651, -24157398, -13631392, -28051003, -11561624, -24613141, -13860782, -31184575, 709464 }, + { 12286395, 13076066, -21775189, -1176622, -25003198, 4057652, -32018128, -8890874, 16102007, 13205847 }, + { 13733362, 5599946, 10557076, 3195751, -5557991, 8536970, -25540170, 8525972, 10151379, 10394400 } + }, + { + { 4024660, -16137551, 22436262, 12276534, -9099015, -2686099, 19698229, 11743039, -33302334, 8934414 }, + { -15879800, -4525240, -8580747, -2934061, 14634845, -698278, -9449077, 3137094, -11536886, 11721158 }, + { 17555939, -5013938, 8268606, 2331751, -22738815, 9761013, 9319229, 8835153, -9205489, -1280045 } + }, + { + { -461409, -7830014, 20614118, 16688288, -7514766, -4807119, 22300304, 505429, 6108462, -6183415 }, + { -5070281, 12367917, -30663534, 3234473, 32617080, -8422642, 29880583, -13483331, -26898490, -7867459 }, + { -31975283, 5726539, 26934134, 10237677, -3173717, -605053, 24199304, 3795095, 7592688, -14992079 } + }, + { + { 21594432, -14964228, 17466408, -4077222, 32537084, 2739898, 6407723, 12018833, -28256052, 4298412 }, + { -20650503, -11961496, -27236275, 570498, 3767144, -1717540, 13891942, -1569194, 13717174, 10805743 }, + { -14676630, -15644296, 15287174, 11927123, 24177847, -8175568, -796431, 14860609, -26938930, -5863836 } + } +}, +{ /* 13/31 */ + { + { 12962541, 5311799, -10060768, 11658280, 18855286, -7954201, 13286263, -12808704, -4381056, 9882022 }, + { 18512079, 11319350, -20123124, 15090309, 18818594, 5271736, -22727904, 3666879, -23967430, -3299429 }, + { -6789020, -3146043, 16192429, 13241070, 15898607, -14206114, -10084880, -6661110, -2403099, 5276065 } + }, + { + { 30169808, -5317648, 26306206, -11750859, 27814964, 7069267, 7152851, 3684982, 1449224, 13082861 }, + { 10342826, 3098505, 2119311, 193222, 25702612, 12233820, 23697382, 15056736, -21016438, -8202000 }, + { -33150110, 3261608, 22745853, 7948688, 19370557, -15177665, -26171976, 6482814, -10300080, -11060101 } + }, + { + { 32869458, -5408545, 25609743, 15678670, -10687769, -15471071, 26112421, 2521008, -22664288, 6904815 }, + { 29506923, 4457497, 3377935, -9796444, -30510046, 12935080, 1561737, 3841096, -29003639, -6657642 }, + { 10340844, -6630377, -18656632, -2278430, 12621151, -13339055, 30878497, -11824370, -25584551, 5181966 } + }, + { + { 25940115, -12658025, 17324188, -10307374, -8671468, 15029094, 24396252, -16450922, -2322852, -12388574 }, + { -21765684, 9916823, -1300409, 4079498, -1028346, 11909559, 1782390, 12641087, 20603771, -6561742 }, + { -18882287, -11673380, 24849422, 11501709, 13161720, -4768874, 1925523, 11914390, 4662781, 7820689 } + }, + { + { 12241050, -425982, 8132691, 9393934, 32846760, -1599620, 29749456, 12172924, 16136752, 15264020 }, + { -10349955, -14680563, -8211979, 2330220, -17662549, -14545780, 10658213, 6671822, 19012087, 3772772 }, + { 3753511, -3421066, 10617074, 2028709, 14841030, -6721664, 28718732, -15762884, 20527771, 12988982 } + }, + { + { -14822485, -5797269, -3707987, 12689773, -898983, -10914866, -24183046, -10564943, 3299665, -12424953 }, + { -16777703, -15253301, -9642417, 4978983, 3308785, 8755439, 6943197, 6461331, -25583147, 8991218 }, + { -17226263, 1816362, -1673288, -6086439, 31783888, -8175991, -32948145, 7417950, -30242287, 1507265 } + }, + { + { 29692663, 6829891, -10498800, 4334896, 20945975, -11906496, -28887608, 8209391, 14606362, -10647073 }, + { -3481570, 8707081, 32188102, 5672294, 22096700, 1711240, -33020695, 9761487, 4170404, -2085325 }, + { -11587470, 14855945, -4127778, -1531857, -26649089, 15084046, 22186522, 16002000, -14276837, -8400798 } + }, + { + { -4811456, 13761029, -31703877, -2483919, -3312471, 7869047, -7113572, -9620092, 13240845, 10965870 }, + { -7742563, -8256762, -14768334, -13656260, -23232383, 12387166, 4498947, 14147411, 29514390, 4302863 }, + { -13413405, -12407859, 20757302, -13801832, 14785143, 8976368, -5061276, -2144373, 17846988, -13971927 } + } +}, +{ /* 14/31 */ + { + { -2244452, -754728, -4597030, -1066309, -6247172, 1455299, -21647728, -9214789, -5222701, 12650267 }, + { -9906797, -16070310, 21134160, 12198166, -27064575, 708126, 387813, 13770293, -19134326, 10958663 }, + { 22470984, 12369526, 23446014, -5441109, -21520802, -9698723, -11772496, -11574455, -25083830, 4271862 } + }, + { + { -25169565, -10053642, -19909332, 15361595, -5984358, 2159192, 75375, -4278529, -32526221, 8469673 }, + { 15854970, 4148314, -8893890, 7259002, 11666551, 13824734, -30531198, 2697372, 24154791, -9460943 }, + { 15446137, -15806644, 29759747, 14019369, 30811221, -9610191, -31582008, 12840104, 24913809, 9815020 } + }, + { + { -4709286, -5614269, -31841498, -12288893, -14443537, 10799414, -9103676, 13438769, 18735128, 9466238 }, + { 11933045, 9281483, 5081055, -5183824, -2628162, -4905629, -7727821, -10896103, -22728655, 16199064 }, + { 14576810, 379472, -26786533, -8317236, -29426508, -10812974, -102766, 1876699, 30801119, 2164795 } + }, + { + { 15995086, 3199873, 13672555, 13712240, -19378835, -4647646, -13081610, -15496269, -13492807, 1268052 }, + { -10290614, -3659039, -3286592, 10948818, 23037027, 3794475, -3470338, -12600221, -17055369, 3565904 }, + { 29210088, -9419337, -5919792, -4952785, 10834811, -13327726, -16512102, -10820713, -27162222, -14030531 } + }, + { + { -13161890, 15508588, 16663704, -8156150, -28349942, 9019123, -29183421, -3769423, 2244111, -14001979 }, + { -5152875, -3800936, -9306475, -6071583, 16243069, 14684434, -25673088, -16180800, 13491506, 4641841 }, + { 10813417, 643330, -19188515, -728916, 30292062, -16600078, 27548447, -7721242, 14476989, -12767431 } + }, + { + { 10292079, 9984945, 6481436, 8279905, -7251514, 7032743, 27282937, -1644259, -27912810, 12651324 }, + { -31185513, -813383, 22271204, 11835308, 10201545, 15351028, 17099662, 3988035, 21721536, -3148940 }, + { 10202177, -6545839, -31373232, -9574638, -32150642, -8119683, -12906320, 3852694, 13216206, 14842320 } + }, + { + { -15815640, -10601066, -6538952, -7258995, -6984659, -6581778, -31500847, 13765824, -27434397, 9900184 }, + { 14465505, -13833331, -32133984, -14738873, -27443187, 12990492, 33046193, 15796406, -7051866, -8040114 }, + { 30924417, -8279620, 6359016, -12816335, 16508377, 9071735, -25488601, 15413635, 9524356, -7018878 } + }, + { + { 12274201, -13175547, 32627641, -1785326, 6736625, 13267305, 5237659, -5109483, 15663516, 4035784 }, + { -2951309, 8903985, 17349946, 601635, -16432815, -4612556, -13732739, -15889334, -22258478, 4659091 }, + { -16916263, -4952973, -30393711, -15158821, 20774812, 15897498, 5736189, 15026997, -2178256, -13455585 } + } +}, +{ /* 15/31 */ + { + { -8858980, -2219056, 28571666, -10155518, -474467, -10105698, -3801496, 278095, 23440562, -290208 }, + { 10226241, -5928702, 15139956, 120818, -14867693, 5218603, 32937275, 11551483, -16571960, -7442864 }, + { 17932739, -12437276, -24039557, 10749060, 11316803, 7535897, 22503767, 5561594, -3646624, 3898661 } + }, + { + { 7749907, -969567, -16339731, -16464, -25018111, 15122143, -1573531, 7152530, 21831162, 1245233 }, + { 26958459, -14658026, 4314586, 8346991, -5677764, 11960072, -32589295, -620035, -30402091, -16716212 }, + { -12165896, 9166947, 33491384, 13673479, 29787085, 13096535, 6280834, 14587357, -22338025, 13987525 } + }, + { + { -24349909, 7778775, 21116000, 15572597, -4833266, -5357778, -4300898, -5124639, -7469781, -2858068 }, + { 9681908, -6737123, -31951644, 13591838, -6883821, 386950, 31622781, 6439245, -14581012, 4091397 }, + { -8426427, 1470727, -28109679, -1596990, 3978627, -5123623, -19622683, 12092163, 29077877, -14741988 } + }, + { + { 5269168, -6859726, -13230211, -8020715, 25932563, 1763552, -5606110, -5505881, -20017847, 2357889 }, + { 32264008, -15407652, -5387735, -1160093, -2091322, -3946900, 23104804, -12869908, 5727338, 189038 }, + { 14609123, -8954470, -6000566, -16622781, -14577387, -7743898, -26745169, 10942115, -25888931, -14884697 } + }, + { + { 20513500, 5557931, -15604613, 7829531, 26413943, -2019404, -21378968, 7471781, 13913677, -5137875 }, + { -25574376, 11967826, 29233242, 12948236, -6754465, 4713227, -8940970, 14059180, 12878652, 8511905 }, + { -25656801, 3393631, -2955415, -7075526, -2250709, 9366908, -30223418, 6812974, 5568676, -3127656 } + }, + { + { 11630004, 12144454, 2116339, 13606037, 27378885, 15676917, -17408753, -13504373, -14395196, 8070818 }, + { 27117696, -10007378, -31282771, -5570088, 1127282, 12772488, -29845906, 10483306, -11552749, -1028714 }, + { 10637467, -5688064, 5674781, 1072708, -26343588, -6982302, -1683975, 9177853, -27493162, 15431203 } + }, + { + { 20525145, 10892566, -12742472, 12779443, -29493034, 16150075, -28240519, 14943142, -15056790, -7935931 }, + { -30024462, 5626926, -551567, -9981087, 753598, 11981191, 25244767, -3239766, -3356550, 9594024 }, + { -23752644, 2636870, -5163910, -10103818, 585134, 7877383, 11345683, -6492290, 13352335, -10977084 } + }, + { + { -1931799, -5407458, 3304649, -12884869, 17015806, -4877091, -29783850, -7752482, -13215537, -319204 }, + { 20239939, 6607058, 6203985, 3483793, -18386976, -779229, -20723742, 15077870, -22750759, 14523817 }, + { 27406042, -6041657, 27423596, -4497394, 4996214, 10002360, -28842031, -4545494, -30172742, -4805667 } + } +}, +{ /* 16/31 */ + { + { 11374242, 12660715, 17861383, -12540833, 10935568, 1099227, -13886076, -9091740, -27727044, 11358504 }, + { -12730809, 10311867, 1510375, 10778093, -2119455, -9145702, 32676003, 11149336, -26123651, 4985768 }, + { -19096303, 341147, -6197485, -239033, 15756973, -8796662, -983043, 13794114, -19414307, -15621255 } + }, + { + { 6490081, 11940286, 25495923, -7726360, 8668373, -8751316, 3367603, 6970005, -1691065, -9004790 }, + { 1656497, 13457317, 15370807, 6364910, 13605745, 8362338, -19174622, -5475723, -16796596, -5031438 }, + { -22273315, -13524424, -64685, -4334223, -18605636, -10921968, -20571065, -7007978, -99853, -10237333 } + }, + { + { 17747465, 10039260, 19368299, -4050591, -20630635, -16041286, 31992683, -15857976, -29260363, -5511971 }, + { 31932027, -4986141, -19612382, 16366580, 22023614, 88450, 11371999, -3744247, 4882242, -10626905 }, + { 29796507, 37186, 19818052, 10115756, -11829032, 3352736, 18551198, 3272828, -5190932, -4162409 } + }, + { + { 12501286, 4044383, -8612957, -13392385, -32430052, 5136599, -19230378, -3529697, 330070, -3659409 }, + { 6384877, 2899513, 17807477, 7663917, -2358888, 12363165, 25366522, -8573892, -271295, 12071499 }, + { -8365515, -4042521, 25133448, -4517355, -6211027, 2265927, -32769618, 1936675, -5159697, 3829363 } + }, + { + { 28425966, -5835433, -577090, -4697198, -14217555, 6870930, 7921550, -6567787, 26333140, 14267664 }, + { -11067219, 11871231, 27385719, -10559544, -4585914, -11189312, 10004786, -8709488, -21761224, 8930324 }, + { -21197785, -16396035, 25654216, -1725397, 12282012, 11008919, 1541940, 4757911, -26491501, -16408940 } + }, + { + { 13537262, -7759490, -20604840, 10961927, -5922820, -13218065, -13156584, 6217254, -15943699, 13814990 }, + { -17422573, 15157790, 18705543, 29619, 24409717, -260476, 27361681, 9257833, -1956526, -1776914 }, + { -25045300, -10191966, 15366585, 15166509, -13105086, 8423556, -29171540, 12361135, -18685978, 4578290 } + }, + { + { 24579768, 3711570, 1342322, -11180126, -27005135, 14124956, -22544529, 14074919, 21964432, 8235257 }, + { -6528613, -2411497, 9442966, -5925588, 12025640, -1487420, -2981514, -1669206, 13006806, 2355433 }, + { -16304899, -13605259, -6632427, -5142349, 16974359, -10911083, 27202044, 1719366, 1141648, -12796236 } + }, + { + { -12863944, -13219986, -8318266, -11018091, -6810145, -4843894, 13475066, -3133972, 32674895, 13715045 }, + { 11423335, -5468059, 32344216, 8962751, 24989809, 9241752, -13265253, 16086212, -28740881, -15642093 }, + { -1409668, 12530728, -6368726, 10847387, 19531186, -14132160, -11709148, 7791794, -27245943, 4383347 } + } +}, +{ /* 17/31 */ + { + { -28970898, 5271447, -1266009, -9736989, -12455236, 16732599, -4862407, -4906449, 27193557, 6245191 }, + { -15193956, 5362278, -1783893, 2695834, 4960227, 12840725, 23061898, 3260492, 22510453, 8577507 }, + { -12632451, 11257346, -32692994, 13548177, -721004, 10879011, 31168030, 13952092, -29571492, -3635906 } + }, + { + { 3877321, -9572739, 32416692, 5405324, -11004407, -13656635, 3759769, 11935320, 5611860, 8164018 }, + { -16275802, 14667797, 15906460, 12155291, -22111149, -9039718, 32003002, -8832289, 5773085, -8422109 }, + { -23788118, -8254300, 1950875, 8937633, 18686727, 16459170, -905725, 12376320, 31632953, 190926 } + }, + { + { -24593607, -16138885, -8423991, 13378746, 14162407, 6901328, -8288749, 4508564, -25341555, -3627528 }, + { 8884438, -5884009, 6023974, 10104341, -6881569, -4941533, 18722941, -14786005, -1672488, 827625 }, + { -32720583, -16289296, -32503547, 7101210, 13354605, 2659080, -1800575, -14108036, -24878478, 1541286 } + }, + { + { 2901347, -1117687, 3880376, -10059388, -17620940, -3612781, -21802117, -3567481, 20456845, -1885033 }, + { 27019610, 12299467, -13658288, -1603234, -12861660, -4861471, -19540150, -5016058, 29439641, 15138866 }, + { 21536104, -6626420, -32447818, -10690208, -22408077, 5175814, -5420040, -16361163, 7779328, 109896 } + }, + { + { 30279744, 14648750, -8044871, 6425558, 13639621, -743509, 28698390, 12180118, 23177719, -554075 }, + { 26572847, 3405927, -31701700, 12890905, -19265668, 5335866, -6493768, 2378492, 4439158, -13279347 }, + { -22716706, 3489070, -9225266, -332753, 18875722, -1140095, 14819434, -12731527, -17717757, -5461437 } + }, + { + { -5056483, 16566551, 15953661, 3767752, -10436499, 15627060, -820954, 2177225, 8550082, -15114165 }, + { -18473302, 16596775, -381660, 15663611, 22860960, 15585581, -27844109, -3582739, -23260460, -8428588 }, + { -32480551, 15707275, -8205912, -5652081, 29464558, 2713815, -22725137, 15860482, -21902570, 1494193 } + }, + { + { -19562091, -14087393, -25583872, -9299552, 13127842, 759709, 21923482, 16529112, 8742704, 12967017 }, + { -28464899, 1553205, 32536856, -10473729, -24691605, -406174, -8914625, -2933896, -29903758, 15553883 }, + { 21877909, 3230008, 9881174, 10539357, -4797115, 2841332, 11543572, 14513274, 19375923, -12647961 } + }, + { + { 8832269, -14495485, 13253511, 5137575, 5037871, 4078777, 24880818, -6222716, 2862653, 9455043 }, + { 29306751, 5123106, 20245049, -14149889, 9592566, 8447059, -2077124, -2990080, 15511449, 4789663 }, + { -20679756, 7004547, 8824831, -9434977, -4045704, -3750736, -5754762, 108893, 23513200, 16652362 } + } +}, +{ /* 18/31 */ + { + { -33256173, 4144782, -4476029, -6579123, 10770039, -7155542, -6650416, -12936300, -18319198, 10212860 }, + { 2756081, 8598110, 7383731, -6859892, 22312759, -1105012, 21179801, 2600940, -9988298, -12506466 }, + { -24645692, 13317462, -30449259, -15653928, 21365574, -10869657, 11344424, 864440, -2499677, -16710063 } + }, + { + { -26432803, 6148329, -17184412, -14474154, 18782929, -275997, -22561534, 211300, 2719757, 4940997 }, + { -1323882, 3911313, -6948744, 14759765, -30027150, 7851207, 21690126, 8518463, 26699843, 5276295 }, + { -13149873, -6429067, 9396249, 365013, 24703301, -10488939, 1321586, 149635, -15452774, 7159369 } + }, + { + { 9987780, -3404759, 17507962, 9505530, 9731535, -2165514, 22356009, 8312176, 22477218, -8403385 }, + { 18155857, -16504990, 19744716, 9006923, 15154154, -10538976, 24256460, -4864995, -22548173, 9334109 }, + { 2986088, -4911893, 10776628, -3473844, 10620590, -7083203, -21413845, 14253545, -22587149, 536906 } + }, + { + { 4377756, 8115836, 24567078, 15495314, 11625074, 13064599, 7390551, 10589625, 10838060, -15420424 }, + { -19342404, 867880, 9277171, -3218459, -14431572, -1986443, 19295826, -15796950, 6378260, 699185 }, + { 7895026, 4057113, -7081772, -13077756, -17886831, -323126, -716039, 15693155, -5045064, -13373962 } + }, + { + { -7737563, -5869402, -14566319, -7406919, 11385654, 13201616, 31730678, -10962840, -3918636, -9669325 }, + { 10188286, -15770834, -7336361, 13427543, 22223443, 14896287, 30743455, 7116568, -21786507, 5427593 }, + { 696102, 13206899, 27047647, -10632082, 15285305, -9853179, 10798490, -4578720, 19236243, 12477404 } + }, + { + { -11229439, 11243796, -17054270, -8040865, -788228, -8167967, -3897669, 11180504, -23169516, 7733644 }, + { 17800790, -14036179, -27000429, -11766671, 23887827, 3149671, 23466177, -10538171, 10322027, 15313801 }, + { 26246234, 11968874, 32263343, -5468728, 6830755, -13323031, -15794704, -101982, -24449242, 10890804 } + }, + { + { -31365647, 10271363, -12660625, -6267268, 16690207, -13062544, -14982212, 16484931, 25180797, -5334884 }, + { -586574, 10376444, -32586414, -11286356, 19801893, 10997610, 2276632, 9482883, 316878, 13820577 }, + { -9882808, -4510367, -2115506, 16457136, -11100081, 11674996, 30756178, -7515054, 30696930, -3712849 } + }, + { + { 32988917, -9603412, 12499366, 7910787, -10617257, -11931514, -7342816, -9985397, -32349517, 7392473 }, + { -8855661, 15927861, 9866406, -3649411, -2396914, -16655781, -30409476, -9134995, 25112947, -2926644 }, + { -2504044, -436966, 25621774, -5678772, 15085042, -5479877, -24884878, -13526194, 5537438, -13914319 } + } +}, +{ /* 19/31 */ + { + { -11225584, 2320285, -9584280, 10149187, -33444663, 5808648, -14876251, -1729667, 31234590, 6090599 }, + { -9633316, 116426, 26083934, 2897444, -6364437, -2688086, 609721, 15878753, -6970405, -9034768 }, + { -27757857, 247744, -15194774, -9002551, 23288161, -10011936, -23869595, 6503646, 20650474, 1804084 } + }, + { + { -27589786, 15456424, 8972517, 8469608, 15640622, 4439847, 3121995, -10329713, 27842616, -202328 }, + { -15306973, 2839644, 22530074, 10026331, 4602058, 5048462, 28248656, 5031932, -11375082, 12714369 }, + { 20807691, -7270825, 29286141, 11421711, -27876523, -13868230, -21227475, 1035546, -19733229, 12796920 } + }, + { + { 12076899, -14301286, -8785001, -11848922, -25012791, 16400684, -17591495, -12899438, 3480665, -15182815 }, + { -32361549, 5457597, 28548107, 7833186, 7303070, -11953545, -24363064, -15921875, -33374054, 2771025 }, + { -21389266, 421932, 26597266, 6860826, 22486084, -6737172, -17137485, -4210226, -24552282, 15673397 } + }, + { + { -20184622, 2338216, 19788685, -9620956, -4001265, -8740893, -20271184, 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8247766, -6710942, -26562381, -7709309, -14401939, -14648910, 4652152, 2488540, 23550156, -271232 }, + { 17294316, -3788438, 7026748, 15626851, 22990044, 113481, 2267737, -5908146, -408818, -137719 } + }, + { + { 16091085, -16253926, 18599252, 7340678, 2137637, -1221657, -3364161, 14550936, 3260525, -7166271 }, + { -4910104, -13332887, 18550887, 10864893, -16459325, -7291596, -23028869, -13204905, -12748722, 2701326 }, + { -8574695, 16099415, 4629974, -16340524, -20786213, -6005432, -10018363, 9276971, 11329923, 1862132 } + }, + { + { 14763076, -15903608, -30918270, 3689867, 3511892, 10313526, -21951088, 12219231, -9037963, -940300 }, + { 8894987, -3446094, 6150753, 3013931, 301220, 15693451, -31981216, -2909717, -15438168, 11595570 }, + { 15214962, 3537601, -26238722, -14058872, 4418657, -15230761, 13947276, 10730794, -13489462, -4363670 } + }, + { + { -2538306, 7682793, 32759013, 263109, -29984731, -7955452, -22332124, -10188635, 977108, 699994 }, + { -12466472, 4195084, -9211532, 550904, -15565337, 12917920, 19118110, -439841, -30534533, -14337913 }, + { 31788461, -14507657, 4799989, 7372237, 8808585, -14747943, 9408237, -10051775, 12493932, -5409317 } + }, + { + { -25680606, 5260744, -19235809, -6284470, -3695942, 16566087, 27218280, 2607121, 29375955, 6024730 }, + { 842132, -2794693, -4763381, -8722815, 26332018, -12405641, 11831880, 6985184, -9940361, 2854096 }, + { -4847262, -7969331, 2516242, -5847713, 9695691, -7221186, 16512645, 960770, 12121869, 16648078 } + }, + { + { -15218652, 14667096, -13336229, 2013717, 30598287, -464137, -31504922, -7882064, 20237806, 2838411 }, + { -19288047, 4453152, 15298546, -16178388, 22115043, -15972604, 12544294, -13470457, 1068881, -12499905 }, + { -9558883, -16518835, 33238498, 13506958, 30505848, -1114596, -8486907, -2630053, 12521378, 4845654 } + }, + { + { -28198521, 10744108, -2958380, 10199664, 7759311, -13088600, 3409348, -873400, -6482306, -12885870 }, + { -23561822, 6230156, -20382013, 10655314, -24040585, -11621172, 10477734, -1240216, -3113227, 13974498 }, + { 12966261, 15550616, -32038948, -1615346, 21025980, -629444, 5642325, 7188737, 18895762, 12629579 } + } +}, +{ /* 21/31 */ + { + { 14741879, -14946887, 22177208, -11721237, 1279741, 8058600, 11758140, 789443, 32195181, 3895677 }, + { 10758205, 15755439, -4509950, 9243698, -4879422, 6879879, -2204575, -3566119, -8982069, 4429647 }, + { -2453894, 15725973, -20436342, -10410672, -5803908, -11040220, -7135870, -11642895, 18047436, -15281743 } + }, + { + { -25173001, -11307165, 29759956, 11776784, -22262383, -15820455, 10993114, -12850837, -17620701, -9408468 }, + { 21987233, 700364, -24505048, 14972008, -7774265, -5718395, 32155026, 2581431, -29958985, 8773375 }, + { -25568350, 454463, -13211935, 16126715, 25240068, 8594567, 20656846, 12017935, -7874389, -13920155 } + }, + { + { 6028182, 6263078, -31011806, -11301710, -818919, 2461772, -31841174, -5468042, -1721788, -2776725 }, + { -12278994, 16624277, 987579, -5922598, 32908203, 1248608, 7719845, -4166698, 28408820, 6816612 }, + { -10358094, -8237829, 19549651, -12169222, 22082623, 16147817, 20613181, 13982702, -10339570, 5067943 } + }, + { + { -30505967, -3821767, 12074681, 13582412, -19877972, 2443951, -19719286, 12746132, 5331210, -10105944 }, + { 30528811, 3601899, -1957090, 4619785, -27361822, -15436388, 24180793, -12570394, 27679908, -1648928 }, + { 9402404, -13957065, 32834043, 10838634, -26580150, -13237195, 26653274, -8685565, 22611444, -12715406 } + }, + { + { 22190590, 1118029, 22736441, 15130463, -30460692, -5991321, 19189625, -4648942, 4854859, 6622139 }, + { -8310738, -2953450, -8262579, -3388049, -10401731, -271929, 13424426, -3567227, 26404409, 13001963 }, + { -31241838, -15415700, -2994250, 8939346, 11562230, -12840670, -26064365, -11621720, -15405155, 11020693 } + }, + { + { 1866042, -7949489, -7898649, -10301010, 12483315, 13477547, 3175636, -12424163, 28761762, 1406734 }, + { -448555, -1777666, 13018551, 3194501, -9580420, -11161737, 24760585, -4347088, 25577411, -13378680 }, + { -24290378, 4759345, -690653, -1852816, 2066747, 10693769, -29595790, 9884936, -9368926, 4745410 } + }, + { + { -9141284, 6049714, -19531061, -4341411, -31260798, 9944276, -15462008, -11311852, 10931924, -11931931 }, + { -16561513, 14112680, -8012645, 4817318, -8040464, -11414606, -22853429, 10856641, -20470770, 13434654 }, + { 22759489, -10073434, -16766264, -1871422, 13637442, -10168091, 1765144, -12654326, 28445307, -5364710 } + }, + { + { 29875063, 12493613, 2795536, -3786330, 1710620, 15181182, -10195717, -8788675, 9074234, 1167180 }, + { -26205683, 11014233, -9842651, -2635485, -26908120, 7532294, -18716888, -9535498, 3843903, 9367684 }, + { -10969595, -6403711, 9591134, 9582310, 11349256, 108879, 16235123, 8601684, -139197, 4242895 } + } +}, +{ /* 22/31 */ + { + { 22092954, -13191123, -2042793, -11968512, 32186753, -11517388, -6574341, 2470660, -27417366, 16625501 }, + { -11057722, 3042016, 13770083, -9257922, 584236, -544855, -7770857, 2602725, -27351616, 14247413 }, + { 6314175, -10264892, -32772502, 15957557, -10157730, 168750, -8618807, 14290061, 27108877, -1180880 } + }, + { + { -8586597, -7170966, 13241782, 10960156, -32991015, -13794596, 33547976, -11058889, -27148451, 981874 }, + { 22833440, 9293594, -32649448, -13618667, -9136966, 14756819, -22928859, -13970780, -10479804, -16197962 }, + { -7768587, 3326786, -28111797, 10783824, 19178761, 14905060, 22680049, 13906969, -15933690, 3797899 } + }, + { + { 21721356, -4212746, -12206123, 9310182, -3882239, -13653110, 23740224, -2709232, 20491983, -8042152 }, + { 9209270, -15135055, -13256557, -6167798, -731016, 15289673, 25947805, 15286587, 30997318, -6703063 }, + { 7392032, 16618386, 23946583, -8039892, -13265164, -1533858, -14197445, -2321576, 17649998, -250080 } + }, + { + { -9301088, -14193827, 30609526, -3049543, -25175069, -1283752, -15241566, -9525724, -2233253, 7662146 }, + { -17558673, 1763594, -33114336, 15908610, -30040870, -12174295, 7335080, -8472199, -3174674, 3440183 }, + { -19889700, -5977008, -24111293, -9688870, 10799743, -16571957, 40450, -4431835, 4862400, 1133 } + }, + { + { -32856209, -7873957, -5422389, 14860950, -16319031, 7956142, 7258061, 311861, -30594991, -7379421 }, + { -3773428, -1565936, 28985340, 7499440, 24445838, 9325937, 29727763, 16527196, 18278453, 15405622 }, + { -4381906, 8508652, -19898366, -3674424, -5984453, 15149970, -13313598, 843523, -21875062, 13626197 } + }, + { + { 2281448, -13487055, -10915418, -2609910, 1879358, 16164207, -10783882, 3953792, 13340839, 15928663 }, + { 31727126, -7179855, -18437503, -8283652, 2875793, -16390330, -25269894, -7014826, -23452306, 5964753 }, + { 4100420, -5959452, -17179337, 6017714, -18705837, 12227141, -26684835, 11344144, 2538215, -7570755 } + }, + { + { -9433605, 6123113, 11159803, -2156608, 30016280, 14966241, -20474983, 1485421, -629256, -15958862 }, + { -26804558, 4260919, 11851389, 9658551, -32017107, 16367492, -20205425, -13191288, 11659922, -11115118 }, + { 26180396, 10015009, -30844224, -8581293, 5418197, 9480663, 2231568, -10170080, 33100372, -1306171 } + }, + { + { 15121113, -5201871, -10389905, 15427821, -27509937, -15992507, 21670947, 4486675, -5931810, -14466380 }, + { 16166486, -9483733, -11104130, 6023908, -31926798, -1364923, 2340060, -16254968, -10735770, -10039824 }, + { 28042865, -3557089, -12126526, 12259706, -3717498, -6945899, 6766453, -8689599, 18036436, 5803270 } + } +}, +{ /* 23/31 */ + { + { -817581, 6763912, 11803561, 1585585, 10958447, -2671165, 23855391, 4598332, -6159431, -14117438 }, + { -31031306, -14256194, 17332029, -2383520, 31312682, -5967183, 696309, 50292, -20095739, 11763584 }, + { -594563, -2514283, -32234153, 12643980, 12650761, 14811489, 665117, -12613632, -19773211, -10713562 } + }, + { + { 30464590, -11262872, -4127476, -12734478, 19835327, -7105613, -24396175, 2075773, -17020157, 992471 }, + { 18357185, -6994433, 7766382, 16342475, -29324918, 411174, 14578841, 8080033, -11574335, -10601610 }, + { 19598397, 10334610, 12555054, 2555664, 18821899, -10339780, 21873263, 16014234, 26224780, 16452269 } + }, + { + { -30223925, 5145196, 5944548, 16385966, 3976735, 2009897, -11377804, -7618186, -20533829, 3698650 }, + { 14187449, 3448569, -10636236, -10810935, -22663880, -3433596, 7268410, -10890444, 27394301, 12015369 }, + { 19695761, 16087646, 28032085, 12999827, 6817792, 11427614, 20244189, -1312777, -13259127, -3402461 } + }, + { + { 30860103, 12735208, -1888245, -4699734, -16974906, 2256940, -8166013, 12298312, -8550524, -10393462 }, + { -5719826, -11245325, -1910649, 15569035, 26642876, -7587760, -5789354, -15118654, -4976164, 12651793 }, + { -2848395, 9953421, 11531313, -5282879, 26895123, -12697089, -13118820, -16517902, 9768698, -2533218 } + }, + { + { -24719459, 1894651, -287698, -4704085, 15348719, -8156530, 32767513, 12765450, 4940095, 10678226 }, + { 18860224, 15980149, -18987240, -1562570, -26233012, -11071856, -7843882, 13944024, -24372348, 16582019 }, + { -15504260, 4970268, -29893044, 4175593, -20993212, -2199756, -11704054, 15444560, -11003761, 7989037 } + }, + { + { 31490452, 5568061, -2412803, 2182383, -32336847, 4531686, -32078269, 6200206, -19686113, -14800171 }, + { -17308668, -15879940, -31522777, -2831, -32887382, 16375549, 8680158, -16371713, 28550068, -6857132 }, + { -28126887, -5688091, 16837845, -1820458, -6850681, 12700016, -30039981, 4364038, 1155602, 5988841 } + }, + { + { 21890435, -13272907, -12624011, 12154349, -7831873, 15300496, 23148983, -4470481, 24618407, 8283181 }, + { -33136107, -10512751, 9975416, 6841041, -31559793, 16356536, 3070187, -7025928, 1466169, 10740210 }, + { -1509399, -15488185, -13503385, -10655916, 32799044, 909394, -13938903, -5779719, -32164649, -15327040 } + }, + { + { 3960823, -14267803, -28026090, -15918051, -19404858, 13146868, 15567327, 951507, -3260321, -573935 }, + { 24740841, 5052253, -30094131, 8961361, 25877428, 6165135, -24368180, 14397372, -7380369, -6144105 }, + { -28888365, 3510803, -28103278, -1158478, -11238128, -10631454, -15441463, -14453128, -1625486, -6494814 } + } +}, +{ /* 24/31 */ + { + { 793299, -9230478, 8836302, -6235707, -27360908, -2369593, 33152843, -4885251, -9906200, -621852 }, + { 5666233, 525582, 20782575, -8038419, -24538499, 14657740, 16099374, 1468826, -6171428, -15186581 }, + { -4859255, -3779343, -2917758, -6748019, 7778750, 11688288, -30404353, -9871238, -1558923, -9863646 } + }, + { + { 10896332, -7719704, 824275, 472601, -19460308, 3009587, 25248958, 14783338, -30581476, -15757844 }, + { 10566929, 12612572, -31944212, 11118703, -12633376, 12362879, 21752402, 8822496, 24003793, 14264025 }, + { 27713862, -7355973, -11008240, 9227530, 27050101, 2504721, 23886875, -13117525, 13958495, -5732453 } + }, + { + { -23481610, 4867226, -27247128, 3900521, 29838369, -8212291, -31889399, -10041781, 7340521, -15410068 }, + { 4646514, -8011124, -22766023, -11532654, 23184553, 8566613, 31366726, -1381061, -15066784, -10375192 }, + { -17270517, 12723032, -16993061, 14878794, 21619651, -6197576, 27584817, 3093888, -8843694, 3849921 } + }, + { + { -9064912, 2103172, 25561640, -15125738, -5239824, 9582958, 32477045, -9017955, 5002294, -15550259 }, + { -12057553, -11177906, 21115585, -13365155, 8808712, -12030708, 16489530, 13378448, -25845716, 12741426 }, + { -5946367, 10645103, -30911586, 15390284, -3286982, -7118677, 24306472, 15852464, 28834118, -7646072 } + }, + { + { -17335748, -9107057, -24531279, 9434953, -8472084, -583362, -13090771, 455841, 20461858, 5491305 }, + { 13669248, -16095482, -12481974, -10203039, -14569770, -11893198, -24995986, 11293807, -28588204, -9421832 }, + { 28497928, 6272777, -33022994, 14470570, 8906179, -1225630, 18504674, -14165166, 29867745, -8795943 } + }, + { + { -16207023, 13517196, -27799630, -13697798, 24009064, -6373891, -6367600, -13175392, 22853429, -4012011 }, + { 24191378, 16712145, -13931797, 15217831, 14542237, 1646131, 18603514, -11037887, 12876623, -2112447 }, + { 17902668, 4518229, -411702, -2829247, 26878217, 5258055, -12860753, 608397, 16031844, 3723494 } + }, + { + { -28632773, 12763728, -20446446, 7577504, 33001348, -13017745, 17558842, -7872890, 23896954, -4314245 }, + { -20005381, -12011952, 31520464, 605201, 2543521, 5991821, -2945064, 7229064, -9919646, -8826859 }, + { 28816045, 298879, -28165016, -15920938, 19000928, -1665890, -12680833, -2949325, -18051778, -2082915 } + }, + { + { 16000882, -344896, 3493092, -11447198, -29504595, -13159789, 12577740, 16041268, -19715240, 7847707 }, + { 10151868, 10572098, 27312476, 7922682, 14825339, 4723128, -32855931, -6519018, -10020567, 3852848 }, + { -11430470, 15697596, -21121557, -4420647, 5386314, 15063598, 16514493, -15932110, 29330899, -15076224 } + } +}, +{ /* 25/31 */ + { + { -25499735, -4378794, -15222908, -6901211, 16615731, 2051784, 3303702, 15490, -27548796, 12314391 }, + { 15683520, -6003043, 18109120, -9980648, 15337968, -5997823, -16717435, 15921866, 16103996, -3731215 }, + { -23169824, -10781249, 13588192, -1628807, -3798557, -1074929, -19273607, 5402699, -29815713, -9841101 } + }, + { + { 23190676, 2384583, -32714340, 3462154, -29903655, -1529132, -11266856, 8911517, -25205859, 2739713 }, + { 21374101, -3554250, -33524649, 9874411, 15377179, 11831242, -33529904, 6134907, 4931255, 11987849 }, + { -7732, -2978858, -16223486, 7277597, 105524, -322051, -31480539, 13861388, -30076310, 10117930 } + }, + { + { -29501170, -10744872, -26163768, 13051539, -25625564, 5089643, -6325503, 6704079, 12890019, 15728940 }, + { -21972360, -11771379, -951059, -4418840, 14704840, 2695116, 903376, -10428139, 12885167, 8311031 }, + { -17516482, 5352194, 10384213, -13811658, 7506451, 13453191, 26423267, 4384730, 1888765, -5435404 } + }, + { + { -25817338, -3107312, -13494599, -3182506, 30896459, -13921729, -32251644, -12707869, -19464434, -3340243 }, + { -23607977, -2665774, -526091, 4651136, 5765089, 4618330, 6092245, 14845197, 17151279, -9854116 }, + { -24830458, -12733720, -15165978, 10367250, -29530908, -265356, 22825805, -7087279, -16866484, 16176525 } + }, + { + { -23583256, 6564961, 20063689, 3798228, -4740178, 7359225, 2006182, -10363426, -28746253, -10197509 }, + { -10626600, -4486402, -13320562, -5125317, 3432136, -6393229, 23632037, -1940610, 32808310, 1099883 }, + { 15030977, 5768825, -27451236, -2887299, -6427378, -15361371, -15277896, -6809350, 2051441, -15225865 } + }, + { + { -3362323, -7239372, 7517890, 9824992, 23555850, 295369, 5148398, -14154188, -22686354, 16633660 }, + { 4577086, -16752288, 13249841, -15304328, 19958763, -14537274, 18559670, -10759549, 8402478, -9864273 }, + { -28406330, -1051581, -26790155, -907698, -17212414, -11030789, 9453451, -14980072, 17983010, 9967138 } + }, + { + { -25762494, 6524722, 26585488, 9969270, 24709298, 1220360, -1677990, 7806337, 17507396, 3651560 }, + { -10420457, -4118111, 14584639, 15971087, -15768321, 8861010, 26556809, -5574557, -18553322, -11357135 }, + { 2839101, 14284142, 4029895, 3472686, 14402957, 12689363, -26642121, 8459447, -5605463, -7621941 } + }, + { + { -4839289, -3535444, 9744961, 2871048, 25113978, 3187018, -25110813, -849066, 17258084, -7977739 }, + { 18164541, -10595176, -17154882, -1542417, 19237078, -9745295, 23357533, -15217008, 26908270, 12150756 }, + { -30264870, -7647865, 5112249, -7036672, -1499807, -6974257, 43168, -5537701, -32302074, 16215819 } + } +}, +{ /* 26/31 */ + { + { -6898905, 9824394, -12304779, -4401089, -31397141, -6276835, 32574489, 12532905, -7503072, -8675347 }, + { -27343522, -16515468, -27151524, -10722951, 946346, 16291093, 254968, 7168080, 21676107, -1943028 }, + { 21260961, -8424752, -16831886, -11920822, -23677961, 3968121, -3651949, -6215466, -3556191, -7913075 } + }, + { + { 16544754, 13250366, -16804428, 15546242, -4583003, 12757258, -2462308, -8680336, -18907032, -9662799 }, + { -2415239, -15577728, 18312303, 4964443, -15272530, -12653564, 26820651, 16690659, 25459437, -4564609 }, + { -25144690, 11425020, 28423002, -11020557, -6144921, -15826224, 9142795, -2391602, -6432418, -1644817 } + }, + { + { -23104652, 6253476, 16964147, -3768872, -25113972, -12296437, -27457225, -16344658, 6335692, 7249989 }, + { -30333227, 13979675, 7503222, -12368314, -11956721, -4621693, -30272269, 2682242, 25993170, -12478523 }, + { 4364628, 5930691, 32304656, -10044554, -8054781, 15091131, 22857016, -10598955, 31820368, 15075278 } + }, + { + { 31879134, -8918693, 17258761, 90626, -8041836, -4917709, 24162788, -9650886, -17970238, 12833045 }, + { 19073683, 14851414, -24403169, -11860168, 7625278, 11091125, -19619190, 2074449, -9413939, 14905377 }, + { 24483667, -11935567, -2518866, -11547418, -1553130, 15355506, -25282080, 9253129, 27628530, -7555480 } + }, + { + { 17597607, 8340603, 19355617, 552187, 26198470, -3176583, 4593324, -9157582, -14110875, 15297016 }, + { 510886, 14337390, -31785257, 16638632, 6328095, 2713355, -20217417, -11864220, 8683221, 2921426 }, + { 18606791, 11874196, 27155355, -5281482, -24031742, 6265446, -25178240, -1278924, 4674690, 13890525 } + }, + { + { 13609624, 13069022, -27372361, -13055908, 24360586, 9592974, 14977157, 9835105, 4389687, 288396 }, + { 9922506, -519394, 13613107, 5883594, -18758345, -434263, -12304062, 8317628, 23388070, 16052080 }, + { 12720016, 11937594, -31970060, -5028689, 26900120, 8561328, -20155687, -11632979, -14754271, -10812892 } + }, + { + { 15961858, 14150409, 26716931, -665832, -22794328, 13603569, 11829573, 7467844, -28822128, 929275 }, + { 11038231, -11582396, -27310482, -7316562, -10498527, -16307831, -23479533, -9371869, -21393143, 2465074 }, + { 20017163, -4323226, 27915242, 1529148, 12396362, 15675764, 13817261, -9658066, 2463391, -4622140 } + }, + { + { -16358878, -12663911, -12065183, 4996454, -1256422, 1073572, 9583558, 12851107, 4003896, 12673717 }, + { -1731589, -15155870, -3262930, 16143082, 19294135, 13385325, 14741514, -9103726, 7903886, 2348101 }, + { 24536016, -16515207, 12715592, -3862155, 1511293, 10047386, -3842346, -7129159, -28377538, 10048127 } + } +}, +{ /* 27/31 */ + { + { -12622226, -6204820, 30718825, 2591312, -10617028, 12192840, 18873298, -7297090, -32297756, 15221632 }, + { -26478122, -11103864, 11546244, -1852483, 9180880, 7656409, -21343950, 2095755, 29769758, 6593415 }, + { -31994208, -2907461, 4176912, 3264766, 12538965, -868111, 26312345, -6118678, 30958054, 8292160 } + }, + { + { 31429822, -13959116, 29173532, 15632448, 12174511, -2760094, 32808831, 3977186, 26143136, -3148876 }, + { 22648901, 1402143, -22799984, 13746059, 7936347, 365344, -8668633, -1674433, -3758243, -2304625 }, + { -15491917, 8012313, -2514730, -12702462, -23965846, -10254029, -1612713, -1535569, -16664475, 8194478 } + }, + { + { 27338066, -7507420, -7414224, 10140405, -19026427, -6589889, 27277191, 8855376, 28572286, 3005164 }, + { 26287124, 4821776, 25476601, -4145903, -3764513, -15788984, -18008582, 1182479, -26094821, -13079595 }, + { -7171154, 3178080, 23970071, 6201893, -17195577, -4489192, -21876275, -13982627, 32208683, -1198248 } + }, + { + { -16657702, 2817643, -10286362, 14811298, 6024667, 13349505, -27315504, -10497842, -27672585, -11539858 }, + { 15941029, -9405932, -21367050, 8062055, 31876073, -238629, -15278393, -1444429, 15397331, -4130193 }, + { 8934485, -13485467, -23286397, -13423241, -32446090, 14047986, 31170398, -1441021, -27505566, 15087184 } + }, + { + { -18357243, -2156491, 24524913, -16677868, 15520427, -6360776, -15502406, 11461896, 16788528, -5868942 }, + { -1947386, 16013773, 21750665, 3714552, -17401782, -16055433, -3770287, -10323320, 31322514, -11615635 }, + { 21426655, -5650218, -13648287, -5347537, -28812189, -4920970, -18275391, -14621414, 13040862, -12112948 } + }, + { + { 11293895, 12478086, -27136401, 15083750, -29307421, 14748872, 14555558, -13417103, 1613711, 4896935 }, + { -25894883, 15323294, -8489791, -8057900, 25967126, -13425460, 2825960, -4897045, -23971776, -11267415 }, + { -15924766, -5229880, -17443532, 6410664, 3622847, 10243618, 20615400, 12405433, -23753030, -8436416 } + }, + { + { -7091295, 12556208, -20191352, 9025187, -17072479, 4333801, 4378436, 2432030, 23097949, -566018 }, + { 4565804, -16025654, 20084412, -7842817, 1724999, 189254, 24767264, 10103221, -18512313, 2424778 }, + { 366633, -11976806, 8173090, -6890119, 30788634, 5745705, -7168678, 1344109, -3642553, 12412659 } + }, + { + { -24001791, 7690286, 14929416, -168257, -32210835, -13412986, 24162697, -15326504, -3141501, 11179385 }, + { 18289522, -14724954, 8056945, 16430056, -21729724, 7842514, -6001441, -1486897, -18684645, -11443503 }, + { 476239, 6601091, -6152790, -9723375, 17503545, -4863900, 27672959, 13403813, 11052904, 5219329 } + } +}, +{ /* 28/31 */ + { + { 20678546, -8375738, -32671898, 8849123, -5009758, 14574752, 31186971, -3973730, 9014762, -8579056 }, + { -13644050, -10350239, -15962508, 5075808, -1514661, -11534600, -33102500, 9160280, 8473550, -3256838 }, + { 24900749, 14435722, 17209120, -15292541, -22592275, 9878983, -7689309, -16335821, -24568481, 11788948 } + }, + { + { -3118155, -11395194, -13802089, 14797441, 9652448, -6845904, -20037437, 10410733, -24568470, -1458691 }, + { -15659161, 16736706, -22467150, 10215878, -9097177, 7563911, 11871841, -12505194, -18513325, 8464118 }, + { -23400612, 8348507, -14585951, -861714, -3950205, -6373419, 14325289, 8628612, 33313881, -8370517 } + }, + { + { -20186973, -4967935, 22367356, 5271547, -1097117, -4788838, -24805667, -10236854, -8940735, -5818269 }, + { -6948785, -1795212, -32625683, -16021179, 32635414, -7374245, 15989197, -12838188, 28358192, -4253904 }, + { -23561781, -2799059, -32351682, -1661963, -9147719, 10429267, -16637684, 4072016, -5351664, 5596589 } + }, + { + { -28236598, -3390048, 12312896, 6213178, 3117142, 16078565, 29266239, 2557221, 1768301, 15373193 }, + { -7243358, -3246960, -4593467, -7553353, -127927, -912245, -1090902, -4504991, -24660491, 3442910 }, + { -30210571, 5124043, 14181784, 8197961, 18964734, -11939093, 22597931, 7176455, -18585478, 13365930 } + }, + { + { -7877390, -1499958, 8324673, 4690079, 6261860, 890446, 24538107, -8570186, -9689599, -3031667 }, + { 25008904, -10771599, -4305031, -9638010, 16265036, 15721635, 683793, -11823784, 15723479, -15163481 }, + { -9660625, 12374379, -27006999, -7026148, -7724114, -12314514, 11879682, 5400171, 519526, -1235876 } + }, + { + { 22258397, -16332233, -7869817, 14613016, -22520255, -2950923, -20353881, 7315967, 16648397, 7605640 }, + { -8081308, -8464597, -8223311, 9719710, 19259459, -15348212, 23994942, -5281555, -9468848, 4763278 }, + { -21699244, 9220969, -15730624, 1084137, -25476107, -2852390, 31088447, -7764523, -11356529, 728112 } + }, + { + { 26047220, -11751471, -6900323, -16521798, 24092068, 9158119, -4273545, -12555558, -29365436, -5498272 }, + { 17510331, -322857, 5854289, 8403524, 17133918, -3112612, -28111007, 12327945, 10750447, 10014012 }, + { -10312768, 3936952, 9156313, -8897683, 16498692, -994647, -27481051, -666732, 3424691, 7540221 } + }, + { + { 30322361, -6964110, 11361005, -4143317, 7433304, 4989748, -7071422, -16317219, -9244265, 15258046 }, + { 13054562, -2779497, 19155474, 469045, -12482797, 4566042, 5631406, 2711395, 1062915, -5136345 }, + { -19240248, -11254599, -29509029, -7499965, -5835763, 13005411, -6066489, 12194497, 32960380, 1459310 } + } +}, +{ /* 29/31 */ + { + { 19852034, 7027924, 23669353, 10020366, 8586503, -6657907, 394197, -6101885, 18638003, -11174937 }, + { 31395534, 15098109, 26581030, 8030562, -16527914, -5007134, 9012486, -7584354, -6643087, -5442636 }, + { -9192165, -2347377, -1997099, 4529534, 25766844, 607986, -13222, 9677543, -32294889, -6456008 } + }, + { + { -2444496, -149937, 29348902, 8186665, 1873760, 12489863, -30934579, -7839692, -7852844, -8138429 }, + { -15236356, -15433509, 7766470, 746860, 26346930, -10221762, -27333451, 10754588, -9431476, 5203576 }, + { 31834314, 14135496, -770007, 5159118, 20917671, -16768096, -7467973, -7337524, 31809243, 7347066 } + }, + { + { -9606723, -11874240, 20414459, 13033986, 13716524, -11691881, 19797970, -12211255, 15192876, -2087490 }, + { -12663563, -2181719, 1168162, -3804809, 26747877, -14138091, 10609330, 12694420, 33473243, -13382104 }, + { 33184999, 11180355, 15832085, -11385430, -1633671, 225884, 15089336, -11023903, -6135662, 14480053 } + }, + { + { 31308717, -5619998, 31030840, -1897099, 15674547, -6582883, 5496208, 13685227, 27595050, 8737275 }, + { -20318852, -15150239, 10933843, -16178022, 8335352, -7546022, -31008351, -12610604, 26498114, 66511 }, + { 22644454, -8761729, -16671776, 4884562, -3105614, -13559366, 30540766, -4286747, -13327787, -7515095 } + }, + { + { -28017847, 9834845, 18617207, -2681312, -3401956, -13307506, 8205540, 13585437, -17127465, 15115439 }, + { 23711543, -672915, 31206561, -8362711, 6164647, -9709987, -33535882, -1426096, 8236921, 16492939 }, + { -23910559, -13515526, -26299483, -4503841, 25005590, -7687270, 19574902, 10071562, 6708380, -6222424 } + }, + { + { 2101391, -4930054, 19702731, 2367575, -15427167, 1047675, 5301017, 9328700, 29955601, -11678310 }, + { 3096359, 9271816, -21620864, -15521844, -14847996, -7592937, -25892142, -12635595, -9917575, 6216608 }, + { -32615849, 338663, -25195611, 2510422, -29213566, -13820213, 24822830, -6146567, -26767480, 7525079 } + }, + { + { -23066649, -13985623, 16133487, -7896178, -3389565, 778788, -910336, -2782495, -19386633, 11994101 }, + { 21691500, -13624626, -641331, -14367021, 3285881, -3483596, -25064666, 9718258, -7477437, 13381418 }, + { 18445390, -4202236, 14979846, 11622458, -1727110, -3582980, 23111648, -6375247, 28535282, 15779576 } + }, + { + { 30098053, 3089662, -9234387, 16662135, -21306940, 11308411, -14068454, 12021730, 9955285, -16303356 }, + { 9734894, -14576830, -7473633, -9138735, 2060392, 11313496, -18426029, 9924399, 20194861, 13380996 }, + { -26378102, -7965207, -22167821, 15789297, -18055342, -6168792, -1984914, 15707771, 26342023, 10146099 } + } +}, +{ /* 30/31 */ + { + { -26016874, -219943, 21339191, -41388, 19745256, -2878700, -29637280, 2227040, 21612326, -545728 }, + { -13077387, 1184228, 23562814, -5970442, -20351244, -6348714, 25764461, 12243797, -20856566, 11649658 }, + { -10031494, 11262626, 27384172, 2271902, 26947504, -15997771, 39944, 6114064, 33514190, 2333242 } + }, + { + { -21433588, -12421821, 8119782, 7219913, -21830522, -9016134, -6679750, -12670638, 24350578, -13450001 }, + { -4116307, -11271533, -23886186, 4843615, -30088339, 690623, -31536088, -10406836, 8317860, 12352766 }, + { 18200138, -14475911, -33087759, -2696619, -23702521, -9102511, -23552096, -2287550, 20712163, 6719373 } + }, + { + { 26656208, 6075253, -7858556, 1886072, -28344043, 4262326, 11117530, -3763210, 26224235, -3297458 }, + { -17168938, -14854097, -3395676, -16369877, -19954045, 14050420, 21728352, 9493610, 18620611, -16428628 }, + { -13323321, 13325349, 11432106, 5964811, 18609221, 6062965, -5269471, -9725556, -30701573, -16479657 } + }, + { + { -23860538, -11233159, 26961357, 1640861, -32413112, -16737940, 12248509, -5240639, 13735342, 1934062 }, + { 25089769, 6742589, 17081145, -13406266, 21909293, -16067981, -15136294, -3765346, -21277997, 5473616 }, + { 31883677, -7961101, 1083432, -11572403, 22828471, 13290673, -7125085, 12469656, 29111212, -5451014 } + }, + { + { 24244947, -15050407, -26262976, 2791540, -14997599, 16666678, 24367466, 6388839, -10295587, 452383 }, + { -25640782, -3417841, 5217916, 16224624, 19987036, -4082269, -24236251, -5915248, 15766062, 8407814 }, + { -20406999, 13990231, 15495425, 16395525, 5377168, 15166495, -8917023, -4388953, -8067909, 2276718 } + }, + { + { 30157918, 12924066, -17712050, 9245753, 19895028, 3368142, -23827587, 5096219, 22740376, -7303417 }, + { 2041139, -14256350, 7783687, 13876377, -25946985, -13352459, 24051124, 13742383, -15637599, 13295222 }, + { 33338237, -8505733, 12532113, 7977527, 9106186, -1715251, -17720195, -4612972, -4451357, -14669444 } + }, + { + { -20045281, 5454097, -14346548, 6447146, 28862071, 1883651, -2469266, -4141880, 7770569, 9620597 }, + { 23208068, 7979712, 33071466, 8149229, 1758231, -10834995, 30945528, -1694323, -33502340, -14767970 }, + { 1439958, -16270480, -1079989, -793782, 4625402, 10647766, -5043801, 1220118, 30494170, -11440799 } + }, + { + { -5037580, -13028295, -2970559, -3061767, 15640974, -6701666, -26739026, 926050, -1684339, -13333647 }, + { 13908495, -3549272, 30919928, -6273825, -21521863, 7989039, 9021034, 9078865, 3353509, 4033511 }, + { -29663431, -15113610, 32259991, -344482, 24295849, -12912123, 23161163, 8839127, 27485041, 7356032 } + } +}, +{ /* 31/31 */ + { + { 9661027, 705443, 11980065, -5370154, -1628543, 14661173, -6346142, 2625015, 28431036, -16771834 }, + { -23839233, -8311415, -25945511, 7480958, -17681669, -8354183, -22545972, 14150565, 15970762, 4099461 }, + { 29262576, 16756590, 26350592, -8793563, 8529671, -11208050, 13617293, -9937143, 11465739, 8317062 } + }, + { + { -25493081, -6962928, 32500200, -9419051, -23038724, -2302222, 14898637, 3848455, 20969334, -5157516 }, + { -20384450, -14347713, -18336405, 13884722, -33039454, 2842114, -21610826, -3649888, 11177095, 14989547 }, + { -24496721, -11716016, 16959896, 2278463, 12066309, 10137771, 13515641, 2581286, -28487508, 9930240 } + }, + { + { -17751622, -2097826, 16544300, -13009300, -15914807, -14949081, 18345767, -13403753, 16291481, -5314038 }, + { -33229194, 2553288, 32678213, 9875984, 8534129, 6889387, -9676774, 6957617, 4368891, 9788741 }, + { 16660756, 7281060, -10830758, 12911820, 20108584, -8101676, -21722536, -8613148, 16250552, -11111103 } + }, + { + { -19765507, 2390526, -16551031, 14161980, 1905286, 6414907, 4689584, 10604807, -30190403, 4782747 }, + { -1354539, 14736941, -7367442, -13292886, 7710542, -14155590, -9981571, 4383045, 22546403, 437323 }, + { 31665577, -12180464, -16186830, 1491339, -18368625, 3294682, 27343084, 2786261, -30633590, -14097016 } + }, + { + { -14467279, -683715, -33374107, 7448552, 19294360, 14334329, -19690631, 2355319, -19284671, -6114373 }, + { 15121312, -15796162, 6377020, -6031361, -10798111, -12957845, 18952177, 15496498, -29380133, 11754228 }, + { -2637277, -13483075, 8488727, -14303896, 12728761, -1622493, 7141596, 11724556, 22761615, -10134141 } + }, + { + { 16918416, 11729663, -18083579, 3022987, -31015732, -13339659, -28741185, -12227393, 32851222, 11717399 }, + { 11166634, 7338049, -6722523, 4531520, -29468672, -7302055, 31474879, 3483633, -1193175, -4030831 }, + { -185635, 9921305, 31456609, -13536438, -12013818, 13348923, 33142652, 6546660, -19985279, -3948376 } + }, + { + { -32460596, 11266712, -11197107, -7899103, 31703694, 3855903, -8537131, -12833048, -30772034, -15486313 }, + { -18006477, 12709068, 3991746, -6479188, -21491523, -10550425, -31135347, -16049879, 10928917, 3011958 }, + { -6957757, -15594337, 31696059, 334240, 29576716, 14796075, -30831056, -12805180, 18008031, 10258577 } + }, + { + { -22448644, 15655569, 7018479, -4410003, -30314266, -1201591, -1853465, 1367120, 25127874, 6671743 }, + { 29701166, -14373934, -10878120, 9279288, -17568, 13127210, 21382910, 11042292, 25838796, 4642684 }, + { -20430234, 14955537, -24126347, 8124619, -5369288, -5990470, 30468147, -13900640, 18423289, 4177476 } + } +} diff --git a/lib/hcrypto/x25519/fe_25_5/base2.h b/lib/hcrypto/x25519/fe_25_5/base2.h new file mode 100644 index 000000000000..90a1457eab04 --- /dev/null +++ b/lib/hcrypto/x25519/fe_25_5/base2.h @@ -0,0 +1,40 @@ +{ + { 25967493, -14356035, 29566456, 3660896, -12694345, 4014787, 27544626, -11754271, -6079156, 2047605 }, + { -12545711, 934262, -2722910, 3049990, -727428, 9406986, 12720692, 5043384, 19500929, -15469378 }, + { -8738181, 4489570, 9688441, -14785194, 10184609, -12363380, 29287919, 11864899, -24514362, -4438546 } +}, +{ + { 15636291, -9688557, 24204773, -7912398, 616977, -16685262, 27787600, -14772189, 28944400, -1550024 }, + { 16568933, 4717097, -11556148, -1102322, 15682896, -11807043, 16354577, -11775962, 7689662, 11199574 }, + { 30464156, -5976125, -11779434, -15670865, 23220365, 15915852, 7512774, 10017326, -17749093, -9920357 } +}, +{ + { 10861363, 11473154, 27284546, 1981175, -30064349, 12577861, 32867885, 14515107, -15438304, 10819380 }, + { 4708026, 6336745, 20377586, 9066809, -11272109, 6594696, -25653668, 12483688, -12668491, 5581306 }, + { 19563160, 16186464, -29386857, 4097519, 10237984, -4348115, 28542350, 13850243, -23678021, -15815942 } +}, +{ + { 5153746, 9909285, 1723747, -2777874, 30523605, 5516873, 19480852, 5230134, -23952439, -15175766 }, + { -30269007, -3463509, 7665486, 10083793, 28475525, 1649722, 20654025, 16520125, 30598449, 7715701 }, + { 28881845, 14381568, 9657904, 3680757, -20181635, 7843316, -31400660, 1370708, 29794553, -1409300 } +}, +{ + { -22518993, -6692182, 14201702, -8745502, -23510406, 8844726, 18474211, -1361450, -13062696, 13821877 }, + { -6455177, -7839871, 3374702, -4740862, -27098617, -10571707, 31655028, -7212327, 18853322, -14220951 }, + { 4566830, -12963868, -28974889, -12240689, -7602672, -2830569, -8514358, -10431137, 2207753, -3209784 } +}, +{ + { -25154831, -4185821, 29681144, 7868801, -6854661, -9423865, -12437364, -663000, -31111463, -16132436 }, + { 25576264, -2703214, 7349804, -11814844, 16472782, 9300885, 3844789, 15725684, 171356, 6466918 }, + { 23103977, 13316479, 9739013, -16149481, 817875, -15038942, 8965339, -14088058, -30714912, 16193877 } +}, +{ + { -33521811, 3180713, -2394130, 14003687, -16903474, -16270840, 17238398, 4729455, -18074513, 9256800 }, + { -25182317, -4174131, 32336398, 5036987, -21236817, 11360617, 22616405, 9761698, -19827198, 630305 }, + { -13720693, 2639453, -24237460, -7406481, 9494427, -5774029, -6554551, -15960994, -2449256, -14291300 } +}, +{ + { -3151181, -5046075, 9282714, 6866145, -31907062, -863023, -18940575, 15033784, 25105118, -7894876 }, + { -24326370, 15950226, -31801215, -14592823, -11662737, -5090925, 1573892, -2625887, 2198790, -15804619 }, + { -3099351, 10324967, -2241613, 7453183, -5446979, -2735503, -13812022, -16236442, -32461234, -12290683 } +} diff --git a/lib/hcrypto/x25519/fe_25_5/constants.h b/lib/hcrypto/x25519/fe_25_5/constants.h new file mode 100644 index 000000000000..dd6da1b87403 --- /dev/null +++ b/lib/hcrypto/x25519/fe_25_5/constants.h @@ -0,0 +1,40 @@ +/* 37095705934669439343138083508754565189542113879843219016388785533085940283555 */ +static const fe25519 d = { + -10913610, 13857413, -15372611, 6949391, 114729, -8787816, -6275908, -3247719, -18696448, -12055116 +}; + +/* 2 * d = + * 16295367250680780974490674513165176452449235426866156013048779062215315747161 + */ +static const fe25519 d2 = { + -21827239, -5839606, -30745221, 13898782, 229458, 15978800, -12551817, -6495438, 29715968, 9444199 }; + +/* sqrt(-1) */ +static const fe25519 sqrtm1 = { + -32595792, -7943725, 9377950, 3500415, 12389472, -272473, -25146209, -2005654, 326686, 11406482 +}; + +/* A = 486662 */ +static const fe25519 curve25519_A = { + 486662, 0, 0, 0, 0, 0, 0, 0, 0, 0 +}; + +/* sqrt(ad - 1) with a = -1 (mod p) */ +static const fe25519 sqrtadm1 = { + 24849947, -153582, -23613485, 6347715, -21072328, -667138, -25271143, -15367704, -870347, 14525639 +}; + +/* 1 / sqrt(a - d) */ +static const fe25519 invsqrtamd = { + 6111485, 4156064, -27798727, 12243468, -25904040, 120897, 20826367, -7060776, 6093568, -1986012 +}; + +/* 1 - d ^ 2 */ +static const fe25519 onemsqd = { + 6275446, -16617371, -22938544, -3773710, 11667077, 7397348, -27922721, 1766195, -24433858, 672203 +}; + +/* (d - 1) ^ 2 */ +static const fe25519 sqdmone = { + 15551795, -11097455, -13425098, -10125071, -11896535, 10178284, -26634327, 4729244, -5282110, -10116402 +}; diff --git a/lib/hcrypto/x25519/fe_25_5/fe.h b/lib/hcrypto/x25519/fe_25_5/fe.h new file mode 100644 index 000000000000..f216669e4e0d --- /dev/null +++ b/lib/hcrypto/x25519/fe_25_5/fe.h @@ -0,0 +1,220 @@ +/* + Ignores top bit of h. + */ + +void +fe25519_frombytes(fe25519 h, const unsigned char *s) +{ + int64_t h0 = load_4(s); + int64_t h1 = load_3(s + 4) << 6; + int64_t h2 = load_3(s + 7) << 5; + int64_t h3 = load_3(s + 10) << 3; + int64_t h4 = load_3(s + 13) << 2; + int64_t h5 = load_4(s + 16); + int64_t h6 = load_3(s + 20) << 7; + int64_t h7 = load_3(s + 23) << 5; + int64_t h8 = load_3(s + 26) << 4; + int64_t h9 = (load_3(s + 29) & 8388607) << 2; + + int64_t carry0; + int64_t carry1; + int64_t carry2; + int64_t carry3; + int64_t carry4; + int64_t carry5; + int64_t carry6; + int64_t carry7; + int64_t carry8; + int64_t carry9; + + carry9 = (h9 + (int64_t)(1L << 24)) >> 25; + h0 += carry9 * 19; + h9 -= carry9 * ((uint64_t) 1L << 25); + carry1 = (h1 + (int64_t)(1L << 24)) >> 25; + h2 += carry1; + h1 -= carry1 * ((uint64_t) 1L << 25); + carry3 = (h3 + (int64_t)(1L << 24)) >> 25; + h4 += carry3; + h3 -= carry3 * ((uint64_t) 1L << 25); + carry5 = (h5 + (int64_t)(1L << 24)) >> 25; + h6 += carry5; + h5 -= carry5 * ((uint64_t) 1L << 25); + carry7 = (h7 + (int64_t)(1L << 24)) >> 25; + h8 += carry7; + h7 -= carry7 * ((uint64_t) 1L << 25); + + carry0 = (h0 + (int64_t)(1L << 25)) >> 26; + h1 += carry0; + h0 -= carry0 * ((uint64_t) 1L << 26); + carry2 = (h2 + (int64_t)(1L << 25)) >> 26; + h3 += carry2; + h2 -= carry2 * ((uint64_t) 1L << 26); + carry4 = (h4 + (int64_t)(1L << 25)) >> 26; + h5 += carry4; + h4 -= carry4 * ((uint64_t) 1L << 26); + carry6 = (h6 + (int64_t)(1L << 25)) >> 26; + h7 += carry6; + h6 -= carry6 * ((uint64_t) 1L << 26); + carry8 = (h8 + (int64_t)(1L << 25)) >> 26; + h9 += carry8; + h8 -= carry8 * ((uint64_t) 1L << 26); + + h[0] = (int32_t) h0; + h[1] = (int32_t) h1; + h[2] = (int32_t) h2; + h[3] = (int32_t) h3; + h[4] = (int32_t) h4; + h[5] = (int32_t) h5; + h[6] = (int32_t) h6; + h[7] = (int32_t) h7; + h[8] = (int32_t) h8; + h[9] = (int32_t) h9; +} + +/* + Preconditions: + |h| bounded by 1.1*2^26,1.1*2^25,1.1*2^26,1.1*2^25,etc. + + Write p=2^255-19; q=floor(h/p). + Basic claim: q = floor(2^(-255)(h + 19 2^(-25)h9 + 2^(-1))). + + Proof: + Have |h|<=p so |q|<=1 so |19^2 2^(-255) q|<1/4. + Also have |h-2^230 h9|<2^231 so |19 2^(-255)(h-2^230 h9)|<1/4. + + Write y=2^(-1)-19^2 2^(-255)q-19 2^(-255)(h-2^230 h9). + Then 0<y<1. + + Write r=h-pq. + Have 0<=r<=p-1=2^255-20. + Thus 0<=r+19(2^-255)r<r+19(2^-255)2^255<=2^255-1. + + Write x=r+19(2^-255)r+y. + Then 0<x<2^255 so floor(2^(-255)x) = 0 so floor(q+2^(-255)x) = q. + + Have q+2^(-255)x = 2^(-255)(h + 19 2^(-25) h9 + 2^(-1)) + so floor(2^(-255)(h + 19 2^(-25) h9 + 2^(-1))) = q. +*/ + +static void +fe25519_reduce(fe25519 h, const fe25519 f) +{ + int32_t h0 = f[0]; + int32_t h1 = f[1]; + int32_t h2 = f[2]; + int32_t h3 = f[3]; + int32_t h4 = f[4]; + int32_t h5 = f[5]; + int32_t h6 = f[6]; + int32_t h7 = f[7]; + int32_t h8 = f[8]; + int32_t h9 = f[9]; + + int32_t q; + int32_t carry0, carry1, carry2, carry3, carry4, carry5, carry6, carry7, carry8, carry9; + + q = (19 * h9 + ((uint32_t) 1L << 24)) >> 25; + q = (h0 + q) >> 26; + q = (h1 + q) >> 25; + q = (h2 + q) >> 26; + q = (h3 + q) >> 25; + q = (h4 + q) >> 26; + q = (h5 + q) >> 25; + q = (h6 + q) >> 26; + q = (h7 + q) >> 25; + q = (h8 + q) >> 26; + q = (h9 + q) >> 25; + + /* Goal: Output h-(2^255-19)q, which is between 0 and 2^255-20. */ + h0 += 19 * q; + /* Goal: Output h-2^255 q, which is between 0 and 2^255-20. */ + + carry0 = h0 >> 26; + h1 += carry0; + h0 -= carry0 * ((uint32_t) 1L << 26); + carry1 = h1 >> 25; + h2 += carry1; + h1 -= carry1 * ((uint32_t) 1L << 25); + carry2 = h2 >> 26; + h3 += carry2; + h2 -= carry2 * ((uint32_t) 1L << 26); + carry3 = h3 >> 25; + h4 += carry3; + h3 -= carry3 * ((uint32_t) 1L << 25); + carry4 = h4 >> 26; + h5 += carry4; + h4 -= carry4 * ((uint32_t) 1L << 26); + carry5 = h5 >> 25; + h6 += carry5; + h5 -= carry5 * ((uint32_t) 1L << 25); + carry6 = h6 >> 26; + h7 += carry6; + h6 -= carry6 * ((uint32_t) 1L << 26); + carry7 = h7 >> 25; + h8 += carry7; + h7 -= carry7 * ((uint32_t) 1L << 25); + carry8 = h8 >> 26; + h9 += carry8; + h8 -= carry8 * ((uint32_t) 1L << 26); + carry9 = h9 >> 25; + h9 -= carry9 * ((uint32_t) 1L << 25); + + h[0] = h0; + h[1] = h1; + h[2] = h2; + h[3] = h3; + h[4] = h4; + h[5] = h5; + h[6] = h6; + h[7] = h7; + h[8] = h8; + h[9] = h9; +} + +/* + Goal: Output h0+...+2^255 h10-2^255 q, which is between 0 and 2^255-20. + Have h0+...+2^230 h9 between 0 and 2^255-1; + evidently 2^255 h10-2^255 q = 0. + + Goal: Output h0+...+2^230 h9. + */ + +void +fe25519_tobytes(unsigned char *s, const fe25519 h) +{ + fe25519 t; + + fe25519_reduce(t, h); + s[0] = t[0] >> 0; + s[1] = t[0] >> 8; + s[2] = t[0] >> 16; + s[3] = (t[0] >> 24) | (t[1] * ((uint32_t) 1 << 2)); + s[4] = t[1] >> 6; + s[5] = t[1] >> 14; + s[6] = (t[1] >> 22) | (t[2] * ((uint32_t) 1 << 3)); + s[7] = t[2] >> 5; + s[8] = t[2] >> 13; + s[9] = (t[2] >> 21) | (t[3] * ((uint32_t) 1 << 5)); + s[10] = t[3] >> 3; + s[11] = t[3] >> 11; + s[12] = (t[3] >> 19) | (t[4] * ((uint32_t) 1 << 6)); + s[13] = t[4] >> 2; + s[14] = t[4] >> 10; + s[15] = t[4] >> 18; + s[16] = t[5] >> 0; + s[17] = t[5] >> 8; + s[18] = t[5] >> 16; + s[19] = (t[5] >> 24) | (t[6] * ((uint32_t) 1 << 1)); + s[20] = t[6] >> 7; + s[21] = t[6] >> 15; + s[22] = (t[6] >> 23) | (t[7] * ((uint32_t) 1 << 3)); + s[23] = t[7] >> 5; + s[24] = t[7] >> 13; + s[25] = (t[7] >> 21) | (t[8] * ((uint32_t) 1 << 4)); + s[26] = t[8] >> 4; + s[27] = t[8] >> 12; + s[28] = (t[8] >> 20) | (t[9] * ((uint32_t) 1 << 6)); + s[29] = t[9] >> 2; + s[30] = t[9] >> 10; + s[31] = t[9] >> 18; +} diff --git a/lib/hcrypto/x25519/fe_51/base.h b/lib/hcrypto/x25519/fe_51/base.h new file mode 100644 index 000000000000..6b3b833e7a6c --- /dev/null +++ b/lib/hcrypto/x25519/fe_51/base.h @@ -0,0 +1,1344 @@ +{ /* 0/31 */ + { + { 1288382639258501, 245678601348599, 269427782077623, 1462984067271730, 137412439391563 }, + { 62697248952638, 204681361388450, 631292143396476, 338455783676468, 1213667448819585 }, + { 301289933810280, 1259582250014073, 1422107436869536, 796239922652654, 1953934009299142 } + }, + { + { 1380971894829527, 790832306631236, 2067202295274102, 1995808275510000, 1566530869037010 }, + { 463307831301544, 432984605774163, 1610641361907204, 750899048855000, 1894842303421586 }, + { 748439484463711, 1033211726465151, 1396005112841647, 1611506220286469, 1972177495910992 } + }, + { + { 1601611775252272, 1720807796594148, 1132070835939856, 1260455018889551, 2147779492816911 }, + { 316559037616741, 2177824224946892, 1459442586438991, 1461528397712656, 751590696113597 }, + { 1850748884277385, 1200145853858453, 1068094770532492, 672251375690438, 1586055907191707 } + }, + { + { 934282339813791, 1846903124198670, 1172395437954843, 1007037127761661, 1830588347719256 }, + { 1694390458783935, 1735906047636159, 705069562067493, 648033061693059, 696214010414170 }, + { 1121406372216585, 192876649532226, 190294192191717, 1994165897297032, 2245000007398739 } + }, + { + { 769950342298419, 132954430919746, 844085933195555, 974092374476333, 726076285546016 }, + { 425251763115706, 608463272472562, 442562545713235, 837766094556764, 374555092627893 }, + { 1086255230780037, 274979815921559, 1960002765731872, 929474102396301, 1190409889297339 } + }, + { + { 1388594989461809, 316767091099457, 394298842192982, 1230079486801005, 1440737038838979 }, + { 7380825640100, 146210432690483, 304903576448906, 1198869323871120, 997689833219095 }, + { 1181317918772081, 114573476638901, 262805072233344, 265712217171332, 294181933805782 } + }, + { + { 665000864555967, 2065379846933859, 370231110385876, 350988370788628, 1233371373142985 }, + { 2019367628972465, 676711900706637, 110710997811333, 1108646842542025, 517791959672113 }, + { 965130719900578, 247011430587952, 526356006571389, 91986625355052, 2157223321444601 } + }, + { + { 2068619540119183, 1966274918058806, 957728544705549, 729906502578991, 159834893065166 }, + { 2073601412052185, 31021124762708, 264500969797082, 248034690651703, 1030252227928288 }, + { 551790716293402, 1989538725166328, 801169423371717, 2052451893578887, 678432056995012 } + } +}, +{ /* 1/31 */ + { + { 1368953770187805, 790347636712921, 437508475667162, 2142576377050580, 1932081720066286 }, + { 953638594433374, 1092333936795051, 1419774766716690, 805677984380077, 859228993502513 }, + { 1200766035879111, 20142053207432, 1465634435977050, 1645256912097844, 295121984874596 } + }, + { + { 1735718747031557, 1248237894295956, 1204753118328107, 976066523550493, 65943769534592 }, + { 1060098822528990, 1586825862073490, 212301317240126, 1975302711403555, 666724059764335 }, + { 1091990273418756, 1572899409348578, 80968014455247, 306009358661350, 1520450739132526 } + }, + { + { 1480517209436112, 1511153322193952, 1244343858991172, 304788150493241, 369136856496443 }, + { 2151330273626164, 762045184746182, 1688074332551515, 823046109005759, 907602769079491 }, + { 2047386910586836, 168470092900250, 1552838872594810, 340951180073789, 360819374702533 } + }, + { + { 1982622644432056, 2014393600336956, 128909208804214, 1617792623929191, 105294281913815 }, + { 980234343912898, 1712256739246056, 588935272190264, 204298813091998, 841798321043288 }, + { 197561292938973, 454817274782871, 1963754960082318, 2113372252160468, 971377527342673 } + }, + { + { 164699448829328, 3127451757672, 1199504971548753, 1766155447043652, 1899238924683527 }, + { 732262946680281, 1674412764227063, 2182456405662809, 1350894754474250, 558458873295247 }, + { 2103305098582922, 1960809151316468, 715134605001343, 1454892949167181, 40827143824949 } + }, + { + { 1239289043050212, 1744654158124578, 758702410031698, 1796762995074688, 1603056663766 }, + { 2232056027107988, 987343914584615, 2115594492994461, 1819598072792159, 1119305654014850 }, + { 320153677847348, 939613871605645, 641883205761567, 1930009789398224, 329165806634126 } + }, + { + { 980930490474130, 1242488692177893, 1251446316964684, 1086618677993530, 1961430968465772 }, + { 276821765317453, 1536835591188030, 1305212741412361, 61473904210175, 2051377036983058 }, + { 833449923882501, 1750270368490475, 1123347002068295, 185477424765687, 278090826653186 } + }, + { + { 794524995833413, 1849907304548286, 53348672473145, 1272368559505217, 1147304168324779 }, + { 1504846112759364, 1203096289004681, 562139421471418, 274333017451844, 1284344053775441 }, + { 483048732424432, 2116063063343382, 30120189902313, 292451576741007, 1156379271702225 } + } +}, +{ /* 2/31 */ + { + { 928372153029038, 2147692869914564, 1455665844462196, 1986737809425946, 185207050258089 }, + { 137732961814206, 706670923917341, 1387038086865771, 1965643813686352, 1384777115696347 }, + { 481144981981577, 2053319313589856, 2065402289827512, 617954271490316, 1106602634668125 } + }, + { + { 696298019648792, 893299659040895, 1148636718636009, 26734077349617, 2203955659340681 }, + { 657390353372855, 998499966885562, 991893336905797, 810470207106761, 343139804608786 }, + { 791736669492960, 934767652997115, 824656780392914, 1759463253018643, 361530362383518 } + }, + { + { 2022541353055597, 2094700262587466, 1551008075025686, 242785517418164, 695985404963562 }, + { 1287487199965223, 2215311941380308, 1552928390931986, 1664859529680196, 1125004975265243 }, + { 677434665154918, 989582503122485, 1817429540898386, 1052904935475344, 1143826298169798 } + }, + { + { 367266328308408, 318431188922404, 695629353755355, 634085657580832, 24581612564426 }, + { 773360688841258, 1815381330538070, 363773437667376, 539629987070205, 783280434248437 }, + { 180820816194166, 168937968377394, 748416242794470, 1227281252254508, 1567587861004268 } + }, + { + { 478775558583645, 2062896624554807, 699391259285399, 358099408427873, 1277310261461761 }, + { 1984740906540026, 1079164179400229, 1056021349262661, 1659958556483663, 1088529069025527 }, + { 580736401511151, 1842931091388998, 1177201471228238, 2075460256527244, 1301133425678027 } + }, + { + { 1515728832059182, 1575261009617579, 1510246567196186, 191078022609704, 116661716289141 }, + { 1295295738269652, 1714742313707026, 545583042462581, 2034411676262552, 1513248090013606 }, + { 230710545179830, 30821514358353, 760704303452229, 390668103790604, 573437871383156 } + }, + { + { 1169380107545646, 263167233745614, 2022901299054448, 819900753251120, 2023898464874585 }, + { 2102254323485823, 1570832666216754, 34696906544624, 1993213739807337, 70638552271463 }, + { 894132856735058, 548675863558441, 845349339503395, 1942269668326667, 1615682209874691 } + }, + { + { 1287670217537834, 1222355136884920, 1846481788678694, 1150426571265110, 1613523400722047 }, + { 793388516527298, 1315457083650035, 1972286999342417, 1901825953052455, 338269477222410 }, + { 550201530671806, 778605267108140, 2063911101902983, 115500557286349, 2041641272971022 } + } +}, +{ /* 3/31 */ + { + { 717255318455100, 519313764361315, 2080406977303708, 541981206705521, 774328150311600 }, + { 261715221532238, 1795354330069993, 1496878026850283, 499739720521052, 389031152673770 }, + { 1997217696294013, 1717306351628065, 1684313917746180, 1644426076011410, 1857378133465451 } + }, + { + { 1475434724792648, 76931896285979, 1116729029771667, 2002544139318042, 725547833803938 }, + { 2022306639183567, 726296063571875, 315345054448644, 1058733329149221, 1448201136060677 }, + { 1710065158525665, 1895094923036397, 123988286168546, 1145519900776355, 1607510767693874 } + }, + { + { 561605375422540, 1071733543815037, 131496498800990, 1946868434569999, 828138133964203 }, + { 1548495173745801, 442310529226540, 998072547000384, 553054358385281, 644824326376171 }, + { 1445526537029440, 2225519789662536, 914628859347385, 1064754194555068, 1660295614401091 } + }, + { + { 1199690223111956, 24028135822341, 66638289244341, 57626156285975, 565093967979607 }, + { 876926774220824, 554618976488214, 1012056309841565, 839961821554611, 1414499340307677 }, + { 703047626104145, 1266841406201770, 165556500219173, 486991595001879, 1011325891650656 } + }, + { + { 1622861044480487, 1156394801573634, 1869132565415504, 327103985777730, 2095342781472284 }, + { 334886927423922, 489511099221528, 129160865966726, 1720809113143481, 619700195649254 }, + { 1646545795166119, 1758370782583567, 714746174550637, 1472693650165135, 898994790308209 } + }, + { + { 333403773039279, 295772542452938, 1693106465353610, 912330357530760, 471235657950362 }, + { 1811196219982022, 1068969825533602, 289602974833439, 1988956043611592, 863562343398367 }, + { 906282429780072, 2108672665779781, 432396390473936, 150625823801893, 1708930497638539 } + }, + { + { 925664675702328, 21416848568684, 1831436641861340, 601157008940113, 371818055044496 }, + { 1479786007267725, 1738881859066675, 68646196476567, 2146507056100328, 1247662817535471 }, + { 52035296774456, 939969390708103, 312023458773250, 59873523517659, 1231345905848899 } + }, + { + { 643355106415761, 290186807495774, 2013561737429023, 319648069511546, 393736678496162 }, + { 129358342392716, 1932811617704777, 1176749390799681, 398040349861790, 1170779668090425 }, + { 2051980782668029, 121859921510665, 2048329875753063, 1235229850149665, 519062146124755 } + } +}, +{ /* 4/31 */ + { + { 1608170971973096, 415809060360428, 1350468408164766, 2038620059057678, 1026904485989112 }, + { 1837656083115103, 1510134048812070, 906263674192061, 1821064197805734, 565375124676301 }, + { 578027192365650, 2034800251375322, 2128954087207123, 478816193810521, 2196171989962750 } + }, + { + { 1633188840273139, 852787172373708, 1548762607215796, 1266275218902681, 1107218203325133 }, + { 462189358480054, 1784816734159228, 1611334301651368, 1303938263943540, 707589560319424 }, + { 1038829280972848, 38176604650029, 753193246598573, 1136076426528122, 595709990562434 } + }, + { + { 1408451820859834, 2194984964010833, 2198361797561729, 1061962440055713, 1645147963442934 }, + { 4701053362120, 1647641066302348, 1047553002242085, 1923635013395977, 206970314902065 }, + { 1750479161778571, 1362553355169293, 1891721260220598, 966109370862782, 1024913988299801 } + }, + { + { 212699049131723, 1117950018299775, 1873945661751056, 1403802921984058, 130896082652698 }, + { 636808533673210, 1262201711667560, 390951380330599, 1663420692697294, 561951321757406 }, + { 520731594438141, 1446301499955692, 273753264629267, 1565101517999256, 1019411827004672 } + }, + { + { 926527492029409, 1191853477411379, 734233225181171, 184038887541270, 1790426146325343 }, + { 1464651961852572, 1483737295721717, 1519450561335517, 1161429831763785, 405914998179977 }, + { 996126634382301, 796204125879525, 127517800546509, 344155944689303, 615279846169038 } + }, + { + { 738724080975276, 2188666632415296, 1961313708559162, 1506545807547587, 1151301638969740 }, + { 622917337413835, 1218989177089035, 1284857712846592, 970502061709359, 351025208117090 }, + { 2067814584765580, 1677855129927492, 2086109782475197, 235286517313238, 1416314046739645 } + }, + { + { 586844262630358, 307444381952195, 458399356043426, 602068024507062, 1028548203415243 }, + { 678489922928203, 2016657584724032, 90977383049628, 1026831907234582, 615271492942522 }, + { 301225714012278, 1094837270268560, 1202288391010439, 644352775178361, 1647055902137983 } + }, + { + { 1210746697896478, 1416608304244708, 686487477217856, 1245131191434135, 1051238336855737 }, + { 1135604073198207, 1683322080485474, 769147804376683, 2086688130589414, 900445683120379 }, + { 1971518477615628, 401909519527336, 448627091057375, 1409486868273821, 1214789035034363 } + } +}, +{ /* 5/31 */ + { + { 1364039144731711, 1897497433586190, 2203097701135459, 145461396811251, 1349844460790699 }, + { 1045230323257973, 818206601145807, 630513189076103, 1672046528998132, 807204017562437 }, + { 439961968385997, 386362664488986, 1382706320807688, 309894000125359, 2207801346498567 } + }, + { + { 1229004686397588, 920643968530863, 123975893911178, 681423993215777, 1400559197080973 }, + { 2003766096898049, 170074059235165, 1141124258967971, 1485419893480973, 1573762821028725 }, + { 729905708611432, 1270323270673202, 123353058984288, 426460209632942, 2195574535456672 } + }, + { + { 1271140255321235, 2044363183174497, 52125387634689, 1445120246694705, 942541986339084 }, + { 1761608437466135, 583360847526804, 1586706389685493, 2157056599579261, 1170692369685772 }, + 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1577022856702685, 2206946542980843, 625883007765001, 279930793512158 }, + { 1076287717051609, 1114455570543035, 187297059715481, 250446884292121, 1885187512550540 }, + { 902497362940219, 76749815795675, 1657927525633846, 1420238379745202, 1340321636548352 } + }, + { + { 1129576631190784, 1281994010027327, 996844254743018, 257876363489249, 1150850742055018 }, + { 628740660038789, 1943038498527841, 467786347793886, 1093341428303375, 235413859513003 }, + { 237425418909360, 469614029179605, 1512389769174935, 1241726368345357, 441602891065214 } + } +}, +{ /* 6/31 */ + { + { 1736417953058555, 726531315520508, 1833335034432527, 1629442561574747, 624418919286085 }, + { 1960754663920689, 497040957888962, 1909832851283095, 1271432136996826, 2219780368020940 }, + { 1537037379417136, 1358865369268262, 2130838645654099, 828733687040705, 1999987652890901 } + }, + { + { 629042105241814, 1098854999137608, 887281544569320, 1423102019874777, 7911258951561 }, + { 1811562332665373, 1501882019007673, 2213763501088999, 359573079719636, 36370565049116 }, + { 218907117361280, 1209298913016966, 1944312619096112, 1130690631451061, 1342327389191701 } + }, + { + { 1369976867854704, 1396479602419169, 1765656654398856, 2203659200586299, 998327836117241 }, + { 2230701885562825, 1348173180338974, 2172856128624598, 1426538746123771, 444193481326151 }, + { 784210426627951, 918204562375674, 1284546780452985, 1324534636134684, 1872449409642708 } + }, + { + { 319638829540294, 596282656808406, 2037902696412608, 1557219121643918, 341938082688094 }, + { 1901860206695915, 2004489122065736, 1625847061568236, 973529743399879, 2075287685312905 }, + { 1371853944110545, 1042332820512553, 1949855697918254, 1791195775521505, 37487364849293 } + }, + { + { 687200189577855, 1082536651125675, 644224940871546, 340923196057951, 343581346747396 }, + { 2082717129583892, 27829425539422, 145655066671970, 1690527209845512, 1865260509673478 }, + { 1059729620568824, 2163709103470266, 1440302280256872, 1769143160546397, 869830310425069 } + }, + { + { 1609516219779025, 777277757338817, 2101121130363987, 550762194946473, 1905542338659364 }, + { 2024821921041576, 426948675450149, 595133284085473, 471860860885970, 600321679413000 }, + { 598474602406721, 1468128276358244, 1191923149557635, 1501376424093216, 1281662691293476 } + }, + { + { 1721138489890707, 1264336102277790, 433064545421287, 1359988423149466, 1561871293409447 }, + { 719520245587143, 393380711632345, 132350400863381, 1543271270810729, 1819543295798660 }, + { 396397949784152, 1811354474471839, 1362679985304303, 2117033964846756, 498041172552279 } + }, + { + { 1812471844975748, 1856491995543149, 126579494584102, 1036244859282620, 1975108050082550 }, + { 650623932407995, 1137551288410575, 2125223403615539, 1725658013221271, 2134892965117796 }, + { 522584000310195, 1241762481390450, 1743702789495384, 2227404127826575, 1686746002148897 } + } +}, +{ /* 7/31 */ + { + { 427904865186312, 1703211129693455, 1585368107547509, 1436984488744336, 761188534613978 }, + { 318101947455002, 248138407995851, 1481904195303927, 309278454311197, 1258516760217879 }, + { 1275068538599310, 513726919533379, 349926553492294, 688428871968420, 1702400196000666 } + }, + { + { 1061864036265233, 961611260325381, 321859632700838, 1045600629959517, 1985130202504038 }, + { 1558816436882417, 1962896332636523, 1337709822062152, 1501413830776938, 294436165831932 }, + { 818359826554971, 1862173000996177, 626821592884859, 573655738872376, 1749691246745455 } + }, + { + { 1988022651432119, 1082111498586040, 1834020786104821, 1454826876423687, 692929915223122 }, + { 2146513703733331, 584788900394667, 464965657279958, 2183973639356127, 238371159456790 }, + { 1129007025494441, 2197883144413266, 265142755578169, 971864464758890, 1983715884903702 } + }, + { + { 1291366624493075, 381456718189114, 1711482489312444, 1815233647702022, 892279782992467 }, + { 444548969917454, 1452286453853356, 2113731441506810, 645188273895859, 810317625309512 }, + { 2242724082797924, 1373354730327868, 1006520110883049, 2147330369940688, 1151816104883620 } + }, + { + { 1745720200383796, 1911723143175317, 2056329390702074, 355227174309849, 879232794371100 }, + { 163723479936298, 115424889803150, 1156016391581227, 1894942220753364, 1970549419986329 }, + { 681981452362484, 267208874112496, 1374683991933094, 638600984916117, 646178654558546 } + }, + { + { 13378654854251, 106237307029567, 1944412051589651, 1841976767925457, 230702819835573 }, + { 260683893467075, 854060306077237, 913639551980112, 4704576840123, 280254810808712 }, + { 715374893080287, 1173334812210491, 1806524662079626, 1894596008000979, 398905715033393 } + }, + { + { 500026409727661, 1596431288195371, 1420380351989370, 985211561521489, 392444930785633 }, + { 2096421546958141, 1922523000950363, 789831022876840, 427295144688779, 320923973161730 }, + { 1927770723575450, 1485792977512719, 1850996108474547, 551696031508956, 2126047405475647 } + }, + { + { 2112099158080148, 742570803909715, 6484558077432, 1951119898618916, 93090382703416 }, + { 383905201636970, 859946997631870, 855623867637644, 1017125780577795, 794250831877809 }, + { 77571826285752, 999304298101753, 487841111777762, 1038031143212339, 339066367948762 } + } +}, +{ /* 8/31 */ + { + { 674994775520533, 266035846330789, 826951213393478, 1405007746162285, 1781791018620876 }, + { 1001412661522686, 348196197067298, 1666614366723946, 888424995032760, 580747687801357 }, + { 1939560076207777, 1409892634407635, 552574736069277, 383854338280405, 190706709864139 } + }, + { + { 2177087163428741, 1439255351721944, 1208070840382793, 2230616362004769, 1396886392021913 }, + { 676962063230039, 1880275537148808, 2046721011602706, 888463247083003, 1318301552024067 }, + { 1466980508178206, 617045217998949, 652303580573628, 757303753529064, 207583137376902 } + }, + { + { 1511056752906902, 105403126891277, 493434892772846, 1091943425335976, 1802717338077427 }, + { 1853982405405128, 1878664056251147, 1528011020803992, 1019626468153565, 1128438412189035 }, + { 1963939888391106, 293456433791664, 697897559513649, 985882796904380, 796244541237972 } + }, + { + { 416770998629779, 389655552427054, 1314476859406756, 1749382513022778, 1161905598739491 }, + { 1428358296490651, 1027115282420478, 304840698058337, 441410174026628, 1819358356278573 }, + { 204943430200135, 1554861433819175, 216426658514651, 264149070665950, 2047097371738319 } + }, + { + { 1934415182909034, 1393285083565062, 516409331772960, 1157690734993892, 121039666594268 }, + { 662035583584445, 286736105093098, 1131773000510616, 818494214211439, 472943792054479 }, + { 665784778135882, 1893179629898606, 808313193813106, 276797254706413, 1563426179676396 } + }, + { + { 945205108984232, 526277562959295, 1324180513733566, 1666970227868664, 153547609289173 }, + { 2031433403516252, 203996615228162, 170487168837083, 981513604791390, 843573964916831 }, + { 1476570093962618, 838514669399805, 1857930577281364, 2017007352225784, 317085545220047 } + }, + { 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1040818725742319, 2018318290311834, 1712060030915354 }, + { 873966876953756, 1090638350350440, 1708559325189137, 672344594801910, 1320437969700239 }, + { 1508590048271766, 1131769479776094, 101550868699323, 428297785557897, 561791648661744 } + } +}, +{ /* 11/31 */ + { + { 756417570499462, 237882279232602, 2136263418594016, 1701968045454886, 703713185137472 }, + { 1781187809325462, 1697624151492346, 1381393690939988, 175194132284669, 1483054666415238 }, + { 2175517777364616, 708781536456029, 955668231122942, 1967557500069555, 2021208005604118 } + }, + { + { 1115135966606887, 224217372950782, 915967306279222, 593866251291540, 561747094208006 }, + { 1443163092879439, 391875531646162, 2180847134654632, 464538543018753, 1594098196837178 }, + { 850858855888869, 319436476624586, 327807784938441, 740785849558761, 17128415486016 } + }, + { + { 2132756334090067, 536247820155645, 48907151276867, 608473197600695, 1261689545022784 }, + { 1525176236978354, 974205476721062, 293436255662638, 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1512388234908357, 1926731583198686, 2041482526432505, 920401122333774 }, + { 1884844597333588, 601480070269079, 620203503079537, 1079527400117915, 1202076693132015 }, + { 840922919763324, 727955812569642, 1303406629750194, 522898432152867, 294161410441865 } + } +}, +{ /* 17/31 */ + { + { 353760790835310, 1598361541848743, 1122905698202299, 1922533590158905, 419107700666580 }, + { 359856369838236, 180914355488683, 861726472646627, 218807937262986, 575626773232501 }, + { 755467689082474, 909202735047934, 730078068932500, 936309075711518, 2007798262842972 } + }, + { + { 1609384177904073, 362745185608627, 1335318541768201, 800965770436248, 547877979267412 }, + { 984339177776787, 815727786505884, 1645154585713747, 1659074964378553, 1686601651984156 }, + { 1697863093781930, 599794399429786, 1104556219769607, 830560774794755, 12812858601017 } + }, + { + { 1168737550514982, 897832437380552, 463140296333799, 302564600022547, 2008360505135501 }, + { 1856930662813910, 678090852002597, 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100273572924182 } + }, + { + { 1306410853171605, 1627717417672447, 50983221088417, 1109249951172250, 870201789081392 }, + { 104233794644221, 1548919791188248, 2224541913267306, 2054909377116478, 1043803389015153 }, + { 216762189468802, 707284285441622, 190678557969733, 973969342604308, 1403009538434867 } + }, + { + { 1279024291038477, 344776835218310, 273722096017199, 1834200436811442, 634517197663804 }, + { 343805853118335, 1302216857414201, 566872543223541, 2051138939539004, 321428858384280 }, + { 470067171324852, 1618629234173951, 2000092177515639, 7307679772789, 1117521120249968 } + } +}, +{ /* 18/31 */ + { + { 278151578291475, 1810282338562947, 1771599529530998, 1383659409671631, 685373414471841 }, + { 577009397403102, 1791440261786291, 2177643735971638, 174546149911960, 1412505077782326 }, + { 893719721537457, 1201282458018197, 1522349501711173, 58011597740583, 1130406465887139 } + }, + { + { 412607348255453, 1280455764199780, 2233277987330768, 14180080401665, 331584698417165 }, 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1590564179491896, 1944527126709657, 837344427345298 } + }, + { + { 754558365378305, 1712186480903618, 1703656826337531, 750310918489786, 518996040250900 }, + { 1309847803895382, 1462151862813074, 211370866671570, 1544595152703681, 1027691798954090 }, + { 803217563745370, 1884799722343599, 1357706345069218, 2244955901722095, 730869460037413 } + }, + { + { 689299471295966, 1831210565161071, 1375187341585438, 1106284977546171, 1893781834054269 }, + { 696351368613042, 1494385251239250, 738037133616932, 636385507851544, 927483222611406 }, + { 1949114198209333, 1104419699537997, 783495707664463, 1747473107602770, 2002634765788641 } + }, + { + { 1607325776830197, 530883941415333, 1451089452727895, 1581691157083423, 496100432831154 }, + { 1068900648804224, 2006891997072550, 1134049269345549, 1638760646180091, 2055396084625778 }, + { 2222475519314561, 1870703901472013, 1884051508440561, 1344072275216753, 1318025677799069 } + } +}, +{ /* 19/31 */ + { + { 155711679280656, 681100400509288, 389811735211209, 2135723811340709, 408733211204125 }, + { 7813206966729, 194444201427550, 2071405409526507, 1065605076176312, 1645486789731291 }, + { 16625790644959, 1647648827778410, 1579910185572704, 436452271048548, 121070048451050 } + }, + { + { 1037263028552531, 568385780377829, 297953104144430, 1558584511931211, 2238221839292471 }, + { 190565267697443, 672855706028058, 338796554369226, 337687268493904, 853246848691734 }, + { 1763863028400139, 766498079432444, 1321118624818005, 69494294452268, 858786744165651 } + }, + { + { 1292056768563024, 1456632109855638, 1100631247050184, 1386133165675321, 1232898350193752 }, + { 366253102478259, 525676242508811, 1449610995265438, 1183300845322183, 185960306491545 }, + { 28315355815982, 460422265558930, 1799675876678724, 1969256312504498, 1051823843138725 } + }, + { + { 156914999361983, 1606148405719949, 1665208410108430, 317643278692271, 1383783705665320 }, + { 54684536365732, 2210010038536222, 1194984798155308, 535239027773705, 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107077591595359, 884959942172345, 27306869797400, 2224911448949390, 964352058245223 }, + { 1730194207717538, 431790042319772, 1831515233279467, 1372080552768581, 1074513929381760 }, + { 1450880638731607, 1019861580989005, 1229729455116861, 1174945729836143, 826083146840706 } + } +}, +{ /* 20/31 */ + { + { 1899935429242705, 1602068751520477, 940583196550370, 82431069053859, 1540863155745696 }, + { 2136688454840028, 2099509000964294, 1690800495246475, 1217643678575476, 828720645084218 }, + { 765548025667841, 462473984016099, 998061409979798, 546353034089527, 2212508972466858 } + }, + { + { 46575283771160, 892570971573071, 1281983193144090, 1491520128287375, 75847005908304 }, + { 1801436127943107, 1734436817907890, 1268728090345068, 167003097070711, 2233597765834956 }, + { 1997562060465113, 1048700225534011, 7615603985628, 1855310849546841, 2242557647635213 } + }, + { + { 1161017320376250, 492624580169043, 2169815802355237, 976496781732542, 1770879511019629 }, + { 1357044908364776, 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64476199777924, 1117233614485261 } + }, + { + { 984292135520292, 135138246951259, 2220652137473167, 1722843421165029, 190482558012909 }, + { 298845952651262, 1166086588952562, 1179896526238434, 1347812759398693, 1412945390096208 }, + { 1143239552672925, 906436640714209, 2177000572812152, 2075299936108548, 325186347798433 } + }, + { + { 721024854374772, 684487861263316, 1373438744094159, 2193186935276995, 1387043709851261 }, + { 418098668140962, 715065997721283, 1471916138376055, 2168570337288357, 937812682637044 }, + { 1043584187226485, 2143395746619356, 2209558562919611, 482427979307092, 847556718384018 } + } +}, +{ /* 21/31 */ + { + { 1248731221520759, 1465200936117687, 540803492710140, 52978634680892, 261434490176109 }, + { 1057329623869501, 620334067429122, 461700859268034, 2012481616501857, 297268569108938 }, + { 1055352180870759, 1553151421852298, 1510903185371259, 1470458349428097, 1226259419062731 } + }, + { + { 1492988790301668, 790326625573331, 1190107028409745, 1389394752159193, 1620408196604194 }, + { 47000654413729, 1004754424173864, 1868044813557703, 173236934059409, 588771199737015 }, + { 30498470091663, 1082245510489825, 576771653181956, 806509986132686, 1317634017056939 } + }, + { + { 420308055751555, 1493354863316002, 165206721528088, 1884845694919786, 2065456951573059 }, + { 1115636332012334, 1854340990964155, 83792697369514, 1972177451994021, 457455116057587 }, + { 1698968457310898, 1435137169051090, 1083661677032510, 938363267483709, 340103887207182 } + }, + { + { 1995325341336574, 911500251774648, 164010755403692, 855378419194762, 1573601397528842 }, + { 241719380661528, 310028521317150, 1215881323380194, 1408214976493624, 2141142156467363 }, + { 1315157046163473, 727368447885818, 1363466668108618, 1668921439990361, 1398483384337907 } + }, + { + { 75029678299646, 1015388206460473, 1849729037055212, 1939814616452984, 444404230394954 }, + { 2053597130993710, 2024431685856332, 2233550957004860, 2012407275509545, 872546993104440 }, + { 1217269667678610, 599909351968693, 1390077048548598, 1471879360694802, 739586172317596 } + }, + { + { 1718318639380794, 1560510726633958, 904462881159922, 1418028351780052, 94404349451937 }, + { 2132502667405250, 214379346175414, 1502748313768060, 1960071701057800, 1353971822643138 }, + { 319394212043702, 2127459436033571, 717646691535162, 663366796076914, 318459064945314 } + }, + { + { 405989424923593, 1960452633787083, 667349034401665, 1492674260767112, 1451061489880787 }, + { 947085906234007, 323284730494107, 1485778563977200, 728576821512394, 901584347702286 }, + { 1575783124125742, 2126210792434375, 1569430791264065, 1402582372904727, 1891780248341114 } + }, + { + { 838432205560695, 1997703511451664, 1018791879907867, 1662001808174331, 78328132957753 }, + { 739152638255629, 2074935399403557, 505483666745895, 1611883356514088, 628654635394878 }, + { 1822054032121349, 643057948186973, 7306757352712, 577249257962099, 284735863382083 } + } +}, +{ /* 22/31 */ + { + { 1366558556363930, 1448606567552086, 1478881020944768, 165803179355898, 1115718458123498 }, + { 204146226972102, 1630511199034723, 2215235214174763, 174665910283542, 956127674017216 }, + { 1562934578796716, 1070893489712745, 11324610642270, 958989751581897, 2172552325473805 } + }, + { + { 1770564423056027, 735523631664565, 1326060113795289, 1509650369341127, 65892421582684 }, + { 623682558650637, 1337866509471512, 990313350206649, 1314236615762469, 1164772974270275 }, + { 223256821462517, 723690150104139, 1000261663630601, 933280913953265, 254872671543046 } + }, + { + { 1969087237026041, 624795725447124, 1335555107635969, 2069986355593023, 1712100149341902 }, + { 1236103475266979, 1837885883267218, 1026072585230455, 1025865513954973, 1801964901432134 }, + { 1115241013365517, 1712251818829143, 2148864332502771, 2096001471438138, 2235017246626125 } + }, + { + { 1299268198601632, 2047148477845621, 2165648650132450, 1612539282026145, 514197911628890 }, + { 118352772338543, 1067608711804704, 1434796676193498, 1683240170548391, 230866769907437 }, + { 1850689576796636, 1601590730430274, 1139674615958142, 1954384401440257, 76039205311 } + }, + { + { 1723387471374172, 997301467038410, 533927635123657, 20928644693965, 1756575222802513 }, + { 2146711623855116, 503278928021499, 625853062251406, 1109121378393107, 1033853809911861 }, + { 571005965509422, 2005213373292546, 1016697270349626, 56607856974274, 914438579435146 } + }, + { + { 1346698876211176, 2076651707527589, 1084761571110205, 265334478828406, 1068954492309671 }, + { 1769967932677654, 1695893319756416, 1151863389675920, 1781042784397689, 400287774418285 }, + { 1851867764003121, 403841933237558, 820549523771987, 761292590207581, 1743735048551143 } + }, + { + { 410915148140008, 2107072311871739, 1004367461876503, 99684895396761, 1180818713503224 }, + { 285945406881439, 648174397347453, 1098403762631981, 1366547441102991, 1505876883139217 }, + { 672095903120153, 1675918957959872, 636236529315028, 1569297300327696, 2164144194785875 } + }, + { + { 1902708175321798, 1035343530915438, 1178560808893263, 301095684058146, 1280977479761118 }, + { 1615357281742403, 404257611616381, 2160201349780978, 1160947379188955, 1578038619549541 }, + { 2013087639791217, 822734930507457, 1785668418619014, 1668650702946164, 389450875221715 } + } +}, +{ /* 23/31 */ + { + { 453918449698368, 106406819929001, 2072540975937135, 308588860670238, 1304394580755385 }, + { 1295082798350326, 2091844511495996, 1851348972587817, 3375039684596, 789440738712837 }, + { 2083069137186154, 848523102004566, 993982213589257, 1405313299916317, 1532824818698468 } + }, + { + { 1495961298852430, 1397203457344779, 1774950217066942, 139302743555696, 66603584342787 }, + { 1782411379088302, 1096724939964781, 27593390721418, 542241850291353, 1540337798439873 }, + { 693543956581437, 171507720360750, 1557908942697227, 1074697073443438, 1104093109037196 } + }, + { + { 345288228393419, 1099643569747172, 134881908403743, 1740551994106740, 248212179299770 }, + { 231429562203065, 1526290236421172, 2021375064026423, 1520954495658041, 806337791525116 }, + { 1079623667189886, 872403650198613, 766894200588288, 2163700860774109, 2023464507911816 } + }, + { + { 854645372543796, 1936406001954827, 151460662541253, 825325739271555, 1554306377287556 }, + { 1497138821904622, 1044820250515590, 1742593886423484, 1237204112746837, 849047450816987 }, + { 667962773375330, 1897271816877105, 1399712621683474, 1143302161683099, 2081798441209593 } + }, + { + { 127147851567005, 1936114012888110, 1704424366552046, 856674880716312, 716603621335359 }, + { 1072409664800960, 2146937497077528, 1508780108920651, 935767602384853, 1112800433544068 }, + { 333549023751292, 280219272863308, 2104176666454852, 1036466864875785, 536135186520207 } + }, + { + { 373666279883137, 146457241530109, 304116267127857, 416088749147715, 1258577131183391 }, + { 1186115062588401, 2251609796968486, 1098944457878953, 1153112761201374, 1791625503417267 }, + { 1870078460219737, 2129630962183380, 852283639691142, 292865602592851, 401904317342226 } + }, + { + { 1361070124828035, 815664541425524, 1026798897364671, 1951790935390647, 555874891834790 }, + { 1546301003424277, 459094500062839, 1097668518375311, 1780297770129643, 720763293687608 }, + { 1212405311403990, 1536693382542438, 61028431067459, 1863929423417129, 1223219538638038 } + }, + { + { 1294303766540260, 1183557465955093, 882271357233093, 63854569425375, 2213283684565087 }, + { 339050984211414, 601386726509773, 413735232134068, 966191255137228, 1839475899458159 }, + { 235605972169408, 2174055643032978, 1538335001838863, 1281866796917192, 1815940222628465 } + } +}, +{ /* 24/31 */ + { + { 1632352921721536, 1833328609514701, 2092779091951987, 1923956201873226, 2210068022482919 }, + { 35271216625062, 1712350667021807, 983664255668860, 98571260373038, 1232645608559836 }, + { 1998172393429622, 1798947921427073, 784387737563581, 1589352214827263, 1589861734168180 } + }, + { + { 1733739258725305, 31715717059538, 201969945218860, 992093044556990, 1194308773174556 }, + { 846415389605137, 746163495539180, 829658752826080, 592067705956946, 957242537821393 }, + { 1758148849754419, 619249044817679, 168089007997045, 1371497636330523, 1867101418880350 } + }, + { + { 326633984209635, 261759506071016, 1700682323676193, 1577907266349064, 1217647663383016 }, + { 1714182387328607, 1477856482074168, 574895689942184, 2159118410227270, 1555532449716575 }, + { 853828206885131, 998498946036955, 1835887550391235, 207627336608048, 258363815956050 } + }, + { + { 141141474651677, 1236728744905256, 643101419899887, 1646615130509173, 1208239602291765 }, + { 1501663228068911, 1354879465566912, 1444432675498247, 897812463852601, 855062598754348 }, + { 714380763546606, 1032824444965790, 1774073483745338, 1063840874947367, 1738680636537158 } + }, + { + { 1640635546696252, 633168953192112, 2212651044092396, 30590958583852, 368515260889378 }, + { 1171650314802029, 1567085444565577, 1453660792008405, 757914533009261, 1619511342778196 }, + { 420958967093237, 971103481109486, 2169549185607107, 1301191633558497, 1661514101014240 } + }, + { + { 907123651818302, 1332556122804146, 1824055253424487, 1367614217442959, 1982558335973172 }, + { 1121533090144639, 1021251337022187, 110469995947421, 1511059774758394, 2110035908131662 }, + { 303213233384524, 2061932261128138, 352862124777736, 40828818670255, 249879468482660 } + }, + { + { 856559257852200, 508517664949010, 1378193767894916, 1723459126947129, 1962275756614521 }, + { 1445691340537320, 40614383122127, 402104303144865, 485134269878232, 1659439323587426 }, + { 20057458979482, 1183363722525800, 2140003847237215, 2053873950687614, 2112017736174909 } + }, + { + { 2228654250927986, 1483591363415267, 1368661293910956, 1076511285177291, 526650682059608 }, + { 709481497028540, 531682216165724, 316963769431931, 1814315888453765, 258560242424104 }, + { 1053447823660455, 1955135194248683, 1010900954918985, 1182614026976701, 1240051576966610 } + } +}, +{ /* 25/31 */ + { + { 1957943897155497, 1788667368028035, 137692910029106, 1039519607062, 826404763313028 }, + { 1848942433095597, 1582009882530495, 1849292741020143, 1068498323302788, 2001402229799484 }, + { 1528282417624269, 2142492439828191, 2179662545816034, 362568973150328, 1591374675250271 } + }, + { + { 160026679434388, 232341189218716, 2149181472355545, 598041771119831, 183859001910173 }, + { 2013278155187349, 662660471354454, 793981225706267, 411706605985744, 804490933124791 }, + { 2051892037280204, 488391251096321, 2230187337030708, 930221970662692, 679002758255210 } + }, + { + { 1530723630438670, 875873929577927, 341560134269988, 449903119530753, 1055551308214179 }, + { 1461835919309432, 1955256480136428, 180866187813063, 1551979252664528, 557743861963950 }, + { 359179641731115, 1324915145732949, 902828372691474, 294254275669987, 1887036027752957 } + }, + { + { 2043271609454323, 2038225437857464, 1317528426475850, 1398989128982787, 2027639881006861 }, + { 2072902725256516, 312132452743412, 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1740300006094761 } + }, + { + { 2014540178270324, 192672779514432, 213877182641530, 2194819933853411, 1716422829364835 }, + { 1540769606609725, 2148289943846077, 1597804156127445, 1230603716683868, 815423458809453 }, + { 1738560251245018, 1779576754536888, 1783765347671392, 1880170990446751, 1088225159617541 } + } +}, +{ /* 26/31 */ + { + { 659303913929492, 1956447718227573, 1830568515922666, 841069049744408, 1669607124206368 }, + { 1143465490433355, 1532194726196059, 1093276745494697, 481041706116088, 2121405433561163 }, + { 1686424298744462, 1451806974487153, 266296068846582, 1834686947542675, 1720762336132256 } + }, + { + { 889217026388959, 1043290623284660, 856125087551909, 1669272323124636, 1603340330827879 }, + { 1206396181488998, 333158148435054, 1402633492821422, 1120091191722026, 1945474114550509 }, + { 766720088232571, 1512222781191002, 1189719893490790, 2091302129467914, 2141418006894941 } + }, + { + { 419663647306612, 1998875112167987, 1426599870253707, 1154928355379510, 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1049075855992603, 2066573052986543, 266904467185534, 2040482348591520 }, + { 94096246544434, 922482381166992, 24517828745563, 2139430508542503, 2097139044231004 }, + { 537697207950515, 1399352016347350, 1563663552106345, 2148749520888918, 549922092988516 } + }, + { + { 1747985413252434, 680511052635695, 1809559829982725, 594274250930054, 201673170745982 }, + { 323583936109569, 1973572998577657, 1192219029966558, 79354804385273, 1374043025560347 }, + { 213277331329947, 416202017849623, 1950535221091783, 1313441578103244, 2171386783823658 } + }, + { + { 189088804229831, 993969372859110, 895870121536987, 1547301535298256, 1477373024911350 }, + { 1620578418245010, 541035331188469, 2235785724453865, 2154865809088198, 1974627268751826 }, + { 1346805451740245, 1350981335690626, 942744349501813, 2155094562545502, 1012483751693409 } + }, + { + { 2107080134091762, 1132567062788208, 1824935377687210, 769194804343737, 1857941799971888 }, + { 1074666112436467, 249279386739593, 1174337926625354, 1559013532006480, 1472287775519121 }, + { 1872620123779532, 1892932666768992, 1921559078394978, 1270573311796160, 1438913646755037 } + }, + { + { 837390187648199, 1012253300223599, 989780015893987, 1351393287739814, 328627746545550 }, + { 1028328827183114, 1711043289969857, 1350832470374933, 1923164689604327, 1495656368846911 }, + { 1900828492104143, 430212361082163, 687437570852799, 832514536673512, 1685641495940794 } + }, + { + { 842632847936398, 605670026766216, 290836444839585, 163210774892356, 2213815011799645 }, + { 1176336383453996, 1725477294339771, 12700622672454, 678015708818208, 162724078519879 }, + { 1448049969043497, 1789411762943521, 385587766217753, 90201620913498, 832999441066823 } + }, + { + { 516086333293313, 2240508292484616, 1351669528166508, 1223255565316488, 750235824427138 }, + { 1263624896582495, 1102602401673328, 526302183714372, 2152015839128799, 1483839308490010 }, + { 442991718646863, 1599275157036458, 1925389027579192, 899514691371390, 350263251085160 } + } +}, +{ /* 28/31 */ + { + { 1689713572022143, 593854559254373, 978095044791970, 1985127338729499, 1676069120347625 }, + { 1557207018622683, 340631692799603, 1477725909476187, 614735951619419, 2033237123746766 }, + { 968764929340557, 1225534776710944, 662967304013036, 1155521416178595, 791142883466590 } + }, + { + { 1487081286167458, 993039441814934, 1792378982844640, 698652444999874, 2153908693179754 }, + { 1123181311102823, 685575944875442, 507605465509927, 1412590462117473, 568017325228626 }, + { 560258797465417, 2193971151466401, 1824086900849026, 579056363542056, 1690063960036441 } + }, + { + { 1918407319222416, 353767553059963, 1930426334528099, 1564816146005724, 1861342381708096 }, + { 2131325168777276, 1176636658428908, 1756922641512981, 1390243617176012, 1966325177038383 }, + { 2063958120364491, 2140267332393533, 699896251574968, 273268351312140, 375580724713232 } + }, + { + { 2024297515263178, 416959329722687, 1079014235017302, 171612225573183, 1031677520051053 }, + { 2033900009388450, 1744902869870788, 2190580087917640, 1949474984254121, 231049754293748 }, + { 343868674606581, 550155864008088, 1450580864229630, 481603765195050, 896972360018042 } + }, + { + { 2151139328380127, 314745882084928, 59756825775204, 1676664391494651, 2048348075599360 }, + { 1528930066340597, 1605003907059576, 1055061081337675, 1458319101947665, 1234195845213142 }, + { 830430507734812, 1780282976102377, 1425386760709037, 362399353095425, 2168861579799910 } + }, + { + { 1155762232730333, 980662895504006, 2053766700883521, 490966214077606, 510405877041357 }, + { 1683750316716132, 652278688286128, 1221798761193539, 1897360681476669, 319658166027343 }, + { 618808732869972, 72755186759744, 2060379135624181, 1730731526741822, 48862757828238 } + }, + { + { 1463171970593505, 1143040711767452, 614590986558883, 1409210575145591, 1882816996436803 }, + { 2230133264691131, 563950955091024, 2042915975426398, 827314356293472, 672028980152815 }, + { 264204366029760, 1654686424479449, 2185050199932931, 2207056159091748, 506015669043634 } + }, + { + { 1784446333136569, 1973746527984364, 334856327359575, 1156769775884610, 1023950124675478 }, + { 2065270940578383, 31477096270353, 306421879113491, 181958643936686, 1907105536686083 }, + { 1496516440779464, 1748485652986458, 872778352227340, 818358834654919, 97932669284220 } + } +}, +{ /* 29/31 */ + { + { 471636015770351, 672455402793577, 1804995246884103, 1842309243470804, 1501862504981682 }, + { 1013216974933691, 538921919682598, 1915776722521558, 1742822441583877, 1886550687916656 }, + { 2094270000643336, 303971879192276, 40801275554748, 649448917027930, 1818544418535447 } + }, + { + { 2241737709499165, 549397817447461, 838180519319392, 1725686958520781, 1705639080897747 }, + { 1216074541925116, 50120933933509, 1565829004133810, 721728156134580, 349206064666188 }, + { 948617110470858, 346222547451945, 1126511960599975, 1759386906004538, 493053284802266 } + }, + { + { 1454933046815146, 874696014266362, 1467170975468588, 1432316382418897, 2111710746366763 }, + { 2105387117364450, 1996463405126433, 1303008614294500, 851908115948209, 1353742049788635 }, + { 750300956351719, 1487736556065813, 15158817002104, 1511998221598392, 971739901354129 } + }, + { + { 1874648163531693, 2124487685930551, 1810030029384882, 918400043048335, 586348627300650 }, + { 1235084464747900, 1166111146432082, 1745394857881591, 1405516473883040, 4463504151617 }, + { 1663810156463827, 327797390285791, 1341846161759410, 1964121122800605, 1747470312055380 } + }, + { + { 660005247548233, 2071860029952887, 1358748199950107, 911703252219107, 1014379923023831 }, + { 2206641276178231, 1690587809721504, 1600173622825126, 2156096097634421, 1106822408548216 }, + { 1344788193552206, 1949552134239140, 1735915881729557, 675891104100469, 1834220014427292 } + }, + { + { 1920949492387964, 158885288387530, 70308263664033, 626038464897817, 1468081726101009 }, + { 622221042073383, 1210146474039168, 1742246422343683, 1403839361379025, 417189490895736 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1418185496130297, 484520167728613, 1646737281442950, 1401487684670265, 1349185550126961 }, + { 1495380034400429, 325049476417173, 46346894893933, 1553408840354856, 828980101835683 }, + { 1280337889310282, 2070832742866672, 1640940617225222, 2098284908289951, 450929509534434 } + }, + { + { 407703353998781, 126572141483652, 286039827513621, 1999255076709338, 2030511179441770 }, + { 1254958221100483, 1153235960999843, 942907704968834, 637105404087392, 1149293270147267 }, + { 894249020470196, 400291701616810, 406878712230981, 1599128793487393, 1145868722604026 } + }, + { + { 1497955250203334, 110116344653260, 1128535642171976, 1900106496009660, 129792717460909 }, + { 452487513298665, 1352120549024569, 1173495883910956, 1999111705922009, 367328130454226 }, + { 1717539401269642, 1475188995688487, 891921989653942, 836824441505699, 1885988485608364 } + }, + { + { 1241784121422547, 187337051947583, 1118481812236193, 428747751936362, 30358898927325 }, + { 2022432361201842, 1088816090685051, 1977843398539868, 1854834215890724, 564238862029357 }, + { 938868489100585, 1100285072929025, 1017806255688848, 1957262154788833, 152787950560442 } + }, + { + { 867319417678923, 620471962942542, 226032203305716, 342001443957629, 1761675818237336 }, + { 1295072362439987, 931227904689414, 1355731432641687, 922235735834035, 892227229410209 }, + { 1680989767906154, 535362787031440, 2136691276706570, 1942228485381244, 1267350086882274 } + }, + { + { 366018233770527, 432660629755596, 126409707644535, 1973842949591662, 645627343442376 }, + { 535509430575217, 546885533737322, 1524675609547799, 2138095752851703, 1260738089896827 }, + { 1159906385590467, 2198530004321610, 714559485023225, 81880727882151, 1484020820037082 } + }, + { + { 1377485731340769, 2046328105512000, 1802058637158797, 62146136768173, 1356993908853901 }, + { 2013612215646735, 1830770575920375, 536135310219832, 609272325580394, 270684344495013 }, + { 1237542585982777, 2228682050256790, 1385281931622824, 593183794882890, 493654978552689 } + } +}, +{ /* 31/31 */ + { + { 47341488007760, 1891414891220257, 983894663308928, 176161768286818, 1126261115179708 }, + { 1694030170963455, 502038567066200, 1691160065225467, 949628319562187, 275110186693066 }, + { 1124515748676336, 1661673816593408, 1499640319059718, 1584929449166988, 558148594103306 } + }, + { + { 1784525599998356, 1619698033617383, 2097300287550715, 258265458103756, 1905684794832758 }, + { 1288941072872766, 931787902039402, 190731008859042, 2006859954667190, 1005931482221702 }, + { 1465551264822703, 152905080555927, 680334307368453, 173227184634745, 666407097159852 } + }, + { + { 2111017076203943, 1378760485794347, 1248583954016456, 1352289194864422, 1895180776543896 }, + { 171348223915638, 662766099800389, 462338943760497, 466917763340314, 656911292869115 }, + { 488623681976577, 866497561541722, 1708105560937768, 1673781214218839, 1506146329818807 } + }, + { + { 160425464456957, 950394373239689, 430497123340934, 711676555398832, 320964687779005 }, + { 988979367990485, 1359729327576302, 1301834257246029, 294141160829308, 29348272277475 }, + { 1434382743317910, 100082049942065, 221102347892623, 186982837860588, 1305765053501834 } + }, + { + { 2205916462268190, 499863829790820, 961960554686616, 158062762756985, 1841471168298305 }, + { 1191737341426592, 1847042034978363, 1382213545049056, 1039952395710448, 788812858896859 }, + { 1346965964571152, 1291881610839830, 2142916164336056, 786821641205979, 1571709146321039 } + }, + { + { 787164375951248, 202869205373189, 1356590421032140, 1431233331032510, 786341368775957 }, + { 492448143532951, 304105152670757, 1761767168301056, 233782684697790, 1981295323106089 }, + { 665807507761866, 1343384868355425, 895831046139653, 439338948736892, 1986828765695105 } + }, + { + { 756096210874553, 1721699973539149, 258765301727885, 1390588532210645, 1212530909934781 }, + { 852891097972275, 1816988871354562, 1543772755726524, 1174710635522444, 202129090724628 }, + { 1205281565824323, 22430498399418, 992947814485516, 1392458699738672, 688441466734558 } + }, + { + { 1050627428414972, 1955849529137135, 2171162376368357, 91745868298214, 447733118757826 }, + { 1287181461435438, 622722465530711, 880952150571872, 741035693459198, 311565274989772 }, + { 1003649078149734, 545233927396469, 1849786171789880, 1318943684880434, 280345687170552 } + } +} diff --git a/lib/hcrypto/x25519/fe_51/base2.h b/lib/hcrypto/x25519/fe_51/base2.h new file mode 100644 index 000000000000..d088241657ac --- /dev/null +++ b/lib/hcrypto/x25519/fe_51/base2.h @@ -0,0 +1,40 @@ +{ + { 1288382639258501, 245678601348599, 269427782077623, 1462984067271730, 137412439391563 }, + { 62697248952638, 204681361388450, 631292143396476, 338455783676468, 1213667448819585 }, + { 301289933810280, 1259582250014073, 1422107436869536, 796239922652654, 1953934009299142 } +}, +{ + { 1601611775252272, 1720807796594148, 1132070835939856, 1260455018889551, 2147779492816911 }, + { 316559037616741, 2177824224946892, 1459442586438991, 1461528397712656, 751590696113597 }, + { 1850748884277385, 1200145853858453, 1068094770532492, 672251375690438, 1586055907191707 } +}, +{ + { 769950342298419, 132954430919746, 844085933195555, 974092374476333, 726076285546016 }, + { 425251763115706, 608463272472562, 442562545713235, 837766094556764, 374555092627893 }, + { 1086255230780037, 274979815921559, 1960002765731872, 929474102396301, 1190409889297339 } +}, +{ + { 665000864555967, 2065379846933859, 370231110385876, 350988370788628, 1233371373142985 }, + { 2019367628972465, 676711900706637, 110710997811333, 1108646842542025, 517791959672113 }, + { 965130719900578, 247011430587952, 526356006571389, 91986625355052, 2157223321444601 } +}, +{ + { 1802695059465007, 1664899123557221, 593559490740857, 2160434469266659, 927570450755031 }, + { 1725674970513508, 1933645953859181, 1542344539275782, 1767788773573747, 1297447965928905 }, + { 1381809363726107, 1430341051343062, 2061843536018959, 1551778050872521, 2036394857967624 } +}, +{ + { 1970894096313054, 528066325833207, 1619374932191227, 2207306624415883, 1169170329061080 }, + { 2070390218572616, 1458919061857835, 624171843017421, 1055332792707765, 433987520732508 }, + { 893653801273833, 1168026499324677, 1242553501121234, 1306366254304474, 1086752658510815 } +}, +{ + { 213454002618221, 939771523987438, 1159882208056014, 317388369627517, 621213314200687 }, + { 1971678598905747, 338026507889165, 762398079972271, 655096486107477, 42299032696322 }, + { 177130678690680, 1754759263300204, 1864311296286618, 1180675631479880, 1292726903152791 } +}, +{ + { 1913163449625248, 460779200291993, 2193883288642314, 1008900146920800, 1721983679009502 }, + { 1070401523076875, 1272492007800961, 1910153608563310, 2075579521696771, 1191169788841221 }, + { 692896803108118, 500174642072499, 2068223309439677, 1162190621851337, 1426986007309901 } +} diff --git a/lib/hcrypto/x25519/fe_51/constants.h b/lib/hcrypto/x25519/fe_51/constants.h new file mode 100644 index 000000000000..24e5cb5ebbe1 --- /dev/null +++ b/lib/hcrypto/x25519/fe_51/constants.h @@ -0,0 +1,41 @@ +/* 37095705934669439343138083508754565189542113879843219016388785533085940283555 */ +static const fe25519 d = { + 929955233495203, 466365720129213, 1662059464998953, 2033849074728123, 1442794654840575 +}; + +/* 2 * d = + * 16295367250680780974490674513165176452449235426866156013048779062215315747161 + */ +static const fe25519 d2 = { + 1859910466990425, 932731440258426, 1072319116312658, 1815898335770999, 633789495995903 +}; + +/* sqrt(-1) */ +static const fe25519 sqrtm1 = { + 1718705420411056, 234908883556509, 2233514472574048, 2117202627021982, 765476049583133 +}; + +/* A = 486662 */ +static const fe25519 curve25519_A = { + 486662, 0, 0, 0, 0 +}; + +/* sqrt(ad - 1) with a = -1 (mod p) */ +static const fe25519 sqrtadm1 = { + 2241493124984347, 425987919032274, 2207028919301688, 1220490630685848, 974799131293748 +}; + +/* 1 / sqrt(a - d) */ +static const fe25519 invsqrtamd = { + 278908739862762, 821645201101625, 8113234426968, 1777959178193151, 2118520810568447 +}; + +/* 1 - d ^ 2 */ +static const fe25519 onemsqd = { + 1136626929484150, 1998550399581263, 496427632559748, 118527312129759, 45110755273534 +}; + +/* (d - 1) ^ 2 */ +static const fe25519 sqdmone = { + 1507062230895904, 1572317787530805, 683053064812840, 317374165784489, 1572899562415810 +}; diff --git a/lib/hcrypto/x25519/fe_51/fe.h b/lib/hcrypto/x25519/fe_51/fe.h new file mode 100644 index 000000000000..de876264c87c --- /dev/null +++ b/lib/hcrypto/x25519/fe_51/fe.h @@ -0,0 +1,116 @@ +/* + Ignores top bit of h. + */ + +void +fe25519_frombytes(fe25519 h, const unsigned char *s) +{ + const uint64_t mask = 0x7ffffffffffffULL; + uint64_t h0, h1, h2, h3, h4; + + h0 = (LOAD64_LE(s ) ) & mask; + h1 = (LOAD64_LE(s + 6) >> 3) & mask; + h2 = (LOAD64_LE(s + 12) >> 6) & mask; + h3 = (LOAD64_LE(s + 19) >> 1) & mask; + h4 = (LOAD64_LE(s + 24) >> 12) & mask; + + h[0] = h0; + h[1] = h1; + h[2] = h2; + h[3] = h3; + h[4] = h4; +} + +static void +fe25519_reduce(fe25519 h, const fe25519 f) +{ + const uint64_t mask = 0x7ffffffffffffULL; + uint128_t t[5]; + + t[0] = f[0]; + t[1] = f[1]; + t[2] = f[2]; + t[3] = f[3]; + t[4] = f[4]; + + t[1] += t[0] >> 51; + t[0] &= mask; + t[2] += t[1] >> 51; + t[1] &= mask; + t[3] += t[2] >> 51; + t[2] &= mask; + t[4] += t[3] >> 51; + t[3] &= mask; + t[0] += 19 * (t[4] >> 51); + t[4] &= mask; + + t[1] += t[0] >> 51; + t[0] &= mask; + t[2] += t[1] >> 51; + t[1] &= mask; + t[3] += t[2] >> 51; + t[2] &= mask; + t[4] += t[3] >> 51; + t[3] &= mask; + t[0] += 19 * (t[4] >> 51); + t[4] &= mask; + + /* now t is between 0 and 2^255-1, properly carried. */ + /* case 1: between 0 and 2^255-20. case 2: between 2^255-19 and 2^255-1. */ + + t[0] += 19ULL; + + t[1] += t[0] >> 51; + t[0] &= mask; + t[2] += t[1] >> 51; + t[1] &= mask; + t[3] += t[2] >> 51; + t[2] &= mask; + t[4] += t[3] >> 51; + t[3] &= mask; + t[0] += 19ULL * (t[4] >> 51); + t[4] &= mask; + + /* now between 19 and 2^255-1 in both cases, and offset by 19. */ + + t[0] += 0x8000000000000 - 19ULL; + t[1] += 0x8000000000000 - 1ULL; + t[2] += 0x8000000000000 - 1ULL; + t[3] += 0x8000000000000 - 1ULL; + t[4] += 0x8000000000000 - 1ULL; + + /* now between 2^255 and 2^256-20, and offset by 2^255. */ + + t[1] += t[0] >> 51; + t[0] &= mask; + t[2] += t[1] >> 51; + t[1] &= mask; + t[3] += t[2] >> 51; + t[2] &= mask; + t[4] += t[3] >> 51; + t[3] &= mask; + t[4] &= mask; + + h[0] = t[0]; + h[1] = t[1]; + h[2] = t[2]; + h[3] = t[3]; + h[4] = t[4]; +} + +void +fe25519_tobytes(unsigned char *s, const fe25519 h) +{ + fe25519 t; + uint64_t t0, t1, t2, t3; + + fe25519_reduce(t, h); + t0 = t[0] | (t[1] << 51); + t1 = (t[1] >> 13) | (t[2] << 38); + t2 = (t[2] >> 26) | (t[3] << 25); + t3 = (t[3] >> 39) | (t[4] << 12); + STORE64_LE(s + 0, t0); + STORE64_LE(s + 8, t1); + STORE64_LE(s + 16, t2); + STORE64_LE(s + 24, t3); +} diff --git a/lib/hcrypto/x25519/x25519_ref10.c b/lib/hcrypto/x25519/x25519_ref10.c new file mode 100644 index 000000000000..d6fced7992c1 --- /dev/null +++ b/lib/hcrypto/x25519/x25519_ref10.c @@ -0,0 +1,209 @@ +/* + * ISC License + * + * Copyright (c) 2013-2019 + * Frank Denis <j at pureftpd dot org> + * + * Permission to use, copy, modify, and/or distribute this software for any + * purpose with or without fee is hereby granted, provided that the above + * copyright notice and this permission notice appear in all copies. + * + * THE SOFTWARE IS PROVIDED "AS IS" AND THE AUTHOR DISCLAIMS ALL WARRANTIES + * WITH REGARD TO THIS SOFTWARE INCLUDING ALL IMPLIED WARRANTIES OF + * MERCHANTABILITY AND FITNESS. IN NO EVENT SHALL THE AUTHOR BE LIABLE FOR + * ANY SPECIAL, DIRECT, INDIRECT, OR CONSEQUENTIAL DAMAGES OR ANY DAMAGES + * WHATSOEVER RESULTING FROM LOSS OF USE, DATA OR PROFITS, WHETHER IN AN + * ACTION OF CONTRACT, NEGLIGENCE OR OTHER TORTIOUS ACTION, ARISING OUT OF + * OR IN CONNECTION WITH THE USE OR PERFORMANCE OF THIS SOFTWARE. + */ + +#include <stddef.h> +#include <stdint.h> + +#include "ed25519_ref10.h" +#include "x25519_ref10.h" +#include "align.h" + +/* + * Reject small order points early to mitigate the implications of + * unexpected optimizations that would affect the ref10 code. + * See https://eprint.iacr.org/2017/806.pdf for reference. + */ +static int +has_small_order(const unsigned char s[32]) +{ + CRYPTO_ALIGN(16) + static const unsigned char blacklist[][32] = { + /* 0 (order 4) */ + { 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00 }, + /* 1 (order 1) */ + { 0x01, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00 }, + /* 325606250916557431795983626356110631294008115727848805560023387167927233504 + (order 8) */ + { 0xe0, 0xeb, 0x7a, 0x7c, 0x3b, 0x41, 0xb8, 0xae, 0x16, 0x56, 0xe3, + 0xfa, 0xf1, 0x9f, 0xc4, 0x6a, 0xda, 0x09, 0x8d, 0xeb, 0x9c, 0x32, + 0xb1, 0xfd, 0x86, 0x62, 0x05, 0x16, 0x5f, 0x49, 0xb8, 0x00 }, + /* 39382357235489614581723060781553021112529911719440698176882885853963445705823 + (order 8) */ + { 0x5f, 0x9c, 0x95, 0xbc, 0xa3, 0x50, 0x8c, 0x24, 0xb1, 0xd0, 0xb1, + 0x55, 0x9c, 0x83, 0xef, 0x5b, 0x04, 0x44, 0x5c, 0xc4, 0x58, 0x1c, + 0x8e, 0x86, 0xd8, 0x22, 0x4e, 0xdd, 0xd0, 0x9f, 0x11, 0x57 }, + /* p-1 (order 2) */ + { 0xec, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, + 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, + 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0x7f }, + /* p (=0, order 4) */ + { 0xed, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, + 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, + 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0x7f }, + /* p+1 (=1, order 1) */ + { 0xee, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, + 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, + 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0x7f } + }; + unsigned char c[7] = { 0 }; + unsigned int k; + size_t i, j; + +#define COMPILER_ASSERT(X) (void) sizeof(char[(X) ? 1 : -1]) + + COMPILER_ASSERT(7 == sizeof blacklist / sizeof blacklist[0]); + for (j = 0; j < 31; j++) { + for (i = 0; i < sizeof blacklist / sizeof blacklist[0]; i++) { + c[i] |= s[j] ^ blacklist[i][j]; + } + } + for (i = 0; i < sizeof blacklist / sizeof blacklist[0]; i++) { + c[i] |= (s[j] & 0x7f) ^ blacklist[i][j]; + } + k = 0; + for (i = 0; i < sizeof blacklist / sizeof blacklist[0]; i++) { + k |= (c[i] - 1); + } + return (int) ((k >> 8) & 1); +} + +static int +crypto_scalarmult_curve25519_ref10(unsigned char *q, + const unsigned char *n, + const unsigned char *p) +{ + unsigned char *t = q; + unsigned int i; + fe25519 x1; + fe25519 x2; + fe25519 z2; + fe25519 x3; + fe25519 z3; + fe25519 tmp0; + fe25519 tmp1; + int pos; + unsigned int swap; + unsigned int b; + + if (has_small_order(p)) { + return -1; + } + for (i = 0; i < 32; i++) { + t[i] = n[i]; + } + t[0] &= 248; + t[31] &= 127; + t[31] |= 64; + fe25519_frombytes(x1, p); + fe25519_1(x2); + fe25519_0(z2); + fe25519_copy(x3, x1); + fe25519_1(z3); + + swap = 0; + for (pos = 254; pos >= 0; --pos) { + b = t[pos / 8] >> (pos & 7); + b &= 1; + swap ^= b; + fe25519_cswap(x2, x3, swap); + fe25519_cswap(z2, z3, swap); + swap = b; + fe25519_sub(tmp0, x3, z3); + fe25519_sub(tmp1, x2, z2); + fe25519_add(x2, x2, z2); + fe25519_add(z2, x3, z3); + fe25519_mul(z3, tmp0, x2); + fe25519_mul(z2, z2, tmp1); + fe25519_sq(tmp0, tmp1); + fe25519_sq(tmp1, x2); + fe25519_add(x3, z3, z2); + fe25519_sub(z2, z3, z2); + fe25519_mul(x2, tmp1, tmp0); + fe25519_sub(tmp1, tmp1, tmp0); + fe25519_sq(z2, z2); + fe25519_scalar_product(z3, tmp1, 121666); + fe25519_sq(x3, x3); + fe25519_add(tmp0, tmp0, z3); + fe25519_mul(z3, x1, z2); + fe25519_mul(z2, tmp1, tmp0); + } + fe25519_cswap(x2, x3, swap); + fe25519_cswap(z2, z3, swap); + + fe25519_invert(z2, z2); + fe25519_mul(x2, x2, z2); + fe25519_tobytes(q, x2); + + return 0; +} + +static void +edwards_to_montgomery(fe25519 montgomeryX, const fe25519 edwardsY, const fe25519 edwardsZ) +{ + fe25519 tempX; + fe25519 tempZ; + + fe25519_add(tempX, edwardsZ, edwardsY); + fe25519_sub(tempZ, edwardsZ, edwardsY); + fe25519_invert(tempZ, tempZ); + fe25519_mul(montgomeryX, tempX, tempZ); +} + +int +crypto_scalarmult_curve25519_base(unsigned char *q, + const unsigned char *n) +{ + unsigned char *t = q; + ge25519_p3 A; + fe25519 pk; + unsigned int i; + + for (i = 0; i < 32; i++) { + t[i] = n[i]; + } + t[0] &= 248; + t[31] &= 127; + t[31] |= 64; + ge25519_scalarmult_base(&A, t); + edwards_to_montgomery(pk, A.Y, A.Z); + fe25519_tobytes(q, pk); + + return 0; +} + +int +crypto_scalarmult_curve25519(unsigned char *q, const unsigned char *n, + const unsigned char *p) +{ + size_t i; + volatile unsigned char d = 0; + + if (crypto_scalarmult_curve25519_ref10(q, n, p) != 0) { + return -1; /* LCOV_EXCL_LINE */ + } + for (i = 0; i < crypto_scalarmult_curve25519_BYTES; i++) { + d |= q[i]; + } + return -(1 & ((d - 1) >> 8)); +} + diff --git a/lib/hcrypto/x25519_ref10.h b/lib/hcrypto/x25519_ref10.h new file mode 100644 index 000000000000..f43cc0236b0a --- /dev/null +++ b/lib/hcrypto/x25519_ref10.h @@ -0,0 +1,55 @@ +/* + * ISC License + * + * Copyright (c) 2013-2019 + * Frank Denis <j at pureftpd dot org> + * + * Permission to use, copy, modify, and/or distribute this software for any + * purpose with or without fee is hereby granted, provided that the above + * copyright notice and this permission notice appear in all copies. + * + * THE SOFTWARE IS PROVIDED "AS IS" AND THE AUTHOR DISCLAIMS ALL WARRANTIES + * WITH REGARD TO THIS SOFTWARE INCLUDING ALL IMPLIED WARRANTIES OF + * MERCHANTABILITY AND FITNESS. IN NO EVENT SHALL THE AUTHOR BE LIABLE FOR + * ANY SPECIAL, DIRECT, INDIRECT, OR CONSEQUENTIAL DAMAGES OR ANY DAMAGES + * WHATSOEVER RESULTING FROM LOSS OF USE, DATA OR PROFITS, WHETHER IN AN + * ACTION OF CONTRACT, NEGLIGENCE OR OTHER TORTIOUS ACTION, ARISING OUT OF + * OR IN CONNECTION WITH THE USE OR PERFORMANCE OF THIS SOFTWARE. + */ + +#ifndef x25519_ref10_H +#define x25519_ref10_H + +#include <stddef.h> + +#ifdef __cplusplus +extern "C" { +#endif + +#define crypto_scalarmult_curve25519_BYTES 32U +size_t crypto_scalarmult_curve25519_bytes(void); + +#define crypto_scalarmult_curve25519_SCALARBYTES 32U +size_t crypto_scalarmult_curve25519_scalarbytes(void); + +/* + * NOTE: Do not use the result of this function directly for key exchange. + * + * Hash the result with the public keys in order to compute a shared + * secret key: H(q || client_pk || server_pk) + * + * Or unless this is not an option, use the crypto_kx() API instead. + */ +#define crypto_scalarmult_curve25519 hc_hcrypto_scalarmult_curve25519 +int crypto_scalarmult_curve25519(unsigned char *q, const unsigned char *n, + const unsigned char *p); + +#define crypto_scalarmult_curve25519_base hc_hcrypto_scalarmult_curve25519_base +int crypto_scalarmult_curve25519_base(unsigned char *q, + const unsigned char *n); + +#ifdef __cplusplus +} +#endif + +#endif |
