diff options
Diffstat (limited to 'crypto/ec/curve25519.c')
| -rw-r--r-- | crypto/ec/curve25519.c | 4541 |
1 files changed, 2340 insertions, 2201 deletions
diff --git a/crypto/ec/curve25519.c b/crypto/ec/curve25519.c index abe9b9cbf6dd..aa999cc5914e 100644 --- a/crypto/ec/curve25519.c +++ b/crypto/ec/curve25519.c @@ -744,91 +744,99 @@ static void x25519_scalar_mult(uint8_t out[32], const uint8_t scalar[32], /* * Reference base 2^25.5 implementation. - */ -/* + * * This code is mostly taken from the ref10 version of Ed25519 in SUPERCOP * 20141124 (http://bench.cr.yp.to/supercop.html). * * The field functions are shared by Ed25519 and X25519 where possible. */ -/* fe means field element. Here the field is \Z/(2^255-19). An element t, +/* + * fe means field element. Here the field is \Z/(2^255-19). An element t, * entries t[0]...t[9], represents the integer t[0]+2^26 t[1]+2^51 t[2]+2^77 * t[3]+2^102 t[4]+...+2^230 t[9]. Bounds on each t[i] vary depending on - * context. */ + * context. + */ typedef int32_t fe[10]; +static const int64_t kBottom21Bits = 0x1fffffLL; static const int64_t kBottom25Bits = 0x1ffffffLL; static const int64_t kBottom26Bits = 0x3ffffffLL; static const int64_t kTop39Bits = 0xfffffffffe000000LL; static const int64_t kTop38Bits = 0xfffffffffc000000LL; -static uint64_t load_3(const uint8_t *in) { - uint64_t result; - result = (uint64_t)in[0]; - result |= ((uint64_t)in[1]) << 8; - result |= ((uint64_t)in[2]) << 16; - return result; +static uint64_t load_3(const uint8_t *in) +{ + uint64_t result; + + result = ((uint64_t)in[0]); + result |= ((uint64_t)in[1]) << 8; + result |= ((uint64_t)in[2]) << 16; + return result; } -static uint64_t load_4(const uint8_t *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; +static uint64_t load_4(const uint8_t *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; } -static void fe_frombytes(fe h, const uint8_t *s) { - /* Ignores top bit of h. */ - 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 + (1 << 24); h0 += (carry9 >> 25) * 19; h9 -= carry9 & kTop39Bits; - carry1 = h1 + (1 << 24); h2 += carry1 >> 25; h1 -= carry1 & kTop39Bits; - carry3 = h3 + (1 << 24); h4 += carry3 >> 25; h3 -= carry3 & kTop39Bits; - carry5 = h5 + (1 << 24); h6 += carry5 >> 25; h5 -= carry5 & kTop39Bits; - carry7 = h7 + (1 << 24); h8 += carry7 >> 25; h7 -= carry7 & kTop39Bits; - - carry0 = h0 + (1 << 25); h1 += carry0 >> 26; h0 -= carry0 & kTop38Bits; - carry2 = h2 + (1 << 25); h3 += carry2 >> 26; h2 -= carry2 & kTop38Bits; - carry4 = h4 + (1 << 25); h5 += carry4 >> 26; h4 -= carry4 & kTop38Bits; - carry6 = h6 + (1 << 25); h7 += carry6 >> 26; h6 -= carry6 & kTop38Bits; - carry8 = h8 + (1 << 25); h9 += carry8 >> 26; h8 -= carry8 & kTop38Bits; - - 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 fe_frombytes(fe h, const uint8_t *s) +{ + /* Ignores top bit of h. */ + 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) & 0x7fffff) << 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 + (1 << 24); h0 += (carry9 >> 25) * 19; h9 -= carry9 & kTop39Bits; + carry1 = h1 + (1 << 24); h2 += carry1 >> 25; h1 -= carry1 & kTop39Bits; + carry3 = h3 + (1 << 24); h4 += carry3 >> 25; h3 -= carry3 & kTop39Bits; + carry5 = h5 + (1 << 24); h6 += carry5 >> 25; h5 -= carry5 & kTop39Bits; + carry7 = h7 + (1 << 24); h8 += carry7 >> 25; h7 -= carry7 & kTop39Bits; + + carry0 = h0 + (1 << 25); h1 += carry0 >> 26; h0 -= carry0 & kTop38Bits; + carry2 = h2 + (1 << 25); h3 += carry2 >> 26; h2 -= carry2 & kTop38Bits; + carry4 = h4 + (1 << 25); h5 += carry4 >> 26; h4 -= carry4 & kTop38Bits; + carry6 = h6 + (1 << 25); h7 += carry6 >> 26; h6 -= carry6 & kTop38Bits; + carry8 = h8 + (1 << 25); h9 += carry8 >> 26; h8 -= carry8 & kTop38Bits; + + 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. +/* + * 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))). @@ -848,102 +856,112 @@ static void fe_frombytes(fe h, const uint8_t *s) { * 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 fe_tobytes(uint8_t *s, const fe h) { - int32_t h0 = h[0]; - int32_t h1 = h[1]; - int32_t h2 = h[2]; - int32_t h3 = h[3]; - int32_t h4 = h[4]; - int32_t h5 = h[5]; - int32_t h6 = h[6]; - int32_t h7 = h[7]; - int32_t h8 = h[8]; - int32_t h9 = h[9]; - int32_t q; - - q = (19 * h9 + (((int32_t) 1) << 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. */ - - h1 += h0 >> 26; h0 &= kBottom26Bits; - h2 += h1 >> 25; h1 &= kBottom25Bits; - h3 += h2 >> 26; h2 &= kBottom26Bits; - h4 += h3 >> 25; h3 &= kBottom25Bits; - h5 += h4 >> 26; h4 &= kBottom26Bits; - h6 += h5 >> 25; h5 &= kBottom25Bits; - h7 += h6 >> 26; h6 &= kBottom26Bits; - h8 += h7 >> 25; h7 &= kBottom25Bits; - h9 += h8 >> 26; h8 &= kBottom26Bits; - h9 &= kBottom25Bits; - /* h10 = carry9 */ - - /* 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. */ - - s[0] = (uint8_t)(h0 >> 0); - s[1] = (uint8_t)(h0 >> 8); - s[2] = (uint8_t)(h0 >> 16); - s[3] = (uint8_t)((h0 >> 24) | ((uint32_t)(h1) << 2)); - s[4] = (uint8_t)(h1 >> 6); - s[5] = (uint8_t)(h1 >> 14); - s[6] = (uint8_t)((h1 >> 22) | ((uint32_t)(h2) << 3)); - s[7] = (uint8_t)(h2 >> 5); - s[8] = (uint8_t)(h2 >> 13); - s[9] = (uint8_t)((h2 >> 21) | ((uint32_t)(h3) << 5)); - s[10] = (uint8_t)(h3 >> 3); - s[11] = (uint8_t)(h3 >> 11); - s[12] = (uint8_t)((h3 >> 19) | ((uint32_t)(h4) << 6)); - s[13] = (uint8_t)(h4 >> 2); - s[14] = (uint8_t)(h4 >> 10); - s[15] = (uint8_t)(h4 >> 18); - s[16] = (uint8_t)(h5 >> 0); - s[17] = (uint8_t)(h5 >> 8); - s[18] = (uint8_t)(h5 >> 16); - s[19] = (uint8_t)((h5 >> 24) | ((uint32_t)(h6) << 1)); - s[20] = (uint8_t)(h6 >> 7); - s[21] = (uint8_t)(h6 >> 15); - s[22] = (uint8_t)((h6 >> 23) | ((uint32_t)(h7) << 3)); - s[23] = (uint8_t)(h7 >> 5); - s[24] = (uint8_t)(h7 >> 13); - s[25] = (uint8_t)((h7 >> 21) | ((uint32_t)(h8) << 4)); - s[26] = (uint8_t)(h8 >> 4); - s[27] = (uint8_t)(h8 >> 12); - s[28] = (uint8_t)((h8 >> 20) | ((uint32_t)(h9) << 6)); - s[29] = (uint8_t)(h9 >> 2); - s[30] = (uint8_t)(h9 >> 10); - s[31] = (uint8_t)(h9 >> 18); + * so floor(2^(-255)(h + 19 2^(-25) h9 + 2^(-1))) = q. + */ +static void fe_tobytes(uint8_t *s, const fe h) +{ + int32_t h0 = h[0]; + int32_t h1 = h[1]; + int32_t h2 = h[2]; + int32_t h3 = h[3]; + int32_t h4 = h[4]; + int32_t h5 = h[5]; + int32_t h6 = h[6]; + int32_t h7 = h[7]; + int32_t h8 = h[8]; + int32_t h9 = h[9]; + int32_t q; + + q = (19 * h9 + (((int32_t) 1) << 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. */ + + h1 += h0 >> 26; h0 &= kBottom26Bits; + h2 += h1 >> 25; h1 &= kBottom25Bits; + h3 += h2 >> 26; h2 &= kBottom26Bits; + h4 += h3 >> 25; h3 &= kBottom25Bits; + h5 += h4 >> 26; h4 &= kBottom26Bits; + h6 += h5 >> 25; h5 &= kBottom25Bits; + h7 += h6 >> 26; h6 &= kBottom26Bits; + h8 += h7 >> 25; h7 &= kBottom25Bits; + h9 += h8 >> 26; h8 &= kBottom26Bits; + h9 &= kBottom25Bits; + /* h10 = carry9 */ + + /* + * 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. + */ + s[ 0] = (uint8_t) (h0 >> 0); + s[ 1] = (uint8_t) (h0 >> 8); + s[ 2] = (uint8_t) (h0 >> 16); + s[ 3] = (uint8_t)((h0 >> 24) | ((uint32_t)(h1) << 2)); + s[ 4] = (uint8_t) (h1 >> 6); + s[ 5] = (uint8_t) (h1 >> 14); + s[ 6] = (uint8_t)((h1 >> 22) | ((uint32_t)(h2) << 3)); + s[ 7] = (uint8_t) (h2 >> 5); + s[ 8] = (uint8_t) (h2 >> 13); + s[ 9] = (uint8_t)((h2 >> 21) | ((uint32_t)(h3) << 5)); + s[10] = (uint8_t) (h3 >> 3); + s[11] = (uint8_t) (h3 >> 11); + s[12] = (uint8_t)((h3 >> 19) | ((uint32_t)(h4) << 6)); + s[13] = (uint8_t) (h4 >> 2); + s[14] = (uint8_t) (h4 >> 10); + s[15] = (uint8_t) (h4 >> 18); + s[16] = (uint8_t) (h5 >> 0); + s[17] = (uint8_t) (h5 >> 8); + s[18] = (uint8_t) (h5 >> 16); + s[19] = (uint8_t)((h5 >> 24) | ((uint32_t)(h6) << 1)); + s[20] = (uint8_t) (h6 >> 7); + s[21] = (uint8_t) (h6 >> 15); + s[22] = (uint8_t)((h6 >> 23) | ((uint32_t)(h7) << 3)); + s[23] = (uint8_t) (h7 >> 5); + s[24] = (uint8_t) (h7 >> 13); + s[25] = (uint8_t)((h7 >> 21) | ((uint32_t)(h8) << 4)); + s[26] = (uint8_t) (h8 >> 4); + s[27] = (uint8_t) (h8 >> 12); + s[28] = (uint8_t)((h8 >> 20) | ((uint32_t)(h9) << 6)); + s[29] = (uint8_t) (h9 >> 2); + s[30] = (uint8_t) (h9 >> 10); + s[31] = (uint8_t) (h9 >> 18); } /* h = f */ -static void fe_copy(fe h, const fe f) { - memmove(h, f, sizeof(int32_t) * 10); +static void fe_copy(fe h, const fe f) +{ + memmove(h, f, sizeof(int32_t) * 10); } /* h = 0 */ -static void fe_0(fe h) { memset(h, 0, sizeof(int32_t) * 10); } +static void fe_0(fe h) +{ + memset(h, 0, sizeof(int32_t) * 10); +} /* h = 1 */ -static void fe_1(fe h) { - memset(h, 0, sizeof(int32_t) * 10); - h[0] = 1; +static void fe_1(fe h) +{ + memset(h, 0, sizeof(int32_t) * 10); + h[0] = 1; } -/* h = f + g +/* + * h = f + g + * * Can overlap h with f or g. * * Preconditions: @@ -951,15 +969,20 @@ static void fe_1(fe h) { * |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 fe_add(fe h, const fe f, const fe g) { - unsigned i; - for (i = 0; i < 10; i++) { - h[i] = f[i] + g[i]; - } + * |h| bounded by 1.1*2^26,1.1*2^25,1.1*2^26,1.1*2^25,etc. + */ +static void fe_add(fe h, const fe f, const fe g) +{ + unsigned i; + + for (i = 0; i < 10; i++) { + h[i] = f[i] + g[i]; + } } -/* h = f - g +/* + * h = f - g + * * Can overlap h with f or g. * * Preconditions: @@ -967,15 +990,20 @@ static void fe_add(fe h, const fe f, const fe g) { * |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 fe_sub(fe h, const fe f, const fe g) { - unsigned i; - for (i = 0; i < 10; i++) { - h[i] = f[i] - g[i]; - } + * |h| bounded by 1.1*2^26,1.1*2^25,1.1*2^26,1.1*2^25,etc. + */ +static void fe_sub(fe h, const fe f, const fe g) +{ + unsigned i; + + for (i = 0; i < 10; i++) { + h[i] = f[i] - g[i]; + } } -/* h = f * g +/* + * h = f * g + * * Can overlap h with f or g. * * Preconditions: @@ -1001,224 +1029,228 @@ static void fe_sub(fe h, const fe f, const fe g) { * 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 fe_mul(fe h, const fe f, const fe 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 + (1 << 25); h1 += carry0 >> 26; h0 -= carry0 & kTop38Bits; - carry4 = h4 + (1 << 25); h5 += carry4 >> 26; h4 -= carry4 & kTop38Bits; - /* |h0| <= 2^25 */ - /* |h4| <= 2^25 */ - /* |h1| <= 1.71*2^59 */ - /* |h5| <= 1.71*2^59 */ - - carry1 = h1 + (1 << 24); h2 += carry1 >> 25; h1 -= carry1 & kTop39Bits; - carry5 = h5 + (1 << 24); h6 += carry5 >> 25; h5 -= carry5 & kTop39Bits; - /* |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 + (1 << 25); h3 += carry2 >> 26; h2 -= carry2 & kTop38Bits; - carry6 = h6 + (1 << 25); h7 += carry6 >> 26; h6 -= carry6 & kTop38Bits; - /* |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 + (1 << 24); h4 += carry3 >> 25; h3 -= carry3 & kTop39Bits; - carry7 = h7 + (1 << 24); h8 += carry7 >> 25; h7 -= carry7 & kTop39Bits; - /* |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 + (1 << 25); h5 += carry4 >> 26; h4 -= carry4 & kTop38Bits; - carry8 = h8 + (1 << 25); h9 += carry8 >> 26; h8 -= carry8 & kTop38Bits; - /* |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 + (1 << 24); h0 += (carry9 >> 25) * 19; h9 -= carry9 & kTop39Bits; - /* |h9| <= 2^24; from now on fits into int32 unchanged */ - /* |h0| <= 1.1*2^39 */ - - carry0 = h0 + (1 << 25); h1 += carry0 >> 26; h0 -= carry0 & kTop38Bits; - /* |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; + * With tighter constraints on inputs can squeeze carries into int32. + */ +static void fe_mul(fe h, const fe f, const fe 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 + (1 << 25); h1 += carry0 >> 26; h0 -= carry0 & kTop38Bits; + carry4 = h4 + (1 << 25); h5 += carry4 >> 26; h4 -= carry4 & kTop38Bits; + /* |h0| <= 2^25 */ + /* |h4| <= 2^25 */ + /* |h1| <= 1.71*2^59 */ + /* |h5| <= 1.71*2^59 */ + + carry1 = h1 + (1 << 24); h2 += carry1 >> 25; h1 -= carry1 & kTop39Bits; + carry5 = h5 + (1 << 24); h6 += carry5 >> 25; h5 -= carry5 & kTop39Bits; + /* |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 + (1 << 25); h3 += carry2 >> 26; h2 -= carry2 & kTop38Bits; + carry6 = h6 + (1 << 25); h7 += carry6 >> 26; h6 -= carry6 & kTop38Bits; + /* |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 + (1 << 24); h4 += carry3 >> 25; h3 -= carry3 & kTop39Bits; + carry7 = h7 + (1 << 24); h8 += carry7 >> 25; h7 -= carry7 & kTop39Bits; + /* |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 + (1 << 25); h5 += carry4 >> 26; h4 -= carry4 & kTop38Bits; + carry8 = h8 + (1 << 25); h9 += carry8 >> 26; h8 -= carry8 & kTop38Bits; + /* |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 + (1 << 24); h0 += (carry9 >> 25) * 19; h9 -= carry9 & kTop39Bits; + /* |h9| <= 2^24; from now on fits into int32 unchanged */ + /* |h0| <= 1.1*2^39 */ + + carry0 = h0 + (1 << 25); h1 += carry0 >> 26; h0 -= carry0 & kTop38Bits; + /* |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 +/* + * h = f * f + * * Can overlap h with f. * * Preconditions: @@ -1227,286 +1259,307 @@ static void fe_mul(fe h, const fe f, const fe g) { * Postconditions: * |h| bounded by 1.01*2^25,1.01*2^24,1.01*2^25,1.01*2^24,etc. * - * See fe_mul.c for discussion of implementation strategy. */ -static void fe_sq(fe h, const fe 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 + (1 << 25); h1 += carry0 >> 26; h0 -= carry0 & kTop38Bits; - carry4 = h4 + (1 << 25); h5 += carry4 >> 26; h4 -= carry4 & kTop38Bits; - - carry1 = h1 + (1 << 24); h2 += carry1 >> 25; h1 -= carry1 & kTop39Bits; - carry5 = h5 + (1 << 24); h6 += carry5 >> 25; h5 -= carry5 & kTop39Bits; - - carry2 = h2 + (1 << 25); h3 += carry2 >> 26; h2 -= carry2 & kTop38Bits; - carry6 = h6 + (1 << 25); h7 += carry6 >> 26; h6 -= carry6 & kTop38Bits; - - carry3 = h3 + (1 << 24); h4 += carry3 >> 25; h3 -= carry3 & kTop39Bits; - carry7 = h7 + (1 << 24); h8 += carry7 >> 25; h7 -= carry7 & kTop39Bits; - - carry4 = h4 + (1 << 25); h5 += carry4 >> 26; h4 -= carry4 & kTop38Bits; - carry8 = h8 + (1 << 25); h9 += carry8 >> 26; h8 -= carry8 & kTop38Bits; - - carry9 = h9 + (1 << 24); h0 += (carry9 >> 25) * 19; h9 -= carry9 & kTop39Bits; - - carry0 = h0 + (1 << 25); h1 += carry0 >> 26; h0 -= carry0 & kTop38Bits; - - 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; + * See fe_mul.c for discussion of implementation strategy. + */ +static void fe_sq(fe h, const fe 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 + (1 << 25); h1 += carry0 >> 26; h0 -= carry0 & kTop38Bits; + carry4 = h4 + (1 << 25); h5 += carry4 >> 26; h4 -= carry4 & kTop38Bits; + + carry1 = h1 + (1 << 24); h2 += carry1 >> 25; h1 -= carry1 & kTop39Bits; + carry5 = h5 + (1 << 24); h6 += carry5 >> 25; h5 -= carry5 & kTop39Bits; + + carry2 = h2 + (1 << 25); h3 += carry2 >> 26; h2 -= carry2 & kTop38Bits; + carry6 = h6 + (1 << 25); h7 += carry6 >> 26; h6 -= carry6 & kTop38Bits; + + carry3 = h3 + (1 << 24); h4 += carry3 >> 25; h3 -= carry3 & kTop39Bits; + carry7 = h7 + (1 << 24); h8 += carry7 >> 25; h7 -= carry7 & kTop39Bits; + + carry4 = h4 + (1 << 25); h5 += carry4 >> 26; h4 -= carry4 & kTop38Bits; + carry8 = h8 + (1 << 25); h9 += carry8 >> 26; h8 -= carry8 & kTop38Bits; + + carry9 = h9 + (1 << 24); h0 += (carry9 >> 25) * 19; h9 -= carry9 & kTop39Bits; + + carry0 = h0 + (1 << 25); h1 += carry0 >> 26; h0 -= carry0 & kTop38Bits; + + 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 fe_invert(fe out, const fe z) { - fe t0; - fe t1; - fe t2; - fe t3; - int i; +static void fe_invert(fe out, const fe z) +{ + fe t0; + fe t1; + fe t2; + fe t3; + int i; - /* - * Compute z ** -1 = z ** (2 ** 255 - 19 - 2) with the exponent as - * 2 ** 255 - 21 = (2 ** 5) * (2 ** 250 - 1) + 11. - */ + /* + * Compute z ** -1 = z ** (2 ** 255 - 19 - 2) with the exponent as + * 2 ** 255 - 21 = (2 ** 5) * (2 ** 250 - 1) + 11. + */ - /* t0 = z ** 2 */ - fe_sq(t0, z); + /* t0 = z ** 2 */ + fe_sq(t0, z); - /* t1 = t0 ** (2 ** 2) = z ** 8 */ - fe_sq(t1, t0); - fe_sq(t1, t1); + /* t1 = t0 ** (2 ** 2) = z ** 8 */ + fe_sq(t1, t0); + fe_sq(t1, t1); - /* t1 = z * t1 = z ** 9 */ - fe_mul(t1, z, t1); - /* t0 = t0 * t1 = z ** 11 -- stash t0 away for the end. */ - fe_mul(t0, t0, t1); + /* t1 = z * t1 = z ** 9 */ + fe_mul(t1, z, t1); + /* t0 = t0 * t1 = z ** 11 -- stash t0 away for the end. */ + fe_mul(t0, t0, t1); - /* t2 = t0 ** 2 = z ** 22 */ - fe_sq(t2, t0); + /* t2 = t0 ** 2 = z ** 22 */ + fe_sq(t2, t0); - /* t1 = t1 * t2 = z ** (2 ** 5 - 1) */ - fe_mul(t1, t1, t2); + /* t1 = t1 * t2 = z ** (2 ** 5 - 1) */ + fe_mul(t1, t1, t2); - /* t2 = t1 ** (2 ** 5) = z ** ((2 ** 5) * (2 ** 5 - 1)) */ - fe_sq(t2, t1); - for (i = 1; i < 5; ++i) { - fe_sq(t2, t2); - } + /* t2 = t1 ** (2 ** 5) = z ** ((2 ** 5) * (2 ** 5 - 1)) */ + fe_sq(t2, t1); + for (i = 1; i < 5; ++i) { + fe_sq(t2, t2); + } - /* t1 = t1 * t2 = z ** ((2 ** 5 + 1) * (2 ** 5 - 1)) = z ** (2 ** 10 - 1) */ - fe_mul(t1, t2, t1); + /* t1 = t1 * t2 = z ** ((2 ** 5 + 1) * (2 ** 5 - 1)) = z ** (2 ** 10 - 1) */ + fe_mul(t1, t2, t1); - /* Continuing similarly... */ + /* Continuing similarly... */ - /* t2 = z ** (2 ** 20 - 1) */ - fe_sq(t2, t1); - for (i = 1; i < 10; ++i) { - fe_sq(t2, t2); - } - fe_mul(t2, t2, t1); - - /* t2 = z ** (2 ** 40 - 1) */ - fe_sq(t3, t2); - for (i = 1; i < 20; ++i) { - fe_sq(t3, t3); - } - fe_mul(t2, t3, t2); - - /* t2 = z ** (2 ** 10) * (2 ** 40 - 1) */ - for (i = 0; i < 10; ++i) { - fe_sq(t2, t2); - } - /* t1 = z ** (2 ** 50 - 1) */ - fe_mul(t1, t2, t1); + /* t2 = z ** (2 ** 20 - 1) */ + fe_sq(t2, t1); + for (i = 1; i < 10; ++i) { + fe_sq(t2, t2); + } + fe_mul(t2, t2, t1); - /* t2 = z ** (2 ** 100 - 1) */ - fe_sq(t2, t1); - for (i = 1; i < 50; ++i) { - fe_sq(t2, t2); - } - fe_mul(t2, t2, t1); - - /* t2 = z ** (2 ** 200 - 1) */ - fe_sq(t3, t2); - for (i = 1; i < 100; ++i) { - fe_sq(t3, t3); - } - fe_mul(t2, t3, t2); - - /* t2 = z ** ((2 ** 50) * (2 ** 200 - 1) */ - fe_sq(t2, t2); - for (i = 1; i < 50; ++i) { + /* t2 = z ** (2 ** 40 - 1) */ + fe_sq(t3, t2); + for (i = 1; i < 20; ++i) { + fe_sq(t3, t3); + } + fe_mul(t2, t3, t2); + + /* t2 = z ** (2 ** 10) * (2 ** 40 - 1) */ + for (i = 0; i < 10; ++i) { + fe_sq(t2, t2); + } + /* t1 = z ** (2 ** 50 - 1) */ + fe_mul(t1, t2, t1); + + /* t2 = z ** (2 ** 100 - 1) */ + fe_sq(t2, t1); + for (i = 1; i < 50; ++i) { + fe_sq(t2, t2); + } + fe_mul(t2, t2, t1); + + /* t2 = z ** (2 ** 200 - 1) */ + fe_sq(t3, t2); + for (i = 1; i < 100; ++i) { + fe_sq(t3, t3); + } + fe_mul(t2, t3, t2); + + /* t2 = z ** ((2 ** 50) * (2 ** 200 - 1) */ fe_sq(t2, t2); - } + for (i = 1; i < 50; ++i) { + fe_sq(t2, t2); + } - /* t1 = z ** (2 ** 250 - 1) */ - fe_mul(t1, t2, t1); + /* t1 = z ** (2 ** 250 - 1) */ + fe_mul(t1, t2, t1); - /* t1 = z ** ((2 ** 5) * (2 ** 250 - 1)) */ - fe_sq(t1, t1); - for (i = 1; i < 5; ++i) { + /* t1 = z ** ((2 ** 5) * (2 ** 250 - 1)) */ fe_sq(t1, t1); - } + for (i = 1; i < 5; ++i) { + fe_sq(t1, t1); + } - /* Recall t0 = z ** 11; out = z ** (2 ** 255 - 21) */ - fe_mul(out, t1, t0); + /* Recall t0 = z ** 11; out = z ** (2 ** 255 - 21) */ + fe_mul(out, t1, t0); } -/* h = -f +/* + * 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 void fe_neg(fe h, const fe f) { - unsigned i; - for (i = 0; i < 10; i++) { - h[i] = -f[i]; - } + * |h| bounded by 1.1*2^25,1.1*2^24,1.1*2^25,1.1*2^24,etc. + */ +static void fe_neg(fe h, const fe f) +{ + unsigned i; + + for (i = 0; i < 10; i++) { + h[i] = -f[i]; + } } -/* Replace (f,g) with (g,g) if b == 1; +/* + * 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 fe_cmov(fe f, const fe g, unsigned b) { - size_t i; - b = 0-b; - for (i = 0; i < 10; i++) { - int32_t x = f[i] ^ g[i]; - x &= b; - f[i] ^= x; - } + * Preconditions: b in {0,1}. + */ +static void fe_cmov(fe f, const fe g, unsigned b) +{ + size_t i; + + b = 0-b; + for (i = 0; i < 10; i++) { + int32_t x = f[i] ^ g[i]; + x &= b; + f[i] ^= x; + } } -/* return 0 if f == 0 +/* + * return 0 if f == 0 * return 1 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 int fe_isnonzero(const fe f) { - uint8_t s[32]; - static const uint8_t zero[32] = {0}; - fe_tobytes(s, f); + * |f| bounded by 1.1*2^26,1.1*2^25,1.1*2^26,1.1*2^25,etc. + */ +static int fe_isnonzero(const fe f) +{ + uint8_t s[32]; + static const uint8_t zero[32] = {0}; - return CRYPTO_memcmp(s, zero, sizeof(zero)) != 0; + fe_tobytes(s, f); + + return CRYPTO_memcmp(s, zero, sizeof(zero)) != 0; } -/* return 1 if f is in {1,3,5,...,q-2} +/* + * 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 int fe_isnegative(const fe f) { - uint8_t s[32]; - fe_tobytes(s, f); - return s[0] & 1; + * |f| bounded by 1.1*2^26,1.1*2^25,1.1*2^26,1.1*2^25,etc. + */ +static int fe_isnegative(const fe f) +{ + uint8_t s[32]; + + fe_tobytes(s, f); + return s[0] & 1; } -/* h = 2 * f * f +/* + * h = 2 * f * f + * * Can overlap h with f. * * Preconditions: @@ -1515,208 +1568,212 @@ static int fe_isnegative(const fe f) { * Postconditions: * |h| bounded by 1.01*2^25,1.01*2^24,1.01*2^25,1.01*2^24,etc. * - * See fe_mul.c for discussion of implementation strategy. */ -static void fe_sq2(fe h, const fe 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 + (1 << 25); h1 += carry0 >> 26; h0 -= carry0 & kTop38Bits; - carry4 = h4 + (1 << 25); h5 += carry4 >> 26; h4 -= carry4 & kTop38Bits; - - carry1 = h1 + (1 << 24); h2 += carry1 >> 25; h1 -= carry1 & kTop39Bits; - carry5 = h5 + (1 << 24); h6 += carry5 >> 25; h5 -= carry5 & kTop39Bits; - - carry2 = h2 + (1 << 25); h3 += carry2 >> 26; h2 -= carry2 & kTop38Bits; - carry6 = h6 + (1 << 25); h7 += carry6 >> 26; h6 -= carry6 & kTop38Bits; - - carry3 = h3 + (1 << 24); h4 += carry3 >> 25; h3 -= carry3 & kTop39Bits; - carry7 = h7 + (1 << 24); h8 += carry7 >> 25; h7 -= carry7 & kTop39Bits; - - carry4 = h4 + (1 << 25); h5 += carry4 >> 26; h4 -= carry4 & kTop38Bits; - carry8 = h8 + (1 << 25); h9 += carry8 >> 26; h8 -= carry8 & kTop38Bits; - - carry9 = h9 + (1 << 24); h0 += (carry9 >> 25) * 19; h9 -= carry9 & kTop39Bits; - - carry0 = h0 + (1 << 25); h1 += carry0 >> 26; h0 -= carry0 & kTop38Bits; - - 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; + * See fe_mul.c for discussion of implementation strategy. + */ +static void fe_sq2(fe h, const fe 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 + (1 << 25); h1 += carry0 >> 26; h0 -= carry0 & kTop38Bits; + carry4 = h4 + (1 << 25); h5 += carry4 >> 26; h4 -= carry4 & kTop38Bits; + + carry1 = h1 + (1 << 24); h2 += carry1 >> 25; h1 -= carry1 & kTop39Bits; + carry5 = h5 + (1 << 24); h6 += carry5 >> 25; h5 -= carry5 & kTop39Bits; + + carry2 = h2 + (1 << 25); h3 += carry2 >> 26; h2 -= carry2 & kTop38Bits; + carry6 = h6 + (1 << 25); h7 += carry6 >> 26; h6 -= carry6 & kTop38Bits; + + carry3 = h3 + (1 << 24); h4 += carry3 >> 25; h3 -= carry3 & kTop39Bits; + carry7 = h7 + (1 << 24); h8 += carry7 >> 25; h7 -= carry7 & kTop39Bits; + + carry4 = h4 + (1 << 25); h5 += carry4 >> 26; h4 -= carry4 & kTop38Bits; + carry8 = h8 + (1 << 25); h9 += carry8 >> 26; h8 -= carry8 & kTop38Bits; + + carry9 = h9 + (1 << 24); h0 += (carry9 >> 25) * 19; h9 -= carry9 & kTop39Bits; + + carry0 = h0 + (1 << 25); h1 += carry0 >> 26; h0 -= carry0 & kTop38Bits; + + 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 fe_pow22523(fe out, const fe z) { - fe t0; - fe t1; - fe t2; - int i; +static void fe_pow22523(fe out, const fe z) +{ + fe t0; + fe t1; + fe t2; + int i; - fe_sq(t0, z); - fe_sq(t1, t0); - for (i = 1; i < 2; ++i) { - fe_sq(t1, t1); - } - fe_mul(t1, z, t1); - fe_mul(t0, t0, t1); - fe_sq(t0, t0); - fe_mul(t0, t1, t0); - fe_sq(t1, t0); - for (i = 1; i < 5; ++i) { - fe_sq(t1, t1); - } - fe_mul(t0, t1, t0); - fe_sq(t1, t0); - for (i = 1; i < 10; ++i) { - fe_sq(t1, t1); - } - fe_mul(t1, t1, t0); - fe_sq(t2, t1); - for (i = 1; i < 20; ++i) { - fe_sq(t2, t2); - } - fe_mul(t1, t2, t1); - fe_sq(t1, t1); - for (i = 1; i < 10; ++i) { - fe_sq(t1, t1); - } - fe_mul(t0, t1, t0); - fe_sq(t1, t0); - for (i = 1; i < 50; ++i) { + fe_sq(t0, z); + fe_sq(t1, t0); + for (i = 1; i < 2; ++i) { + fe_sq(t1, t1); + } + fe_mul(t1, z, t1); + fe_mul(t0, t0, t1); + fe_sq(t0, t0); + fe_mul(t0, t1, t0); + fe_sq(t1, t0); + for (i = 1; i < 5; ++i) { + fe_sq(t1, t1); + } + fe_mul(t0, t1, t0); + fe_sq(t1, t0); + for (i = 1; i < 10; ++i) { + fe_sq(t1, t1); + } + fe_mul(t1, t1, t0); + fe_sq(t2, t1); + for (i = 1; i < 20; ++i) { + fe_sq(t2, t2); + } + fe_mul(t1, t2, t1); fe_sq(t1, t1); - } - fe_mul(t1, t1, t0); - fe_sq(t2, t1); - for (i = 1; i < 100; ++i) { - fe_sq(t2, t2); - } - fe_mul(t1, t2, t1); - fe_sq(t1, t1); - for (i = 1; i < 50; ++i) { + for (i = 1; i < 10; ++i) { + fe_sq(t1, t1); + } + fe_mul(t0, t1, t0); + fe_sq(t1, t0); + for (i = 1; i < 50; ++i) { + fe_sq(t1, t1); + } + fe_mul(t1, t1, t0); + fe_sq(t2, t1); + for (i = 1; i < 100; ++i) { + fe_sq(t2, t2); + } + fe_mul(t1, t2, t1); fe_sq(t1, t1); - } - fe_mul(t0, t1, t0); - fe_sq(t0, t0); - for (i = 1; i < 2; ++i) { + for (i = 1; i < 50; ++i) { + fe_sq(t1, t1); + } + fe_mul(t0, t1, t0); fe_sq(t0, t0); - } - fe_mul(out, t0, z); + for (i = 1; i < 2; ++i) { + fe_sq(t0, t0); + } + fe_mul(out, t0, z); } -/* ge means group element. - +/* + * ge means group element. + * * Here the group is the set of pairs (x,y) of field elements (see fe.h) * satisfying -x^2 + y^2 = 1 + d x^2y^2 * where d = -121665/121666. @@ -1725,268 +1782,292 @@ static void fe_pow22523(fe out, const fe z) { * ge_p2 (projective): (X:Y:Z) satisfying x=X/Z, y=Y/Z * ge_p3 (extended): (X:Y:Z:T) satisfying x=X/Z, y=Y/Z, XY=ZT * ge_p1p1 (completed): ((X:Z),(Y:T)) satisfying x=X/Z, y=Y/T - * ge_precomp (Duif): (y+x,y-x,2dxy) */ - + * ge_precomp (Duif): (y+x,y-x,2dxy) + */ typedef struct { - fe X; - fe Y; - fe Z; + fe X; + fe Y; + fe Z; } ge_p2; typedef struct { - fe X; - fe Y; - fe Z; - fe T; + fe X; + fe Y; + fe Z; + fe T; } ge_p3; typedef struct { - fe X; - fe Y; - fe Z; - fe T; + fe X; + fe Y; + fe Z; + fe T; } ge_p1p1; typedef struct { - fe yplusx; - fe yminusx; - fe xy2d; + fe yplusx; + fe yminusx; + fe xy2d; } ge_precomp; typedef struct { - fe YplusX; - fe YminusX; - fe Z; - fe T2d; + fe YplusX; + fe YminusX; + fe Z; + fe T2d; } ge_cached; -static void ge_tobytes(uint8_t *s, const ge_p2 *h) { - fe recip; - fe x; - fe y; +static void ge_tobytes(uint8_t *s, const ge_p2 *h) +{ + fe recip; + fe x; + fe y; + + fe_invert(recip, h->Z); + fe_mul(x, h->X, recip); + fe_mul(y, h->Y, recip); + fe_tobytes(s, y); + s[31] ^= fe_isnegative(x) << 7; +} - fe_invert(recip, h->Z); - fe_mul(x, h->X, recip); - fe_mul(y, h->Y, recip); - fe_tobytes(s, y); - s[31] ^= fe_isnegative(x) << 7; +static void ge_p3_tobytes(uint8_t *s, const ge_p3 *h) +{ + fe recip; + fe x; + fe y; + + fe_invert(recip, h->Z); + fe_mul(x, h->X, recip); + fe_mul(y, h->Y, recip); + fe_tobytes(s, y); + s[31] ^= fe_isnegative(x) << 7; } -static void ge_p3_tobytes(uint8_t *s, const ge_p3 *h) { - fe recip; - fe x; - fe y; +static const fe d = { + -10913610, 13857413, -15372611, 6949391, 114729, + -8787816, -6275908, -3247719, -18696448, -12055116 +}; - fe_invert(recip, h->Z); - fe_mul(x, h->X, recip); - fe_mul(y, h->Y, recip); - fe_tobytes(s, y); - s[31] ^= fe_isnegative(x) << 7; -} +static const fe sqrtm1 = { + -32595792, -7943725, 9377950, 3500415, 12389472, + -272473, -25146209, -2005654, 326686, 11406482 +}; -static const fe d = {-10913610, 13857413, -15372611, 6949391, 114729, - -8787816, -6275908, -3247719, -18696448, -12055116}; - -static const fe sqrtm1 = {-32595792, -7943725, 9377950, 3500415, 12389472, - -272473, -25146209, -2005654, 326686, 11406482}; - -static int ge_frombytes_vartime(ge_p3 *h, const uint8_t *s) { - fe u; - fe v; - fe v3; - fe vxx; - fe check; - - fe_frombytes(h->Y, s); - fe_1(h->Z); - fe_sq(u, h->Y); - fe_mul(v, u, d); - fe_sub(u, u, h->Z); /* u = y^2-1 */ - fe_add(v, v, h->Z); /* v = dy^2+1 */ - - fe_sq(v3, v); - fe_mul(v3, v3, v); /* v3 = v^3 */ - fe_sq(h->X, v3); - fe_mul(h->X, h->X, v); - fe_mul(h->X, h->X, u); /* x = uv^7 */ - - fe_pow22523(h->X, h->X); /* x = (uv^7)^((q-5)/8) */ - fe_mul(h->X, h->X, v3); - fe_mul(h->X, h->X, u); /* x = uv^3(uv^7)^((q-5)/8) */ - - fe_sq(vxx, h->X); - fe_mul(vxx, vxx, v); - fe_sub(check, vxx, u); /* vx^2-u */ - if (fe_isnonzero(check)) { - fe_add(check, vxx, u); /* vx^2+u */ +static int ge_frombytes_vartime(ge_p3 *h, const uint8_t *s) +{ + fe u; + fe v; + fe v3; + fe vxx; + fe check; + + fe_frombytes(h->Y, s); + fe_1(h->Z); + fe_sq(u, h->Y); + fe_mul(v, u, d); + fe_sub(u, u, h->Z); /* u = y^2-1 */ + fe_add(v, v, h->Z); /* v = dy^2+1 */ + + fe_sq(v3, v); + fe_mul(v3, v3, v); /* v3 = v^3 */ + fe_sq(h->X, v3); + fe_mul(h->X, h->X, v); + fe_mul(h->X, h->X, u); /* x = uv^7 */ + + fe_pow22523(h->X, h->X); /* x = (uv^7)^((q-5)/8) */ + fe_mul(h->X, h->X, v3); + fe_mul(h->X, h->X, u); /* x = uv^3(uv^7)^((q-5)/8) */ + + fe_sq(vxx, h->X); + fe_mul(vxx, vxx, v); + fe_sub(check, vxx, u); /* vx^2-u */ if (fe_isnonzero(check)) { - return -1; + fe_add(check, vxx, u); /* vx^2+u */ + if (fe_isnonzero(check)) { + return -1; + } + fe_mul(h->X, h->X, sqrtm1); } - fe_mul(h->X, h->X, sqrtm1); - } - if (fe_isnegative(h->X) != (s[31] >> 7)) { - fe_neg(h->X, h->X); - } + if (fe_isnegative(h->X) != (s[31] >> 7)) { + fe_neg(h->X, h->X); + } - fe_mul(h->T, h->X, h->Y); - return 0; + fe_mul(h->T, h->X, h->Y); + return 0; } -static void ge_p2_0(ge_p2 *h) { - fe_0(h->X); - fe_1(h->Y); - fe_1(h->Z); +static void ge_p2_0(ge_p2 *h) +{ + fe_0(h->X); + fe_1(h->Y); + fe_1(h->Z); } -static void ge_p3_0(ge_p3 *h) { - fe_0(h->X); - fe_1(h->Y); - fe_1(h->Z); - fe_0(h->T); +static void ge_p3_0(ge_p3 *h) +{ + fe_0(h->X); + fe_1(h->Y); + fe_1(h->Z); + fe_0(h->T); } -static void ge_precomp_0(ge_precomp *h) { - fe_1(h->yplusx); - fe_1(h->yminusx); - fe_0(h->xy2d); +static void ge_precomp_0(ge_precomp *h) +{ + fe_1(h->yplusx); + fe_1(h->yminusx); + fe_0(h->xy2d); } /* r = p */ -static void ge_p3_to_p2(ge_p2 *r, const ge_p3 *p) { - fe_copy(r->X, p->X); - fe_copy(r->Y, p->Y); - fe_copy(r->Z, p->Z); +static void ge_p3_to_p2(ge_p2 *r, const ge_p3 *p) +{ + fe_copy(r->X, p->X); + fe_copy(r->Y, p->Y); + fe_copy(r->Z, p->Z); } -static const fe d2 = {-21827239, -5839606, -30745221, 13898782, 229458, - 15978800, -12551817, -6495438, 29715968, 9444199}; +static const fe d2 = { + -21827239, -5839606, -30745221, 13898782, 229458, + 15978800, -12551817, -6495438, 29715968, 9444199 +}; /* r = p */ -static void ge_p3_to_cached(ge_cached *r, const ge_p3 *p) { - fe_add(r->YplusX, p->Y, p->X); - fe_sub(r->YminusX, p->Y, p->X); - fe_copy(r->Z, p->Z); - fe_mul(r->T2d, p->T, d2); +static void ge_p3_to_cached(ge_cached *r, const ge_p3 *p) +{ + fe_add(r->YplusX, p->Y, p->X); + fe_sub(r->YminusX, p->Y, p->X); + fe_copy(r->Z, p->Z); + fe_mul(r->T2d, p->T, d2); } /* r = p */ -static void ge_p1p1_to_p2(ge_p2 *r, const ge_p1p1 *p) { - fe_mul(r->X, p->X, p->T); - fe_mul(r->Y, p->Y, p->Z); - fe_mul(r->Z, p->Z, p->T); +static void ge_p1p1_to_p2(ge_p2 *r, const ge_p1p1 *p) +{ + fe_mul(r->X, p->X, p->T); + fe_mul(r->Y, p->Y, p->Z); + fe_mul(r->Z, p->Z, p->T); } /* r = p */ -static void ge_p1p1_to_p3(ge_p3 *r, const ge_p1p1 *p) { - fe_mul(r->X, p->X, p->T); - fe_mul(r->Y, p->Y, p->Z); - fe_mul(r->Z, p->Z, p->T); - fe_mul(r->T, p->X, p->Y); +static void ge_p1p1_to_p3(ge_p3 *r, const ge_p1p1 *p) +{ + fe_mul(r->X, p->X, p->T); + fe_mul(r->Y, p->Y, p->Z); + fe_mul(r->Z, p->Z, p->T); + fe_mul(r->T, p->X, p->Y); } /* r = 2 * p */ -static void ge_p2_dbl(ge_p1p1 *r, const ge_p2 *p) { - fe t0; - - fe_sq(r->X, p->X); - fe_sq(r->Z, p->Y); - fe_sq2(r->T, p->Z); - fe_add(r->Y, p->X, p->Y); - fe_sq(t0, r->Y); - fe_add(r->Y, r->Z, r->X); - fe_sub(r->Z, r->Z, r->X); - fe_sub(r->X, t0, r->Y); - fe_sub(r->T, r->T, r->Z); +static void ge_p2_dbl(ge_p1p1 *r, const ge_p2 *p) +{ + fe t0; + + fe_sq(r->X, p->X); + fe_sq(r->Z, p->Y); + fe_sq2(r->T, p->Z); + fe_add(r->Y, p->X, p->Y); + fe_sq(t0, r->Y); + fe_add(r->Y, r->Z, r->X); + fe_sub(r->Z, r->Z, r->X); + fe_sub(r->X, t0, r->Y); + fe_sub(r->T, r->T, r->Z); } /* r = 2 * p */ -static void ge_p3_dbl(ge_p1p1 *r, const ge_p3 *p) { - ge_p2 q; - ge_p3_to_p2(&q, p); - ge_p2_dbl(r, &q); +static void ge_p3_dbl(ge_p1p1 *r, const ge_p3 *p) +{ + ge_p2 q; + ge_p3_to_p2(&q, p); + ge_p2_dbl(r, &q); } /* r = p + q */ -static void ge_madd(ge_p1p1 *r, const ge_p3 *p, const ge_precomp *q) { - fe t0; - - fe_add(r->X, p->Y, p->X); - fe_sub(r->Y, p->Y, p->X); - fe_mul(r->Z, r->X, q->yplusx); - fe_mul(r->Y, r->Y, q->yminusx); - fe_mul(r->T, q->xy2d, p->T); - fe_add(t0, p->Z, p->Z); - fe_sub(r->X, r->Z, r->Y); - fe_add(r->Y, r->Z, r->Y); - fe_add(r->Z, t0, r->T); - fe_sub(r->T, t0, r->T); +static void ge_madd(ge_p1p1 *r, const ge_p3 *p, const ge_precomp *q) +{ + fe t0; + + fe_add(r->X, p->Y, p->X); + fe_sub(r->Y, p->Y, p->X); + fe_mul(r->Z, r->X, q->yplusx); + fe_mul(r->Y, r->Y, q->yminusx); + fe_mul(r->T, q->xy2d, p->T); + fe_add(t0, p->Z, p->Z); + fe_sub(r->X, r->Z, r->Y); + fe_add(r->Y, r->Z, r->Y); + fe_add(r->Z, t0, r->T); + fe_sub(r->T, t0, r->T); } /* r = p - q */ -static void ge_msub(ge_p1p1 *r, const ge_p3 *p, const ge_precomp *q) { - fe t0; - - fe_add(r->X, p->Y, p->X); - fe_sub(r->Y, p->Y, p->X); - fe_mul(r->Z, r->X, q->yminusx); - fe_mul(r->Y, r->Y, q->yplusx); - fe_mul(r->T, q->xy2d, p->T); - fe_add(t0, p->Z, p->Z); - fe_sub(r->X, r->Z, r->Y); - fe_add(r->Y, r->Z, r->Y); - fe_sub(r->Z, t0, r->T); - fe_add(r->T, t0, r->T); +static void ge_msub(ge_p1p1 *r, const ge_p3 *p, const ge_precomp *q) +{ + fe t0; + + fe_add(r->X, p->Y, p->X); + fe_sub(r->Y, p->Y, p->X); + fe_mul(r->Z, r->X, q->yminusx); + fe_mul(r->Y, r->Y, q->yplusx); + fe_mul(r->T, q->xy2d, p->T); + fe_add(t0, p->Z, p->Z); + fe_sub(r->X, r->Z, r->Y); + fe_add(r->Y, r->Z, r->Y); + fe_sub(r->Z, t0, r->T); + fe_add(r->T, t0, r->T); } /* r = p + q */ -static void ge_add(ge_p1p1 *r, const ge_p3 *p, const ge_cached *q) { - fe t0; - - fe_add(r->X, p->Y, p->X); - fe_sub(r->Y, p->Y, p->X); - fe_mul(r->Z, r->X, q->YplusX); - fe_mul(r->Y, r->Y, q->YminusX); - fe_mul(r->T, q->T2d, p->T); - fe_mul(r->X, p->Z, q->Z); - fe_add(t0, r->X, r->X); - fe_sub(r->X, r->Z, r->Y); - fe_add(r->Y, r->Z, r->Y); - fe_add(r->Z, t0, r->T); - fe_sub(r->T, t0, r->T); +static void ge_add(ge_p1p1 *r, const ge_p3 *p, const ge_cached *q) +{ + fe t0; + + fe_add(r->X, p->Y, p->X); + fe_sub(r->Y, p->Y, p->X); + fe_mul(r->Z, r->X, q->YplusX); + fe_mul(r->Y, r->Y, q->YminusX); + fe_mul(r->T, q->T2d, p->T); + fe_mul(r->X, p->Z, q->Z); + fe_add(t0, r->X, r->X); + fe_sub(r->X, r->Z, r->Y); + fe_add(r->Y, r->Z, r->Y); + fe_add(r->Z, t0, r->T); + fe_sub(r->T, t0, r->T); } /* r = p - q */ -static void ge_sub(ge_p1p1 *r, const ge_p3 *p, const ge_cached *q) { - fe t0; - - fe_add(r->X, p->Y, p->X); - fe_sub(r->Y, p->Y, p->X); - fe_mul(r->Z, r->X, q->YminusX); - fe_mul(r->Y, r->Y, q->YplusX); - fe_mul(r->T, q->T2d, p->T); - fe_mul(r->X, p->Z, q->Z); - fe_add(t0, r->X, r->X); - fe_sub(r->X, r->Z, r->Y); - fe_add(r->Y, r->Z, r->Y); - fe_sub(r->Z, t0, r->T); - fe_add(r->T, t0, r->T); +static void ge_sub(ge_p1p1 *r, const ge_p3 *p, const ge_cached *q) +{ + fe t0; + + fe_add(r->X, p->Y, p->X); + fe_sub(r->Y, p->Y, p->X); + fe_mul(r->Z, r->X, q->YminusX); + fe_mul(r->Y, r->Y, q->YplusX); + fe_mul(r->T, q->T2d, p->T); + fe_mul(r->X, p->Z, q->Z); + fe_add(t0, r->X, r->X); + fe_sub(r->X, r->Z, r->Y); + fe_add(r->Y, r->Z, r->Y); + fe_sub(r->Z, t0, r->T); + fe_add(r->T, t0, r->T); } -static uint8_t equal(signed char b, signed char c) { - uint8_t ub = b; - uint8_t uc = c; - uint8_t x = ub ^ uc; /* 0: yes; 1..255: no */ - uint32_t y = x; /* 0: yes; 1..255: no */ - y -= 1; /* 4294967295: yes; 0..254: no */ - y >>= 31; /* 1: yes; 0: no */ - return y; +static uint8_t equal(signed char b, signed char c) +{ + uint8_t ub = b; + uint8_t uc = c; + uint8_t x = ub ^ uc; /* 0: yes; 1..255: no */ + uint32_t y = x; /* 0: yes; 1..255: no */ + y -= 1; /* 4294967295: yes; 0..254: no */ + y >>= 31; /* 1: yes; 0: no */ + return y; } -static void cmov(ge_precomp *t, const ge_precomp *u, uint8_t b) { - fe_cmov(t->yplusx, u->yplusx, b); - fe_cmov(t->yminusx, u->yminusx, b); - fe_cmov(t->xy2d, u->xy2d, b); +static void cmov(ge_precomp *t, const ge_precomp *u, uint8_t b) +{ + fe_cmov(t->yplusx, u->yplusx, b); + fe_cmov(t->yminusx, u->yminusx, b); + fe_cmov(t->xy2d, u->xy2d, b); } /* k25519Precomp[i][j] = (j+1)*256^i*B */ @@ -4105,257 +4186,273 @@ static const ge_precomp k25519Precomp[32][8] = { }, }; -static uint8_t negative(signed char b) { - uint32_t x = b; - x >>= 31; /* 1: yes; 0: no */ - return x; +static uint8_t negative(signed char b) +{ + uint32_t x = b; + + x >>= 31; /* 1: yes; 0: no */ + return x; } -static void table_select(ge_precomp *t, int pos, signed char b) { - ge_precomp minust; - uint8_t bnegative = negative(b); - uint8_t babs = b - ((uint8_t)((-bnegative) & b) << 1); - - ge_precomp_0(t); - cmov(t, &k25519Precomp[pos][0], equal(babs, 1)); - cmov(t, &k25519Precomp[pos][1], equal(babs, 2)); - cmov(t, &k25519Precomp[pos][2], equal(babs, 3)); - cmov(t, &k25519Precomp[pos][3], equal(babs, 4)); - cmov(t, &k25519Precomp[pos][4], equal(babs, 5)); - cmov(t, &k25519Precomp[pos][5], equal(babs, 6)); - cmov(t, &k25519Precomp[pos][6], equal(babs, 7)); - cmov(t, &k25519Precomp[pos][7], equal(babs, 8)); - fe_copy(minust.yplusx, t->yminusx); - fe_copy(minust.yminusx, t->yplusx); - fe_neg(minust.xy2d, t->xy2d); - cmov(t, &minust, bnegative); +static void table_select(ge_precomp *t, int pos, signed char b) +{ + ge_precomp minust; + uint8_t bnegative = negative(b); + uint8_t babs = b - ((uint8_t)((-bnegative) & b) << 1); + + ge_precomp_0(t); + cmov(t, &k25519Precomp[pos][0], equal(babs, 1)); + cmov(t, &k25519Precomp[pos][1], equal(babs, 2)); + cmov(t, &k25519Precomp[pos][2], equal(babs, 3)); + cmov(t, &k25519Precomp[pos][3], equal(babs, 4)); + cmov(t, &k25519Precomp[pos][4], equal(babs, 5)); + cmov(t, &k25519Precomp[pos][5], equal(babs, 6)); + cmov(t, &k25519Precomp[pos][6], equal(babs, 7)); + cmov(t, &k25519Precomp[pos][7], equal(babs, 8)); + fe_copy(minust.yplusx, t->yminusx); + fe_copy(minust.yminusx, t->yplusx); + fe_neg(minust.xy2d, t->xy2d); + cmov(t, &minust, bnegative); } -/* h = a * B +/* + * h = a * B + * * where a = a[0]+256*a[1]+...+256^31 a[31] * B is the Ed25519 base point (x,4/5) with x positive. * * Preconditions: - * a[31] <= 127 */ -static void ge_scalarmult_base(ge_p3 *h, const uint8_t *a) { - signed char e[64]; - signed char carry; - ge_p1p1 r; - ge_p2 s; - ge_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 << 4; - } - e[63] += carry; - /* each e[i] is between -8 and 8 */ - - ge_p3_0(h); - for (i = 1; i < 64; i += 2) { - table_select(&t, i / 2, e[i]); - ge_madd(&r, h, &t); - ge_p1p1_to_p3(h, &r); - } - - ge_p3_dbl(&r, h); - ge_p1p1_to_p2(&s, &r); - ge_p2_dbl(&r, &s); - ge_p1p1_to_p2(&s, &r); - ge_p2_dbl(&r, &s); - ge_p1p1_to_p2(&s, &r); - ge_p2_dbl(&r, &s); - ge_p1p1_to_p3(h, &r); - - for (i = 0; i < 64; i += 2) { - table_select(&t, i / 2, e[i]); - ge_madd(&r, h, &t); + * a[31] <= 127 + */ +static void ge_scalarmult_base(ge_p3 *h, const uint8_t *a) +{ + signed char e[64]; + signed char carry; + ge_p1p1 r; + ge_p2 s; + ge_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 << 4; + } + e[63] += carry; + /* each e[i] is between -8 and 8 */ + + ge_p3_0(h); + for (i = 1; i < 64; i += 2) { + table_select(&t, i / 2, e[i]); + ge_madd(&r, h, &t); + ge_p1p1_to_p3(h, &r); + } + + ge_p3_dbl(&r, h); + ge_p1p1_to_p2(&s, &r); + ge_p2_dbl(&r, &s); + ge_p1p1_to_p2(&s, &r); + ge_p2_dbl(&r, &s); + ge_p1p1_to_p2(&s, &r); + ge_p2_dbl(&r, &s); ge_p1p1_to_p3(h, &r); - } - OPENSSL_cleanse(e, sizeof(e)); + for (i = 0; i < 64; i += 2) { + table_select(&t, i / 2, e[i]); + ge_madd(&r, h, &t); + ge_p1p1_to_p3(h, &r); + } + + OPENSSL_cleanse(e, sizeof(e)); } #if !defined(BASE_2_51_IMPLEMENTED) -/* Replace (f,g) with (g,f) if b == 1; +/* + * 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 fe_cswap(fe f, fe g, unsigned int b) { - size_t i; - b = 0-b; - for (i = 0; i < 10; i++) { - int32_t x = f[i] ^ g[i]; - x &= b; - f[i] ^= x; - g[i] ^= x; - } + * Preconditions: b in {0,1}. + */ +static void fe_cswap(fe f, fe g, unsigned int b) +{ + size_t i; + + b = 0-b; + for (i = 0; i < 10; i++) { + int32_t x = f[i] ^ g[i]; + x &= b; + f[i] ^= x; + g[i] ^= x; + } } -/* h = f * 121666 +/* + * h = f * 121666 + * * Can overlap h with f. * * Preconditions: * |f| bounded by 1.1*2^26,1.1*2^25,1.1*2^26,1.1*2^25,etc. * * Postconditions: - * |h| bounded by 1.1*2^25,1.1*2^24,1.1*2^25,1.1*2^24,etc. */ -static void fe_mul121666(fe h, fe 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]; - int64_t h0 = f0 * (int64_t) 121666; - int64_t h1 = f1 * (int64_t) 121666; - int64_t h2 = f2 * (int64_t) 121666; - int64_t h3 = f3 * (int64_t) 121666; - int64_t h4 = f4 * (int64_t) 121666; - int64_t h5 = f5 * (int64_t) 121666; - int64_t h6 = f6 * (int64_t) 121666; - int64_t h7 = f7 * (int64_t) 121666; - int64_t h8 = f8 * (int64_t) 121666; - int64_t h9 = f9 * (int64_t) 121666; - 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 + (1 << 24); h0 += (carry9 >> 25) * 19; h9 -= carry9 & kTop39Bits; - carry1 = h1 + (1 << 24); h2 += carry1 >> 25; h1 -= carry1 & kTop39Bits; - carry3 = h3 + (1 << 24); h4 += carry3 >> 25; h3 -= carry3 & kTop39Bits; - carry5 = h5 + (1 << 24); h6 += carry5 >> 25; h5 -= carry5 & kTop39Bits; - carry7 = h7 + (1 << 24); h8 += carry7 >> 25; h7 -= carry7 & kTop39Bits; - - carry0 = h0 + (1 << 25); h1 += carry0 >> 26; h0 -= carry0 & kTop38Bits; - carry2 = h2 + (1 << 25); h3 += carry2 >> 26; h2 -= carry2 & kTop38Bits; - carry4 = h4 + (1 << 25); h5 += carry4 >> 26; h4 -= carry4 & kTop38Bits; - carry6 = h6 + (1 << 25); h7 += carry6 >> 26; h6 -= carry6 & kTop38Bits; - carry8 = h8 + (1 << 25); h9 += carry8 >> 26; h8 -= carry8 & kTop38Bits; - - 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| bounded by 1.1*2^25,1.1*2^24,1.1*2^25,1.1*2^24,etc. + */ +static void fe_mul121666(fe h, fe 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]; + int64_t h0 = f0 * (int64_t) 121666; + int64_t h1 = f1 * (int64_t) 121666; + int64_t h2 = f2 * (int64_t) 121666; + int64_t h3 = f3 * (int64_t) 121666; + int64_t h4 = f4 * (int64_t) 121666; + int64_t h5 = f5 * (int64_t) 121666; + int64_t h6 = f6 * (int64_t) 121666; + int64_t h7 = f7 * (int64_t) 121666; + int64_t h8 = f8 * (int64_t) 121666; + int64_t h9 = f9 * (int64_t) 121666; + 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 + (1 << 24); h0 += (carry9 >> 25) * 19; h9 -= carry9 & kTop39Bits; + carry1 = h1 + (1 << 24); h2 += carry1 >> 25; h1 -= carry1 & kTop39Bits; + carry3 = h3 + (1 << 24); h4 += carry3 >> 25; h3 -= carry3 & kTop39Bits; + carry5 = h5 + (1 << 24); h6 += carry5 >> 25; h5 -= carry5 & kTop39Bits; + carry7 = h7 + (1 << 24); h8 += carry7 >> 25; h7 -= carry7 & kTop39Bits; + + carry0 = h0 + (1 << 25); h1 += carry0 >> 26; h0 -= carry0 & kTop38Bits; + carry2 = h2 + (1 << 25); h3 += carry2 >> 26; h2 -= carry2 & kTop38Bits; + carry4 = h4 + (1 << 25); h5 += carry4 >> 26; h4 -= carry4 & kTop38Bits; + carry6 = h6 + (1 << 25); h7 += carry6 >> 26; h6 -= carry6 & kTop38Bits; + carry8 = h8 + (1 << 25); h9 += carry8 >> 26; h8 -= carry8 & kTop38Bits; + + 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 x25519_scalar_mult_generic(uint8_t out[32], const uint8_t scalar[32], const uint8_t point[32]) { - fe x1, x2, z2, x3, z3, tmp0, tmp1; - uint8_t e[32]; - unsigned swap = 0; - int pos; - - memcpy(e, scalar, 32); - e[0] &= 248; - e[31] &= 127; - e[31] |= 64; - fe_frombytes(x1, point); - fe_1(x2); - fe_0(z2); - fe_copy(x3, x1); - fe_1(z3); - - for (pos = 254; pos >= 0; --pos) { - unsigned b = 1 & (e[pos / 8] >> (pos & 7)); - swap ^= b; - fe_cswap(x2, x3, swap); - fe_cswap(z2, z3, swap); - swap = b; - fe_sub(tmp0, x3, z3); - fe_sub(tmp1, x2, z2); - fe_add(x2, x2, z2); - fe_add(z2, x3, z3); - fe_mul(z3, tmp0, x2); - fe_mul(z2, z2, tmp1); - fe_sq(tmp0, tmp1); - fe_sq(tmp1, x2); - fe_add(x3, z3, z2); - fe_sub(z2, z3, z2); - fe_mul(x2, tmp1, tmp0); - fe_sub(tmp1, tmp1, tmp0); - fe_sq(z2, z2); - fe_mul121666(z3, tmp1); - fe_sq(x3, x3); - fe_add(tmp0, tmp0, z3); - fe_mul(z3, x1, z2); - fe_mul(z2, tmp1, tmp0); - } - - fe_invert(z2, z2); - fe_mul(x2, x2, z2); - fe_tobytes(out, x2); - - OPENSSL_cleanse(e, sizeof(e)); + fe x1, x2, z2, x3, z3, tmp0, tmp1; + uint8_t e[32]; + unsigned swap = 0; + int pos; + + memcpy(e, scalar, 32); + e[0] &= 248; + e[31] &= 127; + e[31] |= 64; + fe_frombytes(x1, point); + fe_1(x2); + fe_0(z2); + fe_copy(x3, x1); + fe_1(z3); + + for (pos = 254; pos >= 0; --pos) { + unsigned b = 1 & (e[pos / 8] >> (pos & 7)); + swap ^= b; + fe_cswap(x2, x3, swap); + fe_cswap(z2, z3, swap); + swap = b; + fe_sub(tmp0, x3, z3); + fe_sub(tmp1, x2, z2); + fe_add(x2, x2, z2); + fe_add(z2, x3, z3); + fe_mul(z3, tmp0, x2); + fe_mul(z2, z2, tmp1); + fe_sq(tmp0, tmp1); + fe_sq(tmp1, x2); + fe_add(x3, z3, z2); + fe_sub(z2, z3, z2); + fe_mul(x2, tmp1, tmp0); + fe_sub(tmp1, tmp1, tmp0); + fe_sq(z2, z2); + fe_mul121666(z3, tmp1); + fe_sq(x3, x3); + fe_add(tmp0, tmp0, z3); + fe_mul(z3, x1, z2); + fe_mul(z2, tmp1, tmp0); + } + + fe_invert(z2, z2); + fe_mul(x2, x2, z2); + fe_tobytes(out, x2); + + OPENSSL_cleanse(e, sizeof(e)); } static void x25519_scalar_mult(uint8_t out[32], const uint8_t scalar[32], const uint8_t point[32]) { - x25519_scalar_mult_generic(out, scalar, point); + x25519_scalar_mult_generic(out, scalar, point); } #endif -static void slide(signed char *r, const uint8_t *a) { - int i; - int b; - int k; - - for (i = 0; i < 256; ++i) { - r[i] = 1 & (a[i >> 3] >> (i & 7)); - } - - for (i = 0; i < 256; ++i) { - if (r[i]) { - for (b = 1; b <= 6 && i + b < 256; ++b) { - if (r[i + b]) { - if (r[i] + (r[i + b] << b) <= 15) { - r[i] += r[i + b] << b; - r[i + b] = 0; - } else if (r[i] - (r[i + b] << b) >= -15) { - r[i] -= r[i + b] << b; - for (k = i + b; k < 256; ++k) { - if (!r[k]) { - r[k] = 1; - break; - } - r[k] = 0; +static void slide(signed char *r, const uint8_t *a) +{ + int i; + int b; + int k; + + for (i = 0; i < 256; ++i) { + r[i] = 1 & (a[i >> 3] >> (i & 7)); + } + + for (i = 0; i < 256; ++i) { + if (r[i]) { + for (b = 1; b <= 6 && i + b < 256; ++b) { + if (r[i + b]) { + if (r[i] + (r[i + b] << b) <= 15) { + r[i] += r[i + b] << b; + r[i + b] = 0; + } else if (r[i] - (r[i + b] << b) >= -15) { + r[i] -= r[i + b] << b; + for (k = i + b; k < 256; ++k) { + if (!r[k]) { + r[k] = 1; + break; + } + r[k] = 0; + } + } else { + break; + } + } } - } else { - break; - } } - } } - } } static const ge_precomp Bi[8] = { @@ -4425,1033 +4522,1075 @@ static const ge_precomp Bi[8] = { }, }; -/* r = a * A + b * B +/* + * 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. */ + * B is the Ed25519 base point (x,4/5) with x positive. + */ static void ge_double_scalarmult_vartime(ge_p2 *r, const uint8_t *a, - const ge_p3 *A, const uint8_t *b) { - signed char aslide[256]; - signed char bslide[256]; - ge_cached Ai[8]; /* A,3A,5A,7A,9A,11A,13A,15A */ - ge_p1p1 t; - ge_p3 u; - ge_p3 A2; - int i; - - slide(aslide, a); - slide(bslide, b); - - ge_p3_to_cached(&Ai[0], A); - ge_p3_dbl(&t, A); - ge_p1p1_to_p3(&A2, &t); - ge_add(&t, &A2, &Ai[0]); - ge_p1p1_to_p3(&u, &t); - ge_p3_to_cached(&Ai[1], &u); - ge_add(&t, &A2, &Ai[1]); - ge_p1p1_to_p3(&u, &t); - ge_p3_to_cached(&Ai[2], &u); - ge_add(&t, &A2, &Ai[2]); - ge_p1p1_to_p3(&u, &t); - ge_p3_to_cached(&Ai[3], &u); - ge_add(&t, &A2, &Ai[3]); - ge_p1p1_to_p3(&u, &t); - ge_p3_to_cached(&Ai[4], &u); - ge_add(&t, &A2, &Ai[4]); - ge_p1p1_to_p3(&u, &t); - ge_p3_to_cached(&Ai[5], &u); - ge_add(&t, &A2, &Ai[5]); - ge_p1p1_to_p3(&u, &t); - ge_p3_to_cached(&Ai[6], &u); - ge_add(&t, &A2, &Ai[6]); - ge_p1p1_to_p3(&u, &t); - ge_p3_to_cached(&Ai[7], &u); - - ge_p2_0(r); - - for (i = 255; i >= 0; --i) { - if (aslide[i] || bslide[i]) { - break; + const ge_p3 *A, const uint8_t *b) +{ + signed char aslide[256]; + signed char bslide[256]; + ge_cached Ai[8]; /* A,3A,5A,7A,9A,11A,13A,15A */ + ge_p1p1 t; + ge_p3 u; + ge_p3 A2; + int i; + + slide(aslide, a); + slide(bslide, b); + + ge_p3_to_cached(&Ai[0], A); + ge_p3_dbl(&t, A); + ge_p1p1_to_p3(&A2, &t); + ge_add(&t, &A2, &Ai[0]); + ge_p1p1_to_p3(&u, &t); + ge_p3_to_cached(&Ai[1], &u); + ge_add(&t, &A2, &Ai[1]); + ge_p1p1_to_p3(&u, &t); + ge_p3_to_cached(&Ai[2], &u); + ge_add(&t, &A2, &Ai[2]); + ge_p1p1_to_p3(&u, &t); + ge_p3_to_cached(&Ai[3], &u); + ge_add(&t, &A2, &Ai[3]); + ge_p1p1_to_p3(&u, &t); + ge_p3_to_cached(&Ai[4], &u); + ge_add(&t, &A2, &Ai[4]); + ge_p1p1_to_p3(&u, &t); + ge_p3_to_cached(&Ai[5], &u); + ge_add(&t, &A2, &Ai[5]); + ge_p1p1_to_p3(&u, &t); + ge_p3_to_cached(&Ai[6], &u); + ge_add(&t, &A2, &Ai[6]); + ge_p1p1_to_p3(&u, &t); + ge_p3_to_cached(&Ai[7], &u); + + ge_p2_0(r); + + for (i = 255; i >= 0; --i) { + if (aslide[i] || bslide[i]) { + break; + } } - } - for (; i >= 0; --i) { - ge_p2_dbl(&t, r); + for (; i >= 0; --i) { + ge_p2_dbl(&t, r); - if (aslide[i] > 0) { - ge_p1p1_to_p3(&u, &t); - ge_add(&t, &u, &Ai[aslide[i] / 2]); - } else if (aslide[i] < 0) { - ge_p1p1_to_p3(&u, &t); - ge_sub(&t, &u, &Ai[(-aslide[i]) / 2]); - } + if (aslide[i] > 0) { + ge_p1p1_to_p3(&u, &t); + ge_add(&t, &u, &Ai[aslide[i] / 2]); + } else if (aslide[i] < 0) { + ge_p1p1_to_p3(&u, &t); + ge_sub(&t, &u, &Ai[(-aslide[i]) / 2]); + } - if (bslide[i] > 0) { - ge_p1p1_to_p3(&u, &t); - ge_madd(&t, &u, &Bi[bslide[i] / 2]); - } else if (bslide[i] < 0) { - ge_p1p1_to_p3(&u, &t); - ge_msub(&t, &u, &Bi[(-bslide[i]) / 2]); - } + if (bslide[i] > 0) { + ge_p1p1_to_p3(&u, &t); + ge_madd(&t, &u, &Bi[bslide[i] / 2]); + } else if (bslide[i] < 0) { + ge_p1p1_to_p3(&u, &t); + ge_msub(&t, &u, &Bi[(-bslide[i]) / 2]); + } - ge_p1p1_to_p2(r, &t); - } + ge_p1p1_to_p2(r, &t); + } } -/* The set of scalars is \Z/l - * where l = 2^252 + 27742317777372353535851937790883648493. */ - -/* Input: +/* + * The set of scalars is \Z/l + * where l = 2^252 + 27742317777372353535851937790883648493. + * + * 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. */ -static void x25519_sc_reduce(uint8_t *s) { - 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; - s23 = 0; - - s10 += s22 * 666643; - s11 += s22 * 470296; - s12 += s22 * 654183; - s13 -= s22 * 997805; - s14 += s22 * 136657; - s15 -= s22 * 683901; - s22 = 0; - - s9 += s21 * 666643; - s10 += s21 * 470296; - s11 += s21 * 654183; - s12 -= s21 * 997805; - s13 += s21 * 136657; - s14 -= s21 * 683901; - s21 = 0; - - s8 += s20 * 666643; - s9 += s20 * 470296; - s10 += s20 * 654183; - s11 -= s20 * 997805; - s12 += s20 * 136657; - s13 -= s20 * 683901; - s20 = 0; - - s7 += s19 * 666643; - s8 += s19 * 470296; - s9 += s19 * 654183; - s10 -= s19 * 997805; - s11 += s19 * 136657; - s12 -= s19 * 683901; - s19 = 0; - - s6 += s18 * 666643; - s7 += s18 * 470296; - s8 += s18 * 654183; - s9 -= s18 * 997805; - s10 += s18 * 136657; - s11 -= s18 * 683901; - s18 = 0; - - carry6 = (s6 + (1 << 20)) >> 21; - s7 += carry6; - s6 -= carry6 * (1 << 21); - carry8 = (s8 + (1 << 20)) >> 21; - s9 += carry8; - s8 -= carry8 * (1 << 21); - carry10 = (s10 + (1 << 20)) >> 21; - s11 += carry10; - s10 -= carry10 * (1 << 21); - carry12 = (s12 + (1 << 20)) >> 21; - s13 += carry12; - s12 -= carry12 * (1 << 21); - carry14 = (s14 + (1 << 20)) >> 21; - s15 += carry14; - s14 -= carry14 * (1 << 21); - carry16 = (s16 + (1 << 20)) >> 21; - s17 += carry16; - s16 -= carry16 * (1 << 21); - - carry7 = (s7 + (1 << 20)) >> 21; - s8 += carry7; - s7 -= carry7 * (1 << 21); - carry9 = (s9 + (1 << 20)) >> 21; - s10 += carry9; - s9 -= carry9 * (1 << 21); - carry11 = (s11 + (1 << 20)) >> 21; - s12 += carry11; - s11 -= carry11 * (1 << 21); - carry13 = (s13 + (1 << 20)) >> 21; - s14 += carry13; - s13 -= carry13 * (1 << 21); - carry15 = (s15 + (1 << 20)) >> 21; - s16 += carry15; - s15 -= carry15 * (1 << 21); - - s5 += s17 * 666643; - s6 += s17 * 470296; - s7 += s17 * 654183; - s8 -= s17 * 997805; - s9 += s17 * 136657; - s10 -= s17 * 683901; - s17 = 0; - - s4 += s16 * 666643; - s5 += s16 * 470296; - s6 += s16 * 654183; - s7 -= s16 * 997805; - s8 += s16 * 136657; - s9 -= s16 * 683901; - s16 = 0; - - s3 += s15 * 666643; - s4 += s15 * 470296; - s5 += s15 * 654183; - s6 -= s15 * 997805; - s7 += s15 * 136657; - s8 -= s15 * 683901; - s15 = 0; - - s2 += s14 * 666643; - s3 += s14 * 470296; - s4 += s14 * 654183; - s5 -= s14 * 997805; - s6 += s14 * 136657; - s7 -= s14 * 683901; - s14 = 0; - - s1 += s13 * 666643; - s2 += s13 * 470296; - s3 += s13 * 654183; - s4 -= s13 * 997805; - s5 += s13 * 136657; - s6 -= s13 * 683901; - s13 = 0; - - s0 += s12 * 666643; - s1 += s12 * 470296; - s2 += s12 * 654183; - s3 -= s12 * 997805; - s4 += s12 * 136657; - s5 -= s12 * 683901; - s12 = 0; - - carry0 = (s0 + (1 << 20)) >> 21; - s1 += carry0; - s0 -= carry0 * (1 << 21); - carry2 = (s2 + (1 << 20)) >> 21; - s3 += carry2; - s2 -= carry2 * (1 << 21); - carry4 = (s4 + (1 << 20)) >> 21; - s5 += carry4; - s4 -= carry4 * (1 << 21); - carry6 = (s6 + (1 << 20)) >> 21; - s7 += carry6; - s6 -= carry6 * (1 << 21); - carry8 = (s8 + (1 << 20)) >> 21; - s9 += carry8; - s8 -= carry8 * (1 << 21); - carry10 = (s10 + (1 << 20)) >> 21; - s11 += carry10; - s10 -= carry10 * (1 << 21); - - carry1 = (s1 + (1 << 20)) >> 21; - s2 += carry1; - s1 -= carry1 * (1 << 21); - carry3 = (s3 + (1 << 20)) >> 21; - s4 += carry3; - s3 -= carry3 * (1 << 21); - carry5 = (s5 + (1 << 20)) >> 21; - s6 += carry5; - s5 -= carry5 * (1 << 21); - carry7 = (s7 + (1 << 20)) >> 21; - s8 += carry7; - s7 -= carry7 * (1 << 21); - carry9 = (s9 + (1 << 20)) >> 21; - s10 += carry9; - s9 -= carry9 * (1 << 21); - carry11 = (s11 + (1 << 20)) >> 21; - s12 += carry11; - s11 -= carry11 * (1 << 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 * (1 << 21); - carry1 = s1 >> 21; - s2 += carry1; - s1 -= carry1 * (1 << 21); - carry2 = s2 >> 21; - s3 += carry2; - s2 -= carry2 * (1 << 21); - carry3 = s3 >> 21; - s4 += carry3; - s3 -= carry3 * (1 << 21); - carry4 = s4 >> 21; - s5 += carry4; - s4 -= carry4 * (1 << 21); - carry5 = s5 >> 21; - s6 += carry5; - s5 -= carry5 * (1 << 21); - carry6 = s6 >> 21; - s7 += carry6; - s6 -= carry6 * (1 << 21); - carry7 = s7 >> 21; - s8 += carry7; - s7 -= carry7 * (1 << 21); - carry8 = s8 >> 21; - s9 += carry8; - s8 -= carry8 * (1 << 21); - carry9 = s9 >> 21; - s10 += carry9; - s9 -= carry9 * (1 << 21); - carry10 = s10 >> 21; - s11 += carry10; - s10 -= carry10 * (1 << 21); - carry11 = s11 >> 21; - s12 += carry11; - s11 -= carry11 * (1 << 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 * (1 << 21); - carry1 = s1 >> 21; - s2 += carry1; - s1 -= carry1 * (1 << 21); - carry2 = s2 >> 21; - s3 += carry2; - s2 -= carry2 * (1 << 21); - carry3 = s3 >> 21; - s4 += carry3; - s3 -= carry3 * (1 << 21); - carry4 = s4 >> 21; - s5 += carry4; - s4 -= carry4 * (1 << 21); - carry5 = s5 >> 21; - s6 += carry5; - s5 -= carry5 * (1 << 21); - carry6 = s6 >> 21; - s7 += carry6; - s6 -= carry6 * (1 << 21); - carry7 = s7 >> 21; - s8 += carry7; - s7 -= carry7 * (1 << 21); - carry8 = s8 >> 21; - s9 += carry8; - s8 -= carry8 * (1 << 21); - carry9 = s9 >> 21; - s10 += carry9; - s9 -= carry9 * (1 << 21); - carry10 = s10 >> 21; - s11 += carry10; - s10 -= carry10 * (1 << 21); - - s[0] = (uint8_t)(s0 >> 0); - s[1] = (uint8_t)(s0 >> 8); - s[2] = (uint8_t)((s0 >> 16) | (s1 << 5)); - s[3] = (uint8_t)(s1 >> 3); - s[4] = (uint8_t)(s1 >> 11); - s[5] = (uint8_t)((s1 >> 19) | (s2 << 2)); - s[6] = (uint8_t)(s2 >> 6); - s[7] = (uint8_t)((s2 >> 14) | (s3 << 7)); - s[8] = (uint8_t)(s3 >> 1); - s[9] = (uint8_t)(s3 >> 9); - s[10] = (uint8_t)((s3 >> 17) | (s4 << 4)); - s[11] = (uint8_t)(s4 >> 4); - s[12] = (uint8_t)(s4 >> 12); - s[13] = (uint8_t)((s4 >> 20) | (s5 << 1)); - s[14] = (uint8_t)(s5 >> 7); - s[15] = (uint8_t)((s5 >> 15) | (s6 << 6)); - s[16] = (uint8_t)(s6 >> 2); - s[17] = (uint8_t)(s6 >> 10); - s[18] = (uint8_t)((s6 >> 18) | (s7 << 3)); - s[19] = (uint8_t)(s7 >> 5); - s[20] = (uint8_t)(s7 >> 13); - s[21] = (uint8_t)(s8 >> 0); - s[22] = (uint8_t)(s8 >> 8); - s[23] = (uint8_t)((s8 >> 16) | (s9 << 5)); - s[24] = (uint8_t)(s9 >> 3); - s[25] = (uint8_t)(s9 >> 11); - s[26] = (uint8_t)((s9 >> 19) | (s10 << 2)); - s[27] = (uint8_t)(s10 >> 6); - s[28] = (uint8_t)((s10 >> 14) | (s11 << 7)); - s[29] = (uint8_t)(s11 >> 1); - s[30] = (uint8_t)(s11 >> 9); - s[31] = (uint8_t)(s11 >> 17); + * Overwrites s in place. +*/ +static void x25519_sc_reduce(uint8_t *s) +{ + int64_t s0 = kBottom21Bits & load_3(s); + int64_t s1 = kBottom21Bits & (load_4(s + 2) >> 5); + int64_t s2 = kBottom21Bits & (load_3(s + 5) >> 2); + int64_t s3 = kBottom21Bits & (load_4(s + 7) >> 7); + int64_t s4 = kBottom21Bits & (load_4(s + 10) >> 4); + int64_t s5 = kBottom21Bits & (load_3(s + 13) >> 1); + int64_t s6 = kBottom21Bits & (load_4(s + 15) >> 6); + int64_t s7 = kBottom21Bits & (load_3(s + 18) >> 3); + int64_t s8 = kBottom21Bits & load_3(s + 21); + int64_t s9 = kBottom21Bits & (load_4(s + 23) >> 5); + int64_t s10 = kBottom21Bits & (load_3(s + 26) >> 2); + int64_t s11 = kBottom21Bits & (load_4(s + 28) >> 7); + int64_t s12 = kBottom21Bits & (load_4(s + 31) >> 4); + int64_t s13 = kBottom21Bits & (load_3(s + 34) >> 1); + int64_t s14 = kBottom21Bits & (load_4(s + 36) >> 6); + int64_t s15 = kBottom21Bits & (load_3(s + 39) >> 3); + int64_t s16 = kBottom21Bits & load_3(s + 42); + int64_t s17 = kBottom21Bits & (load_4(s + 44) >> 5); + int64_t s18 = kBottom21Bits & (load_3(s + 47) >> 2); + int64_t s19 = kBottom21Bits & (load_4(s + 49) >> 7); + int64_t s20 = kBottom21Bits & (load_4(s + 52) >> 4); + int64_t s21 = kBottom21Bits & (load_3(s + 55) >> 1); + int64_t s22 = kBottom21Bits & (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; + s23 = 0; + + s10 += s22 * 666643; + s11 += s22 * 470296; + s12 += s22 * 654183; + s13 -= s22 * 997805; + s14 += s22 * 136657; + s15 -= s22 * 683901; + s22 = 0; + + s9 += s21 * 666643; + s10 += s21 * 470296; + s11 += s21 * 654183; + s12 -= s21 * 997805; + s13 += s21 * 136657; + s14 -= s21 * 683901; + s21 = 0; + + s8 += s20 * 666643; + s9 += s20 * 470296; + s10 += s20 * 654183; + s11 -= s20 * 997805; + s12 += s20 * 136657; + s13 -= s20 * 683901; + s20 = 0; + + s7 += s19 * 666643; + s8 += s19 * 470296; + s9 += s19 * 654183; + s10 -= s19 * 997805; + s11 += s19 * 136657; + s12 -= s19 * 683901; + s19 = 0; + + s6 += s18 * 666643; + s7 += s18 * 470296; + s8 += s18 * 654183; + s9 -= s18 * 997805; + s10 += s18 * 136657; + s11 -= s18 * 683901; + s18 = 0; + + carry6 = (s6 + (1 << 20)) >> 21; + s7 += carry6; + s6 -= carry6 * (1 << 21); + carry8 = (s8 + (1 << 20)) >> 21; + s9 += carry8; + s8 -= carry8 * (1 << 21); + carry10 = (s10 + (1 << 20)) >> 21; + s11 += carry10; + s10 -= carry10 * (1 << 21); + carry12 = (s12 + (1 << 20)) >> 21; + s13 += carry12; + s12 -= carry12 * (1 << 21); + carry14 = (s14 + (1 << 20)) >> 21; + s15 += carry14; + s14 -= carry14 * (1 << 21); + carry16 = (s16 + (1 << 20)) >> 21; + s17 += carry16; + s16 -= carry16 * (1 << 21); + + carry7 = (s7 + (1 << 20)) >> 21; + s8 += carry7; + s7 -= carry7 * (1 << 21); + carry9 = (s9 + (1 << 20)) >> 21; + s10 += carry9; + s9 -= carry9 * (1 << 21); + carry11 = (s11 + (1 << 20)) >> 21; + s12 += carry11; + s11 -= carry11 * (1 << 21); + carry13 = (s13 + (1 << 20)) >> 21; + s14 += carry13; + s13 -= carry13 * (1 << 21); + carry15 = (s15 + (1 << 20)) >> 21; + s16 += carry15; + s15 -= carry15 * (1 << 21); + + s5 += s17 * 666643; + s6 += s17 * 470296; + s7 += s17 * 654183; + s8 -= s17 * 997805; + s9 += s17 * 136657; + s10 -= s17 * 683901; + s17 = 0; + + s4 += s16 * 666643; + s5 += s16 * 470296; + s6 += s16 * 654183; + s7 -= s16 * 997805; + s8 += s16 * 136657; + s9 -= s16 * 683901; + s16 = 0; + + s3 += s15 * 666643; + s4 += s15 * 470296; + s5 += s15 * 654183; + s6 -= s15 * 997805; + s7 += s15 * 136657; + s8 -= s15 * 683901; + s15 = 0; + + s2 += s14 * 666643; + s3 += s14 * 470296; + s4 += s14 * 654183; + s5 -= s14 * 997805; + s6 += s14 * 136657; + s7 -= s14 * 683901; + s14 = 0; + + s1 += s13 * 666643; + s2 += s13 * 470296; + s3 += s13 * 654183; + s4 -= s13 * 997805; + s5 += s13 * 136657; + s6 -= s13 * 683901; + s13 = 0; + + s0 += s12 * 666643; + s1 += s12 * 470296; + s2 += s12 * 654183; + s3 -= s12 * 997805; + s4 += s12 * 136657; + s5 -= s12 * 683901; + s12 = 0; + + carry0 = (s0 + (1 << 20)) >> 21; + s1 += carry0; + s0 -= carry0 * (1 << 21); + carry2 = (s2 + (1 << 20)) >> 21; + s3 += carry2; + s2 -= carry2 * (1 << 21); + carry4 = (s4 + (1 << 20)) >> 21; + s5 += carry4; + s4 -= carry4 * (1 << 21); + carry6 = (s6 + (1 << 20)) >> 21; + s7 += carry6; + s6 -= carry6 * (1 << 21); + carry8 = (s8 + (1 << 20)) >> 21; + s9 += carry8; + s8 -= carry8 * (1 << 21); + carry10 = (s10 + (1 << 20)) >> 21; + s11 += carry10; + s10 -= carry10 * (1 << 21); + + carry1 = (s1 + (1 << 20)) >> 21; + s2 += carry1; + s1 -= carry1 * (1 << 21); + carry3 = (s3 + (1 << 20)) >> 21; + s4 += carry3; + s3 -= carry3 * (1 << 21); + carry5 = (s5 + (1 << 20)) >> 21; + s6 += carry5; + s5 -= carry5 * (1 << 21); + carry7 = (s7 + (1 << 20)) >> 21; + s8 += carry7; + s7 -= carry7 * (1 << 21); + carry9 = (s9 + (1 << 20)) >> 21; + s10 += carry9; + s9 -= carry9 * (1 << 21); + carry11 = (s11 + (1 << 20)) >> 21; + s12 += carry11; + s11 -= carry11 * (1 << 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 * (1 << 21); + carry1 = s1 >> 21; + s2 += carry1; + s1 -= carry1 * (1 << 21); + carry2 = s2 >> 21; + s3 += carry2; + s2 -= carry2 * (1 << 21); + carry3 = s3 >> 21; + s4 += carry3; + s3 -= carry3 * (1 << 21); + carry4 = s4 >> 21; + s5 += carry4; + s4 -= carry4 * (1 << 21); + carry5 = s5 >> 21; + s6 += carry5; + s5 -= carry5 * (1 << 21); + carry6 = s6 >> 21; + s7 += carry6; + s6 -= carry6 * (1 << 21); + carry7 = s7 >> 21; + s8 += carry7; + s7 -= carry7 * (1 << 21); + carry8 = s8 >> 21; + s9 += carry8; + s8 -= carry8 * (1 << 21); + carry9 = s9 >> 21; + s10 += carry9; + s9 -= carry9 * (1 << 21); + carry10 = s10 >> 21; + s11 += carry10; + s10 -= carry10 * (1 << 21); + carry11 = s11 >> 21; + s12 += carry11; + s11 -= carry11 * (1 << 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 * (1 << 21); + carry1 = s1 >> 21; + s2 += carry1; + s1 -= carry1 * (1 << 21); + carry2 = s2 >> 21; + s3 += carry2; + s2 -= carry2 * (1 << 21); + carry3 = s3 >> 21; + s4 += carry3; + s3 -= carry3 * (1 << 21); + carry4 = s4 >> 21; + s5 += carry4; + s4 -= carry4 * (1 << 21); + carry5 = s5 >> 21; + s6 += carry5; + s5 -= carry5 * (1 << 21); + carry6 = s6 >> 21; + s7 += carry6; + s6 -= carry6 * (1 << 21); + carry7 = s7 >> 21; + s8 += carry7; + s7 -= carry7 * (1 << 21); + carry8 = s8 >> 21; + s9 += carry8; + s8 -= carry8 * (1 << 21); + carry9 = s9 >> 21; + s10 += carry9; + s9 -= carry9 * (1 << 21); + carry10 = s10 >> 21; + s11 += carry10; + s10 -= carry10 * (1 << 21); + + s[ 0] = (uint8_t) (s0 >> 0); + s[ 1] = (uint8_t) (s0 >> 8); + s[ 2] = (uint8_t)((s0 >> 16) | (s1 << 5)); + s[ 3] = (uint8_t) (s1 >> 3); + s[ 4] = (uint8_t) (s1 >> 11); + s[ 5] = (uint8_t)((s1 >> 19) | (s2 << 2)); + s[ 6] = (uint8_t) (s2 >> 6); + s[ 7] = (uint8_t)((s2 >> 14) | (s3 << 7)); + s[ 8] = (uint8_t) (s3 >> 1); + s[ 9] = (uint8_t) (s3 >> 9); + s[10] = (uint8_t)((s3 >> 17) | (s4 << 4)); + s[11] = (uint8_t) (s4 >> 4); + s[12] = (uint8_t) (s4 >> 12); + s[13] = (uint8_t)((s4 >> 20) | (s5 << 1)); + s[14] = (uint8_t) (s5 >> 7); + s[15] = (uint8_t)((s5 >> 15) | (s6 << 6)); + s[16] = (uint8_t) (s6 >> 2); + s[17] = (uint8_t) (s6 >> 10); + s[18] = (uint8_t)((s6 >> 18) | (s7 << 3)); + s[19] = (uint8_t) (s7 >> 5); + s[20] = (uint8_t) (s7 >> 13); + s[21] = (uint8_t) (s8 >> 0); + s[22] = (uint8_t) (s8 >> 8); + s[23] = (uint8_t)((s8 >> 16) | (s9 << 5)); + s[24] = (uint8_t) (s9 >> 3); + s[25] = (uint8_t) (s9 >> 11); + s[26] = (uint8_t)((s9 >> 19) | (s10 << 2)); + s[27] = (uint8_t) (s10 >> 6); + s[28] = (uint8_t)((s10 >> 14) | (s11 << 7)); + s[29] = (uint8_t) (s11 >> 1); + s[30] = (uint8_t) (s11 >> 9); + s[31] = (uint8_t) (s11 >> 17); } -/* Input: +/* + * 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. */ + * where l = 2^252 + 27742317777372353535851937790883648493. + */ static void sc_muladd(uint8_t *s, const uint8_t *a, const uint8_t *b, - const uint8_t *c) { - 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 + (1 << 20)) >> 21; - s1 += carry0; - s0 -= carry0 * (1 << 21); - carry2 = (s2 + (1 << 20)) >> 21; - s3 += carry2; - s2 -= carry2 * (1 << 21); - carry4 = (s4 + (1 << 20)) >> 21; - s5 += carry4; - s4 -= carry4 * (1 << 21); - carry6 = (s6 + (1 << 20)) >> 21; - s7 += carry6; - s6 -= carry6 * (1 << 21); - carry8 = (s8 + (1 << 20)) >> 21; - s9 += carry8; - s8 -= carry8 * (1 << 21); - carry10 = (s10 + (1 << 20)) >> 21; - s11 += carry10; - s10 -= carry10 * (1 << 21); - carry12 = (s12 + (1 << 20)) >> 21; - s13 += carry12; - s12 -= carry12 * (1 << 21); - carry14 = (s14 + (1 << 20)) >> 21; - s15 += carry14; - s14 -= carry14 * (1 << 21); - carry16 = (s16 + (1 << 20)) >> 21; - s17 += carry16; - s16 -= carry16 * (1 << 21); - carry18 = (s18 + (1 << 20)) >> 21; - s19 += carry18; - s18 -= carry18 * (1 << 21); - carry20 = (s20 + (1 << 20)) >> 21; - s21 += carry20; - s20 -= carry20 * (1 << 21); - carry22 = (s22 + (1 << 20)) >> 21; - s23 += carry22; - s22 -= carry22 * (1 << 21); - - carry1 = (s1 + (1 << 20)) >> 21; - s2 += carry1; - s1 -= carry1 * (1 << 21); - carry3 = (s3 + (1 << 20)) >> 21; - s4 += carry3; - s3 -= carry3 * (1 << 21); - carry5 = (s5 + (1 << 20)) >> 21; - s6 += carry5; - s5 -= carry5 * (1 << 21); - carry7 = (s7 + (1 << 20)) >> 21; - s8 += carry7; - s7 -= carry7 * (1 << 21); - carry9 = (s9 + (1 << 20)) >> 21; - s10 += carry9; - s9 -= carry9 * (1 << 21); - carry11 = (s11 + (1 << 20)) >> 21; - s12 += carry11; - s11 -= carry11 * (1 << 21); - carry13 = (s13 + (1 << 20)) >> 21; - s14 += carry13; - s13 -= carry13 * (1 << 21); - carry15 = (s15 + (1 << 20)) >> 21; - s16 += carry15; - s15 -= carry15 * (1 << 21); - carry17 = (s17 + (1 << 20)) >> 21; - s18 += carry17; - s17 -= carry17 * (1 << 21); - carry19 = (s19 + (1 << 20)) >> 21; - s20 += carry19; - s19 -= carry19 * (1 << 21); - carry21 = (s21 + (1 << 20)) >> 21; - s22 += carry21; - s21 -= carry21 * (1 << 21); - - s11 += s23 * 666643; - s12 += s23 * 470296; - s13 += s23 * 654183; - s14 -= s23 * 997805; - s15 += s23 * 136657; - s16 -= s23 * 683901; - s23 = 0; - - s10 += s22 * 666643; - s11 += s22 * 470296; - s12 += s22 * 654183; - s13 -= s22 * 997805; - s14 += s22 * 136657; - s15 -= s22 * 683901; - s22 = 0; - - s9 += s21 * 666643; - s10 += s21 * 470296; - s11 += s21 * 654183; - s12 -= s21 * 997805; - s13 += s21 * 136657; - s14 -= s21 * 683901; - s21 = 0; - - s8 += s20 * 666643; - s9 += s20 * 470296; - s10 += s20 * 654183; - s11 -= s20 * 997805; - s12 += s20 * 136657; - s13 -= s20 * 683901; - s20 = 0; - - s7 += s19 * 666643; - s8 += s19 * 470296; - s9 += s19 * 654183; - s10 -= s19 * 997805; - s11 += s19 * 136657; - s12 -= s19 * 683901; - s19 = 0; - - s6 += s18 * 666643; - s7 += s18 * 470296; - s8 += s18 * 654183; - s9 -= s18 * 997805; - s10 += s18 * 136657; - s11 -= s18 * 683901; - s18 = 0; - - carry6 = (s6 + (1 << 20)) >> 21; - s7 += carry6; - s6 -= carry6 * (1 << 21); - carry8 = (s8 + (1 << 20)) >> 21; - s9 += carry8; - s8 -= carry8 * (1 << 21); - carry10 = (s10 + (1 << 20)) >> 21; - s11 += carry10; - s10 -= carry10 * (1 << 21); - carry12 = (s12 + (1 << 20)) >> 21; - s13 += carry12; - s12 -= carry12 * (1 << 21); - carry14 = (s14 + (1 << 20)) >> 21; - s15 += carry14; - s14 -= carry14 * (1 << 21); - carry16 = (s16 + (1 << 20)) >> 21; - s17 += carry16; - s16 -= carry16 * (1 << 21); - - carry7 = (s7 + (1 << 20)) >> 21; - s8 += carry7; - s7 -= carry7 * (1 << 21); - carry9 = (s9 + (1 << 20)) >> 21; - s10 += carry9; - s9 -= carry9 * (1 << 21); - carry11 = (s11 + (1 << 20)) >> 21; - s12 += carry11; - s11 -= carry11 * (1 << 21); - carry13 = (s13 + (1 << 20)) >> 21; - s14 += carry13; - s13 -= carry13 * (1 << 21); - carry15 = (s15 + (1 << 20)) >> 21; - s16 += carry15; - s15 -= carry15 * (1 << 21); - - s5 += s17 * 666643; - s6 += s17 * 470296; - s7 += s17 * 654183; - s8 -= s17 * 997805; - s9 += s17 * 136657; - s10 -= s17 * 683901; - s17 = 0; - - s4 += s16 * 666643; - s5 += s16 * 470296; - s6 += s16 * 654183; - s7 -= s16 * 997805; - s8 += s16 * 136657; - s9 -= s16 * 683901; - s16 = 0; - - s3 += s15 * 666643; - s4 += s15 * 470296; - s5 += s15 * 654183; - s6 -= s15 * 997805; - s7 += s15 * 136657; - s8 -= s15 * 683901; - s15 = 0; - - s2 += s14 * 666643; - s3 += s14 * 470296; - s4 += s14 * 654183; - s5 -= s14 * 997805; - s6 += s14 * 136657; - s7 -= s14 * 683901; - s14 = 0; - - s1 += s13 * 666643; - s2 += s13 * 470296; - s3 += s13 * 654183; - s4 -= s13 * 997805; - s5 += s13 * 136657; - s6 -= s13 * 683901; - s13 = 0; - - s0 += s12 * 666643; - s1 += s12 * 470296; - s2 += s12 * 654183; - s3 -= s12 * 997805; - s4 += s12 * 136657; - s5 -= s12 * 683901; - s12 = 0; - - carry0 = (s0 + (1 << 20)) >> 21; - s1 += carry0; - s0 -= carry0 * (1 << 21); - carry2 = (s2 + (1 << 20)) >> 21; - s3 += carry2; - s2 -= carry2 * (1 << 21); - carry4 = (s4 + (1 << 20)) >> 21; - s5 += carry4; - s4 -= carry4 * (1 << 21); - carry6 = (s6 + (1 << 20)) >> 21; - s7 += carry6; - s6 -= carry6 * (1 << 21); - carry8 = (s8 + (1 << 20)) >> 21; - s9 += carry8; - s8 -= carry8 * (1 << 21); - carry10 = (s10 + (1 << 20)) >> 21; - s11 += carry10; - s10 -= carry10 * (1 << 21); - - carry1 = (s1 + (1 << 20)) >> 21; - s2 += carry1; - s1 -= carry1 * (1 << 21); - carry3 = (s3 + (1 << 20)) >> 21; - s4 += carry3; - s3 -= carry3 * (1 << 21); - carry5 = (s5 + (1 << 20)) >> 21; - s6 += carry5; - s5 -= carry5 * (1 << 21); - carry7 = (s7 + (1 << 20)) >> 21; - s8 += carry7; - s7 -= carry7 * (1 << 21); - carry9 = (s9 + (1 << 20)) >> 21; - s10 += carry9; - s9 -= carry9 * (1 << 21); - carry11 = (s11 + (1 << 20)) >> 21; - s12 += carry11; - s11 -= carry11 * (1 << 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 * (1 << 21); - carry1 = s1 >> 21; - s2 += carry1; - s1 -= carry1 * (1 << 21); - carry2 = s2 >> 21; - s3 += carry2; - s2 -= carry2 * (1 << 21); - carry3 = s3 >> 21; - s4 += carry3; - s3 -= carry3 * (1 << 21); - carry4 = s4 >> 21; - s5 += carry4; - s4 -= carry4 * (1 << 21); - carry5 = s5 >> 21; - s6 += carry5; - s5 -= carry5 * (1 << 21); - carry6 = s6 >> 21; - s7 += carry6; - s6 -= carry6 * (1 << 21); - carry7 = s7 >> 21; - s8 += carry7; - s7 -= carry7 * (1 << 21); - carry8 = s8 >> 21; - s9 += carry8; - s8 -= carry8 * (1 << 21); - carry9 = s9 >> 21; - s10 += carry9; - s9 -= carry9 * (1 << 21); - carry10 = s10 >> 21; - s11 += carry10; - s10 -= carry10 * (1 << 21); - carry11 = s11 >> 21; - s12 += carry11; - s11 -= carry11 * (1 << 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 * (1 << 21); - carry1 = s1 >> 21; - s2 += carry1; - s1 -= carry1 * (1 << 21); - carry2 = s2 >> 21; - s3 += carry2; - s2 -= carry2 * (1 << 21); - carry3 = s3 >> 21; - s4 += carry3; - s3 -= carry3 * (1 << 21); - carry4 = s4 >> 21; - s5 += carry4; - s4 -= carry4 * (1 << 21); - carry5 = s5 >> 21; - s6 += carry5; - s5 -= carry5 * (1 << 21); - carry6 = s6 >> 21; - s7 += carry6; - s6 -= carry6 * (1 << 21); - carry7 = s7 >> 21; - s8 += carry7; - s7 -= carry7 * (1 << 21); - carry8 = s8 >> 21; - s9 += carry8; - s8 -= carry8 * (1 << 21); - carry9 = s9 >> 21; - s10 += carry9; - s9 -= carry9 * (1 << 21); - carry10 = s10 >> 21; - s11 += carry10; - s10 -= carry10 * (1 << 21); - - s[0] = (uint8_t)(s0 >> 0); - s[1] = (uint8_t)(s0 >> 8); - s[2] = (uint8_t)((s0 >> 16) | (s1 << 5)); - s[3] = (uint8_t)(s1 >> 3); - s[4] = (uint8_t)(s1 >> 11); - s[5] = (uint8_t)((s1 >> 19) | (s2 << 2)); - s[6] = (uint8_t)(s2 >> 6); - s[7] = (uint8_t)((s2 >> 14) | (s3 << 7)); - s[8] = (uint8_t)(s3 >> 1); - s[9] = (uint8_t)(s3 >> 9); - s[10] = (uint8_t)((s3 >> 17) | (s4 << 4)); - s[11] = (uint8_t)(s4 >> 4); - s[12] = (uint8_t)(s4 >> 12); - s[13] = (uint8_t)((s4 >> 20) | (s5 << 1)); - s[14] = (uint8_t)(s5 >> 7); - s[15] = (uint8_t)((s5 >> 15) | (s6 << 6)); - s[16] = (uint8_t)(s6 >> 2); - s[17] = (uint8_t)(s6 >> 10); - s[18] = (uint8_t)((s6 >> 18) | (s7 << 3)); - s[19] = (uint8_t)(s7 >> 5); - s[20] = (uint8_t)(s7 >> 13); - s[21] = (uint8_t)(s8 >> 0); - s[22] = (uint8_t)(s8 >> 8); - s[23] = (uint8_t)((s8 >> 16) | (s9 << 5)); - s[24] = (uint8_t)(s9 >> 3); - s[25] = (uint8_t)(s9 >> 11); - s[26] = (uint8_t)((s9 >> 19) | (s10 << 2)); - s[27] = (uint8_t)(s10 >> 6); - s[28] = (uint8_t)((s10 >> 14) | (s11 << 7)); - s[29] = (uint8_t)(s11 >> 1); - s[30] = (uint8_t)(s11 >> 9); - s[31] = (uint8_t)(s11 >> 17); + const uint8_t *c) +{ + int64_t a0 = kBottom21Bits & load_3(a); + int64_t a1 = kBottom21Bits & (load_4(a + 2) >> 5); + int64_t a2 = kBottom21Bits & (load_3(a + 5) >> 2); + int64_t a3 = kBottom21Bits & (load_4(a + 7) >> 7); + int64_t a4 = kBottom21Bits & (load_4(a + 10) >> 4); + int64_t a5 = kBottom21Bits & (load_3(a + 13) >> 1); + int64_t a6 = kBottom21Bits & (load_4(a + 15) >> 6); + int64_t a7 = kBottom21Bits & (load_3(a + 18) >> 3); + int64_t a8 = kBottom21Bits & load_3(a + 21); + int64_t a9 = kBottom21Bits & (load_4(a + 23) >> 5); + int64_t a10 = kBottom21Bits & (load_3(a + 26) >> 2); + int64_t a11 = (load_4(a + 28) >> 7); + int64_t b0 = kBottom21Bits & load_3(b); + int64_t b1 = kBottom21Bits & (load_4(b + 2) >> 5); + int64_t b2 = kBottom21Bits & (load_3(b + 5) >> 2); + int64_t b3 = kBottom21Bits & (load_4(b + 7) >> 7); + int64_t b4 = kBottom21Bits & (load_4(b + 10) >> 4); + int64_t b5 = kBottom21Bits & (load_3(b + 13) >> 1); + int64_t b6 = kBottom21Bits & (load_4(b + 15) >> 6); + int64_t b7 = kBottom21Bits & (load_3(b + 18) >> 3); + int64_t b8 = kBottom21Bits & load_3(b + 21); + int64_t b9 = kBottom21Bits & (load_4(b + 23) >> 5); + int64_t b10 = kBottom21Bits & (load_3(b + 26) >> 2); + int64_t b11 = (load_4(b + 28) >> 7); + int64_t c0 = kBottom21Bits & load_3(c); + int64_t c1 = kBottom21Bits & (load_4(c + 2) >> 5); + int64_t c2 = kBottom21Bits & (load_3(c + 5) >> 2); + int64_t c3 = kBottom21Bits & (load_4(c + 7) >> 7); + int64_t c4 = kBottom21Bits & (load_4(c + 10) >> 4); + int64_t c5 = kBottom21Bits & (load_3(c + 13) >> 1); + int64_t c6 = kBottom21Bits & (load_4(c + 15) >> 6); + int64_t c7 = kBottom21Bits & (load_3(c + 18) >> 3); + int64_t c8 = kBottom21Bits & load_3(c + 21); + int64_t c9 = kBottom21Bits & (load_4(c + 23) >> 5); + int64_t c10 = kBottom21Bits & (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 + (1 << 20)) >> 21; + s1 += carry0; + s0 -= carry0 * (1 << 21); + carry2 = (s2 + (1 << 20)) >> 21; + s3 += carry2; + s2 -= carry2 * (1 << 21); + carry4 = (s4 + (1 << 20)) >> 21; + s5 += carry4; + s4 -= carry4 * (1 << 21); + carry6 = (s6 + (1 << 20)) >> 21; + s7 += carry6; + s6 -= carry6 * (1 << 21); + carry8 = (s8 + (1 << 20)) >> 21; + s9 += carry8; + s8 -= carry8 * (1 << 21); + carry10 = (s10 + (1 << 20)) >> 21; + s11 += carry10; + s10 -= carry10 * (1 << 21); + carry12 = (s12 + (1 << 20)) >> 21; + s13 += carry12; + s12 -= carry12 * (1 << 21); + carry14 = (s14 + (1 << 20)) >> 21; + s15 += carry14; + s14 -= carry14 * (1 << 21); + carry16 = (s16 + (1 << 20)) >> 21; + s17 += carry16; + s16 -= carry16 * (1 << 21); + carry18 = (s18 + (1 << 20)) >> 21; + s19 += carry18; + s18 -= carry18 * (1 << 21); + carry20 = (s20 + (1 << 20)) >> 21; + s21 += carry20; + s20 -= carry20 * (1 << 21); + carry22 = (s22 + (1 << 20)) >> 21; + s23 += carry22; + s22 -= carry22 * (1 << 21); + + carry1 = (s1 + (1 << 20)) >> 21; + s2 += carry1; + s1 -= carry1 * (1 << 21); + carry3 = (s3 + (1 << 20)) >> 21; + s4 += carry3; + s3 -= carry3 * (1 << 21); + carry5 = (s5 + (1 << 20)) >> 21; + s6 += carry5; + s5 -= carry5 * (1 << 21); + carry7 = (s7 + (1 << 20)) >> 21; + s8 += carry7; + s7 -= carry7 * (1 << 21); + carry9 = (s9 + (1 << 20)) >> 21; + s10 += carry9; + s9 -= carry9 * (1 << 21); + carry11 = (s11 + (1 << 20)) >> 21; + s12 += carry11; + s11 -= carry11 * (1 << 21); + carry13 = (s13 + (1 << 20)) >> 21; + s14 += carry13; + s13 -= carry13 * (1 << 21); + carry15 = (s15 + (1 << 20)) >> 21; + s16 += carry15; + s15 -= carry15 * (1 << 21); + carry17 = (s17 + (1 << 20)) >> 21; + s18 += carry17; + s17 -= carry17 * (1 << 21); + carry19 = (s19 + (1 << 20)) >> 21; + s20 += carry19; + s19 -= carry19 * (1 << 21); + carry21 = (s21 + (1 << 20)) >> 21; + s22 += carry21; + s21 -= carry21 * (1 << 21); + + s11 += s23 * 666643; + s12 += s23 * 470296; + s13 += s23 * 654183; + s14 -= s23 * 997805; + s15 += s23 * 136657; + s16 -= s23 * 683901; + s23 = 0; + + s10 += s22 * 666643; + s11 += s22 * 470296; + s12 += s22 * 654183; + s13 -= s22 * 997805; + s14 += s22 * 136657; + s15 -= s22 * 683901; + s22 = 0; + + s9 += s21 * 666643; + s10 += s21 * 470296; + s11 += s21 * 654183; + s12 -= s21 * 997805; + s13 += s21 * 136657; + s14 -= s21 * 683901; + s21 = 0; + + s8 += s20 * 666643; + s9 += s20 * 470296; + s10 += s20 * 654183; + s11 -= s20 * 997805; + s12 += s20 * 136657; + s13 -= s20 * 683901; + s20 = 0; + + s7 += s19 * 666643; + s8 += s19 * 470296; + s9 += s19 * 654183; + s10 -= s19 * 997805; + s11 += s19 * 136657; + s12 -= s19 * 683901; + s19 = 0; + + s6 += s18 * 666643; + s7 += s18 * 470296; + s8 += s18 * 654183; + s9 -= s18 * 997805; + s10 += s18 * 136657; + s11 -= s18 * 683901; + s18 = 0; + + carry6 = (s6 + (1 << 20)) >> 21; + s7 += carry6; + s6 -= carry6 * (1 << 21); + carry8 = (s8 + (1 << 20)) >> 21; + s9 += carry8; + s8 -= carry8 * (1 << 21); + carry10 = (s10 + (1 << 20)) >> 21; + s11 += carry10; + s10 -= carry10 * (1 << 21); + carry12 = (s12 + (1 << 20)) >> 21; + s13 += carry12; + s12 -= carry12 * (1 << 21); + carry14 = (s14 + (1 << 20)) >> 21; + s15 += carry14; + s14 -= carry14 * (1 << 21); + carry16 = (s16 + (1 << 20)) >> 21; + s17 += carry16; + s16 -= carry16 * (1 << 21); + + carry7 = (s7 + (1 << 20)) >> 21; + s8 += carry7; + s7 -= carry7 * (1 << 21); + carry9 = (s9 + (1 << 20)) >> 21; + s10 += carry9; + s9 -= carry9 * (1 << 21); + carry11 = (s11 + (1 << 20)) >> 21; + s12 += carry11; + s11 -= carry11 * (1 << 21); + carry13 = (s13 + (1 << 20)) >> 21; + s14 += carry13; + s13 -= carry13 * (1 << 21); + carry15 = (s15 + (1 << 20)) >> 21; + s16 += carry15; + s15 -= carry15 * (1 << 21); + + s5 += s17 * 666643; + s6 += s17 * 470296; + s7 += s17 * 654183; + s8 -= s17 * 997805; + s9 += s17 * 136657; + s10 -= s17 * 683901; + s17 = 0; + + s4 += s16 * 666643; + s5 += s16 * 470296; + s6 += s16 * 654183; + s7 -= s16 * 997805; + s8 += s16 * 136657; + s9 -= s16 * 683901; + s16 = 0; + + s3 += s15 * 666643; + s4 += s15 * 470296; + s5 += s15 * 654183; + s6 -= s15 * 997805; + s7 += s15 * 136657; + s8 -= s15 * 683901; + s15 = 0; + + s2 += s14 * 666643; + s3 += s14 * 470296; + s4 += s14 * 654183; + s5 -= s14 * 997805; + s6 += s14 * 136657; + s7 -= s14 * 683901; + s14 = 0; + + s1 += s13 * 666643; + s2 += s13 * 470296; + s3 += s13 * 654183; + s4 -= s13 * 997805; + s5 += s13 * 136657; + s6 -= s13 * 683901; + s13 = 0; + + s0 += s12 * 666643; + s1 += s12 * 470296; + s2 += s12 * 654183; + s3 -= s12 * 997805; + s4 += s12 * 136657; + s5 -= s12 * 683901; + s12 = 0; + + carry0 = (s0 + (1 << 20)) >> 21; + s1 += carry0; + s0 -= carry0 * (1 << 21); + carry2 = (s2 + (1 << 20)) >> 21; + s3 += carry2; + s2 -= carry2 * (1 << 21); + carry4 = (s4 + (1 << 20)) >> 21; + s5 += carry4; + s4 -= carry4 * (1 << 21); + carry6 = (s6 + (1 << 20)) >> 21; + s7 += carry6; + s6 -= carry6 * (1 << 21); + carry8 = (s8 + (1 << 20)) >> 21; + s9 += carry8; + s8 -= carry8 * (1 << 21); + carry10 = (s10 + (1 << 20)) >> 21; + s11 += carry10; + s10 -= carry10 * (1 << 21); + + carry1 = (s1 + (1 << 20)) >> 21; + s2 += carry1; + s1 -= carry1 * (1 << 21); + carry3 = (s3 + (1 << 20)) >> 21; + s4 += carry3; + s3 -= carry3 * (1 << 21); + carry5 = (s5 + (1 << 20)) >> 21; + s6 += carry5; + s5 -= carry5 * (1 << 21); + carry7 = (s7 + (1 << 20)) >> 21; + s8 += carry7; + s7 -= carry7 * (1 << 21); + carry9 = (s9 + (1 << 20)) >> 21; + s10 += carry9; + s9 -= carry9 * (1 << 21); + carry11 = (s11 + (1 << 20)) >> 21; + s12 += carry11; + s11 -= carry11 * (1 << 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 * (1 << 21); + carry1 = s1 >> 21; + s2 += carry1; + s1 -= carry1 * (1 << 21); + carry2 = s2 >> 21; + s3 += carry2; + s2 -= carry2 * (1 << 21); + carry3 = s3 >> 21; + s4 += carry3; + s3 -= carry3 * (1 << 21); + carry4 = s4 >> 21; + s5 += carry4; + s4 -= carry4 * (1 << 21); + carry5 = s5 >> 21; + s6 += carry5; + s5 -= carry5 * (1 << 21); + carry6 = s6 >> 21; + s7 += carry6; + s6 -= carry6 * (1 << 21); + carry7 = s7 >> 21; + s8 += carry7; + s7 -= carry7 * (1 << 21); + carry8 = s8 >> 21; + s9 += carry8; + s8 -= carry8 * (1 << 21); + carry9 = s9 >> 21; + s10 += carry9; + s9 -= carry9 * (1 << 21); + carry10 = s10 >> 21; + s11 += carry10; + s10 -= carry10 * (1 << 21); + carry11 = s11 >> 21; + s12 += carry11; + s11 -= carry11 * (1 << 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 * (1 << 21); + carry1 = s1 >> 21; + s2 += carry1; + s1 -= carry1 * (1 << 21); + carry2 = s2 >> 21; + s3 += carry2; + s2 -= carry2 * (1 << 21); + carry3 = s3 >> 21; + s4 += carry3; + s3 -= carry3 * (1 << 21); + carry4 = s4 >> 21; + s5 += carry4; + s4 -= carry4 * (1 << 21); + carry5 = s5 >> 21; + s6 += carry5; + s5 -= carry5 * (1 << 21); + carry6 = s6 >> 21; + s7 += carry6; + s6 -= carry6 * (1 << 21); + carry7 = s7 >> 21; + s8 += carry7; + s7 -= carry7 * (1 << 21); + carry8 = s8 >> 21; + s9 += carry8; + s8 -= carry8 * (1 << 21); + carry9 = s9 >> 21; + s10 += carry9; + s9 -= carry9 * (1 << 21); + carry10 = s10 >> 21; + s11 += carry10; + s10 -= carry10 * (1 << 21); + + s[ 0] = (uint8_t) (s0 >> 0); + s[ 1] = (uint8_t) (s0 >> 8); + s[ 2] = (uint8_t)((s0 >> 16) | (s1 << 5)); + s[ 3] = (uint8_t) (s1 >> 3); + s[ 4] = (uint8_t) (s1 >> 11); + s[ 5] = (uint8_t)((s1 >> 19) | (s2 << 2)); + s[ 6] = (uint8_t) (s2 >> 6); + s[ 7] = (uint8_t)((s2 >> 14) | (s3 << 7)); + s[ 8] = (uint8_t) (s3 >> 1); + s[ 9] = (uint8_t) (s3 >> 9); + s[10] = (uint8_t)((s3 >> 17) | (s4 << 4)); + s[11] = (uint8_t) (s4 >> 4); + s[12] = (uint8_t) (s4 >> 12); + s[13] = (uint8_t)((s4 >> 20) | (s5 << 1)); + s[14] = (uint8_t) (s5 >> 7); + s[15] = (uint8_t)((s5 >> 15) | (s6 << 6)); + s[16] = (uint8_t) (s6 >> 2); + s[17] = (uint8_t) (s6 >> 10); + s[18] = (uint8_t)((s6 >> 18) | (s7 << 3)); + s[19] = (uint8_t) (s7 >> 5); + s[20] = (uint8_t) (s7 >> 13); + s[21] = (uint8_t) (s8 >> 0); + s[22] = (uint8_t) (s8 >> 8); + s[23] = (uint8_t)((s8 >> 16) | (s9 << 5)); + s[24] = (uint8_t) (s9 >> 3); + s[25] = (uint8_t) (s9 >> 11); + s[26] = (uint8_t)((s9 >> 19) | (s10 << 2)); + s[27] = (uint8_t) (s10 >> 6); + s[28] = (uint8_t)((s10 >> 14) | (s11 << 7)); + s[29] = (uint8_t) (s11 >> 1); + s[30] = (uint8_t) (s11 >> 9); + s[31] = (uint8_t) (s11 >> 17); } int ED25519_sign(uint8_t *out_sig, const uint8_t *message, size_t message_len, - const uint8_t public_key[32], const uint8_t private_key[32]) { - uint8_t az[SHA512_DIGEST_LENGTH]; - uint8_t nonce[SHA512_DIGEST_LENGTH]; - ge_p3 R; - uint8_t hram[SHA512_DIGEST_LENGTH]; - SHA512_CTX hash_ctx; - - SHA512_Init(&hash_ctx); - SHA512_Update(&hash_ctx, private_key, 32); - SHA512_Final(az, &hash_ctx); - - az[0] &= 248; - az[31] &= 63; - az[31] |= 64; - - SHA512_Init(&hash_ctx); - SHA512_Update(&hash_ctx, az + 32, 32); - SHA512_Update(&hash_ctx, message, message_len); - SHA512_Final(nonce, &hash_ctx); - - x25519_sc_reduce(nonce); - ge_scalarmult_base(&R, nonce); - ge_p3_tobytes(out_sig, &R); - - SHA512_Init(&hash_ctx); - SHA512_Update(&hash_ctx, out_sig, 32); - SHA512_Update(&hash_ctx, public_key, 32); - SHA512_Update(&hash_ctx, message, message_len); - SHA512_Final(hram, &hash_ctx); - - x25519_sc_reduce(hram); - sc_muladd(out_sig + 32, hram, az, nonce); - - OPENSSL_cleanse(&hash_ctx, sizeof(hash_ctx)); - OPENSSL_cleanse(nonce, sizeof(nonce)); - OPENSSL_cleanse(az, sizeof(az)); - - return 1; + const uint8_t public_key[32], const uint8_t private_key[32]) +{ + uint8_t az[SHA512_DIGEST_LENGTH]; + uint8_t nonce[SHA512_DIGEST_LENGTH]; + ge_p3 R; + uint8_t hram[SHA512_DIGEST_LENGTH]; + SHA512_CTX hash_ctx; + + SHA512_Init(&hash_ctx); + SHA512_Update(&hash_ctx, private_key, 32); + SHA512_Final(az, &hash_ctx); + + az[0] &= 248; + az[31] &= 63; + az[31] |= 64; + + SHA512_Init(&hash_ctx); + SHA512_Update(&hash_ctx, az + 32, 32); + SHA512_Update(&hash_ctx, message, message_len); + SHA512_Final(nonce, &hash_ctx); + + x25519_sc_reduce(nonce); + ge_scalarmult_base(&R, nonce); + ge_p3_tobytes(out_sig, &R); + + SHA512_Init(&hash_ctx); + SHA512_Update(&hash_ctx, out_sig, 32); + SHA512_Update(&hash_ctx, public_key, 32); + SHA512_Update(&hash_ctx, message, message_len); + SHA512_Final(hram, &hash_ctx); + + x25519_sc_reduce(hram); + sc_muladd(out_sig + 32, hram, az, nonce); + + OPENSSL_cleanse(&hash_ctx, sizeof(hash_ctx)); + OPENSSL_cleanse(nonce, sizeof(nonce)); + OPENSSL_cleanse(az, sizeof(az)); + + return 1; } +static const char allzeroes[15]; + int ED25519_verify(const uint8_t *message, size_t message_len, - const uint8_t signature[64], const uint8_t public_key[32]) { - ge_p3 A; - uint8_t rcopy[32]; - uint8_t scopy[32]; - SHA512_CTX hash_ctx; - ge_p2 R; - uint8_t rcheck[32]; - uint8_t h[SHA512_DIGEST_LENGTH]; - - if ((signature[63] & 224) != 0 || - ge_frombytes_vartime(&A, public_key) != 0) { - return 0; - } + const uint8_t signature[64], const uint8_t public_key[32]) +{ + int i; + ge_p3 A; + const uint8_t *r, *s; + SHA512_CTX hash_ctx; + ge_p2 R; + uint8_t rcheck[32]; + uint8_t h[SHA512_DIGEST_LENGTH]; + /* 27742317777372353535851937790883648493 in little endian format */ + const uint8_t l_low[16] = { + 0xED, 0xD3, 0xF5, 0x5C, 0x1A, 0x63, 0x12, 0x58, 0xD6, 0x9C, 0xF7, 0xA2, + 0xDE, 0xF9, 0xDE, 0x14 + }; + + r = signature; + s = signature + 32; + + /* + * Check 0 <= s < L where L = 2^252 + 27742317777372353535851937790883648493 + * + * If not the signature is publicly invalid. Since it's public we can do the + * check in variable time. + * + * First check the most significant byte + */ + if (s[31] > 0x10) + return 0; + if (s[31] == 0x10) { + /* + * Most significant byte indicates a value close to 2^252 so check the + * rest + */ + if (memcmp(s + 16, allzeroes, sizeof(allzeroes)) != 0) + return 0; + for (i = 15; i >= 0; i--) { + if (s[i] < l_low[i]) + break; + if (s[i] > l_low[i]) + return 0; + } + if (i < 0) + return 0; + } - fe_neg(A.X, A.X); - fe_neg(A.T, A.T); + if (ge_frombytes_vartime(&A, public_key) != 0) { + return 0; + } - memcpy(rcopy, signature, 32); - memcpy(scopy, signature + 32, 32); + fe_neg(A.X, A.X); + fe_neg(A.T, A.T); - SHA512_Init(&hash_ctx); - SHA512_Update(&hash_ctx, signature, 32); - SHA512_Update(&hash_ctx, public_key, 32); - SHA512_Update(&hash_ctx, message, message_len); - SHA512_Final(h, &hash_ctx); + SHA512_Init(&hash_ctx); + SHA512_Update(&hash_ctx, r, 32); + SHA512_Update(&hash_ctx, public_key, 32); + SHA512_Update(&hash_ctx, message, message_len); + SHA512_Final(h, &hash_ctx); - x25519_sc_reduce(h); + x25519_sc_reduce(h); - ge_double_scalarmult_vartime(&R, h, &A, scopy); + ge_double_scalarmult_vartime(&R, h, &A, s); - ge_tobytes(rcheck, &R); + ge_tobytes(rcheck, &R); - return CRYPTO_memcmp(rcheck, rcopy, sizeof(rcheck)) == 0; + return CRYPTO_memcmp(rcheck, r, sizeof(rcheck)) == 0; } void ED25519_public_from_private(uint8_t out_public_key[32], - const uint8_t private_key[32]) { - uint8_t az[SHA512_DIGEST_LENGTH]; - ge_p3 A; + const uint8_t private_key[32]) +{ + uint8_t az[SHA512_DIGEST_LENGTH]; + ge_p3 A; - SHA512(private_key, 32, az); + SHA512(private_key, 32, az); - az[0] &= 248; - az[31] &= 63; - az[31] |= 64; + az[0] &= 248; + az[31] &= 63; + az[31] |= 64; - ge_scalarmult_base(&A, az); - ge_p3_tobytes(out_public_key, &A); + ge_scalarmult_base(&A, az); + ge_p3_tobytes(out_public_key, &A); - OPENSSL_cleanse(az, sizeof(az)); + OPENSSL_cleanse(az, sizeof(az)); } int X25519(uint8_t out_shared_key[32], const uint8_t private_key[32], - const uint8_t peer_public_value[32]) { - static const uint8_t kZeros[32] = {0}; - x25519_scalar_mult(out_shared_key, private_key, peer_public_value); - /* The all-zero output results when the input is a point of small order. */ - return CRYPTO_memcmp(kZeros, out_shared_key, 32) != 0; + const uint8_t peer_public_value[32]) +{ + static const uint8_t kZeros[32] = {0}; + x25519_scalar_mult(out_shared_key, private_key, peer_public_value); + /* The all-zero output results when the input is a point of small order. */ + return CRYPTO_memcmp(kZeros, out_shared_key, 32) != 0; } void X25519_public_from_private(uint8_t out_public_value[32], - const uint8_t private_key[32]) { - uint8_t e[32]; - ge_p3 A; - fe zplusy, zminusy, zminusy_inv; - - memcpy(e, private_key, 32); - e[0] &= 248; - e[31] &= 127; - e[31] |= 64; - - ge_scalarmult_base(&A, e); - - /* We only need the u-coordinate of the curve25519 point. The map is - * u=(y+1)/(1-y). Since y=Y/Z, this gives u=(Z+Y)/(Z-Y). */ - fe_add(zplusy, A.Z, A.Y); - fe_sub(zminusy, A.Z, A.Y); - fe_invert(zminusy_inv, zminusy); - fe_mul(zplusy, zplusy, zminusy_inv); - fe_tobytes(out_public_value, zplusy); - - OPENSSL_cleanse(e, sizeof(e)); + const uint8_t private_key[32]) +{ + uint8_t e[32]; + ge_p3 A; + fe zplusy, zminusy, zminusy_inv; + + memcpy(e, private_key, 32); + e[0] &= 248; + e[31] &= 127; + e[31] |= 64; + + ge_scalarmult_base(&A, e); + + /* + * We only need the u-coordinate of the curve25519 point. + * The map is u=(y+1)/(1-y). Since y=Y/Z, this gives + * u=(Z+Y)/(Z-Y). + */ + fe_add(zplusy, A.Z, A.Y); + fe_sub(zminusy, A.Z, A.Y); + fe_invert(zminusy_inv, zminusy); + fe_mul(zplusy, zplusy, zminusy_inv); + fe_tobytes(out_public_value, zplusy); + + OPENSSL_cleanse(e, sizeof(e)); } |