diff options
Diffstat (limited to 'crypto/ec/ecp_smpl.c')
-rw-r--r-- | crypto/ec/ecp_smpl.c | 309 |
1 files changed, 169 insertions, 140 deletions
diff --git a/crypto/ec/ecp_smpl.c b/crypto/ec/ecp_smpl.c index b354bfe9ce9e..b3110ec89dbe 100644 --- a/crypto/ec/ecp_smpl.c +++ b/crypto/ec/ecp_smpl.c @@ -1,5 +1,5 @@ /* - * Copyright 2001-2019 The OpenSSL Project Authors. All Rights Reserved. + * Copyright 2001-2020 The OpenSSL Project Authors. All Rights Reserved. * Copyright (c) 2002, Oracle and/or its affiliates. All rights reserved * * Licensed under the OpenSSL license (the "License"). You may not use @@ -1372,6 +1372,7 @@ int ec_GFp_simple_field_sqr(const EC_GROUP *group, BIGNUM *r, const BIGNUM *a, * Computes the multiplicative inverse of a in GF(p), storing the result in r. * If a is zero (or equivalent), you'll get a EC_R_CANNOT_INVERT error. * Since we don't have a Mont structure here, SCA hardening is with blinding. + * NB: "a" must be in _decoded_ form. (i.e. field_decode must precede.) */ int ec_GFp_simple_field_inv(const EC_GROUP *group, BIGNUM *r, const BIGNUM *a, BN_CTX *ctx) @@ -1431,112 +1432,133 @@ int ec_GFp_simple_blind_coordinates(const EC_GROUP *group, EC_POINT *p, temp = BN_CTX_get(ctx); if (temp == NULL) { ECerr(EC_F_EC_GFP_SIMPLE_BLIND_COORDINATES, ERR_R_MALLOC_FAILURE); - goto err; + goto end; } - /* make sure lambda is not zero */ + /*- + * Make sure lambda is not zero. + * If the RNG fails, we cannot blind but nevertheless want + * code to continue smoothly and not clobber the error stack. + */ do { - if (!BN_priv_rand_range(lambda, group->field)) { - ECerr(EC_F_EC_GFP_SIMPLE_BLIND_COORDINATES, ERR_R_BN_LIB); - goto err; + ERR_set_mark(); + ret = BN_priv_rand_range(lambda, group->field); + ERR_pop_to_mark(); + if (ret == 0) { + ret = 1; + goto end; } } while (BN_is_zero(lambda)); /* if field_encode defined convert between representations */ - if (group->meth->field_encode != NULL - && !group->meth->field_encode(group, lambda, lambda, ctx)) - goto err; - if (!group->meth->field_mul(group, p->Z, p->Z, lambda, ctx)) - goto err; - if (!group->meth->field_sqr(group, temp, lambda, ctx)) - goto err; - if (!group->meth->field_mul(group, p->X, p->X, temp, ctx)) - goto err; - if (!group->meth->field_mul(group, temp, temp, lambda, ctx)) - goto err; - if (!group->meth->field_mul(group, p->Y, p->Y, temp, ctx)) - goto err; - p->Z_is_one = 0; + if ((group->meth->field_encode != NULL + && !group->meth->field_encode(group, lambda, lambda, ctx)) + || !group->meth->field_mul(group, p->Z, p->Z, lambda, ctx) + || !group->meth->field_sqr(group, temp, lambda, ctx) + || !group->meth->field_mul(group, p->X, p->X, temp, ctx) + || !group->meth->field_mul(group, temp, temp, lambda, ctx) + || !group->meth->field_mul(group, p->Y, p->Y, temp, ctx)) + goto end; + p->Z_is_one = 0; ret = 1; - err: + end: BN_CTX_end(ctx); return ret; } /*- - * Set s := p, r := 2p. + * Input: + * - p: affine coordinates + * + * Output: + * - s := p, r := 2p: blinded projective (homogeneous) coordinates * * For doubling we use Formula 3 from Izu-Takagi "A fast parallel elliptic curve - * multiplication resistant against side channel attacks" appendix, as described - * at + * multiplication resistant against side channel attacks" appendix, described at * https://hyperelliptic.org/EFD/g1p/auto-shortw-xz.html#doubling-dbl-2002-it-2 + * simplified for Z1=1. * - * The input point p will be in randomized Jacobian projective coords: - * x = X/Z**2, y=Y/Z**3 - * - * The output points p, s, and r are converted to standard (homogeneous) - * projective coords: - * x = X/Z, y=Y/Z + * Blinding uses the equivalence relation (\lambda X, \lambda Y, \lambda Z) + * for any non-zero \lambda that holds for projective (homogeneous) coords. */ int ec_GFp_simple_ladder_pre(const EC_GROUP *group, EC_POINT *r, EC_POINT *s, EC_POINT *p, BN_CTX *ctx) { - BIGNUM *t1, *t2, *t3, *t4, *t5, *t6 = NULL; + BIGNUM *t1, *t2, *t3, *t4, *t5 = NULL; - t1 = r->Z; - t2 = r->Y; + t1 = s->Z; + t2 = r->Z; t3 = s->X; t4 = r->X; t5 = s->Y; - t6 = s->Z; - - /* convert p: (X,Y,Z) -> (XZ,Y,Z**3) */ - if (!group->meth->field_mul(group, p->X, p->X, p->Z, ctx) - || !group->meth->field_sqr(group, t1, p->Z, ctx) - || !group->meth->field_mul(group, p->Z, p->Z, t1, ctx) - /* r := 2p */ - || !group->meth->field_sqr(group, t2, p->X, ctx) - || !group->meth->field_sqr(group, t3, p->Z, ctx) - || !group->meth->field_mul(group, t4, t3, group->a, ctx) - || !BN_mod_sub_quick(t5, t2, t4, group->field) - || !BN_mod_add_quick(t2, t2, t4, group->field) - || !group->meth->field_sqr(group, t5, t5, ctx) - || !group->meth->field_mul(group, t6, t3, group->b, ctx) - || !group->meth->field_mul(group, t1, p->X, p->Z, ctx) - || !group->meth->field_mul(group, t4, t1, t6, ctx) - || !BN_mod_lshift_quick(t4, t4, 3, group->field) + + if (!p->Z_is_one /* r := 2p */ + || !group->meth->field_sqr(group, t3, p->X, ctx) + || !BN_mod_sub_quick(t4, t3, group->a, group->field) + || !group->meth->field_sqr(group, t4, t4, ctx) + || !group->meth->field_mul(group, t5, p->X, group->b, ctx) + || !BN_mod_lshift_quick(t5, t5, 3, group->field) /* r->X coord output */ - || !BN_mod_sub_quick(r->X, t5, t4, group->field) - || !group->meth->field_mul(group, t1, t1, t2, ctx) - || !group->meth->field_mul(group, t2, t3, t6, ctx) - || !BN_mod_add_quick(t1, t1, t2, group->field) + || !BN_mod_sub_quick(r->X, t4, t5, group->field) + || !BN_mod_add_quick(t1, t3, group->a, group->field) + || !group->meth->field_mul(group, t2, p->X, t1, ctx) + || !BN_mod_add_quick(t2, group->b, t2, group->field) /* r->Z coord output */ - || !BN_mod_lshift_quick(r->Z, t1, 2, group->field) - || !EC_POINT_copy(s, p)) + || !BN_mod_lshift_quick(r->Z, t2, 2, group->field)) + return 0; + + /* make sure lambda (r->Y here for storage) is not zero */ + do { + if (!BN_priv_rand_range(r->Y, group->field)) + return 0; + } while (BN_is_zero(r->Y)); + + /* make sure lambda (s->Z here for storage) is not zero */ + do { + if (!BN_priv_rand_range(s->Z, group->field)) + return 0; + } while (BN_is_zero(s->Z)); + + /* if field_encode defined convert between representations */ + if (group->meth->field_encode != NULL + && (!group->meth->field_encode(group, r->Y, r->Y, ctx) + || !group->meth->field_encode(group, s->Z, s->Z, ctx))) + return 0; + + /* blind r and s independently */ + if (!group->meth->field_mul(group, r->Z, r->Z, r->Y, ctx) + || !group->meth->field_mul(group, r->X, r->X, r->Y, ctx) + || !group->meth->field_mul(group, s->X, p->X, s->Z, ctx)) /* s := p */ return 0; r->Z_is_one = 0; s->Z_is_one = 0; - p->Z_is_one = 0; return 1; } /*- - * Differential addition-and-doubling using Eq. (9) and (10) from Izu-Takagi + * Input: + * - s, r: projective (homogeneous) coordinates + * - p: affine coordinates + * + * Output: + * - s := r + s, r := 2r: projective (homogeneous) coordinates + * + * Differential addition-and-doubling using Eq. (9) and (10) from Izu-Takagi * "A fast parallel elliptic curve multiplication resistant against side channel * attacks", as described at - * https://hyperelliptic.org/EFD/g1p/auto-shortw-xz.html#ladder-ladd-2002-it-4 + * https://hyperelliptic.org/EFD/g1p/auto-shortw-xz.html#ladder-mladd-2002-it-4 */ int ec_GFp_simple_ladder_step(const EC_GROUP *group, EC_POINT *r, EC_POINT *s, EC_POINT *p, BN_CTX *ctx) { int ret = 0; - BIGNUM *t0, *t1, *t2, *t3, *t4, *t5, *t6, *t7 = NULL; + BIGNUM *t0, *t1, *t2, *t3, *t4, *t5, *t6 = NULL; BN_CTX_start(ctx); t0 = BN_CTX_get(ctx); @@ -1546,50 +1568,47 @@ int ec_GFp_simple_ladder_step(const EC_GROUP *group, t4 = BN_CTX_get(ctx); t5 = BN_CTX_get(ctx); t6 = BN_CTX_get(ctx); - t7 = BN_CTX_get(ctx); - if (t7 == NULL - || !group->meth->field_mul(group, t0, r->X, s->X, ctx) - || !group->meth->field_mul(group, t1, r->Z, s->Z, ctx) - || !group->meth->field_mul(group, t2, r->X, s->Z, ctx) + if (t6 == NULL + || !group->meth->field_mul(group, t6, r->X, s->X, ctx) + || !group->meth->field_mul(group, t0, r->Z, s->Z, ctx) + || !group->meth->field_mul(group, t4, r->X, s->Z, ctx) || !group->meth->field_mul(group, t3, r->Z, s->X, ctx) - || !group->meth->field_mul(group, t4, group->a, t1, ctx) - || !BN_mod_add_quick(t0, t0, t4, group->field) - || !BN_mod_add_quick(t4, t3, t2, group->field) - || !group->meth->field_mul(group, t0, t4, t0, ctx) - || !group->meth->field_sqr(group, t1, t1, ctx) - || !BN_mod_lshift_quick(t7, group->b, 2, group->field) - || !group->meth->field_mul(group, t1, t7, t1, ctx) - || !BN_mod_lshift1_quick(t0, t0, group->field) - || !BN_mod_add_quick(t0, t1, t0, group->field) - || !BN_mod_sub_quick(t1, t2, t3, group->field) - || !group->meth->field_sqr(group, t1, t1, ctx) - || !group->meth->field_mul(group, t3, t1, p->X, ctx) - || !group->meth->field_mul(group, t0, p->Z, t0, ctx) - /* s->X coord output */ - || !BN_mod_sub_quick(s->X, t0, t3, group->field) - /* s->Z coord output */ - || !group->meth->field_mul(group, s->Z, p->Z, t1, ctx) - || !group->meth->field_sqr(group, t3, r->X, ctx) - || !group->meth->field_sqr(group, t2, r->Z, ctx) - || !group->meth->field_mul(group, t4, t2, group->a, ctx) - || !BN_mod_add_quick(t5, r->X, r->Z, group->field) - || !group->meth->field_sqr(group, t5, t5, ctx) - || !BN_mod_sub_quick(t5, t5, t3, group->field) - || !BN_mod_sub_quick(t5, t5, t2, group->field) - || !BN_mod_sub_quick(t6, t3, t4, group->field) - || !group->meth->field_sqr(group, t6, t6, ctx) - || !group->meth->field_mul(group, t0, t2, t5, ctx) - || !group->meth->field_mul(group, t0, t7, t0, ctx) - /* r->X coord output */ - || !BN_mod_sub_quick(r->X, t6, t0, group->field) + || !group->meth->field_mul(group, t5, group->a, t0, ctx) + || !BN_mod_add_quick(t5, t6, t5, group->field) || !BN_mod_add_quick(t6, t3, t4, group->field) - || !group->meth->field_sqr(group, t3, t2, ctx) - || !group->meth->field_mul(group, t7, t3, t7, ctx) - || !group->meth->field_mul(group, t5, t5, t6, ctx) + || !group->meth->field_mul(group, t5, t6, t5, ctx) + || !group->meth->field_sqr(group, t0, t0, ctx) + || !BN_mod_lshift_quick(t2, group->b, 2, group->field) + || !group->meth->field_mul(group, t0, t2, t0, ctx) || !BN_mod_lshift1_quick(t5, t5, group->field) + || !BN_mod_sub_quick(t3, t4, t3, group->field) + /* s->Z coord output */ + || !group->meth->field_sqr(group, s->Z, t3, ctx) + || !group->meth->field_mul(group, t4, s->Z, p->X, ctx) + || !BN_mod_add_quick(t0, t0, t5, group->field) + /* s->X coord output */ + || !BN_mod_sub_quick(s->X, t0, t4, group->field) + || !group->meth->field_sqr(group, t4, r->X, ctx) + || !group->meth->field_sqr(group, t5, r->Z, ctx) + || !group->meth->field_mul(group, t6, t5, group->a, ctx) + || !BN_mod_add_quick(t1, r->X, r->Z, group->field) + || !group->meth->field_sqr(group, t1, t1, ctx) + || !BN_mod_sub_quick(t1, t1, t4, group->field) + || !BN_mod_sub_quick(t1, t1, t5, group->field) + || !BN_mod_sub_quick(t3, t4, t6, group->field) + || !group->meth->field_sqr(group, t3, t3, ctx) + || !group->meth->field_mul(group, t0, t5, t1, ctx) + || !group->meth->field_mul(group, t0, t2, t0, ctx) + /* r->X coord output */ + || !BN_mod_sub_quick(r->X, t3, t0, group->field) + || !BN_mod_add_quick(t3, t4, t6, group->field) + || !group->meth->field_sqr(group, t4, t5, ctx) + || !group->meth->field_mul(group, t4, t4, t2, ctx) + || !group->meth->field_mul(group, t1, t1, t3, ctx) + || !BN_mod_lshift1_quick(t1, t1, group->field) /* r->Z coord output */ - || !BN_mod_add_quick(r->Z, t7, t5, group->field)) + || !BN_mod_add_quick(r->Z, t4, t1, group->field)) goto err; ret = 1; @@ -1600,17 +1619,23 @@ int ec_GFp_simple_ladder_step(const EC_GROUP *group, } /*- + * Input: + * - s, r: projective (homogeneous) coordinates + * - p: affine coordinates + * + * Output: + * - r := (x,y): affine coordinates + * * Recovers the y-coordinate of r using Eq. (8) from Brier-Joye, "Weierstrass - * Elliptic Curves and Side-Channel Attacks", modified to work in projective - * coordinates and return r in Jacobian projective coordinates. + * Elliptic Curves and Side-Channel Attacks", modified to work in mixed + * projective coords, i.e. p is affine and (r,s) in projective (homogeneous) + * coords, and return r in affine coordinates. * - * X4 = two*Y1*X2*Z3*Z2*Z1; - * Y4 = two*b*Z3*SQR(Z2*Z1) + Z3*(a*Z2*Z1+X1*X2)*(X1*Z2+X2*Z1) - X3*SQR(X1*Z2-X2*Z1); - * Z4 = two*Y1*Z3*SQR(Z2)*Z1; + * X4 = two*Y1*X2*Z3*Z2; + * Y4 = two*b*Z3*SQR(Z2) + Z3*(a*Z2+X1*X2)*(X1*Z2+X2) - X3*SQR(X1*Z2-X2); + * Z4 = two*Y1*Z3*SQR(Z2); * * Z4 != 0 because: - * - Z1==0 implies p is at infinity, which would have caused an early exit in - * the caller; * - Z2==0 implies r is at infinity (handled by the BN_is_zero(r->Z) branch); * - Z3==0 implies s is at infinity (handled by the BN_is_zero(s->Z) branch); * - Y1==0 implies p has order 2, so either r or s are infinity and handled by @@ -1627,11 +1652,7 @@ int ec_GFp_simple_ladder_post(const EC_GROUP *group, return EC_POINT_set_to_infinity(group, r); if (BN_is_zero(s->Z)) { - /* (X,Y,Z) -> (XZ,YZ**2,Z) */ - if (!group->meth->field_mul(group, r->X, p->X, p->Z, ctx) - || !group->meth->field_sqr(group, r->Z, p->Z, ctx) - || !group->meth->field_mul(group, r->Y, p->Y, r->Z, ctx) - || !BN_copy(r->Z, p->Z) + if (!EC_POINT_copy(r, p) || !EC_POINT_invert(group, r, ctx)) return 0; return 1; @@ -1647,38 +1668,46 @@ int ec_GFp_simple_ladder_post(const EC_GROUP *group, t6 = BN_CTX_get(ctx); if (t6 == NULL - || !BN_mod_lshift1_quick(t0, p->Y, group->field) - || !group->meth->field_mul(group, t1, r->X, p->Z, ctx) - || !group->meth->field_mul(group, t2, r->Z, s->Z, ctx) - || !group->meth->field_mul(group, t2, t1, t2, ctx) - || !group->meth->field_mul(group, t3, t2, t0, ctx) - || !group->meth->field_mul(group, t2, r->Z, p->Z, ctx) - || !group->meth->field_sqr(group, t4, t2, ctx) - || !BN_mod_lshift1_quick(t5, group->b, group->field) - || !group->meth->field_mul(group, t4, t4, t5, ctx) - || !group->meth->field_mul(group, t6, t2, group->a, ctx) - || !group->meth->field_mul(group, t5, r->X, p->X, ctx) - || !BN_mod_add_quick(t5, t6, t5, group->field) - || !group->meth->field_mul(group, t6, r->Z, p->X, ctx) - || !BN_mod_add_quick(t2, t6, t1, group->field) - || !group->meth->field_mul(group, t5, t5, t2, ctx) - || !BN_mod_sub_quick(t6, t6, t1, group->field) - || !group->meth->field_sqr(group, t6, t6, ctx) - || !group->meth->field_mul(group, t6, t6, s->X, ctx) - || !BN_mod_add_quick(t4, t5, t4, group->field) - || !group->meth->field_mul(group, t4, t4, s->Z, ctx) - || !BN_mod_sub_quick(t4, t4, t6, group->field) - || !group->meth->field_sqr(group, t5, r->Z, ctx) - || !group->meth->field_mul(group, r->Z, p->Z, s->Z, ctx) - || !group->meth->field_mul(group, r->Z, t5, r->Z, ctx) - || !group->meth->field_mul(group, r->Z, r->Z, t0, ctx) - /* t3 := X, t4 := Y */ - /* (X,Y,Z) -> (XZ,YZ**2,Z) */ - || !group->meth->field_mul(group, r->X, t3, r->Z, ctx) + || !BN_mod_lshift1_quick(t4, p->Y, group->field) + || !group->meth->field_mul(group, t6, r->X, t4, ctx) + || !group->meth->field_mul(group, t6, s->Z, t6, ctx) + || !group->meth->field_mul(group, t5, r->Z, t6, ctx) + || !BN_mod_lshift1_quick(t1, group->b, group->field) + || !group->meth->field_mul(group, t1, s->Z, t1, ctx) || !group->meth->field_sqr(group, t3, r->Z, ctx) - || !group->meth->field_mul(group, r->Y, t4, t3, ctx)) + || !group->meth->field_mul(group, t2, t3, t1, ctx) + || !group->meth->field_mul(group, t6, r->Z, group->a, ctx) + || !group->meth->field_mul(group, t1, p->X, r->X, ctx) + || !BN_mod_add_quick(t1, t1, t6, group->field) + || !group->meth->field_mul(group, t1, s->Z, t1, ctx) + || !group->meth->field_mul(group, t0, p->X, r->Z, ctx) + || !BN_mod_add_quick(t6, r->X, t0, group->field) + || !group->meth->field_mul(group, t6, t6, t1, ctx) + || !BN_mod_add_quick(t6, t6, t2, group->field) + || !BN_mod_sub_quick(t0, t0, r->X, group->field) + || !group->meth->field_sqr(group, t0, t0, ctx) + || !group->meth->field_mul(group, t0, t0, s->X, ctx) + || !BN_mod_sub_quick(t0, t6, t0, group->field) + || !group->meth->field_mul(group, t1, s->Z, t4, ctx) + || !group->meth->field_mul(group, t1, t3, t1, ctx) + || (group->meth->field_decode != NULL + && !group->meth->field_decode(group, t1, t1, ctx)) + || !group->meth->field_inv(group, t1, t1, ctx) + || (group->meth->field_encode != NULL + && !group->meth->field_encode(group, t1, t1, ctx)) + || !group->meth->field_mul(group, r->X, t5, t1, ctx) + || !group->meth->field_mul(group, r->Y, t0, t1, ctx)) goto err; + if (group->meth->field_set_to_one != NULL) { + if (!group->meth->field_set_to_one(group, r->Z, ctx)) + goto err; + } else { + if (!BN_one(r->Z)) + goto err; + } + + r->Z_is_one = 1; ret = 1; err: |