From: Billy Brumley Date: Sat, 28 Mar 2020 18:35:43 +0000 (+0200) Subject: [crypto/ec] Ladder tweaks X-Git-Tag: openssl-3.0.0-alpha1~177 X-Git-Url: https://git.librecmc.org/?a=commitdiff_plain;h=a4a93bbfb0e679eaa249f77c7c4e7e823ca870ef;p=oweals%2Fopenssl.git [crypto/ec] Ladder tweaks - Convert to affine coords on ladder entry. This lets us use more efficient ladder step formulae. - Convert to affine coords on ladder exit. This prevents the current code awkwardness where conversion happens twice during serialization: first to fetch the buffer size, then again to fetch the coords. - Instead of projectively blinding the input point, blind both accumulators independently. Reviewed-by: Nicola Tuveri Reviewed-by: Bernd Edlinger (Merged from https://github.com/openssl/openssl/pull/11435) --- diff --git a/crypto/ec/ec_mult.c b/crypto/ec/ec_mult.c index 17aacf877b..2d3fc50acf 100644 --- a/crypto/ec/ec_mult.c +++ b/crypto/ec/ec_mult.c @@ -266,17 +266,10 @@ int ec_scalar_mul_ladder(const EC_GROUP *group, EC_POINT *r, goto err; } - /*- - * Apply coordinate blinding for EC_POINT. - * - * The underlying EC_METHOD can optionally implement this function: - * ec_point_blind_coordinates() returns 0 in case of errors or 1 on - * success or if coordinate blinding is not implemented for this - * group. - */ - if (!ec_point_blind_coordinates(group, p, ctx)) { - ECerr(EC_F_EC_SCALAR_MUL_LADDER, EC_R_POINT_COORDINATES_BLIND_FAILURE); - goto err; + /* ensure input point is in affine coords for ladder step efficiency */ + if (!p->Z_is_one && !EC_POINT_make_affine(group, p, ctx)) { + ECerr(EC_F_EC_SCALAR_MUL_LADDER, ERR_R_EC_LIB); + goto err; } /* Initialize the Montgomery ladder */ diff --git a/crypto/ec/ecp_smpl.c b/crypto/ec/ecp_smpl.c index 005ab1ec65..9eaa887f21 100644 --- a/crypto/ec/ecp_smpl.c +++ b/crypto/ec/ecp_smpl.c @@ -1381,6 +1381,7 @@ 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) @@ -1476,77 +1477,96 @@ int ec_GFp_simple_blind_coordinates(const EC_GROUP *group, EC_POINT *p, } /*- - * 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_ex(r->Y, group->field, ctx)) + 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_ex(s->Z, group->field, ctx)) + 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); @@ -1556,50 +1576,47 @@ 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; @@ -1610,17 +1627,23 @@ 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 @@ -1637,11 +1660,7 @@ 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; @@ -1657,38 +1676,46 @@ 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: