/* Originally written by Bodo Moeller for the OpenSSL project. * ==================================================================== * Copyright (c) 1998-2005 The OpenSSL Project. All rights reserved. * * Redistribution and use in source and binary forms, with or without * modification, are permitted provided that the following conditions * are met: * * 1. Redistributions of source code must retain the above copyright * notice, this list of conditions and the following disclaimer. * * 2. Redistributions in binary form must reproduce the above copyright * notice, this list of conditions and the following disclaimer in * the documentation and/or other materials provided with the * distribution. * * 3. All advertising materials mentioning features or use of this * software must display the following acknowledgment: * "This product includes software developed by the OpenSSL Project * for use in the OpenSSL Toolkit. (http://www.openssl.org/)" * * 4. The names "OpenSSL Toolkit" and "OpenSSL Project" must not be used to * endorse or promote products derived from this software without * prior written permission. For written permission, please contact * openssl-core@openssl.org. * * 5. Products derived from this software may not be called "OpenSSL" * nor may "OpenSSL" appear in their names without prior written * permission of the OpenSSL Project. * * 6. Redistributions of any form whatsoever must retain the following * acknowledgment: * "This product includes software developed by the OpenSSL Project * for use in the OpenSSL Toolkit (http://www.openssl.org/)" * * THIS SOFTWARE IS PROVIDED BY THE OpenSSL PROJECT ``AS IS'' AND ANY * EXPRESSED OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR * PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE OpenSSL PROJECT OR * ITS CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, * SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT * NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; * LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, * STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) * ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED * OF THE POSSIBILITY OF SUCH DAMAGE. * ==================================================================== * * This product includes cryptographic software written by Eric Young * (eay@cryptsoft.com). This product includes software written by Tim * Hudson (tjh@cryptsoft.com). * */ /* ==================================================================== * Copyright 2002 Sun Microsystems, Inc. ALL RIGHTS RESERVED. * * Portions of the attached software ("Contribution") are developed by * SUN MICROSYSTEMS, INC., and are contributed to the OpenSSL project. * * The Contribution is licensed pursuant to the OpenSSL open source * license provided above. * * The elliptic curve binary polynomial software is originally written by * Sheueling Chang Shantz and Douglas Stebila of Sun Microsystems * Laboratories. */ #include #include #include #include #include #include #include #include "internal.h" #include "../../internal.h" #include "../bn/internal.h" #include "../delocate.h" #include "builtin_curves.h" static void ec_point_free(EC_POINT *point, int free_group); static void ec_group_init_static_mont(BN_MONT_CTX *mont, size_t num_words, const BN_ULONG *modulus, const BN_ULONG *rr, uint64_t n0) { bn_set_static_words(&mont->N, modulus, num_words); bn_set_static_words(&mont->RR, rr, num_words); #if defined(OPENSSL_64_BIT) mont->n0[0] = n0; #elif defined(OPENSSL_32_BIT) mont->n0[0] = (uint32_t)n0; mont->n0[1] = (uint32_t)(n0 >> 32); #else #error "unknown word length" #endif } static void ec_group_set_a_minus3(EC_GROUP *group) { const EC_FELEM *one = ec_felem_one(group); group->a_is_minus3 = 1; ec_felem_neg(group, &group->a, one); ec_felem_sub(group, &group->a, &group->a, one); ec_felem_sub(group, &group->a, &group->a, one); } static void ec_group_set_a_zero(EC_GROUP *group) { group->a_is_minus3 = 0; OPENSSL_memset(group->a.words, 0, sizeof(EC_FELEM)); } DEFINE_METHOD_FUNCTION(EC_GROUP, EC_group_p224) { out->curve_name = NID_secp224r1; out->comment = "NIST P-224"; // 1.3.132.0.33 static const uint8_t kOIDP224[] = {0x2b, 0x81, 0x04, 0x00, 0x21}; OPENSSL_memcpy(out->oid, kOIDP224, sizeof(kOIDP224)); out->oid_len = sizeof(kOIDP224); ec_group_init_static_mont(&out->field, OPENSSL_ARRAY_SIZE(kP224Field), kP224Field, kP224FieldRR, kP224FieldN0); ec_group_init_static_mont(&out->order, OPENSSL_ARRAY_SIZE(kP224Order), kP224Order, kP224OrderRR, kP224OrderN0); #if defined(BORINGSSL_HAS_UINT128) && !defined(OPENSSL_SMALL) out->meth = EC_GFp_nistp224_method(); OPENSSL_memcpy(out->generator.raw.X.words, kP224GX, sizeof(kP224GX)); OPENSSL_memcpy(out->generator.raw.Y.words, kP224GY, sizeof(kP224GY)); out->generator.raw.Z.words[0] = 1; OPENSSL_memcpy(out->b.words, kP224B, sizeof(kP224B)); #else out->meth = EC_GFp_mont_method(); OPENSSL_memcpy(out->generator.raw.X.words, kP224MontGX, sizeof(kP224MontGX)); OPENSSL_memcpy(out->generator.raw.Y.words, kP224MontGY, sizeof(kP224MontGY)); OPENSSL_memcpy(out->generator.raw.Z.words, kP224FieldR, sizeof(kP224FieldR)); OPENSSL_memcpy(out->b.words, kP224MontB, sizeof(kP224MontB)); #endif out->generator.group = out; ec_group_set_a_minus3(out); out->has_order = 1; out->field_greater_than_order = 1; } DEFINE_METHOD_FUNCTION(EC_GROUP, EC_group_p256) { out->curve_name = NID_X9_62_prime256v1; out->comment = "NIST P-256"; // 1.2.840.10045.3.1.7 static const uint8_t kOIDP256[] = {0x2a, 0x86, 0x48, 0xce, 0x3d, 0x03, 0x01, 0x07}; OPENSSL_memcpy(out->oid, kOIDP256, sizeof(kOIDP256)); out->oid_len = sizeof(kOIDP256); ec_group_init_static_mont(&out->field, OPENSSL_ARRAY_SIZE(kP256Field), kP256Field, kP256FieldRR, kP256FieldN0); ec_group_init_static_mont(&out->order, OPENSSL_ARRAY_SIZE(kP256Order), kP256Order, kP256OrderRR, kP256OrderN0); #if !defined(OPENSSL_NO_ASM) && \ (defined(OPENSSL_X86_64) || defined(OPENSSL_AARCH64)) && \ !defined(OPENSSL_SMALL) out->meth = EC_GFp_nistz256_method(); #else out->meth = EC_GFp_nistp256_method(); #endif out->generator.group = out; OPENSSL_memcpy(out->generator.raw.X.words, kP256MontGX, sizeof(kP256MontGX)); OPENSSL_memcpy(out->generator.raw.Y.words, kP256MontGY, sizeof(kP256MontGY)); OPENSSL_memcpy(out->generator.raw.Z.words, kP256FieldR, sizeof(kP256FieldR)); OPENSSL_memcpy(out->b.words, kP256MontB, sizeof(kP256MontB)); ec_group_set_a_minus3(out); out->has_order = 1; out->field_greater_than_order = 1; } DEFINE_METHOD_FUNCTION(EC_GROUP, EC_group_p384) { out->curve_name = NID_secp384r1; out->comment = "NIST P-384"; // 1.3.132.0.34 static const uint8_t kOIDP384[] = {0x2b, 0x81, 0x04, 0x00, 0x22}; OPENSSL_memcpy(out->oid, kOIDP384, sizeof(kOIDP384)); out->oid_len = sizeof(kOIDP384); ec_group_init_static_mont(&out->field, OPENSSL_ARRAY_SIZE(kP384Field), kP384Field, kP384FieldRR, kP384FieldN0); ec_group_init_static_mont(&out->order, OPENSSL_ARRAY_SIZE(kP384Order), kP384Order, kP384OrderRR, kP384OrderN0); #if !defined(OPENSSL_SMALL) out->meth = EC_GFp_nistp384_method(); #else out->meth = EC_GFp_mont_method(); #endif out->generator.group = out; OPENSSL_memcpy(out->generator.raw.X.words, kP384MontGX, sizeof(kP384MontGX)); OPENSSL_memcpy(out->generator.raw.Y.words, kP384MontGY, sizeof(kP384MontGY)); OPENSSL_memcpy(out->generator.raw.Z.words, kP384FieldR, sizeof(kP384FieldR)); OPENSSL_memcpy(out->b.words, kP384MontB, sizeof(kP384MontB)); ec_group_set_a_minus3(out); out->has_order = 1; out->field_greater_than_order = 1; } DEFINE_METHOD_FUNCTION(EC_GROUP, EC_group_p521) { out->curve_name = NID_secp521r1; out->comment = "NIST P-521"; // 1.3.132.0.35 static const uint8_t kOIDP521[] = {0x2b, 0x81, 0x04, 0x00, 0x23}; OPENSSL_memcpy(out->oid, kOIDP521, sizeof(kOIDP521)); out->oid_len = sizeof(kOIDP521); ec_group_init_static_mont(&out->field, OPENSSL_ARRAY_SIZE(kP521Field), kP521Field, kP521FieldRR, kP521FieldN0); ec_group_init_static_mont(&out->order, OPENSSL_ARRAY_SIZE(kP521Order), kP521Order, kP521OrderRR, kP521OrderN0); #if !defined(OPENSSL_SMALL) out->meth = EC_GFp_nistp521_method(); OPENSSL_memcpy(out->generator.raw.X.words, kP521GX, sizeof(kP521GX)); OPENSSL_memcpy(out->generator.raw.Y.words, kP521GY, sizeof(kP521GY)); out->generator.raw.Z.words[0] = 1; OPENSSL_memcpy(out->b.words, kP521B, sizeof(kP521B)); #else out->meth = EC_GFp_mont_method(); OPENSSL_memcpy(out->generator.raw.X.words, kP521MontGX, sizeof(kP521MontGX)); OPENSSL_memcpy(out->generator.raw.Y.words, kP521MontGY, sizeof(kP521MontGY)); OPENSSL_memcpy(out->generator.raw.Z.words, kP521FieldR, sizeof(kP521FieldR)); OPENSSL_memcpy(out->b.words, kP521MontB, sizeof(kP521MontB)); #endif out->generator.group = out; ec_group_set_a_minus3(out); out->has_order = 1; out->field_greater_than_order = 1; } DEFINE_METHOD_FUNCTION(EC_GROUP, EC_group_secp256k1) { out->curve_name = NID_secp256k1; out->comment = "secp256k1"; // 1.3.132.0.10 static const uint8_t kOIDP256K1[] = {0x2b, 0x81, 0x04, 0x00, 0x0a}; OPENSSL_memcpy(out->oid, kOIDP256K1, sizeof(kOIDP256K1)); out->oid_len = sizeof(kOIDP256K1); ec_group_init_static_mont(&out->field, OPENSSL_ARRAY_SIZE(ksecp256k1Field), ksecp256k1Field, ksecp256k1FieldRR, ksecp256k1FieldN0); ec_group_init_static_mont(&out->order, OPENSSL_ARRAY_SIZE(ksecp256k1Order), ksecp256k1Order, ksecp256k1OrderRR, ksecp256k1OrderN0); out->meth = EC_GFp_mont_method(); out->generator.group = out; OPENSSL_memcpy(out->generator.raw.X.words, ksecp256k1MontGX, sizeof(ksecp256k1MontGX)); OPENSSL_memcpy(out->generator.raw.Y.words, ksecp256k1MontGY, sizeof(ksecp256k1MontGY)); OPENSSL_memcpy(out->generator.raw.Z.words, ksecp256k1FieldR, sizeof(ksecp256k1FieldR)); OPENSSL_memcpy(out->b.words, ksecp256k1MontB, sizeof(ksecp256k1MontB)); ec_group_set_a_zero(out); out->has_order = 1; out->field_greater_than_order = 1; } EC_GROUP *EC_GROUP_new_curve_GFp(const BIGNUM *p, const BIGNUM *a, const BIGNUM *b, BN_CTX *ctx) { if (BN_num_bytes(p) > EC_MAX_BYTES) { OPENSSL_PUT_ERROR(EC, EC_R_INVALID_FIELD); return NULL; } BN_CTX *new_ctx = NULL; if (ctx == NULL) { ctx = new_ctx = BN_CTX_new(); if (ctx == NULL) { return NULL; } } // Historically, |a| and |b| were not required to be fully reduced. // TODO(davidben): Can this be removed? EC_GROUP *ret = NULL; BN_CTX_start(ctx); BIGNUM *a_reduced = BN_CTX_get(ctx); BIGNUM *b_reduced = BN_CTX_get(ctx); if (a_reduced == NULL || b_reduced == NULL || !BN_nnmod(a_reduced, a, p, ctx) || !BN_nnmod(b_reduced, b, p, ctx)) { goto err; } ret = OPENSSL_zalloc(sizeof(EC_GROUP)); if (ret == NULL) { return NULL; } ret->references = 1; ret->meth = EC_GFp_mont_method(); bn_mont_ctx_init(&ret->field); bn_mont_ctx_init(&ret->order); ret->generator.group = ret; if (!ec_GFp_simple_group_set_curve(ret, p, a_reduced, b_reduced, ctx)) { EC_GROUP_free(ret); ret = NULL; goto err; } err: BN_CTX_end(ctx); BN_CTX_free(new_ctx); return ret; } int EC_GROUP_set_generator(EC_GROUP *group, const EC_POINT *generator, const BIGNUM *order, const BIGNUM *cofactor) { if (group->curve_name != NID_undef || group->has_order || generator->group != group) { // |EC_GROUP_set_generator| may only be used with |EC_GROUP|s returned by // |EC_GROUP_new_curve_GFp| and may only used once on each group. // |generator| must have been created from |EC_GROUP_new_curve_GFp|, not a // copy, so that |generator->group->generator| is set correctly. OPENSSL_PUT_ERROR(EC, ERR_R_SHOULD_NOT_HAVE_BEEN_CALLED); return 0; } if (BN_num_bytes(order) > EC_MAX_BYTES) { OPENSSL_PUT_ERROR(EC, EC_R_INVALID_GROUP_ORDER); return 0; } // Require a cofactor of one for custom curves, which implies prime order. if (!BN_is_one(cofactor)) { OPENSSL_PUT_ERROR(EC, EC_R_INVALID_COFACTOR); return 0; } // Require that p < 2×order. This simplifies some ECDSA operations. // // Note any curve which did not satisfy this must have been invalid or use a // tiny prime (less than 17). See the proof in |field_element_to_scalar| in // the ECDSA implementation. int ret = 0; BIGNUM *tmp = BN_new(); if (tmp == NULL || !BN_lshift1(tmp, order)) { goto err; } if (BN_cmp(tmp, &group->field.N) <= 0) { OPENSSL_PUT_ERROR(EC, EC_R_INVALID_GROUP_ORDER); goto err; } EC_AFFINE affine; if (!ec_jacobian_to_affine(group, &affine, &generator->raw) || !BN_MONT_CTX_set(&group->order, order, NULL)) { goto err; } group->field_greater_than_order = BN_cmp(&group->field.N, order) > 0; group->generator.raw.X = affine.X; group->generator.raw.Y = affine.Y; // |raw.Z| was set to 1 by |EC_GROUP_new_curve_GFp|. group->has_order = 1; ret = 1; err: BN_free(tmp); return ret; } EC_GROUP *EC_GROUP_new_by_curve_name(int nid) { switch (nid) { case NID_secp224r1: return (EC_GROUP *)EC_group_p224(); case NID_X9_62_prime256v1: return (EC_GROUP *)EC_group_p256(); case NID_secp384r1: return (EC_GROUP *)EC_group_p384(); case NID_secp521r1: return (EC_GROUP *)EC_group_p521(); case NID_secp256k1: return (EC_GROUP *)EC_group_secp256k1(); default: OPENSSL_PUT_ERROR(EC, EC_R_UNKNOWN_GROUP); return NULL; } } void EC_GROUP_free(EC_GROUP *group) { if (group == NULL || // Built-in curves are static. group->curve_name != NID_undef || !CRYPTO_refcount_dec_and_test_zero(&group->references)) { return; } bn_mont_ctx_cleanup(&group->order); bn_mont_ctx_cleanup(&group->field); OPENSSL_free(group); } EC_GROUP *EC_GROUP_dup(const EC_GROUP *a) { if (a == NULL || // Built-in curves are static. a->curve_name != NID_undef) { return (EC_GROUP *)a; } // Groups are logically immutable (but for |EC_GROUP_set_generator| which must // be called early on), so we simply take a reference. EC_GROUP *group = (EC_GROUP *)a; CRYPTO_refcount_inc(&group->references); return group; } int EC_GROUP_cmp(const EC_GROUP *a, const EC_GROUP *b, BN_CTX *ignored) { // Note this function returns 0 if equal and non-zero otherwise. if (a == b) { return 0; } if (a->curve_name != b->curve_name) { return 1; } if (a->curve_name != NID_undef) { // Built-in curves may be compared by curve name alone. return 0; } // |a| and |b| are both custom curves. We compare the entire curve // structure. If |a| or |b| is incomplete (due to legacy OpenSSL mistakes, // custom curve construction is sadly done in two parts) but otherwise not the // same object, we consider them always unequal. return a->meth != b->meth || // !a->has_order || !b->has_order || BN_cmp(&a->order.N, &b->order.N) != 0 || BN_cmp(&a->field.N, &b->field.N) != 0 || !ec_felem_equal(a, &a->a, &b->a) || // !ec_felem_equal(a, &a->b, &b->b) || !ec_GFp_simple_points_equal(a, &a->generator.raw, &b->generator.raw); } const EC_POINT *EC_GROUP_get0_generator(const EC_GROUP *group) { return group->has_order ? &group->generator : NULL; } const BIGNUM *EC_GROUP_get0_order(const EC_GROUP *group) { assert(group->has_order); return &group->order.N; } int EC_GROUP_get_order(const EC_GROUP *group, BIGNUM *order, BN_CTX *ctx) { if (BN_copy(order, EC_GROUP_get0_order(group)) == NULL) { return 0; } return 1; } int EC_GROUP_order_bits(const EC_GROUP *group) { return BN_num_bits(&group->order.N); } int EC_GROUP_get_cofactor(const EC_GROUP *group, BIGNUM *cofactor, BN_CTX *ctx) { // All |EC_GROUP|s have cofactor 1. return BN_set_word(cofactor, 1); } int EC_GROUP_get_curve_GFp(const EC_GROUP *group, BIGNUM *out_p, BIGNUM *out_a, BIGNUM *out_b, BN_CTX *ctx) { return ec_GFp_simple_group_get_curve(group, out_p, out_a, out_b); } int EC_GROUP_get_curve_name(const EC_GROUP *group) { return group->curve_name; } unsigned EC_GROUP_get_degree(const EC_GROUP *group) { return BN_num_bits(&group->field.N); } const char *EC_curve_nid2nist(int nid) { switch (nid) { case NID_secp224r1: return "P-224"; case NID_X9_62_prime256v1: return "P-256"; case NID_secp384r1: return "P-384"; case NID_secp521r1: return "P-521"; } return NULL; } int EC_curve_nist2nid(const char *name) { if (strcmp(name, "P-224") == 0) { return NID_secp224r1; } if (strcmp(name, "P-256") == 0) { return NID_X9_62_prime256v1; } if (strcmp(name, "P-384") == 0) { return NID_secp384r1; } if (strcmp(name, "P-521") == 0) { return NID_secp521r1; } return NID_undef; } EC_POINT *EC_POINT_new(const EC_GROUP *group) { if (group == NULL) { OPENSSL_PUT_ERROR(EC, ERR_R_PASSED_NULL_PARAMETER); return NULL; } EC_POINT *ret = OPENSSL_malloc(sizeof *ret); if (ret == NULL) { return NULL; } ret->group = EC_GROUP_dup(group); ec_GFp_simple_point_init(&ret->raw); return ret; } static void ec_point_free(EC_POINT *point, int free_group) { if (!point) { return; } if (free_group) { EC_GROUP_free(point->group); } OPENSSL_free(point); } void EC_POINT_free(EC_POINT *point) { ec_point_free(point, 1 /* free group */); } void EC_POINT_clear_free(EC_POINT *point) { EC_POINT_free(point); } int EC_POINT_copy(EC_POINT *dest, const EC_POINT *src) { if (EC_GROUP_cmp(dest->group, src->group, NULL) != 0) { OPENSSL_PUT_ERROR(EC, EC_R_INCOMPATIBLE_OBJECTS); return 0; } if (dest == src) { return 1; } ec_GFp_simple_point_copy(&dest->raw, &src->raw); return 1; } EC_POINT *EC_POINT_dup(const EC_POINT *a, const EC_GROUP *group) { if (a == NULL) { return NULL; } EC_POINT *ret = EC_POINT_new(group); if (ret == NULL || !EC_POINT_copy(ret, a)) { EC_POINT_free(ret); return NULL; } return ret; } int EC_POINT_set_to_infinity(const EC_GROUP *group, EC_POINT *point) { if (EC_GROUP_cmp(group, point->group, NULL) != 0) { OPENSSL_PUT_ERROR(EC, EC_R_INCOMPATIBLE_OBJECTS); return 0; } ec_GFp_simple_point_set_to_infinity(group, &point->raw); return 1; } int EC_POINT_is_at_infinity(const EC_GROUP *group, const EC_POINT *point) { if (EC_GROUP_cmp(group, point->group, NULL) != 0) { OPENSSL_PUT_ERROR(EC, EC_R_INCOMPATIBLE_OBJECTS); return 0; } return ec_GFp_simple_is_at_infinity(group, &point->raw); } int EC_POINT_is_on_curve(const EC_GROUP *group, const EC_POINT *point, BN_CTX *ctx) { if (EC_GROUP_cmp(group, point->group, NULL) != 0) { OPENSSL_PUT_ERROR(EC, EC_R_INCOMPATIBLE_OBJECTS); return 0; } return ec_GFp_simple_is_on_curve(group, &point->raw); } int EC_POINT_cmp(const EC_GROUP *group, const EC_POINT *a, const EC_POINT *b, BN_CTX *ctx) { if (EC_GROUP_cmp(group, a->group, NULL) != 0 || EC_GROUP_cmp(group, b->group, NULL) != 0) { OPENSSL_PUT_ERROR(EC, EC_R_INCOMPATIBLE_OBJECTS); return -1; } // Note |EC_POINT_cmp| returns zero for equality and non-zero for inequality. return ec_GFp_simple_points_equal(group, &a->raw, &b->raw) ? 0 : 1; } int EC_POINT_get_affine_coordinates_GFp(const EC_GROUP *group, const EC_POINT *point, BIGNUM *x, BIGNUM *y, BN_CTX *ctx) { if (group->meth->point_get_affine_coordinates == 0) { OPENSSL_PUT_ERROR(EC, ERR_R_SHOULD_NOT_HAVE_BEEN_CALLED); return 0; } if (EC_GROUP_cmp(group, point->group, NULL) != 0) { OPENSSL_PUT_ERROR(EC, EC_R_INCOMPATIBLE_OBJECTS); return 0; } EC_FELEM x_felem, y_felem; if (!group->meth->point_get_affine_coordinates(group, &point->raw, x == NULL ? NULL : &x_felem, y == NULL ? NULL : &y_felem) || (x != NULL && !ec_felem_to_bignum(group, x, &x_felem)) || (y != NULL && !ec_felem_to_bignum(group, y, &y_felem))) { return 0; } return 1; } int EC_POINT_get_affine_coordinates(const EC_GROUP *group, const EC_POINT *point, BIGNUM *x, BIGNUM *y, BN_CTX *ctx) { return EC_POINT_get_affine_coordinates_GFp(group, point, x, y, ctx); } void ec_affine_to_jacobian(const EC_GROUP *group, EC_JACOBIAN *out, const EC_AFFINE *p) { out->X = p->X; out->Y = p->Y; out->Z = *ec_felem_one(group); } int ec_jacobian_to_affine(const EC_GROUP *group, EC_AFFINE *out, const EC_JACOBIAN *p) { return group->meth->point_get_affine_coordinates(group, p, &out->X, &out->Y); } int ec_jacobian_to_affine_batch(const EC_GROUP *group, EC_AFFINE *out, const EC_JACOBIAN *in, size_t num) { if (group->meth->jacobian_to_affine_batch == NULL) { OPENSSL_PUT_ERROR(EC, ERR_R_SHOULD_NOT_HAVE_BEEN_CALLED); return 0; } return group->meth->jacobian_to_affine_batch(group, out, in, num); } int ec_point_set_affine_coordinates(const EC_GROUP *group, EC_AFFINE *out, const EC_FELEM *x, const EC_FELEM *y) { void (*const felem_mul)(const EC_GROUP *, EC_FELEM *r, const EC_FELEM *a, const EC_FELEM *b) = group->meth->felem_mul; void (*const felem_sqr)(const EC_GROUP *, EC_FELEM *r, const EC_FELEM *a) = group->meth->felem_sqr; // Check if the point is on the curve. EC_FELEM lhs, rhs; felem_sqr(group, &lhs, y); // lhs = y^2 felem_sqr(group, &rhs, x); // rhs = x^2 ec_felem_add(group, &rhs, &rhs, &group->a); // rhs = x^2 + a felem_mul(group, &rhs, &rhs, x); // rhs = x^3 + ax ec_felem_add(group, &rhs, &rhs, &group->b); // rhs = x^3 + ax + b if (!ec_felem_equal(group, &lhs, &rhs)) { OPENSSL_PUT_ERROR(EC, EC_R_POINT_IS_NOT_ON_CURVE); // In the event of an error, defend against the caller not checking the // return value by setting a known safe value. Note this may not be possible // if the caller is in the process of constructing an arbitrary group and // the generator is missing. if (group->has_order) { out->X = group->generator.raw.X; out->Y = group->generator.raw.Y; } return 0; } out->X = *x; out->Y = *y; return 1; } int EC_POINT_set_affine_coordinates_GFp(const EC_GROUP *group, EC_POINT *point, const BIGNUM *x, const BIGNUM *y, BN_CTX *ctx) { if (EC_GROUP_cmp(group, point->group, NULL) != 0) { OPENSSL_PUT_ERROR(EC, EC_R_INCOMPATIBLE_OBJECTS); return 0; } if (x == NULL || y == NULL) { OPENSSL_PUT_ERROR(EC, ERR_R_PASSED_NULL_PARAMETER); return 0; } EC_FELEM x_felem, y_felem; EC_AFFINE affine; if (!ec_bignum_to_felem(group, &x_felem, x) || !ec_bignum_to_felem(group, &y_felem, y) || !ec_point_set_affine_coordinates(group, &affine, &x_felem, &y_felem)) { // In the event of an error, defend against the caller not checking the // return value by setting a known safe value. ec_set_to_safe_point(group, &point->raw); return 0; } ec_affine_to_jacobian(group, &point->raw, &affine); return 1; } int EC_POINT_set_affine_coordinates(const EC_GROUP *group, EC_POINT *point, const BIGNUM *x, const BIGNUM *y, BN_CTX *ctx) { return EC_POINT_set_affine_coordinates_GFp(group, point, x, y, ctx); } int EC_POINT_add(const EC_GROUP *group, EC_POINT *r, const EC_POINT *a, const EC_POINT *b, BN_CTX *ctx) { if (EC_GROUP_cmp(group, r->group, NULL) != 0 || EC_GROUP_cmp(group, a->group, NULL) != 0 || EC_GROUP_cmp(group, b->group, NULL) != 0) { OPENSSL_PUT_ERROR(EC, EC_R_INCOMPATIBLE_OBJECTS); return 0; } group->meth->add(group, &r->raw, &a->raw, &b->raw); return 1; } int EC_POINT_dbl(const EC_GROUP *group, EC_POINT *r, const EC_POINT *a, BN_CTX *ctx) { if (EC_GROUP_cmp(group, r->group, NULL) != 0 || EC_GROUP_cmp(group, a->group, NULL) != 0) { OPENSSL_PUT_ERROR(EC, EC_R_INCOMPATIBLE_OBJECTS); return 0; } group->meth->dbl(group, &r->raw, &a->raw); return 1; } int EC_POINT_invert(const EC_GROUP *group, EC_POINT *a, BN_CTX *ctx) { if (EC_GROUP_cmp(group, a->group, NULL) != 0) { OPENSSL_PUT_ERROR(EC, EC_R_INCOMPATIBLE_OBJECTS); return 0; } ec_GFp_simple_invert(group, &a->raw); return 1; } static int arbitrary_bignum_to_scalar(const EC_GROUP *group, EC_SCALAR *out, const BIGNUM *in, BN_CTX *ctx) { if (ec_bignum_to_scalar(group, out, in)) { return 1; } ERR_clear_error(); // This is an unusual input, so we do not guarantee constant-time processing. BN_CTX_start(ctx); BIGNUM *tmp = BN_CTX_get(ctx); int ok = tmp != NULL && BN_nnmod(tmp, in, EC_GROUP_get0_order(group), ctx) && ec_bignum_to_scalar(group, out, tmp); BN_CTX_end(ctx); return ok; } int ec_point_mul_no_self_test(const EC_GROUP *group, EC_POINT *r, const BIGNUM *g_scalar, const EC_POINT *p, const BIGNUM *p_scalar, BN_CTX *ctx) { // Previously, this function set |r| to the point at infinity if there was // nothing to multiply. But, nobody should be calling this function with // nothing to multiply in the first place. if ((g_scalar == NULL && p_scalar == NULL) || (p == NULL) != (p_scalar == NULL)) { OPENSSL_PUT_ERROR(EC, ERR_R_PASSED_NULL_PARAMETER); return 0; } if (EC_GROUP_cmp(group, r->group, NULL) != 0 || (p != NULL && EC_GROUP_cmp(group, p->group, NULL) != 0)) { OPENSSL_PUT_ERROR(EC, EC_R_INCOMPATIBLE_OBJECTS); return 0; } int ret = 0; BN_CTX *new_ctx = NULL; if (ctx == NULL) { new_ctx = BN_CTX_new(); if (new_ctx == NULL) { goto err; } ctx = new_ctx; } // If both |g_scalar| and |p_scalar| are non-NULL, // |ec_point_mul_scalar_public| would share the doublings between the two // products, which would be more efficient. However, we conservatively assume // the caller needs a constant-time operation. (ECDSA verification does not // use this function.) // // Previously, the low-level constant-time multiplication function aligned // with this function's calling convention, but this was misleading. Curves // which combined the two multiplications did not avoid the doubling case // in the incomplete addition formula and were not constant-time. if (g_scalar != NULL) { EC_SCALAR scalar; if (!arbitrary_bignum_to_scalar(group, &scalar, g_scalar, ctx) || !ec_point_mul_scalar_base(group, &r->raw, &scalar)) { goto err; } } if (p_scalar != NULL) { EC_SCALAR scalar; EC_JACOBIAN tmp; if (!arbitrary_bignum_to_scalar(group, &scalar, p_scalar, ctx) || !ec_point_mul_scalar(group, &tmp, &p->raw, &scalar)) { goto err; } if (g_scalar == NULL) { OPENSSL_memcpy(&r->raw, &tmp, sizeof(EC_JACOBIAN)); } else { group->meth->add(group, &r->raw, &r->raw, &tmp); } } ret = 1; err: BN_CTX_free(new_ctx); return ret; } int EC_POINT_mul(const EC_GROUP *group, EC_POINT *r, const BIGNUM *g_scalar, const EC_POINT *p, const BIGNUM *p_scalar, BN_CTX *ctx) { boringssl_ensure_ecc_self_test(); SET_DIT_AUTO_RESET; return ec_point_mul_no_self_test(group, r, g_scalar, p, p_scalar, ctx); } int ec_point_mul_scalar_public(const EC_GROUP *group, EC_JACOBIAN *r, const EC_SCALAR *g_scalar, const EC_JACOBIAN *p, const EC_SCALAR *p_scalar) { if (g_scalar == NULL || p_scalar == NULL || p == NULL) { OPENSSL_PUT_ERROR(EC, ERR_R_PASSED_NULL_PARAMETER); return 0; } if (group->meth->mul_public == NULL) { return group->meth->mul_public_batch(group, r, g_scalar, p, p_scalar, 1); } group->meth->mul_public(group, r, g_scalar, p, p_scalar); return 1; } int ec_point_mul_scalar_public_batch(const EC_GROUP *group, EC_JACOBIAN *r, const EC_SCALAR *g_scalar, const EC_JACOBIAN *points, const EC_SCALAR *scalars, size_t num) { if (group->meth->mul_public_batch == NULL) { OPENSSL_PUT_ERROR(EC, ERR_R_SHOULD_NOT_HAVE_BEEN_CALLED); return 0; } return group->meth->mul_public_batch(group, r, g_scalar, points, scalars, num); } int ec_point_mul_scalar(const EC_GROUP *group, EC_JACOBIAN *r, const EC_JACOBIAN *p, const EC_SCALAR *scalar) { SET_DIT_AUTO_RESET; if (p == NULL || scalar == NULL) { OPENSSL_PUT_ERROR(EC, ERR_R_PASSED_NULL_PARAMETER); return 0; } group->meth->mul(group, r, p, scalar); // Check the result is on the curve to defend against fault attacks or bugs. // This has negligible cost compared to the multiplication. if (!ec_GFp_simple_is_on_curve(group, r)) { OPENSSL_PUT_ERROR(EC, ERR_R_INTERNAL_ERROR); return 0; } return 1; } int ec_point_mul_scalar_base(const EC_GROUP *group, EC_JACOBIAN *r, const EC_SCALAR *scalar) { SET_DIT_AUTO_RESET; if (scalar == NULL) { OPENSSL_PUT_ERROR(EC, ERR_R_PASSED_NULL_PARAMETER); return 0; } group->meth->mul_base(group, r, scalar); // Check the result is on the curve to defend against fault attacks or bugs. // This has negligible cost compared to the multiplication. This can only // happen on bug or CPU fault, so it is okay to leak this information (if the // computed point is on the curve or not). The alternative would be to // proceed with bad data. if (!constant_time_declassify_int(ec_GFp_simple_is_on_curve(group, r))) { OPENSSL_PUT_ERROR(EC, ERR_R_INTERNAL_ERROR); return 0; } return 1; } int ec_point_mul_scalar_batch(const EC_GROUP *group, EC_JACOBIAN *r, const EC_JACOBIAN *p0, const EC_SCALAR *scalar0, const EC_JACOBIAN *p1, const EC_SCALAR *scalar1, const EC_JACOBIAN *p2, const EC_SCALAR *scalar2) { if (group->meth->mul_batch == NULL) { OPENSSL_PUT_ERROR(EC, ERR_R_SHOULD_NOT_HAVE_BEEN_CALLED); return 0; } group->meth->mul_batch(group, r, p0, scalar0, p1, scalar1, p2, scalar2); // Check the result is on the curve to defend against fault attacks or bugs. // This has negligible cost compared to the multiplication. if (!ec_GFp_simple_is_on_curve(group, r)) { OPENSSL_PUT_ERROR(EC, ERR_R_INTERNAL_ERROR); return 0; } return 1; } int ec_init_precomp(const EC_GROUP *group, EC_PRECOMP *out, const EC_JACOBIAN *p) { if (group->meth->init_precomp == NULL) { OPENSSL_PUT_ERROR(EC, ERR_R_SHOULD_NOT_HAVE_BEEN_CALLED); return 0; } return group->meth->init_precomp(group, out, p); } int ec_point_mul_scalar_precomp(const EC_GROUP *group, EC_JACOBIAN *r, const EC_PRECOMP *p0, const EC_SCALAR *scalar0, const EC_PRECOMP *p1, const EC_SCALAR *scalar1, const EC_PRECOMP *p2, const EC_SCALAR *scalar2) { if (group->meth->mul_precomp == NULL) { OPENSSL_PUT_ERROR(EC, ERR_R_SHOULD_NOT_HAVE_BEEN_CALLED); return 0; } group->meth->mul_precomp(group, r, p0, scalar0, p1, scalar1, p2, scalar2); // Check the result is on the curve to defend against fault attacks or bugs. // This has negligible cost compared to the multiplication. if (!ec_GFp_simple_is_on_curve(group, r)) { OPENSSL_PUT_ERROR(EC, ERR_R_INTERNAL_ERROR); return 0; } return 1; } void ec_point_select(const EC_GROUP *group, EC_JACOBIAN *out, BN_ULONG mask, const EC_JACOBIAN *a, const EC_JACOBIAN *b) { ec_felem_select(group, &out->X, mask, &a->X, &b->X); ec_felem_select(group, &out->Y, mask, &a->Y, &b->Y); ec_felem_select(group, &out->Z, mask, &a->Z, &b->Z); } void ec_affine_select(const EC_GROUP *group, EC_AFFINE *out, BN_ULONG mask, const EC_AFFINE *a, const EC_AFFINE *b) { ec_felem_select(group, &out->X, mask, &a->X, &b->X); ec_felem_select(group, &out->Y, mask, &a->Y, &b->Y); } void ec_precomp_select(const EC_GROUP *group, EC_PRECOMP *out, BN_ULONG mask, const EC_PRECOMP *a, const EC_PRECOMP *b) { OPENSSL_STATIC_ASSERT(sizeof(out->comb) == sizeof(*out), out_comb_does_not_span_the_entire_structure) for (size_t i = 0; i < OPENSSL_ARRAY_SIZE(out->comb); i++) { ec_affine_select(group, &out->comb[i], mask, &a->comb[i], &b->comb[i]); } } int ec_cmp_x_coordinate(const EC_GROUP *group, const EC_JACOBIAN *p, const EC_SCALAR *r) { return group->meth->cmp_x_coordinate(group, p, r); } int ec_get_x_coordinate_as_scalar(const EC_GROUP *group, EC_SCALAR *out, const EC_JACOBIAN *p) { uint8_t bytes[EC_MAX_BYTES]; size_t len; if (!ec_get_x_coordinate_as_bytes(group, bytes, &len, sizeof(bytes), p)) { return 0; } // The x-coordinate is bounded by p, but we need a scalar, bounded by the // order. These may not have the same size. However, we must have p < 2×order, // assuming p is not tiny (p >= 17). // // Thus |bytes| will fit in |order.width + 1| words, and we can reduce by // performing at most one subtraction. // // Proof: We only work with prime order curves, so the number of points on // the curve is the order. Thus Hasse's theorem gives: // // |order - (p + 1)| <= 2×sqrt(p) // p + 1 - order <= 2×sqrt(p) // p + 1 - 2×sqrt(p) <= order // p + 1 - 2×(p/4) < order (p/4 > sqrt(p) for p >= 17) // p/2 < p/2 + 1 < order // p < 2×order // // Additionally, one can manually check this property for built-in curves. It // is enforced for legacy custom curves in |EC_GROUP_set_generator|. const BIGNUM *order = EC_GROUP_get0_order(group); BN_ULONG words[EC_MAX_WORDS + 1] = {0}; bn_big_endian_to_words(words, order->width + 1, bytes, len); bn_reduce_once(out->words, words, /*carry=*/words[order->width], order->d, order->width); return 1; } int ec_get_x_coordinate_as_bytes(const EC_GROUP *group, uint8_t *out, size_t *out_len, size_t max_out, const EC_JACOBIAN *p) { size_t len = BN_num_bytes(&group->field.N); assert(len <= EC_MAX_BYTES); if (max_out < len) { OPENSSL_PUT_ERROR(EC, EC_R_BUFFER_TOO_SMALL); return 0; } EC_FELEM x; if (!group->meth->point_get_affine_coordinates(group, p, &x, NULL)) { return 0; } ec_felem_to_bytes(group, out, out_len, &x); *out_len = len; return 1; } void ec_set_to_safe_point(const EC_GROUP *group, EC_JACOBIAN *out) { if (group->has_order) { ec_GFp_simple_point_copy(out, &group->generator.raw); } else { // The generator can be missing if the caller is in the process of // constructing an arbitrary group. In this case, we give up and use the // point at infinity. ec_GFp_simple_point_set_to_infinity(group, out); } } void EC_GROUP_set_asn1_flag(EC_GROUP *group, int flag) {} int EC_GROUP_get_asn1_flag(const EC_GROUP *group) { return OPENSSL_EC_NAMED_CURVE; } const EC_METHOD *EC_GROUP_method_of(const EC_GROUP *group) { // This function exists purely to give callers a way to call // |EC_METHOD_get_field_type|. cryptography.io crashes if |EC_GROUP_method_of| // returns NULL, so return some other garbage pointer. return (const EC_METHOD *)0x12340000; } int EC_METHOD_get_field_type(const EC_METHOD *meth) { return NID_X9_62_prime_field; } void EC_GROUP_set_point_conversion_form(EC_GROUP *group, point_conversion_form_t form) { /* NO-OP. However, abort if consumer attempts to set a representation that is * not supported. */ if (form != POINT_CONVERSION_UNCOMPRESSED && form != POINT_CONVERSION_COMPRESSED) { abort(); } } size_t EC_GROUP_set_seed(EC_GROUP *group, const unsigned char *seed, size_t len) { return 0; } unsigned char *EC_GROUP_get0_seed(const EC_GROUP *group) { return NULL; } size_t EC_GROUP_get_seed_len(const EC_GROUP *group) { return 0; }