diff options
Diffstat (limited to 'thirdparty/openssl/crypto/ec/ecp_smpl.c')
| -rw-r--r-- | thirdparty/openssl/crypto/ec/ecp_smpl.c | 1418 |
1 files changed, 0 insertions, 1418 deletions
diff --git a/thirdparty/openssl/crypto/ec/ecp_smpl.c b/thirdparty/openssl/crypto/ec/ecp_smpl.c deleted file mode 100644 index 2b848216d7..0000000000 --- a/thirdparty/openssl/crypto/ec/ecp_smpl.c +++ /dev/null @@ -1,1418 +0,0 @@ -/* crypto/ec/ecp_smpl.c */ -/* - * Includes code written by Lenka Fibikova <fibikova@exp-math.uni-essen.de> - * for the OpenSSL project. Includes code written by Bodo Moeller for the - * OpenSSL project. - */ -/* ==================================================================== - * Copyright (c) 1998-2002 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 this software developed by SUN MICROSYSTEMS, INC., - * and contributed to the OpenSSL project. - */ - -#include <openssl/err.h> -#include <openssl/symhacks.h> - -#ifdef OPENSSL_FIPS -# include <openssl/fips.h> -#endif - -#include "ec_lcl.h" - -const EC_METHOD *EC_GFp_simple_method(void) -{ - static const EC_METHOD ret = { - EC_FLAGS_DEFAULT_OCT, - NID_X9_62_prime_field, - ec_GFp_simple_group_init, - ec_GFp_simple_group_finish, - ec_GFp_simple_group_clear_finish, - ec_GFp_simple_group_copy, - ec_GFp_simple_group_set_curve, - ec_GFp_simple_group_get_curve, - ec_GFp_simple_group_get_degree, - ec_GFp_simple_group_check_discriminant, - ec_GFp_simple_point_init, - ec_GFp_simple_point_finish, - ec_GFp_simple_point_clear_finish, - ec_GFp_simple_point_copy, - ec_GFp_simple_point_set_to_infinity, - ec_GFp_simple_set_Jprojective_coordinates_GFp, - ec_GFp_simple_get_Jprojective_coordinates_GFp, - ec_GFp_simple_point_set_affine_coordinates, - ec_GFp_simple_point_get_affine_coordinates, - 0, 0, 0, - ec_GFp_simple_add, - ec_GFp_simple_dbl, - ec_GFp_simple_invert, - ec_GFp_simple_is_at_infinity, - ec_GFp_simple_is_on_curve, - ec_GFp_simple_cmp, - ec_GFp_simple_make_affine, - ec_GFp_simple_points_make_affine, - 0 /* mul */ , - 0 /* precompute_mult */ , - 0 /* have_precompute_mult */ , - ec_GFp_simple_field_mul, - ec_GFp_simple_field_sqr, - 0 /* field_div */ , - 0 /* field_encode */ , - 0 /* field_decode */ , - 0 /* field_set_to_one */ - }; - -#ifdef OPENSSL_FIPS - if (FIPS_mode()) - return fips_ec_gfp_simple_method(); -#endif - - return &ret; -} - -/* - * Most method functions in this file are designed to work with - * non-trivial representations of field elements if necessary - * (see ecp_mont.c): while standard modular addition and subtraction - * are used, the field_mul and field_sqr methods will be used for - * multiplication, and field_encode and field_decode (if defined) - * will be used for converting between representations. - * - * Functions ec_GFp_simple_points_make_affine() and - * ec_GFp_simple_point_get_affine_coordinates() specifically assume - * that if a non-trivial representation is used, it is a Montgomery - * representation (i.e. 'encoding' means multiplying by some factor R). - */ - -int ec_GFp_simple_group_init(EC_GROUP *group) -{ - BN_init(&group->field); - BN_init(&group->a); - BN_init(&group->b); - group->a_is_minus3 = 0; - return 1; -} - -void ec_GFp_simple_group_finish(EC_GROUP *group) -{ - BN_free(&group->field); - BN_free(&group->a); - BN_free(&group->b); -} - -void ec_GFp_simple_group_clear_finish(EC_GROUP *group) -{ - BN_clear_free(&group->field); - BN_clear_free(&group->a); - BN_clear_free(&group->b); -} - -int ec_GFp_simple_group_copy(EC_GROUP *dest, const EC_GROUP *src) -{ - if (!BN_copy(&dest->field, &src->field)) - return 0; - if (!BN_copy(&dest->a, &src->a)) - return 0; - if (!BN_copy(&dest->b, &src->b)) - return 0; - - dest->a_is_minus3 = src->a_is_minus3; - - return 1; -} - -int ec_GFp_simple_group_set_curve(EC_GROUP *group, - const BIGNUM *p, const BIGNUM *a, - const BIGNUM *b, BN_CTX *ctx) -{ - int ret = 0; - BN_CTX *new_ctx = NULL; - BIGNUM *tmp_a; - - /* p must be a prime > 3 */ - if (BN_num_bits(p) <= 2 || !BN_is_odd(p)) { - ECerr(EC_F_EC_GFP_SIMPLE_GROUP_SET_CURVE, EC_R_INVALID_FIELD); - return 0; - } - - if (ctx == NULL) { - ctx = new_ctx = BN_CTX_new(); - if (ctx == NULL) - return 0; - } - - BN_CTX_start(ctx); - tmp_a = BN_CTX_get(ctx); - if (tmp_a == NULL) - goto err; - - /* group->field */ - if (!BN_copy(&group->field, p)) - goto err; - BN_set_negative(&group->field, 0); - - /* group->a */ - if (!BN_nnmod(tmp_a, a, p, ctx)) - goto err; - if (group->meth->field_encode) { - if (!group->meth->field_encode(group, &group->a, tmp_a, ctx)) - goto err; - } else if (!BN_copy(&group->a, tmp_a)) - goto err; - - /* group->b */ - if (!BN_nnmod(&group->b, b, p, ctx)) - goto err; - if (group->meth->field_encode) - if (!group->meth->field_encode(group, &group->b, &group->b, ctx)) - goto err; - - /* group->a_is_minus3 */ - if (!BN_add_word(tmp_a, 3)) - goto err; - group->a_is_minus3 = (0 == BN_cmp(tmp_a, &group->field)); - - ret = 1; - - err: - BN_CTX_end(ctx); - if (new_ctx != NULL) - BN_CTX_free(new_ctx); - return ret; -} - -int ec_GFp_simple_group_get_curve(const EC_GROUP *group, BIGNUM *p, BIGNUM *a, - BIGNUM *b, BN_CTX *ctx) -{ - int ret = 0; - BN_CTX *new_ctx = NULL; - - if (p != NULL) { - if (!BN_copy(p, &group->field)) - return 0; - } - - if (a != NULL || b != NULL) { - if (group->meth->field_decode) { - if (ctx == NULL) { - ctx = new_ctx = BN_CTX_new(); - if (ctx == NULL) - return 0; - } - if (a != NULL) { - if (!group->meth->field_decode(group, a, &group->a, ctx)) - goto err; - } - if (b != NULL) { - if (!group->meth->field_decode(group, b, &group->b, ctx)) - goto err; - } - } else { - if (a != NULL) { - if (!BN_copy(a, &group->a)) - goto err; - } - if (b != NULL) { - if (!BN_copy(b, &group->b)) - goto err; - } - } - } - - ret = 1; - - err: - if (new_ctx) - BN_CTX_free(new_ctx); - return ret; -} - -int ec_GFp_simple_group_get_degree(const EC_GROUP *group) -{ - return BN_num_bits(&group->field); -} - -int ec_GFp_simple_group_check_discriminant(const EC_GROUP *group, BN_CTX *ctx) -{ - int ret = 0; - BIGNUM *a, *b, *order, *tmp_1, *tmp_2; - const BIGNUM *p = &group->field; - BN_CTX *new_ctx = NULL; - - if (ctx == NULL) { - ctx = new_ctx = BN_CTX_new(); - if (ctx == NULL) { - ECerr(EC_F_EC_GFP_SIMPLE_GROUP_CHECK_DISCRIMINANT, - ERR_R_MALLOC_FAILURE); - goto err; - } - } - BN_CTX_start(ctx); - a = BN_CTX_get(ctx); - b = BN_CTX_get(ctx); - tmp_1 = BN_CTX_get(ctx); - tmp_2 = BN_CTX_get(ctx); - order = BN_CTX_get(ctx); - if (order == NULL) - goto err; - - if (group->meth->field_decode) { - if (!group->meth->field_decode(group, a, &group->a, ctx)) - goto err; - if (!group->meth->field_decode(group, b, &group->b, ctx)) - goto err; - } else { - if (!BN_copy(a, &group->a)) - goto err; - if (!BN_copy(b, &group->b)) - goto err; - } - - /*- - * check the discriminant: - * y^2 = x^3 + a*x + b is an elliptic curve <=> 4*a^3 + 27*b^2 != 0 (mod p) - * 0 =< a, b < p - */ - if (BN_is_zero(a)) { - if (BN_is_zero(b)) - goto err; - } else if (!BN_is_zero(b)) { - if (!BN_mod_sqr(tmp_1, a, p, ctx)) - goto err; - if (!BN_mod_mul(tmp_2, tmp_1, a, p, ctx)) - goto err; - if (!BN_lshift(tmp_1, tmp_2, 2)) - goto err; - /* tmp_1 = 4*a^3 */ - - if (!BN_mod_sqr(tmp_2, b, p, ctx)) - goto err; - if (!BN_mul_word(tmp_2, 27)) - goto err; - /* tmp_2 = 27*b^2 */ - - if (!BN_mod_add(a, tmp_1, tmp_2, p, ctx)) - goto err; - if (BN_is_zero(a)) - goto err; - } - ret = 1; - - err: - if (ctx != NULL) - BN_CTX_end(ctx); - if (new_ctx != NULL) - BN_CTX_free(new_ctx); - return ret; -} - -int ec_GFp_simple_point_init(EC_POINT *point) -{ - BN_init(&point->X); - BN_init(&point->Y); - BN_init(&point->Z); - point->Z_is_one = 0; - - return 1; -} - -void ec_GFp_simple_point_finish(EC_POINT *point) -{ - BN_free(&point->X); - BN_free(&point->Y); - BN_free(&point->Z); -} - -void ec_GFp_simple_point_clear_finish(EC_POINT *point) -{ - BN_clear_free(&point->X); - BN_clear_free(&point->Y); - BN_clear_free(&point->Z); - point->Z_is_one = 0; -} - -int ec_GFp_simple_point_copy(EC_POINT *dest, const EC_POINT *src) -{ - if (!BN_copy(&dest->X, &src->X)) - return 0; - if (!BN_copy(&dest->Y, &src->Y)) - return 0; - if (!BN_copy(&dest->Z, &src->Z)) - return 0; - dest->Z_is_one = src->Z_is_one; - - return 1; -} - -int ec_GFp_simple_point_set_to_infinity(const EC_GROUP *group, - EC_POINT *point) -{ - point->Z_is_one = 0; - BN_zero(&point->Z); - return 1; -} - -int ec_GFp_simple_set_Jprojective_coordinates_GFp(const EC_GROUP *group, - EC_POINT *point, - const BIGNUM *x, - const BIGNUM *y, - const BIGNUM *z, - BN_CTX *ctx) -{ - BN_CTX *new_ctx = NULL; - int ret = 0; - - if (ctx == NULL) { - ctx = new_ctx = BN_CTX_new(); - if (ctx == NULL) - return 0; - } - - if (x != NULL) { - if (!BN_nnmod(&point->X, x, &group->field, ctx)) - goto err; - if (group->meth->field_encode) { - if (!group->meth->field_encode(group, &point->X, &point->X, ctx)) - goto err; - } - } - - if (y != NULL) { - if (!BN_nnmod(&point->Y, y, &group->field, ctx)) - goto err; - if (group->meth->field_encode) { - if (!group->meth->field_encode(group, &point->Y, &point->Y, ctx)) - goto err; - } - } - - if (z != NULL) { - int Z_is_one; - - if (!BN_nnmod(&point->Z, z, &group->field, ctx)) - goto err; - Z_is_one = BN_is_one(&point->Z); - if (group->meth->field_encode) { - if (Z_is_one && (group->meth->field_set_to_one != 0)) { - if (!group->meth->field_set_to_one(group, &point->Z, ctx)) - goto err; - } else { - if (!group-> - meth->field_encode(group, &point->Z, &point->Z, ctx)) - goto err; - } - } - point->Z_is_one = Z_is_one; - } - - ret = 1; - - err: - if (new_ctx != NULL) - BN_CTX_free(new_ctx); - return ret; -} - -int ec_GFp_simple_get_Jprojective_coordinates_GFp(const EC_GROUP *group, - const EC_POINT *point, - BIGNUM *x, BIGNUM *y, - BIGNUM *z, BN_CTX *ctx) -{ - BN_CTX *new_ctx = NULL; - int ret = 0; - - if (group->meth->field_decode != 0) { - if (ctx == NULL) { - ctx = new_ctx = BN_CTX_new(); - if (ctx == NULL) - return 0; - } - - if (x != NULL) { - if (!group->meth->field_decode(group, x, &point->X, ctx)) - goto err; - } - if (y != NULL) { - if (!group->meth->field_decode(group, y, &point->Y, ctx)) - goto err; - } - if (z != NULL) { - if (!group->meth->field_decode(group, z, &point->Z, ctx)) - goto err; - } - } else { - if (x != NULL) { - if (!BN_copy(x, &point->X)) - goto err; - } - if (y != NULL) { - if (!BN_copy(y, &point->Y)) - goto err; - } - if (z != NULL) { - if (!BN_copy(z, &point->Z)) - goto err; - } - } - - ret = 1; - - err: - if (new_ctx != NULL) - BN_CTX_free(new_ctx); - return ret; -} - -int ec_GFp_simple_point_set_affine_coordinates(const EC_GROUP *group, - EC_POINT *point, - const BIGNUM *x, - const BIGNUM *y, BN_CTX *ctx) -{ - if (x == NULL || y == NULL) { - /* - * unlike for projective coordinates, we do not tolerate this - */ - ECerr(EC_F_EC_GFP_SIMPLE_POINT_SET_AFFINE_COORDINATES, - ERR_R_PASSED_NULL_PARAMETER); - return 0; - } - - return EC_POINT_set_Jprojective_coordinates_GFp(group, point, x, y, - BN_value_one(), ctx); -} - -int ec_GFp_simple_point_get_affine_coordinates(const EC_GROUP *group, - const EC_POINT *point, - BIGNUM *x, BIGNUM *y, - BN_CTX *ctx) -{ - BN_CTX *new_ctx = NULL; - BIGNUM *Z, *Z_1, *Z_2, *Z_3; - const BIGNUM *Z_; - int ret = 0; - - if (EC_POINT_is_at_infinity(group, point)) { - ECerr(EC_F_EC_GFP_SIMPLE_POINT_GET_AFFINE_COORDINATES, - EC_R_POINT_AT_INFINITY); - return 0; - } - - if (ctx == NULL) { - ctx = new_ctx = BN_CTX_new(); - if (ctx == NULL) - return 0; - } - - BN_CTX_start(ctx); - Z = BN_CTX_get(ctx); - Z_1 = BN_CTX_get(ctx); - Z_2 = BN_CTX_get(ctx); - Z_3 = BN_CTX_get(ctx); - if (Z_3 == NULL) - goto err; - - /* transform (X, Y, Z) into (x, y) := (X/Z^2, Y/Z^3) */ - - if (group->meth->field_decode) { - if (!group->meth->field_decode(group, Z, &point->Z, ctx)) - goto err; - Z_ = Z; - } else { - Z_ = &point->Z; - } - - if (BN_is_one(Z_)) { - if (group->meth->field_decode) { - if (x != NULL) { - if (!group->meth->field_decode(group, x, &point->X, ctx)) - goto err; - } - if (y != NULL) { - if (!group->meth->field_decode(group, y, &point->Y, ctx)) - goto err; - } - } else { - if (x != NULL) { - if (!BN_copy(x, &point->X)) - goto err; - } - if (y != NULL) { - if (!BN_copy(y, &point->Y)) - goto err; - } - } - } else { - if (!BN_mod_inverse(Z_1, Z_, &group->field, ctx)) { - ECerr(EC_F_EC_GFP_SIMPLE_POINT_GET_AFFINE_COORDINATES, - ERR_R_BN_LIB); - goto err; - } - - if (group->meth->field_encode == 0) { - /* field_sqr works on standard representation */ - if (!group->meth->field_sqr(group, Z_2, Z_1, ctx)) - goto err; - } else { - if (!BN_mod_sqr(Z_2, Z_1, &group->field, ctx)) - goto err; - } - - if (x != NULL) { - /* - * in the Montgomery case, field_mul will cancel out Montgomery - * factor in X: - */ - if (!group->meth->field_mul(group, x, &point->X, Z_2, ctx)) - goto err; - } - - if (y != NULL) { - if (group->meth->field_encode == 0) { - /* - * field_mul works on standard representation - */ - if (!group->meth->field_mul(group, Z_3, Z_2, Z_1, ctx)) - goto err; - } else { - if (!BN_mod_mul(Z_3, Z_2, Z_1, &group->field, ctx)) - goto err; - } - - /* - * in the Montgomery case, field_mul will cancel out Montgomery - * factor in Y: - */ - if (!group->meth->field_mul(group, y, &point->Y, Z_3, ctx)) - goto err; - } - } - - ret = 1; - - err: - BN_CTX_end(ctx); - if (new_ctx != NULL) - BN_CTX_free(new_ctx); - return ret; -} - -int ec_GFp_simple_add(const EC_GROUP *group, EC_POINT *r, const EC_POINT *a, - const EC_POINT *b, BN_CTX *ctx) -{ - int (*field_mul) (const EC_GROUP *, BIGNUM *, const BIGNUM *, - const BIGNUM *, BN_CTX *); - int (*field_sqr) (const EC_GROUP *, BIGNUM *, const BIGNUM *, BN_CTX *); - const BIGNUM *p; - BN_CTX *new_ctx = NULL; - BIGNUM *n0, *n1, *n2, *n3, *n4, *n5, *n6; - int ret = 0; - - if (a == b) - return EC_POINT_dbl(group, r, a, ctx); - if (EC_POINT_is_at_infinity(group, a)) - return EC_POINT_copy(r, b); - if (EC_POINT_is_at_infinity(group, b)) - return EC_POINT_copy(r, a); - - field_mul = group->meth->field_mul; - field_sqr = group->meth->field_sqr; - p = &group->field; - - if (ctx == NULL) { - ctx = new_ctx = BN_CTX_new(); - if (ctx == NULL) - return 0; - } - - BN_CTX_start(ctx); - n0 = BN_CTX_get(ctx); - n1 = BN_CTX_get(ctx); - n2 = BN_CTX_get(ctx); - n3 = BN_CTX_get(ctx); - n4 = BN_CTX_get(ctx); - n5 = BN_CTX_get(ctx); - n6 = BN_CTX_get(ctx); - if (n6 == NULL) - goto end; - - /* - * Note that in this function we must not read components of 'a' or 'b' - * once we have written the corresponding components of 'r'. ('r' might - * be one of 'a' or 'b'.) - */ - - /* n1, n2 */ - if (b->Z_is_one) { - if (!BN_copy(n1, &a->X)) - goto end; - if (!BN_copy(n2, &a->Y)) - goto end; - /* n1 = X_a */ - /* n2 = Y_a */ - } else { - if (!field_sqr(group, n0, &b->Z, ctx)) - goto end; - if (!field_mul(group, n1, &a->X, n0, ctx)) - goto end; - /* n1 = X_a * Z_b^2 */ - - if (!field_mul(group, n0, n0, &b->Z, ctx)) - goto end; - if (!field_mul(group, n2, &a->Y, n0, ctx)) - goto end; - /* n2 = Y_a * Z_b^3 */ - } - - /* n3, n4 */ - if (a->Z_is_one) { - if (!BN_copy(n3, &b->X)) - goto end; - if (!BN_copy(n4, &b->Y)) - goto end; - /* n3 = X_b */ - /* n4 = Y_b */ - } else { - if (!field_sqr(group, n0, &a->Z, ctx)) - goto end; - if (!field_mul(group, n3, &b->X, n0, ctx)) - goto end; - /* n3 = X_b * Z_a^2 */ - - if (!field_mul(group, n0, n0, &a->Z, ctx)) - goto end; - if (!field_mul(group, n4, &b->Y, n0, ctx)) - goto end; - /* n4 = Y_b * Z_a^3 */ - } - - /* n5, n6 */ - if (!BN_mod_sub_quick(n5, n1, n3, p)) - goto end; - if (!BN_mod_sub_quick(n6, n2, n4, p)) - goto end; - /* n5 = n1 - n3 */ - /* n6 = n2 - n4 */ - - if (BN_is_zero(n5)) { - if (BN_is_zero(n6)) { - /* a is the same point as b */ - BN_CTX_end(ctx); - ret = EC_POINT_dbl(group, r, a, ctx); - ctx = NULL; - goto end; - } else { - /* a is the inverse of b */ - BN_zero(&r->Z); - r->Z_is_one = 0; - ret = 1; - goto end; - } - } - - /* 'n7', 'n8' */ - if (!BN_mod_add_quick(n1, n1, n3, p)) - goto end; - if (!BN_mod_add_quick(n2, n2, n4, p)) - goto end; - /* 'n7' = n1 + n3 */ - /* 'n8' = n2 + n4 */ - - /* Z_r */ - if (a->Z_is_one && b->Z_is_one) { - if (!BN_copy(&r->Z, n5)) - goto end; - } else { - if (a->Z_is_one) { - if (!BN_copy(n0, &b->Z)) - goto end; - } else if (b->Z_is_one) { - if (!BN_copy(n0, &a->Z)) - goto end; - } else { - if (!field_mul(group, n0, &a->Z, &b->Z, ctx)) - goto end; - } - if (!field_mul(group, &r->Z, n0, n5, ctx)) - goto end; - } - r->Z_is_one = 0; - /* Z_r = Z_a * Z_b * n5 */ - - /* X_r */ - if (!field_sqr(group, n0, n6, ctx)) - goto end; - if (!field_sqr(group, n4, n5, ctx)) - goto end; - if (!field_mul(group, n3, n1, n4, ctx)) - goto end; - if (!BN_mod_sub_quick(&r->X, n0, n3, p)) - goto end; - /* X_r = n6^2 - n5^2 * 'n7' */ - - /* 'n9' */ - if (!BN_mod_lshift1_quick(n0, &r->X, p)) - goto end; - if (!BN_mod_sub_quick(n0, n3, n0, p)) - goto end; - /* n9 = n5^2 * 'n7' - 2 * X_r */ - - /* Y_r */ - if (!field_mul(group, n0, n0, n6, ctx)) - goto end; - if (!field_mul(group, n5, n4, n5, ctx)) - goto end; /* now n5 is n5^3 */ - if (!field_mul(group, n1, n2, n5, ctx)) - goto end; - if (!BN_mod_sub_quick(n0, n0, n1, p)) - goto end; - if (BN_is_odd(n0)) - if (!BN_add(n0, n0, p)) - goto end; - /* now 0 <= n0 < 2*p, and n0 is even */ - if (!BN_rshift1(&r->Y, n0)) - goto end; - /* Y_r = (n6 * 'n9' - 'n8' * 'n5^3') / 2 */ - - ret = 1; - - end: - if (ctx) /* otherwise we already called BN_CTX_end */ - BN_CTX_end(ctx); - if (new_ctx != NULL) - BN_CTX_free(new_ctx); - return ret; -} - -int ec_GFp_simple_dbl(const EC_GROUP *group, EC_POINT *r, const EC_POINT *a, - BN_CTX *ctx) -{ - int (*field_mul) (const EC_GROUP *, BIGNUM *, const BIGNUM *, - const BIGNUM *, BN_CTX *); - int (*field_sqr) (const EC_GROUP *, BIGNUM *, const BIGNUM *, BN_CTX *); - const BIGNUM *p; - BN_CTX *new_ctx = NULL; - BIGNUM *n0, *n1, *n2, *n3; - int ret = 0; - - if (EC_POINT_is_at_infinity(group, a)) { - BN_zero(&r->Z); - r->Z_is_one = 0; - return 1; - } - - field_mul = group->meth->field_mul; - field_sqr = group->meth->field_sqr; - p = &group->field; - - if (ctx == NULL) { - ctx = new_ctx = BN_CTX_new(); - if (ctx == NULL) - return 0; - } - - BN_CTX_start(ctx); - n0 = BN_CTX_get(ctx); - n1 = BN_CTX_get(ctx); - n2 = BN_CTX_get(ctx); - n3 = BN_CTX_get(ctx); - if (n3 == NULL) - goto err; - - /* - * Note that in this function we must not read components of 'a' once we - * have written the corresponding components of 'r'. ('r' might the same - * as 'a'.) - */ - - /* n1 */ - if (a->Z_is_one) { - if (!field_sqr(group, n0, &a->X, ctx)) - goto err; - if (!BN_mod_lshift1_quick(n1, n0, p)) - goto err; - if (!BN_mod_add_quick(n0, n0, n1, p)) - goto err; - if (!BN_mod_add_quick(n1, n0, &group->a, p)) - goto err; - /* n1 = 3 * X_a^2 + a_curve */ - } else if (group->a_is_minus3) { - if (!field_sqr(group, n1, &a->Z, ctx)) - goto err; - if (!BN_mod_add_quick(n0, &a->X, n1, p)) - goto err; - if (!BN_mod_sub_quick(n2, &a->X, n1, p)) - goto err; - if (!field_mul(group, n1, n0, n2, ctx)) - goto err; - if (!BN_mod_lshift1_quick(n0, n1, p)) - goto err; - if (!BN_mod_add_quick(n1, n0, n1, p)) - goto err; - /*- - * n1 = 3 * (X_a + Z_a^2) * (X_a - Z_a^2) - * = 3 * X_a^2 - 3 * Z_a^4 - */ - } else { - if (!field_sqr(group, n0, &a->X, ctx)) - goto err; - if (!BN_mod_lshift1_quick(n1, n0, p)) - goto err; - if (!BN_mod_add_quick(n0, n0, n1, p)) - goto err; - if (!field_sqr(group, n1, &a->Z, ctx)) - goto err; - if (!field_sqr(group, n1, n1, ctx)) - goto err; - if (!field_mul(group, n1, n1, &group->a, ctx)) - goto err; - if (!BN_mod_add_quick(n1, n1, n0, p)) - goto err; - /* n1 = 3 * X_a^2 + a_curve * Z_a^4 */ - } - - /* Z_r */ - if (a->Z_is_one) { - if (!BN_copy(n0, &a->Y)) - goto err; - } else { - if (!field_mul(group, n0, &a->Y, &a->Z, ctx)) - goto err; - } - if (!BN_mod_lshift1_quick(&r->Z, n0, p)) - goto err; - r->Z_is_one = 0; - /* Z_r = 2 * Y_a * Z_a */ - - /* n2 */ - if (!field_sqr(group, n3, &a->Y, ctx)) - goto err; - if (!field_mul(group, n2, &a->X, n3, ctx)) - goto err; - if (!BN_mod_lshift_quick(n2, n2, 2, p)) - goto err; - /* n2 = 4 * X_a * Y_a^2 */ - - /* X_r */ - if (!BN_mod_lshift1_quick(n0, n2, p)) - goto err; - if (!field_sqr(group, &r->X, n1, ctx)) - goto err; - if (!BN_mod_sub_quick(&r->X, &r->X, n0, p)) - goto err; - /* X_r = n1^2 - 2 * n2 */ - - /* n3 */ - if (!field_sqr(group, n0, n3, ctx)) - goto err; - if (!BN_mod_lshift_quick(n3, n0, 3, p)) - goto err; - /* n3 = 8 * Y_a^4 */ - - /* Y_r */ - if (!BN_mod_sub_quick(n0, n2, &r->X, p)) - goto err; - if (!field_mul(group, n0, n1, n0, ctx)) - goto err; - if (!BN_mod_sub_quick(&r->Y, n0, n3, p)) - goto err; - /* Y_r = n1 * (n2 - X_r) - n3 */ - - ret = 1; - - err: - BN_CTX_end(ctx); - if (new_ctx != NULL) - BN_CTX_free(new_ctx); - return ret; -} - -int ec_GFp_simple_invert(const EC_GROUP *group, EC_POINT *point, BN_CTX *ctx) -{ - if (EC_POINT_is_at_infinity(group, point) || BN_is_zero(&point->Y)) - /* point is its own inverse */ - return 1; - - return BN_usub(&point->Y, &group->field, &point->Y); -} - -int ec_GFp_simple_is_at_infinity(const EC_GROUP *group, const EC_POINT *point) -{ - return BN_is_zero(&point->Z); -} - -int ec_GFp_simple_is_on_curve(const EC_GROUP *group, const EC_POINT *point, - BN_CTX *ctx) -{ - int (*field_mul) (const EC_GROUP *, BIGNUM *, const BIGNUM *, - const BIGNUM *, BN_CTX *); - int (*field_sqr) (const EC_GROUP *, BIGNUM *, const BIGNUM *, BN_CTX *); - const BIGNUM *p; - BN_CTX *new_ctx = NULL; - BIGNUM *rh, *tmp, *Z4, *Z6; - int ret = -1; - - if (EC_POINT_is_at_infinity(group, point)) - return 1; - - field_mul = group->meth->field_mul; - field_sqr = group->meth->field_sqr; - p = &group->field; - - if (ctx == NULL) { - ctx = new_ctx = BN_CTX_new(); - if (ctx == NULL) - return -1; - } - - BN_CTX_start(ctx); - rh = BN_CTX_get(ctx); - tmp = BN_CTX_get(ctx); - Z4 = BN_CTX_get(ctx); - Z6 = BN_CTX_get(ctx); - if (Z6 == NULL) - goto err; - - /*- - * We have a curve defined by a Weierstrass equation - * y^2 = x^3 + a*x + b. - * The point to consider is given in Jacobian projective coordinates - * where (X, Y, Z) represents (x, y) = (X/Z^2, Y/Z^3). - * Substituting this and multiplying by Z^6 transforms the above equation into - * Y^2 = X^3 + a*X*Z^4 + b*Z^6. - * To test this, we add up the right-hand side in 'rh'. - */ - - /* rh := X^2 */ - if (!field_sqr(group, rh, &point->X, ctx)) - goto err; - - if (!point->Z_is_one) { - if (!field_sqr(group, tmp, &point->Z, ctx)) - goto err; - if (!field_sqr(group, Z4, tmp, ctx)) - goto err; - if (!field_mul(group, Z6, Z4, tmp, ctx)) - goto err; - - /* rh := (rh + a*Z^4)*X */ - if (group->a_is_minus3) { - if (!BN_mod_lshift1_quick(tmp, Z4, p)) - goto err; - if (!BN_mod_add_quick(tmp, tmp, Z4, p)) - goto err; - if (!BN_mod_sub_quick(rh, rh, tmp, p)) - goto err; - if (!field_mul(group, rh, rh, &point->X, ctx)) - goto err; - } else { - if (!field_mul(group, tmp, Z4, &group->a, ctx)) - goto err; - if (!BN_mod_add_quick(rh, rh, tmp, p)) - goto err; - if (!field_mul(group, rh, rh, &point->X, ctx)) - goto err; - } - - /* rh := rh + b*Z^6 */ - if (!field_mul(group, tmp, &group->b, Z6, ctx)) - goto err; - if (!BN_mod_add_quick(rh, rh, tmp, p)) - goto err; - } else { - /* point->Z_is_one */ - - /* rh := (rh + a)*X */ - if (!BN_mod_add_quick(rh, rh, &group->a, p)) - goto err; - if (!field_mul(group, rh, rh, &point->X, ctx)) - goto err; - /* rh := rh + b */ - if (!BN_mod_add_quick(rh, rh, &group->b, p)) - goto err; - } - - /* 'lh' := Y^2 */ - if (!field_sqr(group, tmp, &point->Y, ctx)) - goto err; - - ret = (0 == BN_ucmp(tmp, rh)); - - err: - BN_CTX_end(ctx); - if (new_ctx != NULL) - BN_CTX_free(new_ctx); - return ret; -} - -int ec_GFp_simple_cmp(const EC_GROUP *group, const EC_POINT *a, - const EC_POINT *b, BN_CTX *ctx) -{ - /*- - * return values: - * -1 error - * 0 equal (in affine coordinates) - * 1 not equal - */ - - int (*field_mul) (const EC_GROUP *, BIGNUM *, const BIGNUM *, - const BIGNUM *, BN_CTX *); - int (*field_sqr) (const EC_GROUP *, BIGNUM *, const BIGNUM *, BN_CTX *); - BN_CTX *new_ctx = NULL; - BIGNUM *tmp1, *tmp2, *Za23, *Zb23; - const BIGNUM *tmp1_, *tmp2_; - int ret = -1; - - if (EC_POINT_is_at_infinity(group, a)) { - return EC_POINT_is_at_infinity(group, b) ? 0 : 1; - } - - if (EC_POINT_is_at_infinity(group, b)) - return 1; - - if (a->Z_is_one && b->Z_is_one) { - return ((BN_cmp(&a->X, &b->X) == 0) - && BN_cmp(&a->Y, &b->Y) == 0) ? 0 : 1; - } - - field_mul = group->meth->field_mul; - field_sqr = group->meth->field_sqr; - - if (ctx == NULL) { - ctx = new_ctx = BN_CTX_new(); - if (ctx == NULL) - return -1; - } - - BN_CTX_start(ctx); - tmp1 = BN_CTX_get(ctx); - tmp2 = BN_CTX_get(ctx); - Za23 = BN_CTX_get(ctx); - Zb23 = BN_CTX_get(ctx); - if (Zb23 == NULL) - goto end; - - /*- - * We have to decide whether - * (X_a/Z_a^2, Y_a/Z_a^3) = (X_b/Z_b^2, Y_b/Z_b^3), - * or equivalently, whether - * (X_a*Z_b^2, Y_a*Z_b^3) = (X_b*Z_a^2, Y_b*Z_a^3). - */ - - if (!b->Z_is_one) { - if (!field_sqr(group, Zb23, &b->Z, ctx)) - goto end; - if (!field_mul(group, tmp1, &a->X, Zb23, ctx)) - goto end; - tmp1_ = tmp1; - } else - tmp1_ = &a->X; - if (!a->Z_is_one) { - if (!field_sqr(group, Za23, &a->Z, ctx)) - goto end; - if (!field_mul(group, tmp2, &b->X, Za23, ctx)) - goto end; - tmp2_ = tmp2; - } else - tmp2_ = &b->X; - - /* compare X_a*Z_b^2 with X_b*Z_a^2 */ - if (BN_cmp(tmp1_, tmp2_) != 0) { - ret = 1; /* points differ */ - goto end; - } - - if (!b->Z_is_one) { - if (!field_mul(group, Zb23, Zb23, &b->Z, ctx)) - goto end; - if (!field_mul(group, tmp1, &a->Y, Zb23, ctx)) - goto end; - /* tmp1_ = tmp1 */ - } else - tmp1_ = &a->Y; - if (!a->Z_is_one) { - if (!field_mul(group, Za23, Za23, &a->Z, ctx)) - goto end; - if (!field_mul(group, tmp2, &b->Y, Za23, ctx)) - goto end; - /* tmp2_ = tmp2 */ - } else - tmp2_ = &b->Y; - - /* compare Y_a*Z_b^3 with Y_b*Z_a^3 */ - if (BN_cmp(tmp1_, tmp2_) != 0) { - ret = 1; /* points differ */ - goto end; - } - - /* points are equal */ - ret = 0; - - end: - BN_CTX_end(ctx); - if (new_ctx != NULL) - BN_CTX_free(new_ctx); - return ret; -} - -int ec_GFp_simple_make_affine(const EC_GROUP *group, EC_POINT *point, - BN_CTX *ctx) -{ - BN_CTX *new_ctx = NULL; - BIGNUM *x, *y; - int ret = 0; - - if (point->Z_is_one || EC_POINT_is_at_infinity(group, point)) - return 1; - - if (ctx == NULL) { - ctx = new_ctx = BN_CTX_new(); - if (ctx == NULL) - return 0; - } - - BN_CTX_start(ctx); - x = BN_CTX_get(ctx); - y = BN_CTX_get(ctx); - if (y == NULL) - goto err; - - if (!EC_POINT_get_affine_coordinates_GFp(group, point, x, y, ctx)) - goto err; - if (!EC_POINT_set_affine_coordinates_GFp(group, point, x, y, ctx)) - goto err; - if (!point->Z_is_one) { - ECerr(EC_F_EC_GFP_SIMPLE_MAKE_AFFINE, ERR_R_INTERNAL_ERROR); - goto err; - } - - ret = 1; - - err: - BN_CTX_end(ctx); - if (new_ctx != NULL) - BN_CTX_free(new_ctx); - return ret; -} - -int ec_GFp_simple_points_make_affine(const EC_GROUP *group, size_t num, - EC_POINT *points[], BN_CTX *ctx) -{ - BN_CTX *new_ctx = NULL; - BIGNUM *tmp, *tmp_Z; - BIGNUM **prod_Z = NULL; - size_t i; - int ret = 0; - - if (num == 0) - return 1; - - if (ctx == NULL) { - ctx = new_ctx = BN_CTX_new(); - if (ctx == NULL) - return 0; - } - - BN_CTX_start(ctx); - tmp = BN_CTX_get(ctx); - tmp_Z = BN_CTX_get(ctx); - if (tmp == NULL || tmp_Z == NULL) - goto err; - - prod_Z = OPENSSL_malloc(num * sizeof prod_Z[0]); - if (prod_Z == NULL) - goto err; - for (i = 0; i < num; i++) { - prod_Z[i] = BN_new(); - if (prod_Z[i] == NULL) - goto err; - } - - /* - * Set each prod_Z[i] to the product of points[0]->Z .. points[i]->Z, - * skipping any zero-valued inputs (pretend that they're 1). - */ - - if (!BN_is_zero(&points[0]->Z)) { - if (!BN_copy(prod_Z[0], &points[0]->Z)) - goto err; - } else { - if (group->meth->field_set_to_one != 0) { - if (!group->meth->field_set_to_one(group, prod_Z[0], ctx)) - goto err; - } else { - if (!BN_one(prod_Z[0])) - goto err; - } - } - - for (i = 1; i < num; i++) { - if (!BN_is_zero(&points[i]->Z)) { - if (!group->meth->field_mul(group, prod_Z[i], prod_Z[i - 1], - &points[i]->Z, ctx)) - goto err; - } else { - if (!BN_copy(prod_Z[i], prod_Z[i - 1])) - goto err; - } - } - - /* - * Now use a single explicit inversion to replace every non-zero - * points[i]->Z by its inverse. - */ - - if (!BN_mod_inverse(tmp, prod_Z[num - 1], &group->field, ctx)) { - ECerr(EC_F_EC_GFP_SIMPLE_POINTS_MAKE_AFFINE, ERR_R_BN_LIB); - goto err; - } - if (group->meth->field_encode != 0) { - /* - * In the Montgomery case, we just turned R*H (representing H) into - * 1/(R*H), but we need R*(1/H) (representing 1/H); i.e. we need to - * multiply by the Montgomery factor twice. - */ - if (!group->meth->field_encode(group, tmp, tmp, ctx)) - goto err; - if (!group->meth->field_encode(group, tmp, tmp, ctx)) - goto err; - } - - for (i = num - 1; i > 0; --i) { - /* - * Loop invariant: tmp is the product of the inverses of points[0]->Z - * .. points[i]->Z (zero-valued inputs skipped). - */ - if (!BN_is_zero(&points[i]->Z)) { - /* - * Set tmp_Z to the inverse of points[i]->Z (as product of Z - * inverses 0 .. i, Z values 0 .. i - 1). - */ - if (!group-> - meth->field_mul(group, tmp_Z, prod_Z[i - 1], tmp, ctx)) - goto err; - /* - * Update tmp to satisfy the loop invariant for i - 1. - */ - if (!group->meth->field_mul(group, tmp, tmp, &points[i]->Z, ctx)) - goto err; - /* Replace points[i]->Z by its inverse. */ - if (!BN_copy(&points[i]->Z, tmp_Z)) - goto err; - } - } - - if (!BN_is_zero(&points[0]->Z)) { - /* Replace points[0]->Z by its inverse. */ - if (!BN_copy(&points[0]->Z, tmp)) - goto err; - } - - /* Finally, fix up the X and Y coordinates for all points. */ - - for (i = 0; i < num; i++) { - EC_POINT *p = points[i]; - - if (!BN_is_zero(&p->Z)) { - /* turn (X, Y, 1/Z) into (X/Z^2, Y/Z^3, 1) */ - - if (!group->meth->field_sqr(group, tmp, &p->Z, ctx)) - goto err; - if (!group->meth->field_mul(group, &p->X, &p->X, tmp, ctx)) - goto err; - - if (!group->meth->field_mul(group, tmp, tmp, &p->Z, ctx)) - goto err; - if (!group->meth->field_mul(group, &p->Y, &p->Y, tmp, ctx)) - goto err; - - if (group->meth->field_set_to_one != 0) { - if (!group->meth->field_set_to_one(group, &p->Z, ctx)) - goto err; - } else { - if (!BN_one(&p->Z)) - goto err; - } - p->Z_is_one = 1; - } - } - - ret = 1; - - err: - BN_CTX_end(ctx); - if (new_ctx != NULL) - BN_CTX_free(new_ctx); - if (prod_Z != NULL) { - for (i = 0; i < num; i++) { - if (prod_Z[i] == NULL) - break; - BN_clear_free(prod_Z[i]); - } - OPENSSL_free(prod_Z); - } - return ret; -} - -int ec_GFp_simple_field_mul(const EC_GROUP *group, BIGNUM *r, const BIGNUM *a, - const BIGNUM *b, BN_CTX *ctx) -{ - return BN_mod_mul(r, a, b, &group->field, ctx); -} - -int ec_GFp_simple_field_sqr(const EC_GROUP *group, BIGNUM *r, const BIGNUM *a, - BN_CTX *ctx) -{ - return BN_mod_sqr(r, a, &group->field, ctx); -} |