X-Git-Url: https://git.openssl.org/?a=blobdiff_plain;f=crypto%2Fec%2Fecp_smpl.c;h=7e8fe4fbbe3119ed874f6f60ce38c8dda85cf523;hb=5dc40a83c74be579575a512b30d9c1e0364e6a7b;hp=d6c3f635e5621a87e9d9d1918ea9964e74e2227e;hpb=1d5bd6cf71b1e4aedda0264905a9ddc64d8c1d76;p=openssl.git diff --git a/crypto/ec/ecp_smpl.c b/crypto/ec/ecp_smpl.c index d6c3f635e5..7e8fe4fbbe 100644 --- a/crypto/ec/ecp_smpl.c +++ b/crypto/ec/ecp_smpl.c @@ -1,1177 +1,1644 @@ -/* crypto/ec/ecp_smpl.c */ -/* Includes code written by Lenka Fibikova - * for the OpenSSL project. */ -/* ==================================================================== - * Copyright (c) 1998-2001 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 2001-2018 The OpenSSL Project Authors. All Rights Reserved. + * Copyright (c) 2002, Oracle and/or its affiliates. All rights reserved * + * Licensed under the Apache License 2.0 (the "License"). You may not use + * this file except in compliance with the License. You can obtain a copy + * in the file LICENSE in the source distribution or at + * https://www.openssl.org/source/license.html */ #include +#include #include "ec_lcl.h" - const EC_METHOD *EC_GFp_simple_method(void) - { - static const EC_METHOD ret = { - ec_GFp_simple_group_init, - ec_GFp_simple_group_set_curve_GFp, - ec_GFp_simple_group_finish, - ec_GFp_simple_group_clear_finish, - ec_GFp_simple_group_copy, - ec_GFp_simple_group_set_generator, - /* TODO: 'set' and 'get' functions for EC_GROUPs */ - 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_GFp, - ec_GFp_simple_point_get_affine_coordinates_GFp, - ec_GFp_simple_set_compressed_coordinates_GFp, - ec_GFp_simple_point2oct, - ec_GFp_simple_oct2point, - 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_field_mul, - ec_GFp_simple_field_sqr, - 0 /* field_encode */, - 0 /* field_decode */ }; - - return &ret; - } - +{ + 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_group_simple_order_bits, + 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 */ + ec_key_simple_priv2oct, + ec_key_simple_oct2priv, + 0, /* set private */ + ec_key_simple_generate_key, + ec_key_simple_check_key, + ec_key_simple_generate_public_key, + 0, /* keycopy */ + 0, /* keyfinish */ + ecdh_simple_compute_key, + 0, /* field_inverse_mod_ord */ + ec_GFp_simple_blind_coordinates, + ec_GFp_simple_ladder_pre, + ec_GFp_simple_ladder_step, + ec_GFp_simple_ladder_post + }; + + 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; - group->generator = NULL; - BN_init(&group->order); - BN_init(&group->cofactor); - return 1; - } - - -int ec_GFp_simple_group_set_curve_GFp(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_GFP, 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; - group->field.neg = 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; - } - +{ + group->field = BN_new(); + group->a = BN_new(); + group->b = BN_new(); + if (group->field == NULL || group->a == NULL || group->b == NULL) { + BN_free(group->field); + BN_free(group->a); + BN_free(group->b); + return 0; + } + 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); - if (group->generator != NULL) - EC_POINT_free(group->generator); - BN_free(&group->order); - BN_free(&group->cofactor); - } - +{ + 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); - if (group->generator != NULL) - { - EC_POINT_clear_free(group->generator); - group->generator = NULL; - } - BN_clear_free(&group->order); - BN_clear_free(&group->cofactor); - } - +{ + 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; - - if (src->generator != NULL) - { - if (dest->generator == NULL) - { - dest->generator = EC_POINT_new(dest); - if (dest->generator == NULL) return 0; - } - if (!EC_POINT_copy(dest->generator, src->generator)) return 0; - } - else - { - /* src->generator == NULL */ - if (dest->generator != NULL) - { - EC_POINT_clear_free(dest->generator); - dest->generator = NULL; - } - } - - if (!BN_copy(&dest->order, &src->order)) return 0; - if (!BN_copy(&dest->cofactor, &src->cofactor)) return 0; - - return 1; - } - - -int ec_GFp_simple_group_set_generator(EC_GROUP *group, const EC_POINT *generator, - const BIGNUM *order, const BIGNUM *cofactor) - { - if (generator) - { - ECerr(EC_F_EC_GFP_SIMPLE_GROUP_SET_GENERATOR, ERR_R_PASSED_NULL_PARAMETER); - return 0 ; - } - - if (group->generator == NULL) - { - group->generator = EC_POINT_new(group); - if (group->generator == NULL) return 0; - } - if (!EC_POINT_copy(group->generator, generator)) return 0; - - if (order != NULL) - { if (!BN_copy(&group->order, order)) return 0; } - else - { if (!BN_zero(&group->order)) return 0; } - - if (cofactor != NULL) - { if (!BN_copy(&group->cofactor, cofactor)) return 0; } - else - { if (!BN_zero(&group->cofactor)) return 0; } - - return 1; - } - - -/* TODO: 'set' and 'get' functions for EC_GROUPs */ +{ + 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); + 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; -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; + err: + 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; - return 1; - } + err: + if (ctx != NULL) + BN_CTX_end(ctx); + BN_CTX_free(new_ctx); + return ret; +} +int ec_GFp_simple_point_init(EC_POINT *point) +{ + point->X = BN_new(); + point->Y = BN_new(); + point->Z = BN_new(); + point->Z_is_one = 0; + + if (point->X == NULL || point->Y == NULL || point->Z == NULL) { + BN_free(point->X); + BN_free(point->Y); + BN_free(point->Z); + return 0; + } + return 1; +} void ec_GFp_simple_point_finish(EC_POINT *point) - { - BN_free(&point->X); - BN_free(&point->Y); - BN_free(&point->Z); - } - +{ + 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; - } - +{ + 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; - return (BN_zero(&point->Z)); - } - - -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); -/* TODO */ - - -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); -/* TODO */ - - -int ec_GFp_simple_point_set_affine_coordinates_GFp(const EC_GROUP *group, EC_POINT *point, - const BIGNUM *x, const BIGNUM *y, BN_CTX *ctx) - { - BN_CTX *new_ctx = NULL; - int ret = 0; - - if (!BN_copy(&point->X, x)) goto err; - if (!BN_copy(&point->Y, y)) goto err; - if (!BN_one(&point->Z)) goto err; - - if (group->meth->field_encode) - { - if (ctx == NULL) - { - ctx = new_ctx = BN_CTX_new(); - if (ctx == NULL) - return 0; - } - - if (!group->meth->field_encode(group, &point->X, &point->X, ctx)) goto err; - if (!group->meth->field_encode(group, &point->Y, &point->Y, ctx)) goto err; - if (!group->meth->field_encode(group, &point->Z, &point->Z, ctx)) goto err; - } - - point->Z_is_one = 1; - - err: - if (new_ctx != NULL) - BN_CTX_free(new_ctx); - return ret; - } - - -int ec_GFp_simple_point_get_affine_coordinates_GFp(const EC_GROUP *group, const EC_POINT *point, - BIGNUM *x, BIGNUM *y, BN_CTX *ctx) - { - BN_CTX *new_ctx = NULL; - BIGNUM *X, *Y, *Z, *Z_1, *Z_2, *Z_3; - const BIGNUM *X_, *Y_, *Z_; - int ret = 0; - - if (EC_POINT_is_at_infinity(group, point)) - { - ECerr(EC_F_EC_GFP_SIMPLE_POINT_GET_AFFINE_COORDINATES_GFP, 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); - X = BN_CTX_get(ctx); - Y = BN_CTX_get(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, X, &point->X, ctx)) goto err; - if (!group->meth->field_decode(group, Y, &point->Y, ctx)) goto err; - if (!group->meth->field_decode(group, Z, &point->Z, ctx)) goto err; - X_ = X; Y_ = Y; Z_ = Z; - } - else - { - X_ = &point->X; - Y_ = &point->Y; - Z_ = &point->Z; - } - - if (BN_is_one(Z_)) - { - if (x != NULL) - { - if (!BN_copy(x, X_)) goto err; - } - if (y != NULL) - { - if (!BN_copy(y, Y_)) goto err; - } - } - else - { - if (!BN_mod_inverse(Z_1, Z_, &group->field, ctx)) - { - ECerr(EC_F_EC_GFP_SIMPLE_POINT_GET_AFFINE_COORDINATES_GFP, ERR_R_BN_LIB); - goto err; - } - if (!BN_mod_sqr(Z_2, Z_1, &group->field, ctx)) goto err; - - if (x != NULL) - { - if (!BN_mod_mul(x, X_, Z_2, &group->field, ctx)) goto err; - } - - if (y != NULL) - { - if (!BN_mod_mul(Z_3, Z_2, Z_1, &group->field, ctx)) goto err; - if (!BN_mod_mul(y, Y_, Z_3, &group->field, ctx)) goto err; - } - } - - ret = 1; +{ + 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; + dest->curve_name = src->curve_name; + + 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: - BN_CTX_end(ctx); - if (new_ctx != NULL) - BN_CTX_free(new_ctx); - return ret; - } - - -int ec_GFp_simple_set_compressed_coordinates_GFp(const EC_GROUP *group, EC_POINT *point, - const BIGNUM *x, int y_bit, BN_CTX *); -/* TODO */ - - -size_t ec_GFp_simple_point2oct(const EC_GROUP *group, const EC_POINT *point, point_conversion_form_t form, - unsigned char *buf, size_t len, BN_CTX *ctx) - { - size_t ret; - BN_CTX *new_ctx = NULL; - int used_ctx = 0; - BIGNUM *x, *y; - size_t field_len, i, skip; - - if ((form != POINT_CONVERSION_COMPRESSED) - && (form != POINT_CONVERSION_UNCOMPRESSED) - && (form != POINT_CONVERSION_HYBRID)) - { - ECerr(EC_F_EC_GFP_SIMPLE_POINT2OCT, EC_R_INVALID_FORM); - goto err; - } - - if (EC_POINT_is_at_infinity(group, point)) - { - /* encodes to a single 0 octet */ - if (buf != NULL) - { - if (len < 1) - { - ECerr(EC_F_EC_GFP_SIMPLE_POINT2OCT, EC_R_BUFFER_TOO_SMALL); - return 0; - } - buf[0] = 0; - } - return 1; - } - - - /* ret := required output buffer length */ - field_len = BN_num_bytes(&group->field); - ret = (form == POINT_CONVERSION_COMPRESSED) ? 1 + field_len : 1 + 2*field_len; - - /* if 'buf' is NULL, just return required length */ - if (buf != NULL) - { - if (len < ret) - { - ECerr(EC_F_EC_GFP_SIMPLE_POINT2OCT, EC_R_BUFFER_TOO_SMALL); - goto err; - } - - if (ctx == NULL) - { - ctx = new_ctx = BN_CTX_new(); - if (ctx == NULL) - return 0; - } - - BN_CTX_start(ctx); - used_ctx = 1; - 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 ((form == POINT_CONVERSION_COMPRESSED || form == POINT_CONVERSION_HYBRID) && BN_is_odd(y)) - buf[0] = form + 1; - else - buf[0] = form; - - i = 1; - - skip = field_len - BN_num_bytes(x); - if (skip > field_len) - { - ECerr(EC_F_EC_GFP_SIMPLE_POINT2OCT, ERR_R_INTERNAL_ERROR); - goto err; - } - while (skip > 0) - { - buf[i++] = 0; - skip--; - } - skip = BN_bn2bin(x, buf + i); - i += skip; - if (i != 1 + field_len) - { - ECerr(EC_F_EC_GFP_SIMPLE_POINT2OCT, ERR_R_INTERNAL_ERROR); - goto err; - } - - if (form == POINT_CONVERSION_UNCOMPRESSED || form == POINT_CONVERSION_HYBRID) - { - skip = field_len - BN_num_bytes(y); - if (skip > field_len) - { - ECerr(EC_F_EC_GFP_SIMPLE_POINT2OCT, ERR_R_INTERNAL_ERROR); - goto err; - } - while (skip > 0) - { - buf[i++] = 0; - skip--; - } - skip = BN_bn2bin(y, buf + i); - i += skip; - } - - if (i != ret) - { - ECerr(EC_F_EC_GFP_SIMPLE_POINT2OCT, ERR_R_INTERNAL_ERROR); - goto err; - } - } - - if (used_ctx) - BN_CTX_end(ctx); - if (new_ctx != NULL) - BN_CTX_free(new_ctx); - return ret; + 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 (used_ctx) - BN_CTX_end(ctx); - if (new_ctx != NULL) - BN_CTX_free(new_ctx); - return 0; - } - - -int ec_GFp_simple_oct2point(const EC_GROUP *group, EC_POINT *point, - const unsigned char *buf, size_t len, BN_CTX *ctx) - { - point_conversion_form_t form; - int y_bit; - BN_CTX *new_ctx = NULL; - BIGNUM *x, *y; - size_t field_len, enc_len; - int ret = 0; - - if (len <= 0) - { - ECerr(EC_F_EC_GFP_SIMPLE_OCT2POINT, EC_R_BUFFER_TOO_SMALL); - return 0; - } - form = buf[0]; - y_bit = form & 1; - form = form & ~1; - if ((form != 0) && (form != POINT_CONVERSION_COMPRESSED) - && (form != POINT_CONVERSION_UNCOMPRESSED) - && (form != POINT_CONVERSION_HYBRID)) - { - ECerr(EC_F_EC_GFP_SIMPLE_OCT2POINT, EC_R_INVALID_ENCODING); - return 0; - } - if ((form == 0 || form == POINT_CONVERSION_UNCOMPRESSED) && y_bit) - { - ECerr(EC_F_EC_GFP_SIMPLE_OCT2POINT, EC_R_INVALID_ENCODING); - return 0; - } - - if (form == 0) - { - if (len != 1) - { - ECerr(EC_F_EC_GFP_SIMPLE_OCT2POINT, EC_R_INVALID_ENCODING); - return 0; - } - - return EC_POINT_set_to_infinity(group, point); - } - - field_len = BN_num_bytes(&group->field); - enc_len = (form == POINT_CONVERSION_COMPRESSED) ? 1 + field_len : 1 + 2*field_len; - - if (len != enc_len) - { - ECerr(EC_F_EC_GFP_SIMPLE_OCT2POINT, EC_R_INVALID_ENCODING); - return 0; - } - - 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 (!BN_bin2bn(buf + 1, field_len, x)) goto err; - if (BN_ucmp(x, &group->field) >= 0) - { - ECerr(EC_F_EC_GFP_SIMPLE_OCT2POINT, EC_R_INVALID_ENCODING); - goto err; - } - - if (form != POINT_CONVERSION_COMPRESSED) - { - if (!BN_bin2bn(buf + 1 + field_len, field_len, y)) goto err; - if (BN_ucmp(y, &group->field) >= 0) - { - ECerr(EC_F_EC_GFP_SIMPLE_OCT2POINT, EC_R_INVALID_ENCODING); - goto err; - } - if (form == POINT_CONVERSION_HYBRID) - { - if (y_bit != BN_is_odd(y)) - { - ECerr(EC_F_EC_GFP_SIMPLE_OCT2POINT, EC_R_INVALID_ENCODING); - goto err; - } - } - } - - if (form == POINT_CONVERSION_COMPRESSED) - { - /* Recover y. We have a Weierstrass equation - * y^2 = x^3 + a*x + b, - * so y is one of the square roots of x^3 + a*x + b. - */ - - BIGNUM *tmp1, *tmp2; - - tmp1 = BN_CTX_get(ctx); - tmp2 = BN_CTX_get(ctx); - if (tmp2 == NULL) goto err; - - /* tmp1 := x^3 */ - if (!BN_mod_sqr(tmp2, x, &group->field, ctx)) goto err; - if (!BN_mod_mul(tmp1, tmp2, x, &group->field, ctx)) goto err; - - /* tmp1 := tmp1 + a*x */ - if (group->a_is_minus3) - { - if (!BN_mod_lshift1_quick(tmp2, x, &group->field)) goto err; - if (!BN_mod_add_quick(tmp2, tmp2, x, &group->field)) goto err; - if (!BN_mod_sub_quick(tmp1, tmp1, tmp2, &group->field)) goto err; - } - else - { - if (!BN_mod_mul(tmp2, &group->a, x, &group->field, ctx)) goto err; - if (!BN_mod_add_quick(tmp1, tmp1, tmp2, &group->field)) goto err; - } - - /* tmp1 := tmp1 + b */ - if (!BN_mod_add_quick(tmp1, tmp1, &group->b, &group->field)) goto err; - - if (!BN_mod_sqrt(y, tmp1, &group->field, ctx)) - { - ECerr(EC_F_EC_GFP_SIMPLE_OCT2POINT, ERR_R_BN_LIB); - goto err; - } - - if (y_bit != BN_is_odd(y)) - { - if (BN_is_zero(y)) - { - ECerr(EC_F_EC_GFP_SIMPLE_OCT2POINT, EC_R_INVALID_ENCODING); - goto err; - } - if (!BN_usub(y, &group->field, y)) goto err; - } - if (y_bit != BN_is_odd(y)) - { - ECerr(EC_F_EC_GFP_SIMPLE_OCT2POINT, ERR_R_INTERNAL_ERROR); - goto err; - } - } - - if (!EC_POINT_set_affine_coordinates_GFp(group, point, x, y, ctx)) goto err; - - if (!EC_POINT_is_on_curve(group, point, ctx)) /* test required by X9.62 */ - { - ECerr(EC_F_EC_GFP_SIMPLE_OCT2POINT, EC_R_POINT_IS_NOT_ON_CURVE); - goto err; - } - - ret = 1; - + 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 */ - if (!BN_zero(&r->Z)) goto end; - 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; + BN_CTX_end(ctx); + 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)) - { - if (!BN_zero(&r->Z)) return 0; - 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; + if (ctx) /* otherwise we already called BN_CTX_end */ + BN_CTX_end(ctx); + 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; - } - + BN_CTX_end(ctx); + BN_CTX_free(new_ctx); + return ret; +} -int ec_GFp_simple_invert(const EC_GROUP *group, EC_POINT *point, BN_CTX *ctx); -/* TODO */ +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, *tmp1, *tmp2, *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); - tmp1 = BN_CTX_get(ctx); - tmp2 = 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^3 */ - if (!field_sqr(group, rh, &point->X, ctx)) goto err; - if (!field_mul(group, rh, rh, &point->X, ctx)) goto err; - - if (!point->Z_is_one) - { - if (!field_sqr(group, tmp1, &point->Z, ctx)) goto err; - if (!field_sqr(group, Z4, tmp1, ctx)) goto err; - if (!field_mul(group, Z6, Z4, tmp1, ctx)) goto err; - - /* rh := rh + a*X*Z^4 */ - if (!field_mul(group, tmp1, &point->X, Z4, ctx)) goto err; - if (&group->a_is_minus3) - { - if (!BN_mod_lshift1_quick(tmp2, tmp1, p)) goto err; - if (!BN_mod_add_quick(tmp2, tmp2, tmp1, p)) goto err; - if (!BN_mod_sub_quick(rh, rh, tmp2, p)) goto err; - } - else - { - if (!field_mul(group, tmp2, tmp1, &group->a, ctx)) goto err; - if (!BN_mod_add_quick(rh, rh, tmp2, p)) goto err; - } - - /* rh := rh + b*Z^6 */ - if (!field_mul(group, tmp1, &group->b, Z6, ctx)) goto err; - if (!BN_mod_add_quick(rh, rh, tmp1, p)) goto err; - } - else - { - /* point->Z_is_one */ - - /* rh := rh + a*X */ - if (&group->a_is_minus3) - { - if (!BN_mod_lshift1_quick(tmp2, &point->X, p)) goto err; - if (!BN_mod_add_quick(tmp2, tmp2, &point->X, p)) goto err; - if (!BN_mod_sub_quick(rh, rh, tmp2, p)) goto err; - } - else - { - if (!field_mul(group, tmp2, &point->X, &group->a, ctx)) goto err; - if (!BN_mod_add_quick(rh, rh, tmp2, p)) goto err; - } - - /* rh := rh + b */ - if (!BN_mod_add_quick(rh, rh, &group->b, p)) goto err; - } - - /* 'lh' := Y^2 */ - if (!field_sqr(group, tmp1, &point->Y, ctx)) goto err; - - ret = (0 == BN_cmp(tmp1, rh)); +{ + 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 *, const EC_POINT *a, const EC_POINT *b, BN_CTX *); -/* TODO */ - - -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; + BN_CTX_end(ctx); + 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); + 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(group, point, x, y, ctx)) + goto err; + if (!EC_POINT_set_affine_coordinates(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; - } + BN_CTX_end(ctx); + 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_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); + 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); +} + +/*- + * Apply randomization of EC point projective coordinates: + * + * (X, Y ,Z ) = (lambda^2*X, lambda^3*Y, lambda*Z) + * lambda = [1,group->field) + * + */ +int ec_GFp_simple_blind_coordinates(const EC_GROUP *group, EC_POINT *p, + BN_CTX *ctx) +{ + int ret = 0; + BIGNUM *lambda = NULL; + BIGNUM *temp = NULL; + + BN_CTX_start(ctx); + lambda = BN_CTX_get(ctx); + temp = BN_CTX_get(ctx); + if (temp == NULL) { + ECerr(EC_F_EC_GFP_SIMPLE_BLIND_COORDINATES, ERR_R_MALLOC_FAILURE); + goto err; + } + + /* make sure lambda is not zero */ + do { + if (!BN_priv_rand_range(lambda, group->field)) { + ECerr(EC_F_EC_GFP_SIMPLE_BLIND_COORDINATES, ERR_R_BN_LIB); + goto err; + } + } 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; + + ret = 1; -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); - } + err: + BN_CTX_end(ctx); + return ret; +} +/*- + * Set s := p, r := 2p. + * + * For doubling we use Formula 3 from Izu-Takagi "A fast parallel elliptic curve + * multiplication resistant against side channel attacks" appendix, as described + * at + * https://hyperelliptic.org/EFD/g1p/auto-shortw-xz.html#doubling-dbl-2002-it-2 + * + * 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 + */ +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; + + t1 = r->Z; + t2 = r->Y; + 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) + /* 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) + /* r->Z coord output */ + || !BN_mod_lshift_quick(r->Z, t1, 2, group->field) + || !EC_POINT_copy(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 + * "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 + */ +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; + + BN_CTX_start(ctx); + t0 = BN_CTX_get(ctx); + t1 = BN_CTX_get(ctx); + t2 = BN_CTX_get(ctx); + t3 = BN_CTX_get(ctx); + 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) + || !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) + || !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) + || !BN_mod_lshift1_quick(t5, t5, group->field) + /* r->Z coord output */ + || !BN_mod_add_quick(r->Z, t7, t5, group->field)) + goto err; + + ret = 1; -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); - } + err: + BN_CTX_end(ctx); + return ret; +} + +/*- + * 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. + * + * 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; + * + * 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 + * one of the BN_is_zero(...) branches. + */ +int ec_GFp_simple_ladder_post(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 = NULL; + + if (BN_is_zero(r->Z)) + 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) + || !EC_POINT_invert(group, r, ctx)) + return 0; + return 1; + } + + BN_CTX_start(ctx); + t0 = BN_CTX_get(ctx); + t1 = BN_CTX_get(ctx); + t2 = BN_CTX_get(ctx); + t3 = BN_CTX_get(ctx); + t4 = BN_CTX_get(ctx); + t5 = BN_CTX_get(ctx); + 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) + || !group->meth->field_sqr(group, t3, r->Z, ctx) + || !group->meth->field_mul(group, r->Y, t4, t3, ctx)) + goto err; + + ret = 1; + + err: + BN_CTX_end(ctx); + return ret; +}