1717 lines
48 KiB
C
1717 lines
48 KiB
C
/*
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* Copyright 2001-2020 The OpenSSL Project Authors. All Rights Reserved.
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* Copyright (c) 2002, Oracle and/or its affiliates. All rights reserved
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*
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* Licensed under the OpenSSL license (the "License"). You may not use
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* this file except in compliance with the License. You can obtain a copy
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* in the file LICENSE in the source distribution or at
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* https://www.openssl.org/source/license.html
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*/
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#include <openssl/err.h>
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#include <openssl/symhacks.h>
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#include "ec_local.h"
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const EC_METHOD *EC_GFp_simple_method(void)
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{
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static const EC_METHOD ret = {
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EC_FLAGS_DEFAULT_OCT,
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NID_X9_62_prime_field,
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ec_GFp_simple_group_init,
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ec_GFp_simple_group_finish,
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ec_GFp_simple_group_clear_finish,
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ec_GFp_simple_group_copy,
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ec_GFp_simple_group_set_curve,
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ec_GFp_simple_group_get_curve,
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ec_GFp_simple_group_get_degree,
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ec_group_simple_order_bits,
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ec_GFp_simple_group_check_discriminant,
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ec_GFp_simple_point_init,
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ec_GFp_simple_point_finish,
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ec_GFp_simple_point_clear_finish,
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ec_GFp_simple_point_copy,
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ec_GFp_simple_point_set_to_infinity,
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ec_GFp_simple_set_Jprojective_coordinates_GFp,
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ec_GFp_simple_get_Jprojective_coordinates_GFp,
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ec_GFp_simple_point_set_affine_coordinates,
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ec_GFp_simple_point_get_affine_coordinates,
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0, 0, 0,
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ec_GFp_simple_add,
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ec_GFp_simple_dbl,
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ec_GFp_simple_invert,
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ec_GFp_simple_is_at_infinity,
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ec_GFp_simple_is_on_curve,
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ec_GFp_simple_cmp,
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ec_GFp_simple_make_affine,
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ec_GFp_simple_points_make_affine,
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0 /* mul */ ,
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0 /* precompute_mult */ ,
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0 /* have_precompute_mult */ ,
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ec_GFp_simple_field_mul,
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ec_GFp_simple_field_sqr,
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0 /* field_div */ ,
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ec_GFp_simple_field_inv,
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0 /* field_encode */ ,
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0 /* field_decode */ ,
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0, /* field_set_to_one */
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ec_key_simple_priv2oct,
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ec_key_simple_oct2priv,
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0, /* set private */
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ec_key_simple_generate_key,
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ec_key_simple_check_key,
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ec_key_simple_generate_public_key,
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0, /* keycopy */
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0, /* keyfinish */
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ecdh_simple_compute_key,
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0, /* field_inverse_mod_ord */
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ec_GFp_simple_blind_coordinates,
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ec_GFp_simple_ladder_pre,
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ec_GFp_simple_ladder_step,
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ec_GFp_simple_ladder_post
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};
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return &ret;
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}
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/*
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* Most method functions in this file are designed to work with
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* non-trivial representations of field elements if necessary
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* (see ecp_mont.c): while standard modular addition and subtraction
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* are used, the field_mul and field_sqr methods will be used for
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* multiplication, and field_encode and field_decode (if defined)
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* will be used for converting between representations.
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*
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* Functions ec_GFp_simple_points_make_affine() and
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* ec_GFp_simple_point_get_affine_coordinates() specifically assume
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* that if a non-trivial representation is used, it is a Montgomery
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* representation (i.e. 'encoding' means multiplying by some factor R).
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*/
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int ec_GFp_simple_group_init(EC_GROUP *group)
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{
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group->field = BN_new();
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group->a = BN_new();
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group->b = BN_new();
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if (group->field == NULL || group->a == NULL || group->b == NULL) {
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BN_free(group->field);
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BN_free(group->a);
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BN_free(group->b);
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return 0;
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}
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group->a_is_minus3 = 0;
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return 1;
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}
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void ec_GFp_simple_group_finish(EC_GROUP *group)
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{
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BN_free(group->field);
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BN_free(group->a);
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BN_free(group->b);
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}
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void ec_GFp_simple_group_clear_finish(EC_GROUP *group)
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{
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BN_clear_free(group->field);
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BN_clear_free(group->a);
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BN_clear_free(group->b);
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}
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int ec_GFp_simple_group_copy(EC_GROUP *dest, const EC_GROUP *src)
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{
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if (!BN_copy(dest->field, src->field))
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return 0;
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if (!BN_copy(dest->a, src->a))
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return 0;
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if (!BN_copy(dest->b, src->b))
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return 0;
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dest->a_is_minus3 = src->a_is_minus3;
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return 1;
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}
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int ec_GFp_simple_group_set_curve(EC_GROUP *group,
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const BIGNUM *p, const BIGNUM *a,
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const BIGNUM *b, BN_CTX *ctx)
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{
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int ret = 0;
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BN_CTX *new_ctx = NULL;
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BIGNUM *tmp_a;
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/* p must be a prime > 3 */
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if (BN_num_bits(p) <= 2 || !BN_is_odd(p)) {
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ECerr(EC_F_EC_GFP_SIMPLE_GROUP_SET_CURVE, EC_R_INVALID_FIELD);
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return 0;
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}
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if (ctx == NULL) {
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ctx = new_ctx = BN_CTX_new();
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if (ctx == NULL)
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return 0;
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}
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BN_CTX_start(ctx);
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tmp_a = BN_CTX_get(ctx);
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if (tmp_a == NULL)
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goto err;
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/* group->field */
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if (!BN_copy(group->field, p))
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goto err;
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BN_set_negative(group->field, 0);
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/* group->a */
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if (!BN_nnmod(tmp_a, a, p, ctx))
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goto err;
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if (group->meth->field_encode) {
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if (!group->meth->field_encode(group, group->a, tmp_a, ctx))
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goto err;
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} else if (!BN_copy(group->a, tmp_a))
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goto err;
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/* group->b */
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if (!BN_nnmod(group->b, b, p, ctx))
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goto err;
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if (group->meth->field_encode)
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if (!group->meth->field_encode(group, group->b, group->b, ctx))
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goto err;
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/* group->a_is_minus3 */
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if (!BN_add_word(tmp_a, 3))
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goto err;
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group->a_is_minus3 = (0 == BN_cmp(tmp_a, group->field));
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ret = 1;
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err:
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BN_CTX_end(ctx);
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BN_CTX_free(new_ctx);
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return ret;
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}
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int ec_GFp_simple_group_get_curve(const EC_GROUP *group, BIGNUM *p, BIGNUM *a,
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BIGNUM *b, BN_CTX *ctx)
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{
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int ret = 0;
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BN_CTX *new_ctx = NULL;
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if (p != NULL) {
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if (!BN_copy(p, group->field))
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return 0;
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}
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if (a != NULL || b != NULL) {
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if (group->meth->field_decode) {
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if (ctx == NULL) {
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ctx = new_ctx = BN_CTX_new();
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if (ctx == NULL)
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return 0;
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}
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if (a != NULL) {
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if (!group->meth->field_decode(group, a, group->a, ctx))
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goto err;
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}
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if (b != NULL) {
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if (!group->meth->field_decode(group, b, group->b, ctx))
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goto err;
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}
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} else {
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if (a != NULL) {
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if (!BN_copy(a, group->a))
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goto err;
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}
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if (b != NULL) {
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if (!BN_copy(b, group->b))
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goto err;
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}
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}
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}
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ret = 1;
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err:
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BN_CTX_free(new_ctx);
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return ret;
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}
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int ec_GFp_simple_group_get_degree(const EC_GROUP *group)
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{
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return BN_num_bits(group->field);
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}
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int ec_GFp_simple_group_check_discriminant(const EC_GROUP *group, BN_CTX *ctx)
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{
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int ret = 0;
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BIGNUM *a, *b, *order, *tmp_1, *tmp_2;
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const BIGNUM *p = group->field;
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BN_CTX *new_ctx = NULL;
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if (ctx == NULL) {
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ctx = new_ctx = BN_CTX_new();
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if (ctx == NULL) {
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ECerr(EC_F_EC_GFP_SIMPLE_GROUP_CHECK_DISCRIMINANT,
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ERR_R_MALLOC_FAILURE);
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goto err;
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}
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}
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BN_CTX_start(ctx);
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a = BN_CTX_get(ctx);
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b = BN_CTX_get(ctx);
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tmp_1 = BN_CTX_get(ctx);
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tmp_2 = BN_CTX_get(ctx);
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order = BN_CTX_get(ctx);
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if (order == NULL)
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goto err;
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if (group->meth->field_decode) {
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if (!group->meth->field_decode(group, a, group->a, ctx))
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goto err;
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if (!group->meth->field_decode(group, b, group->b, ctx))
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goto err;
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} else {
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if (!BN_copy(a, group->a))
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goto err;
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if (!BN_copy(b, group->b))
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goto err;
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}
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/*-
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* check the discriminant:
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* y^2 = x^3 + a*x + b is an elliptic curve <=> 4*a^3 + 27*b^2 != 0 (mod p)
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* 0 =< a, b < p
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*/
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if (BN_is_zero(a)) {
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if (BN_is_zero(b))
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goto err;
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} else if (!BN_is_zero(b)) {
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if (!BN_mod_sqr(tmp_1, a, p, ctx))
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goto err;
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if (!BN_mod_mul(tmp_2, tmp_1, a, p, ctx))
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goto err;
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if (!BN_lshift(tmp_1, tmp_2, 2))
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goto err;
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/* tmp_1 = 4*a^3 */
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if (!BN_mod_sqr(tmp_2, b, p, ctx))
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goto err;
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if (!BN_mul_word(tmp_2, 27))
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goto err;
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/* tmp_2 = 27*b^2 */
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if (!BN_mod_add(a, tmp_1, tmp_2, p, ctx))
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goto err;
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if (BN_is_zero(a))
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goto err;
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}
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ret = 1;
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err:
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BN_CTX_end(ctx);
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BN_CTX_free(new_ctx);
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return ret;
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}
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int ec_GFp_simple_point_init(EC_POINT *point)
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{
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point->X = BN_new();
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point->Y = BN_new();
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point->Z = BN_new();
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point->Z_is_one = 0;
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if (point->X == NULL || point->Y == NULL || point->Z == NULL) {
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BN_free(point->X);
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BN_free(point->Y);
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BN_free(point->Z);
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return 0;
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}
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return 1;
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}
|
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void ec_GFp_simple_point_finish(EC_POINT *point)
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{
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BN_free(point->X);
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BN_free(point->Y);
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BN_free(point->Z);
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}
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void ec_GFp_simple_point_clear_finish(EC_POINT *point)
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{
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BN_clear_free(point->X);
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BN_clear_free(point->Y);
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BN_clear_free(point->Z);
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point->Z_is_one = 0;
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}
|
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int ec_GFp_simple_point_copy(EC_POINT *dest, const EC_POINT *src)
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{
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if (!BN_copy(dest->X, src->X))
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return 0;
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if (!BN_copy(dest->Y, src->Y))
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return 0;
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if (!BN_copy(dest->Z, src->Z))
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return 0;
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dest->Z_is_one = src->Z_is_one;
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dest->curve_name = src->curve_name;
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|
|
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return 1;
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|
}
|
|
|
|
int ec_GFp_simple_point_set_to_infinity(const EC_GROUP *group,
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EC_POINT *point)
|
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{
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|
point->Z_is_one = 0;
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BN_zero(point->Z);
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return 1;
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|
}
|
|
|
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int ec_GFp_simple_set_Jprojective_coordinates_GFp(const EC_GROUP *group,
|
|
EC_POINT *point,
|
|
const BIGNUM *x,
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|
const BIGNUM *y,
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const BIGNUM *z,
|
|
BN_CTX *ctx)
|
|
{
|
|
BN_CTX *new_ctx = NULL;
|
|
int ret = 0;
|
|
|
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if (ctx == NULL) {
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|
ctx = new_ctx = BN_CTX_new();
|
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if (ctx == NULL)
|
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return 0;
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}
|
|
|
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if (x != NULL) {
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if (!BN_nnmod(point->X, x, group->field, ctx))
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goto err;
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if (group->meth->field_encode) {
|
|
if (!group->meth->field_encode(group, point->X, point->X, ctx))
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goto err;
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}
|
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}
|
|
|
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if (y != NULL) {
|
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if (!BN_nnmod(point->Y, y, group->field, ctx))
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|
goto err;
|
|
if (group->meth->field_encode) {
|
|
if (!group->meth->field_encode(group, point->Y, point->Y, ctx))
|
|
goto err;
|
|
}
|
|
}
|
|
|
|
if (z != NULL) {
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|
int Z_is_one;
|
|
|
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if (!BN_nnmod(point->Z, z, group->field, ctx))
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goto err;
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Z_is_one = BN_is_one(point->Z);
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if (group->meth->field_encode) {
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if (Z_is_one && (group->meth->field_set_to_one != 0)) {
|
|
if (!group->meth->field_set_to_one(group, point->Z, ctx))
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|
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_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:
|
|
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 (!group->meth->field_inv(group, Z_1, Z_, 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);
|
|
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:
|
|
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);
|
|
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);
|
|
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);
|
|
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 (!group->meth->field_inv(group, tmp, prod_Z[num - 1], 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);
|
|
}
|
|
|
|
/*-
|
|
* Computes the multiplicative inverse of a in GF(p), storing the result in r.
|
|
* If a is zero (or equivalent), you'll get a EC_R_CANNOT_INVERT error.
|
|
* Since we don't have a Mont structure here, SCA hardening is with blinding.
|
|
* NB: "a" must be in _decoded_ form. (i.e. field_decode must precede.)
|
|
*/
|
|
int ec_GFp_simple_field_inv(const EC_GROUP *group, BIGNUM *r, const BIGNUM *a,
|
|
BN_CTX *ctx)
|
|
{
|
|
BIGNUM *e = NULL;
|
|
BN_CTX *new_ctx = NULL;
|
|
int ret = 0;
|
|
|
|
if (ctx == NULL && (ctx = new_ctx = BN_CTX_secure_new()) == NULL)
|
|
return 0;
|
|
|
|
BN_CTX_start(ctx);
|
|
if ((e = BN_CTX_get(ctx)) == NULL)
|
|
goto err;
|
|
|
|
do {
|
|
if (!BN_priv_rand_range(e, group->field))
|
|
goto err;
|
|
} while (BN_is_zero(e));
|
|
|
|
/* r := a * e */
|
|
if (!group->meth->field_mul(group, r, a, e, ctx))
|
|
goto err;
|
|
/* r := 1/(a * e) */
|
|
if (!BN_mod_inverse(r, r, group->field, ctx)) {
|
|
ECerr(EC_F_EC_GFP_SIMPLE_FIELD_INV, EC_R_CANNOT_INVERT);
|
|
goto err;
|
|
}
|
|
/* r := e/(a * e) = 1/a */
|
|
if (!group->meth->field_mul(group, r, r, e, ctx))
|
|
goto err;
|
|
|
|
ret = 1;
|
|
|
|
err:
|
|
BN_CTX_end(ctx);
|
|
BN_CTX_free(new_ctx);
|
|
return ret;
|
|
}
|
|
|
|
/*-
|
|
* 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 end;
|
|
}
|
|
|
|
/*-
|
|
* Make sure lambda is not zero.
|
|
* If the RNG fails, we cannot blind but nevertheless want
|
|
* code to continue smoothly and not clobber the error stack.
|
|
*/
|
|
do {
|
|
ERR_set_mark();
|
|
ret = BN_priv_rand_range(lambda, group->field);
|
|
ERR_pop_to_mark();
|
|
if (ret == 0) {
|
|
ret = 1;
|
|
goto end;
|
|
}
|
|
} while (BN_is_zero(lambda));
|
|
|
|
/* if field_encode defined convert between representations */
|
|
if ((group->meth->field_encode != NULL
|
|
&& !group->meth->field_encode(group, lambda, lambda, ctx))
|
|
|| !group->meth->field_mul(group, p->Z, p->Z, lambda, ctx)
|
|
|| !group->meth->field_sqr(group, temp, lambda, ctx)
|
|
|| !group->meth->field_mul(group, p->X, p->X, temp, ctx)
|
|
|| !group->meth->field_mul(group, temp, temp, lambda, ctx)
|
|
|| !group->meth->field_mul(group, p->Y, p->Y, temp, ctx))
|
|
goto end;
|
|
|
|
p->Z_is_one = 0;
|
|
ret = 1;
|
|
|
|
end:
|
|
BN_CTX_end(ctx);
|
|
return ret;
|
|
}
|
|
|
|
/*-
|
|
* Input:
|
|
* - p: affine coordinates
|
|
*
|
|
* Output:
|
|
* - s := p, r := 2p: blinded projective (homogeneous) coordinates
|
|
*
|
|
* For doubling we use Formula 3 from Izu-Takagi "A fast parallel elliptic curve
|
|
* multiplication resistant against side channel attacks" appendix, described at
|
|
* https://hyperelliptic.org/EFD/g1p/auto-shortw-xz.html#doubling-dbl-2002-it-2
|
|
* simplified for Z1=1.
|
|
*
|
|
* Blinding uses the equivalence relation (\lambda X, \lambda Y, \lambda Z)
|
|
* for any non-zero \lambda that holds for projective (homogeneous) coords.
|
|
*/
|
|
int ec_GFp_simple_ladder_pre(const EC_GROUP *group,
|
|
EC_POINT *r, EC_POINT *s,
|
|
EC_POINT *p, BN_CTX *ctx)
|
|
{
|
|
BIGNUM *t1, *t2, *t3, *t4, *t5 = NULL;
|
|
|
|
t1 = s->Z;
|
|
t2 = r->Z;
|
|
t3 = s->X;
|
|
t4 = r->X;
|
|
t5 = s->Y;
|
|
|
|
if (!p->Z_is_one /* r := 2p */
|
|
|| !group->meth->field_sqr(group, t3, p->X, ctx)
|
|
|| !BN_mod_sub_quick(t4, t3, group->a, group->field)
|
|
|| !group->meth->field_sqr(group, t4, t4, ctx)
|
|
|| !group->meth->field_mul(group, t5, p->X, group->b, ctx)
|
|
|| !BN_mod_lshift_quick(t5, t5, 3, group->field)
|
|
/* r->X coord output */
|
|
|| !BN_mod_sub_quick(r->X, t4, t5, group->field)
|
|
|| !BN_mod_add_quick(t1, t3, group->a, group->field)
|
|
|| !group->meth->field_mul(group, t2, p->X, t1, ctx)
|
|
|| !BN_mod_add_quick(t2, group->b, t2, group->field)
|
|
/* r->Z coord output */
|
|
|| !BN_mod_lshift_quick(r->Z, t2, 2, group->field))
|
|
return 0;
|
|
|
|
/* make sure lambda (r->Y here for storage) is not zero */
|
|
do {
|
|
if (!BN_priv_rand_range(r->Y, group->field))
|
|
return 0;
|
|
} while (BN_is_zero(r->Y));
|
|
|
|
/* make sure lambda (s->Z here for storage) is not zero */
|
|
do {
|
|
if (!BN_priv_rand_range(s->Z, group->field))
|
|
return 0;
|
|
} while (BN_is_zero(s->Z));
|
|
|
|
/* if field_encode defined convert between representations */
|
|
if (group->meth->field_encode != NULL
|
|
&& (!group->meth->field_encode(group, r->Y, r->Y, ctx)
|
|
|| !group->meth->field_encode(group, s->Z, s->Z, ctx)))
|
|
return 0;
|
|
|
|
/* blind r and s independently */
|
|
if (!group->meth->field_mul(group, r->Z, r->Z, r->Y, ctx)
|
|
|| !group->meth->field_mul(group, r->X, r->X, r->Y, ctx)
|
|
|| !group->meth->field_mul(group, s->X, p->X, s->Z, ctx)) /* s := p */
|
|
return 0;
|
|
|
|
r->Z_is_one = 0;
|
|
s->Z_is_one = 0;
|
|
|
|
return 1;
|
|
}
|
|
|
|
/*-
|
|
* Input:
|
|
* - s, r: projective (homogeneous) coordinates
|
|
* - p: affine coordinates
|
|
*
|
|
* Output:
|
|
* - s := r + s, r := 2r: projective (homogeneous) coordinates
|
|
*
|
|
* Differential addition-and-doubling using Eq. (9) and (10) from Izu-Takagi
|
|
* "A fast parallel elliptic curve multiplication resistant against side channel
|
|
* attacks", as described at
|
|
* https://hyperelliptic.org/EFD/g1p/auto-shortw-xz.html#ladder-mladd-2002-it-4
|
|
*/
|
|
int ec_GFp_simple_ladder_step(const EC_GROUP *group,
|
|
EC_POINT *r, EC_POINT *s,
|
|
EC_POINT *p, BN_CTX *ctx)
|
|
{
|
|
int ret = 0;
|
|
BIGNUM *t0, *t1, *t2, *t3, *t4, *t5, *t6 = 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);
|
|
|
|
if (t6 == NULL
|
|
|| !group->meth->field_mul(group, t6, r->X, s->X, ctx)
|
|
|| !group->meth->field_mul(group, t0, r->Z, s->Z, ctx)
|
|
|| !group->meth->field_mul(group, t4, r->X, s->Z, ctx)
|
|
|| !group->meth->field_mul(group, t3, r->Z, s->X, ctx)
|
|
|| !group->meth->field_mul(group, t5, group->a, t0, ctx)
|
|
|| !BN_mod_add_quick(t5, t6, t5, group->field)
|
|
|| !BN_mod_add_quick(t6, t3, t4, group->field)
|
|
|| !group->meth->field_mul(group, t5, t6, t5, ctx)
|
|
|| !group->meth->field_sqr(group, t0, t0, ctx)
|
|
|| !BN_mod_lshift_quick(t2, group->b, 2, group->field)
|
|
|| !group->meth->field_mul(group, t0, t2, t0, ctx)
|
|
|| !BN_mod_lshift1_quick(t5, t5, group->field)
|
|
|| !BN_mod_sub_quick(t3, t4, t3, group->field)
|
|
/* s->Z coord output */
|
|
|| !group->meth->field_sqr(group, s->Z, t3, ctx)
|
|
|| !group->meth->field_mul(group, t4, s->Z, p->X, ctx)
|
|
|| !BN_mod_add_quick(t0, t0, t5, group->field)
|
|
/* s->X coord output */
|
|
|| !BN_mod_sub_quick(s->X, t0, t4, group->field)
|
|
|| !group->meth->field_sqr(group, t4, r->X, ctx)
|
|
|| !group->meth->field_sqr(group, t5, r->Z, ctx)
|
|
|| !group->meth->field_mul(group, t6, t5, group->a, ctx)
|
|
|| !BN_mod_add_quick(t1, r->X, r->Z, group->field)
|
|
|| !group->meth->field_sqr(group, t1, t1, ctx)
|
|
|| !BN_mod_sub_quick(t1, t1, t4, group->field)
|
|
|| !BN_mod_sub_quick(t1, t1, t5, group->field)
|
|
|| !BN_mod_sub_quick(t3, t4, t6, group->field)
|
|
|| !group->meth->field_sqr(group, t3, t3, ctx)
|
|
|| !group->meth->field_mul(group, t0, t5, t1, ctx)
|
|
|| !group->meth->field_mul(group, t0, t2, t0, ctx)
|
|
/* r->X coord output */
|
|
|| !BN_mod_sub_quick(r->X, t3, t0, group->field)
|
|
|| !BN_mod_add_quick(t3, t4, t6, group->field)
|
|
|| !group->meth->field_sqr(group, t4, t5, ctx)
|
|
|| !group->meth->field_mul(group, t4, t4, t2, ctx)
|
|
|| !group->meth->field_mul(group, t1, t1, t3, ctx)
|
|
|| !BN_mod_lshift1_quick(t1, t1, group->field)
|
|
/* r->Z coord output */
|
|
|| !BN_mod_add_quick(r->Z, t4, t1, group->field))
|
|
goto err;
|
|
|
|
ret = 1;
|
|
|
|
err:
|
|
BN_CTX_end(ctx);
|
|
return ret;
|
|
}
|
|
|
|
/*-
|
|
* Input:
|
|
* - s, r: projective (homogeneous) coordinates
|
|
* - p: affine coordinates
|
|
*
|
|
* Output:
|
|
* - r := (x,y): affine coordinates
|
|
*
|
|
* Recovers the y-coordinate of r using Eq. (8) from Brier-Joye, "Weierstrass
|
|
* Elliptic Curves and Side-Channel Attacks", modified to work in mixed
|
|
* projective coords, i.e. p is affine and (r,s) in projective (homogeneous)
|
|
* coords, and return r in affine coordinates.
|
|
*
|
|
* X4 = two*Y1*X2*Z3*Z2;
|
|
* Y4 = two*b*Z3*SQR(Z2) + Z3*(a*Z2+X1*X2)*(X1*Z2+X2) - X3*SQR(X1*Z2-X2);
|
|
* Z4 = two*Y1*Z3*SQR(Z2);
|
|
*
|
|
* Z4 != 0 because:
|
|
* - 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)) {
|
|
if (!EC_POINT_copy(r, p)
|
|
|| !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(t4, p->Y, group->field)
|
|
|| !group->meth->field_mul(group, t6, r->X, t4, ctx)
|
|
|| !group->meth->field_mul(group, t6, s->Z, t6, ctx)
|
|
|| !group->meth->field_mul(group, t5, r->Z, t6, ctx)
|
|
|| !BN_mod_lshift1_quick(t1, group->b, group->field)
|
|
|| !group->meth->field_mul(group, t1, s->Z, t1, ctx)
|
|
|| !group->meth->field_sqr(group, t3, r->Z, ctx)
|
|
|| !group->meth->field_mul(group, t2, t3, t1, ctx)
|
|
|| !group->meth->field_mul(group, t6, r->Z, group->a, ctx)
|
|
|| !group->meth->field_mul(group, t1, p->X, r->X, ctx)
|
|
|| !BN_mod_add_quick(t1, t1, t6, group->field)
|
|
|| !group->meth->field_mul(group, t1, s->Z, t1, ctx)
|
|
|| !group->meth->field_mul(group, t0, p->X, r->Z, ctx)
|
|
|| !BN_mod_add_quick(t6, r->X, t0, group->field)
|
|
|| !group->meth->field_mul(group, t6, t6, t1, ctx)
|
|
|| !BN_mod_add_quick(t6, t6, t2, group->field)
|
|
|| !BN_mod_sub_quick(t0, t0, r->X, group->field)
|
|
|| !group->meth->field_sqr(group, t0, t0, ctx)
|
|
|| !group->meth->field_mul(group, t0, t0, s->X, ctx)
|
|
|| !BN_mod_sub_quick(t0, t6, t0, group->field)
|
|
|| !group->meth->field_mul(group, t1, s->Z, t4, ctx)
|
|
|| !group->meth->field_mul(group, t1, t3, t1, ctx)
|
|
|| (group->meth->field_decode != NULL
|
|
&& !group->meth->field_decode(group, t1, t1, ctx))
|
|
|| !group->meth->field_inv(group, t1, t1, ctx)
|
|
|| (group->meth->field_encode != NULL
|
|
&& !group->meth->field_encode(group, t1, t1, ctx))
|
|
|| !group->meth->field_mul(group, r->X, t5, t1, ctx)
|
|
|| !group->meth->field_mul(group, r->Y, t0, t1, ctx))
|
|
goto err;
|
|
|
|
if (group->meth->field_set_to_one != NULL) {
|
|
if (!group->meth->field_set_to_one(group, r->Z, ctx))
|
|
goto err;
|
|
} else {
|
|
if (!BN_one(r->Z))
|
|
goto err;
|
|
}
|
|
|
|
r->Z_is_one = 1;
|
|
ret = 1;
|
|
|
|
err:
|
|
BN_CTX_end(ctx);
|
|
return ret;
|
|
}
|