/* Originally written by Bodo Moeller and Nils Larsch for the OpenSSL project.
* ====================================================================
* Copyright (c) 1998-2005 The OpenSSL Project. All rights reserved.
*
* Redistribution and use in source and binary forms, with or without
* modification, are permitted provided that the following conditions
* are met:
*
* 1. Redistributions of source code must retain the above copyright
* notice, this list of conditions and the following disclaimer.
*
* 2. Redistributions in binary form must reproduce the above copyright
* notice, this list of conditions and the following disclaimer in
* the documentation and/or other materials provided with the
* distribution.
*
* 3. All advertising materials mentioning features or use of this
* software must display the following acknowledgment:
* "This product includes software developed by the OpenSSL Project
* for use in the OpenSSL Toolkit. (http://www.openssl.org/)"
*
* 4. The names "OpenSSL Toolkit" and "OpenSSL Project" must not be used to
* endorse or promote products derived from this software without
* prior written permission. For written permission, please contact
* openssl-core@openssl.org.
*
* 5. Products derived from this software may not be called "OpenSSL"
* nor may "OpenSSL" appear in their names without prior written
* permission of the OpenSSL Project.
*
* 6. Redistributions of any form whatsoever must retain the following
* acknowledgment:
* "This product includes software developed by the OpenSSL Project
* for use in the OpenSSL Toolkit (http://www.openssl.org/)"
*
* THIS SOFTWARE IS PROVIDED BY THE OpenSSL PROJECT ``AS IS'' AND ANY
* EXPRESSED OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
* IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR
* PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE OpenSSL PROJECT OR
* ITS CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL,
* SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT
* NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES;
* LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
* HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT,
* STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE)
* ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED
* OF THE POSSIBILITY OF SUCH DAMAGE.
* ====================================================================
*
* This product includes cryptographic software written by Eric Young
* (eay@cryptsoft.com). This product includes software written by Tim
* Hudson (tjh@cryptsoft.com).
*
*/
/* ====================================================================
* Copyright 2002 Sun Microsystems, Inc. ALL RIGHTS RESERVED.
*
* Portions of the attached software ("Contribution") are developed by
* SUN MICROSYSTEMS, INC., and are contributed to the OpenSSL project.
*
* The Contribution is licensed pursuant to the OpenSSL open source
* license provided above.
*
* The elliptic curve binary polynomial software is originally written by
* Sheueling Chang Shantz and Douglas Stebila of Sun Microsystems
* Laboratories. */
#include <openssl/ec.h>
#include <openssl/bn.h>
#include <openssl/err.h>
#include <openssl/mem.h>
#include "../bn/internal.h"
#include "../delocate.h"
#include "internal.h"
int ec_GFp_mont_group_init(EC_GROUP *group) {
int ok;
ok = ec_GFp_simple_group_init(group);
group->mont = NULL;
return ok;
}
void ec_GFp_mont_group_finish(EC_GROUP *group) {
BN_MONT_CTX_free(group->mont);
group->mont = NULL;
ec_GFp_simple_group_finish(group);
}
int ec_GFp_mont_group_set_curve(EC_GROUP *group, const BIGNUM *p,
const BIGNUM *a, const BIGNUM *b, BN_CTX *ctx) {
BN_CTX *new_ctx = NULL;
int ret = 0;
BN_MONT_CTX_free(group->mont);
group->mont = NULL;
if (ctx == NULL) {
ctx = new_ctx = BN_CTX_new();
if (ctx == NULL) {
return 0;
}
}
group->mont = BN_MONT_CTX_new_for_modulus(p, ctx);
if (group->mont == NULL) {
OPENSSL_PUT_ERROR(EC, ERR_R_BN_LIB);
goto err;
}
ret = ec_GFp_simple_group_set_curve(group, p, a, b, ctx);
if (!ret) {
BN_MONT_CTX_free(group->mont);
group->mont = NULL;
}
err:
BN_CTX_free(new_ctx);
return ret;
}
int ec_GFp_mont_field_mul(const EC_GROUP *group, BIGNUM *r, const BIGNUM *a,
const BIGNUM *b, BN_CTX *ctx) {
if (group->mont == NULL) {
OPENSSL_PUT_ERROR(EC, EC_R_NOT_INITIALIZED);
return 0;
}
return BN_mod_mul_montgomery(r, a, b, group->mont, ctx);
}
int ec_GFp_mont_field_sqr(const EC_GROUP *group, BIGNUM *r, const BIGNUM *a,
BN_CTX *ctx) {
if (group->mont == NULL) {
OPENSSL_PUT_ERROR(EC, EC_R_NOT_INITIALIZED);
return 0;
}
return BN_mod_mul_montgomery(r, a, a, group->mont, ctx);
}
int ec_GFp_mont_field_encode(const EC_GROUP *group, BIGNUM *r, const BIGNUM *a,
BN_CTX *ctx) {
if (group->mont == NULL) {
OPENSSL_PUT_ERROR(EC, EC_R_NOT_INITIALIZED);
return 0;
}
return BN_to_montgomery(r, a, group->mont, ctx);
}
int ec_GFp_mont_field_decode(const EC_GROUP *group, BIGNUM *r, const BIGNUM *a,
BN_CTX *ctx) {
if (group->mont == NULL) {
OPENSSL_PUT_ERROR(EC, EC_R_NOT_INITIALIZED);
return 0;
}
return BN_from_montgomery(r, a, group->mont, ctx);
}
static int ec_GFp_mont_point_get_affine_coordinates(const EC_GROUP *group,
const EC_POINT *point,
BIGNUM *x, BIGNUM *y,
BN_CTX *ctx) {
if (EC_POINT_is_at_infinity(group, point)) {
OPENSSL_PUT_ERROR(EC, EC_R_POINT_AT_INFINITY);
return 0;
}
BN_CTX *new_ctx = NULL;
if (ctx == NULL) {
ctx = new_ctx = BN_CTX_new();
if (ctx == NULL) {
return 0;
}
}
int ret = 0;
BN_CTX_start(ctx);
if (BN_cmp(&point->Z, &group->one) == 0) {
// |point| is already affine.
if (x != NULL && !BN_from_montgomery(x, &point->X, group->mont, ctx)) {
goto err;
}
if (y != NULL && !BN_from_montgomery(y, &point->Y, group->mont, ctx)) {
goto err;
}
} else {
// transform (X, Y, Z) into (x, y) := (X/Z^2, Y/Z^3)
BIGNUM *Z_1 = BN_CTX_get(ctx);
BIGNUM *Z_2 = BN_CTX_get(ctx);
BIGNUM *Z_3 = BN_CTX_get(ctx);
if (Z_1 == NULL ||
Z_2 == NULL ||
Z_3 == NULL) {
goto err;
}
// The straightforward way to calculate the inverse of a Montgomery-encoded
// value where the result is Montgomery-encoded is:
//
// |BN_from_montgomery| + invert + |BN_to_montgomery|.
//
// This is equivalent, but more efficient, because |BN_from_montgomery|
// is more efficient (at least in theory) than |BN_to_montgomery|, since it
// doesn't have to do the multiplication before the reduction.
//
// Use Fermat's Little Theorem instead of |BN_mod_inverse_odd| since this
// inversion may be done as the final step of private key operations.
// Unfortunately, this is suboptimal for ECDSA verification.
if (!BN_from_montgomery(Z_1, &point->Z, group->mont, ctx) ||
!BN_from_montgomery(Z_1, Z_1, group->mont, ctx) ||
!bn_mod_inverse_prime(Z_1, Z_1, &group->field, ctx, group->mont)) {
goto err;
}
if (!BN_mod_mul_montgomery(Z_2, Z_1, Z_1, group->mont, ctx)) {
goto err;
}
// Instead of using |BN_from_montgomery| to convert the |x| coordinate
// and then calling |BN_from_montgomery| again to convert the |y|
// coordinate below, convert the common factor |Z_2| once now, saving one
// reduction.
if (!BN_from_montgomery(Z_2, Z_2, group->mont, ctx)) {
goto err;
}
if (x != NULL) {
if (!BN_mod_mul_montgomery(x, &point->X, Z_2, group->mont, ctx)) {
goto err;
}
}
if (y != NULL) {
if (!BN_mod_mul_montgomery(Z_3, Z_2, Z_1, group->mont, ctx) ||
!BN_mod_mul_montgomery(y, &point->Y, Z_3, group->mont, ctx)) {
goto err;
}
}
}
ret = 1;
err:
BN_CTX_end(ctx);
BN_CTX_free(new_ctx);
return ret;
}
DEFINE_METHOD_FUNCTION(EC_METHOD, EC_GFp_mont_method) {
out->group_init = ec_GFp_mont_group_init;
out->group_finish = ec_GFp_mont_group_finish;
out->group_set_curve = ec_GFp_mont_group_set_curve;
out->point_get_affine_coordinates = ec_GFp_mont_point_get_affine_coordinates;
out->mul = ec_wNAF_mul /* XXX: Not constant time. */;
out->mul_public = ec_wNAF_mul;
out->field_mul = ec_GFp_mont_field_mul;
out->field_sqr = ec_GFp_mont_field_sqr;
out->field_encode = ec_GFp_mont_field_encode;
out->field_decode = ec_GFp_mont_field_decode;
}