| /* 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 "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_copy(EC_GROUP *dest, const EC_GROUP *src) { |
| BN_MONT_CTX_free(dest->mont); |
| dest->mont = NULL; |
| |
| if (!ec_GFp_simple_group_copy(dest, src)) { |
| return 0; |
| } |
| |
| if (src->mont != NULL) { |
| dest->mont = BN_MONT_CTX_new(); |
| if (dest->mont == NULL) { |
| return 0; |
| } |
| if (!BN_MONT_CTX_copy(dest->mont, src->mont)) { |
| goto err; |
| } |
| } |
| |
| return 1; |
| |
| err: |
| BN_MONT_CTX_free(dest->mont); |
| dest->mont = NULL; |
| return 0; |
| } |
| |
| 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; |
| BN_MONT_CTX *mont = 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; |
| } |
| } |
| |
| mont = BN_MONT_CTX_new(); |
| if (mont == NULL) { |
| goto err; |
| } |
| if (!BN_MONT_CTX_set(mont, p, ctx)) { |
| OPENSSL_PUT_ERROR(EC, ERR_R_BN_LIB); |
| goto err; |
| } |
| |
| group->mont = mont; |
| mont = NULL; |
| |
| 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); |
| BN_MONT_CTX_free(mont); |
| 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); |
| BIGNUM *field_minus_2 = BN_CTX_get(ctx); |
| if (Z_1 == NULL || |
| Z_2 == NULL || |
| Z_3 == NULL || |
| field_minus_2 == 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 with |BN_mod_exp_mont_consttime| 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_copy(field_minus_2, &group->field) || |
| !BN_sub_word(field_minus_2, 2) || |
| !BN_mod_exp_mont_consttime(Z_1, Z_1, field_minus_2, &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; |
| } |
| |
| const EC_METHOD EC_GFp_mont_method = { |
| ec_GFp_mont_group_init, |
| ec_GFp_mont_group_finish, |
| ec_GFp_mont_group_copy, |
| ec_GFp_mont_group_set_curve, |
| ec_GFp_mont_point_get_affine_coordinates, |
| ec_wNAF_mul /* XXX: Not constant time. */, |
| ec_GFp_mont_field_mul, |
| ec_GFp_mont_field_sqr, |
| ec_GFp_mont_field_encode, |
| ec_GFp_mont_field_decode, |
| }; |