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1418 lines
39 KiB
1418 lines
39 KiB
/* crypto/ec/ecp_smpl.c */ |
|
/* |
|
* Includes code written by Lenka Fibikova <fibikova@exp-math.uni-essen.de> |
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* for the OpenSSL project. Includes code written by Bodo Moeller for the |
|
* OpenSSL project. |
|
*/ |
|
/* ==================================================================== |
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* Copyright (c) 1998-2002 The OpenSSL Project. All rights reserved. |
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* |
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* Redistribution and use in source and binary forms, with or without |
|
* modification, are permitted provided that the following conditions |
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* are met: |
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* |
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* 1. Redistributions of source code must retain the above copyright |
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* notice, this list of conditions and the following disclaimer. |
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* |
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* 2. Redistributions in binary form must reproduce the above copyright |
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* notice, this list of conditions and the following disclaimer in |
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* the documentation and/or other materials provided with the |
|
* distribution. |
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* |
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* 3. All advertising materials mentioning features or use of this |
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* software must display the following acknowledgment: |
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* "This product includes software developed by the OpenSSL Project |
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* for use in the OpenSSL Toolkit. (http://www.openssl.org/)" |
|
* |
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* 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. |
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* |
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* 5. Products derived from this software may not be called "OpenSSL" |
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* nor may "OpenSSL" appear in their names without prior written |
|
* permission of the OpenSSL Project. |
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* |
|
* 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/)" |
|
* |
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* THIS SOFTWARE IS PROVIDED BY THE OpenSSL PROJECT ``AS IS'' AND ANY |
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* EXPRESSED OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE |
|
* IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR |
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* PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE OpenSSL PROJECT OR |
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* ITS CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, |
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* SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT |
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* NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; |
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* LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) |
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* HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, |
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* STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) |
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* ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED |
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* OF THE POSSIBILITY OF SUCH DAMAGE. |
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* ==================================================================== |
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* |
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* This product includes cryptographic software written by Eric Young |
|
* (eay@cryptsoft.com). This product includes software written by Tim |
|
* Hudson (tjh@cryptsoft.com). |
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* |
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*/ |
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/* ==================================================================== |
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* Copyright 2002 Sun Microsystems, Inc. ALL RIGHTS RESERVED. |
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* Portions of this software developed by SUN MICROSYSTEMS, INC., |
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* and contributed to the OpenSSL project. |
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*/ |
|
|
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#include <openssl/err.h> |
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#include <openssl/symhacks.h> |
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|
|
#ifdef OPENSSL_FIPS |
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# include <openssl/fips.h> |
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#endif |
|
|
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#include "ec_lcl.h" |
|
|
|
const EC_METHOD *EC_GFp_simple_method(void) |
|
{ |
|
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, |
|
ec_GFp_simple_group_finish, |
|
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_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, |
|
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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0 /* field_encode */ , |
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0 /* field_decode */ , |
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0 /* field_set_to_one */ |
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}; |
|
|
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#ifdef OPENSSL_FIPS |
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if (FIPS_mode()) |
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return fips_ec_gfp_simple_method(); |
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#endif |
|
|
|
return &ret; |
|
} |
|
|
|
/* |
|
* Most method functions in this file are designed to work with |
|
* non-trivial representations of field elements if necessary |
|
* (see ecp_mont.c): while standard modular addition and subtraction |
|
* are used, the field_mul and field_sqr methods will be used for |
|
* multiplication, and field_encode and field_decode (if defined) |
|
* will be used for converting between representations. |
|
* |
|
* Functions ec_GFp_simple_points_make_affine() and |
|
* ec_GFp_simple_point_get_affine_coordinates() specifically assume |
|
* that if a non-trivial representation is used, it is a Montgomery |
|
* representation (i.e. 'encoding' means multiplying by some factor R). |
|
*/ |
|
|
|
int ec_GFp_simple_group_init(EC_GROUP *group) |
|
{ |
|
BN_init(&group->field); |
|
BN_init(&group->a); |
|
BN_init(&group->b); |
|
group->a_is_minus3 = 0; |
|
return 1; |
|
} |
|
|
|
void ec_GFp_simple_group_finish(EC_GROUP *group) |
|
{ |
|
BN_free(&group->field); |
|
BN_free(&group->a); |
|
BN_free(&group->b); |
|
} |
|
|
|
void ec_GFp_simple_group_clear_finish(EC_GROUP *group) |
|
{ |
|
BN_clear_free(&group->field); |
|
BN_clear_free(&group->a); |
|
BN_clear_free(&group->b); |
|
} |
|
|
|
int ec_GFp_simple_group_copy(EC_GROUP *dest, const EC_GROUP *src) |
|
{ |
|
if (!BN_copy(&dest->field, &src->field)) |
|
return 0; |
|
if (!BN_copy(&dest->a, &src->a)) |
|
return 0; |
|
if (!BN_copy(&dest->b, &src->b)) |
|
return 0; |
|
|
|
dest->a_is_minus3 = src->a_is_minus3; |
|
|
|
return 1; |
|
} |
|
|
|
int ec_GFp_simple_group_set_curve(EC_GROUP *group, |
|
const BIGNUM *p, const BIGNUM *a, |
|
const BIGNUM *b, BN_CTX *ctx) |
|
{ |
|
int ret = 0; |
|
BN_CTX *new_ctx = NULL; |
|
BIGNUM *tmp_a; |
|
|
|
/* p must be a prime > 3 */ |
|
if (BN_num_bits(p) <= 2 || !BN_is_odd(p)) { |
|
ECerr(EC_F_EC_GFP_SIMPLE_GROUP_SET_CURVE, EC_R_INVALID_FIELD); |
|
return 0; |
|
} |
|
|
|
if (ctx == NULL) { |
|
ctx = new_ctx = BN_CTX_new(); |
|
if (ctx == NULL) |
|
return 0; |
|
} |
|
|
|
BN_CTX_start(ctx); |
|
tmp_a = BN_CTX_get(ctx); |
|
if (tmp_a == NULL) |
|
goto err; |
|
|
|
/* group->field */ |
|
if (!BN_copy(&group->field, p)) |
|
goto err; |
|
BN_set_negative(&group->field, 0); |
|
|
|
/* group->a */ |
|
if (!BN_nnmod(tmp_a, a, p, ctx)) |
|
goto err; |
|
if (group->meth->field_encode) { |
|
if (!group->meth->field_encode(group, &group->a, tmp_a, ctx)) |
|
goto err; |
|
} else if (!BN_copy(&group->a, tmp_a)) |
|
goto err; |
|
|
|
/* group->b */ |
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if (!BN_nnmod(&group->b, b, p, ctx)) |
|
goto err; |
|
if (group->meth->field_encode) |
|
if (!group->meth->field_encode(group, &group->b, &group->b, ctx)) |
|
goto err; |
|
|
|
/* group->a_is_minus3 */ |
|
if (!BN_add_word(tmp_a, 3)) |
|
goto err; |
|
group->a_is_minus3 = (0 == BN_cmp(tmp_a, &group->field)); |
|
|
|
ret = 1; |
|
|
|
err: |
|
BN_CTX_end(ctx); |
|
if (new_ctx != NULL) |
|
BN_CTX_free(new_ctx); |
|
return ret; |
|
} |
|
|
|
int ec_GFp_simple_group_get_curve(const EC_GROUP *group, BIGNUM *p, BIGNUM *a, |
|
BIGNUM *b, BN_CTX *ctx) |
|
{ |
|
int ret = 0; |
|
BN_CTX *new_ctx = NULL; |
|
|
|
if (p != NULL) { |
|
if (!BN_copy(p, &group->field)) |
|
return 0; |
|
} |
|
|
|
if (a != NULL || b != NULL) { |
|
if (group->meth->field_decode) { |
|
if (ctx == NULL) { |
|
ctx = new_ctx = BN_CTX_new(); |
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if (ctx == NULL) |
|
return 0; |
|
} |
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if (a != NULL) { |
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if (!group->meth->field_decode(group, a, &group->a, ctx)) |
|
goto err; |
|
} |
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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; |
|
} |
|
} else { |
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if (a != NULL) { |
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if (!BN_copy(a, &group->a)) |
|
goto err; |
|
} |
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if (b != NULL) { |
|
if (!BN_copy(b, &group->b)) |
|
goto err; |
|
} |
|
} |
|
} |
|
|
|
ret = 1; |
|
|
|
err: |
|
if (new_ctx) |
|
BN_CTX_free(new_ctx); |
|
return ret; |
|
} |
|
|
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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) { |
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ctx = new_ctx = BN_CTX_new(); |
|
if (ctx == NULL) { |
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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; |
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if (!BN_mod_mul(tmp_2, tmp_1, a, p, ctx)) |
|
goto err; |
|
if (!BN_lshift(tmp_1, tmp_2, 2)) |
|
goto err; |
|
/* tmp_1 = 4*a^3 */ |
|
|
|
if (!BN_mod_sqr(tmp_2, b, p, ctx)) |
|
goto err; |
|
if (!BN_mul_word(tmp_2, 27)) |
|
goto err; |
|
/* tmp_2 = 27*b^2 */ |
|
|
|
if (!BN_mod_add(a, tmp_1, tmp_2, p, ctx)) |
|
goto err; |
|
if (BN_is_zero(a)) |
|
goto err; |
|
} |
|
ret = 1; |
|
|
|
err: |
|
if (ctx != NULL) |
|
BN_CTX_end(ctx); |
|
if (new_ctx != NULL) |
|
BN_CTX_free(new_ctx); |
|
return ret; |
|
} |
|
|
|
int ec_GFp_simple_point_init(EC_POINT *point) |
|
{ |
|
BN_init(&point->X); |
|
BN_init(&point->Y); |
|
BN_init(&point->Z); |
|
point->Z_is_one = 0; |
|
|
|
return 1; |
|
} |
|
|
|
void ec_GFp_simple_point_finish(EC_POINT *point) |
|
{ |
|
BN_free(&point->X); |
|
BN_free(&point->Y); |
|
BN_free(&point->Z); |
|
} |
|
|
|
void ec_GFp_simple_point_clear_finish(EC_POINT *point) |
|
{ |
|
BN_clear_free(&point->X); |
|
BN_clear_free(&point->Y); |
|
BN_clear_free(&point->Z); |
|
point->Z_is_one = 0; |
|
} |
|
|
|
int ec_GFp_simple_point_copy(EC_POINT *dest, const EC_POINT *src) |
|
{ |
|
if (!BN_copy(&dest->X, &src->X)) |
|
return 0; |
|
if (!BN_copy(&dest->Y, &src->Y)) |
|
return 0; |
|
if (!BN_copy(&dest->Z, &src->Z)) |
|
return 0; |
|
dest->Z_is_one = src->Z_is_one; |
|
|
|
return 1; |
|
} |
|
|
|
int ec_GFp_simple_point_set_to_infinity(const EC_GROUP *group, |
|
EC_POINT *point) |
|
{ |
|
point->Z_is_one = 0; |
|
BN_zero(&point->Z); |
|
return 1; |
|
} |
|
|
|
int ec_GFp_simple_set_Jprojective_coordinates_GFp(const EC_GROUP *group, |
|
EC_POINT *point, |
|
const BIGNUM *x, |
|
const BIGNUM *y, |
|
const BIGNUM *z, |
|
BN_CTX *ctx) |
|
{ |
|
BN_CTX *new_ctx = NULL; |
|
int ret = 0; |
|
|
|
if (ctx == NULL) { |
|
ctx = new_ctx = BN_CTX_new(); |
|
if (ctx == NULL) |
|
return 0; |
|
} |
|
|
|
if (x != NULL) { |
|
if (!BN_nnmod(&point->X, x, &group->field, ctx)) |
|
goto err; |
|
if (group->meth->field_encode) { |
|
if (!group->meth->field_encode(group, &point->X, &point->X, ctx)) |
|
goto err; |
|
} |
|
} |
|
|
|
if (y != NULL) { |
|
if (!BN_nnmod(&point->Y, y, &group->field, ctx)) |
|
goto err; |
|
if (group->meth->field_encode) { |
|
if (!group->meth->field_encode(group, &point->Y, &point->Y, ctx)) |
|
goto err; |
|
} |
|
} |
|
|
|
if (z != NULL) { |
|
int Z_is_one; |
|
|
|
if (!BN_nnmod(&point->Z, z, &group->field, ctx)) |
|
goto err; |
|
Z_is_one = BN_is_one(&point->Z); |
|
if (group->meth->field_encode) { |
|
if (Z_is_one && (group->meth->field_set_to_one != 0)) { |
|
if (!group->meth->field_set_to_one(group, &point->Z, ctx)) |
|
goto err; |
|
} else { |
|
if (!group-> |
|
meth->field_encode(group, &point->Z, &point->Z, ctx)) |
|
goto err; |
|
} |
|
} |
|
point->Z_is_one = Z_is_one; |
|
} |
|
|
|
ret = 1; |
|
|
|
err: |
|
if (new_ctx != NULL) |
|
BN_CTX_free(new_ctx); |
|
return ret; |
|
} |
|
|
|
int ec_GFp_simple_get_Jprojective_coordinates_GFp(const EC_GROUP *group, |
|
const EC_POINT *point, |
|
BIGNUM *x, BIGNUM *y, |
|
BIGNUM *z, BN_CTX *ctx) |
|
{ |
|
BN_CTX *new_ctx = NULL; |
|
int ret = 0; |
|
|
|
if (group->meth->field_decode != 0) { |
|
if (ctx == NULL) { |
|
ctx = new_ctx = BN_CTX_new(); |
|
if (ctx == NULL) |
|
return 0; |
|
} |
|
|
|
if (x != NULL) { |
|
if (!group->meth->field_decode(group, x, &point->X, ctx)) |
|
goto err; |
|
} |
|
if (y != NULL) { |
|
if (!group->meth->field_decode(group, y, &point->Y, ctx)) |
|
goto err; |
|
} |
|
if (z != NULL) { |
|
if (!group->meth->field_decode(group, z, &point->Z, ctx)) |
|
goto err; |
|
} |
|
} else { |
|
if (x != NULL) { |
|
if (!BN_copy(x, &point->X)) |
|
goto err; |
|
} |
|
if (y != NULL) { |
|
if (!BN_copy(y, &point->Y)) |
|
goto err; |
|
} |
|
if (z != NULL) { |
|
if (!BN_copy(z, &point->Z)) |
|
goto err; |
|
} |
|
} |
|
|
|
ret = 1; |
|
|
|
err: |
|
if (new_ctx != NULL) |
|
BN_CTX_free(new_ctx); |
|
return ret; |
|
} |
|
|
|
int ec_GFp_simple_point_set_affine_coordinates(const EC_GROUP *group, |
|
EC_POINT *point, |
|
const BIGNUM *x, |
|
const BIGNUM *y, BN_CTX *ctx) |
|
{ |
|
if (x == NULL || y == NULL) { |
|
/* |
|
* unlike for projective coordinates, we do not tolerate this |
|
*/ |
|
ECerr(EC_F_EC_GFP_SIMPLE_POINT_SET_AFFINE_COORDINATES, |
|
ERR_R_PASSED_NULL_PARAMETER); |
|
return 0; |
|
} |
|
|
|
return EC_POINT_set_Jprojective_coordinates_GFp(group, point, x, y, |
|
BN_value_one(), ctx); |
|
} |
|
|
|
int ec_GFp_simple_point_get_affine_coordinates(const EC_GROUP *group, |
|
const EC_POINT *point, |
|
BIGNUM *x, BIGNUM *y, |
|
BN_CTX *ctx) |
|
{ |
|
BN_CTX *new_ctx = NULL; |
|
BIGNUM *Z, *Z_1, *Z_2, *Z_3; |
|
const BIGNUM *Z_; |
|
int ret = 0; |
|
|
|
if (EC_POINT_is_at_infinity(group, point)) { |
|
ECerr(EC_F_EC_GFP_SIMPLE_POINT_GET_AFFINE_COORDINATES, |
|
EC_R_POINT_AT_INFINITY); |
|
return 0; |
|
} |
|
|
|
if (ctx == NULL) { |
|
ctx = new_ctx = BN_CTX_new(); |
|
if (ctx == NULL) |
|
return 0; |
|
} |
|
|
|
BN_CTX_start(ctx); |
|
Z = BN_CTX_get(ctx); |
|
Z_1 = BN_CTX_get(ctx); |
|
Z_2 = BN_CTX_get(ctx); |
|
Z_3 = BN_CTX_get(ctx); |
|
if (Z_3 == NULL) |
|
goto err; |
|
|
|
/* transform (X, Y, Z) into (x, y) := (X/Z^2, Y/Z^3) */ |
|
|
|
if (group->meth->field_decode) { |
|
if (!group->meth->field_decode(group, Z, &point->Z, ctx)) |
|
goto err; |
|
Z_ = Z; |
|
} else { |
|
Z_ = &point->Z; |
|
} |
|
|
|
if (BN_is_one(Z_)) { |
|
if (group->meth->field_decode) { |
|
if (x != NULL) { |
|
if (!group->meth->field_decode(group, x, &point->X, ctx)) |
|
goto err; |
|
} |
|
if (y != NULL) { |
|
if (!group->meth->field_decode(group, y, &point->Y, ctx)) |
|
goto err; |
|
} |
|
} else { |
|
if (x != NULL) { |
|
if (!BN_copy(x, &point->X)) |
|
goto err; |
|
} |
|
if (y != NULL) { |
|
if (!BN_copy(y, &point->Y)) |
|
goto err; |
|
} |
|
} |
|
} else { |
|
if (!BN_mod_inverse(Z_1, Z_, &group->field, ctx)) { |
|
ECerr(EC_F_EC_GFP_SIMPLE_POINT_GET_AFFINE_COORDINATES, |
|
ERR_R_BN_LIB); |
|
goto err; |
|
} |
|
|
|
if (group->meth->field_encode == 0) { |
|
/* field_sqr works on standard representation */ |
|
if (!group->meth->field_sqr(group, Z_2, Z_1, ctx)) |
|
goto err; |
|
} else { |
|
if (!BN_mod_sqr(Z_2, Z_1, &group->field, ctx)) |
|
goto err; |
|
} |
|
|
|
if (x != NULL) { |
|
/* |
|
* in the Montgomery case, field_mul will cancel out Montgomery |
|
* factor in X: |
|
*/ |
|
if (!group->meth->field_mul(group, x, &point->X, Z_2, ctx)) |
|
goto err; |
|
} |
|
|
|
if (y != NULL) { |
|
if (group->meth->field_encode == 0) { |
|
/* |
|
* field_mul works on standard representation |
|
*/ |
|
if (!group->meth->field_mul(group, Z_3, Z_2, Z_1, ctx)) |
|
goto err; |
|
} else { |
|
if (!BN_mod_mul(Z_3, Z_2, Z_1, &group->field, ctx)) |
|
goto err; |
|
} |
|
|
|
/* |
|
* in the Montgomery case, field_mul will cancel out Montgomery |
|
* factor in Y: |
|
*/ |
|
if (!group->meth->field_mul(group, y, &point->Y, Z_3, ctx)) |
|
goto err; |
|
} |
|
} |
|
|
|
ret = 1; |
|
|
|
err: |
|
BN_CTX_end(ctx); |
|
if (new_ctx != NULL) |
|
BN_CTX_free(new_ctx); |
|
return ret; |
|
} |
|
|
|
int ec_GFp_simple_add(const EC_GROUP *group, EC_POINT *r, const EC_POINT *a, |
|
const EC_POINT *b, BN_CTX *ctx) |
|
{ |
|
int (*field_mul) (const EC_GROUP *, BIGNUM *, const BIGNUM *, |
|
const BIGNUM *, BN_CTX *); |
|
int (*field_sqr) (const EC_GROUP *, BIGNUM *, const BIGNUM *, BN_CTX *); |
|
const BIGNUM *p; |
|
BN_CTX *new_ctx = NULL; |
|
BIGNUM *n0, *n1, *n2, *n3, *n4, *n5, *n6; |
|
int ret = 0; |
|
|
|
if (a == b) |
|
return EC_POINT_dbl(group, r, a, ctx); |
|
if (EC_POINT_is_at_infinity(group, a)) |
|
return EC_POINT_copy(r, b); |
|
if (EC_POINT_is_at_infinity(group, b)) |
|
return EC_POINT_copy(r, a); |
|
|
|
field_mul = group->meth->field_mul; |
|
field_sqr = group->meth->field_sqr; |
|
p = &group->field; |
|
|
|
if (ctx == NULL) { |
|
ctx = new_ctx = BN_CTX_new(); |
|
if (ctx == NULL) |
|
return 0; |
|
} |
|
|
|
BN_CTX_start(ctx); |
|
n0 = BN_CTX_get(ctx); |
|
n1 = BN_CTX_get(ctx); |
|
n2 = BN_CTX_get(ctx); |
|
n3 = BN_CTX_get(ctx); |
|
n4 = BN_CTX_get(ctx); |
|
n5 = BN_CTX_get(ctx); |
|
n6 = BN_CTX_get(ctx); |
|
if (n6 == NULL) |
|
goto end; |
|
|
|
/* |
|
* Note that in this function we must not read components of 'a' or 'b' |
|
* once we have written the corresponding components of 'r'. ('r' might |
|
* be one of 'a' or 'b'.) |
|
*/ |
|
|
|
/* n1, n2 */ |
|
if (b->Z_is_one) { |
|
if (!BN_copy(n1, &a->X)) |
|
goto end; |
|
if (!BN_copy(n2, &a->Y)) |
|
goto end; |
|
/* n1 = X_a */ |
|
/* n2 = Y_a */ |
|
} else { |
|
if (!field_sqr(group, n0, &b->Z, ctx)) |
|
goto end; |
|
if (!field_mul(group, n1, &a->X, n0, ctx)) |
|
goto end; |
|
/* n1 = X_a * Z_b^2 */ |
|
|
|
if (!field_mul(group, n0, n0, &b->Z, ctx)) |
|
goto end; |
|
if (!field_mul(group, n2, &a->Y, n0, ctx)) |
|
goto end; |
|
/* n2 = Y_a * Z_b^3 */ |
|
} |
|
|
|
/* n3, n4 */ |
|
if (a->Z_is_one) { |
|
if (!BN_copy(n3, &b->X)) |
|
goto end; |
|
if (!BN_copy(n4, &b->Y)) |
|
goto end; |
|
/* n3 = X_b */ |
|
/* n4 = Y_b */ |
|
} else { |
|
if (!field_sqr(group, n0, &a->Z, ctx)) |
|
goto end; |
|
if (!field_mul(group, n3, &b->X, n0, ctx)) |
|
goto end; |
|
/* n3 = X_b * Z_a^2 */ |
|
|
|
if (!field_mul(group, n0, n0, &a->Z, ctx)) |
|
goto end; |
|
if (!field_mul(group, n4, &b->Y, n0, ctx)) |
|
goto end; |
|
/* n4 = Y_b * Z_a^3 */ |
|
} |
|
|
|
/* n5, n6 */ |
|
if (!BN_mod_sub_quick(n5, n1, n3, p)) |
|
goto end; |
|
if (!BN_mod_sub_quick(n6, n2, n4, p)) |
|
goto end; |
|
/* n5 = n1 - n3 */ |
|
/* n6 = n2 - n4 */ |
|
|
|
if (BN_is_zero(n5)) { |
|
if (BN_is_zero(n6)) { |
|
/* a is the same point as b */ |
|
BN_CTX_end(ctx); |
|
ret = EC_POINT_dbl(group, r, a, ctx); |
|
ctx = NULL; |
|
goto end; |
|
} else { |
|
/* a is the inverse of b */ |
|
BN_zero(&r->Z); |
|
r->Z_is_one = 0; |
|
ret = 1; |
|
goto end; |
|
} |
|
} |
|
|
|
/* 'n7', 'n8' */ |
|
if (!BN_mod_add_quick(n1, n1, n3, p)) |
|
goto end; |
|
if (!BN_mod_add_quick(n2, n2, n4, p)) |
|
goto end; |
|
/* 'n7' = n1 + n3 */ |
|
/* 'n8' = n2 + n4 */ |
|
|
|
/* Z_r */ |
|
if (a->Z_is_one && b->Z_is_one) { |
|
if (!BN_copy(&r->Z, n5)) |
|
goto end; |
|
} else { |
|
if (a->Z_is_one) { |
|
if (!BN_copy(n0, &b->Z)) |
|
goto end; |
|
} else if (b->Z_is_one) { |
|
if (!BN_copy(n0, &a->Z)) |
|
goto end; |
|
} else { |
|
if (!field_mul(group, n0, &a->Z, &b->Z, ctx)) |
|
goto end; |
|
} |
|
if (!field_mul(group, &r->Z, n0, n5, ctx)) |
|
goto end; |
|
} |
|
r->Z_is_one = 0; |
|
/* Z_r = Z_a * Z_b * n5 */ |
|
|
|
/* X_r */ |
|
if (!field_sqr(group, n0, n6, ctx)) |
|
goto end; |
|
if (!field_sqr(group, n4, n5, ctx)) |
|
goto end; |
|
if (!field_mul(group, n3, n1, n4, ctx)) |
|
goto end; |
|
if (!BN_mod_sub_quick(&r->X, n0, n3, p)) |
|
goto end; |
|
/* X_r = n6^2 - n5^2 * 'n7' */ |
|
|
|
/* 'n9' */ |
|
if (!BN_mod_lshift1_quick(n0, &r->X, p)) |
|
goto end; |
|
if (!BN_mod_sub_quick(n0, n3, n0, p)) |
|
goto end; |
|
/* n9 = n5^2 * 'n7' - 2 * X_r */ |
|
|
|
/* Y_r */ |
|
if (!field_mul(group, n0, n0, n6, ctx)) |
|
goto end; |
|
if (!field_mul(group, n5, n4, n5, ctx)) |
|
goto end; /* now n5 is n5^3 */ |
|
if (!field_mul(group, n1, n2, n5, ctx)) |
|
goto end; |
|
if (!BN_mod_sub_quick(n0, n0, n1, p)) |
|
goto end; |
|
if (BN_is_odd(n0)) |
|
if (!BN_add(n0, n0, p)) |
|
goto end; |
|
/* now 0 <= n0 < 2*p, and n0 is even */ |
|
if (!BN_rshift1(&r->Y, n0)) |
|
goto end; |
|
/* Y_r = (n6 * 'n9' - 'n8' * 'n5^3') / 2 */ |
|
|
|
ret = 1; |
|
|
|
end: |
|
if (ctx) /* otherwise we already called BN_CTX_end */ |
|
BN_CTX_end(ctx); |
|
if (new_ctx != NULL) |
|
BN_CTX_free(new_ctx); |
|
return ret; |
|
} |
|
|
|
int ec_GFp_simple_dbl(const EC_GROUP *group, EC_POINT *r, const EC_POINT *a, |
|
BN_CTX *ctx) |
|
{ |
|
int (*field_mul) (const EC_GROUP *, BIGNUM *, const BIGNUM *, |
|
const BIGNUM *, BN_CTX *); |
|
int (*field_sqr) (const EC_GROUP *, BIGNUM *, const BIGNUM *, BN_CTX *); |
|
const BIGNUM *p; |
|
BN_CTX *new_ctx = NULL; |
|
BIGNUM *n0, *n1, *n2, *n3; |
|
int ret = 0; |
|
|
|
if (EC_POINT_is_at_infinity(group, a)) { |
|
BN_zero(&r->Z); |
|
r->Z_is_one = 0; |
|
return 1; |
|
} |
|
|
|
field_mul = group->meth->field_mul; |
|
field_sqr = group->meth->field_sqr; |
|
p = &group->field; |
|
|
|
if (ctx == NULL) { |
|
ctx = new_ctx = BN_CTX_new(); |
|
if (ctx == NULL) |
|
return 0; |
|
} |
|
|
|
BN_CTX_start(ctx); |
|
n0 = BN_CTX_get(ctx); |
|
n1 = BN_CTX_get(ctx); |
|
n2 = BN_CTX_get(ctx); |
|
n3 = BN_CTX_get(ctx); |
|
if (n3 == NULL) |
|
goto err; |
|
|
|
/* |
|
* Note that in this function we must not read components of 'a' once we |
|
* have written the corresponding components of 'r'. ('r' might the same |
|
* as 'a'.) |
|
*/ |
|
|
|
/* n1 */ |
|
if (a->Z_is_one) { |
|
if (!field_sqr(group, n0, &a->X, ctx)) |
|
goto err; |
|
if (!BN_mod_lshift1_quick(n1, n0, p)) |
|
goto err; |
|
if (!BN_mod_add_quick(n0, n0, n1, p)) |
|
goto err; |
|
if (!BN_mod_add_quick(n1, n0, &group->a, p)) |
|
goto err; |
|
/* n1 = 3 * X_a^2 + a_curve */ |
|
} else if (group->a_is_minus3) { |
|
if (!field_sqr(group, n1, &a->Z, ctx)) |
|
goto err; |
|
if (!BN_mod_add_quick(n0, &a->X, n1, p)) |
|
goto err; |
|
if (!BN_mod_sub_quick(n2, &a->X, n1, p)) |
|
goto err; |
|
if (!field_mul(group, n1, n0, n2, ctx)) |
|
goto err; |
|
if (!BN_mod_lshift1_quick(n0, n1, p)) |
|
goto err; |
|
if (!BN_mod_add_quick(n1, n0, n1, p)) |
|
goto err; |
|
/*- |
|
* n1 = 3 * (X_a + Z_a^2) * (X_a - Z_a^2) |
|
* = 3 * X_a^2 - 3 * Z_a^4 |
|
*/ |
|
} else { |
|
if (!field_sqr(group, n0, &a->X, ctx)) |
|
goto err; |
|
if (!BN_mod_lshift1_quick(n1, n0, p)) |
|
goto err; |
|
if (!BN_mod_add_quick(n0, n0, n1, p)) |
|
goto err; |
|
if (!field_sqr(group, n1, &a->Z, ctx)) |
|
goto err; |
|
if (!field_sqr(group, n1, n1, ctx)) |
|
goto err; |
|
if (!field_mul(group, n1, n1, &group->a, ctx)) |
|
goto err; |
|
if (!BN_mod_add_quick(n1, n1, n0, p)) |
|
goto err; |
|
/* n1 = 3 * X_a^2 + a_curve * Z_a^4 */ |
|
} |
|
|
|
/* Z_r */ |
|
if (a->Z_is_one) { |
|
if (!BN_copy(n0, &a->Y)) |
|
goto err; |
|
} else { |
|
if (!field_mul(group, n0, &a->Y, &a->Z, ctx)) |
|
goto err; |
|
} |
|
if (!BN_mod_lshift1_quick(&r->Z, n0, p)) |
|
goto err; |
|
r->Z_is_one = 0; |
|
/* Z_r = 2 * Y_a * Z_a */ |
|
|
|
/* n2 */ |
|
if (!field_sqr(group, n3, &a->Y, ctx)) |
|
goto err; |
|
if (!field_mul(group, n2, &a->X, n3, ctx)) |
|
goto err; |
|
if (!BN_mod_lshift_quick(n2, n2, 2, p)) |
|
goto err; |
|
/* n2 = 4 * X_a * Y_a^2 */ |
|
|
|
/* X_r */ |
|
if (!BN_mod_lshift1_quick(n0, n2, p)) |
|
goto err; |
|
if (!field_sqr(group, &r->X, n1, ctx)) |
|
goto err; |
|
if (!BN_mod_sub_quick(&r->X, &r->X, n0, p)) |
|
goto err; |
|
/* X_r = n1^2 - 2 * n2 */ |
|
|
|
/* n3 */ |
|
if (!field_sqr(group, n0, n3, ctx)) |
|
goto err; |
|
if (!BN_mod_lshift_quick(n3, n0, 3, p)) |
|
goto err; |
|
/* n3 = 8 * Y_a^4 */ |
|
|
|
/* Y_r */ |
|
if (!BN_mod_sub_quick(n0, n2, &r->X, p)) |
|
goto err; |
|
if (!field_mul(group, n0, n1, n0, ctx)) |
|
goto err; |
|
if (!BN_mod_sub_quick(&r->Y, n0, n3, p)) |
|
goto err; |
|
/* Y_r = n1 * (n2 - X_r) - n3 */ |
|
|
|
ret = 1; |
|
|
|
err: |
|
BN_CTX_end(ctx); |
|
if (new_ctx != NULL) |
|
BN_CTX_free(new_ctx); |
|
return ret; |
|
} |
|
|
|
int ec_GFp_simple_invert(const EC_GROUP *group, EC_POINT *point, BN_CTX *ctx) |
|
{ |
|
if (EC_POINT_is_at_infinity(group, point) || BN_is_zero(&point->Y)) |
|
/* point is its own inverse */ |
|
return 1; |
|
|
|
return BN_usub(&point->Y, &group->field, &point->Y); |
|
} |
|
|
|
int ec_GFp_simple_is_at_infinity(const EC_GROUP *group, const EC_POINT *point) |
|
{ |
|
return BN_is_zero(&point->Z); |
|
} |
|
|
|
int ec_GFp_simple_is_on_curve(const EC_GROUP *group, const EC_POINT *point, |
|
BN_CTX *ctx) |
|
{ |
|
int (*field_mul) (const EC_GROUP *, BIGNUM *, const BIGNUM *, |
|
const BIGNUM *, BN_CTX *); |
|
int (*field_sqr) (const EC_GROUP *, BIGNUM *, const BIGNUM *, BN_CTX *); |
|
const BIGNUM *p; |
|
BN_CTX *new_ctx = NULL; |
|
BIGNUM *rh, *tmp, *Z4, *Z6; |
|
int ret = -1; |
|
|
|
if (EC_POINT_is_at_infinity(group, point)) |
|
return 1; |
|
|
|
field_mul = group->meth->field_mul; |
|
field_sqr = group->meth->field_sqr; |
|
p = &group->field; |
|
|
|
if (ctx == NULL) { |
|
ctx = new_ctx = BN_CTX_new(); |
|
if (ctx == NULL) |
|
return -1; |
|
} |
|
|
|
BN_CTX_start(ctx); |
|
rh = BN_CTX_get(ctx); |
|
tmp = BN_CTX_get(ctx); |
|
Z4 = BN_CTX_get(ctx); |
|
Z6 = BN_CTX_get(ctx); |
|
if (Z6 == NULL) |
|
goto err; |
|
|
|
/*- |
|
* We have a curve defined by a Weierstrass equation |
|
* y^2 = x^3 + a*x + b. |
|
* The point to consider is given in Jacobian projective coordinates |
|
* where (X, Y, Z) represents (x, y) = (X/Z^2, Y/Z^3). |
|
* Substituting this and multiplying by Z^6 transforms the above equation into |
|
* Y^2 = X^3 + a*X*Z^4 + b*Z^6. |
|
* To test this, we add up the right-hand side in 'rh'. |
|
*/ |
|
|
|
/* rh := X^2 */ |
|
if (!field_sqr(group, rh, &point->X, ctx)) |
|
goto err; |
|
|
|
if (!point->Z_is_one) { |
|
if (!field_sqr(group, tmp, &point->Z, ctx)) |
|
goto err; |
|
if (!field_sqr(group, Z4, tmp, ctx)) |
|
goto err; |
|
if (!field_mul(group, Z6, Z4, tmp, ctx)) |
|
goto err; |
|
|
|
/* rh := (rh + a*Z^4)*X */ |
|
if (group->a_is_minus3) { |
|
if (!BN_mod_lshift1_quick(tmp, Z4, p)) |
|
goto err; |
|
if (!BN_mod_add_quick(tmp, tmp, Z4, p)) |
|
goto err; |
|
if (!BN_mod_sub_quick(rh, rh, tmp, p)) |
|
goto err; |
|
if (!field_mul(group, rh, rh, &point->X, ctx)) |
|
goto err; |
|
} else { |
|
if (!field_mul(group, tmp, Z4, &group->a, ctx)) |
|
goto err; |
|
if (!BN_mod_add_quick(rh, rh, tmp, p)) |
|
goto err; |
|
if (!field_mul(group, rh, rh, &point->X, ctx)) |
|
goto err; |
|
} |
|
|
|
/* rh := rh + b*Z^6 */ |
|
if (!field_mul(group, tmp, &group->b, Z6, ctx)) |
|
goto err; |
|
if (!BN_mod_add_quick(rh, rh, tmp, p)) |
|
goto err; |
|
} else { |
|
/* point->Z_is_one */ |
|
|
|
/* rh := (rh + a)*X */ |
|
if (!BN_mod_add_quick(rh, rh, &group->a, p)) |
|
goto err; |
|
if (!field_mul(group, rh, rh, &point->X, ctx)) |
|
goto err; |
|
/* rh := rh + b */ |
|
if (!BN_mod_add_quick(rh, rh, &group->b, p)) |
|
goto err; |
|
} |
|
|
|
/* 'lh' := Y^2 */ |
|
if (!field_sqr(group, tmp, &point->Y, ctx)) |
|
goto err; |
|
|
|
ret = (0 == BN_ucmp(tmp, rh)); |
|
|
|
err: |
|
BN_CTX_end(ctx); |
|
if (new_ctx != NULL) |
|
BN_CTX_free(new_ctx); |
|
return ret; |
|
} |
|
|
|
int ec_GFp_simple_cmp(const EC_GROUP *group, const EC_POINT *a, |
|
const EC_POINT *b, BN_CTX *ctx) |
|
{ |
|
/*- |
|
* return values: |
|
* -1 error |
|
* 0 equal (in affine coordinates) |
|
* 1 not equal |
|
*/ |
|
|
|
int (*field_mul) (const EC_GROUP *, BIGNUM *, const BIGNUM *, |
|
const BIGNUM *, BN_CTX *); |
|
int (*field_sqr) (const EC_GROUP *, BIGNUM *, const BIGNUM *, BN_CTX *); |
|
BN_CTX *new_ctx = NULL; |
|
BIGNUM *tmp1, *tmp2, *Za23, *Zb23; |
|
const BIGNUM *tmp1_, *tmp2_; |
|
int ret = -1; |
|
|
|
if (EC_POINT_is_at_infinity(group, a)) { |
|
return EC_POINT_is_at_infinity(group, b) ? 0 : 1; |
|
} |
|
|
|
if (EC_POINT_is_at_infinity(group, b)) |
|
return 1; |
|
|
|
if (a->Z_is_one && b->Z_is_one) { |
|
return ((BN_cmp(&a->X, &b->X) == 0) |
|
&& BN_cmp(&a->Y, &b->Y) == 0) ? 0 : 1; |
|
} |
|
|
|
field_mul = group->meth->field_mul; |
|
field_sqr = group->meth->field_sqr; |
|
|
|
if (ctx == NULL) { |
|
ctx = new_ctx = BN_CTX_new(); |
|
if (ctx == NULL) |
|
return -1; |
|
} |
|
|
|
BN_CTX_start(ctx); |
|
tmp1 = BN_CTX_get(ctx); |
|
tmp2 = BN_CTX_get(ctx); |
|
Za23 = BN_CTX_get(ctx); |
|
Zb23 = BN_CTX_get(ctx); |
|
if (Zb23 == NULL) |
|
goto end; |
|
|
|
/*- |
|
* We have to decide whether |
|
* (X_a/Z_a^2, Y_a/Z_a^3) = (X_b/Z_b^2, Y_b/Z_b^3), |
|
* or equivalently, whether |
|
* (X_a*Z_b^2, Y_a*Z_b^3) = (X_b*Z_a^2, Y_b*Z_a^3). |
|
*/ |
|
|
|
if (!b->Z_is_one) { |
|
if (!field_sqr(group, Zb23, &b->Z, ctx)) |
|
goto end; |
|
if (!field_mul(group, tmp1, &a->X, Zb23, ctx)) |
|
goto end; |
|
tmp1_ = tmp1; |
|
} else |
|
tmp1_ = &a->X; |
|
if (!a->Z_is_one) { |
|
if (!field_sqr(group, Za23, &a->Z, ctx)) |
|
goto end; |
|
if (!field_mul(group, tmp2, &b->X, Za23, ctx)) |
|
goto end; |
|
tmp2_ = tmp2; |
|
} else |
|
tmp2_ = &b->X; |
|
|
|
/* compare X_a*Z_b^2 with X_b*Z_a^2 */ |
|
if (BN_cmp(tmp1_, tmp2_) != 0) { |
|
ret = 1; /* points differ */ |
|
goto end; |
|
} |
|
|
|
if (!b->Z_is_one) { |
|
if (!field_mul(group, Zb23, Zb23, &b->Z, ctx)) |
|
goto end; |
|
if (!field_mul(group, tmp1, &a->Y, Zb23, ctx)) |
|
goto end; |
|
/* tmp1_ = tmp1 */ |
|
} else |
|
tmp1_ = &a->Y; |
|
if (!a->Z_is_one) { |
|
if (!field_mul(group, Za23, Za23, &a->Z, ctx)) |
|
goto end; |
|
if (!field_mul(group, tmp2, &b->Y, Za23, ctx)) |
|
goto end; |
|
/* tmp2_ = tmp2 */ |
|
} else |
|
tmp2_ = &b->Y; |
|
|
|
/* compare Y_a*Z_b^3 with Y_b*Z_a^3 */ |
|
if (BN_cmp(tmp1_, tmp2_) != 0) { |
|
ret = 1; /* points differ */ |
|
goto end; |
|
} |
|
|
|
/* points are equal */ |
|
ret = 0; |
|
|
|
end: |
|
BN_CTX_end(ctx); |
|
if (new_ctx != NULL) |
|
BN_CTX_free(new_ctx); |
|
return ret; |
|
} |
|
|
|
int ec_GFp_simple_make_affine(const EC_GROUP *group, EC_POINT *point, |
|
BN_CTX *ctx) |
|
{ |
|
BN_CTX *new_ctx = NULL; |
|
BIGNUM *x, *y; |
|
int ret = 0; |
|
|
|
if (point->Z_is_one || EC_POINT_is_at_infinity(group, point)) |
|
return 1; |
|
|
|
if (ctx == NULL) { |
|
ctx = new_ctx = BN_CTX_new(); |
|
if (ctx == NULL) |
|
return 0; |
|
} |
|
|
|
BN_CTX_start(ctx); |
|
x = BN_CTX_get(ctx); |
|
y = BN_CTX_get(ctx); |
|
if (y == NULL) |
|
goto err; |
|
|
|
if (!EC_POINT_get_affine_coordinates_GFp(group, point, x, y, ctx)) |
|
goto err; |
|
if (!EC_POINT_set_affine_coordinates_GFp(group, point, x, y, ctx)) |
|
goto err; |
|
if (!point->Z_is_one) { |
|
ECerr(EC_F_EC_GFP_SIMPLE_MAKE_AFFINE, ERR_R_INTERNAL_ERROR); |
|
goto err; |
|
} |
|
|
|
ret = 1; |
|
|
|
err: |
|
BN_CTX_end(ctx); |
|
if (new_ctx != NULL) |
|
BN_CTX_free(new_ctx); |
|
return ret; |
|
} |
|
|
|
int ec_GFp_simple_points_make_affine(const EC_GROUP *group, size_t num, |
|
EC_POINT *points[], BN_CTX *ctx) |
|
{ |
|
BN_CTX *new_ctx = NULL; |
|
BIGNUM *tmp, *tmp_Z; |
|
BIGNUM **prod_Z = NULL; |
|
size_t i; |
|
int ret = 0; |
|
|
|
if (num == 0) |
|
return 1; |
|
|
|
if (ctx == NULL) { |
|
ctx = new_ctx = BN_CTX_new(); |
|
if (ctx == NULL) |
|
return 0; |
|
} |
|
|
|
BN_CTX_start(ctx); |
|
tmp = BN_CTX_get(ctx); |
|
tmp_Z = BN_CTX_get(ctx); |
|
if (tmp == NULL || tmp_Z == NULL) |
|
goto err; |
|
|
|
prod_Z = OPENSSL_malloc(num * sizeof prod_Z[0]); |
|
if (prod_Z == NULL) |
|
goto err; |
|
for (i = 0; i < num; i++) { |
|
prod_Z[i] = BN_new(); |
|
if (prod_Z[i] == NULL) |
|
goto err; |
|
} |
|
|
|
/* |
|
* Set each prod_Z[i] to the product of points[0]->Z .. points[i]->Z, |
|
* skipping any zero-valued inputs (pretend that they're 1). |
|
*/ |
|
|
|
if (!BN_is_zero(&points[0]->Z)) { |
|
if (!BN_copy(prod_Z[0], &points[0]->Z)) |
|
goto err; |
|
} else { |
|
if (group->meth->field_set_to_one != 0) { |
|
if (!group->meth->field_set_to_one(group, prod_Z[0], ctx)) |
|
goto err; |
|
} else { |
|
if (!BN_one(prod_Z[0])) |
|
goto err; |
|
} |
|
} |
|
|
|
for (i = 1; i < num; i++) { |
|
if (!BN_is_zero(&points[i]->Z)) { |
|
if (!group->meth->field_mul(group, prod_Z[i], prod_Z[i - 1], |
|
&points[i]->Z, ctx)) |
|
goto err; |
|
} else { |
|
if (!BN_copy(prod_Z[i], prod_Z[i - 1])) |
|
goto err; |
|
} |
|
} |
|
|
|
/* |
|
* Now use a single explicit inversion to replace every non-zero |
|
* points[i]->Z by its inverse. |
|
*/ |
|
|
|
if (!BN_mod_inverse(tmp, prod_Z[num - 1], &group->field, ctx)) { |
|
ECerr(EC_F_EC_GFP_SIMPLE_POINTS_MAKE_AFFINE, ERR_R_BN_LIB); |
|
goto err; |
|
} |
|
if (group->meth->field_encode != 0) { |
|
/* |
|
* In the Montgomery case, we just turned R*H (representing H) into |
|
* 1/(R*H), but we need R*(1/H) (representing 1/H); i.e. we need to |
|
* multiply by the Montgomery factor twice. |
|
*/ |
|
if (!group->meth->field_encode(group, tmp, tmp, ctx)) |
|
goto err; |
|
if (!group->meth->field_encode(group, tmp, tmp, ctx)) |
|
goto err; |
|
} |
|
|
|
for (i = num - 1; i > 0; --i) { |
|
/* |
|
* Loop invariant: tmp is the product of the inverses of points[0]->Z |
|
* .. points[i]->Z (zero-valued inputs skipped). |
|
*/ |
|
if (!BN_is_zero(&points[i]->Z)) { |
|
/* |
|
* Set tmp_Z to the inverse of points[i]->Z (as product of Z |
|
* inverses 0 .. i, Z values 0 .. i - 1). |
|
*/ |
|
if (!group-> |
|
meth->field_mul(group, tmp_Z, prod_Z[i - 1], tmp, ctx)) |
|
goto err; |
|
/* |
|
* Update tmp to satisfy the loop invariant for i - 1. |
|
*/ |
|
if (!group->meth->field_mul(group, tmp, tmp, &points[i]->Z, ctx)) |
|
goto err; |
|
/* Replace points[i]->Z by its inverse. */ |
|
if (!BN_copy(&points[i]->Z, tmp_Z)) |
|
goto err; |
|
} |
|
} |
|
|
|
if (!BN_is_zero(&points[0]->Z)) { |
|
/* Replace points[0]->Z by its inverse. */ |
|
if (!BN_copy(&points[0]->Z, tmp)) |
|
goto err; |
|
} |
|
|
|
/* Finally, fix up the X and Y coordinates for all points. */ |
|
|
|
for (i = 0; i < num; i++) { |
|
EC_POINT *p = points[i]; |
|
|
|
if (!BN_is_zero(&p->Z)) { |
|
/* turn (X, Y, 1/Z) into (X/Z^2, Y/Z^3, 1) */ |
|
|
|
if (!group->meth->field_sqr(group, tmp, &p->Z, ctx)) |
|
goto err; |
|
if (!group->meth->field_mul(group, &p->X, &p->X, tmp, ctx)) |
|
goto err; |
|
|
|
if (!group->meth->field_mul(group, tmp, tmp, &p->Z, ctx)) |
|
goto err; |
|
if (!group->meth->field_mul(group, &p->Y, &p->Y, tmp, ctx)) |
|
goto err; |
|
|
|
if (group->meth->field_set_to_one != 0) { |
|
if (!group->meth->field_set_to_one(group, &p->Z, ctx)) |
|
goto err; |
|
} else { |
|
if (!BN_one(&p->Z)) |
|
goto err; |
|
} |
|
p->Z_is_one = 1; |
|
} |
|
} |
|
|
|
ret = 1; |
|
|
|
err: |
|
BN_CTX_end(ctx); |
|
if (new_ctx != NULL) |
|
BN_CTX_free(new_ctx); |
|
if (prod_Z != NULL) { |
|
for (i = 0; i < num; i++) { |
|
if (prod_Z[i] == NULL) |
|
break; |
|
BN_clear_free(prod_Z[i]); |
|
} |
|
OPENSSL_free(prod_Z); |
|
} |
|
return ret; |
|
} |
|
|
|
int ec_GFp_simple_field_mul(const EC_GROUP *group, BIGNUM *r, const BIGNUM *a, |
|
const BIGNUM *b, BN_CTX *ctx) |
|
{ |
|
return BN_mod_mul(r, a, b, &group->field, ctx); |
|
} |
|
|
|
int ec_GFp_simple_field_sqr(const EC_GROUP *group, BIGNUM *r, const BIGNUM *a, |
|
BN_CTX *ctx) |
|
{ |
|
return BN_mod_sqr(r, a, &group->field, ctx); |
|
}
|
|
|