/
ecp_smpl.c
1560 lines (1350 loc) · 37.2 KB
/
ecp_smpl.c
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/* $OpenBSD: ecp_smpl.c,v 1.56 2023/08/03 18:53:56 tb Exp $ */
/* Includes code written by Lenka Fibikova <fibikova@exp-math.uni-essen.de>
* for the OpenSSL project.
* Includes code written by Bodo Moeller for the OpenSSL project.
*/
/* ====================================================================
* Copyright (c) 1998-2002 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 this software developed by SUN MICROSYSTEMS, INC.,
* and contributed to the OpenSSL project.
*/
#include <openssl/err.h>
#include "bn_local.h"
#include "ec_local.h"
/*
* 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);
}
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;
}
static int
ec_decode_scalar(const EC_GROUP *group, BIGNUM *bn, const BIGNUM *x, BN_CTX *ctx)
{
if (bn == NULL)
return 1;
if (group->meth->field_decode != NULL)
return group->meth->field_decode(group, bn, x, ctx);
return bn_copy(bn, x);
}
static int
ec_encode_scalar(const EC_GROUP *group, BIGNUM *bn, const BIGNUM *x, BN_CTX *ctx)
{
if (!BN_nnmod(bn, x, &group->field, ctx))
return 0;
if (group->meth->field_encode != NULL)
return group->meth->field_encode(group, bn, bn, ctx);
return 1;
}
static int
ec_encode_z_coordinate(const EC_GROUP *group, BIGNUM *bn, int *is_one,
const BIGNUM *z, BN_CTX *ctx)
{
if (!BN_nnmod(bn, z, &group->field, ctx))
return 0;
*is_one = BN_is_one(bn);
if (*is_one && group->meth->field_set_to_one != NULL)
return group->meth->field_set_to_one(group, bn, ctx);
if (group->meth->field_encode != NULL)
return group->meth->field_encode(group, bn, bn, ctx);
return 1;
}
int
ec_GFp_simple_group_set_curve(EC_GROUP *group,
const BIGNUM *p, const BIGNUM *a, const BIGNUM *b, BN_CTX *ctx)
{
BIGNUM *a_plus_3;
int ret = 0;
/* p must be a prime > 3 */
if (BN_num_bits(p) <= 2 || !BN_is_odd(p)) {
ECerror(EC_R_INVALID_FIELD);
return 0;
}
BN_CTX_start(ctx);
if ((a_plus_3 = BN_CTX_get(ctx)) == NULL)
goto err;
if (!bn_copy(&group->field, p))
goto err;
BN_set_negative(&group->field, 0);
if (!ec_encode_scalar(group, &group->a, a, ctx))
goto err;
if (!ec_encode_scalar(group, &group->b, b, ctx))
goto err;
if (!BN_set_word(a_plus_3, 3))
goto err;
if (!BN_mod_add(a_plus_3, a_plus_3, a, &group->field, ctx))
goto err;
group->a_is_minus3 = BN_is_zero(a_plus_3);
ret = 1;
err:
BN_CTX_end(ctx);
return ret;
}
int
ec_GFp_simple_group_get_curve(const EC_GROUP *group, BIGNUM *p, BIGNUM *a,
BIGNUM *b, BN_CTX *ctx)
{
if (p != NULL) {
if (!bn_copy(p, &group->field))
return 0;
}
if (!ec_decode_scalar(group, a, &group->a, ctx))
return 0;
if (!ec_decode_scalar(group, b, &group->b, ctx))
return 0;
return 1;
}
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)
{
BIGNUM *p, *a, *b, *discriminant;
int ret = 0;
BN_CTX_start(ctx);
if ((p = BN_CTX_get(ctx)) == NULL)
goto err;
if ((a = BN_CTX_get(ctx)) == NULL)
goto err;
if ((b = BN_CTX_get(ctx)) == NULL)
goto err;
if ((discriminant = BN_CTX_get(ctx)) == NULL)
goto err;
if (!EC_GROUP_get_curve(group, p, a, b, ctx))
goto err;
/*
* Check that the discriminant 4a^3 + 27b^2 is non-zero modulo p.
*/
if (BN_is_zero(a) && BN_is_zero(b))
goto err;
if (BN_is_zero(a) || BN_is_zero(b))
goto done;
/* Compute the discriminant: first 4a^3, then 27b^2, then their sum. */
if (!BN_mod_sqr(discriminant, a, p, ctx))
goto err;
if (!BN_mod_mul(discriminant, discriminant, a, p, ctx))
goto err;
if (!BN_lshift(discriminant, discriminant, 2))
goto err;
if (!BN_mod_sqr(b, b, p, ctx))
goto err;
if (!BN_mul_word(b, 27))
goto err;
if (!BN_mod_add(discriminant, discriminant, b, p, ctx))
goto err;
if (BN_is_zero(discriminant))
goto err;
done:
ret = 1;
err:
BN_CTX_end(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);
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(const EC_GROUP *group,
EC_POINT *point, const BIGNUM *x, const BIGNUM *y, const BIGNUM *z,
BN_CTX *ctx)
{
int ret = 0;
/*
* Setting individual coordinates allows the creation of bad points.
* EC_POINT_set_Jprojective_coordinates() checks at the API boundary.
*/
if (x != NULL) {
if (!ec_encode_scalar(group, &point->X, x, ctx))
goto err;
}
if (y != NULL) {
if (!ec_encode_scalar(group, &point->Y, y, ctx))
goto err;
}
if (z != NULL) {
if (!ec_encode_z_coordinate(group, &point->Z, &point->Z_is_one,
z, ctx))
goto err;
}
ret = 1;
err:
return ret;
}
int
ec_GFp_simple_get_Jprojective_coordinates(const EC_GROUP *group,
const EC_POINT *point, BIGNUM *x, BIGNUM *y, BIGNUM *z, BN_CTX *ctx)
{
int ret = 0;
if (!ec_decode_scalar(group, x, &point->X, ctx))
goto err;
if (!ec_decode_scalar(group, y, &point->Y, ctx))
goto err;
if (!ec_decode_scalar(group, z, &point->Z, ctx))
goto err;
ret = 1;
err:
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 */
ECerror(ERR_R_PASSED_NULL_PARAMETER);
return 0;
}
return EC_POINT_set_Jprojective_coordinates(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)
{
BIGNUM *z, *Z, *Z_1, *Z_2, *Z_3;
int ret = 0;
if (EC_POINT_is_at_infinity(group, point) > 0) {
ECerror(EC_R_POINT_AT_INFINITY);
return 0;
}
BN_CTX_start(ctx);
if ((z = BN_CTX_get(ctx)) == NULL)
goto err;
if ((Z = BN_CTX_get(ctx)) == NULL)
goto err;
if ((Z_1 = BN_CTX_get(ctx)) == NULL)
goto err;
if ((Z_2 = BN_CTX_get(ctx)) == NULL)
goto err;
if ((Z_3 = BN_CTX_get(ctx)) == NULL)
goto err;
/* Convert from projective coordinates (X, Y, Z) into (X/Z^2, Y/Z^3). */
if (!ec_decode_scalar(group, z, &point->Z, ctx))
goto err;
if (BN_is_one(z)) {
if (!ec_decode_scalar(group, x, &point->X, ctx))
goto err;
if (!ec_decode_scalar(group, y, &point->Y, ctx))
goto err;
goto done;
}
if (BN_mod_inverse_ct(Z_1, z, &group->field, ctx) == NULL) {
ECerror(ERR_R_BN_LIB);
goto err;
}
if (group->meth->field_encode == NULL) {
/* 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 == NULL) {
/* 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;
}
done:
ret = 1;
err:
BN_CTX_end(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 *);
BIGNUM *n0, *n1, *n2, *n3, *n4, *n5, *n6;
const BIGNUM *p;
int ret = 0;
if (a == b)
return EC_POINT_dbl(group, r, a, ctx);
if (EC_POINT_is_at_infinity(group, a) > 0)
return EC_POINT_copy(r, b);
if (EC_POINT_is_at_infinity(group, b) > 0)
return EC_POINT_copy(r, a);
field_mul = group->meth->field_mul;
field_sqr = group->meth->field_sqr;
p = &group->field;
BN_CTX_start(ctx);
if ((n0 = BN_CTX_get(ctx)) == NULL)
goto end;
if ((n1 = BN_CTX_get(ctx)) == NULL)
goto end;
if ((n2 = BN_CTX_get(ctx)) == NULL)
goto end;
if ((n3 = BN_CTX_get(ctx)) == NULL)
goto end;
if ((n4 = BN_CTX_get(ctx)) == NULL)
goto end;
if ((n5 = BN_CTX_get(ctx)) == NULL)
goto end;
if ((n6 = BN_CTX_get(ctx)) == 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);
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;
BIGNUM *n0, *n1, *n2, *n3;
int ret = 0;
if (EC_POINT_is_at_infinity(group, a) > 0)
return EC_POINT_set_to_infinity(group, r);
field_mul = group->meth->field_mul;
field_sqr = group->meth->field_sqr;
p = &group->field;
BN_CTX_start(ctx);
if ((n0 = BN_CTX_get(ctx)) == NULL)
goto err;
if ((n1 = BN_CTX_get(ctx)) == NULL)
goto err;
if ((n2 = BN_CTX_get(ctx)) == NULL)
goto err;
if ((n3 = BN_CTX_get(ctx)) == 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);
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) > 0 || 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;
BIGNUM *rh, *tmp, *Z4, *Z6;
int ret = -1;
if (EC_POINT_is_at_infinity(group, point) > 0)
return 1;
field_mul = group->meth->field_mul;
field_sqr = group->meth->field_sqr;
p = &group->field;
BN_CTX_start(ctx);
if ((rh = BN_CTX_get(ctx)) == NULL)
goto err;
if ((tmp = BN_CTX_get(ctx)) == NULL)
goto err;
if ((Z4 = BN_CTX_get(ctx)) == NULL)
goto err;
if ((Z6 = BN_CTX_get(ctx)) == 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);
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 *);
BIGNUM *tmp1, *tmp2, *Za23, *Zb23;
const BIGNUM *tmp1_, *tmp2_;
int ret = -1;
if (EC_POINT_is_at_infinity(group, a) > 0)
return EC_POINT_is_at_infinity(group, b) > 0 ? 0 : 1;
if (EC_POINT_is_at_infinity(group, b) > 0)
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;
BN_CTX_start(ctx);
if ((tmp1 = BN_CTX_get(ctx)) == NULL)
goto end;
if ((tmp2 = BN_CTX_get(ctx)) == NULL)
goto end;
if ((Za23 = BN_CTX_get(ctx)) == NULL)
goto end;
if ((Zb23 = BN_CTX_get(ctx)) == 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);
return ret;
}
int
ec_GFp_simple_make_affine(const EC_GROUP *group, EC_POINT *point, BN_CTX *ctx)
{
BIGNUM *x, *y;
int ret = 0;