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openssl/crypto/ec/ecp_smpl.c
Bodo Moeller 16602b5cd5 Further improve/fix ec_GFp_simple_points_make_affine (ecp_smpl.c) and 
group_order_tests (ectest.c).  Also fix the EC_POINTs_mul documentation (ec.h).

Reviewed-by: emilia@openssl.org
2014-08-13 17:37:19 +02:00

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/* crypto/ec/ecp_smpl.c */
/* 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.
*/
#define OPENSSL_FIPSAPI
#include <openssl/err.h>
#include <openssl/symhacks.h>
#include "ec_lcl.h"
const EC_METHOD *EC_GFp_simple_method(void)
{
static const EC_METHOD ret = {
EC_FLAGS_DEFAULT_OCT,
NID_X9_62_prime_field,
ec_GFp_simple_group_init,
ec_GFp_simple_group_finish,
ec_GFp_simple_group_clear_finish,
ec_GFp_simple_group_copy,
ec_GFp_simple_group_set_curve,
ec_GFp_simple_group_get_curve,
ec_GFp_simple_group_get_degree,
ec_GFp_simple_group_check_discriminant,
ec_GFp_simple_point_init,
ec_GFp_simple_point_finish,
ec_GFp_simple_point_clear_finish,
ec_GFp_simple_point_copy,
ec_GFp_simple_point_set_to_infinity,
ec_GFp_simple_set_Jprojective_coordinates_GFp,
ec_GFp_simple_get_Jprojective_coordinates_GFp,
ec_GFp_simple_point_set_affine_coordinates,
ec_GFp_simple_point_get_affine_coordinates,
0,0,0,
ec_GFp_simple_add,
ec_GFp_simple_dbl,
ec_GFp_simple_invert,
ec_GFp_simple_is_at_infinity,
ec_GFp_simple_is_on_curve,
ec_GFp_simple_cmp,
ec_GFp_simple_make_affine,
ec_GFp_simple_points_make_affine,
0 /* mul */,
0 /* precompute_mult */,
0 /* have_precompute_mult */,
ec_GFp_simple_field_mul,
ec_GFp_simple_field_sqr,
0 /* field_div */,
0 /* field_encode */,
0 /* field_decode */,
0 /* field_set_to_one */ };
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 */
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();
if (ctx == NULL)
return 0;
}
if (a != NULL)
{
if (!group->meth->field_decode(group, a, &group->a, ctx)) goto err;
}
if (b != NULL)
{
if (!group->meth->field_decode(group, b, &group->b, ctx)) goto err;
}
}
else
{
if (a != NULL)
{
if (!BN_copy(a, &group->a)) goto err;
}
if (b != NULL)
{
if (!BN_copy(b, &group->b)) goto err;
}
}
}
ret = 1;
err:
if (new_ctx)
BN_CTX_free(new_ctx);
return ret;
}
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)
{
ctx = new_ctx = BN_CTX_new();
if (ctx == NULL)
{
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;
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);
}
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