/* crypto/ec/ec2_smpl.c */
/* ====================================================================
* Copyright 2002 Sun Microsystems, Inc. ALL RIGHTS RESERVED.
*
* The Elliptic Curve Public-Key Crypto Library (ECC Code) included
* herein is developed by SUN MICROSYSTEMS, INC., and is contributed
* to the OpenSSL project.
*
* The ECC Code is licensed pursuant to the OpenSSL open source
* license provided below.
*
* The software is originally written by Sheueling Chang Shantz and
* Douglas Stebila of Sun Microsystems Laboratories.
*
*/
/* ====================================================================
* Copyright (c) 1998-2005 The OpenSSL Project. All rights reserved.
*
* Redistribution and use in source and binary forms, with or without
* modification, are permitted provided that the following conditions
* are met:
*
* 1. Redistributions of source code must retain the above copyright
* notice, this list of conditions and the following disclaimer.
*
* 2. Redistributions in binary form must reproduce the above copyright
* notice, this list of conditions and the following disclaimer in
* the documentation and/or other materials provided with the
* distribution.
*
* 3. All advertising materials mentioning features or use of this
* software must display the following acknowledgment:
* "This product includes software developed by the OpenSSL Project
* for use in the OpenSSL Toolkit. (http://www.openssl.org/)"
*
* 4. The names "OpenSSL Toolkit" and "OpenSSL Project" must not be used to
* endorse or promote products derived from this software without
* prior written permission. For written permission, please contact
* openssl-core@openssl.org.
*
* 5. Products derived from this software may not be called "OpenSSL"
* nor may "OpenSSL" appear in their names without prior written
* permission of the OpenSSL Project.
*
* 6. Redistributions of any form whatsoever must retain the following
* acknowledgment:
* "This product includes software developed by the OpenSSL Project
* for use in the OpenSSL Toolkit (http://www.openssl.org/)"
*
* THIS SOFTWARE IS PROVIDED BY THE OpenSSL PROJECT ``AS IS'' AND ANY
* EXPRESSED OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
* IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR
* PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE OpenSSL PROJECT OR
* ITS CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL,
* SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT
* NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES;
* LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
* HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT,
* STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE)
* ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED
* OF THE POSSIBILITY OF SUCH DAMAGE.
* ====================================================================
*
* This product includes cryptographic software written by Eric Young
* (eay@cryptsoft.com). This product includes software written by Tim
* Hudson (tjh@cryptsoft.com).
*
*/
#include <openssl/err.h>
#include "ec_lcl.h"
#ifndef OPENSSL_NO_EC2M
#ifdef OPENSSL_FIPS
#include <openssl/fips.h>
#endif
const EC_METHOD *EC_GF2m_simple_method(void)
{
#ifdef OPENSSL_FIPS
return fips_ec_gf2m_simple_method();
#else
static const EC_METHOD ret = {
EC_FLAGS_DEFAULT_OCT,
NID_X9_62_characteristic_two_field,
ec_GF2m_simple_group_init,
ec_GF2m_simple_group_finish,
ec_GF2m_simple_group_clear_finish,
ec_GF2m_simple_group_copy,
ec_GF2m_simple_group_set_curve,
ec_GF2m_simple_group_get_curve,
ec_GF2m_simple_group_get_degree,
ec_GF2m_simple_group_check_discriminant,
ec_GF2m_simple_point_init,
ec_GF2m_simple_point_finish,
ec_GF2m_simple_point_clear_finish,
ec_GF2m_simple_point_copy,
ec_GF2m_simple_point_set_to_infinity,
0 /* set_Jprojective_coordinates_GFp */,
0 /* get_Jprojective_coordinates_GFp */,
ec_GF2m_simple_point_set_affine_coordinates,
ec_GF2m_simple_point_get_affine_coordinates,
0,0,0,
ec_GF2m_simple_add,
ec_GF2m_simple_dbl,
ec_GF2m_simple_invert,
ec_GF2m_simple_is_at_infinity,
ec_GF2m_simple_is_on_curve,
ec_GF2m_simple_cmp,
ec_GF2m_simple_make_affine,
ec_GF2m_simple_points_make_affine,
/* the following three method functions are defined in ec2_mult.c */
ec_GF2m_simple_mul,
ec_GF2m_precompute_mult,
ec_GF2m_have_precompute_mult,
ec_GF2m_simple_field_mul,
ec_GF2m_simple_field_sqr,
ec_GF2m_simple_field_div,
0 /* field_encode */,
0 /* field_decode */,
0 /* field_set_to_one */ };
return &ret;
#endif
}
/* Initialize a GF(2^m)-based EC_GROUP structure.
* Note that all other members are handled by EC_GROUP_new.
*/
int ec_GF2m_simple_group_init(EC_GROUP *group)
{
BN_init(&group->field);
BN_init(&group->a);
BN_init(&group->b);
return 1;
}
/* Free a GF(2^m)-based EC_GROUP structure.
* Note that all other members are handled by EC_GROUP_free.
*/
void ec_GF2m_simple_group_finish(EC_GROUP *group)
{
BN_free(&group->field);
BN_free(&group->a);
BN_free(&group->b);
}
/* Clear and free a GF(2^m)-based EC_GROUP structure.
* Note that all other members are handled by EC_GROUP_clear_free.
*/
void ec_GF2m_simple_group_clear_finish(EC_GROUP *group)
{
BN_clear_free(&group->field);
BN_clear_free(&group->a);
BN_clear_free(&group->b);
group->poly[0] = 0;
group->poly[1] = 0;
group->poly[2] = 0;
group->poly[3] = 0;
group->poly[4] = 0;
group->poly[5] = -1;
}
/* Copy a GF(2^m)-based EC_GROUP structure.
* Note that all other members are handled by EC_GROUP_copy.
*/
int ec_GF2m_simple_group_copy(EC_GROUP *dest, const EC_GROUP *src)
{
int i;
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->poly[0] = src->poly[0];
dest->poly[1] = src->poly[1];
dest->poly[2] = src->poly[2];
dest->poly[3] = src->poly[3];
dest->poly[4] = src->poly[4];
dest->poly[5] = src->poly[5];
if (bn_wexpand(&dest->a, (int)(dest->poly[0] + BN_BITS2 - 1) / BN_BITS2) == NULL) return 0;
if (bn_wexpand(&dest->b, (int)(dest->poly[0] + BN_BITS2 - 1) / BN_BITS2) == NULL) return 0;
for (i = dest->a.top; i < dest->a.dmax; i++) dest->a.d[i] = 0;
for (i = dest->b.top; i < dest->b.dmax; i++) dest->b.d[i] = 0;
return 1;
}
/* Set the curve parameters of an EC_GROUP structure. */
int ec_GF2m_simple_group_set_curve(EC_GROUP *group,
const BIGNUM *p, const BIGNUM *a, const BIGNUM *b, BN_CTX *ctx)
{
int ret = 0, i;
/* group->field */
if (!BN_copy(&group->field, p)) goto err;
i = BN_GF2m_poly2arr(&group->field, group->poly, 6) - 1;
if ((i != 5) && (i != 3))
{
ECerr(EC_F_EC_GF2M_SIMPLE_GROUP_SET_CURVE, EC_R_UNSUPPORTED_FIELD);
goto err;
}
/* group->a */
if (!BN_GF2m_mod_arr(&group->a, a, group->poly)) goto err;
if(bn_wexpand(&group->a, (int)(group->poly[0] + BN_BITS2 - 1) / BN_BITS2) == NULL) goto err;
for (i = group->a.top; i < group->a.dmax; i++) group->a.d[i] = 0;
/* group->b */
if (!BN_GF2m_mod_arr(&group->b, b, group->poly)) goto err;
if(bn_wexpand(&group->b, (int)(group->poly[0] + BN_BITS2 - 1) / BN_BITS2) == NULL) goto err;
for (i = group->b.top; i < group->b.dmax; i++) group->b.d[i] = 0;
ret = 1;
err:
return ret;
}
/* Get the curve parameters of an EC_GROUP structure.
* If p, a, or b are NULL then there values will not be set but the method will return with success.
*/
int ec_GF2m_simple_group_get_curve(const EC_GROUP *group, BIGNUM *p, BIGNUM *a, BIGNUM *b, BN_CTX *ctx)
{
int ret = 0;
if (p != NULL)
{
if (!BN_copy(p, &group->field)) return 0;
}
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:
return ret;
}
/* Gets the degree of the field. For a curve over GF(2^m) this is the value m. */
int ec_GF2m_simple_group_get_degree(const EC_GROUP *group)
{
return BN_num_bits(&group->field)-1;
}
/* Checks the discriminant of the curve.
* y^2 + x*y = x^3 + a*x^2 + b is an elliptic curve <=> b != 0 (mod p)
*/
int ec_GF2m_simple_group_check_discriminant(const EC_GROUP *group, BN_CTX *ctx)
{
int ret = 0;
BIGNUM *b;
BN_CTX *new_ctx = NULL;
if (ctx == NULL)
{
ctx = new_ctx = BN_CTX_new();
if (ctx == NULL)
{
ECerr(EC_F_EC_GF2M_SIMPLE_GROUP_CHECK_DISCRIMINANT, ERR_R_MALLOC_FAILURE);
goto err;
}
}
BN_CTX_start(ctx);
b = BN_CTX_get(ctx);
if (b == NULL) goto err;
if (!BN_GF2m_mod_arr(b, &group->b, group->poly)) goto err;
/* check the discriminant:
* y^2 + x*y = x^3 + a*x^2 + b is an elliptic curve <=> b != 0 (mod p)
*/
if (BN_is_zero(b)) goto err;
ret = 1;
err:
if (ctx != NULL)
BN_CTX_end(ctx);
if (new_ctx != NULL)
BN_CTX_free(new_ctx);
return ret;
}
/* Initializes an EC_POINT. */
int ec_GF2m_simple_point_init(EC_POINT *point)
{
BN_init(&point->X);
BN_init(&point->Y);
BN_init(&point->Z);
return 1;
}
/* Frees an EC_POINT. */
void ec_GF2m_simple_point_finish(EC_POINT *point)
{
BN_free(&point->X);
BN_free(&point->Y);
BN_free(&point->Z);
}
/* Clears and frees an EC_POINT. */
void ec_GF2m_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;
}
/* Copy the contents of one EC_POINT into another. Assumes dest is initialized. */
int ec_GF2m_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;
}
/* Set an EC_POINT to the point at infinity.
* A point at infinity is represented by having Z=0.
*/
int ec_GF2m_simple_point_set_to_infinity(const EC_GROUP *group, EC_POINT *point)
{
point->Z_is_one = 0;
BN_zero(&point->Z);
return 1;
}
/* Set the coordinates of an EC_POINT using affine coordinates.
* Note that the simple implementation only uses affine coordinates.
*/
int ec_GF2m_simple_point_set_affine_coordinates(const EC_GROUP *group, EC_POINT *point,
const BIGNUM *x, const BIGNUM *y, BN_CTX *ctx)
{
int ret = 0;
if (x == NULL || y == NULL)
{
ECerr(EC_F_EC_GF2M_SIMPLE_POINT_SET_AFFINE_COORDINATES, ERR_R_PASSED_NULL_PARAMETER);
return 0;
}
if (!BN_copy(&point->X, x)) goto err;
BN_set_negative(&point->X, 0);
if (!BN_copy(&point->Y, y)) goto err;
BN_set_negative(&point->Y, 0);
if (!BN_copy(&point->Z, BN_value_one())) goto err;
BN_set_negative(&point->Z, 0);
point->Z_is_one = 1;
ret = 1;
err:
return ret;
}
/* Gets the affine coordinates of an EC_POINT.
* Note that the simple implementation only uses affine coordinates.
*/
int ec_GF2m_simple_point_get_affine_coordinates(const EC_GROUP *group, const EC_POINT *point,
BIGNUM *x, BIGNUM *y, BN_CTX *ctx)
{
int ret = 0;
if (EC_POINT_is_at_infinity(group, point))
{
ECerr(EC_F_EC_GF2M_SIMPLE_POINT_GET_AFFINE_COORDINATES, EC_R_POINT_AT_INFINITY);
return 0;
}
if (BN_cmp(&point->Z, BN_value_one()))
{
ECerr(EC_F_EC_GF2M_SIMPLE_POINT_GET_AFFINE_COORDINATES, ERR_R_SHOULD_NOT_HAVE_BEEN_CALLED);
return 0;
}
if (x != NULL)
{
if (!BN_copy(x, &point->X)) goto err;
BN_set_negative(x, 0);
}
if (y != NULL)
{
if (!BN_copy(y, &point->Y)) goto err;
BN_set_negative(y, 0);
}
ret = 1;
err:
return ret;
}
/* Computes a + b and stores the result in r. r could be a or b, a could be b.
* Uses algorithm A.10.2 of IEEE P1363.
*/
int ec_GF2m_simple_add(const EC_GROUP *group, EC_POINT *r, const EC_POINT *a, const EC_POINT *b, BN_CTX *ctx)
{
BN_CTX *new_ctx = NULL;
BIGNUM *x0, *y0, *x1, *y1, *x2, *y2, *s, *t;
int ret = 0;
if (EC_POINT_is_at_infinity(group, a))
{
if (!EC_POINT_copy(r, b)) return 0;
return 1;
}
if (EC_POINT_is_at_infinity(group, b))
{
if (!EC_POINT_copy(r, a)) return 0;
return 1;
}
if (ctx == NULL)
{
ctx = new_ctx = BN_CTX_new();
if (ctx == NULL)
return 0;
}
BN_CTX_start(ctx);
x0 = BN_CTX_get(ctx);
y0 = BN_CTX_get(ctx);
x1 = BN_CTX_get(ctx);
y1 = BN_CTX_get(ctx);
x2 = BN_CTX_get(ctx);
y2 = BN_CTX_get(ctx);
s = BN_CTX_get(ctx);
t = BN_CTX_get(ctx);
if (t == NULL) goto err;
if (a->Z_is_one)
{
if (!BN_copy(x0, &a->X)) goto err;
if (!BN_copy(y0, &a->Y)) goto err;
}
else
{
if (!EC_POINT_get_affine_coordinates_GF2m(group, a, x0, y0, ctx)) goto err;
}
if (b->Z_is_one)
{
if (!BN_copy(x1, &b->X)) goto err;
if (!BN_copy(y1, &b->Y)) goto err;
}
else
{
if (!EC_POINT_get_affine_coordinates_GF2m(group, b, x1, y1, ctx)) goto err;
}
if (BN_GF2m_cmp(x0, x1))
{
if (!BN_GF2m_add(t, x0, x1)) goto err;
if (!BN_GF2m_add(s, y0, y1)) goto err;
if (!group->meth->field_div(group, s, s, t, ctx)) goto err;
if (!group->meth->field_sqr(group, x2, s, ctx)) goto err;
if (!BN_GF2m_add(x2, x2, &group->a)) goto err;
if (!BN_GF2m_add(x2, x2, s)) goto err;
if (!BN_GF2m_add(x2, x2, t)) goto err;
}
else
{
if (BN_GF2m_cmp(y0, y1) || BN_is_zero(x1))
{
if (!EC_POINT_set_to_infinity(group, r)) goto err;
ret = 1;
goto err;
}
if (!group->meth->field_div(group, s, y1, x1, ctx)) goto err;
if (!BN_GF2m_add(s, s, x1)) goto err;
if (!group->meth->field_sqr(group, x2, s, ctx)) goto err;
if (!BN_GF2m_add(x2, x2, s)) goto err;
if (!BN_GF2m_add(x2, x2, &group->a)) goto err;
}
if (!BN_GF2m_add(y2, x1, x2)) goto err;
if (!group->meth->field_mul(group, y2, y2, s, ctx)) goto err;
if (!BN_GF2m_add(y2, y2, x2)) goto err;
if (!BN_GF2m_add(y2, y2, y1)) goto err;
if (!EC_POINT_set_affine_coordinates_GF2m(group, r, x2, y2, ctx)) goto err;
ret = 1;
err:
BN_CTX_end(ctx);
if (new_ctx != NULL)
BN_CTX_free(new_ctx);
return ret;
}
/* Computes 2 * a and stores the result in r. r could be a.
* Uses algorithm A.10.2 of IEEE P1363.
*/
int ec_GF2m_simple_dbl(const EC_GROUP *group, EC_POINT *r, const EC_POINT *a, BN_CTX *ctx)
{
return ec_GF2m_simple_add(group, r, a, a, ctx);
}
int ec_GF2m_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;
if (!EC_POINT_make_affine(group, point, ctx)) return 0;
return BN_GF2m_add(&point->Y, &point->X, &point->Y);
}
/* Indicates whether the given point is the point at infinity. */
int ec_GF2m_simple_is_at_infinity(const EC_GROUP *group, const EC_POINT *point)
{
return BN_is_zero(&point->Z);
}
/* Determines whether the given EC_POINT is an actual point on the curve defined
* in the EC_GROUP. A point is valid if it satisfies the Weierstrass equation:
* y^2 + x*y = x^3 + a*x^2 + b.
*/
int ec_GF2m_simple_is_on_curve(const EC_GROUP *group, const EC_POINT *point, BN_CTX *ctx)
{
int ret = -1;
BN_CTX *new_ctx = NULL;
BIGNUM *lh, *y2;
int (*field_mul)(const EC_GROUP *, BIGNUM *, const BIGNUM *, const BIGNUM *, BN_CTX *);
int (*field_sqr)(const EC_GROUP *, BIGNUM *, const BIGNUM *, BN_CTX *);
if (EC_POINT_is_at_infinity(group, point))
return 1;
field_mul = group->meth->field_mul;
field_sqr = group->meth->field_sqr;
/* only support affine coordinates */
if (!point->Z_is_one) return -1;
if (ctx == NULL)
{
ctx = new_ctx = BN_CTX_new();
if (ctx == NULL)
return -1;
}
BN_CTX_start(ctx);
y2 = BN_CTX_get(ctx);
lh = BN_CTX_get(ctx);
if (lh == NULL) goto err;
/* We have a curve defined by a Weierstrass equation
* y^2 + x*y = x^3 + a*x^2 + b.
* <=> x^3 + a*x^2 + x*y + b + y^2 = 0
* <=> ((x + a) * x + y ) * x + b + y^2 = 0
*/
if (!BN_GF2m_add(lh, &point->X, &group->a)) goto err;
if (!field_mul(group, lh, lh, &point->X, ctx)) goto err;
if (!BN_GF2m_add(lh, lh, &point->Y)) goto err;
if (!field_mul(group, lh, lh, &point->X, ctx)) goto err;
if (!BN_GF2m_add(lh, lh, &group->b)) goto err;
if (!field_sqr(group, y2, &point->Y, ctx)) goto err;
if (!BN_GF2m_add(lh, lh, y2)) goto err;
ret = BN_is_zero(lh);
err:
if (ctx) BN_CTX_end(ctx);
if (new_ctx) BN_CTX_free(new_ctx);
return ret;
}
/* Indicates whether two points are equal.
* Return values:
* -1 error
* 0 equal (in affine coordinates)
* 1 not equal
*/
int ec_GF2m_simple_cmp(const EC_GROUP *group, const EC_POINT *a, const EC_POINT *b, BN_CTX *ctx)
{
BIGNUM *aX, *aY, *bX, *bY;
BN_CTX *new_ctx = NULL;
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;
}
if (ctx == NULL)
{
ctx = new_ctx = BN_CTX_new();
if (ctx == NULL)
return -1;
}
BN_CTX_start(ctx);
aX = BN_CTX_get(ctx);
aY = BN_CTX_get(ctx);
bX = BN_CTX_get(ctx);
bY = BN_CTX_get(ctx);
if (bY == NULL) goto err;
if (!EC_POINT_get_affine_coordinates_GF2m(group, a, aX, aY, ctx)) goto err;
if (!EC_POINT_get_affine_coordinates_GF2m(group, b, bX, bY, ctx)) goto err;
ret = ((BN_cmp(aX, bX) == 0) && BN_cmp(aY, bY) == 0) ? 0 : 1;
err:
if (ctx) BN_CTX_end(ctx);
if (new_ctx) BN_CTX_free(new_ctx);
return ret;
}
/* Forces the given EC_POINT to internally use affine coordinates. */
int ec_GF2m_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_GF2m(group, point, x, y, ctx)) goto err;
if (!BN_copy(&point->X, x)) goto err;
if (!BN_copy(&point->Y, y)) goto err;
if (!BN_one(&point->Z)) goto err;
ret = 1;
err:
if (ctx) BN_CTX_end(ctx);
if (new_ctx) BN_CTX_free(new_ctx);
return ret;
}
/* Forces each of the EC_POINTs in the given array to use affine coordinates. */
int ec_GF2m_simple_points_make_affine(const EC_GROUP *group, size_t num, EC_POINT *points[], BN_CTX *ctx)
{
size_t i;
for (i = 0; i < num; i++)
{
if (!group->meth->make_affine(group, points[i], ctx)) return 0;
}
return 1;
}
/* Wrapper to simple binary polynomial field multiplication implementation. */
int ec_GF2m_simple_field_mul(const EC_GROUP *group, BIGNUM *r, const BIGNUM *a, const BIGNUM *b, BN_CTX *ctx)
{
return BN_GF2m_mod_mul_arr(r, a, b, group->poly, ctx);
}
/* Wrapper to simple binary polynomial field squaring implementation. */
int ec_GF2m_simple_field_sqr(const EC_GROUP *group, BIGNUM *r, const BIGNUM *a, BN_CTX *ctx)
{
return BN_GF2m_mod_sqr_arr(r, a, group->poly, ctx);
}
/* Wrapper to simple binary polynomial field division implementation. */
int ec_GF2m_simple_field_div(const EC_GROUP *group, BIGNUM *r, const BIGNUM *a, const BIGNUM *b, BN_CTX *ctx)
{
return BN_GF2m_mod_div(r, a, b, &group->field, ctx);
}
#endif