ecp_smpl.c

OpenSSL 0.9.8k 最新版OpenSSL

/* crypto/ec/ecp_smpl.c */
/* Includes code written by Lenka Fibikova <[e-mail]>
 * 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
 *    [e-mail].
 *
 * 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
 * ([e-mail]).  This product includes software written by Tim
 * Hudson ([e-mail]).
 *
 */
/* ====================================================================
 * 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 <openssl/symhacks.h>

#include "ec_lcl.h"

const EC_METHOD *EC_GFp_simple_method(void)
	{
	static const EC_METHOD ret = {
		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,
		ec_GFp_simple_set_compressed_coordinates,
		ec_GFp_simple_point2oct,
		ec_GFp_simple_oct2point,
		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;
				}
			}