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1042 lines
26 KiB
1042 lines
26 KiB
/* crypto/ec/ec2_smpl.c */
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/* ====================================================================
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* Copyright 2002 Sun Microsystems, Inc. ALL RIGHTS RESERVED.
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*
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* The Elliptic Curve Public-Key Crypto Library (ECC Code) included
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* herein is developed by SUN MICROSYSTEMS, INC., and is contributed
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* to the OpenSSL project.
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*
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* The ECC Code is licensed pursuant to the OpenSSL open source
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* license provided below.
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*
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* The software is originally written by Sheueling Chang Shantz and
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* Douglas Stebila of Sun Microsystems Laboratories.
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*
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*/
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/* ====================================================================
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* Copyright (c) 1998-2005 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
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* 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
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* 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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*
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* 4. The names "OpenSSL Toolkit" and "OpenSSL Project" must not be used to
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* endorse or promote products derived from this software without
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* prior written permission. For written permission, please contact
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* 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
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* permission of the OpenSSL Project.
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*
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* 6. Redistributions of any form whatsoever must retain the following
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* 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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*
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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
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* 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
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* (eay@cryptsoft.com). This product includes software written by Tim
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* Hudson (tjh@cryptsoft.com).
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*
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*/
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#include <openssl/err.h>
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#include "ec_lcl.h"
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const EC_METHOD *EC_GF2m_simple_method(void)
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{
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static const EC_METHOD ret = {
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NID_X9_62_characteristic_two_field,
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ec_GF2m_simple_group_init,
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ec_GF2m_simple_group_finish,
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ec_GF2m_simple_group_clear_finish,
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ec_GF2m_simple_group_copy,
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ec_GF2m_simple_group_set_curve,
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ec_GF2m_simple_group_get_curve,
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ec_GF2m_simple_group_get_degree,
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ec_GF2m_simple_group_check_discriminant,
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ec_GF2m_simple_point_init,
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ec_GF2m_simple_point_finish,
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ec_GF2m_simple_point_clear_finish,
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ec_GF2m_simple_point_copy,
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ec_GF2m_simple_point_set_to_infinity,
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0 /* set_Jprojective_coordinates_GFp */,
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0 /* get_Jprojective_coordinates_GFp */,
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ec_GF2m_simple_point_set_affine_coordinates,
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ec_GF2m_simple_point_get_affine_coordinates,
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ec_GF2m_simple_set_compressed_coordinates,
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ec_GF2m_simple_point2oct,
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ec_GF2m_simple_oct2point,
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ec_GF2m_simple_add,
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ec_GF2m_simple_dbl,
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ec_GF2m_simple_invert,
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ec_GF2m_simple_is_at_infinity,
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ec_GF2m_simple_is_on_curve,
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ec_GF2m_simple_cmp,
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ec_GF2m_simple_make_affine,
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ec_GF2m_simple_points_make_affine,
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/* the following three method functions are defined in ec2_mult.c */
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ec_GF2m_simple_mul,
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ec_GF2m_precompute_mult,
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ec_GF2m_have_precompute_mult,
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ec_GF2m_simple_field_mul,
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ec_GF2m_simple_field_sqr,
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ec_GF2m_simple_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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return &ret;
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}
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/* Initialize a GF(2^m)-based EC_GROUP structure.
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* Note that all other members are handled by EC_GROUP_new.
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*/
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int ec_GF2m_simple_group_init(EC_GROUP *group)
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{
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BN_init(&group->field);
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BN_init(&group->a);
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BN_init(&group->b);
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return 1;
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}
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/* Free a GF(2^m)-based EC_GROUP structure.
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* Note that all other members are handled by EC_GROUP_free.
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*/
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void ec_GF2m_simple_group_finish(EC_GROUP *group)
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{
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BN_free(&group->field);
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BN_free(&group->a);
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BN_free(&group->b);
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}
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/* Clear and free a GF(2^m)-based EC_GROUP structure.
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* Note that all other members are handled by EC_GROUP_clear_free.
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*/
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void ec_GF2m_simple_group_clear_finish(EC_GROUP *group)
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{
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BN_clear_free(&group->field);
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BN_clear_free(&group->a);
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BN_clear_free(&group->b);
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group->poly[0] = 0;
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group->poly[1] = 0;
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group->poly[2] = 0;
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group->poly[3] = 0;
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group->poly[4] = 0;
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group->poly[5] = -1;
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}
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/* Copy a GF(2^m)-based EC_GROUP structure.
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* Note that all other members are handled by EC_GROUP_copy.
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*/
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int ec_GF2m_simple_group_copy(EC_GROUP *dest, const EC_GROUP *src)
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{
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int i;
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if (!BN_copy(&dest->field, &src->field)) return 0;
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if (!BN_copy(&dest->a, &src->a)) return 0;
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if (!BN_copy(&dest->b, &src->b)) return 0;
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dest->poly[0] = src->poly[0];
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dest->poly[1] = src->poly[1];
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dest->poly[2] = src->poly[2];
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dest->poly[3] = src->poly[3];
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dest->poly[4] = src->poly[4];
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dest->poly[5] = src->poly[5];
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if (bn_wexpand(&dest->a, (int)(dest->poly[0] + BN_BITS2 - 1) / BN_BITS2) == NULL) return 0;
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if (bn_wexpand(&dest->b, (int)(dest->poly[0] + BN_BITS2 - 1) / BN_BITS2) == NULL) return 0;
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for (i = dest->a.top; i < dest->a.dmax; i++) dest->a.d[i] = 0;
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for (i = dest->b.top; i < dest->b.dmax; i++) dest->b.d[i] = 0;
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return 1;
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}
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/* Set the curve parameters of an EC_GROUP structure. */
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int ec_GF2m_simple_group_set_curve(EC_GROUP *group,
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const BIGNUM *p, const BIGNUM *a, const BIGNUM *b, BN_CTX *ctx)
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{
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int ret = 0, i;
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/* group->field */
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if (!BN_copy(&group->field, p)) goto err;
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i = BN_GF2m_poly2arr(&group->field, group->poly, 6) - 1;
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if ((i != 5) && (i != 3))
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{
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ECerr(EC_F_EC_GF2M_SIMPLE_GROUP_SET_CURVE, EC_R_UNSUPPORTED_FIELD);
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goto err;
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}
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/* group->a */
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if (!BN_GF2m_mod_arr(&group->a, a, group->poly)) goto err;
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if(bn_wexpand(&group->a, (int)(group->poly[0] + BN_BITS2 - 1) / BN_BITS2) == NULL) goto err;
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for (i = group->a.top; i < group->a.dmax; i++) group->a.d[i] = 0;
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/* group->b */
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if (!BN_GF2m_mod_arr(&group->b, b, group->poly)) goto err;
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if(bn_wexpand(&group->b, (int)(group->poly[0] + BN_BITS2 - 1) / BN_BITS2) == NULL) goto err;
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for (i = group->b.top; i < group->b.dmax; i++) group->b.d[i] = 0;
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ret = 1;
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err:
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return ret;
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}
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/* Get the curve parameters of an EC_GROUP structure.
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* If p, a, or b are NULL then there values will not be set but the method will return with success.
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*/
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int ec_GF2m_simple_group_get_curve(const EC_GROUP *group, BIGNUM *p, BIGNUM *a, BIGNUM *b, BN_CTX *ctx)
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{
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int ret = 0;
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if (p != NULL)
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{
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if (!BN_copy(p, &group->field)) return 0;
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}
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if (a != NULL)
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{
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if (!BN_copy(a, &group->a)) goto err;
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}
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if (b != NULL)
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{
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if (!BN_copy(b, &group->b)) goto err;
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}
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ret = 1;
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err:
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return ret;
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}
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/* Gets the degree of the field. For a curve over GF(2^m) this is the value m. */
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int ec_GF2m_simple_group_get_degree(const EC_GROUP *group)
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{
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return BN_num_bits(&group->field)-1;
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}
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/* Checks the discriminant of the curve.
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* y^2 + x*y = x^3 + a*x^2 + b is an elliptic curve <=> b != 0 (mod p)
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*/
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int ec_GF2m_simple_group_check_discriminant(const EC_GROUP *group, BN_CTX *ctx)
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{
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int ret = 0;
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BIGNUM *b;
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BN_CTX *new_ctx = NULL;
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if (ctx == NULL)
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{
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ctx = new_ctx = BN_CTX_new();
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if (ctx == NULL)
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{
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ECerr(EC_F_EC_GF2M_SIMPLE_GROUP_CHECK_DISCRIMINANT, ERR_R_MALLOC_FAILURE);
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goto err;
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}
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}
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BN_CTX_start(ctx);
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b = BN_CTX_get(ctx);
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if (b == NULL) goto err;
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if (!BN_GF2m_mod_arr(b, &group->b, group->poly)) goto err;
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/* check the discriminant:
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* y^2 + x*y = x^3 + a*x^2 + b is an elliptic curve <=> b != 0 (mod p)
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*/
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if (BN_is_zero(b)) goto err;
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ret = 1;
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err:
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if (ctx != NULL)
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BN_CTX_end(ctx);
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if (new_ctx != NULL)
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BN_CTX_free(new_ctx);
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return ret;
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}
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/* Initializes an EC_POINT. */
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int ec_GF2m_simple_point_init(EC_POINT *point)
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{
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BN_init(&point->X);
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BN_init(&point->Y);
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BN_init(&point->Z);
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return 1;
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}
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/* Frees an EC_POINT. */
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void ec_GF2m_simple_point_finish(EC_POINT *point)
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{
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BN_free(&point->X);
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BN_free(&point->Y);
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BN_free(&point->Z);
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}
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/* Clears and frees an EC_POINT. */
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void ec_GF2m_simple_point_clear_finish(EC_POINT *point)
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{
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BN_clear_free(&point->X);
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BN_clear_free(&point->Y);
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BN_clear_free(&point->Z);
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point->Z_is_one = 0;
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}
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/* Copy the contents of one EC_POINT into another. Assumes dest is initialized. */
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int ec_GF2m_simple_point_copy(EC_POINT *dest, const EC_POINT *src)
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{
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if (!BN_copy(&dest->X, &src->X)) return 0;
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if (!BN_copy(&dest->Y, &src->Y)) return 0;
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if (!BN_copy(&dest->Z, &src->Z)) return 0;
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dest->Z_is_one = src->Z_is_one;
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return 1;
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}
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|
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/* Set an EC_POINT to the point at infinity.
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* A point at infinity is represented by having Z=0.
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*/
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int ec_GF2m_simple_point_set_to_infinity(const EC_GROUP *group, EC_POINT *point)
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{
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point->Z_is_one = 0;
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BN_zero(&point->Z);
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return 1;
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}
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|
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/* Set the coordinates of an EC_POINT using affine coordinates.
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* Note that the simple implementation only uses affine coordinates.
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*/
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int ec_GF2m_simple_point_set_affine_coordinates(const EC_GROUP *group, EC_POINT *point,
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const BIGNUM *x, const BIGNUM *y, BN_CTX *ctx)
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{
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int ret = 0;
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if (x == NULL || y == NULL)
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{
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ECerr(EC_F_EC_GF2M_SIMPLE_POINT_SET_AFFINE_COORDINATES, ERR_R_PASSED_NULL_PARAMETER);
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return 0;
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}
|
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if (!BN_copy(&point->X, x)) goto err;
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BN_set_negative(&point->X, 0);
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if (!BN_copy(&point->Y, y)) goto err;
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BN_set_negative(&point->Y, 0);
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if (!BN_copy(&point->Z, BN_value_one())) goto err;
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BN_set_negative(&point->Z, 0);
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point->Z_is_one = 1;
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ret = 1;
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|
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err:
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return ret;
|
|
}
|
|
|
|
|
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/* Gets the affine coordinates of an EC_POINT.
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* Note that the simple implementation only uses affine coordinates.
|
|
*/
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int ec_GF2m_simple_point_get_affine_coordinates(const EC_GROUP *group, const EC_POINT *point,
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BIGNUM *x, BIGNUM *y, BN_CTX *ctx)
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{
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int ret = 0;
|
|
|
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if (EC_POINT_is_at_infinity(group, point))
|
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{
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ECerr(EC_F_EC_GF2M_SIMPLE_POINT_GET_AFFINE_COORDINATES, EC_R_POINT_AT_INFINITY);
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|
return 0;
|
|
}
|
|
|
|
if (BN_cmp(&point->Z, BN_value_one()))
|
|
{
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|
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;
|
|
}
|
|
|
|
|
|
/* Calculates and sets the affine coordinates of an EC_POINT from the given
|
|
* compressed coordinates. Uses algorithm 2.3.4 of SEC 1.
|
|
* Note that the simple implementation only uses affine coordinates.
|
|
*
|
|
* The method is from the following publication:
|
|
*
|
|
* Harper, Menezes, Vanstone:
|
|
* "Public-Key Cryptosystems with Very Small Key Lengths",
|
|
* EUROCRYPT '92, Springer-Verlag LNCS 658,
|
|
* published February 1993
|
|
*
|
|
* US Patents 6,141,420 and 6,618,483 (Vanstone, Mullin, Agnew) describe
|
|
* the same method, but claim no priority date earlier than July 29, 1994
|
|
* (and additionally fail to cite the EUROCRYPT '92 publication as prior art).
|
|
*/
|
|
int ec_GF2m_simple_set_compressed_coordinates(const EC_GROUP *group, EC_POINT *point,
|
|
const BIGNUM *x_, int y_bit, BN_CTX *ctx)
|
|
{
|
|
BN_CTX *new_ctx = NULL;
|
|
BIGNUM *tmp, *x, *y, *z;
|
|
int ret = 0, z0;
|
|
|
|
/* clear error queue */
|
|
ERR_clear_error();
|
|
|
|
if (ctx == NULL)
|
|
{
|
|
ctx = new_ctx = BN_CTX_new();
|
|
if (ctx == NULL)
|
|
return 0;
|
|
}
|
|
|
|
y_bit = (y_bit != 0) ? 1 : 0;
|
|
|
|
BN_CTX_start(ctx);
|
|
tmp = BN_CTX_get(ctx);
|
|
x = BN_CTX_get(ctx);
|
|
y = BN_CTX_get(ctx);
|
|
z = BN_CTX_get(ctx);
|
|
if (z == NULL) goto err;
|
|
|
|
if (!BN_GF2m_mod_arr(x, x_, group->poly)) goto err;
|
|
if (BN_is_zero(x))
|
|
{
|
|
if (!BN_GF2m_mod_sqrt_arr(y, &group->b, group->poly, ctx)) goto err;
|
|
}
|
|
else
|
|
{
|
|
if (!group->meth->field_sqr(group, tmp, x, ctx)) goto err;
|
|
if (!group->meth->field_div(group, tmp, &group->b, tmp, ctx)) goto err;
|
|
if (!BN_GF2m_add(tmp, &group->a, tmp)) goto err;
|
|
if (!BN_GF2m_add(tmp, x, tmp)) goto err;
|
|
if (!BN_GF2m_mod_solve_quad_arr(z, tmp, group->poly, ctx))
|
|
{
|
|
unsigned long err = ERR_peek_last_error();
|
|
|
|
if (ERR_GET_LIB(err) == ERR_LIB_BN && ERR_GET_REASON(err) == BN_R_NO_SOLUTION)
|
|
{
|
|
ERR_clear_error();
|
|
ECerr(EC_F_EC_GF2M_SIMPLE_SET_COMPRESSED_COORDINATES, EC_R_INVALID_COMPRESSED_POINT);
|
|
}
|
|
else
|
|
ECerr(EC_F_EC_GF2M_SIMPLE_SET_COMPRESSED_COORDINATES, ERR_R_BN_LIB);
|
|
goto err;
|
|
}
|
|
z0 = (BN_is_odd(z)) ? 1 : 0;
|
|
if (!group->meth->field_mul(group, y, x, z, ctx)) goto err;
|
|
if (z0 != y_bit)
|
|
{
|
|
if (!BN_GF2m_add(y, y, x)) goto err;
|
|
}
|
|
}
|
|
|
|
if (!EC_POINT_set_affine_coordinates_GF2m(group, point, x, y, ctx)) goto err;
|
|
|
|
ret = 1;
|
|
|
|
err:
|
|
BN_CTX_end(ctx);
|
|
if (new_ctx != NULL)
|
|
BN_CTX_free(new_ctx);
|
|
return ret;
|
|
}
|
|
|
|
|
|
/* Converts an EC_POINT to an octet string.
|
|
* If buf is NULL, the encoded length will be returned.
|
|
* If the length len of buf is smaller than required an error will be returned.
|
|
*/
|
|
size_t ec_GF2m_simple_point2oct(const EC_GROUP *group, const EC_POINT *point, point_conversion_form_t form,
|
|
unsigned char *buf, size_t len, BN_CTX *ctx)
|
|
{
|
|
size_t ret;
|
|
BN_CTX *new_ctx = NULL;
|
|
int used_ctx = 0;
|
|
BIGNUM *x, *y, *yxi;
|
|
size_t field_len, i, skip;
|
|
|
|
if ((form != POINT_CONVERSION_COMPRESSED)
|
|
&& (form != POINT_CONVERSION_UNCOMPRESSED)
|
|
&& (form != POINT_CONVERSION_HYBRID))
|
|
{
|
|
ECerr(EC_F_EC_GF2M_SIMPLE_POINT2OCT, EC_R_INVALID_FORM);
|
|
goto err;
|
|
}
|
|
|
|
if (EC_POINT_is_at_infinity(group, point))
|
|
{
|
|
/* encodes to a single 0 octet */
|
|
if (buf != NULL)
|
|
{
|
|
if (len < 1)
|
|
{
|
|
ECerr(EC_F_EC_GF2M_SIMPLE_POINT2OCT, EC_R_BUFFER_TOO_SMALL);
|
|
return 0;
|
|
}
|
|
buf[0] = 0;
|
|
}
|
|
return 1;
|
|
}
|
|
|
|
|
|
/* ret := required output buffer length */
|
|
field_len = (EC_GROUP_get_degree(group) + 7) / 8;
|
|
ret = (form == POINT_CONVERSION_COMPRESSED) ? 1 + field_len : 1 + 2*field_len;
|
|
|
|
/* if 'buf' is NULL, just return required length */
|
|
if (buf != NULL)
|
|
{
|
|
if (len < ret)
|
|
{
|
|
ECerr(EC_F_EC_GF2M_SIMPLE_POINT2OCT, EC_R_BUFFER_TOO_SMALL);
|
|
goto err;
|
|
}
|
|
|
|
if (ctx == NULL)
|
|
{
|
|
ctx = new_ctx = BN_CTX_new();
|
|
if (ctx == NULL)
|
|
return 0;
|
|
}
|
|
|
|
BN_CTX_start(ctx);
|
|
used_ctx = 1;
|
|
x = BN_CTX_get(ctx);
|
|
y = BN_CTX_get(ctx);
|
|
yxi = BN_CTX_get(ctx);
|
|
if (yxi == NULL) goto err;
|
|
|
|
if (!EC_POINT_get_affine_coordinates_GF2m(group, point, x, y, ctx)) goto err;
|
|
|
|
buf[0] = form;
|
|
if ((form != POINT_CONVERSION_UNCOMPRESSED) && !BN_is_zero(x))
|
|
{
|
|
if (!group->meth->field_div(group, yxi, y, x, ctx)) goto err;
|
|
if (BN_is_odd(yxi)) buf[0]++;
|
|
}
|
|
|
|
i = 1;
|
|
|
|
skip = field_len - BN_num_bytes(x);
|
|
if (skip > field_len)
|
|
{
|
|
ECerr(EC_F_EC_GF2M_SIMPLE_POINT2OCT, ERR_R_INTERNAL_ERROR);
|
|
goto err;
|
|
}
|
|
while (skip > 0)
|
|
{
|
|
buf[i++] = 0;
|
|
skip--;
|
|
}
|
|
skip = BN_bn2bin(x, buf + i);
|
|
i += skip;
|
|
if (i != 1 + field_len)
|
|
{
|
|
ECerr(EC_F_EC_GF2M_SIMPLE_POINT2OCT, ERR_R_INTERNAL_ERROR);
|
|
goto err;
|
|
}
|
|
|
|
if (form == POINT_CONVERSION_UNCOMPRESSED || form == POINT_CONVERSION_HYBRID)
|
|
{
|
|
skip = field_len - BN_num_bytes(y);
|
|
if (skip > field_len)
|
|
{
|
|
ECerr(EC_F_EC_GF2M_SIMPLE_POINT2OCT, ERR_R_INTERNAL_ERROR);
|
|
goto err;
|
|
}
|
|
while (skip > 0)
|
|
{
|
|
buf[i++] = 0;
|
|
skip--;
|
|
}
|
|
skip = BN_bn2bin(y, buf + i);
|
|
i += skip;
|
|
}
|
|
|
|
if (i != ret)
|
|
{
|
|
ECerr(EC_F_EC_GF2M_SIMPLE_POINT2OCT, ERR_R_INTERNAL_ERROR);
|
|
goto err;
|
|
}
|
|
}
|
|
|
|
if (used_ctx)
|
|
BN_CTX_end(ctx);
|
|
if (new_ctx != NULL)
|
|
BN_CTX_free(new_ctx);
|
|
return ret;
|
|
|
|
err:
|
|
if (used_ctx)
|
|
BN_CTX_end(ctx);
|
|
if (new_ctx != NULL)
|
|
BN_CTX_free(new_ctx);
|
|
return 0;
|
|
}
|
|
|
|
|
|
/* Converts an octet string representation to an EC_POINT.
|
|
* Note that the simple implementation only uses affine coordinates.
|
|
*/
|
|
int ec_GF2m_simple_oct2point(const EC_GROUP *group, EC_POINT *point,
|
|
const unsigned char *buf, size_t len, BN_CTX *ctx)
|
|
{
|
|
point_conversion_form_t form;
|
|
int y_bit;
|
|
BN_CTX *new_ctx = NULL;
|
|
BIGNUM *x, *y, *yxi;
|
|
size_t field_len, enc_len;
|
|
int ret = 0;
|
|
|
|
if (len == 0)
|
|
{
|
|
ECerr(EC_F_EC_GF2M_SIMPLE_OCT2POINT, EC_R_BUFFER_TOO_SMALL);
|
|
return 0;
|
|
}
|
|
form = buf[0];
|
|
y_bit = form & 1;
|
|
form = form & ~1U;
|
|
if ((form != 0) && (form != POINT_CONVERSION_COMPRESSED)
|
|
&& (form != POINT_CONVERSION_UNCOMPRESSED)
|
|
&& (form != POINT_CONVERSION_HYBRID))
|
|
{
|
|
ECerr(EC_F_EC_GF2M_SIMPLE_OCT2POINT, EC_R_INVALID_ENCODING);
|
|
return 0;
|
|
}
|
|
if ((form == 0 || form == POINT_CONVERSION_UNCOMPRESSED) && y_bit)
|
|
{
|
|
ECerr(EC_F_EC_GF2M_SIMPLE_OCT2POINT, EC_R_INVALID_ENCODING);
|
|
return 0;
|
|
}
|
|
|
|
if (form == 0)
|
|
{
|
|
if (len != 1)
|
|
{
|
|
ECerr(EC_F_EC_GF2M_SIMPLE_OCT2POINT, EC_R_INVALID_ENCODING);
|
|
return 0;
|
|
}
|
|
|
|
return EC_POINT_set_to_infinity(group, point);
|
|
}
|
|
|
|
field_len = (EC_GROUP_get_degree(group) + 7) / 8;
|
|
enc_len = (form == POINT_CONVERSION_COMPRESSED) ? 1 + field_len : 1 + 2*field_len;
|
|
|
|
if (len != enc_len)
|
|
{
|
|
ECerr(EC_F_EC_GF2M_SIMPLE_OCT2POINT, EC_R_INVALID_ENCODING);
|
|
return 0;
|
|
}
|
|
|
|
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);
|
|
yxi = BN_CTX_get(ctx);
|
|
if (yxi == NULL) goto err;
|
|
|
|
if (!BN_bin2bn(buf + 1, field_len, x)) goto err;
|
|
if (BN_ucmp(x, &group->field) >= 0)
|
|
{
|
|
ECerr(EC_F_EC_GF2M_SIMPLE_OCT2POINT, EC_R_INVALID_ENCODING);
|
|
goto err;
|
|
}
|
|
|
|
if (form == POINT_CONVERSION_COMPRESSED)
|
|
{
|
|
if (!EC_POINT_set_compressed_coordinates_GF2m(group, point, x, y_bit, ctx)) goto err;
|
|
}
|
|
else
|
|
{
|
|
if (!BN_bin2bn(buf + 1 + field_len, field_len, y)) goto err;
|
|
if (BN_ucmp(y, &group->field) >= 0)
|
|
{
|
|
ECerr(EC_F_EC_GF2M_SIMPLE_OCT2POINT, EC_R_INVALID_ENCODING);
|
|
goto err;
|
|
}
|
|
if (form == POINT_CONVERSION_HYBRID)
|
|
{
|
|
if (!group->meth->field_div(group, yxi, y, x, ctx)) goto err;
|
|
if (y_bit != BN_is_odd(yxi))
|
|
{
|
|
ECerr(EC_F_EC_GF2M_SIMPLE_OCT2POINT, EC_R_INVALID_ENCODING);
|
|
goto err;
|
|
}
|
|
}
|
|
|
|
if (!EC_POINT_set_affine_coordinates_GF2m(group, point, x, y, ctx)) goto err;
|
|
}
|
|
|
|
if (!EC_POINT_is_on_curve(group, point, ctx)) /* test required by X9.62 */
|
|
{
|
|
ECerr(EC_F_EC_GF2M_SIMPLE_OCT2POINT, EC_R_POINT_IS_NOT_ON_CURVE);
|
|
goto err;
|
|
}
|
|
|
|
ret = 1;
|
|
|
|
err:
|
|
BN_CTX_end(ctx);
|
|
if (new_ctx != NULL)
|
|
BN_CTX_free(new_ctx);
|
|
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) goto err;
|
|
|
|
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);
|
|
}
|
|
|