/src/libressl/crypto/ec/ec2_mult.c

Source (jump to first uncovered line)
/* $OpenBSD: ec2_mult.c,v 1.13 2018/07/23 18:24:22 tb Exp $ */
/* ====================================================================
 * 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) 1998-2003 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/opensslconf.h>

#include <openssl/err.h>

#include "bn_lcl.h"
#include "ec_lcl.h"

#ifndef OPENSSL_NO_EC2M


/* Compute the x-coordinate x/z for the point 2*(x/z) in Montgomery projective
 * coordinates.
 * Uses algorithm Mdouble in appendix of
 *     Lopez, J. and Dahab, R.  "Fast multiplication on elliptic curves over
 *     GF(2^m) without precomputation" (CHES '99, LNCS 1717).
 * modified to not require precomputation of c=b^{2^{m-1}}.
 */
static int
gf2m_Mdouble(const EC_GROUP *group, BIGNUM *x, BIGNUM *z, BN_CTX *ctx)
{
  BIGNUM *t1;
  int ret = 0;

  /* Since Mdouble is static we can guarantee that ctx != NULL. */
  BN_CTX_start(ctx);
  if ((t1 = BN_CTX_get(ctx)) == NULL)
    goto err;

  if (!group->meth->field_sqr(group, x, x, ctx))
    goto err;
  if (!group->meth->field_sqr(group, t1, z, ctx))
    goto err;
  if (!group->meth->field_mul(group, z, x, t1, ctx))
    goto err;
  if (!group->meth->field_sqr(group, x, x, ctx))
    goto err;
  if (!group->meth->field_sqr(group, t1, t1, ctx))
    goto err;
  if (!group->meth->field_mul(group, t1, &group->b, t1, ctx))
    goto err;
  if (!BN_GF2m_add(x, x, t1))
    goto err;

  ret = 1;

 err:
  BN_CTX_end(ctx);
  return ret;
}

/* Compute the x-coordinate x1/z1 for the point (x1/z1)+(x2/x2) in Montgomery
 * projective coordinates.
 * Uses algorithm Madd in appendix of
 *     Lopez, J. and Dahab, R.  "Fast multiplication on elliptic curves over
 *     GF(2^m) without precomputation" (CHES '99, LNCS 1717).
 */
static int
gf2m_Madd(const EC_GROUP *group, const BIGNUM *x, BIGNUM *x1, BIGNUM *z1,
    const BIGNUM *x2, const BIGNUM *z2, BN_CTX *ctx)
{
  BIGNUM *t1, *t2;
  int ret = 0;

  /* Since Madd is static we can guarantee that ctx != NULL. */
  BN_CTX_start(ctx);
  if ((t1 = BN_CTX_get(ctx)) == NULL)
    goto err;
  if ((t2 = BN_CTX_get(ctx)) == NULL)
    goto err;

  if (!BN_copy(t1, x))
    goto err;
  if (!group->meth->field_mul(group, x1, x1, z2, ctx))
    goto err;
  if (!group->meth->field_mul(group, z1, z1, x2, ctx))
    goto err;
  if (!group->meth->field_mul(group, t2, x1, z1, ctx))
    goto err;
  if (!BN_GF2m_add(z1, z1, x1))
    goto err;
  if (!group->meth->field_sqr(group, z1, z1, ctx))
    goto err;
  if (!group->meth->field_mul(group, x1, z1, t1, ctx))
    goto err;
  if (!BN_GF2m_add(x1, x1, t2))
    goto err;

  ret = 1;

 err:
  BN_CTX_end(ctx);
  return ret;
}

/* Compute the x, y affine coordinates from the point (x1, z1) (x2, z2)
 * using Montgomery point multiplication algorithm Mxy() in appendix of
 *     Lopez, J. and Dahab, R.  "Fast multiplication on elliptic curves over
 *     GF(2^m) without precomputation" (CHES '99, LNCS 1717).
 * Returns:
 *     0 on error
 *     1 if return value should be the point at infinity
 *     2 otherwise
 */
static int
gf2m_Mxy(const EC_GROUP *group, const BIGNUM *x, const BIGNUM *y, BIGNUM *x1,
    BIGNUM *z1, BIGNUM *x2, BIGNUM *z2, BN_CTX *ctx)
{
  BIGNUM *t3, *t4, *t5;
  int ret = 0;

  if (BN_is_zero(z1)) {
    BN_zero(x2);
    BN_zero(z2);
    return 1;
  }
  if (BN_is_zero(z2)) {
    if (!BN_copy(x2, x))
      return 0;
    if (!BN_GF2m_add(z2, x, y))
      return 0;
    return 2;
  }
  /* Since Mxy is static we can guarantee that ctx != NULL. */
  BN_CTX_start(ctx);
  if ((t3 = BN_CTX_get(ctx)) == NULL)
    goto err;
  if ((t4 = BN_CTX_get(ctx)) == NULL)
    goto err;
  if ((t5 = BN_CTX_get(ctx)) == NULL)
    goto err;

  if (!BN_one(t5))
    goto err;

  if (!group->meth->field_mul(group, t3, z1, z2, ctx))
    goto err;

  if (!group->meth->field_mul(group, z1, z1, x, ctx))
    goto err;
  if (!BN_GF2m_add(z1, z1, x1))
    goto err;
  if (!group->meth->field_mul(group, z2, z2, x, ctx))
    goto err;
  if (!group->meth->field_mul(group, x1, z2, x1, ctx))
    goto err;
  if (!BN_GF2m_add(z2, z2, x2))
    goto err;

  if (!group->meth->field_mul(group, z2, z2, z1, ctx))
    goto err;
  if (!group->meth->field_sqr(group, t4, x, ctx))
    goto err;
  if (!BN_GF2m_add(t4, t4, y))
    goto err;
  if (!group->meth->field_mul(group, t4, t4, t3, ctx))
    goto err;
  if (!BN_GF2m_add(t4, t4, z2))
    goto err;

  if (!group->meth->field_mul(group, t3, t3, x, ctx))
    goto err;
  if (!group->meth->field_div(group, t3, t5, t3, ctx))
    goto err;
  if (!group->meth->field_mul(group, t4, t3, t4, ctx))
    goto err;
  if (!group->meth->field_mul(group, x2, x1, t3, ctx))
    goto err;
  if (!BN_GF2m_add(z2, x2, x))
    goto err;

  if (!group->meth->field_mul(group, z2, z2, t4, ctx))
    goto err;
  if (!BN_GF2m_add(z2, z2, y))
    goto err;

  ret = 2;

 err:
  BN_CTX_end(ctx);
  return ret;
}


/* Computes scalar*point and stores the result in r.
 * point can not equal r.
 * Uses a modified algorithm 2P of
 *     Lopez, J. and Dahab, R.  "Fast multiplication on elliptic curves over
 *     GF(2^m) without precomputation" (CHES '99, LNCS 1717).
 *
 * To protect against side-channel attack the function uses constant time swap,
 * avoiding conditional branches.
 */
static int
ec_GF2m_montgomery_point_multiply(const EC_GROUP *group, EC_POINT *r,
    const BIGNUM *scalar, const EC_POINT *point, BN_CTX *ctx)
{
  BIGNUM *x1, *x2, *z1, *z2;
  int ret = 0, i;
  BN_ULONG mask, word;

  if (r == point) {
    ECerror(EC_R_INVALID_ARGUMENT);
    return 0;
  }
  /* if result should be point at infinity */
  if ((scalar == NULL) || BN_is_zero(scalar) || (point == NULL) ||
      EC_POINT_is_at_infinity(group, point) > 0) {
    return EC_POINT_set_to_infinity(group, r);
  }
  /* only support affine coordinates */
  if (!point->Z_is_one)
    return 0;

  /* Since point_multiply is static we can guarantee that ctx != NULL. */
  BN_CTX_start(ctx);
  if ((x1 = BN_CTX_get(ctx)) == NULL)
    goto err;
  if ((z1 = BN_CTX_get(ctx)) == NULL)
    goto err;

  x2 = &r->X;
  z2 = &r->Y;

  if (!bn_wexpand(x1, group->field.top))
                goto err;
  if (!bn_wexpand(z1, group->field.top))
                goto err;
  if (!bn_wexpand(x2, group->field.top))
                goto err;
  if (!bn_wexpand(z2, group->field.top))
                goto err;

  if (!BN_GF2m_mod_arr(x1, &point->X, group->poly))
    goto err; /* x1 = x */
  if (!BN_one(z1))
    goto err; /* z1 = 1 */
  if (!group->meth->field_sqr(group, z2, x1, ctx))
    goto err; /* z2 = x1^2 = x^2 */
  if (!group->meth->field_sqr(group, x2, z2, ctx))
    goto err;
  if (!BN_GF2m_add(x2, x2, &group->b))
    goto err; /* x2 = x^4 + b */

  /* find top most bit and go one past it */
  i = scalar->top - 1;
  mask = BN_TBIT;
  word = scalar->d[i];
  while (!(word & mask))
    mask >>= 1;
  mask >>= 1;
  /* if top most bit was at word break, go to next word */
  if (!mask) {
    i--;
    mask = BN_TBIT;
  }
  for (; i >= 0; i--) {
    word = scalar->d[i];
    while (mask) {
      if (!BN_swap_ct(word & mask, x1, x2, group->field.top))
        goto err;
      if (!BN_swap_ct(word & mask, z1, z2, group->field.top))
        goto err;
      if (!gf2m_Madd(group, &point->X, x2, z2, x1, z1, ctx))
        goto err;
      if (!gf2m_Mdouble(group, x1, z1, ctx))
        goto err;
      if (!BN_swap_ct(word & mask, x1, x2, group->field.top))
        goto err;
      if (!BN_swap_ct(word & mask, z1, z2, group->field.top))
        goto err;
      mask >>= 1;
    }
    mask = BN_TBIT;
  }

  /* convert out of "projective" coordinates */
  i = gf2m_Mxy(group, &point->X, &point->Y, x1, z1, x2, z2, ctx);
  if (i == 0)
    goto err;
  else if (i == 1) {
    if (!EC_POINT_set_to_infinity(group, r))
      goto err;
  } else {
    if (!BN_one(&r->Z))
      goto err;
    r->Z_is_one = 1;
  }

  /* GF(2^m) field elements should always have BIGNUM::neg = 0 */
  BN_set_negative(&r->X, 0);
  BN_set_negative(&r->Y, 0);

  ret = 1;

 err:
  BN_CTX_end(ctx);
  return ret;
}


/* Computes the sum
 *     scalar*group->generator + scalars[0]*points[0] + ... + scalars[num-1]*points[num-1]
 * gracefully ignoring NULL scalar values.
 */
int
ec_GF2m_simple_mul(const EC_GROUP *group, EC_POINT *r, const BIGNUM *scalar,
    size_t num, const EC_POINT *points[], const BIGNUM *scalars[], BN_CTX *ctx)
{
  BN_CTX *new_ctx = NULL;
  int ret = 0;
  size_t i;
  EC_POINT *p = NULL;
  EC_POINT *acc = NULL;

  if (ctx == NULL) {
    ctx = new_ctx = BN_CTX_new();
    if (ctx == NULL)
      return 0;
  }
  /*
   * This implementation is more efficient than the wNAF implementation
   * for 2 or fewer points.  Use the ec_wNAF_mul implementation for 3
   * or more points, or if we can perform a fast multiplication based
   * on precomputation.
   */
  if ((scalar && (num > 1)) || (num > 2) ||
      (num == 0 && EC_GROUP_have_precompute_mult(group))) {
    ret = ec_wNAF_mul(group, r, scalar, num, points, scalars, ctx);
    goto err;
  }
  if ((p = EC_POINT_new(group)) == NULL)
    goto err;
  if ((acc = EC_POINT_new(group)) == NULL)
    goto err;

  if (!EC_POINT_set_to_infinity(group, acc))
    goto err;

  if (scalar) {
    if (!ec_GF2m_montgomery_point_multiply(group, p, scalar, group->generator, ctx))
      goto err;
    if (BN_is_negative(scalar))
      if (!group->meth->invert(group, p, ctx))
        goto err;
    if (!group->meth->add(group, acc, acc, p, ctx))
      goto err;
  }
  for (i = 0; i < num; i++) {
    if (!ec_GF2m_montgomery_point_multiply(group, p, scalars[i], points[i], ctx))
      goto err;
    if (BN_is_negative(scalars[i]))
      if (!group->meth->invert(group, p, ctx))
        goto err;
    if (!group->meth->add(group, acc, acc, p, ctx))
      goto err;
  }

  if (!EC_POINT_copy(r, acc))
    goto err;

  ret = 1;

 err:
  EC_POINT_free(p);
  EC_POINT_free(acc);
  BN_CTX_free(new_ctx);
  return ret;
}


/* Precomputation for point multiplication: fall back to wNAF methods
 * because ec_GF2m_simple_mul() uses ec_wNAF_mul() if appropriate */

int
ec_GF2m_precompute_mult(EC_GROUP * group, BN_CTX * ctx)
{
  return ec_wNAF_precompute_mult(group, ctx);
}

int
ec_GF2m_have_precompute_mult(const EC_GROUP * group)
{
  return ec_wNAF_have_precompute_mult(group);
}

#endif

Coverage Report

Created: 2022-08-24 06:30

Line	Count	Source (jump to first uncovered line)
1		/* $OpenBSD: ec2_mult.c,v 1.13 2018/07/23 18:24:22 tb Exp $ */
2		/* ====================================================================
3		* Copyright 2002 Sun Microsystems, Inc. ALL RIGHTS RESERVED.
4		*
5		* The Elliptic Curve Public-Key Crypto Library (ECC Code) included
6		* herein is developed by SUN MICROSYSTEMS, INC., and is contributed
7		* to the OpenSSL project.
8		*
9		* The ECC Code is licensed pursuant to the OpenSSL open source
10		* license provided below.
11		*
12		* The software is originally written by Sheueling Chang Shantz and
13		* Douglas Stebila of Sun Microsystems Laboratories.
14		*
15		*/
16		/* ====================================================================
17		* Copyright (c) 1998-2003 The OpenSSL Project. All rights reserved.
18		*
19		* Redistribution and use in source and binary forms, with or without
20		* modification, are permitted provided that the following conditions
21		* are met:
22		*
23		* 1. Redistributions of source code must retain the above copyright
24		* notice, this list of conditions and the following disclaimer.
25		*
26		* 2. Redistributions in binary form must reproduce the above copyright
27		* notice, this list of conditions and the following disclaimer in
28		* the documentation and/or other materials provided with the
29		* distribution.
30		*
31		* 3. All advertising materials mentioning features or use of this
32		* software must display the following acknowledgment:
33		* "This product includes software developed by the OpenSSL Project
34		* for use in the OpenSSL Toolkit. (http://www.openssl.org/)"
35		*
36		* 4. The names "OpenSSL Toolkit" and "OpenSSL Project" must not be used to
37		* endorse or promote products derived from this software without
38		* prior written permission. For written permission, please contact
39		* openssl-core@openssl.org.
40		*
41		* 5. Products derived from this software may not be called "OpenSSL"
42		* nor may "OpenSSL" appear in their names without prior written
43		* permission of the OpenSSL Project.
44		*
45		* 6. Redistributions of any form whatsoever must retain the following
46		* acknowledgment:
47		* "This product includes software developed by the OpenSSL Project
48		* for use in the OpenSSL Toolkit (http://www.openssl.org/)"
49		*
50		* THIS SOFTWARE IS PROVIDED BY THE OpenSSL PROJECT ``AS IS'' AND ANY
51		* EXPRESSED OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
52		* IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR
53		* PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE OpenSSL PROJECT OR
54		* ITS CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL,
55		* SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT
56		* NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES;
57		* LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
58		* HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT,
59		* STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE)
60		* ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED
61		* OF THE POSSIBILITY OF SUCH DAMAGE.
62		* ====================================================================
63		*
64		* This product includes cryptographic software written by Eric Young
65		* (eay@cryptsoft.com). This product includes software written by Tim
66		* Hudson (tjh@cryptsoft.com).
67		*
68		*/
69
70		#include <openssl/opensslconf.h>
71
72		#include <openssl/err.h>
73
74		#include "bn_lcl.h"
75		#include "ec_lcl.h"
76
77		#ifndef OPENSSL_NO_EC2M
78
79
80		/* Compute the x-coordinate x/z for the point 2*(x/z) in Montgomery projective
81		* coordinates.
82		* Uses algorithm Mdouble in appendix of
83		* Lopez, J. and Dahab, R. "Fast multiplication on elliptic curves over
84		* GF(2^m) without precomputation" (CHES '99, LNCS 1717).
85		* modified to not require precomputation of c=b^{2^{m-1}}.
86		*/
87		static int
88		gf2m_Mdouble(const EC_GROUP group, BIGNUM x, BIGNUM z, BN_CTX ctx)
89	0	{
90	0	BIGNUM *t1;
91	0	int ret = 0;
92
93		/* Since Mdouble is static we can guarantee that ctx != NULL. */
94	0	BN_CTX_start(ctx);
95	0	if ((t1 = BN_CTX_get(ctx)) == NULL)
96	0	goto err;
97
98	0	if (!group->meth->field_sqr(group, x, x, ctx))
99	0	goto err;
100	0	if (!group->meth->field_sqr(group, t1, z, ctx))
101	0	goto err;
102	0	if (!group->meth->field_mul(group, z, x, t1, ctx))
103	0	goto err;
104	0	if (!group->meth->field_sqr(group, x, x, ctx))
105	0	goto err;
106	0	if (!group->meth->field_sqr(group, t1, t1, ctx))
107	0	goto err;
108	0	if (!group->meth->field_mul(group, t1, &group->b, t1, ctx))
109	0	goto err;
110	0	if (!BN_GF2m_add(x, x, t1))
111	0	goto err;
112
113	0	ret = 1;
114
115	0	err:
116	0	BN_CTX_end(ctx);
117	0	return ret;
118	0	}
119
120		/* Compute the x-coordinate x1/z1 for the point (x1/z1)+(x2/x2) in Montgomery
121		* projective coordinates.
122		* Uses algorithm Madd in appendix of
123		* Lopez, J. and Dahab, R. "Fast multiplication on elliptic curves over
124		* GF(2^m) without precomputation" (CHES '99, LNCS 1717).
125		*/
126		static int
127		gf2m_Madd(const EC_GROUP group, const BIGNUM x, BIGNUM x1, BIGNUM z1,
128		const BIGNUM x2, const BIGNUM z2, BN_CTX *ctx)
129	0	{
130	0	BIGNUM t1, t2;
131	0	int ret = 0;
132
133		/* Since Madd is static we can guarantee that ctx != NULL. */
134	0	BN_CTX_start(ctx);
135	0	if ((t1 = BN_CTX_get(ctx)) == NULL)
136	0	goto err;
137	0	if ((t2 = BN_CTX_get(ctx)) == NULL)
138	0	goto err;
139
140	0	if (!BN_copy(t1, x))
141	0	goto err;
142	0	if (!group->meth->field_mul(group, x1, x1, z2, ctx))
143	0	goto err;
144	0	if (!group->meth->field_mul(group, z1, z1, x2, ctx))
145	0	goto err;
146	0	if (!group->meth->field_mul(group, t2, x1, z1, ctx))
147	0	goto err;
148	0	if (!BN_GF2m_add(z1, z1, x1))
149	0	goto err;
150	0	if (!group->meth->field_sqr(group, z1, z1, ctx))
151	0	goto err;
152	0	if (!group->meth->field_mul(group, x1, z1, t1, ctx))
153	0	goto err;
154	0	if (!BN_GF2m_add(x1, x1, t2))
155	0	goto err;
156
157	0	ret = 1;
158
159	0	err:
160	0	BN_CTX_end(ctx);
161	0	return ret;
162	0	}
163
164		/* Compute the x, y affine coordinates from the point (x1, z1) (x2, z2)
165		* using Montgomery point multiplication algorithm Mxy() in appendix of
166		* Lopez, J. and Dahab, R. "Fast multiplication on elliptic curves over
167		* GF(2^m) without precomputation" (CHES '99, LNCS 1717).
168		* Returns:
169		* 0 on error
170		* 1 if return value should be the point at infinity
171		* 2 otherwise
172		*/
173		static int
174		gf2m_Mxy(const EC_GROUP group, const BIGNUM x, const BIGNUM y, BIGNUM x1,
175		BIGNUM z1, BIGNUM x2, BIGNUM z2, BN_CTX ctx)
176	0	{
177	0	BIGNUM t3, t4, *t5;
178	0	int ret = 0;
179
180	0	if (BN_is_zero(z1)) {
181	0	BN_zero(x2);
182	0	BN_zero(z2);
183	0	return 1;
184	0	}
185	0	if (BN_is_zero(z2)) {
186	0	if (!BN_copy(x2, x))
187	0	return 0;
188	0	if (!BN_GF2m_add(z2, x, y))
189	0	return 0;
190	0	return 2;
191	0	}
192		/* Since Mxy is static we can guarantee that ctx != NULL. */
193	0	BN_CTX_start(ctx);
194	0	if ((t3 = BN_CTX_get(ctx)) == NULL)
195	0	goto err;
196	0	if ((t4 = BN_CTX_get(ctx)) == NULL)
197	0	goto err;
198	0	if ((t5 = BN_CTX_get(ctx)) == NULL)
199	0	goto err;
200
201	0	if (!BN_one(t5))
202	0	goto err;
203
204	0	if (!group->meth->field_mul(group, t3, z1, z2, ctx))
205	0	goto err;
206
207	0	if (!group->meth->field_mul(group, z1, z1, x, ctx))
208	0	goto err;
209	0	if (!BN_GF2m_add(z1, z1, x1))
210	0	goto err;
211	0	if (!group->meth->field_mul(group, z2, z2, x, ctx))
212	0	goto err;
213	0	if (!group->meth->field_mul(group, x1, z2, x1, ctx))
214	0	goto err;
215	0	if (!BN_GF2m_add(z2, z2, x2))
216	0	goto err;
217
218	0	if (!group->meth->field_mul(group, z2, z2, z1, ctx))
219	0	goto err;
220	0	if (!group->meth->field_sqr(group, t4, x, ctx))
221	0	goto err;
222	0	if (!BN_GF2m_add(t4, t4, y))
223	0	goto err;
224	0	if (!group->meth->field_mul(group, t4, t4, t3, ctx))
225	0	goto err;
226	0	if (!BN_GF2m_add(t4, t4, z2))
227	0	goto err;
228
229	0	if (!group->meth->field_mul(group, t3, t3, x, ctx))
230	0	goto err;
231	0	if (!group->meth->field_div(group, t3, t5, t3, ctx))
232	0	goto err;
233	0	if (!group->meth->field_mul(group, t4, t3, t4, ctx))
234	0	goto err;
235	0	if (!group->meth->field_mul(group, x2, x1, t3, ctx))
236	0	goto err;
237	0	if (!BN_GF2m_add(z2, x2, x))
238	0	goto err;
239
240	0	if (!group->meth->field_mul(group, z2, z2, t4, ctx))
241	0	goto err;
242	0	if (!BN_GF2m_add(z2, z2, y))
243	0	goto err;
244
245	0	ret = 2;
246
247	0	err:
248	0	BN_CTX_end(ctx);
249	0	return ret;
250	0	}
251
252
253		/* Computes scalar*point and stores the result in r.
254		* point can not equal r.
255		* Uses a modified algorithm 2P of
256		* Lopez, J. and Dahab, R. "Fast multiplication on elliptic curves over
257		* GF(2^m) without precomputation" (CHES '99, LNCS 1717).
258		*
259		* To protect against side-channel attack the function uses constant time swap,
260		* avoiding conditional branches.
261		*/
262		static int
263		ec_GF2m_montgomery_point_multiply(const EC_GROUP group, EC_POINT r,
264		const BIGNUM scalar, const EC_POINT point, BN_CTX *ctx)
265	0	{
266	0	BIGNUM x1, x2, z1, z2;
267	0	int ret = 0, i;
268	0	BN_ULONG mask, word;
269
270	0	if (r == point) {
271	0	ECerror(EC_R_INVALID_ARGUMENT);
272	0	return 0;
273	0	}
274		/* if result should be point at infinity */
275	0	if ((scalar == NULL) \|\| BN_is_zero(scalar) \|\| (point == NULL) \|\|
276	0	EC_POINT_is_at_infinity(group, point) > 0) {
277	0	return EC_POINT_set_to_infinity(group, r);
278	0	}
279		/* only support affine coordinates */
280	0	if (!point->Z_is_one)
281	0	return 0;
282
283		/* Since point_multiply is static we can guarantee that ctx != NULL. */
284	0	BN_CTX_start(ctx);
285	0	if ((x1 = BN_CTX_get(ctx)) == NULL)
286	0	goto err;
287	0	if ((z1 = BN_CTX_get(ctx)) == NULL)
288	0	goto err;
289
290	0	x2 = &r->X;
291	0	z2 = &r->Y;
292
293	0	if (!bn_wexpand(x1, group->field.top))
294	0	goto err;
295	0	if (!bn_wexpand(z1, group->field.top))
296	0	goto err;
297	0	if (!bn_wexpand(x2, group->field.top))
298	0	goto err;
299	0	if (!bn_wexpand(z2, group->field.top))
300	0	goto err;
301
302	0	if (!BN_GF2m_mod_arr(x1, &point->X, group->poly))
303	0	goto err; /* x1 = x */
304	0	if (!BN_one(z1))
305	0	goto err; /* z1 = 1 */
306	0	if (!group->meth->field_sqr(group, z2, x1, ctx))
307	0	goto err; /* z2 = x1^2 = x^2 */
308	0	if (!group->meth->field_sqr(group, x2, z2, ctx))
309	0	goto err;
310	0	if (!BN_GF2m_add(x2, x2, &group->b))
311	0	goto err; /* x2 = x^4 + b */
312
313		/* find top most bit and go one past it */
314	0	i = scalar->top - 1;
315	0	mask = BN_TBIT;
316	0	word = scalar->d[i];
317	0	while (!(word & mask))
318	0	mask >>= 1;
319	0	mask >>= 1;
320		/* if top most bit was at word break, go to next word */
321	0	if (!mask) {
322	0	i--;
323	0	mask = BN_TBIT;
324	0	}
325	0	for (; i >= 0; i--) {
326	0	word = scalar->d[i];
327	0	while (mask) {
328	0	if (!BN_swap_ct(word & mask, x1, x2, group->field.top))
329	0	goto err;
330	0	if (!BN_swap_ct(word & mask, z1, z2, group->field.top))
331	0	goto err;
332	0	if (!gf2m_Madd(group, &point->X, x2, z2, x1, z1, ctx))
333	0	goto err;
334	0	if (!gf2m_Mdouble(group, x1, z1, ctx))
335	0	goto err;
336	0	if (!BN_swap_ct(word & mask, x1, x2, group->field.top))
337	0	goto err;
338	0	if (!BN_swap_ct(word & mask, z1, z2, group->field.top))
339	0	goto err;
340	0	mask >>= 1;
341	0	}
342	0	mask = BN_TBIT;
343	0	}
344
345		/* convert out of "projective" coordinates */
346	0	i = gf2m_Mxy(group, &point->X, &point->Y, x1, z1, x2, z2, ctx);
347	0	if (i == 0)
348	0	goto err;
349	0	else if (i == 1) {
350	0	if (!EC_POINT_set_to_infinity(group, r))
351	0	goto err;
352	0	} else {
353	0	if (!BN_one(&r->Z))
354	0	goto err;
355	0	r->Z_is_one = 1;
356	0	}
357
358		/* GF(2^m) field elements should always have BIGNUM::neg = 0 */
359	0	BN_set_negative(&r->X, 0);
360	0	BN_set_negative(&r->Y, 0);
361
362	0	ret = 1;
363
364	0	err:
365	0	BN_CTX_end(ctx);
366	0	return ret;
367	0	}
368
369
370		/* Computes the sum
371		* scalargroup->generator + scalars[0]points[0] + ... + scalars[num-1]*points[num-1]
372		* gracefully ignoring NULL scalar values.
373		*/
374		int
375		ec_GF2m_simple_mul(const EC_GROUP group, EC_POINT r, const BIGNUM *scalar,
376		size_t num, const EC_POINT points[], const BIGNUM scalars[], BN_CTX *ctx)
377	0	{
378	0	BN_CTX *new_ctx = NULL;
379	0	int ret = 0;
380	0	size_t i;
381	0	EC_POINT *p = NULL;
382	0	EC_POINT *acc = NULL;
383
384	0	if (ctx == NULL) {
385	0	ctx = new_ctx = BN_CTX_new();
386	0	if (ctx == NULL)
387	0	return 0;
388	0	}
389		/*
390		* This implementation is more efficient than the wNAF implementation
391		* for 2 or fewer points. Use the ec_wNAF_mul implementation for 3
392		* or more points, or if we can perform a fast multiplication based
393		* on precomputation.
394		*/
395	0	if ((scalar && (num > 1)) \|\| (num > 2) \|\|
396	0	(num == 0 && EC_GROUP_have_precompute_mult(group))) {
397	0	ret = ec_wNAF_mul(group, r, scalar, num, points, scalars, ctx);
398	0	goto err;
399	0	}
400	0	if ((p = EC_POINT_new(group)) == NULL)
401	0	goto err;
402	0	if ((acc = EC_POINT_new(group)) == NULL)
403	0	goto err;
404
405	0	if (!EC_POINT_set_to_infinity(group, acc))
406	0	goto err;
407
408	0	if (scalar) {
409	0	if (!ec_GF2m_montgomery_point_multiply(group, p, scalar, group->generator, ctx))
410	0	goto err;
411	0	if (BN_is_negative(scalar))
412	0	if (!group->meth->invert(group, p, ctx))
413	0	goto err;
414	0	if (!group->meth->add(group, acc, acc, p, ctx))
415	0	goto err;
416	0	}
417	0	for (i = 0; i < num; i++) {
418	0	if (!ec_GF2m_montgomery_point_multiply(group, p, scalars[i], points[i], ctx))
419	0	goto err;
420	0	if (BN_is_negative(scalars[i]))
421	0	if (!group->meth->invert(group, p, ctx))
422	0	goto err;
423	0	if (!group->meth->add(group, acc, acc, p, ctx))
424	0	goto err;
425	0	}
426
427	0	if (!EC_POINT_copy(r, acc))
428	0	goto err;
429
430	0	ret = 1;
431
432	0	err:
433	0	EC_POINT_free(p);
434	0	EC_POINT_free(acc);
435	0	BN_CTX_free(new_ctx);
436	0	return ret;
437	0	}
438
439
440		/* Precomputation for point multiplication: fall back to wNAF methods
441		* because ec_GF2m_simple_mul() uses ec_wNAF_mul() if appropriate */
442
443		int
444		ec_GF2m_precompute_mult(EC_GROUP * group, BN_CTX * ctx)
445	0	{
446	0	return ec_wNAF_precompute_mult(group, ctx);
447	0	}
448
449		int
450		ec_GF2m_have_precompute_mult(const EC_GROUP * group)
451	0	{
452	0	return ec_wNAF_have_precompute_mult(group);
453	0	}
454
455		#endif