Head

GCC Code Coverage Report

Directory:	./		Exec	Total	Coverage
File:	lib/libcrypto/crypto/../../libssl/src/crypto/ec/ec2_mult.c	Lines:	150	228	65.8 %
Date:	2016-12-06	Branches:	108	188	57.4 %


/* $OpenBSD: ec2_mult.c,v 1.8 2016/03/12 21:44:11 bcook 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 "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) {
		ECerr(EC_F_EC_GF2M_MONTGOMERY_POINT_MULTIPLY, 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) {
			BN_consttime_swap(word & mask, x1, x2, group->field.top);
			BN_consttime_swap(word & mask, z1, z2, group->field.top);
			if (!gf2m_Madd(group, &point->X, x2, z2, x1, z1, ctx))
				goto err;
			if (!gf2m_Mdouble(group, x1, z1, ctx))
				goto err;
			BN_consttime_swap(word & mask, x1, x2, group->field.top);
			BN_consttime_swap(word & mask, z1, z2, group->field.top);
			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


Generated by: GCOVR (Version 3.3)

Line	Branch	Exec	Source
1			/* $OpenBSD: ec2_mult.c,v 1.8 2016/03/12 21:44:11 bcook 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 "ec_lcl.h"
75
76			#ifndef OPENSSL_NO_EC2M
77
78
79			/* Compute the x-coordinate x/z for the point 2*(x/z) in Montgomery projective
80			* coordinates.
81			* Uses algorithm Mdouble in appendix of
82			* Lopez, J. and Dahab, R. "Fast multiplication on elliptic curves over
83			* GF(2^m) without precomputation" (CHES '99, LNCS 1717).
84			* modified to not require precomputation of c=b^{2^{m-1}}.
85			*/
86			static int
87			gf2m_Mdouble(const EC_GROUP group, BIGNUM x, BIGNUM z, BN_CTX ctx)
88		153560	{
89			BIGNUM *t1;
90		153560	int ret = 0;
91
92			/* Since Mdouble is static we can guarantee that ctx != NULL. */
93		153560	BN_CTX_start(ctx);
94	✗✓	153560	if ((t1 = BN_CTX_get(ctx)) == NULL)
95			goto err;
96
97	✗✓	153560	if (!group->meth->field_sqr(group, x, x, ctx))
98			goto err;
99	✗✓	153560	if (!group->meth->field_sqr(group, t1, z, ctx))
100			goto err;
101	✗✓	153560	if (!group->meth->field_mul(group, z, x, t1, ctx))
102			goto err;
103	✗✓	153560	if (!group->meth->field_sqr(group, x, x, ctx))
104			goto err;
105	✗✓	153560	if (!group->meth->field_sqr(group, t1, t1, ctx))
106			goto err;
107	✗✓	153560	if (!group->meth->field_mul(group, t1, &group->b, t1, ctx))
108			goto err;
109	✗✓	153560	if (!BN_GF2m_add(x, x, t1))
110			goto err;
111
112		153560	ret = 1;
113
114		153560	err:
115		153560	BN_CTX_end(ctx);
116		153560	return ret;
117			}
118
119			/* Compute the x-coordinate x1/z1 for the point (x1/z1)+(x2/x2) in Montgomery
120			* projective coordinates.
121			* Uses algorithm Madd in appendix of
122			* Lopez, J. and Dahab, R. "Fast multiplication on elliptic curves over
123			* GF(2^m) without precomputation" (CHES '99, LNCS 1717).
124			*/
125			static int
126			gf2m_Madd(const EC_GROUP group, const BIGNUM x, BIGNUM x1, BIGNUM z1,
127			const BIGNUM x2, const BIGNUM z2, BN_CTX *ctx)
128		153560	{
129			BIGNUM t1, t2;
130		153560	int ret = 0;
131
132			/* Since Madd is static we can guarantee that ctx != NULL. */
133		153560	BN_CTX_start(ctx);
134	✗✓	153560	if ((t1 = BN_CTX_get(ctx)) == NULL)
135			goto err;
136	✗✓	153560	if ((t2 = BN_CTX_get(ctx)) == NULL)
137			goto err;
138
139	✗✓	153560	if (!BN_copy(t1, x))
140			goto err;
141	✗✓	153560	if (!group->meth->field_mul(group, x1, x1, z2, ctx))
142			goto err;
143	✗✓	153560	if (!group->meth->field_mul(group, z1, z1, x2, ctx))
144			goto err;
145	✗✓	153560	if (!group->meth->field_mul(group, t2, x1, z1, ctx))
146			goto err;
147	✗✓	153560	if (!BN_GF2m_add(z1, z1, x1))
148			goto err;
149	✗✓	153560	if (!group->meth->field_sqr(group, z1, z1, ctx))
150			goto err;
151	✗✓	153560	if (!group->meth->field_mul(group, x1, z1, t1, ctx))
152			goto err;
153	✗✓	153560	if (!BN_GF2m_add(x1, x1, t2))
154			goto err;
155
156		153560	ret = 1;
157
158		153560	err:
159		153560	BN_CTX_end(ctx);
160		153560	return ret;
161			}
162
163			/* Compute the x, y affine coordinates from the point (x1, z1) (x2, z2)
164			* using Montgomery point multiplication algorithm Mxy() in appendix of
165			* Lopez, J. and Dahab, R. "Fast multiplication on elliptic curves over
166			* GF(2^m) without precomputation" (CHES '99, LNCS 1717).
167			* Returns:
168			* 0 on error
169			* 1 if return value should be the point at infinity
170			* 2 otherwise
171			*/
172			static int
173			gf2m_Mxy(const EC_GROUP group, const BIGNUM x, const BIGNUM y, BIGNUM x1,
174			BIGNUM z1, BIGNUM x2, BIGNUM z2, BN_CTX ctx)
175		593	{
176			BIGNUM t3, t4, *t5;
177		593	int ret = 0;
178
179	✓✓	593	if (BN_is_zero(z1)) {
180		77	BN_zero(x2);
181		77	BN_zero(z2);
182		77	return 1;
183			}
184	✗✓	516	if (BN_is_zero(z2)) {
185			if (!BN_copy(x2, x))
186			return 0;
187			if (!BN_GF2m_add(z2, x, y))
188			return 0;
189			return 2;
190			}
191			/* Since Mxy is static we can guarantee that ctx != NULL. */
192		516	BN_CTX_start(ctx);
193	✗✓	516	if ((t3 = BN_CTX_get(ctx)) == NULL)
194			goto err;
195	✗✓	516	if ((t4 = BN_CTX_get(ctx)) == NULL)
196			goto err;
197	✗✓	516	if ((t5 = BN_CTX_get(ctx)) == NULL)
198			goto err;
199
200	✗✓	516	if (!BN_one(t5))
201			goto err;
202
203	✗✓	516	if (!group->meth->field_mul(group, t3, z1, z2, ctx))
204			goto err;
205
206	✗✓	516	if (!group->meth->field_mul(group, z1, z1, x, ctx))
207			goto err;
208	✗✓	516	if (!BN_GF2m_add(z1, z1, x1))
209			goto err;
210	✗✓	516	if (!group->meth->field_mul(group, z2, z2, x, ctx))
211			goto err;
212	✗✓	516	if (!group->meth->field_mul(group, x1, z2, x1, ctx))
213			goto err;
214	✗✓	516	if (!BN_GF2m_add(z2, z2, x2))
215			goto err;
216
217	✗✓	516	if (!group->meth->field_mul(group, z2, z2, z1, ctx))
218			goto err;
219	✗✓	516	if (!group->meth->field_sqr(group, t4, x, ctx))
220			goto err;
221	✗✓	516	if (!BN_GF2m_add(t4, t4, y))
222			goto err;
223	✗✓	516	if (!group->meth->field_mul(group, t4, t4, t3, ctx))
224			goto err;
225	✗✓	516	if (!BN_GF2m_add(t4, t4, z2))
226			goto err;
227
228	✗✓	516	if (!group->meth->field_mul(group, t3, t3, x, ctx))
229			goto err;
230	✗✓	516	if (!group->meth->field_div(group, t3, t5, t3, ctx))
231			goto err;
232	✗✓	516	if (!group->meth->field_mul(group, t4, t3, t4, ctx))
233			goto err;
234	✗✓	516	if (!group->meth->field_mul(group, x2, x1, t3, ctx))
235			goto err;
236	✗✓	516	if (!BN_GF2m_add(z2, x2, x))
237			goto err;
238
239	✗✓	516	if (!group->meth->field_mul(group, z2, z2, t4, ctx))
240			goto err;
241	✗✓	516	if (!BN_GF2m_add(z2, z2, y))
242			goto err;
243
244		516	ret = 2;
245
246		516	err:
247		516	BN_CTX_end(ctx);
248		516	return ret;
249			}
250
251
252			/* Computes scalar*point and stores the result in r.
253			* point can not equal r.
254			* Uses a modified algorithm 2P of
255			* Lopez, J. and Dahab, R. "Fast multiplication on elliptic curves over
256			* GF(2^m) without precomputation" (CHES '99, LNCS 1717).
257			*
258			* To protect against side-channel attack the function uses constant time swap,
259			* avoiding conditional branches.
260			*/
261			static int
262			ec_GF2m_montgomery_point_multiply(const EC_GROUP group, EC_POINT r,
263			const BIGNUM scalar, const EC_POINT point, BN_CTX *ctx)
264		623	{
265			BIGNUM x1, x2, z1, z2;
266		623	int ret = 0, i;
267			BN_ULONG mask, word;
268
269	✗✓	623	if (r == point) {
270			ECerr(EC_F_EC_GF2M_MONTGOMERY_POINT_MULTIPLY, EC_R_INVALID_ARGUMENT);
271			return 0;
272			}
273			/* if result should be point at infinity */
274	✓✗✓✗ ✓✓	623	if ((scalar == NULL) \|\| BN_is_zero(scalar) \|\| (point == NULL) \|\|
275			EC_POINT_is_at_infinity(group, point) > 0) {
276		30	return EC_POINT_set_to_infinity(group, r);
277			}
278			/* only support affine coordinates */
279	✗✓	593	if (!point->Z_is_one)
280			return 0;
281
282			/* Since point_multiply is static we can guarantee that ctx != NULL. */
283		593	BN_CTX_start(ctx);
284	✗✓	593	if ((x1 = BN_CTX_get(ctx)) == NULL)
285			goto err;
286	✗✓	593	if ((z1 = BN_CTX_get(ctx)) == NULL)
287			goto err;
288
289		593	x2 = &r->X;
290		593	z2 = &r->Y;
291
292	✓✓✗✓	593	if (!bn_wexpand(x1, group->field.top))
293			goto err;
294	✓✓✗✓	593	if (!bn_wexpand(z1, group->field.top))
295			goto err;
296	✓✓✗✓	593	if (!bn_wexpand(x2, group->field.top))
297			goto err;
298	✓✓✗✓	593	if (!bn_wexpand(z2, group->field.top))
299			goto err;
300
301	✗✓	593	if (!BN_GF2m_mod_arr(x1, &point->X, group->poly))
302			goto err; /* x1 = x */
303	✗✓	593	if (!BN_one(z1))
304			goto err; /* z1 = 1 */
305	✗✓	593	if (!group->meth->field_sqr(group, z2, x1, ctx))
306			goto err; /* z2 = x1^2 = x^2 */
307	✗✓	593	if (!group->meth->field_sqr(group, x2, z2, ctx))
308			goto err;
309	✗✓	593	if (!BN_GF2m_add(x2, x2, &group->b))
310			goto err; /* x2 = x^4 + b */
311
312			/* find top most bit and go one past it */
313		593	i = scalar->top - 1;
314		593	mask = BN_TBIT;
315		593	word = scalar->d[i];
316	✓✓	15673	while (!(word & mask))
317		14487	mask >>= 1;
318		593	mask >>= 1;
319			/* if top most bit was at word break, go to next word */
320	✓✓	593	if (!mask) {
321		8	i--;
322		8	mask = BN_TBIT;
323			}
324	✓✓	2627	for (; i >= 0; i--) {
325		2627	word = scalar->d[i];
326	✓✓	158814	while (mask) {
327		153560	BN_consttime_swap(word & mask, x1, x2, group->field.top);
328		153560	BN_consttime_swap(word & mask, z1, z2, group->field.top);
329	✗✓	153560	if (!gf2m_Madd(group, &point->X, x2, z2, x1, z1, ctx))
330			goto err;
331	✗✓	153560	if (!gf2m_Mdouble(group, x1, z1, ctx))
332			goto err;
333		153560	BN_consttime_swap(word & mask, x1, x2, group->field.top);
334		153560	BN_consttime_swap(word & mask, z1, z2, group->field.top);
335		153560	mask >>= 1;
336			}
337		2627	mask = BN_TBIT;
338			}
339
340			/* convert out of "projective" coordinates */
341		593	i = gf2m_Mxy(group, &point->X, &point->Y, x1, z1, x2, z2, ctx);
342	✗✓	593	if (i == 0)
343			goto err;
344	✓✓	593	else if (i == 1) {
345	✗✓	77	if (!EC_POINT_set_to_infinity(group, r))
346			goto err;
347			} else {
348	✗✓	516	if (!BN_one(&r->Z))
349			goto err;
350		516	r->Z_is_one = 1;
351			}
352
353			/* GF(2^m) field elements should always have BIGNUM::neg = 0 */
354		593	BN_set_negative(&r->X, 0);
355		593	BN_set_negative(&r->Y, 0);
356
357		593	ret = 1;
358
359		593	err:
360		593	BN_CTX_end(ctx);
361		593	return ret;
362			}
363
364
365			/* Computes the sum
366			* scalargroup->generator + scalars[0]points[0] + ... + scalars[num-1]*points[num-1]
367			* gracefully ignoring NULL scalar values.
368			*/
369			int
370			ec_GF2m_simple_mul(const EC_GROUP group, EC_POINT r, const BIGNUM *scalar,
371			size_t num, const EC_POINT points[], const BIGNUM scalars[], BN_CTX *ctx)
372		474	{
373		474	BN_CTX *new_ctx = NULL;
374		474	int ret = 0;
375			size_t i;
376		474	EC_POINT *p = NULL;
377		474	EC_POINT *acc = NULL;
378
379	✗✓	474	if (ctx == NULL) {
380			ctx = new_ctx = BN_CTX_new();
381			if (ctx == NULL)
382			return 0;
383			}
384			/*
385			* This implementation is more efficient than the wNAF implementation
386			* for 2 or fewer points. Use the ec_wNAF_mul implementation for 3
387			* or more points, or if we can perform a fast multiplication based
388			* on precomputation.
389			*/
390	✓✓✓✓ ✓✓✓✓	474	if ((scalar && (num > 1)) \|\| (num > 2) \|\|
391			(num == 0 && EC_GROUP_have_precompute_mult(group))) {
392		21	ret = ec_wNAF_mul(group, r, scalar, num, points, scalars, ctx);
393		21	goto err;
394			}
395	✗✓	453	if ((p = EC_POINT_new(group)) == NULL)
396			goto err;
397	✗✓	453	if ((acc = EC_POINT_new(group)) == NULL)
398			goto err;
399
400	✗✓	453	if (!EC_POINT_set_to_infinity(group, acc))
401			goto err;
402
403	✓✓	453	if (scalar) {
404	✗✓	367	if (!ec_GF2m_montgomery_point_multiply(group, p, scalar, group->generator, ctx))
405			goto err;
406	✗✓	367	if (BN_is_negative(scalar))
407			if (!group->meth->invert(group, p, ctx))
408			goto err;
409	✗✓	367	if (!group->meth->add(group, acc, acc, p, ctx))
410			goto err;
411			}
412	✓✓	709	for (i = 0; i < num; i++) {
413	✗✓	256	if (!ec_GF2m_montgomery_point_multiply(group, p, scalars[i], points[i], ctx))
414			goto err;
415	✓✓	256	if (BN_is_negative(scalars[i]))
416	✗✓	21	if (!group->meth->invert(group, p, ctx))
417			goto err;
418	✗✓	256	if (!group->meth->add(group, acc, acc, p, ctx))
419			goto err;
420			}
421
422	✗✓	453	if (!EC_POINT_copy(r, acc))
423			goto err;
424
425		453	ret = 1;
426
427		474	err:
428		474	EC_POINT_free(p);
429		474	EC_POINT_free(acc);
430		474	BN_CTX_free(new_ctx);
431		474	return ret;
432			}
433
434
435			/* Precomputation for point multiplication: fall back to wNAF methods
436			* because ec_GF2m_simple_mul() uses ec_wNAF_mul() if appropriate */
437
438			int
439			ec_GF2m_precompute_mult(EC_GROUP * group, BN_CTX * ctx)
440		10	{
441		10	return ec_wNAF_precompute_mult(group, ctx);
442			}
443
444			int
445			ec_GF2m_have_precompute_mult(const EC_GROUP * group)
446		218	{
447		218	return ec_wNAF_have_precompute_mult(group);
448			}
449
450			#endif