/src/openssl/crypto/ec/ec2_mult.c

Source (jump to first uncovered line)
/* crypto/ec/ec2_mult.c */
/* ====================================================================
 * Copyright 2002 Sun Microsystems, Inc. ALL RIGHTS RESERVED.
 *
 * The Elliptic Curve Public-Key Crypto Library (ECC Code) included
 * herein is developed by SUN MICROSYSTEMS, INC., and is contributed
 * to the OpenSSL project.
 *
 * The ECC Code is licensed pursuant to the OpenSSL open source
 * license provided below.
 *
 * The software is originally written by Sheueling Chang Shantz and
 * Douglas Stebila of Sun Microsystems Laboratories.
 *
 */
/* ====================================================================
 * Copyright (c) 1998-2003 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/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);
    t1 = BN_CTX_get(ctx);
    if (t1 == 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);
    t1 = BN_CTX_get(ctx);
    t2 = BN_CTX_get(ctx);
    if (t2 == 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);
    t3 = BN_CTX_get(ctx);
    t4 = BN_CTX_get(ctx);
    t5 = BN_CTX_get(ctx);
    if (t5 == 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, group_top;
    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)) {
        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);
    x1 = BN_CTX_get(ctx);
    z1 = BN_CTX_get(ctx);
    if (z1 == NULL)
        goto err;

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

    group_top = group->field.top;
    if (bn_wexpand(x1, group_top) == NULL
        || bn_wexpand(z1, group_top) == NULL
        || bn_wexpand(x2, group_top) == NULL
        || bn_wexpand(z2, group_top) == NULL)
        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_top);
            BN_consttime_swap(word & mask, z1, z2, group_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_top);
            BN_consttime_swap(word & mask, z1, z2, group_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:
    if (p)
        EC_POINT_free(p);
    if (acc)
        EC_POINT_free(acc);
    if (new_ctx != NULL)
        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: 2022-11-30 06:20

Line	Count	Source (jump to first uncovered line)
1		/* crypto/ec/ec2_mult.c */
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/err.h>
71
72		#include "ec_lcl.h"
73
74		#ifndef OPENSSL_NO_EC2M
75
76		/*-
77		* Compute the x-coordinate x/z for the point 2*(x/z) in Montgomery projective
78		* coordinates.
79		* Uses algorithm Mdouble in appendix of
80		* Lopez, J. and Dahab, R. "Fast multiplication on elliptic curves over
81		* GF(2^m) without precomputation" (CHES '99, LNCS 1717).
82		* modified to not require precomputation of c=b^{2^{m-1}}.
83		*/
84		static int gf2m_Mdouble(const EC_GROUP group, BIGNUM x, BIGNUM *z,
85		BN_CTX *ctx)
86	0	{
87	0	BIGNUM *t1;
88	0	int ret = 0;
89
90		/* Since Mdouble is static we can guarantee that ctx != NULL. */
91	0	BN_CTX_start(ctx);
92	0	t1 = BN_CTX_get(ctx);
93	0	if (t1 == NULL)
94	0	goto err;
95
96	0	if (!group->meth->field_sqr(group, x, x, ctx))
97	0	goto err;
98	0	if (!group->meth->field_sqr(group, t1, z, ctx))
99	0	goto err;
100	0	if (!group->meth->field_mul(group, z, x, t1, ctx))
101	0	goto err;
102	0	if (!group->meth->field_sqr(group, x, x, ctx))
103	0	goto err;
104	0	if (!group->meth->field_sqr(group, t1, t1, ctx))
105	0	goto err;
106	0	if (!group->meth->field_mul(group, t1, &group->b, t1, ctx))
107	0	goto err;
108	0	if (!BN_GF2m_add(x, x, t1))
109	0	goto err;
110
111	0	ret = 1;
112
113	0	err:
114	0	BN_CTX_end(ctx);
115	0	return ret;
116	0	}
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 gf2m_Madd(const EC_GROUP group, const BIGNUM x, BIGNUM *x1,
126		BIGNUM z1, const BIGNUM x2, const BIGNUM *z2,
127		BN_CTX *ctx)
128	0	{
129	0	BIGNUM t1, t2;
130	0	int ret = 0;
131
132		/* Since Madd is static we can guarantee that ctx != NULL. */
133	0	BN_CTX_start(ctx);
134	0	t1 = BN_CTX_get(ctx);
135	0	t2 = BN_CTX_get(ctx);
136	0	if (t2 == NULL)
137	0	goto err;
138
139	0	if (!BN_copy(t1, x))
140	0	goto err;
141	0	if (!group->meth->field_mul(group, x1, x1, z2, ctx))
142	0	goto err;
143	0	if (!group->meth->field_mul(group, z1, z1, x2, ctx))
144	0	goto err;
145	0	if (!group->meth->field_mul(group, t2, x1, z1, ctx))
146	0	goto err;
147	0	if (!BN_GF2m_add(z1, z1, x1))
148	0	goto err;
149	0	if (!group->meth->field_sqr(group, z1, z1, ctx))
150	0	goto err;
151	0	if (!group->meth->field_mul(group, x1, z1, t1, ctx))
152	0	goto err;
153	0	if (!BN_GF2m_add(x1, x1, t2))
154	0	goto err;
155
156	0	ret = 1;
157
158	0	err:
159	0	BN_CTX_end(ctx);
160	0	return ret;
161	0	}
162
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 gf2m_Mxy(const EC_GROUP group, const BIGNUM x, const BIGNUM *y,
174		BIGNUM x1, BIGNUM z1, BIGNUM x2, BIGNUM z2,
175		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
186	0	if (BN_is_zero(z2)) {
187	0	if (!BN_copy(x2, x))
188	0	return 0;
189	0	if (!BN_GF2m_add(z2, x, y))
190	0	return 0;
191	0	return 2;
192	0	}
193
194		/* Since Mxy is static we can guarantee that ctx != NULL. */
195	0	BN_CTX_start(ctx);
196	0	t3 = BN_CTX_get(ctx);
197	0	t4 = BN_CTX_get(ctx);
198	0	t5 = BN_CTX_get(ctx);
199	0	if (t5 == NULL)
200	0	goto err;
201
202	0	if (!BN_one(t5))
203	0	goto err;
204
205	0	if (!group->meth->field_mul(group, t3, z1, z2, ctx))
206	0	goto err;
207
208	0	if (!group->meth->field_mul(group, z1, z1, x, ctx))
209	0	goto err;
210	0	if (!BN_GF2m_add(z1, z1, x1))
211	0	goto err;
212	0	if (!group->meth->field_mul(group, z2, z2, x, ctx))
213	0	goto err;
214	0	if (!group->meth->field_mul(group, x1, z2, x1, ctx))
215	0	goto err;
216	0	if (!BN_GF2m_add(z2, z2, x2))
217	0	goto err;
218
219	0	if (!group->meth->field_mul(group, z2, z2, z1, ctx))
220	0	goto err;
221	0	if (!group->meth->field_sqr(group, t4, x, ctx))
222	0	goto err;
223	0	if (!BN_GF2m_add(t4, t4, y))
224	0	goto err;
225	0	if (!group->meth->field_mul(group, t4, t4, t3, ctx))
226	0	goto err;
227	0	if (!BN_GF2m_add(t4, t4, z2))
228	0	goto err;
229
230	0	if (!group->meth->field_mul(group, t3, t3, x, ctx))
231	0	goto err;
232	0	if (!group->meth->field_div(group, t3, t5, t3, ctx))
233	0	goto err;
234	0	if (!group->meth->field_mul(group, t4, t3, t4, ctx))
235	0	goto err;
236	0	if (!group->meth->field_mul(group, x2, x1, t3, ctx))
237	0	goto err;
238	0	if (!BN_GF2m_add(z2, x2, x))
239	0	goto err;
240
241	0	if (!group->meth->field_mul(group, z2, z2, t4, ctx))
242	0	goto err;
243	0	if (!BN_GF2m_add(z2, z2, y))
244	0	goto err;
245
246	0	ret = 2;
247
248	0	err:
249	0	BN_CTX_end(ctx);
250	0	return ret;
251	0	}
252
253		/*-
254		* Computes scalar*point and stores the result in r.
255		* point can not equal r.
256		* Uses a modified algorithm 2P of
257		* Lopez, J. and Dahab, R. "Fast multiplication on elliptic curves over
258		* GF(2^m) without precomputation" (CHES '99, LNCS 1717).
259		*
260		* To protect against side-channel attack the function uses constant time swap,
261		* avoiding conditional branches.
262		*/
263		static int ec_GF2m_montgomery_point_multiply(const EC_GROUP *group,
264		EC_POINT *r,
265		const BIGNUM *scalar,
266		const EC_POINT *point,
267		BN_CTX *ctx)
268	0	{
269	0	BIGNUM x1, x2, z1, z2;
270	0	int ret = 0, i, group_top;
271	0	BN_ULONG mask, word;
272
273	0	if (r == point) {
274	0	ECerr(EC_F_EC_GF2M_MONTGOMERY_POINT_MULTIPLY, EC_R_INVALID_ARGUMENT);
275	0	return 0;
276	0	}
277
278		/* if result should be point at infinity */
279	0	if ((scalar == NULL) \|\| BN_is_zero(scalar) \|\| (point == NULL) \|\|
280	0	EC_POINT_is_at_infinity(group, point)) {
281	0	return EC_POINT_set_to_infinity(group, r);
282	0	}
283
284		/* only support affine coordinates */
285	0	if (!point->Z_is_one)
286	0	return 0;
287
288		/*
289		* Since point_multiply is static we can guarantee that ctx != NULL.
290		*/
291	0	BN_CTX_start(ctx);
292	0	x1 = BN_CTX_get(ctx);
293	0	z1 = BN_CTX_get(ctx);
294	0	if (z1 == NULL)
295	0	goto err;
296
297	0	x2 = &r->X;
298	0	z2 = &r->Y;
299
300	0	group_top = group->field.top;
301	0	if (bn_wexpand(x1, group_top) == NULL
302	0	\|\| bn_wexpand(z1, group_top) == NULL
303	0	\|\| bn_wexpand(x2, group_top) == NULL
304	0	\|\| bn_wexpand(z2, group_top) == NULL)
305	0	goto err;
306
307	0	if (!BN_GF2m_mod_arr(x1, &point->X, group->poly))
308	0	goto err; /* x1 = x */
309	0	if (!BN_one(z1))
310	0	goto err; /* z1 = 1 */
311	0	if (!group->meth->field_sqr(group, z2, x1, ctx))
312	0	goto err; /* z2 = x1^2 = x^2 */
313	0	if (!group->meth->field_sqr(group, x2, z2, ctx))
314	0	goto err;
315	0	if (!BN_GF2m_add(x2, x2, &group->b))
316	0	goto err; /* x2 = x^4 + b */
317
318		/* find top most bit and go one past it */
319	0	i = scalar->top - 1;
320	0	mask = BN_TBIT;
321	0	word = scalar->d[i];
322	0	while (!(word & mask))
323	0	mask >>= 1;
324	0	mask >>= 1;
325		/* if top most bit was at word break, go to next word */
326	0	if (!mask) {
327	0	i--;
328	0	mask = BN_TBIT;
329	0	}
330
331	0	for (; i >= 0; i--) {
332	0	word = scalar->d[i];
333	0	while (mask) {
334	0	BN_consttime_swap(word & mask, x1, x2, group_top);
335	0	BN_consttime_swap(word & mask, z1, z2, group_top);
336	0	if (!gf2m_Madd(group, &point->X, x2, z2, x1, z1, ctx))
337	0	goto err;
338	0	if (!gf2m_Mdouble(group, x1, z1, ctx))
339	0	goto err;
340	0	BN_consttime_swap(word & mask, x1, x2, group_top);
341	0	BN_consttime_swap(word & mask, z1, z2, group_top);
342	0	mask >>= 1;
343	0	}
344	0	mask = BN_TBIT;
345	0	}
346
347		/* convert out of "projective" coordinates */
348	0	i = gf2m_Mxy(group, &point->X, &point->Y, x1, z1, x2, z2, ctx);
349	0	if (i == 0)
350	0	goto err;
351	0	else if (i == 1) {
352	0	if (!EC_POINT_set_to_infinity(group, r))
353	0	goto err;
354	0	} else {
355	0	if (!BN_one(&r->Z))
356	0	goto err;
357	0	r->Z_is_one = 1;
358	0	}
359
360		/* GF(2^m) field elements should always have BIGNUM::neg = 0 */
361	0	BN_set_negative(&r->X, 0);
362	0	BN_set_negative(&r->Y, 0);
363
364	0	ret = 1;
365
366	0	err:
367	0	BN_CTX_end(ctx);
368	0	return ret;
369	0	}
370
371		/*-
372		* Computes the sum
373		* scalargroup->generator + scalars[0]points[0] + ... + scalars[num-1]*points[num-1]
374		* gracefully ignoring NULL scalar values.
375		*/
376		int ec_GF2m_simple_mul(const EC_GROUP group, EC_POINT r,
377		const BIGNUM *scalar, size_t num,
378		const EC_POINT points[], const BIGNUM scalars[],
379		BN_CTX *ctx)
380	0	{
381	0	BN_CTX *new_ctx = NULL;
382	0	int ret = 0;
383	0	size_t i;
384	0	EC_POINT *p = NULL;
385	0	EC_POINT *acc = NULL;
386
387	0	if (ctx == NULL) {
388	0	ctx = new_ctx = BN_CTX_new();
389	0	if (ctx == NULL)
390	0	return 0;
391	0	}
392
393		/*
394		* This implementation is more efficient than the wNAF implementation for
395		* 2 or fewer points. Use the ec_wNAF_mul implementation for 3 or more
396		* points, or if we can perform a fast multiplication based on
397		* precomputation.
398		*/
399	0	if ((scalar && (num > 1)) \|\| (num > 2)
400	0	\|\| (num == 0 && EC_GROUP_have_precompute_mult(group))) {
401	0	ret = ec_wNAF_mul(group, r, scalar, num, points, scalars, ctx);
402	0	goto err;
403	0	}
404
405	0	if ((p = EC_POINT_new(group)) == NULL)
406	0	goto err;
407	0	if ((acc = EC_POINT_new(group)) == NULL)
408	0	goto err;
409
410	0	if (!EC_POINT_set_to_infinity(group, acc))
411	0	goto err;
412
413	0	if (scalar) {
414	0	if (!ec_GF2m_montgomery_point_multiply
415	0	(group, p, scalar, group->generator, ctx))
416	0	goto err;
417	0	if (BN_is_negative(scalar))
418	0	if (!group->meth->invert(group, p, ctx))
419	0	goto err;
420	0	if (!group->meth->add(group, acc, acc, p, ctx))
421	0	goto err;
422	0	}
423
424	0	for (i = 0; i < num; i++) {
425	0	if (!ec_GF2m_montgomery_point_multiply
426	0	(group, p, scalars[i], points[i], ctx))
427	0	goto err;
428	0	if (BN_is_negative(scalars[i]))
429	0	if (!group->meth->invert(group, p, ctx))
430	0	goto err;
431	0	if (!group->meth->add(group, acc, acc, p, ctx))
432	0	goto err;
433	0	}
434
435	0	if (!EC_POINT_copy(r, acc))
436	0	goto err;
437
438	0	ret = 1;
439
440	0	err:
441	0	if (p)
442	0	EC_POINT_free(p);
443	0	if (acc)
444	0	EC_POINT_free(acc);
445	0	if (new_ctx != NULL)
446	0	BN_CTX_free(new_ctx);
447	0	return ret;
448	0	}
449
450		/*
451		* Precomputation for point multiplication: fall back to wNAF methods because
452		* ec_GF2m_simple_mul() uses ec_wNAF_mul() if appropriate
453		*/
454
455		int ec_GF2m_precompute_mult(EC_GROUP group, BN_CTX ctx)
456	0	{
457	0	return ec_wNAF_precompute_mult(group, ctx);
458	0	}
459
460		int ec_GF2m_have_precompute_mult(const EC_GROUP *group)
461	0	{
462	0	return ec_wNAF_have_precompute_mult(group);
463	0	}
464
465		#endif