1 /* crypto/ec/ec2_mult.c */
2 /* ====================================================================
3 * Copyright 2002 Sun Microsystems, Inc. ALL RIGHTS RESERVED.
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.
9 * The ECC Code is licensed pursuant to the OpenSSL open source
10 * license provided below.
12 * The software is originally written by Sheueling Chang Shantz and
13 * Douglas Stebila of Sun Microsystems Laboratories.
16 /* ====================================================================
17 * Copyright (c) 1998-2003 The OpenSSL Project. All rights reserved.
19 * Redistribution and use in source and binary forms, with or without
20 * modification, are permitted provided that the following conditions
23 * 1. Redistributions of source code must retain the above copyright
24 * notice, this list of conditions and the following disclaimer.
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
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/)"
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.
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.
45 * 6. Redistributions of any form whatsoever must retain the following
47 * "This product includes software developed by the OpenSSL Project
48 * for use in the OpenSSL Toolkit (http://www.openssl.org/)"
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 * ====================================================================
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).
70 #include <openssl/err.h>
72 #include "internal/bn_int.h"
75 #ifndef OPENSSL_NO_EC2M
78 * Compute the x-coordinate x/z for the point 2*(x/z) in Montgomery projective
80 * Uses algorithm Mdouble in appendix of
81 * Lopez, J. and Dahab, R. "Fast multiplication on elliptic curves over
82 * GF(2^m) without precomputation" (CHES '99, LNCS 1717).
83 * modified to not require precomputation of c=b^{2^{m-1}}.
85 static int gf2m_Mdouble(const EC_GROUP *group, BIGNUM *x, BIGNUM *z,
91 /* Since Mdouble is static we can guarantee that ctx != NULL. */
97 if (!group->meth->field_sqr(group, x, x, ctx))
99 if (!group->meth->field_sqr(group, t1, z, ctx))
101 if (!group->meth->field_mul(group, z, x, t1, ctx))
103 if (!group->meth->field_sqr(group, x, x, ctx))
105 if (!group->meth->field_sqr(group, t1, t1, ctx))
107 if (!group->meth->field_mul(group, t1, group->b, t1, ctx))
109 if (!BN_GF2m_add(x, x, t1))
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).
126 static int gf2m_Madd(const EC_GROUP *group, const BIGNUM *x, BIGNUM *x1,
127 BIGNUM *z1, const BIGNUM *x2, const BIGNUM *z2,
133 /* Since Madd is static we can guarantee that ctx != NULL. */
135 t1 = BN_CTX_get(ctx);
136 t2 = BN_CTX_get(ctx);
142 if (!group->meth->field_mul(group, x1, x1, z2, ctx))
144 if (!group->meth->field_mul(group, z1, z1, x2, ctx))
146 if (!group->meth->field_mul(group, t2, x1, z1, ctx))
148 if (!BN_GF2m_add(z1, z1, x1))
150 if (!group->meth->field_sqr(group, z1, z1, ctx))
152 if (!group->meth->field_mul(group, x1, z1, t1, ctx))
154 if (!BN_GF2m_add(x1, x1, t2))
165 * Compute the x, y affine coordinates from the point (x1, z1) (x2, z2)
166 * using Montgomery point multiplication algorithm Mxy() in appendix of
167 * Lopez, J. and Dahab, R. "Fast multiplication on elliptic curves over
168 * GF(2^m) without precomputation" (CHES '99, LNCS 1717).
171 * 1 if return value should be the point at infinity
174 static int gf2m_Mxy(const EC_GROUP *group, const BIGNUM *x, const BIGNUM *y,
175 BIGNUM *x1, BIGNUM *z1, BIGNUM *x2, BIGNUM *z2,
178 BIGNUM *t3, *t4, *t5;
181 if (BN_is_zero(z1)) {
187 if (BN_is_zero(z2)) {
190 if (!BN_GF2m_add(z2, x, y))
195 /* Since Mxy is static we can guarantee that ctx != NULL. */
197 t3 = BN_CTX_get(ctx);
198 t4 = BN_CTX_get(ctx);
199 t5 = BN_CTX_get(ctx);
206 if (!group->meth->field_mul(group, t3, z1, z2, ctx))
209 if (!group->meth->field_mul(group, z1, z1, x, ctx))
211 if (!BN_GF2m_add(z1, z1, x1))
213 if (!group->meth->field_mul(group, z2, z2, x, ctx))
215 if (!group->meth->field_mul(group, x1, z2, x1, ctx))
217 if (!BN_GF2m_add(z2, z2, x2))
220 if (!group->meth->field_mul(group, z2, z2, z1, ctx))
222 if (!group->meth->field_sqr(group, t4, x, ctx))
224 if (!BN_GF2m_add(t4, t4, y))
226 if (!group->meth->field_mul(group, t4, t4, t3, ctx))
228 if (!BN_GF2m_add(t4, t4, z2))
231 if (!group->meth->field_mul(group, t3, t3, x, ctx))
233 if (!group->meth->field_div(group, t3, t5, t3, ctx))
235 if (!group->meth->field_mul(group, t4, t3, t4, ctx))
237 if (!group->meth->field_mul(group, x2, x1, t3, ctx))
239 if (!BN_GF2m_add(z2, x2, x))
242 if (!group->meth->field_mul(group, z2, z2, t4, ctx))
244 if (!BN_GF2m_add(z2, z2, y))
255 * Computes scalar*point and stores the result in r.
256 * point can not equal r.
257 * Uses a modified algorithm 2P of
258 * Lopez, J. and Dahab, R. "Fast multiplication on elliptic curves over
259 * GF(2^m) without precomputation" (CHES '99, LNCS 1717).
261 * To protect against side-channel attack the function uses constant time swap,
262 * avoiding conditional branches.
264 static int ec_GF2m_montgomery_point_multiply(const EC_GROUP *group,
266 const BIGNUM *scalar,
267 const EC_POINT *point,
270 BIGNUM *x1, *x2, *z1, *z2;
275 ECerr(EC_F_EC_GF2M_MONTGOMERY_POINT_MULTIPLY, EC_R_INVALID_ARGUMENT);
279 /* if result should be point at infinity */
280 if ((scalar == NULL) || BN_is_zero(scalar) || (point == NULL) ||
281 EC_POINT_is_at_infinity(group, point)) {
282 return EC_POINT_set_to_infinity(group, r);
285 /* only support affine coordinates */
286 if (!point->Z_is_one)
290 * Since point_multiply is static we can guarantee that ctx != NULL.
293 x1 = BN_CTX_get(ctx);
294 z1 = BN_CTX_get(ctx);
301 bn_wexpand(x1, bn_get_top(group->field));
302 bn_wexpand(z1, bn_get_top(group->field));
303 bn_wexpand(x2, bn_get_top(group->field));
304 bn_wexpand(z2, bn_get_top(group->field));
306 if (!BN_GF2m_mod_arr(x1, point->X, group->poly))
307 goto err; /* x1 = x */
309 goto err; /* z1 = 1 */
310 if (!group->meth->field_sqr(group, z2, x1, ctx))
311 goto err; /* z2 = x1^2 = x^2 */
312 if (!group->meth->field_sqr(group, x2, z2, ctx))
314 if (!BN_GF2m_add(x2, x2, group->b))
315 goto err; /* x2 = x^4 + b */
317 /* find top most bit and go one past it */
318 i = bn_get_top(scalar) - 1;
320 word = bn_get_words(scalar)[i];
321 while (!(word & mask))
324 /* if top most bit was at word break, go to next word */
330 for (; i >= 0; i--) {
331 word = bn_get_words(scalar)[i];
333 BN_consttime_swap(word & mask, x1, x2, bn_get_top(group->field));
334 BN_consttime_swap(word & mask, z1, z2, bn_get_top(group->field));
335 if (!gf2m_Madd(group, point->X, x2, z2, x1, z1, ctx))
337 if (!gf2m_Mdouble(group, x1, z1, ctx))
339 BN_consttime_swap(word & mask, x1, x2, bn_get_top(group->field));
340 BN_consttime_swap(word & mask, z1, z2, bn_get_top(group->field));
346 /* convert out of "projective" coordinates */
347 i = gf2m_Mxy(group, point->X, point->Y, x1, z1, x2, z2, ctx);
351 if (!EC_POINT_set_to_infinity(group, r))
359 /* GF(2^m) field elements should always have BIGNUM::neg = 0 */
360 BN_set_negative(r->X, 0);
361 BN_set_negative(r->Y, 0);
372 * scalar*group->generator + scalars[0]*points[0] + ... + scalars[num-1]*points[num-1]
373 * gracefully ignoring NULL scalar values.
375 int ec_GF2m_simple_mul(const EC_GROUP *group, EC_POINT *r,
376 const BIGNUM *scalar, size_t num,
377 const EC_POINT *points[], const BIGNUM *scalars[],
380 BN_CTX *new_ctx = NULL;
384 EC_POINT *acc = NULL;
387 ctx = new_ctx = BN_CTX_new();
393 * This implementation is more efficient than the wNAF implementation for
394 * 2 or fewer points. Use the ec_wNAF_mul implementation for 3 or more
395 * points, or if we can perform a fast multiplication based on
398 if ((scalar && (num > 1)) || (num > 2)
399 || (num == 0 && EC_GROUP_have_precompute_mult(group))) {
400 ret = ec_wNAF_mul(group, r, scalar, num, points, scalars, ctx);
404 if ((p = EC_POINT_new(group)) == NULL)
406 if ((acc = EC_POINT_new(group)) == NULL)
409 if (!EC_POINT_set_to_infinity(group, acc))
413 if (!ec_GF2m_montgomery_point_multiply
414 (group, p, scalar, group->generator, ctx))
416 if (BN_is_negative(scalar))
417 if (!group->meth->invert(group, p, ctx))
419 if (!group->meth->add(group, acc, acc, p, ctx))
423 for (i = 0; i < num; i++) {
424 if (!ec_GF2m_montgomery_point_multiply
425 (group, p, scalars[i], points[i], ctx))
427 if (BN_is_negative(scalars[i]))
428 if (!group->meth->invert(group, p, ctx))
430 if (!group->meth->add(group, acc, acc, p, ctx))
434 if (!EC_POINT_copy(r, acc))
443 BN_CTX_free(new_ctx);
448 * Precomputation for point multiplication: fall back to wNAF methods because
449 * ec_GF2m_simple_mul() uses ec_wNAF_mul() if appropriate
452 int ec_GF2m_precompute_mult(EC_GROUP *group, BN_CTX *ctx)
454 return ec_wNAF_precompute_mult(group, ctx);
457 int ec_GF2m_have_precompute_mult(const EC_GROUP *group)
459 return ec_wNAF_have_precompute_mult(group);