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diff --git a/src/lib/libcrypto/ec/ec2_mult.c b/src/lib/libcrypto/ec/ec2_mult.c
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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 */
86static int
87gf2m_Mdouble(const EC_GROUP *group, BIGNUM *x, BIGNUM *z, BN_CTX *ctx)
88{
89 BIGNUM *t1;
90 int ret = 0;
91
92 /* Since Mdouble is static we can guarantee that ctx != NULL. */
93 BN_CTX_start(ctx);
94 if ((t1 = BN_CTX_get(ctx)) == NULL)
95 goto err;
96
97 if (!group->meth->field_sqr(group, x, x, ctx))
98 goto err;
99 if (!group->meth->field_sqr(group, t1, z, ctx))
100 goto err;
101 if (!group->meth->field_mul(group, z, x, t1, ctx))
102 goto err;
103 if (!group->meth->field_sqr(group, x, x, ctx))
104 goto err;
105 if (!group->meth->field_sqr(group, t1, t1, ctx))
106 goto err;
107 if (!group->meth->field_mul(group, t1, &group->b, t1, ctx))
108 goto err;
109 if (!BN_GF2m_add(x, x, t1))
110 goto err;
111
112 ret = 1;
113
114err:
115 BN_CTX_end(ctx);
116 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 */
125static int
126gf2m_Madd(const EC_GROUP *group, const BIGNUM *x, BIGNUM *x1, BIGNUM *z1,
127 const BIGNUM *x2, const BIGNUM *z2, BN_CTX *ctx)
128{
129 BIGNUM *t1, *t2;
130 int ret = 0;
131
132 /* Since Madd is static we can guarantee that ctx != NULL. */
133 BN_CTX_start(ctx);
134 if ((t1 = BN_CTX_get(ctx)) == NULL)
135 goto err;
136 if ((t2 = BN_CTX_get(ctx)) == NULL)
137 goto err;
138
139 if (!BN_copy(t1, x))
140 goto err;
141 if (!group->meth->field_mul(group, x1, x1, z2, ctx))
142 goto err;
143 if (!group->meth->field_mul(group, z1, z1, x2, ctx))
144 goto err;
145 if (!group->meth->field_mul(group, t2, x1, z1, ctx))
146 goto err;
147 if (!BN_GF2m_add(z1, z1, x1))
148 goto err;
149 if (!group->meth->field_sqr(group, z1, z1, ctx))
150 goto err;
151 if (!group->meth->field_mul(group, x1, z1, t1, ctx))
152 goto err;
153 if (!BN_GF2m_add(x1, x1, t2))
154 goto err;
155
156 ret = 1;
157
158err:
159 BN_CTX_end(ctx);
160 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 */
172static int
173gf2m_Mxy(const EC_GROUP *group, const BIGNUM *x, const BIGNUM *y, BIGNUM *x1,
174 BIGNUM *z1, BIGNUM *x2, BIGNUM *z2, BN_CTX *ctx)
175{
176 BIGNUM *t3, *t4, *t5;
177 int ret = 0;
178
179 if (BN_is_zero(z1)) {
180 BN_zero(x2);
181 BN_zero(z2);
182 return 1;
183 }
184 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 BN_CTX_start(ctx);
193 if ((t3 = BN_CTX_get(ctx)) == NULL)
194 goto err;
195 if ((t4 = BN_CTX_get(ctx)) == NULL)
196 goto err;
197 if ((t5 = BN_CTX_get(ctx)) == NULL)
198 goto err;
199
200 if (!BN_one(t5))
201 goto err;
202
203 if (!group->meth->field_mul(group, t3, z1, z2, ctx))
204 goto err;
205
206 if (!group->meth->field_mul(group, z1, z1, x, ctx))
207 goto err;
208 if (!BN_GF2m_add(z1, z1, x1))
209 goto err;
210 if (!group->meth->field_mul(group, z2, z2, x, ctx))
211 goto err;
212 if (!group->meth->field_mul(group, x1, z2, x1, ctx))
213 goto err;
214 if (!BN_GF2m_add(z2, z2, x2))
215 goto err;
216
217 if (!group->meth->field_mul(group, z2, z2, z1, ctx))
218 goto err;
219 if (!group->meth->field_sqr(group, t4, x, ctx))
220 goto err;
221 if (!BN_GF2m_add(t4, t4, y))
222 goto err;
223 if (!group->meth->field_mul(group, t4, t4, t3, ctx))
224 goto err;
225 if (!BN_GF2m_add(t4, t4, z2))
226 goto err;
227
228 if (!group->meth->field_mul(group, t3, t3, x, ctx))
229 goto err;
230 if (!group->meth->field_div(group, t3, t5, t3, ctx))
231 goto err;
232 if (!group->meth->field_mul(group, t4, t3, t4, ctx))
233 goto err;
234 if (!group->meth->field_mul(group, x2, x1, t3, ctx))
235 goto err;
236 if (!BN_GF2m_add(z2, x2, x))
237 goto err;
238
239 if (!group->meth->field_mul(group, z2, z2, t4, ctx))
240 goto err;
241 if (!BN_GF2m_add(z2, z2, y))
242 goto err;
243
244 ret = 2;
245
246err:
247 BN_CTX_end(ctx);
248 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 */
261static int
262ec_GF2m_montgomery_point_multiply(const EC_GROUP *group, EC_POINT *r,
263 const BIGNUM *scalar, const EC_POINT *point, BN_CTX *ctx)
264{
265 BIGNUM *x1, *x2, *z1, *z2;
266 int ret = 0, i;
267 BN_ULONG mask, word;
268
269 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 if ((scalar == NULL) || BN_is_zero(scalar) || (point == NULL) ||
275 EC_POINT_is_at_infinity(group, point) > 0) {
276 return EC_POINT_set_to_infinity(group, r);
277 }
278 /* only support affine coordinates */
279 if (!point->Z_is_one)
280 return 0;
281
282 /* Since point_multiply is static we can guarantee that ctx != NULL. */
283 BN_CTX_start(ctx);
284 if ((x1 = BN_CTX_get(ctx)) == NULL)
285 goto err;
286 if ((z1 = BN_CTX_get(ctx)) == NULL)
287 goto err;
288
289 x2 = &r->X;
290 z2 = &r->Y;
291
292 if (!bn_wexpand(x1, group->field.top))
293 goto err;
294 if (!bn_wexpand(z1, group->field.top))
295 goto err;
296 if (!bn_wexpand(x2, group->field.top))
297 goto err;
298 if (!bn_wexpand(z2, group->field.top))
299 goto err;
300
301 if (!BN_GF2m_mod_arr(x1, &point->X, group->poly))
302 goto err; /* x1 = x */
303 if (!BN_one(z1))
304 goto err; /* z1 = 1 */
305 if (!group->meth->field_sqr(group, z2, x1, ctx))
306 goto err; /* z2 = x1^2 = x^2 */
307 if (!group->meth->field_sqr(group, x2, z2, ctx))
308 goto err;
309 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 i = scalar->top - 1;
314 mask = BN_TBIT;
315 word = scalar->d[i];
316 while (!(word & mask))
317 mask >>= 1;
318 mask >>= 1;
319 /* if top most bit was at word break, go to next word */
320 if (!mask) {
321 i--;
322 mask = BN_TBIT;
323 }
324 for (; i >= 0; i--) {
325 word = scalar->d[i];
326 while (mask) {
327 BN_consttime_swap(word & mask, x1, x2, group->field.top);
328 BN_consttime_swap(word & mask, z1, z2, group->field.top);
329 if (!gf2m_Madd(group, &point->X, x2, z2, x1, z1, ctx))
330 goto err;
331 if (!gf2m_Mdouble(group, x1, z1, ctx))
332 goto err;
333 BN_consttime_swap(word & mask, x1, x2, group->field.top);
334 BN_consttime_swap(word & mask, z1, z2, group->field.top);
335 mask >>= 1;
336 }
337 mask = BN_TBIT;
338 }
339
340 /* convert out of "projective" coordinates */
341 i = gf2m_Mxy(group, &point->X, &point->Y, x1, z1, x2, z2, ctx);
342 if (i == 0)
343 goto err;
344 else if (i == 1) {
345 if (!EC_POINT_set_to_infinity(group, r))
346 goto err;
347 } else {
348 if (!BN_one(&r->Z))
349 goto err;
350 r->Z_is_one = 1;
351 }
352
353 /* GF(2^m) field elements should always have BIGNUM::neg = 0 */
354 BN_set_negative(&r->X, 0);
355 BN_set_negative(&r->Y, 0);
356
357 ret = 1;
358
359err:
360 BN_CTX_end(ctx);
361 return ret;
362}
363
364
365/* Computes the sum
366 * scalar*group->generator + scalars[0]*points[0] + ... + scalars[num-1]*points[num-1]
367 * gracefully ignoring NULL scalar values.
368 */
369int
370ec_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{
373 BN_CTX *new_ctx = NULL;
374 int ret = 0;
375 size_t i;
376 EC_POINT *p = NULL;
377 EC_POINT *acc = NULL;
378
379 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 if ((scalar && (num > 1)) || (num > 2) ||
391 (num == 0 && EC_GROUP_have_precompute_mult(group))) {
392 ret = ec_wNAF_mul(group, r, scalar, num, points, scalars, ctx);
393 goto err;
394 }
395 if ((p = EC_POINT_new(group)) == NULL)
396 goto err;
397 if ((acc = EC_POINT_new(group)) == NULL)
398 goto err;
399
400 if (!EC_POINT_set_to_infinity(group, acc))
401 goto err;
402
403 if (scalar) {
404 if (!ec_GF2m_montgomery_point_multiply(group, p, scalar, group->generator, ctx))
405 goto err;
406 if (BN_is_negative(scalar))
407 if (!group->meth->invert(group, p, ctx))
408 goto err;
409 if (!group->meth->add(group, acc, acc, p, ctx))
410 goto err;
411 }
412 for (i = 0; i < num; i++) {
413 if (!ec_GF2m_montgomery_point_multiply(group, p, scalars[i], points[i], ctx))
414 goto err;
415 if (BN_is_negative(scalars[i]))
416 if (!group->meth->invert(group, p, ctx))
417 goto err;
418 if (!group->meth->add(group, acc, acc, p, ctx))
419 goto err;
420 }
421
422 if (!EC_POINT_copy(r, acc))
423 goto err;
424
425 ret = 1;
426
427err:
428 EC_POINT_free(p);
429 EC_POINT_free(acc);
430 BN_CTX_free(new_ctx);
431 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
438int
439ec_GF2m_precompute_mult(EC_GROUP * group, BN_CTX * ctx)
440{
441 return ec_wNAF_precompute_mult(group, ctx);
442}
443
444int
445ec_GF2m_have_precompute_mult(const EC_GROUP * group)
446{
447 return ec_wNAF_have_precompute_mult(group);
448}
449
450#endif
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