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authorcvs2svn <admin@example.com>2015-08-02 21:54:22 +0000
committercvs2svn <admin@example.com>2015-08-02 21:54:22 +0000
commited3760bf4be4a96a89233fb8f8b84a0d44725862 (patch)
tree5609c82060f75c53af0a7641d9b33a88574876cd /src/lib/libcrypto/ec/ec2_mult.c
parentf8b563fb5ba1524c821d37308f4e6abfc866bc3f (diff)
downloadopenbsd-OPENBSD_5_8_BASE.tar.gz
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This commit was manufactured by cvs2git to create tag 'OPENBSD_5_8_BASE'.OPENBSD_5_8_BASE
Diffstat (limited to 'src/lib/libcrypto/ec/ec2_mult.c')
-rw-r--r--src/lib/libcrypto/ec/ec2_mult.c446
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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 1.7 2015/02/09 15:49:22 jsing 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 bn_wexpand(x1, group->field.top);
293 bn_wexpand(z1, group->field.top);
294 bn_wexpand(x2, group->field.top);
295 bn_wexpand(z2, group->field.top);
296
297 if (!BN_GF2m_mod_arr(x1, &point->X, group->poly))
298 goto err; /* x1 = x */
299 if (!BN_one(z1))
300 goto err; /* z1 = 1 */
301 if (!group->meth->field_sqr(group, z2, x1, ctx))
302 goto err; /* z2 = x1^2 = x^2 */
303 if (!group->meth->field_sqr(group, x2, z2, ctx))
304 goto err;
305 if (!BN_GF2m_add(x2, x2, &group->b))
306 goto err; /* x2 = x^4 + b */
307
308 /* find top most bit and go one past it */
309 i = scalar->top - 1;
310 mask = BN_TBIT;
311 word = scalar->d[i];
312 while (!(word & mask))
313 mask >>= 1;
314 mask >>= 1;
315 /* if top most bit was at word break, go to next word */
316 if (!mask) {
317 i--;
318 mask = BN_TBIT;
319 }
320 for (; i >= 0; i--) {
321 word = scalar->d[i];
322 while (mask) {
323 BN_consttime_swap(word & mask, x1, x2, group->field.top);
324 BN_consttime_swap(word & mask, z1, z2, group->field.top);
325 if (!gf2m_Madd(group, &point->X, x2, z2, x1, z1, ctx))
326 goto err;
327 if (!gf2m_Mdouble(group, x1, z1, ctx))
328 goto err;
329 BN_consttime_swap(word & mask, x1, x2, group->field.top);
330 BN_consttime_swap(word & mask, z1, z2, group->field.top);
331 mask >>= 1;
332 }
333 mask = BN_TBIT;
334 }
335
336 /* convert out of "projective" coordinates */
337 i = gf2m_Mxy(group, &point->X, &point->Y, x1, z1, x2, z2, ctx);
338 if (i == 0)
339 goto err;
340 else if (i == 1) {
341 if (!EC_POINT_set_to_infinity(group, r))
342 goto err;
343 } else {
344 if (!BN_one(&r->Z))
345 goto err;
346 r->Z_is_one = 1;
347 }
348
349 /* GF(2^m) field elements should always have BIGNUM::neg = 0 */
350 BN_set_negative(&r->X, 0);
351 BN_set_negative(&r->Y, 0);
352
353 ret = 1;
354
355err:
356 BN_CTX_end(ctx);
357 return ret;
358}
359
360
361/* Computes the sum
362 * scalar*group->generator + scalars[0]*points[0] + ... + scalars[num-1]*points[num-1]
363 * gracefully ignoring NULL scalar values.
364 */
365int
366ec_GF2m_simple_mul(const EC_GROUP *group, EC_POINT *r, const BIGNUM *scalar,
367 size_t num, const EC_POINT *points[], const BIGNUM *scalars[], BN_CTX *ctx)
368{
369 BN_CTX *new_ctx = NULL;
370 int ret = 0;
371 size_t i;
372 EC_POINT *p = NULL;
373 EC_POINT *acc = NULL;
374
375 if (ctx == NULL) {
376 ctx = new_ctx = BN_CTX_new();
377 if (ctx == NULL)
378 return 0;
379 }
380 /*
381 * This implementation is more efficient than the wNAF implementation
382 * for 2 or fewer points. Use the ec_wNAF_mul implementation for 3
383 * or more points, or if we can perform a fast multiplication based
384 * on precomputation.
385 */
386 if ((scalar && (num > 1)) || (num > 2) ||
387 (num == 0 && EC_GROUP_have_precompute_mult(group))) {
388 ret = ec_wNAF_mul(group, r, scalar, num, points, scalars, ctx);
389 goto err;
390 }
391 if ((p = EC_POINT_new(group)) == NULL)
392 goto err;
393 if ((acc = EC_POINT_new(group)) == NULL)
394 goto err;
395
396 if (!EC_POINT_set_to_infinity(group, acc))
397 goto err;
398
399 if (scalar) {
400 if (!ec_GF2m_montgomery_point_multiply(group, p, scalar, group->generator, ctx))
401 goto err;
402 if (BN_is_negative(scalar))
403 if (!group->meth->invert(group, p, ctx))
404 goto err;
405 if (!group->meth->add(group, acc, acc, p, ctx))
406 goto err;
407 }
408 for (i = 0; i < num; i++) {
409 if (!ec_GF2m_montgomery_point_multiply(group, p, scalars[i], points[i], ctx))
410 goto err;
411 if (BN_is_negative(scalars[i]))
412 if (!group->meth->invert(group, p, ctx))
413 goto err;
414 if (!group->meth->add(group, acc, acc, p, ctx))
415 goto err;
416 }
417
418 if (!EC_POINT_copy(r, acc))
419 goto err;
420
421 ret = 1;
422
423err:
424 EC_POINT_free(p);
425 EC_POINT_free(acc);
426 BN_CTX_free(new_ctx);
427 return ret;
428}
429
430
431/* Precomputation for point multiplication: fall back to wNAF methods
432 * because ec_GF2m_simple_mul() uses ec_wNAF_mul() if appropriate */
433
434int
435ec_GF2m_precompute_mult(EC_GROUP * group, BN_CTX * ctx)
436{
437 return ec_wNAF_precompute_mult(group, ctx);
438}
439
440int
441ec_GF2m_have_precompute_mult(const EC_GROUP * group)
442{
443 return ec_wNAF_have_precompute_mult(group);
444}
445
446#endif
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