Line data Source code
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 0 : static int gf2m_Mdouble(const EC_GROUP *group, BIGNUM *x, BIGNUM *z,
85 : BN_CTX *ctx)
86 : {
87 : BIGNUM *t1;
88 : 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 : goto err;
95 :
96 0 : if (!group->meth->field_sqr(group, x, x, ctx))
97 : goto err;
98 0 : if (!group->meth->field_sqr(group, t1, z, ctx))
99 : goto err;
100 0 : if (!group->meth->field_mul(group, z, x, t1, ctx))
101 : goto err;
102 0 : if (!group->meth->field_sqr(group, x, x, ctx))
103 : goto err;
104 0 : if (!group->meth->field_sqr(group, t1, t1, ctx))
105 : goto err;
106 0 : if (!group->meth->field_mul(group, t1, &group->b, t1, ctx))
107 : goto err;
108 0 : if (!BN_GF2m_add(x, x, t1))
109 : goto err;
110 :
111 : ret = 1;
112 :
113 : err:
114 0 : BN_CTX_end(ctx);
115 0 : return ret;
116 : }
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 0 : 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 : {
129 : BIGNUM *t1, *t2;
130 : 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 : goto err;
138 :
139 0 : if (!BN_copy(t1, x))
140 : goto err;
141 0 : if (!group->meth->field_mul(group, x1, x1, z2, ctx))
142 : goto err;
143 0 : if (!group->meth->field_mul(group, z1, z1, x2, ctx))
144 : goto err;
145 0 : if (!group->meth->field_mul(group, t2, x1, z1, ctx))
146 : goto err;
147 0 : if (!BN_GF2m_add(z1, z1, x1))
148 : goto err;
149 0 : if (!group->meth->field_sqr(group, z1, z1, ctx))
150 : goto err;
151 0 : if (!group->meth->field_mul(group, x1, z1, t1, ctx))
152 : goto err;
153 0 : if (!BN_GF2m_add(x1, x1, t2))
154 : goto err;
155 :
156 : ret = 1;
157 :
158 : err:
159 0 : BN_CTX_end(ctx);
160 0 : return ret;
161 : }
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 0 : 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 : {
177 : BIGNUM *t3, *t4, *t5;
178 : 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 : }
185 :
186 0 : if (BN_is_zero(z2)) {
187 0 : if (!BN_copy(x2, x))
188 : return 0;
189 0 : if (!BN_GF2m_add(z2, x, y))
190 : return 0;
191 0 : return 2;
192 : }
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 : goto err;
201 :
202 0 : if (!BN_one(t5))
203 : goto err;
204 :
205 0 : if (!group->meth->field_mul(group, t3, z1, z2, ctx))
206 : goto err;
207 :
208 0 : if (!group->meth->field_mul(group, z1, z1, x, ctx))
209 : goto err;
210 0 : if (!BN_GF2m_add(z1, z1, x1))
211 : goto err;
212 0 : if (!group->meth->field_mul(group, z2, z2, x, ctx))
213 : goto err;
214 0 : if (!group->meth->field_mul(group, x1, z2, x1, ctx))
215 : goto err;
216 0 : if (!BN_GF2m_add(z2, z2, x2))
217 : goto err;
218 :
219 0 : if (!group->meth->field_mul(group, z2, z2, z1, ctx))
220 : goto err;
221 0 : if (!group->meth->field_sqr(group, t4, x, ctx))
222 : goto err;
223 0 : if (!BN_GF2m_add(t4, t4, y))
224 : goto err;
225 0 : if (!group->meth->field_mul(group, t4, t4, t3, ctx))
226 : goto err;
227 0 : if (!BN_GF2m_add(t4, t4, z2))
228 : goto err;
229 :
230 0 : if (!group->meth->field_mul(group, t3, t3, x, ctx))
231 : goto err;
232 0 : if (!group->meth->field_div(group, t3, t5, t3, ctx))
233 : goto err;
234 0 : if (!group->meth->field_mul(group, t4, t3, t4, ctx))
235 : goto err;
236 0 : if (!group->meth->field_mul(group, x2, x1, t3, ctx))
237 : goto err;
238 0 : if (!BN_GF2m_add(z2, x2, x))
239 : goto err;
240 :
241 0 : if (!group->meth->field_mul(group, z2, z2, t4, ctx))
242 : goto err;
243 0 : if (!BN_GF2m_add(z2, z2, y))
244 : goto err;
245 :
246 : ret = 2;
247 :
248 : err:
249 0 : BN_CTX_end(ctx);
250 0 : return ret;
251 : }
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 0 : 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 : {
269 : BIGNUM *x1, *x2, *z1, *z2;
270 : int ret = 0, i;
271 : 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 : }
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 : }
283 :
284 : /* only support affine coordinates */
285 0 : if (!point->Z_is_one)
286 : 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 : goto err;
296 :
297 0 : x2 = &r->X;
298 0 : z2 = &r->Y;
299 :
300 0 : bn_wexpand(x1, group->field.top);
301 0 : bn_wexpand(z1, group->field.top);
302 0 : bn_wexpand(x2, group->field.top);
303 0 : bn_wexpand(z2, group->field.top);
304 :
305 0 : if (!BN_GF2m_mod_arr(x1, &point->X, group->poly))
306 : goto err; /* x1 = x */
307 0 : if (!BN_one(z1))
308 : goto err; /* z1 = 1 */
309 0 : if (!group->meth->field_sqr(group, z2, x1, ctx))
310 : goto err; /* z2 = x1^2 = x^2 */
311 0 : if (!group->meth->field_sqr(group, x2, z2, ctx))
312 : goto err;
313 0 : if (!BN_GF2m_add(x2, x2, &group->b))
314 : goto err; /* x2 = x^4 + b */
315 :
316 : /* find top most bit and go one past it */
317 0 : i = scalar->top - 1;
318 : mask = BN_TBIT;
319 0 : word = scalar->d[i];
320 0 : while (!(word & mask))
321 0 : mask >>= 1;
322 0 : mask >>= 1;
323 : /* if top most bit was at word break, go to next word */
324 0 : if (!mask) {
325 0 : i--;
326 : mask = BN_TBIT;
327 : }
328 :
329 0 : for (; i >= 0; i--) {
330 0 : word = scalar->d[i];
331 0 : while (mask) {
332 0 : BN_consttime_swap(word & mask, x1, x2, group->field.top);
333 0 : BN_consttime_swap(word & mask, z1, z2, group->field.top);
334 0 : if (!gf2m_Madd(group, &point->X, x2, z2, x1, z1, ctx))
335 : goto err;
336 0 : if (!gf2m_Mdouble(group, x1, z1, ctx))
337 : goto err;
338 0 : BN_consttime_swap(word & mask, x1, x2, group->field.top);
339 0 : BN_consttime_swap(word & mask, z1, z2, group->field.top);
340 0 : mask >>= 1;
341 : }
342 : mask = BN_TBIT;
343 : }
344 :
345 : /* convert out of "projective" coordinates */
346 0 : i = gf2m_Mxy(group, &point->X, &point->Y, x1, z1, x2, z2, ctx);
347 0 : if (i == 0)
348 : goto err;
349 0 : else if (i == 1) {
350 0 : if (!EC_POINT_set_to_infinity(group, r))
351 : goto err;
352 : } else {
353 0 : if (!BN_one(&r->Z))
354 : goto err;
355 0 : r->Z_is_one = 1;
356 : }
357 :
358 : /* GF(2^m) field elements should always have BIGNUM::neg = 0 */
359 0 : BN_set_negative(&r->X, 0);
360 0 : BN_set_negative(&r->Y, 0);
361 :
362 : ret = 1;
363 :
364 : err:
365 0 : BN_CTX_end(ctx);
366 0 : return ret;
367 : }
368 :
369 : /*-
370 : * Computes the sum
371 : * scalar*group->generator + scalars[0]*points[0] + ... + scalars[num-1]*points[num-1]
372 : * gracefully ignoring NULL scalar values.
373 : */
374 0 : int ec_GF2m_simple_mul(const EC_GROUP *group, EC_POINT *r,
375 : const BIGNUM *scalar, size_t num,
376 : const EC_POINT *points[], const BIGNUM *scalars[],
377 : BN_CTX *ctx)
378 : {
379 : BN_CTX *new_ctx = NULL;
380 : int ret = 0;
381 : size_t i;
382 : EC_POINT *p = NULL;
383 : EC_POINT *acc = NULL;
384 :
385 0 : if (ctx == NULL) {
386 0 : ctx = new_ctx = BN_CTX_new();
387 0 : if (ctx == NULL)
388 : return 0;
389 : }
390 :
391 : /*
392 : * This implementation is more efficient than the wNAF implementation for
393 : * 2 or fewer points. Use the ec_wNAF_mul implementation for 3 or more
394 : * points, or if we can perform a fast multiplication based on
395 : * precomputation.
396 : */
397 0 : if ((scalar && (num > 1)) || (num > 2)
398 0 : || (num == 0 && EC_GROUP_have_precompute_mult(group))) {
399 0 : ret = ec_wNAF_mul(group, r, scalar, num, points, scalars, ctx);
400 0 : goto err;
401 : }
402 :
403 0 : if ((p = EC_POINT_new(group)) == NULL)
404 : goto err;
405 0 : if ((acc = EC_POINT_new(group)) == NULL)
406 : goto err;
407 :
408 0 : if (!EC_POINT_set_to_infinity(group, acc))
409 : goto err;
410 :
411 0 : if (scalar) {
412 0 : if (!ec_GF2m_montgomery_point_multiply
413 0 : (group, p, scalar, group->generator, ctx))
414 : goto err;
415 0 : if (BN_is_negative(scalar))
416 0 : if (!group->meth->invert(group, p, ctx))
417 : goto err;
418 0 : if (!group->meth->add(group, acc, acc, p, ctx))
419 : goto err;
420 : }
421 :
422 0 : for (i = 0; i < num; i++) {
423 0 : if (!ec_GF2m_montgomery_point_multiply
424 0 : (group, p, scalars[i], points[i], ctx))
425 : goto err;
426 0 : if (BN_is_negative(scalars[i]))
427 0 : if (!group->meth->invert(group, p, ctx))
428 : goto err;
429 0 : if (!group->meth->add(group, acc, acc, p, ctx))
430 : goto err;
431 : }
432 :
433 0 : if (!EC_POINT_copy(r, acc))
434 : goto err;
435 :
436 : ret = 1;
437 :
438 : err:
439 0 : if (p)
440 0 : EC_POINT_free(p);
441 0 : if (acc)
442 0 : EC_POINT_free(acc);
443 0 : if (new_ctx != NULL)
444 0 : BN_CTX_free(new_ctx);
445 0 : return ret;
446 : }
447 :
448 : /*
449 : * Precomputation for point multiplication: fall back to wNAF methods because
450 : * ec_GF2m_simple_mul() uses ec_wNAF_mul() if appropriate
451 : */
452 :
453 0 : int ec_GF2m_precompute_mult(EC_GROUP *group, BN_CTX *ctx)
454 : {
455 0 : return ec_wNAF_precompute_mult(group, ctx);
456 : }
457 :
458 0 : int ec_GF2m_have_precompute_mult(const EC_GROUP *group)
459 : {
460 0 : return ec_wNAF_have_precompute_mult(group);
461 : }
462 :
463 : #endif
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