1 /* Originally written by Bodo Moeller for the OpenSSL project.
2 * ====================================================================
3 * Copyright (c) 1998-2005 The OpenSSL Project. All rights reserved.
4 *
5 * Redistribution and use in source and binary forms, with or without
6 * modification, are permitted provided that the following conditions
7 * are met:
8 *
9 * 1. Redistributions of source code must retain the above copyright
10 * notice, this list of conditions and the following disclaimer.
11 *
12 * 2. Redistributions in binary form must reproduce the above copyright
13 * notice, this list of conditions and the following disclaimer in
14 * the documentation and/or other materials provided with the
15 * distribution.
16 *
17 * 3. All advertising materials mentioning features or use of this
18 * software must display the following acknowledgment:
19 * "This product includes software developed by the OpenSSL Project
20 * for use in the OpenSSL Toolkit. (http://www.openssl.org/)"
21 *
22 * 4. The names "OpenSSL Toolkit" and "OpenSSL Project" must not be used to
23 * endorse or promote products derived from this software without
24 * prior written permission. For written permission, please contact
25 * openssl-core@openssl.org.
26 *
27 * 5. Products derived from this software may not be called "OpenSSL"
28 * nor may "OpenSSL" appear in their names without prior written
29 * permission of the OpenSSL Project.
30 *
31 * 6. Redistributions of any form whatsoever must retain the following
32 * acknowledgment:
33 * "This product includes software developed by the OpenSSL Project
34 * for use in the OpenSSL Toolkit (http://www.openssl.org/)"
35 *
36 * THIS SOFTWARE IS PROVIDED BY THE OpenSSL PROJECT ``AS IS'' AND ANY
37 * EXPRESSED OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
38 * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR
39 * PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE OpenSSL PROJECT OR
40 * ITS CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL,
41 * SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT
42 * NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES;
43 * LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
44 * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT,
45 * STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE)
46 * ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED
47 * OF THE POSSIBILITY OF SUCH DAMAGE.
48 * ====================================================================
49 *
50 * This product includes cryptographic software written by Eric Young
51 * (eay@cryptsoft.com). This product includes software written by Tim
52 * Hudson (tjh@cryptsoft.com).
53 *
54 */
55 /* ====================================================================
56 * Copyright 2002 Sun Microsystems, Inc. ALL RIGHTS RESERVED.
57 *
58 * Portions of the attached software ("Contribution") are developed by
59 * SUN MICROSYSTEMS, INC., and are contributed to the OpenSSL project.
60 *
61 * The Contribution is licensed pursuant to the OpenSSL open source
62 * license provided above.
63 *
64 * The elliptic curve binary polynomial software is originally written by
65 * Sheueling Chang Shantz and Douglas Stebila of Sun Microsystems
66 * Laboratories. */
67
68 #include <openssl/ec.h>
69
70 #include <string.h>
71
72 #include <openssl/bn.h>
73 #include <openssl/err.h>
74 #include <openssl/mem.h>
75
76 #include "internal.h"
77
78
79 /* Most method functions in this file are designed to work with non-trivial
80 * representations of field elements if necessary (see ecp_mont.c): while
81 * standard modular addition and subtraction are used, the field_mul and
82 * field_sqr methods will be used for multiplication, and field_encode and
83 * field_decode (if defined) will be used for converting between
84 * representations.
85
86 * Functions ec_GFp_simple_points_make_affine() and
87 * ec_GFp_simple_point_get_affine_coordinates() specifically assume that if a
88 * non-trivial representation is used, it is a Montgomery representation (i.e.
89 * 'encoding' means multiplying by some factor R). */
90
ec_GFp_simple_group_init(EC_GROUP * group)91 int ec_GFp_simple_group_init(EC_GROUP *group) {
92 BN_init(&group->field);
93 BN_init(&group->a);
94 BN_init(&group->b);
95 group->a_is_minus3 = 0;
96 return 1;
97 }
98
ec_GFp_simple_group_finish(EC_GROUP * group)99 void ec_GFp_simple_group_finish(EC_GROUP *group) {
100 BN_free(&group->field);
101 BN_free(&group->a);
102 BN_free(&group->b);
103 }
104
ec_GFp_simple_group_clear_finish(EC_GROUP * group)105 void ec_GFp_simple_group_clear_finish(EC_GROUP *group) {
106 BN_clear_free(&group->field);
107 BN_clear_free(&group->a);
108 BN_clear_free(&group->b);
109 }
110
ec_GFp_simple_group_copy(EC_GROUP * dest,const EC_GROUP * src)111 int ec_GFp_simple_group_copy(EC_GROUP *dest, const EC_GROUP *src) {
112 if (!BN_copy(&dest->field, &src->field) ||
113 !BN_copy(&dest->a, &src->a) ||
114 !BN_copy(&dest->b, &src->b)) {
115 return 0;
116 }
117
118 dest->a_is_minus3 = src->a_is_minus3;
119 return 1;
120 }
121
ec_GFp_simple_group_set_curve(EC_GROUP * group,const BIGNUM * p,const BIGNUM * a,const BIGNUM * b,BN_CTX * ctx)122 int ec_GFp_simple_group_set_curve(EC_GROUP *group, const BIGNUM *p,
123 const BIGNUM *a, const BIGNUM *b,
124 BN_CTX *ctx) {
125 int ret = 0;
126 BN_CTX *new_ctx = NULL;
127 BIGNUM *tmp_a;
128
129 /* p must be a prime > 3 */
130 if (BN_num_bits(p) <= 2 || !BN_is_odd(p)) {
131 OPENSSL_PUT_ERROR(EC, EC_R_INVALID_FIELD);
132 return 0;
133 }
134
135 if (ctx == NULL) {
136 ctx = new_ctx = BN_CTX_new();
137 if (ctx == NULL) {
138 return 0;
139 }
140 }
141
142 BN_CTX_start(ctx);
143 tmp_a = BN_CTX_get(ctx);
144 if (tmp_a == NULL) {
145 goto err;
146 }
147
148 /* group->field */
149 if (!BN_copy(&group->field, p)) {
150 goto err;
151 }
152 BN_set_negative(&group->field, 0);
153
154 /* group->a */
155 if (!BN_nnmod(tmp_a, a, p, ctx)) {
156 goto err;
157 }
158 if (group->meth->field_encode) {
159 if (!group->meth->field_encode(group, &group->a, tmp_a, ctx)) {
160 goto err;
161 }
162 } else if (!BN_copy(&group->a, tmp_a)) {
163 goto err;
164 }
165
166 /* group->b */
167 if (!BN_nnmod(&group->b, b, p, ctx)) {
168 goto err;
169 }
170 if (group->meth->field_encode &&
171 !group->meth->field_encode(group, &group->b, &group->b, ctx)) {
172 goto err;
173 }
174
175 /* group->a_is_minus3 */
176 if (!BN_add_word(tmp_a, 3)) {
177 goto err;
178 }
179 group->a_is_minus3 = (0 == BN_cmp(tmp_a, &group->field));
180
181 ret = 1;
182
183 err:
184 BN_CTX_end(ctx);
185 BN_CTX_free(new_ctx);
186 return ret;
187 }
188
ec_GFp_simple_group_get_curve(const EC_GROUP * group,BIGNUM * p,BIGNUM * a,BIGNUM * b,BN_CTX * ctx)189 int ec_GFp_simple_group_get_curve(const EC_GROUP *group, BIGNUM *p, BIGNUM *a,
190 BIGNUM *b, BN_CTX *ctx) {
191 int ret = 0;
192 BN_CTX *new_ctx = NULL;
193
194 if (p != NULL && !BN_copy(p, &group->field)) {
195 return 0;
196 }
197
198 if (a != NULL || b != NULL) {
199 if (group->meth->field_decode) {
200 if (ctx == NULL) {
201 ctx = new_ctx = BN_CTX_new();
202 if (ctx == NULL) {
203 return 0;
204 }
205 }
206 if (a != NULL && !group->meth->field_decode(group, a, &group->a, ctx)) {
207 goto err;
208 }
209 if (b != NULL && !group->meth->field_decode(group, b, &group->b, ctx)) {
210 goto err;
211 }
212 } else {
213 if (a != NULL && !BN_copy(a, &group->a)) {
214 goto err;
215 }
216 if (b != NULL && !BN_copy(b, &group->b)) {
217 goto err;
218 }
219 }
220 }
221
222 ret = 1;
223
224 err:
225 BN_CTX_free(new_ctx);
226 return ret;
227 }
228
ec_GFp_simple_group_get_degree(const EC_GROUP * group)229 unsigned ec_GFp_simple_group_get_degree(const EC_GROUP *group) {
230 return BN_num_bits(&group->field);
231 }
232
ec_GFp_simple_group_check_discriminant(const EC_GROUP * group,BN_CTX * ctx)233 int ec_GFp_simple_group_check_discriminant(const EC_GROUP *group, BN_CTX *ctx) {
234 int ret = 0;
235 BIGNUM *a, *b, *order, *tmp_1, *tmp_2;
236 const BIGNUM *p = &group->field;
237 BN_CTX *new_ctx = NULL;
238
239 if (ctx == NULL) {
240 ctx = new_ctx = BN_CTX_new();
241 if (ctx == NULL) {
242 OPENSSL_PUT_ERROR(EC, ERR_R_MALLOC_FAILURE);
243 goto err;
244 }
245 }
246 BN_CTX_start(ctx);
247 a = BN_CTX_get(ctx);
248 b = BN_CTX_get(ctx);
249 tmp_1 = BN_CTX_get(ctx);
250 tmp_2 = BN_CTX_get(ctx);
251 order = BN_CTX_get(ctx);
252 if (order == NULL) {
253 goto err;
254 }
255
256 if (group->meth->field_decode) {
257 if (!group->meth->field_decode(group, a, &group->a, ctx) ||
258 !group->meth->field_decode(group, b, &group->b, ctx)) {
259 goto err;
260 }
261 } else {
262 if (!BN_copy(a, &group->a) || !BN_copy(b, &group->b)) {
263 goto err;
264 }
265 }
266
267 /* check the discriminant:
268 * y^2 = x^3 + a*x + b is an elliptic curve <=> 4*a^3 + 27*b^2 != 0 (mod p)
269 * 0 =< a, b < p */
270 if (BN_is_zero(a)) {
271 if (BN_is_zero(b)) {
272 goto err;
273 }
274 } else if (!BN_is_zero(b)) {
275 if (!BN_mod_sqr(tmp_1, a, p, ctx) ||
276 !BN_mod_mul(tmp_2, tmp_1, a, p, ctx) ||
277 !BN_lshift(tmp_1, tmp_2, 2)) {
278 goto err;
279 }
280 /* tmp_1 = 4*a^3 */
281
282 if (!BN_mod_sqr(tmp_2, b, p, ctx) ||
283 !BN_mul_word(tmp_2, 27)) {
284 goto err;
285 }
286 /* tmp_2 = 27*b^2 */
287
288 if (!BN_mod_add(a, tmp_1, tmp_2, p, ctx) ||
289 BN_is_zero(a)) {
290 goto err;
291 }
292 }
293 ret = 1;
294
295 err:
296 if (ctx != NULL) {
297 BN_CTX_end(ctx);
298 }
299 BN_CTX_free(new_ctx);
300 return ret;
301 }
302
ec_GFp_simple_point_init(EC_POINT * point)303 int ec_GFp_simple_point_init(EC_POINT *point) {
304 BN_init(&point->X);
305 BN_init(&point->Y);
306 BN_init(&point->Z);
307 point->Z_is_one = 0;
308
309 return 1;
310 }
311
ec_GFp_simple_point_finish(EC_POINT * point)312 void ec_GFp_simple_point_finish(EC_POINT *point) {
313 BN_free(&point->X);
314 BN_free(&point->Y);
315 BN_free(&point->Z);
316 }
317
ec_GFp_simple_point_clear_finish(EC_POINT * point)318 void ec_GFp_simple_point_clear_finish(EC_POINT *point) {
319 BN_clear_free(&point->X);
320 BN_clear_free(&point->Y);
321 BN_clear_free(&point->Z);
322 point->Z_is_one = 0;
323 }
324
ec_GFp_simple_point_copy(EC_POINT * dest,const EC_POINT * src)325 int ec_GFp_simple_point_copy(EC_POINT *dest, const EC_POINT *src) {
326 if (!BN_copy(&dest->X, &src->X) ||
327 !BN_copy(&dest->Y, &src->Y) ||
328 !BN_copy(&dest->Z, &src->Z)) {
329 return 0;
330 }
331 dest->Z_is_one = src->Z_is_one;
332
333 return 1;
334 }
335
ec_GFp_simple_point_set_to_infinity(const EC_GROUP * group,EC_POINT * point)336 int ec_GFp_simple_point_set_to_infinity(const EC_GROUP *group,
337 EC_POINT *point) {
338 point->Z_is_one = 0;
339 BN_zero(&point->Z);
340 return 1;
341 }
342
ec_GFp_simple_set_Jprojective_coordinates_GFp(const EC_GROUP * group,EC_POINT * point,const BIGNUM * x,const BIGNUM * y,const BIGNUM * z,BN_CTX * ctx)343 int ec_GFp_simple_set_Jprojective_coordinates_GFp(
344 const EC_GROUP *group, EC_POINT *point, const BIGNUM *x, const BIGNUM *y,
345 const BIGNUM *z, BN_CTX *ctx) {
346 BN_CTX *new_ctx = NULL;
347 int ret = 0;
348
349 if (ctx == NULL) {
350 ctx = new_ctx = BN_CTX_new();
351 if (ctx == NULL) {
352 return 0;
353 }
354 }
355
356 if (x != NULL) {
357 if (!BN_nnmod(&point->X, x, &group->field, ctx)) {
358 goto err;
359 }
360 if (group->meth->field_encode &&
361 !group->meth->field_encode(group, &point->X, &point->X, ctx)) {
362 goto err;
363 }
364 }
365
366 if (y != NULL) {
367 if (!BN_nnmod(&point->Y, y, &group->field, ctx)) {
368 goto err;
369 }
370 if (group->meth->field_encode &&
371 !group->meth->field_encode(group, &point->Y, &point->Y, ctx)) {
372 goto err;
373 }
374 }
375
376 if (z != NULL) {
377 int Z_is_one;
378
379 if (!BN_nnmod(&point->Z, z, &group->field, ctx)) {
380 goto err;
381 }
382 Z_is_one = BN_is_one(&point->Z);
383 if (group->meth->field_encode) {
384 if (Z_is_one && (group->meth->field_set_to_one != 0)) {
385 if (!group->meth->field_set_to_one(group, &point->Z, ctx)) {
386 goto err;
387 }
388 } else if (!group->meth->field_encode(group, &point->Z, &point->Z, ctx)) {
389 goto err;
390 }
391 }
392 point->Z_is_one = Z_is_one;
393 }
394
395 ret = 1;
396
397 err:
398 BN_CTX_free(new_ctx);
399 return ret;
400 }
401
ec_GFp_simple_get_Jprojective_coordinates_GFp(const EC_GROUP * group,const EC_POINT * point,BIGNUM * x,BIGNUM * y,BIGNUM * z,BN_CTX * ctx)402 int ec_GFp_simple_get_Jprojective_coordinates_GFp(const EC_GROUP *group,
403 const EC_POINT *point,
404 BIGNUM *x, BIGNUM *y,
405 BIGNUM *z, BN_CTX *ctx) {
406 BN_CTX *new_ctx = NULL;
407 int ret = 0;
408
409 if (group->meth->field_decode != 0) {
410 if (ctx == NULL) {
411 ctx = new_ctx = BN_CTX_new();
412 if (ctx == NULL) {
413 return 0;
414 }
415 }
416
417 if (x != NULL && !group->meth->field_decode(group, x, &point->X, ctx)) {
418 goto err;
419 }
420 if (y != NULL && !group->meth->field_decode(group, y, &point->Y, ctx)) {
421 goto err;
422 }
423 if (z != NULL && !group->meth->field_decode(group, z, &point->Z, ctx)) {
424 goto err;
425 }
426 } else {
427 if (x != NULL && !BN_copy(x, &point->X)) {
428 goto err;
429 }
430 if (y != NULL && !BN_copy(y, &point->Y)) {
431 goto err;
432 }
433 if (z != NULL && !BN_copy(z, &point->Z)) {
434 goto err;
435 }
436 }
437
438 ret = 1;
439
440 err:
441 BN_CTX_free(new_ctx);
442 return ret;
443 }
444
ec_GFp_simple_point_set_affine_coordinates(const EC_GROUP * group,EC_POINT * point,const BIGNUM * x,const BIGNUM * y,BN_CTX * ctx)445 int ec_GFp_simple_point_set_affine_coordinates(const EC_GROUP *group,
446 EC_POINT *point, const BIGNUM *x,
447 const BIGNUM *y, BN_CTX *ctx) {
448 if (x == NULL || y == NULL) {
449 /* unlike for projective coordinates, we do not tolerate this */
450 OPENSSL_PUT_ERROR(EC, ERR_R_PASSED_NULL_PARAMETER);
451 return 0;
452 }
453
454 return ec_point_set_Jprojective_coordinates_GFp(group, point, x, y,
455 BN_value_one(), ctx);
456 }
457
ec_GFp_simple_point_get_affine_coordinates(const EC_GROUP * group,const EC_POINT * point,BIGNUM * x,BIGNUM * y,BN_CTX * ctx)458 int ec_GFp_simple_point_get_affine_coordinates(const EC_GROUP *group,
459 const EC_POINT *point, BIGNUM *x,
460 BIGNUM *y, BN_CTX *ctx) {
461 BN_CTX *new_ctx = NULL;
462 BIGNUM *Z, *Z_1, *Z_2, *Z_3;
463 const BIGNUM *Z_;
464 int ret = 0;
465
466 if (EC_POINT_is_at_infinity(group, point)) {
467 OPENSSL_PUT_ERROR(EC, EC_R_POINT_AT_INFINITY);
468 return 0;
469 }
470
471 if (ctx == NULL) {
472 ctx = new_ctx = BN_CTX_new();
473 if (ctx == NULL) {
474 return 0;
475 }
476 }
477
478 BN_CTX_start(ctx);
479 Z = BN_CTX_get(ctx);
480 Z_1 = BN_CTX_get(ctx);
481 Z_2 = BN_CTX_get(ctx);
482 Z_3 = BN_CTX_get(ctx);
483 if (Z == NULL || Z_1 == NULL || Z_2 == NULL || Z_3 == NULL) {
484 goto err;
485 }
486
487 /* transform (X, Y, Z) into (x, y) := (X/Z^2, Y/Z^3) */
488
489 if (group->meth->field_decode) {
490 if (!group->meth->field_decode(group, Z, &point->Z, ctx)) {
491 goto err;
492 }
493 Z_ = Z;
494 } else {
495 Z_ = &point->Z;
496 }
497
498 if (BN_is_one(Z_)) {
499 if (group->meth->field_decode) {
500 if (x != NULL && !group->meth->field_decode(group, x, &point->X, ctx)) {
501 goto err;
502 }
503 if (y != NULL && !group->meth->field_decode(group, y, &point->Y, ctx)) {
504 goto err;
505 }
506 } else {
507 if (x != NULL && !BN_copy(x, &point->X)) {
508 goto err;
509 }
510 if (y != NULL && !BN_copy(y, &point->Y)) {
511 goto err;
512 }
513 }
514 } else {
515 if (!BN_mod_inverse(Z_1, Z_, &group->field, ctx)) {
516 OPENSSL_PUT_ERROR(EC, ERR_R_BN_LIB);
517 goto err;
518 }
519
520 if (group->meth->field_encode == 0) {
521 /* field_sqr works on standard representation */
522 if (!group->meth->field_sqr(group, Z_2, Z_1, ctx)) {
523 goto err;
524 }
525 } else if (!BN_mod_sqr(Z_2, Z_1, &group->field, ctx)) {
526 goto err;
527 }
528
529 /* in the Montgomery case, field_mul will cancel out Montgomery factor in
530 * X: */
531 if (x != NULL && !group->meth->field_mul(group, x, &point->X, Z_2, ctx)) {
532 goto err;
533 }
534
535 if (y != NULL) {
536 if (group->meth->field_encode == 0) {
537 /* field_mul works on standard representation */
538 if (!group->meth->field_mul(group, Z_3, Z_2, Z_1, ctx)) {
539 goto err;
540 }
541 } else if (!BN_mod_mul(Z_3, Z_2, Z_1, &group->field, ctx)) {
542 goto err;
543 }
544
545 /* in the Montgomery case, field_mul will cancel out Montgomery factor in
546 * Y: */
547 if (!group->meth->field_mul(group, y, &point->Y, Z_3, ctx)) {
548 goto err;
549 }
550 }
551 }
552
553 ret = 1;
554
555 err:
556 BN_CTX_end(ctx);
557 BN_CTX_free(new_ctx);
558 return ret;
559 }
560
ec_GFp_simple_add(const EC_GROUP * group,EC_POINT * r,const EC_POINT * a,const EC_POINT * b,BN_CTX * ctx)561 int ec_GFp_simple_add(const EC_GROUP *group, EC_POINT *r, const EC_POINT *a,
562 const EC_POINT *b, BN_CTX *ctx) {
563 int (*field_mul)(const EC_GROUP *, BIGNUM *, const BIGNUM *, const BIGNUM *,
564 BN_CTX *);
565 int (*field_sqr)(const EC_GROUP *, BIGNUM *, const BIGNUM *, BN_CTX *);
566 const BIGNUM *p;
567 BN_CTX *new_ctx = NULL;
568 BIGNUM *n0, *n1, *n2, *n3, *n4, *n5, *n6;
569 int ret = 0;
570
571 if (a == b) {
572 return EC_POINT_dbl(group, r, a, ctx);
573 }
574 if (EC_POINT_is_at_infinity(group, a)) {
575 return EC_POINT_copy(r, b);
576 }
577 if (EC_POINT_is_at_infinity(group, b)) {
578 return EC_POINT_copy(r, a);
579 }
580
581 field_mul = group->meth->field_mul;
582 field_sqr = group->meth->field_sqr;
583 p = &group->field;
584
585 if (ctx == NULL) {
586 ctx = new_ctx = BN_CTX_new();
587 if (ctx == NULL) {
588 return 0;
589 }
590 }
591
592 BN_CTX_start(ctx);
593 n0 = BN_CTX_get(ctx);
594 n1 = BN_CTX_get(ctx);
595 n2 = BN_CTX_get(ctx);
596 n3 = BN_CTX_get(ctx);
597 n4 = BN_CTX_get(ctx);
598 n5 = BN_CTX_get(ctx);
599 n6 = BN_CTX_get(ctx);
600 if (n6 == NULL) {
601 goto end;
602 }
603
604 /* Note that in this function we must not read components of 'a' or 'b'
605 * once we have written the corresponding components of 'r'.
606 * ('r' might be one of 'a' or 'b'.)
607 */
608
609 /* n1, n2 */
610 if (b->Z_is_one) {
611 if (!BN_copy(n1, &a->X) || !BN_copy(n2, &a->Y)) {
612 goto end;
613 }
614 /* n1 = X_a */
615 /* n2 = Y_a */
616 } else {
617 if (!field_sqr(group, n0, &b->Z, ctx) ||
618 !field_mul(group, n1, &a->X, n0, ctx)) {
619 goto end;
620 }
621 /* n1 = X_a * Z_b^2 */
622
623 if (!field_mul(group, n0, n0, &b->Z, ctx) ||
624 !field_mul(group, n2, &a->Y, n0, ctx)) {
625 goto end;
626 }
627 /* n2 = Y_a * Z_b^3 */
628 }
629
630 /* n3, n4 */
631 if (a->Z_is_one) {
632 if (!BN_copy(n3, &b->X) || !BN_copy(n4, &b->Y)) {
633 goto end;
634 }
635 /* n3 = X_b */
636 /* n4 = Y_b */
637 } else {
638 if (!field_sqr(group, n0, &a->Z, ctx) ||
639 !field_mul(group, n3, &b->X, n0, ctx)) {
640 goto end;
641 }
642 /* n3 = X_b * Z_a^2 */
643
644 if (!field_mul(group, n0, n0, &a->Z, ctx) ||
645 !field_mul(group, n4, &b->Y, n0, ctx)) {
646 goto end;
647 }
648 /* n4 = Y_b * Z_a^3 */
649 }
650
651 /* n5, n6 */
652 if (!BN_mod_sub_quick(n5, n1, n3, p) ||
653 !BN_mod_sub_quick(n6, n2, n4, p)) {
654 goto end;
655 }
656 /* n5 = n1 - n3 */
657 /* n6 = n2 - n4 */
658
659 if (BN_is_zero(n5)) {
660 if (BN_is_zero(n6)) {
661 /* a is the same point as b */
662 BN_CTX_end(ctx);
663 ret = EC_POINT_dbl(group, r, a, ctx);
664 ctx = NULL;
665 goto end;
666 } else {
667 /* a is the inverse of b */
668 BN_zero(&r->Z);
669 r->Z_is_one = 0;
670 ret = 1;
671 goto end;
672 }
673 }
674
675 /* 'n7', 'n8' */
676 if (!BN_mod_add_quick(n1, n1, n3, p) ||
677 !BN_mod_add_quick(n2, n2, n4, p)) {
678 goto end;
679 }
680 /* 'n7' = n1 + n3 */
681 /* 'n8' = n2 + n4 */
682
683 /* Z_r */
684 if (a->Z_is_one && b->Z_is_one) {
685 if (!BN_copy(&r->Z, n5)) {
686 goto end;
687 }
688 } else {
689 if (a->Z_is_one) {
690 if (!BN_copy(n0, &b->Z)) {
691 goto end;
692 }
693 } else if (b->Z_is_one) {
694 if (!BN_copy(n0, &a->Z)) {
695 goto end;
696 }
697 } else if (!field_mul(group, n0, &a->Z, &b->Z, ctx)) {
698 goto end;
699 }
700 if (!field_mul(group, &r->Z, n0, n5, ctx)) {
701 goto end;
702 }
703 }
704 r->Z_is_one = 0;
705 /* Z_r = Z_a * Z_b * n5 */
706
707 /* X_r */
708 if (!field_sqr(group, n0, n6, ctx) ||
709 !field_sqr(group, n4, n5, ctx) ||
710 !field_mul(group, n3, n1, n4, ctx) ||
711 !BN_mod_sub_quick(&r->X, n0, n3, p)) {
712 goto end;
713 }
714 /* X_r = n6^2 - n5^2 * 'n7' */
715
716 /* 'n9' */
717 if (!BN_mod_lshift1_quick(n0, &r->X, p) ||
718 !BN_mod_sub_quick(n0, n3, n0, p)) {
719 goto end;
720 }
721 /* n9 = n5^2 * 'n7' - 2 * X_r */
722
723 /* Y_r */
724 if (!field_mul(group, n0, n0, n6, ctx) ||
725 !field_mul(group, n5, n4, n5, ctx)) {
726 goto end; /* now n5 is n5^3 */
727 }
728 if (!field_mul(group, n1, n2, n5, ctx) ||
729 !BN_mod_sub_quick(n0, n0, n1, p)) {
730 goto end;
731 }
732 if (BN_is_odd(n0) && !BN_add(n0, n0, p)) {
733 goto end;
734 }
735 /* now 0 <= n0 < 2*p, and n0 is even */
736 if (!BN_rshift1(&r->Y, n0)) {
737 goto end;
738 }
739 /* Y_r = (n6 * 'n9' - 'n8' * 'n5^3') / 2 */
740
741 ret = 1;
742
743 end:
744 if (ctx) {
745 /* otherwise we already called BN_CTX_end */
746 BN_CTX_end(ctx);
747 }
748 BN_CTX_free(new_ctx);
749 return ret;
750 }
751
ec_GFp_simple_dbl(const EC_GROUP * group,EC_POINT * r,const EC_POINT * a,BN_CTX * ctx)752 int ec_GFp_simple_dbl(const EC_GROUP *group, EC_POINT *r, const EC_POINT *a,
753 BN_CTX *ctx) {
754 int (*field_mul)(const EC_GROUP *, BIGNUM *, const BIGNUM *, const BIGNUM *,
755 BN_CTX *);
756 int (*field_sqr)(const EC_GROUP *, BIGNUM *, const BIGNUM *, BN_CTX *);
757 const BIGNUM *p;
758 BN_CTX *new_ctx = NULL;
759 BIGNUM *n0, *n1, *n2, *n3;
760 int ret = 0;
761
762 if (EC_POINT_is_at_infinity(group, a)) {
763 BN_zero(&r->Z);
764 r->Z_is_one = 0;
765 return 1;
766 }
767
768 field_mul = group->meth->field_mul;
769 field_sqr = group->meth->field_sqr;
770 p = &group->field;
771
772 if (ctx == NULL) {
773 ctx = new_ctx = BN_CTX_new();
774 if (ctx == NULL) {
775 return 0;
776 }
777 }
778
779 BN_CTX_start(ctx);
780 n0 = BN_CTX_get(ctx);
781 n1 = BN_CTX_get(ctx);
782 n2 = BN_CTX_get(ctx);
783 n3 = BN_CTX_get(ctx);
784 if (n3 == NULL) {
785 goto err;
786 }
787
788 /* Note that in this function we must not read components of 'a'
789 * once we have written the corresponding components of 'r'.
790 * ('r' might the same as 'a'.)
791 */
792
793 /* n1 */
794 if (a->Z_is_one) {
795 if (!field_sqr(group, n0, &a->X, ctx) ||
796 !BN_mod_lshift1_quick(n1, n0, p) ||
797 !BN_mod_add_quick(n0, n0, n1, p) ||
798 !BN_mod_add_quick(n1, n0, &group->a, p)) {
799 goto err;
800 }
801 /* n1 = 3 * X_a^2 + a_curve */
802 } else if (group->a_is_minus3) {
803 if (!field_sqr(group, n1, &a->Z, ctx) ||
804 !BN_mod_add_quick(n0, &a->X, n1, p) ||
805 !BN_mod_sub_quick(n2, &a->X, n1, p) ||
806 !field_mul(group, n1, n0, n2, ctx) ||
807 !BN_mod_lshift1_quick(n0, n1, p) ||
808 !BN_mod_add_quick(n1, n0, n1, p)) {
809 goto err;
810 }
811 /* n1 = 3 * (X_a + Z_a^2) * (X_a - Z_a^2)
812 * = 3 * X_a^2 - 3 * Z_a^4 */
813 } else {
814 if (!field_sqr(group, n0, &a->X, ctx) ||
815 !BN_mod_lshift1_quick(n1, n0, p) ||
816 !BN_mod_add_quick(n0, n0, n1, p) ||
817 !field_sqr(group, n1, &a->Z, ctx) ||
818 !field_sqr(group, n1, n1, ctx) ||
819 !field_mul(group, n1, n1, &group->a, ctx) ||
820 !BN_mod_add_quick(n1, n1, n0, p)) {
821 goto err;
822 }
823 /* n1 = 3 * X_a^2 + a_curve * Z_a^4 */
824 }
825
826 /* Z_r */
827 if (a->Z_is_one) {
828 if (!BN_copy(n0, &a->Y)) {
829 goto err;
830 }
831 } else if (!field_mul(group, n0, &a->Y, &a->Z, ctx)) {
832 goto err;
833 }
834 if (!BN_mod_lshift1_quick(&r->Z, n0, p)) {
835 goto err;
836 }
837 r->Z_is_one = 0;
838 /* Z_r = 2 * Y_a * Z_a */
839
840 /* n2 */
841 if (!field_sqr(group, n3, &a->Y, ctx) ||
842 !field_mul(group, n2, &a->X, n3, ctx) ||
843 !BN_mod_lshift_quick(n2, n2, 2, p)) {
844 goto err;
845 }
846 /* n2 = 4 * X_a * Y_a^2 */
847
848 /* X_r */
849 if (!BN_mod_lshift1_quick(n0, n2, p) ||
850 !field_sqr(group, &r->X, n1, ctx) ||
851 !BN_mod_sub_quick(&r->X, &r->X, n0, p)) {
852 goto err;
853 }
854 /* X_r = n1^2 - 2 * n2 */
855
856 /* n3 */
857 if (!field_sqr(group, n0, n3, ctx) ||
858 !BN_mod_lshift_quick(n3, n0, 3, p)) {
859 goto err;
860 }
861 /* n3 = 8 * Y_a^4 */
862
863 /* Y_r */
864 if (!BN_mod_sub_quick(n0, n2, &r->X, p) ||
865 !field_mul(group, n0, n1, n0, ctx) ||
866 !BN_mod_sub_quick(&r->Y, n0, n3, p)) {
867 goto err;
868 }
869 /* Y_r = n1 * (n2 - X_r) - n3 */
870
871 ret = 1;
872
873 err:
874 BN_CTX_end(ctx);
875 BN_CTX_free(new_ctx);
876 return ret;
877 }
878
ec_GFp_simple_invert(const EC_GROUP * group,EC_POINT * point,BN_CTX * ctx)879 int ec_GFp_simple_invert(const EC_GROUP *group, EC_POINT *point, BN_CTX *ctx) {
880 if (EC_POINT_is_at_infinity(group, point) || BN_is_zero(&point->Y)) {
881 /* point is its own inverse */
882 return 1;
883 }
884
885 return BN_usub(&point->Y, &group->field, &point->Y);
886 }
887
ec_GFp_simple_is_at_infinity(const EC_GROUP * group,const EC_POINT * point)888 int ec_GFp_simple_is_at_infinity(const EC_GROUP *group, const EC_POINT *point) {
889 return !point->Z_is_one && BN_is_zero(&point->Z);
890 }
891
ec_GFp_simple_is_on_curve(const EC_GROUP * group,const EC_POINT * point,BN_CTX * ctx)892 int ec_GFp_simple_is_on_curve(const EC_GROUP *group, const EC_POINT *point,
893 BN_CTX *ctx) {
894 int (*field_mul)(const EC_GROUP *, BIGNUM *, const BIGNUM *, const BIGNUM *,
895 BN_CTX *);
896 int (*field_sqr)(const EC_GROUP *, BIGNUM *, const BIGNUM *, BN_CTX *);
897 const BIGNUM *p;
898 BN_CTX *new_ctx = NULL;
899 BIGNUM *rh, *tmp, *Z4, *Z6;
900 int ret = -1;
901
902 if (EC_POINT_is_at_infinity(group, point)) {
903 return 1;
904 }
905
906 field_mul = group->meth->field_mul;
907 field_sqr = group->meth->field_sqr;
908 p = &group->field;
909
910 if (ctx == NULL) {
911 ctx = new_ctx = BN_CTX_new();
912 if (ctx == NULL) {
913 return -1;
914 }
915 }
916
917 BN_CTX_start(ctx);
918 rh = BN_CTX_get(ctx);
919 tmp = BN_CTX_get(ctx);
920 Z4 = BN_CTX_get(ctx);
921 Z6 = BN_CTX_get(ctx);
922 if (Z6 == NULL) {
923 goto err;
924 }
925
926 /* We have a curve defined by a Weierstrass equation
927 * y^2 = x^3 + a*x + b.
928 * The point to consider is given in Jacobian projective coordinates
929 * where (X, Y, Z) represents (x, y) = (X/Z^2, Y/Z^3).
930 * Substituting this and multiplying by Z^6 transforms the above equation
931 * into
932 * Y^2 = X^3 + a*X*Z^4 + b*Z^6.
933 * To test this, we add up the right-hand side in 'rh'.
934 */
935
936 /* rh := X^2 */
937 if (!field_sqr(group, rh, &point->X, ctx)) {
938 goto err;
939 }
940
941 if (!point->Z_is_one) {
942 if (!field_sqr(group, tmp, &point->Z, ctx) ||
943 !field_sqr(group, Z4, tmp, ctx) ||
944 !field_mul(group, Z6, Z4, tmp, ctx)) {
945 goto err;
946 }
947
948 /* rh := (rh + a*Z^4)*X */
949 if (group->a_is_minus3) {
950 if (!BN_mod_lshift1_quick(tmp, Z4, p) ||
951 !BN_mod_add_quick(tmp, tmp, Z4, p) ||
952 !BN_mod_sub_quick(rh, rh, tmp, p) ||
953 !field_mul(group, rh, rh, &point->X, ctx)) {
954 goto err;
955 }
956 } else {
957 if (!field_mul(group, tmp, Z4, &group->a, ctx) ||
958 !BN_mod_add_quick(rh, rh, tmp, p) ||
959 !field_mul(group, rh, rh, &point->X, ctx)) {
960 goto err;
961 }
962 }
963
964 /* rh := rh + b*Z^6 */
965 if (!field_mul(group, tmp, &group->b, Z6, ctx) ||
966 !BN_mod_add_quick(rh, rh, tmp, p)) {
967 goto err;
968 }
969 } else {
970 /* point->Z_is_one */
971
972 /* rh := (rh + a)*X */
973 if (!BN_mod_add_quick(rh, rh, &group->a, p) ||
974 !field_mul(group, rh, rh, &point->X, ctx)) {
975 goto err;
976 }
977 /* rh := rh + b */
978 if (!BN_mod_add_quick(rh, rh, &group->b, p)) {
979 goto err;
980 }
981 }
982
983 /* 'lh' := Y^2 */
984 if (!field_sqr(group, tmp, &point->Y, ctx)) {
985 goto err;
986 }
987
988 ret = (0 == BN_ucmp(tmp, rh));
989
990 err:
991 BN_CTX_end(ctx);
992 BN_CTX_free(new_ctx);
993 return ret;
994 }
995
ec_GFp_simple_cmp(const EC_GROUP * group,const EC_POINT * a,const EC_POINT * b,BN_CTX * ctx)996 int ec_GFp_simple_cmp(const EC_GROUP *group, const EC_POINT *a,
997 const EC_POINT *b, BN_CTX *ctx) {
998 /* return values:
999 * -1 error
1000 * 0 equal (in affine coordinates)
1001 * 1 not equal
1002 */
1003
1004 int (*field_mul)(const EC_GROUP *, BIGNUM *, const BIGNUM *, const BIGNUM *,
1005 BN_CTX *);
1006 int (*field_sqr)(const EC_GROUP *, BIGNUM *, const BIGNUM *, BN_CTX *);
1007 BN_CTX *new_ctx = NULL;
1008 BIGNUM *tmp1, *tmp2, *Za23, *Zb23;
1009 const BIGNUM *tmp1_, *tmp2_;
1010 int ret = -1;
1011
1012 if (EC_POINT_is_at_infinity(group, a)) {
1013 return EC_POINT_is_at_infinity(group, b) ? 0 : 1;
1014 }
1015
1016 if (EC_POINT_is_at_infinity(group, b)) {
1017 return 1;
1018 }
1019
1020 if (a->Z_is_one && b->Z_is_one) {
1021 return ((BN_cmp(&a->X, &b->X) == 0) && BN_cmp(&a->Y, &b->Y) == 0) ? 0 : 1;
1022 }
1023
1024 field_mul = group->meth->field_mul;
1025 field_sqr = group->meth->field_sqr;
1026
1027 if (ctx == NULL) {
1028 ctx = new_ctx = BN_CTX_new();
1029 if (ctx == NULL) {
1030 return -1;
1031 }
1032 }
1033
1034 BN_CTX_start(ctx);
1035 tmp1 = BN_CTX_get(ctx);
1036 tmp2 = BN_CTX_get(ctx);
1037 Za23 = BN_CTX_get(ctx);
1038 Zb23 = BN_CTX_get(ctx);
1039 if (Zb23 == NULL) {
1040 goto end;
1041 }
1042
1043 /* We have to decide whether
1044 * (X_a/Z_a^2, Y_a/Z_a^3) = (X_b/Z_b^2, Y_b/Z_b^3),
1045 * or equivalently, whether
1046 * (X_a*Z_b^2, Y_a*Z_b^3) = (X_b*Z_a^2, Y_b*Z_a^3).
1047 */
1048
1049 if (!b->Z_is_one) {
1050 if (!field_sqr(group, Zb23, &b->Z, ctx) ||
1051 !field_mul(group, tmp1, &a->X, Zb23, ctx)) {
1052 goto end;
1053 }
1054 tmp1_ = tmp1;
1055 } else {
1056 tmp1_ = &a->X;
1057 }
1058 if (!a->Z_is_one) {
1059 if (!field_sqr(group, Za23, &a->Z, ctx) ||
1060 !field_mul(group, tmp2, &b->X, Za23, ctx)) {
1061 goto end;
1062 }
1063 tmp2_ = tmp2;
1064 } else {
1065 tmp2_ = &b->X;
1066 }
1067
1068 /* compare X_a*Z_b^2 with X_b*Z_a^2 */
1069 if (BN_cmp(tmp1_, tmp2_) != 0) {
1070 ret = 1; /* points differ */
1071 goto end;
1072 }
1073
1074
1075 if (!b->Z_is_one) {
1076 if (!field_mul(group, Zb23, Zb23, &b->Z, ctx) ||
1077 !field_mul(group, tmp1, &a->Y, Zb23, ctx)) {
1078 goto end;
1079 }
1080 /* tmp1_ = tmp1 */
1081 } else {
1082 tmp1_ = &a->Y;
1083 }
1084 if (!a->Z_is_one) {
1085 if (!field_mul(group, Za23, Za23, &a->Z, ctx) ||
1086 !field_mul(group, tmp2, &b->Y, Za23, ctx)) {
1087 goto end;
1088 }
1089 /* tmp2_ = tmp2 */
1090 } else {
1091 tmp2_ = &b->Y;
1092 }
1093
1094 /* compare Y_a*Z_b^3 with Y_b*Z_a^3 */
1095 if (BN_cmp(tmp1_, tmp2_) != 0) {
1096 ret = 1; /* points differ */
1097 goto end;
1098 }
1099
1100 /* points are equal */
1101 ret = 0;
1102
1103 end:
1104 BN_CTX_end(ctx);
1105 BN_CTX_free(new_ctx);
1106 return ret;
1107 }
1108
ec_GFp_simple_make_affine(const EC_GROUP * group,EC_POINT * point,BN_CTX * ctx)1109 int ec_GFp_simple_make_affine(const EC_GROUP *group, EC_POINT *point,
1110 BN_CTX *ctx) {
1111 BN_CTX *new_ctx = NULL;
1112 BIGNUM *x, *y;
1113 int ret = 0;
1114
1115 if (point->Z_is_one || EC_POINT_is_at_infinity(group, point)) {
1116 return 1;
1117 }
1118
1119 if (ctx == NULL) {
1120 ctx = new_ctx = BN_CTX_new();
1121 if (ctx == NULL) {
1122 return 0;
1123 }
1124 }
1125
1126 BN_CTX_start(ctx);
1127 x = BN_CTX_get(ctx);
1128 y = BN_CTX_get(ctx);
1129 if (y == NULL) {
1130 goto err;
1131 }
1132
1133 if (!EC_POINT_get_affine_coordinates_GFp(group, point, x, y, ctx) ||
1134 !EC_POINT_set_affine_coordinates_GFp(group, point, x, y, ctx)) {
1135 goto err;
1136 }
1137 if (!point->Z_is_one) {
1138 OPENSSL_PUT_ERROR(EC, ERR_R_INTERNAL_ERROR);
1139 goto err;
1140 }
1141
1142 ret = 1;
1143
1144 err:
1145 BN_CTX_end(ctx);
1146 BN_CTX_free(new_ctx);
1147 return ret;
1148 }
1149
ec_GFp_simple_points_make_affine(const EC_GROUP * group,size_t num,EC_POINT * points[],BN_CTX * ctx)1150 int ec_GFp_simple_points_make_affine(const EC_GROUP *group, size_t num,
1151 EC_POINT *points[], BN_CTX *ctx) {
1152 BN_CTX *new_ctx = NULL;
1153 BIGNUM *tmp, *tmp_Z;
1154 BIGNUM **prod_Z = NULL;
1155 size_t i;
1156 int ret = 0;
1157
1158 if (num == 0) {
1159 return 1;
1160 }
1161
1162 if (ctx == NULL) {
1163 ctx = new_ctx = BN_CTX_new();
1164 if (ctx == NULL) {
1165 return 0;
1166 }
1167 }
1168
1169 BN_CTX_start(ctx);
1170 tmp = BN_CTX_get(ctx);
1171 tmp_Z = BN_CTX_get(ctx);
1172 if (tmp == NULL || tmp_Z == NULL) {
1173 goto err;
1174 }
1175
1176 prod_Z = OPENSSL_malloc(num * sizeof(prod_Z[0]));
1177 if (prod_Z == NULL) {
1178 goto err;
1179 }
1180 memset(prod_Z, 0, num * sizeof(prod_Z[0]));
1181 for (i = 0; i < num; i++) {
1182 prod_Z[i] = BN_new();
1183 if (prod_Z[i] == NULL) {
1184 goto err;
1185 }
1186 }
1187
1188 /* Set each prod_Z[i] to the product of points[0]->Z .. points[i]->Z,
1189 * skipping any zero-valued inputs (pretend that they're 1). */
1190
1191 if (!BN_is_zero(&points[0]->Z)) {
1192 if (!BN_copy(prod_Z[0], &points[0]->Z)) {
1193 goto err;
1194 }
1195 } else {
1196 if (group->meth->field_set_to_one != 0) {
1197 if (!group->meth->field_set_to_one(group, prod_Z[0], ctx)) {
1198 goto err;
1199 }
1200 } else {
1201 if (!BN_one(prod_Z[0])) {
1202 goto err;
1203 }
1204 }
1205 }
1206
1207 for (i = 1; i < num; i++) {
1208 if (!BN_is_zero(&points[i]->Z)) {
1209 if (!group->meth->field_mul(group, prod_Z[i], prod_Z[i - 1],
1210 &points[i]->Z, ctx)) {
1211 goto err;
1212 }
1213 } else {
1214 if (!BN_copy(prod_Z[i], prod_Z[i - 1])) {
1215 goto err;
1216 }
1217 }
1218 }
1219
1220 /* Now use a single explicit inversion to replace every
1221 * non-zero points[i]->Z by its inverse. */
1222
1223 if (!BN_mod_inverse(tmp, prod_Z[num - 1], &group->field, ctx)) {
1224 OPENSSL_PUT_ERROR(EC, ERR_R_BN_LIB);
1225 goto err;
1226 }
1227
1228 if (group->meth->field_encode != NULL) {
1229 /* In the Montgomery case, we just turned R*H (representing H)
1230 * into 1/(R*H), but we need R*(1/H) (representing 1/H);
1231 * i.e. we need to multiply by the Montgomery factor twice. */
1232 if (!group->meth->field_encode(group, tmp, tmp, ctx) ||
1233 !group->meth->field_encode(group, tmp, tmp, ctx)) {
1234 goto err;
1235 }
1236 }
1237
1238 for (i = num - 1; i > 0; --i) {
1239 /* Loop invariant: tmp is the product of the inverses of
1240 * points[0]->Z .. points[i]->Z (zero-valued inputs skipped). */
1241 if (BN_is_zero(&points[i]->Z)) {
1242 continue;
1243 }
1244
1245 /* Set tmp_Z to the inverse of points[i]->Z (as product
1246 * of Z inverses 0 .. i, Z values 0 .. i - 1). */
1247 if (!group->meth->field_mul(group, tmp_Z, prod_Z[i - 1], tmp, ctx) ||
1248 /* Update tmp to satisfy the loop invariant for i - 1. */
1249 !group->meth->field_mul(group, tmp, tmp, &points[i]->Z, ctx) ||
1250 /* Replace points[i]->Z by its inverse. */
1251 !BN_copy(&points[i]->Z, tmp_Z)) {
1252 goto err;
1253 }
1254 }
1255
1256 /* Replace points[0]->Z by its inverse. */
1257 if (!BN_is_zero(&points[0]->Z) && !BN_copy(&points[0]->Z, tmp)) {
1258 goto err;
1259 }
1260
1261 /* Finally, fix up the X and Y coordinates for all points. */
1262 for (i = 0; i < num; i++) {
1263 EC_POINT *p = points[i];
1264
1265 if (!BN_is_zero(&p->Z)) {
1266 /* turn (X, Y, 1/Z) into (X/Z^2, Y/Z^3, 1). */
1267 if (!group->meth->field_sqr(group, tmp, &p->Z, ctx) ||
1268 !group->meth->field_mul(group, &p->X, &p->X, tmp, ctx) ||
1269 !group->meth->field_mul(group, tmp, tmp, &p->Z, ctx) ||
1270 !group->meth->field_mul(group, &p->Y, &p->Y, tmp, ctx)) {
1271 goto err;
1272 }
1273
1274 if (group->meth->field_set_to_one != NULL) {
1275 if (!group->meth->field_set_to_one(group, &p->Z, ctx)) {
1276 goto err;
1277 }
1278 } else {
1279 if (!BN_one(&p->Z)) {
1280 goto err;
1281 }
1282 }
1283 p->Z_is_one = 1;
1284 }
1285 }
1286
1287 ret = 1;
1288
1289 err:
1290 BN_CTX_end(ctx);
1291 BN_CTX_free(new_ctx);
1292 if (prod_Z != NULL) {
1293 for (i = 0; i < num; i++) {
1294 if (prod_Z[i] == NULL) {
1295 break;
1296 }
1297 BN_clear_free(prod_Z[i]);
1298 }
1299 OPENSSL_free(prod_Z);
1300 }
1301
1302 return ret;
1303 }
1304
ec_GFp_simple_field_mul(const EC_GROUP * group,BIGNUM * r,const BIGNUM * a,const BIGNUM * b,BN_CTX * ctx)1305 int ec_GFp_simple_field_mul(const EC_GROUP *group, BIGNUM *r, const BIGNUM *a,
1306 const BIGNUM *b, BN_CTX *ctx) {
1307 return BN_mod_mul(r, a, b, &group->field, ctx);
1308 }
1309
ec_GFp_simple_field_sqr(const EC_GROUP * group,BIGNUM * r,const BIGNUM * a,BN_CTX * ctx)1310 int ec_GFp_simple_field_sqr(const EC_GROUP *group, BIGNUM *r, const BIGNUM *a,
1311 BN_CTX *ctx) {
1312 return BN_mod_sqr(r, a, &group->field, ctx);
1313 }
1314