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Save and restore the Windows error around TlsGetValue.
[thirdparty/openssl.git] / crypto / ec / ecp_smpl.c
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0f113f3e 1/*
edea42c6 2 * Copyright 2001-2017 The OpenSSL Project Authors. All Rights Reserved.
aa8f3d76 3 * Copyright (c) 2002, Oracle and/or its affiliates. All rights reserved
f8fe20e0 4 *
aa6bb135
RS		 5 * Licensed under the OpenSSL license (the "License"). You may not use
6 * this file except in compliance with the License. You can obtain a copy
7 * in the file LICENSE in the source distribution or at
8 * https://www.openssl.org/source/license.html
f8fe20e0 9 */
aa6bb135 10
60428dbf 11#include <openssl/err.h>
02cbedc3 12#include <openssl/symhacks.h>
60428dbf 13
f8fe20e0 14#include "ec_lcl.h"
0657bf9c 15
0657bf9c 16const EC_METHOD *EC_GFp_simple_method(void)
0f113f3e
MC		 17{
18 static const EC_METHOD ret = {
19 EC_FLAGS_DEFAULT_OCT,
20 NID_X9_62_prime_field,
21 ec_GFp_simple_group_init,
22 ec_GFp_simple_group_finish,
23 ec_GFp_simple_group_clear_finish,
24 ec_GFp_simple_group_copy,
25 ec_GFp_simple_group_set_curve,
26 ec_GFp_simple_group_get_curve,
27 ec_GFp_simple_group_get_degree,
9ff9bccc 28 ec_group_simple_order_bits,
0f113f3e
MC		 29 ec_GFp_simple_group_check_discriminant,
30 ec_GFp_simple_point_init,
31 ec_GFp_simple_point_finish,
32 ec_GFp_simple_point_clear_finish,
33 ec_GFp_simple_point_copy,
34 ec_GFp_simple_point_set_to_infinity,
35 ec_GFp_simple_set_Jprojective_coordinates_GFp,
36 ec_GFp_simple_get_Jprojective_coordinates_GFp,
37 ec_GFp_simple_point_set_affine_coordinates,
38 ec_GFp_simple_point_get_affine_coordinates,
39 0, 0, 0,
40 ec_GFp_simple_add,
41 ec_GFp_simple_dbl,
42 ec_GFp_simple_invert,
43 ec_GFp_simple_is_at_infinity,
44 ec_GFp_simple_is_on_curve,
45 ec_GFp_simple_cmp,
46 ec_GFp_simple_make_affine,
47 ec_GFp_simple_points_make_affine,
48 0 /* mul */ ,
49 0 /* precompute_mult */ ,
50 0 /* have_precompute_mult */ ,
51 ec_GFp_simple_field_mul,
52 ec_GFp_simple_field_sqr,
53 0 /* field_div */ ,
54 0 /* field_encode */ ,
55 0 /* field_decode */ ,
9ff9bccc
DSH		 56 0, /* field_set_to_one */
57 ec_key_simple_priv2oct,
58 ec_key_simple_oct2priv,
59 0, /* set private */
60 ec_key_simple_generate_key,
61 ec_key_simple_check_key,
62 ec_key_simple_generate_public_key,
63 0, /* keycopy */
64 0, /* keyfinish */
65 ecdh_simple_compute_key
0f113f3e
MC		 66 };
67
68 return &ret;
69}
60428dbf 70
3a83462d
MC		 71/*
72 * Most method functions in this file are designed to work with
922fa76e
BM		 73 * non-trivial representations of field elements if necessary
74 * (see ecp_mont.c): while standard modular addition and subtraction
75 * are used, the field_mul and field_sqr methods will be used for
76 * multiplication, and field_encode and field_decode (if defined)
77 * will be used for converting between representations.
3a83462d 78 *
922fa76e
BM		 79 * Functions ec_GFp_simple_points_make_affine() and
80 * ec_GFp_simple_point_get_affine_coordinates() specifically assume
81 * that if a non-trivial representation is used, it is a Montgomery
82 * representation (i.e. 'encoding' means multiplying by some factor R).
83 */
84
60428dbf 85int ec_GFp_simple_group_init(EC_GROUP *group)
0f113f3e
MC		 86{
87 group->field = BN_new();
88 group->a = BN_new();
89 group->b = BN_new();
90945fa3 90 if (group->field == NULL || group->a == NULL || group->b == NULL) {
a3853772
RS		 91 BN_free(group->field);
92 BN_free(group->a);
93 BN_free(group->b);
0f113f3e
MC		 94 return 0;
95 }
96 group->a_is_minus3 = 0;
97 return 1;
98}
60428dbf 99
bb62a8b0 100void ec_GFp_simple_group_finish(EC_GROUP *group)
0f113f3e
MC		 101{
102 BN_free(group->field);
103 BN_free(group->a);
104 BN_free(group->b);
105}
bb62a8b0
BM		 106
107void ec_GFp_simple_group_clear_finish(EC_GROUP *group)
0f113f3e
MC		 108{
109 BN_clear_free(group->field);
110 BN_clear_free(group->a);
111 BN_clear_free(group->b);
112}
bb62a8b0
BM		 113
114int ec_GFp_simple_group_copy(EC_GROUP *dest, const EC_GROUP *src)
0f113f3e
MC		 115{
116 if (!BN_copy(dest->field, src->field))
117 return 0;
118 if (!BN_copy(dest->a, src->a))
119 return 0;
120 if (!BN_copy(dest->b, src->b))
121 return 0;
bb62a8b0 122
0f113f3e 123 dest->a_is_minus3 = src->a_is_minus3;
bb62a8b0 124
0f113f3e
MC		 125 return 1;
126}
bb62a8b0 127
35b73a1f 128int ec_GFp_simple_group_set_curve(EC_GROUP *group,
0f113f3e
MC		 129 const BIGNUM *p, const BIGNUM *a,
130 const BIGNUM *b, BN_CTX *ctx)
131{
132 int ret = 0;
133 BN_CTX *new_ctx = NULL;
134 BIGNUM *tmp_a;
135
136 /* p must be a prime > 3 */
137 if (BN_num_bits(p) <= 2 || !BN_is_odd(p)) {
138 ECerr(EC_F_EC_GFP_SIMPLE_GROUP_SET_CURVE, EC_R_INVALID_FIELD);
139 return 0;
140 }
141
142 if (ctx == NULL) {
143 ctx = new_ctx = BN_CTX_new();
144 if (ctx == NULL)
145 return 0;
146 }
147
148 BN_CTX_start(ctx);
149 tmp_a = BN_CTX_get(ctx);
150 if (tmp_a == NULL)
151 goto err;
152
153 /* group->field */
154 if (!BN_copy(group->field, p))
155 goto err;
156 BN_set_negative(group->field, 0);
157
158 /* group->a */
159 if (!BN_nnmod(tmp_a, a, p, ctx))
160 goto err;
161 if (group->meth->field_encode) {
162 if (!group->meth->field_encode(group, group->a, tmp_a, ctx))
163 goto err;
164 } else if (!BN_copy(group->a, tmp_a))
165 goto err;
166
167 /* group->b */
168 if (!BN_nnmod(group->b, b, p, ctx))
169 goto err;
170 if (group->meth->field_encode)
171 if (!group->meth->field_encode(group, group->b, group->b, ctx))
172 goto err;
173
174 /* group->a_is_minus3 */
175 if (!BN_add_word(tmp_a, 3))
176 goto err;
177 group->a_is_minus3 = (0 == BN_cmp(tmp_a, group->field));
178
179 ret = 1;
60428dbf
BM		 180
181 err:
0f113f3e 182 BN_CTX_end(ctx);
23a1d5e9 183 BN_CTX_free(new_ctx);
0f113f3e
MC		 184 return ret;
185}
186
187int ec_GFp_simple_group_get_curve(const EC_GROUP *group, BIGNUM *p, BIGNUM *a,
188 BIGNUM *b, BN_CTX *ctx)
189{
190 int ret = 0;
191 BN_CTX *new_ctx = NULL;
192
193 if (p != NULL) {
194 if (!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 if (a != NULL) {
206 if (!group->meth->field_decode(group, a, group->a, ctx))
207 goto err;
208 }
209 if (b != NULL) {
210 if (!group->meth->field_decode(group, b, group->b, ctx))
211 goto err;
212 }
213 } else {
214 if (a != NULL) {
215 if (!BN_copy(a, group->a))
216 goto err;
217 }
218 if (b != NULL) {
219 if (!BN_copy(b, group->b))
220 goto err;
221 }
222 }
223 }
224
225 ret = 1;
60428dbf 226
0f113f3e 227 err:
23a1d5e9 228 BN_CTX_free(new_ctx);
0f113f3e
MC		 229 return ret;
230}
60428dbf 231
7793f30e 232int ec_GFp_simple_group_get_degree(const EC_GROUP *group)
0f113f3e
MC		 233{
234 return BN_num_bits(group->field);
235}
7793f30e 236
17d6bb81 237int ec_GFp_simple_group_check_discriminant(const EC_GROUP *group, BN_CTX *ctx)
0f113f3e
MC		 238{
239 int ret = 0;
240 BIGNUM *a, *b, *order, *tmp_1, *tmp_2;
241 const BIGNUM *p = group->field;
242 BN_CTX *new_ctx = NULL;
243
244 if (ctx == NULL) {
245 ctx = new_ctx = BN_CTX_new();
246 if (ctx == NULL) {
247 ECerr(EC_F_EC_GFP_SIMPLE_GROUP_CHECK_DISCRIMINANT,
248 ERR_R_MALLOC_FAILURE);
249 goto err;
250 }
251 }
252 BN_CTX_start(ctx);
253 a = BN_CTX_get(ctx);
254 b = BN_CTX_get(ctx);
255 tmp_1 = BN_CTX_get(ctx);
256 tmp_2 = BN_CTX_get(ctx);
257 order = BN_CTX_get(ctx);
258 if (order == NULL)
259 goto err;
260
261 if (group->meth->field_decode) {
262 if (!group->meth->field_decode(group, a, group->a, ctx))
263 goto err;
264 if (!group->meth->field_decode(group, b, group->b, ctx))
265 goto err;
266 } else {
267 if (!BN_copy(a, group->a))
268 goto err;
269 if (!BN_copy(b, group->b))
270 goto err;
271 }
272
50e735f9
MC		 273 /*-
274 * check the discriminant:
275 * y^2 = x^3 + a*x + b is an elliptic curve <=> 4*a^3 + 27*b^2 != 0 (mod p)
276 * 0 =< a, b < p
277 */
0f113f3e
MC		 278 if (BN_is_zero(a)) {
279 if (BN_is_zero(b))
280 goto err;
281 } else if (!BN_is_zero(b)) {
282 if (!BN_mod_sqr(tmp_1, a, p, ctx))
283 goto err;
284 if (!BN_mod_mul(tmp_2, tmp_1, a, p, ctx))
285 goto err;
286 if (!BN_lshift(tmp_1, tmp_2, 2))
287 goto err;
288 /* tmp_1 = 4*a^3 */
289
290 if (!BN_mod_sqr(tmp_2, b, p, ctx))
291 goto err;
292 if (!BN_mul_word(tmp_2, 27))
293 goto err;
294 /* tmp_2 = 27*b^2 */
295
296 if (!BN_mod_add(a, tmp_1, tmp_2, p, ctx))
297 goto err;
298 if (BN_is_zero(a))
299 goto err;
300 }
301 ret = 1;
af28dd6c 302
0f113f3e
MC		 303 err:
304 if (ctx != NULL)
305 BN_CTX_end(ctx);
23a1d5e9 306 BN_CTX_free(new_ctx);
0f113f3e
MC		 307 return ret;
308}
af28dd6c 309
60428dbf 310int ec_GFp_simple_point_init(EC_POINT *point)
0f113f3e
MC		 311{
312 point->X = BN_new();
313 point->Y = BN_new();
314 point->Z = BN_new();
315 point->Z_is_one = 0;
316
90945fa3 317 if (point->X == NULL || point->Y == NULL || point->Z == NULL) {
23a1d5e9
RS		 318 BN_free(point->X);
319 BN_free(point->Y);
320 BN_free(point->Z);
0f113f3e
MC		 321 return 0;
322 }
323 return 1;
324}
60428dbf
BM		 325
326void ec_GFp_simple_point_finish(EC_POINT *point)
0f113f3e
MC		 327{
328 BN_free(point->X);
329 BN_free(point->Y);
330 BN_free(point->Z);
331}
60428dbf
BM		 332
333void ec_GFp_simple_point_clear_finish(EC_POINT *point)
0f113f3e
MC		 334{
335 BN_clear_free(point->X);
336 BN_clear_free(point->Y);
337 BN_clear_free(point->Z);
338 point->Z_is_one = 0;
339}
60428dbf
BM		 340
341int ec_GFp_simple_point_copy(EC_POINT *dest, const EC_POINT *src)
0f113f3e
MC		 342{
343 if (!BN_copy(dest->X, src->X))
344 return 0;
345 if (!BN_copy(dest->Y, src->Y))
346 return 0;
347 if (!BN_copy(dest->Z, src->Z))
348 return 0;
349 dest->Z_is_one = src->Z_is_one;
350
351 return 1;
352}
353
354int ec_GFp_simple_point_set_to_infinity(const EC_GROUP *group,
355 EC_POINT *point)
356{
357 point->Z_is_one = 0;
358 BN_zero(point->Z);
359 return 1;
360}
361
362int ec_GFp_simple_set_Jprojective_coordinates_GFp(const EC_GROUP *group,
363 EC_POINT *point,
364 const BIGNUM *x,
365 const BIGNUM *y,
366 const BIGNUM *z,
367 BN_CTX *ctx)
368{
369 BN_CTX *new_ctx = NULL;
370 int ret = 0;
371
372 if (ctx == NULL) {
373 ctx = new_ctx = BN_CTX_new();
374 if (ctx == NULL)
375 return 0;
376 }
377
378 if (x != NULL) {
379 if (!BN_nnmod(point->X, x, group->field, ctx))
380 goto err;
381 if (group->meth->field_encode) {
382 if (!group->meth->field_encode(group, point->X, point->X, ctx))
383 goto err;
384 }
385 }
386
387 if (y != NULL) {
388 if (!BN_nnmod(point->Y, y, group->field, ctx))
389 goto err;
390 if (group->meth->field_encode) {
391 if (!group->meth->field_encode(group, point->Y, point->Y, ctx))
392 goto err;
393 }
394 }
395
396 if (z != NULL) {
397 int Z_is_one;
398
399 if (!BN_nnmod(point->Z, z, group->field, ctx))
400 goto err;
401 Z_is_one = BN_is_one(point->Z);
402 if (group->meth->field_encode) {
403 if (Z_is_one && (group->meth->field_set_to_one != 0)) {
404 if (!group->meth->field_set_to_one(group, point->Z, ctx))
405 goto err;
406 } else {
407 if (!group->
408 meth->field_encode(group, point->Z, point->Z, ctx))
409 goto err;
410 }
411 }
412 point->Z_is_one = Z_is_one;
413 }
414
415 ret = 1;
416
bb62a8b0 417 err:
23a1d5e9 418 BN_CTX_free(new_ctx);
0f113f3e
MC		 419 return ret;
420}
421
422int ec_GFp_simple_get_Jprojective_coordinates_GFp(const EC_GROUP *group,
423 const EC_POINT *point,
424 BIGNUM *x, BIGNUM *y,
425 BIGNUM *z, BN_CTX *ctx)
426{
427 BN_CTX *new_ctx = NULL;
428 int ret = 0;
429
430 if (group->meth->field_decode != 0) {
431 if (ctx == NULL) {
432 ctx = new_ctx = BN_CTX_new();
433 if (ctx == NULL)
434 return 0;
435 }
436
437 if (x != NULL) {
438 if (!group->meth->field_decode(group, x, point->X, ctx))
439 goto err;
440 }
441 if (y != NULL) {
442 if (!group->meth->field_decode(group, y, point->Y, ctx))
443 goto err;
444 }
445 if (z != NULL) {
446 if (!group->meth->field_decode(group, z, point->Z, ctx))
447 goto err;
448 }
449 } else {
450 if (x != NULL) {
451 if (!BN_copy(x, point->X))
452 goto err;
453 }
454 if (y != NULL) {
455 if (!BN_copy(y, point->Y))
456 goto err;
457 }
458 if (z != NULL) {
459 if (!BN_copy(z, point->Z))
460 goto err;
461 }
462 }
463
464 ret = 1;
bb62a8b0 465
226cc7de 466 err:
23a1d5e9 467 BN_CTX_free(new_ctx);
0f113f3e
MC		 468 return ret;
469}
470
471int ec_GFp_simple_point_set_affine_coordinates(const EC_GROUP *group,
472 EC_POINT *point,
473 const BIGNUM *x,
474 const BIGNUM *y, BN_CTX *ctx)
475{
476 if (x == NULL || y == NULL) {
477 /*
478 * unlike for projective coordinates, we do not tolerate this
479 */
480 ECerr(EC_F_EC_GFP_SIMPLE_POINT_SET_AFFINE_COORDINATES,
481 ERR_R_PASSED_NULL_PARAMETER);
482 return 0;
483 }
484
485 return EC_POINT_set_Jprojective_coordinates_GFp(group, point, x, y,
486 BN_value_one(), ctx);
487}
488
489int ec_GFp_simple_point_get_affine_coordinates(const EC_GROUP *group,
490 const EC_POINT *point,
491 BIGNUM *x, BIGNUM *y,
492 BN_CTX *ctx)
493{
494 BN_CTX *new_ctx = NULL;
495 BIGNUM *Z, *Z_1, *Z_2, *Z_3;
496 const BIGNUM *Z_;
497 int ret = 0;
498
499 if (EC_POINT_is_at_infinity(group, point)) {
500 ECerr(EC_F_EC_GFP_SIMPLE_POINT_GET_AFFINE_COORDINATES,
501 EC_R_POINT_AT_INFINITY);
502 return 0;
503 }
504
505 if (ctx == NULL) {
506 ctx = new_ctx = BN_CTX_new();
507 if (ctx == NULL)
508 return 0;
509 }
510
511 BN_CTX_start(ctx);
512 Z = BN_CTX_get(ctx);
513 Z_1 = BN_CTX_get(ctx);
514 Z_2 = BN_CTX_get(ctx);
515 Z_3 = BN_CTX_get(ctx);
516 if (Z_3 == NULL)
517 goto err;
518
519 /* transform (X, Y, Z) into (x, y) := (X/Z^2, Y/Z^3) */
520
521 if (group->meth->field_decode) {
522 if (!group->meth->field_decode(group, Z, point->Z, ctx))
523 goto err;
524 Z_ = Z;
525 } else {
526 Z_ = point->Z;
527 }
528
529 if (BN_is_one(Z_)) {
530 if (group->meth->field_decode) {
531 if (x != NULL) {
532 if (!group->meth->field_decode(group, x, point->X, ctx))
533 goto err;
534 }
535 if (y != NULL) {
536 if (!group->meth->field_decode(group, y, point->Y, ctx))
537 goto err;
538 }
539 } else {
540 if (x != NULL) {
541 if (!BN_copy(x, point->X))
542 goto err;
543 }
544 if (y != NULL) {
545 if (!BN_copy(y, point->Y))
546 goto err;
547 }
548 }
549 } else {
550 if (!BN_mod_inverse(Z_1, Z_, group->field, ctx)) {
551 ECerr(EC_F_EC_GFP_SIMPLE_POINT_GET_AFFINE_COORDINATES,
552 ERR_R_BN_LIB);
553 goto err;
554 }
555
556 if (group->meth->field_encode == 0) {
557 /* field_sqr works on standard representation */
558 if (!group->meth->field_sqr(group, Z_2, Z_1, ctx))
559 goto err;
560 } else {
561 if (!BN_mod_sqr(Z_2, Z_1, group->field, ctx))
562 goto err;
563 }
564
565 if (x != NULL) {
566 /*
567 * in the Montgomery case, field_mul will cancel out Montgomery
568 * factor in X:
569 */
570 if (!group->meth->field_mul(group, x, point->X, Z_2, ctx))
571 goto err;
572 }
573
574 if (y != NULL) {
575 if (group->meth->field_encode == 0) {
576 /*
577 * field_mul works on standard representation
578 */
579 if (!group->meth->field_mul(group, Z_3, Z_2, Z_1, ctx))
580 goto err;
581 } else {
582 if (!BN_mod_mul(Z_3, Z_2, Z_1, group->field, ctx))
583 goto err;
584 }
585
586 /*
587 * in the Montgomery case, field_mul will cancel out Montgomery
588 * factor in Y:
589 */
590 if (!group->meth->field_mul(group, y, point->Y, Z_3, ctx))
591 goto err;
592 }
593 }
594
595 ret = 1;
226cc7de
BM		 596
597 err:
0f113f3e 598 BN_CTX_end(ctx);
23a1d5e9 599 BN_CTX_free(new_ctx);
0f113f3e
MC		 600 return ret;
601}
602
603int ec_GFp_simple_add(const EC_GROUP *group, EC_POINT *r, const EC_POINT *a,
604 const EC_POINT *b, BN_CTX *ctx)
605{
606 int (*field_mul) (const EC_GROUP *, BIGNUM *, const BIGNUM *,
607 const BIGNUM *, BN_CTX *);
608 int (*field_sqr) (const EC_GROUP *, BIGNUM *, const BIGNUM *, BN_CTX *);
609 const BIGNUM *p;
610 BN_CTX *new_ctx = NULL;
611 BIGNUM *n0, *n1, *n2, *n3, *n4, *n5, *n6;
612 int ret = 0;
613
614 if (a == b)
615 return EC_POINT_dbl(group, r, a, ctx);
616 if (EC_POINT_is_at_infinity(group, a))
617 return EC_POINT_copy(r, b);
618 if (EC_POINT_is_at_infinity(group, b))
619 return EC_POINT_copy(r, a);
620
621 field_mul = group->meth->field_mul;
622 field_sqr = group->meth->field_sqr;
623 p = group->field;
624
625 if (ctx == NULL) {
626 ctx = new_ctx = BN_CTX_new();
627 if (ctx == NULL)
628 return 0;
629 }
630
631 BN_CTX_start(ctx);
632 n0 = BN_CTX_get(ctx);
633 n1 = BN_CTX_get(ctx);
634 n2 = BN_CTX_get(ctx);
635 n3 = BN_CTX_get(ctx);
636 n4 = BN_CTX_get(ctx);
637 n5 = BN_CTX_get(ctx);
638 n6 = BN_CTX_get(ctx);
639 if (n6 == NULL)
640 goto end;
641
642 /*
643 * Note that in this function we must not read components of 'a' or 'b'
644 * once we have written the corresponding components of 'r'. ('r' might
645 * be one of 'a' or 'b'.)
646 */
647
648 /* n1, n2 */
649 if (b->Z_is_one) {
650 if (!BN_copy(n1, a->X))
651 goto end;
652 if (!BN_copy(n2, a->Y))
653 goto end;
654 /* n1 = X_a */
655 /* n2 = Y_a */
656 } else {
657 if (!field_sqr(group, n0, b->Z, ctx))
658 goto end;
659 if (!field_mul(group, n1, a->X, n0, ctx))
660 goto end;
661 /* n1 = X_a * Z_b^2 */
662
663 if (!field_mul(group, n0, n0, b->Z, ctx))
664 goto end;
665 if (!field_mul(group, n2, a->Y, n0, ctx))
666 goto end;
667 /* n2 = Y_a * Z_b^3 */
668 }
669
670 /* n3, n4 */
671 if (a->Z_is_one) {
672 if (!BN_copy(n3, b->X))
673 goto end;
674 if (!BN_copy(n4, b->Y))
675 goto end;
676 /* n3 = X_b */
677 /* n4 = Y_b */
678 } else {
679 if (!field_sqr(group, n0, a->Z, ctx))
680 goto end;
681 if (!field_mul(group, n3, b->X, n0, ctx))
682 goto end;
683 /* n3 = X_b * Z_a^2 */
684
685 if (!field_mul(group, n0, n0, a->Z, ctx))
686 goto end;
687 if (!field_mul(group, n4, b->Y, n0, ctx))
688 goto end;
689 /* n4 = Y_b * Z_a^3 */
690 }
691
692 /* n5, n6 */
693 if (!BN_mod_sub_quick(n5, n1, n3, p))
694 goto end;
695 if (!BN_mod_sub_quick(n6, n2, n4, p))
696 goto end;
697 /* n5 = n1 - n3 */
698 /* n6 = n2 - n4 */
699
700 if (BN_is_zero(n5)) {
701 if (BN_is_zero(n6)) {
702 /* a is the same point as b */
703 BN_CTX_end(ctx);
704 ret = EC_POINT_dbl(group, r, a, ctx);
705 ctx = NULL;
706 goto end;
707 } else {
708 /* a is the inverse of b */
709 BN_zero(r->Z);
710 r->Z_is_one = 0;
711 ret = 1;
712 goto end;
713 }
714 }
715
716 /* 'n7', 'n8' */
717 if (!BN_mod_add_quick(n1, n1, n3, p))
718 goto end;
719 if (!BN_mod_add_quick(n2, n2, n4, p))
720 goto end;
721 /* 'n7' = n1 + n3 */
722 /* 'n8' = n2 + n4 */
723
724 /* Z_r */
725 if (a->Z_is_one && b->Z_is_one) {
726 if (!BN_copy(r->Z, n5))
727 goto end;
728 } else {
729 if (a->Z_is_one) {
730 if (!BN_copy(n0, b->Z))
731 goto end;
732 } else if (b->Z_is_one) {
733 if (!BN_copy(n0, a->Z))
734 goto end;
735 } else {
736 if (!field_mul(group, n0, a->Z, b->Z, ctx))
737 goto end;
738 }
739 if (!field_mul(group, r->Z, n0, n5, ctx))
740 goto end;
741 }
742 r->Z_is_one = 0;
743 /* Z_r = Z_a * Z_b * n5 */
744
745 /* X_r */
746 if (!field_sqr(group, n0, n6, ctx))
747 goto end;
748 if (!field_sqr(group, n4, n5, ctx))
749 goto end;
750 if (!field_mul(group, n3, n1, n4, ctx))
751 goto end;
752 if (!BN_mod_sub_quick(r->X, n0, n3, p))
753 goto end;
754 /* X_r = n6^2 - n5^2 * 'n7' */
755
756 /* 'n9' */
757 if (!BN_mod_lshift1_quick(n0, r->X, p))
758 goto end;
759 if (!BN_mod_sub_quick(n0, n3, n0, p))
760 goto end;
761 /* n9 = n5^2 * 'n7' - 2 * X_r */
762
763 /* Y_r */
764 if (!field_mul(group, n0, n0, n6, ctx))
765 goto end;
766 if (!field_mul(group, n5, n4, n5, ctx))
767 goto end; /* now n5 is n5^3 */
768 if (!field_mul(group, n1, n2, n5, ctx))
769 goto end;
770 if (!BN_mod_sub_quick(n0, n0, n1, p))
771 goto end;
772 if (BN_is_odd(n0))
773 if (!BN_add(n0, n0, p))
774 goto end;
775 /* now 0 <= n0 < 2*p, and n0 is even */
776 if (!BN_rshift1(r->Y, n0))
777 goto end;
778 /* Y_r = (n6 * 'n9' - 'n8' * 'n5^3') / 2 */
779
780 ret = 1;
60428dbf
BM		 781
782 end:
0f113f3e
MC		 783 if (ctx) /* otherwise we already called BN_CTX_end */
784 BN_CTX_end(ctx);
23a1d5e9 785 BN_CTX_free(new_ctx);
0f113f3e
MC		 786 return ret;
787}
788
789int ec_GFp_simple_dbl(const EC_GROUP *group, EC_POINT *r, const EC_POINT *a,
790 BN_CTX *ctx)
791{
792 int (*field_mul) (const EC_GROUP *, BIGNUM *, const BIGNUM *,
793 const BIGNUM *, BN_CTX *);
794 int (*field_sqr) (const EC_GROUP *, BIGNUM *, const BIGNUM *, BN_CTX *);
795 const BIGNUM *p;
796 BN_CTX *new_ctx = NULL;
797 BIGNUM *n0, *n1, *n2, *n3;
798 int ret = 0;
799
800 if (EC_POINT_is_at_infinity(group, a)) {
801 BN_zero(r->Z);
802 r->Z_is_one = 0;
803 return 1;
804 }
805
806 field_mul = group->meth->field_mul;
807 field_sqr = group->meth->field_sqr;
808 p = group->field;
809
810 if (ctx == NULL) {
811 ctx = new_ctx = BN_CTX_new();
812 if (ctx == NULL)
813 return 0;
814 }
815
816 BN_CTX_start(ctx);
817 n0 = BN_CTX_get(ctx);
818 n1 = BN_CTX_get(ctx);
819 n2 = BN_CTX_get(ctx);
820 n3 = BN_CTX_get(ctx);
821 if (n3 == NULL)
822 goto err;
823
824 /*
825 * Note that in this function we must not read components of 'a' once we
826 * have written the corresponding components of 'r'. ('r' might the same
827 * as 'a'.)
828 */
829
830 /* n1 */
831 if (a->Z_is_one) {
832 if (!field_sqr(group, n0, a->X, ctx))
833 goto err;
834 if (!BN_mod_lshift1_quick(n1, n0, p))
835 goto err;
836 if (!BN_mod_add_quick(n0, n0, n1, p))
837 goto err;
838 if (!BN_mod_add_quick(n1, n0, group->a, p))
839 goto err;
840 /* n1 = 3 * X_a^2 + a_curve */
841 } else if (group->a_is_minus3) {
842 if (!field_sqr(group, n1, a->Z, ctx))
843 goto err;
844 if (!BN_mod_add_quick(n0, a->X, n1, p))
845 goto err;
846 if (!BN_mod_sub_quick(n2, a->X, n1, p))
847 goto err;
848 if (!field_mul(group, n1, n0, n2, ctx))
849 goto err;
850 if (!BN_mod_lshift1_quick(n0, n1, p))
851 goto err;
852 if (!BN_mod_add_quick(n1, n0, n1, p))
853 goto err;
35a1cc90
MC		 854 /*-
855 * n1 = 3 * (X_a + Z_a^2) * (X_a - Z_a^2)
856 * = 3 * X_a^2 - 3 * Z_a^4
857 */
0f113f3e
MC		 858 } else {
859 if (!field_sqr(group, n0, a->X, ctx))
860 goto err;
861 if (!BN_mod_lshift1_quick(n1, n0, p))
862 goto err;
863 if (!BN_mod_add_quick(n0, n0, n1, p))
864 goto err;
865 if (!field_sqr(group, n1, a->Z, ctx))
866 goto err;
867 if (!field_sqr(group, n1, n1, ctx))
868 goto err;
869 if (!field_mul(group, n1, n1, group->a, ctx))
870 goto err;
871 if (!BN_mod_add_quick(n1, n1, n0, p))
872 goto err;
873 /* n1 = 3 * X_a^2 + a_curve * Z_a^4 */
874 }
875
876 /* Z_r */
877 if (a->Z_is_one) {
878 if (!BN_copy(n0, a->Y))
879 goto err;
880 } else {
881 if (!field_mul(group, n0, a->Y, a->Z, ctx))
882 goto err;
883 }
884 if (!BN_mod_lshift1_quick(r->Z, n0, p))
885 goto err;
886 r->Z_is_one = 0;
887 /* Z_r = 2 * Y_a * Z_a */
888
889 /* n2 */
890 if (!field_sqr(group, n3, a->Y, ctx))
891 goto err;
892 if (!field_mul(group, n2, a->X, n3, ctx))
893 goto err;
894 if (!BN_mod_lshift_quick(n2, n2, 2, p))
895 goto err;
896 /* n2 = 4 * X_a * Y_a^2 */
897
898 /* X_r */
899 if (!BN_mod_lshift1_quick(n0, n2, p))
900 goto err;
901 if (!field_sqr(group, r->X, n1, ctx))
902 goto err;
903 if (!BN_mod_sub_quick(r->X, r->X, n0, p))
904 goto err;
905 /* X_r = n1^2 - 2 * n2 */
906
907 /* n3 */
908 if (!field_sqr(group, n0, n3, ctx))
909 goto err;
910 if (!BN_mod_lshift_quick(n3, n0, 3, p))
911 goto err;
912 /* n3 = 8 * Y_a^4 */
913
914 /* Y_r */
915 if (!BN_mod_sub_quick(n0, n2, r->X, p))
916 goto err;
917 if (!field_mul(group, n0, n1, n0, ctx))
918 goto err;
919 if (!BN_mod_sub_quick(r->Y, n0, n3, p))
920 goto err;
921 /* Y_r = n1 * (n2 - X_r) - n3 */
922
923 ret = 1;
60428dbf
BM		 924
925 err:
0f113f3e 926 BN_CTX_end(ctx);
23a1d5e9 927 BN_CTX_free(new_ctx);
0f113f3e
MC		 928 return ret;
929}
60428dbf 930
bb62a8b0 931int ec_GFp_simple_invert(const EC_GROUP *group, EC_POINT *point, BN_CTX *ctx)
0f113f3e
MC		 932{
933 if (EC_POINT_is_at_infinity(group, point) || BN_is_zero(point->Y))
934 /* point is its own inverse */
935 return 1;
1d5bd6cf 936
0f113f3e
MC		 937 return BN_usub(point->Y, group->field, point->Y);
938}
1d5bd6cf 939
60428dbf 940int ec_GFp_simple_is_at_infinity(const EC_GROUP *group, const EC_POINT *point)
0f113f3e
MC		 941{
942 return BN_is_zero(point->Z);
943}
944
945int ec_GFp_simple_is_on_curve(const EC_GROUP *group, const EC_POINT *point,
946 BN_CTX *ctx)
947{
948 int (*field_mul) (const EC_GROUP *, BIGNUM *, const BIGNUM *,
949 const BIGNUM *, BN_CTX *);
950 int (*field_sqr) (const EC_GROUP *, BIGNUM *, const BIGNUM *, BN_CTX *);
951 const BIGNUM *p;
952 BN_CTX *new_ctx = NULL;
953 BIGNUM *rh, *tmp, *Z4, *Z6;
954 int ret = -1;
955
956 if (EC_POINT_is_at_infinity(group, point))
957 return 1;
958
959 field_mul = group->meth->field_mul;
960 field_sqr = group->meth->field_sqr;
961 p = group->field;
962
963 if (ctx == NULL) {
964 ctx = new_ctx = BN_CTX_new();
965 if (ctx == NULL)
966 return -1;
967 }
968
969 BN_CTX_start(ctx);
970 rh = BN_CTX_get(ctx);
971 tmp = BN_CTX_get(ctx);
972 Z4 = BN_CTX_get(ctx);
973 Z6 = BN_CTX_get(ctx);
974 if (Z6 == NULL)
975 goto err;
976
35a1cc90
MC		 977 /*-
978 * We have a curve defined by a Weierstrass equation
979 * y^2 = x^3 + a*x + b.
980 * The point to consider is given in Jacobian projective coordinates
981 * where (X, Y, Z) represents (x, y) = (X/Z^2, Y/Z^3).
982 * Substituting this and multiplying by Z^6 transforms the above equation into
983 * Y^2 = X^3 + a*X*Z^4 + b*Z^6.
984 * To test this, we add up the right-hand side in 'rh'.
985 */
0f113f3e
MC		 986
987 /* rh := X^2 */
988 if (!field_sqr(group, rh, point->X, ctx))
989 goto err;
990
991 if (!point->Z_is_one) {
992 if (!field_sqr(group, tmp, point->Z, ctx))
993 goto err;
994 if (!field_sqr(group, Z4, tmp, ctx))
995 goto err;
996 if (!field_mul(group, Z6, Z4, tmp, ctx))
997 goto err;
998
999 /* rh := (rh + a*Z^4)*X */
1000 if (group->a_is_minus3) {
1001 if (!BN_mod_lshift1_quick(tmp, Z4, p))
1002 goto err;
1003 if (!BN_mod_add_quick(tmp, tmp, Z4, p))
1004 goto err;
1005 if (!BN_mod_sub_quick(rh, rh, tmp, p))
1006 goto err;
1007 if (!field_mul(group, rh, rh, point->X, ctx))
1008 goto err;
1009 } else {
1010 if (!field_mul(group, tmp, Z4, group->a, ctx))
1011 goto err;
1012 if (!BN_mod_add_quick(rh, rh, tmp, p))
1013 goto err;
1014 if (!field_mul(group, rh, rh, point->X, ctx))
1015 goto err;
1016 }
1017
1018 /* rh := rh + b*Z^6 */
1019 if (!field_mul(group, tmp, group->b, Z6, ctx))
1020 goto err;
1021 if (!BN_mod_add_quick(rh, rh, tmp, p))
1022 goto err;
1023 } else {
1024 /* point->Z_is_one */
1025
1026 /* rh := (rh + a)*X */
1027 if (!BN_mod_add_quick(rh, rh, group->a, p))
1028 goto err;
1029 if (!field_mul(group, rh, rh, point->X, ctx))
1030 goto err;
1031 /* rh := rh + b */
1032 if (!BN_mod_add_quick(rh, rh, group->b, p))
1033 goto err;
1034 }
1035
1036 /* 'lh' := Y^2 */
1037 if (!field_sqr(group, tmp, point->Y, ctx))
1038 goto err;
1039
1040 ret = (0 == BN_ucmp(tmp, rh));
e869d4bd
BM		 1041
1042 err:
0f113f3e 1043 BN_CTX_end(ctx);
23a1d5e9 1044 BN_CTX_free(new_ctx);
0f113f3e
MC		 1045 return ret;
1046}
1047
1048int ec_GFp_simple_cmp(const EC_GROUP *group, const EC_POINT *a,
1049 const EC_POINT *b, BN_CTX *ctx)
1050{
35a1cc90
MC		 1051 /*-
1052 * return values:
1053 * -1 error
1054 * 0 equal (in affine coordinates)
1055 * 1 not equal
1056 */
0f113f3e
MC		 1057
1058 int (*field_mul) (const EC_GROUP *, BIGNUM *, const BIGNUM *,
1059 const BIGNUM *, BN_CTX *);
1060 int (*field_sqr) (const EC_GROUP *, BIGNUM *, const BIGNUM *, BN_CTX *);
1061 BN_CTX *new_ctx = NULL;
1062 BIGNUM *tmp1, *tmp2, *Za23, *Zb23;
1063 const BIGNUM *tmp1_, *tmp2_;
1064 int ret = -1;
1065
1066 if (EC_POINT_is_at_infinity(group, a)) {
1067 return EC_POINT_is_at_infinity(group, b) ? 0 : 1;
1068 }
1069
1070 if (EC_POINT_is_at_infinity(group, b))
1071 return 1;
1072
1073 if (a->Z_is_one && b->Z_is_one) {
1074 return ((BN_cmp(a->X, b->X) == 0) && BN_cmp(a->Y, b->Y) == 0) ? 0 : 1;
1075 }
1076
1077 field_mul = group->meth->field_mul;
1078 field_sqr = group->meth->field_sqr;
1079
1080 if (ctx == NULL) {
1081 ctx = new_ctx = BN_CTX_new();
1082 if (ctx == NULL)
1083 return -1;
1084 }
1085
1086 BN_CTX_start(ctx);
1087 tmp1 = BN_CTX_get(ctx);
1088 tmp2 = BN_CTX_get(ctx);
1089 Za23 = BN_CTX_get(ctx);
1090 Zb23 = BN_CTX_get(ctx);
1091 if (Zb23 == NULL)
1092 goto end;
1093
35a1cc90
MC		 1094 /*-
1095 * We have to decide whether
1096 * (X_a/Z_a^2, Y_a/Z_a^3) = (X_b/Z_b^2, Y_b/Z_b^3),
1097 * or equivalently, whether
1098 * (X_a*Z_b^2, Y_a*Z_b^3) = (X_b*Z_a^2, Y_b*Z_a^3).
1099 */
0f113f3e
MC		 1100
1101 if (!b->Z_is_one) {
1102 if (!field_sqr(group, Zb23, b->Z, ctx))
1103 goto end;
1104 if (!field_mul(group, tmp1, a->X, Zb23, ctx))
1105 goto end;
1106 tmp1_ = tmp1;
1107 } else
1108 tmp1_ = a->X;
1109 if (!a->Z_is_one) {
1110 if (!field_sqr(group, Za23, a->Z, ctx))
1111 goto end;
1112 if (!field_mul(group, tmp2, b->X, Za23, ctx))
1113 goto end;
1114 tmp2_ = tmp2;
1115 } else
1116 tmp2_ = b->X;
1117
1118 /* compare X_a*Z_b^2 with X_b*Z_a^2 */
1119 if (BN_cmp(tmp1_, tmp2_) != 0) {
1120 ret = 1; /* points differ */
1121 goto end;
1122 }
1123
1124 if (!b->Z_is_one) {
1125 if (!field_mul(group, Zb23, Zb23, b->Z, ctx))
1126 goto end;
1127 if (!field_mul(group, tmp1, a->Y, Zb23, ctx))
1128 goto end;
1129 /* tmp1_ = tmp1 */
1130 } else
1131 tmp1_ = a->Y;
1132 if (!a->Z_is_one) {
1133 if (!field_mul(group, Za23, Za23, a->Z, ctx))
1134 goto end;
1135 if (!field_mul(group, tmp2, b->Y, Za23, ctx))
1136 goto end;
1137 /* tmp2_ = tmp2 */
1138 } else
1139 tmp2_ = b->Y;
1140
1141 /* compare Y_a*Z_b^3 with Y_b*Z_a^3 */
1142 if (BN_cmp(tmp1_, tmp2_) != 0) {
1143 ret = 1; /* points differ */
1144 goto end;
1145 }
1146
1147 /* points are equal */
1148 ret = 0;
bb62a8b0
BM		 1149
1150 end:
0f113f3e 1151 BN_CTX_end(ctx);
23a1d5e9 1152 BN_CTX_free(new_ctx);
0f113f3e
MC		 1153 return ret;
1154}
1155
1156int ec_GFp_simple_make_affine(const EC_GROUP *group, EC_POINT *point,
1157 BN_CTX *ctx)
1158{
1159 BN_CTX *new_ctx = NULL;
1160 BIGNUM *x, *y;
1161 int ret = 0;
1162
1163 if (point->Z_is_one || EC_POINT_is_at_infinity(group, point))
1164 return 1;
1165
1166 if (ctx == NULL) {
1167 ctx = new_ctx = BN_CTX_new();
1168 if (ctx == NULL)
1169 return 0;
1170 }
1171
1172 BN_CTX_start(ctx);
1173 x = BN_CTX_get(ctx);
1174 y = BN_CTX_get(ctx);
1175 if (y == NULL)
1176 goto err;
1177
1178 if (!EC_POINT_get_affine_coordinates_GFp(group, point, x, y, ctx))
1179 goto err;
1180 if (!EC_POINT_set_affine_coordinates_GFp(group, point, x, y, ctx))
1181 goto err;
1182 if (!point->Z_is_one) {
1183 ECerr(EC_F_EC_GFP_SIMPLE_MAKE_AFFINE, ERR_R_INTERNAL_ERROR);
1184 goto err;
1185 }
1186
1187 ret = 1;
e869d4bd 1188
226cc7de 1189 err:
0f113f3e 1190 BN_CTX_end(ctx);
23a1d5e9 1191 BN_CTX_free(new_ctx);
0f113f3e
MC		 1192 return ret;
1193}
1194
1195int ec_GFp_simple_points_make_affine(const EC_GROUP *group, size_t num,
1196 EC_POINT *points[], BN_CTX *ctx)
1197{
1198 BN_CTX *new_ctx = NULL;
1199 BIGNUM *tmp, *tmp_Z;
1200 BIGNUM **prod_Z = NULL;
1201 size_t i;
1202 int ret = 0;
1203
1204 if (num == 0)
1205 return 1;
1206
1207 if (ctx == NULL) {
1208 ctx = new_ctx = BN_CTX_new();
1209 if (ctx == NULL)
1210 return 0;
1211 }
1212
1213 BN_CTX_start(ctx);
1214 tmp = BN_CTX_get(ctx);
1215 tmp_Z = BN_CTX_get(ctx);
edea42c6 1216 if (tmp_Z == NULL)
0f113f3e
MC		 1217 goto err;
1218
cbe29648 1219 prod_Z = OPENSSL_malloc(num * sizeof(prod_Z[0]));
0f113f3e
MC		 1220 if (prod_Z == NULL)
1221 goto err;
1222 for (i = 0; i < num; i++) {
1223 prod_Z[i] = BN_new();
1224 if (prod_Z[i] == NULL)
1225 goto err;
1226 }
1227
1228 /*
1229 * Set each prod_Z[i] to the product of points[0]->Z .. points[i]->Z,
1230 * skipping any zero-valued inputs (pretend that they're 1).
1231 */
1232
1233 if (!BN_is_zero(points[0]->Z)) {
1234 if (!BN_copy(prod_Z[0], points[0]->Z))
1235 goto err;
1236 } else {
1237 if (group->meth->field_set_to_one != 0) {
1238 if (!group->meth->field_set_to_one(group, prod_Z[0], ctx))
1239 goto err;
1240 } else {
1241 if (!BN_one(prod_Z[0]))
1242 goto err;
1243 }
1244 }
1245
1246 for (i = 1; i < num; i++) {
1247 if (!BN_is_zero(points[i]->Z)) {
1248 if (!group->
1249 meth->field_mul(group, prod_Z[i], prod_Z[i - 1], points[i]->Z,
1250 ctx))
1251 goto err;
1252 } else {
1253 if (!BN_copy(prod_Z[i], prod_Z[i - 1]))
1254 goto err;
1255 }
1256 }
1257
1258 /*
1259 * Now use a single explicit inversion to replace every non-zero
1260 * points[i]->Z by its inverse.
1261 */
1262
1263 if (!BN_mod_inverse(tmp, prod_Z[num - 1], group->field, ctx)) {
1264 ECerr(EC_F_EC_GFP_SIMPLE_POINTS_MAKE_AFFINE, ERR_R_BN_LIB);
1265 goto err;
1266 }
1267 if (group->meth->field_encode != 0) {
1268 /*
1269 * In the Montgomery case, we just turned R*H (representing H) into
1270 * 1/(R*H), but we need R*(1/H) (representing 1/H); i.e. we need to
1271 * multiply by the Montgomery factor twice.
1272 */
1273 if (!group->meth->field_encode(group, tmp, tmp, ctx))
1274 goto err;
1275 if (!group->meth->field_encode(group, tmp, tmp, ctx))
1276 goto err;
1277 }
1278
1279 for (i = num - 1; i > 0; --i) {
1280 /*
1281 * Loop invariant: tmp is the product of the inverses of points[0]->Z
1282 * .. points[i]->Z (zero-valued inputs skipped).
1283 */
1284 if (!BN_is_zero(points[i]->Z)) {
1285 /*
1286 * Set tmp_Z to the inverse of points[i]->Z (as product of Z
1287 * inverses 0 .. i, Z values 0 .. i - 1).
1288 */
1289 if (!group->
1290 meth->field_mul(group, tmp_Z, prod_Z[i - 1], tmp, ctx))
1291 goto err;
1292 /*
1293 * Update tmp to satisfy the loop invariant for i - 1.
1294 */
1295 if (!group->meth->field_mul(group, tmp, tmp, points[i]->Z, ctx))
1296 goto err;
1297 /* Replace points[i]->Z by its inverse. */
1298 if (!BN_copy(points[i]->Z, tmp_Z))
1299 goto err;
1300 }
1301 }
1302
1303 if (!BN_is_zero(points[0]->Z)) {
1304 /* Replace points[0]->Z by its inverse. */
1305 if (!BN_copy(points[0]->Z, tmp))
1306 goto err;
1307 }
1308
1309 /* Finally, fix up the X and Y coordinates for all points. */
1310
1311 for (i = 0; i < num; i++) {
1312 EC_POINT *p = points[i];
1313
1314 if (!BN_is_zero(p->Z)) {
1315 /* turn (X, Y, 1/Z) into (X/Z^2, Y/Z^3, 1) */
1316
1317 if (!group->meth->field_sqr(group, tmp, p->Z, ctx))
1318 goto err;
1319 if (!group->meth->field_mul(group, p->X, p->X, tmp, ctx))
1320 goto err;
1321
1322 if (!group->meth->field_mul(group, tmp, tmp, p->Z, ctx))
1323 goto err;
1324 if (!group->meth->field_mul(group, p->Y, p->Y, tmp, ctx))
1325 goto err;
1326
1327 if (group->meth->field_set_to_one != 0) {
1328 if (!group->meth->field_set_to_one(group, p->Z, ctx))
1329 goto err;
1330 } else {
1331 if (!BN_one(p->Z))
1332 goto err;
1333 }
1334 p->Z_is_one = 1;
1335 }
1336 }
1337
1338 ret = 1;
0fe73d6c 1339
48fe4d62 1340 err:
0f113f3e 1341 BN_CTX_end(ctx);
23a1d5e9 1342 BN_CTX_free(new_ctx);
0f113f3e
MC		 1343 if (prod_Z != NULL) {
1344 for (i = 0; i < num; i++) {
1345 if (prod_Z[i] == NULL)
1346 break;
1347 BN_clear_free(prod_Z[i]);
1348 }
1349 OPENSSL_free(prod_Z);
1350 }
1351 return ret;
1352}
1353
1354int ec_GFp_simple_field_mul(const EC_GROUP *group, BIGNUM *r, const BIGNUM *a,
1355 const BIGNUM *b, BN_CTX *ctx)
1356{
1357 return BN_mod_mul(r, a, b, group->field, ctx);
1358}
1359
1360int ec_GFp_simple_field_sqr(const EC_GROUP *group, BIGNUM *r, const BIGNUM *a,
1361 BN_CTX *ctx)
1362{
1363 return BN_mod_sqr(r, a, group->field, ctx);
1364}
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