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diff --git a/src/lib/libcrypto/ec/ecp_smpl.c b/src/lib/libcrypto/ec/ecp_smpl.c
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1/* crypto/ec/ecp_smpl.c */
2/* Includes code written by Lenka Fibikova <fibikova@exp-math.uni-essen.de>
3 * for the OpenSSL project.
4 * Includes code written by Bodo Moeller for the OpenSSL project.
5*/
6/* ====================================================================
7 * Copyright (c) 1998-2002 The OpenSSL Project. All rights reserved.
8 *
9 * Redistribution and use in source and binary forms, with or without
10 * modification, are permitted provided that the following conditions
11 * are met:
12 *
13 * 1. Redistributions of source code must retain the above copyright
14 * notice, this list of conditions and the following disclaimer.
15 *
16 * 2. Redistributions in binary form must reproduce the above copyright
17 * notice, this list of conditions and the following disclaimer in
18 * the documentation and/or other materials provided with the
19 * distribution.
20 *
21 * 3. All advertising materials mentioning features or use of this
22 * software must display the following acknowledgment:
23 * "This product includes software developed by the OpenSSL Project
24 * for use in the OpenSSL Toolkit. (http://www.openssl.org/)"
25 *
26 * 4. The names "OpenSSL Toolkit" and "OpenSSL Project" must not be used to
27 * endorse or promote products derived from this software without
28 * prior written permission. For written permission, please contact
29 * openssl-core@openssl.org.
30 *
31 * 5. Products derived from this software may not be called "OpenSSL"
32 * nor may "OpenSSL" appear in their names without prior written
33 * permission of the OpenSSL Project.
34 *
35 * 6. Redistributions of any form whatsoever must retain the following
36 * acknowledgment:
37 * "This product includes software developed by the OpenSSL Project
38 * for use in the OpenSSL Toolkit (http://www.openssl.org/)"
39 *
40 * THIS SOFTWARE IS PROVIDED BY THE OpenSSL PROJECT ``AS IS'' AND ANY
41 * EXPRESSED OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
42 * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR
43 * PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE OpenSSL PROJECT OR
44 * ITS CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL,
45 * SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT
46 * NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES;
47 * LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
48 * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT,
49 * STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE)
50 * ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED
51 * OF THE POSSIBILITY OF SUCH DAMAGE.
52 * ====================================================================
53 *
54 * This product includes cryptographic software written by Eric Young
55 * (eay@cryptsoft.com). This product includes software written by Tim
56 * Hudson (tjh@cryptsoft.com).
57 *
58 */
59/* ====================================================================
60 * Copyright 2002 Sun Microsystems, Inc. ALL RIGHTS RESERVED.
61 * Portions of this software developed by SUN MICROSYSTEMS, INC.,
62 * and contributed to the OpenSSL project.
63 */
64
65#include <openssl/err.h>
66#include <openssl/symhacks.h>
67
68#ifdef OPENSSL_FIPS
69#include <openssl/fips.h>
70#endif
71
72#include "ec_lcl.h"
73
74const EC_METHOD *EC_GFp_simple_method(void)
75 {
76#ifdef OPENSSL_FIPS
77 return fips_ec_gfp_simple_method();
78#else
79 static const EC_METHOD ret = {
80 EC_FLAGS_DEFAULT_OCT,
81 NID_X9_62_prime_field,
82 ec_GFp_simple_group_init,
83 ec_GFp_simple_group_finish,
84 ec_GFp_simple_group_clear_finish,
85 ec_GFp_simple_group_copy,
86 ec_GFp_simple_group_set_curve,
87 ec_GFp_simple_group_get_curve,
88 ec_GFp_simple_group_get_degree,
89 ec_GFp_simple_group_check_discriminant,
90 ec_GFp_simple_point_init,
91 ec_GFp_simple_point_finish,
92 ec_GFp_simple_point_clear_finish,
93 ec_GFp_simple_point_copy,
94 ec_GFp_simple_point_set_to_infinity,
95 ec_GFp_simple_set_Jprojective_coordinates_GFp,
96 ec_GFp_simple_get_Jprojective_coordinates_GFp,
97 ec_GFp_simple_point_set_affine_coordinates,
98 ec_GFp_simple_point_get_affine_coordinates,
99 0,0,0,
100 ec_GFp_simple_add,
101 ec_GFp_simple_dbl,
102 ec_GFp_simple_invert,
103 ec_GFp_simple_is_at_infinity,
104 ec_GFp_simple_is_on_curve,
105 ec_GFp_simple_cmp,
106 ec_GFp_simple_make_affine,
107 ec_GFp_simple_points_make_affine,
108 0 /* mul */,
109 0 /* precompute_mult */,
110 0 /* have_precompute_mult */,
111 ec_GFp_simple_field_mul,
112 ec_GFp_simple_field_sqr,
113 0 /* field_div */,
114 0 /* field_encode */,
115 0 /* field_decode */,
116 0 /* field_set_to_one */ };
117
118 return &ret;
119#endif
120 }
121
122
123/* Most method functions in this file are designed to work with
124 * non-trivial representations of field elements if necessary
125 * (see ecp_mont.c): while standard modular addition and subtraction
126 * are used, the field_mul and field_sqr methods will be used for
127 * multiplication, and field_encode and field_decode (if defined)
128 * will be used for converting between representations.
129
130 * Functions ec_GFp_simple_points_make_affine() and
131 * ec_GFp_simple_point_get_affine_coordinates() specifically assume
132 * that if a non-trivial representation is used, it is a Montgomery
133 * representation (i.e. 'encoding' means multiplying by some factor R).
134 */
135
136
137int ec_GFp_simple_group_init(EC_GROUP *group)
138 {
139 BN_init(&group->field);
140 BN_init(&group->a);
141 BN_init(&group->b);
142 group->a_is_minus3 = 0;
143 return 1;
144 }
145
146
147void ec_GFp_simple_group_finish(EC_GROUP *group)
148 {
149 BN_free(&group->field);
150 BN_free(&group->a);
151 BN_free(&group->b);
152 }
153
154
155void ec_GFp_simple_group_clear_finish(EC_GROUP *group)
156 {
157 BN_clear_free(&group->field);
158 BN_clear_free(&group->a);
159 BN_clear_free(&group->b);
160 }
161
162
163int ec_GFp_simple_group_copy(EC_GROUP *dest, const EC_GROUP *src)
164 {
165 if (!BN_copy(&dest->field, &src->field)) return 0;
166 if (!BN_copy(&dest->a, &src->a)) return 0;
167 if (!BN_copy(&dest->b, &src->b)) return 0;
168
169 dest->a_is_minus3 = src->a_is_minus3;
170
171 return 1;
172 }
173
174
175int ec_GFp_simple_group_set_curve(EC_GROUP *group,
176 const BIGNUM *p, const BIGNUM *a, const BIGNUM *b, BN_CTX *ctx)
177 {
178 int ret = 0;
179 BN_CTX *new_ctx = NULL;
180 BIGNUM *tmp_a;
181
182 /* p must be a prime > 3 */
183 if (BN_num_bits(p) <= 2 || !BN_is_odd(p))
184 {
185 ECerr(EC_F_EC_GFP_SIMPLE_GROUP_SET_CURVE, EC_R_INVALID_FIELD);
186 return 0;
187 }
188
189 if (ctx == NULL)
190 {
191 ctx = new_ctx = BN_CTX_new();
192 if (ctx == NULL)
193 return 0;
194 }
195
196 BN_CTX_start(ctx);
197 tmp_a = BN_CTX_get(ctx);
198 if (tmp_a == NULL) goto err;
199
200 /* group->field */
201 if (!BN_copy(&group->field, p)) goto err;
202 BN_set_negative(&group->field, 0);
203
204 /* group->a */
205 if (!BN_nnmod(tmp_a, a, p, ctx)) goto err;
206 if (group->meth->field_encode)
207 { if (!group->meth->field_encode(group, &group->a, tmp_a, ctx)) goto err; }
208 else
209 if (!BN_copy(&group->a, tmp_a)) goto err;
210
211 /* group->b */
212 if (!BN_nnmod(&group->b, b, p, ctx)) goto err;
213 if (group->meth->field_encode)
214 if (!group->meth->field_encode(group, &group->b, &group->b, ctx)) goto err;
215
216 /* group->a_is_minus3 */
217 if (!BN_add_word(tmp_a, 3)) goto err;
218 group->a_is_minus3 = (0 == BN_cmp(tmp_a, &group->field));
219
220 ret = 1;
221
222 err:
223 BN_CTX_end(ctx);
224 if (new_ctx != NULL)
225 BN_CTX_free(new_ctx);
226 return ret;
227 }
228
229
230int ec_GFp_simple_group_get_curve(const EC_GROUP *group, BIGNUM *p, BIGNUM *a, BIGNUM *b, BN_CTX *ctx)
231 {
232 int ret = 0;
233 BN_CTX *new_ctx = NULL;
234
235 if (p != NULL)
236 {
237 if (!BN_copy(p, &group->field)) return 0;
238 }
239
240 if (a != NULL || b != NULL)
241 {
242 if (group->meth->field_decode)
243 {
244 if (ctx == NULL)
245 {
246 ctx = new_ctx = BN_CTX_new();
247 if (ctx == NULL)
248 return 0;
249 }
250 if (a != NULL)
251 {
252 if (!group->meth->field_decode(group, a, &group->a, ctx)) goto err;
253 }
254 if (b != NULL)
255 {
256 if (!group->meth->field_decode(group, b, &group->b, ctx)) goto err;
257 }
258 }
259 else
260 {
261 if (a != NULL)
262 {
263 if (!BN_copy(a, &group->a)) goto err;
264 }
265 if (b != NULL)
266 {
267 if (!BN_copy(b, &group->b)) goto err;
268 }
269 }
270 }
271
272 ret = 1;
273
274 err:
275 if (new_ctx)
276 BN_CTX_free(new_ctx);
277 return ret;
278 }
279
280
281int ec_GFp_simple_group_get_degree(const EC_GROUP *group)
282 {
283 return BN_num_bits(&group->field);
284 }
285
286
287int ec_GFp_simple_group_check_discriminant(const EC_GROUP *group, BN_CTX *ctx)
288 {
289 int ret = 0;
290 BIGNUM *a,*b,*order,*tmp_1,*tmp_2;
291 const BIGNUM *p = &group->field;
292 BN_CTX *new_ctx = NULL;
293
294 if (ctx == NULL)
295 {
296 ctx = new_ctx = BN_CTX_new();
297 if (ctx == NULL)
298 {
299 ECerr(EC_F_EC_GFP_SIMPLE_GROUP_CHECK_DISCRIMINANT, ERR_R_MALLOC_FAILURE);
300 goto err;
301 }
302 }
303 BN_CTX_start(ctx);
304 a = BN_CTX_get(ctx);
305 b = BN_CTX_get(ctx);
306 tmp_1 = BN_CTX_get(ctx);
307 tmp_2 = BN_CTX_get(ctx);
308 order = BN_CTX_get(ctx);
309 if (order == NULL) goto err;
310
311 if (group->meth->field_decode)
312 {
313 if (!group->meth->field_decode(group, a, &group->a, ctx)) goto err;
314 if (!group->meth->field_decode(group, b, &group->b, ctx)) goto err;
315 }
316 else
317 {
318 if (!BN_copy(a, &group->a)) goto err;
319 if (!BN_copy(b, &group->b)) goto err;
320 }
321
322 /* check the discriminant:
323 * y^2 = x^3 + a*x + b is an elliptic curve <=> 4*a^3 + 27*b^2 != 0 (mod p)
324 * 0 =< a, b < p */
325 if (BN_is_zero(a))
326 {
327 if (BN_is_zero(b)) goto err;
328 }
329 else if (!BN_is_zero(b))
330 {
331 if (!BN_mod_sqr(tmp_1, a, p, ctx)) goto err;
332 if (!BN_mod_mul(tmp_2, tmp_1, a, p, ctx)) goto err;
333 if (!BN_lshift(tmp_1, tmp_2, 2)) goto err;
334 /* tmp_1 = 4*a^3 */
335
336 if (!BN_mod_sqr(tmp_2, b, p, ctx)) goto err;
337 if (!BN_mul_word(tmp_2, 27)) goto err;
338 /* tmp_2 = 27*b^2 */
339
340 if (!BN_mod_add(a, tmp_1, tmp_2, p, ctx)) goto err;
341 if (BN_is_zero(a)) goto err;
342 }
343 ret = 1;
344
345err:
346 if (ctx != NULL)
347 BN_CTX_end(ctx);
348 if (new_ctx != NULL)
349 BN_CTX_free(new_ctx);
350 return ret;
351 }
352
353
354int ec_GFp_simple_point_init(EC_POINT *point)
355 {
356 BN_init(&point->X);
357 BN_init(&point->Y);
358 BN_init(&point->Z);
359 point->Z_is_one = 0;
360
361 return 1;
362 }
363
364
365void ec_GFp_simple_point_finish(EC_POINT *point)
366 {
367 BN_free(&point->X);
368 BN_free(&point->Y);
369 BN_free(&point->Z);
370 }
371
372
373void ec_GFp_simple_point_clear_finish(EC_POINT *point)
374 {
375 BN_clear_free(&point->X);
376 BN_clear_free(&point->Y);
377 BN_clear_free(&point->Z);
378 point->Z_is_one = 0;
379 }
380
381
382int ec_GFp_simple_point_copy(EC_POINT *dest, const EC_POINT *src)
383 {
384 if (!BN_copy(&dest->X, &src->X)) return 0;
385 if (!BN_copy(&dest->Y, &src->Y)) return 0;
386 if (!BN_copy(&dest->Z, &src->Z)) return 0;
387 dest->Z_is_one = src->Z_is_one;
388
389 return 1;
390 }
391
392
393int ec_GFp_simple_point_set_to_infinity(const EC_GROUP *group, EC_POINT *point)
394 {
395 point->Z_is_one = 0;
396 BN_zero(&point->Z);
397 return 1;
398 }
399
400
401int ec_GFp_simple_set_Jprojective_coordinates_GFp(const EC_GROUP *group, EC_POINT *point,
402 const BIGNUM *x, const BIGNUM *y, const BIGNUM *z, BN_CTX *ctx)
403 {
404 BN_CTX *new_ctx = NULL;
405 int ret = 0;
406
407 if (ctx == NULL)
408 {
409 ctx = new_ctx = BN_CTX_new();
410 if (ctx == NULL)
411 return 0;
412 }
413
414 if (x != NULL)
415 {
416 if (!BN_nnmod(&point->X, x, &group->field, ctx)) goto err;
417 if (group->meth->field_encode)
418 {
419 if (!group->meth->field_encode(group, &point->X, &point->X, ctx)) goto err;
420 }
421 }
422
423 if (y != NULL)
424 {
425 if (!BN_nnmod(&point->Y, y, &group->field, ctx)) goto err;
426 if (group->meth->field_encode)
427 {
428 if (!group->meth->field_encode(group, &point->Y, &point->Y, ctx)) goto err;
429 }
430 }
431
432 if (z != NULL)
433 {
434 int Z_is_one;
435
436 if (!BN_nnmod(&point->Z, z, &group->field, ctx)) goto err;
437 Z_is_one = BN_is_one(&point->Z);
438 if (group->meth->field_encode)
439 {
440 if (Z_is_one && (group->meth->field_set_to_one != 0))
441 {
442 if (!group->meth->field_set_to_one(group, &point->Z, ctx)) goto err;
443 }
444 else
445 {
446 if (!group->meth->field_encode(group, &point->Z, &point->Z, ctx)) goto err;
447 }
448 }
449 point->Z_is_one = Z_is_one;
450 }
451
452 ret = 1;
453
454 err:
455 if (new_ctx != NULL)
456 BN_CTX_free(new_ctx);
457 return ret;
458 }
459
460
461int ec_GFp_simple_get_Jprojective_coordinates_GFp(const EC_GROUP *group, const EC_POINT *point,
462 BIGNUM *x, BIGNUM *y, BIGNUM *z, BN_CTX *ctx)
463 {
464 BN_CTX *new_ctx = NULL;
465 int ret = 0;
466
467 if (group->meth->field_decode != 0)
468 {
469 if (ctx == NULL)
470 {
471 ctx = new_ctx = BN_CTX_new();
472 if (ctx == NULL)
473 return 0;
474 }
475
476 if (x != NULL)
477 {
478 if (!group->meth->field_decode(group, x, &point->X, ctx)) goto err;
479 }
480 if (y != NULL)
481 {
482 if (!group->meth->field_decode(group, y, &point->Y, ctx)) goto err;
483 }
484 if (z != NULL)
485 {
486 if (!group->meth->field_decode(group, z, &point->Z, ctx)) goto err;
487 }
488 }
489 else
490 {
491 if (x != NULL)
492 {
493 if (!BN_copy(x, &point->X)) goto err;
494 }
495 if (y != NULL)
496 {
497 if (!BN_copy(y, &point->Y)) goto err;
498 }
499 if (z != NULL)
500 {
501 if (!BN_copy(z, &point->Z)) goto err;
502 }
503 }
504
505 ret = 1;
506
507 err:
508 if (new_ctx != NULL)
509 BN_CTX_free(new_ctx);
510 return ret;
511 }
512
513
514int ec_GFp_simple_point_set_affine_coordinates(const EC_GROUP *group, EC_POINT *point,
515 const BIGNUM *x, const BIGNUM *y, BN_CTX *ctx)
516 {
517 if (x == NULL || y == NULL)
518 {
519 /* unlike for projective coordinates, we do not tolerate this */
520 ECerr(EC_F_EC_GFP_SIMPLE_POINT_SET_AFFINE_COORDINATES, ERR_R_PASSED_NULL_PARAMETER);
521 return 0;
522 }
523
524 return EC_POINT_set_Jprojective_coordinates_GFp(group, point, x, y, BN_value_one(), ctx);
525 }
526
527
528int ec_GFp_simple_point_get_affine_coordinates(const EC_GROUP *group, const EC_POINT *point,
529 BIGNUM *x, BIGNUM *y, BN_CTX *ctx)
530 {
531 BN_CTX *new_ctx = NULL;
532 BIGNUM *Z, *Z_1, *Z_2, *Z_3;
533 const BIGNUM *Z_;
534 int ret = 0;
535
536 if (EC_POINT_is_at_infinity(group, point))
537 {
538 ECerr(EC_F_EC_GFP_SIMPLE_POINT_GET_AFFINE_COORDINATES, EC_R_POINT_AT_INFINITY);
539 return 0;
540 }
541
542 if (ctx == NULL)
543 {
544 ctx = new_ctx = BN_CTX_new();
545 if (ctx == NULL)
546 return 0;
547 }
548
549 BN_CTX_start(ctx);
550 Z = BN_CTX_get(ctx);
551 Z_1 = BN_CTX_get(ctx);
552 Z_2 = BN_CTX_get(ctx);
553 Z_3 = BN_CTX_get(ctx);
554 if (Z_3 == NULL) goto err;
555
556 /* transform (X, Y, Z) into (x, y) := (X/Z^2, Y/Z^3) */
557
558 if (group->meth->field_decode)
559 {
560 if (!group->meth->field_decode(group, Z, &point->Z, ctx)) goto err;
561 Z_ = Z;
562 }
563 else
564 {
565 Z_ = &point->Z;
566 }
567
568 if (BN_is_one(Z_))
569 {
570 if (group->meth->field_decode)
571 {
572 if (x != NULL)
573 {
574 if (!group->meth->field_decode(group, x, &point->X, ctx)) goto err;
575 }
576 if (y != NULL)
577 {
578 if (!group->meth->field_decode(group, y, &point->Y, ctx)) goto err;
579 }
580 }
581 else
582 {
583 if (x != NULL)
584 {
585 if (!BN_copy(x, &point->X)) goto err;
586 }
587 if (y != NULL)
588 {
589 if (!BN_copy(y, &point->Y)) goto err;
590 }
591 }
592 }
593 else
594 {
595 if (!BN_mod_inverse(Z_1, Z_, &group->field, ctx))
596 {
597 ECerr(EC_F_EC_GFP_SIMPLE_POINT_GET_AFFINE_COORDINATES, ERR_R_BN_LIB);
598 goto err;
599 }
600
601 if (group->meth->field_encode == 0)
602 {
603 /* field_sqr works on standard representation */
604 if (!group->meth->field_sqr(group, Z_2, Z_1, ctx)) goto err;
605 }
606 else
607 {
608 if (!BN_mod_sqr(Z_2, Z_1, &group->field, ctx)) goto err;
609 }
610
611 if (x != NULL)
612 {
613 /* in the Montgomery case, field_mul will cancel out Montgomery factor in X: */
614 if (!group->meth->field_mul(group, x, &point->X, Z_2, ctx)) goto err;
615 }
616
617 if (y != NULL)
618 {
619 if (group->meth->field_encode == 0)
620 {
621 /* field_mul works on standard representation */
622 if (!group->meth->field_mul(group, Z_3, Z_2, Z_1, ctx)) goto err;
623 }
624 else
625 {
626 if (!BN_mod_mul(Z_3, Z_2, Z_1, &group->field, ctx)) goto err;
627 }
628
629 /* in the Montgomery case, field_mul will cancel out Montgomery factor in Y: */
630 if (!group->meth->field_mul(group, y, &point->Y, Z_3, ctx)) goto err;
631 }
632 }
633
634 ret = 1;
635
636 err:
637 BN_CTX_end(ctx);
638 if (new_ctx != NULL)
639 BN_CTX_free(new_ctx);
640 return ret;
641 }
642
643int ec_GFp_simple_add(const EC_GROUP *group, EC_POINT *r, const EC_POINT *a, const EC_POINT *b, BN_CTX *ctx)
644 {
645 int (*field_mul)(const EC_GROUP *, BIGNUM *, const BIGNUM *, const BIGNUM *, BN_CTX *);
646 int (*field_sqr)(const EC_GROUP *, BIGNUM *, const BIGNUM *, BN_CTX *);
647 const BIGNUM *p;
648 BN_CTX *new_ctx = NULL;
649 BIGNUM *n0, *n1, *n2, *n3, *n4, *n5, *n6;
650 int ret = 0;
651
652 if (a == b)
653 return EC_POINT_dbl(group, r, a, ctx);
654 if (EC_POINT_is_at_infinity(group, a))
655 return EC_POINT_copy(r, b);
656 if (EC_POINT_is_at_infinity(group, b))
657 return EC_POINT_copy(r, a);
658
659 field_mul = group->meth->field_mul;
660 field_sqr = group->meth->field_sqr;
661 p = &group->field;
662
663 if (ctx == NULL)
664 {
665 ctx = new_ctx = BN_CTX_new();
666 if (ctx == NULL)
667 return 0;
668 }
669
670 BN_CTX_start(ctx);
671 n0 = BN_CTX_get(ctx);
672 n1 = BN_CTX_get(ctx);
673 n2 = BN_CTX_get(ctx);
674 n3 = BN_CTX_get(ctx);
675 n4 = BN_CTX_get(ctx);
676 n5 = BN_CTX_get(ctx);
677 n6 = BN_CTX_get(ctx);
678 if (n6 == NULL) goto end;
679
680 /* Note that in this function we must not read components of 'a' or 'b'
681 * once we have written the corresponding components of 'r'.
682 * ('r' might be one of 'a' or 'b'.)
683 */
684
685 /* n1, n2 */
686 if (b->Z_is_one)
687 {
688 if (!BN_copy(n1, &a->X)) goto end;
689 if (!BN_copy(n2, &a->Y)) goto end;
690 /* n1 = X_a */
691 /* n2 = Y_a */
692 }
693 else
694 {
695 if (!field_sqr(group, n0, &b->Z, ctx)) goto end;
696 if (!field_mul(group, n1, &a->X, n0, ctx)) goto end;
697 /* n1 = X_a * Z_b^2 */
698
699 if (!field_mul(group, n0, n0, &b->Z, ctx)) goto end;
700 if (!field_mul(group, n2, &a->Y, n0, ctx)) goto end;
701 /* n2 = Y_a * Z_b^3 */
702 }
703
704 /* n3, n4 */
705 if (a->Z_is_one)
706 {
707 if (!BN_copy(n3, &b->X)) goto end;
708 if (!BN_copy(n4, &b->Y)) goto end;
709 /* n3 = X_b */
710 /* n4 = Y_b */
711 }
712 else
713 {
714 if (!field_sqr(group, n0, &a->Z, ctx)) goto end;
715 if (!field_mul(group, n3, &b->X, n0, ctx)) goto end;
716 /* n3 = X_b * Z_a^2 */
717
718 if (!field_mul(group, n0, n0, &a->Z, ctx)) goto end;
719 if (!field_mul(group, n4, &b->Y, n0, ctx)) goto end;
720 /* n4 = Y_b * Z_a^3 */
721 }
722
723 /* n5, n6 */
724 if (!BN_mod_sub_quick(n5, n1, n3, p)) goto end;
725 if (!BN_mod_sub_quick(n6, n2, n4, p)) goto end;
726 /* n5 = n1 - n3 */
727 /* n6 = n2 - n4 */
728
729 if (BN_is_zero(n5))
730 {
731 if (BN_is_zero(n6))
732 {
733 /* a is the same point as b */
734 BN_CTX_end(ctx);
735 ret = EC_POINT_dbl(group, r, a, ctx);
736 ctx = NULL;
737 goto end;
738 }
739 else
740 {
741 /* a is the inverse of b */
742 BN_zero(&r->Z);
743 r->Z_is_one = 0;
744 ret = 1;
745 goto end;
746 }
747 }
748
749 /* 'n7', 'n8' */
750 if (!BN_mod_add_quick(n1, n1, n3, p)) goto end;
751 if (!BN_mod_add_quick(n2, n2, n4, p)) goto end;
752 /* 'n7' = n1 + n3 */
753 /* 'n8' = n2 + n4 */
754
755 /* Z_r */
756 if (a->Z_is_one && b->Z_is_one)
757 {
758 if (!BN_copy(&r->Z, n5)) goto end;
759 }
760 else
761 {
762 if (a->Z_is_one)
763 { if (!BN_copy(n0, &b->Z)) goto end; }
764 else if (b->Z_is_one)
765 { if (!BN_copy(n0, &a->Z)) goto end; }
766 else
767 { if (!field_mul(group, n0, &a->Z, &b->Z, ctx)) goto end; }
768 if (!field_mul(group, &r->Z, n0, n5, ctx)) goto end;
769 }
770 r->Z_is_one = 0;
771 /* Z_r = Z_a * Z_b * n5 */
772
773 /* X_r */
774 if (!field_sqr(group, n0, n6, ctx)) goto end;
775 if (!field_sqr(group, n4, n5, ctx)) goto end;
776 if (!field_mul(group, n3, n1, n4, ctx)) goto end;
777 if (!BN_mod_sub_quick(&r->X, n0, n3, p)) goto end;
778 /* X_r = n6^2 - n5^2 * 'n7' */
779
780 /* 'n9' */
781 if (!BN_mod_lshift1_quick(n0, &r->X, p)) goto end;
782 if (!BN_mod_sub_quick(n0, n3, n0, p)) goto end;
783 /* n9 = n5^2 * 'n7' - 2 * X_r */
784
785 /* Y_r */
786 if (!field_mul(group, n0, n0, n6, ctx)) goto end;
787 if (!field_mul(group, n5, n4, n5, ctx)) goto end; /* now n5 is n5^3 */
788 if (!field_mul(group, n1, n2, n5, ctx)) goto end;
789 if (!BN_mod_sub_quick(n0, n0, n1, p)) goto end;
790 if (BN_is_odd(n0))
791 if (!BN_add(n0, n0, p)) goto end;
792 /* now 0 <= n0 < 2*p, and n0 is even */
793 if (!BN_rshift1(&r->Y, n0)) goto end;
794 /* Y_r = (n6 * 'n9' - 'n8' * 'n5^3') / 2 */
795
796 ret = 1;
797
798 end:
799 if (ctx) /* otherwise we already called BN_CTX_end */
800 BN_CTX_end(ctx);
801 if (new_ctx != NULL)
802 BN_CTX_free(new_ctx);
803 return ret;
804 }
805
806
807int ec_GFp_simple_dbl(const EC_GROUP *group, EC_POINT *r, const EC_POINT *a, BN_CTX *ctx)
808 {
809 int (*field_mul)(const EC_GROUP *, BIGNUM *, const BIGNUM *, const BIGNUM *, BN_CTX *);
810 int (*field_sqr)(const EC_GROUP *, BIGNUM *, const BIGNUM *, BN_CTX *);
811 const BIGNUM *p;
812 BN_CTX *new_ctx = NULL;
813 BIGNUM *n0, *n1, *n2, *n3;
814 int ret = 0;
815
816 if (EC_POINT_is_at_infinity(group, a))
817 {
818 BN_zero(&r->Z);
819 r->Z_is_one = 0;
820 return 1;
821 }
822
823 field_mul = group->meth->field_mul;
824 field_sqr = group->meth->field_sqr;
825 p = &group->field;
826
827 if (ctx == NULL)
828 {
829 ctx = new_ctx = BN_CTX_new();
830 if (ctx == NULL)
831 return 0;
832 }
833
834 BN_CTX_start(ctx);
835 n0 = BN_CTX_get(ctx);
836 n1 = BN_CTX_get(ctx);
837 n2 = BN_CTX_get(ctx);
838 n3 = BN_CTX_get(ctx);
839 if (n3 == NULL) goto err;
840
841 /* Note that in this function we must not read components of 'a'
842 * once we have written the corresponding components of 'r'.
843 * ('r' might the same as 'a'.)
844 */
845
846 /* n1 */
847 if (a->Z_is_one)
848 {
849 if (!field_sqr(group, n0, &a->X, ctx)) goto err;
850 if (!BN_mod_lshift1_quick(n1, n0, p)) goto err;
851 if (!BN_mod_add_quick(n0, n0, n1, p)) goto err;
852 if (!BN_mod_add_quick(n1, n0, &group->a, p)) goto err;
853 /* n1 = 3 * X_a^2 + a_curve */
854 }
855 else if (group->a_is_minus3)
856 {
857 if (!field_sqr(group, n1, &a->Z, ctx)) goto err;
858 if (!BN_mod_add_quick(n0, &a->X, n1, p)) goto err;
859 if (!BN_mod_sub_quick(n2, &a->X, n1, p)) goto err;
860 if (!field_mul(group, n1, n0, n2, ctx)) goto err;
861 if (!BN_mod_lshift1_quick(n0, n1, p)) goto err;
862 if (!BN_mod_add_quick(n1, n0, n1, p)) goto err;
863 /* n1 = 3 * (X_a + Z_a^2) * (X_a - Z_a^2)
864 * = 3 * X_a^2 - 3 * Z_a^4 */
865 }
866 else
867 {
868 if (!field_sqr(group, n0, &a->X, ctx)) goto err;
869 if (!BN_mod_lshift1_quick(n1, n0, p)) goto err;
870 if (!BN_mod_add_quick(n0, n0, n1, p)) goto err;
871 if (!field_sqr(group, n1, &a->Z, ctx)) goto err;
872 if (!field_sqr(group, n1, n1, ctx)) goto err;
873 if (!field_mul(group, n1, n1, &group->a, ctx)) goto err;
874 if (!BN_mod_add_quick(n1, n1, n0, p)) goto err;
875 /* n1 = 3 * X_a^2 + a_curve * Z_a^4 */
876 }
877
878 /* Z_r */
879 if (a->Z_is_one)
880 {
881 if (!BN_copy(n0, &a->Y)) goto err;
882 }
883 else
884 {
885 if (!field_mul(group, n0, &a->Y, &a->Z, ctx)) goto err;
886 }
887 if (!BN_mod_lshift1_quick(&r->Z, n0, p)) goto err;
888 r->Z_is_one = 0;
889 /* Z_r = 2 * Y_a * Z_a */
890
891 /* n2 */
892 if (!field_sqr(group, n3, &a->Y, ctx)) goto err;
893 if (!field_mul(group, n2, &a->X, n3, ctx)) goto err;
894 if (!BN_mod_lshift_quick(n2, n2, 2, p)) goto err;
895 /* n2 = 4 * X_a * Y_a^2 */
896
897 /* X_r */
898 if (!BN_mod_lshift1_quick(n0, n2, p)) goto err;
899 if (!field_sqr(group, &r->X, n1, ctx)) goto err;
900 if (!BN_mod_sub_quick(&r->X, &r->X, n0, p)) goto err;
901 /* X_r = n1^2 - 2 * n2 */
902
903 /* n3 */
904 if (!field_sqr(group, n0, n3, ctx)) goto err;
905 if (!BN_mod_lshift_quick(n3, n0, 3, p)) goto err;
906 /* n3 = 8 * Y_a^4 */
907
908 /* Y_r */
909 if (!BN_mod_sub_quick(n0, n2, &r->X, p)) goto err;
910 if (!field_mul(group, n0, n1, n0, ctx)) goto err;
911 if (!BN_mod_sub_quick(&r->Y, n0, n3, p)) goto err;
912 /* Y_r = n1 * (n2 - X_r) - n3 */
913
914 ret = 1;
915
916 err:
917 BN_CTX_end(ctx);
918 if (new_ctx != NULL)
919 BN_CTX_free(new_ctx);
920 return ret;
921 }
922
923
924int ec_GFp_simple_invert(const EC_GROUP *group, EC_POINT *point, BN_CTX *ctx)
925 {
926 if (EC_POINT_is_at_infinity(group, point) || BN_is_zero(&point->Y))
927 /* point is its own inverse */
928 return 1;
929
930 return BN_usub(&point->Y, &group->field, &point->Y);
931 }
932
933
934int ec_GFp_simple_is_at_infinity(const EC_GROUP *group, const EC_POINT *point)
935 {
936 return BN_is_zero(&point->Z);
937 }
938
939
940int ec_GFp_simple_is_on_curve(const EC_GROUP *group, const EC_POINT *point, BN_CTX *ctx)
941 {
942 int (*field_mul)(const EC_GROUP *, BIGNUM *, const BIGNUM *, const BIGNUM *, BN_CTX *);
943 int (*field_sqr)(const EC_GROUP *, BIGNUM *, const BIGNUM *, BN_CTX *);
944 const BIGNUM *p;
945 BN_CTX *new_ctx = NULL;
946 BIGNUM *rh, *tmp, *Z4, *Z6;
947 int ret = -1;
948
949 if (EC_POINT_is_at_infinity(group, point))
950 return 1;
951
952 field_mul = group->meth->field_mul;
953 field_sqr = group->meth->field_sqr;
954 p = &group->field;
955
956 if (ctx == NULL)
957 {
958 ctx = new_ctx = BN_CTX_new();
959 if (ctx == NULL)
960 return -1;
961 }
962
963 BN_CTX_start(ctx);
964 rh = BN_CTX_get(ctx);
965 tmp = BN_CTX_get(ctx);
966 Z4 = BN_CTX_get(ctx);
967 Z6 = BN_CTX_get(ctx);
968 if (Z6 == NULL) goto err;
969
970 /* We have a curve defined by a Weierstrass equation
971 * y^2 = x^3 + a*x + b.
972 * The point to consider is given in Jacobian projective coordinates
973 * where (X, Y, Z) represents (x, y) = (X/Z^2, Y/Z^3).
974 * Substituting this and multiplying by Z^6 transforms the above equation into
975 * Y^2 = X^3 + a*X*Z^4 + b*Z^6.
976 * To test this, we add up the right-hand side in 'rh'.
977 */
978
979 /* rh := X^2 */
980 if (!field_sqr(group, rh, &point->X, ctx)) goto err;
981
982 if (!point->Z_is_one)
983 {
984 if (!field_sqr(group, tmp, &point->Z, ctx)) goto err;
985 if (!field_sqr(group, Z4, tmp, ctx)) goto err;
986 if (!field_mul(group, Z6, Z4, tmp, ctx)) goto err;
987
988 /* rh := (rh + a*Z^4)*X */
989 if (group->a_is_minus3)
990 {
991 if (!BN_mod_lshift1_quick(tmp, Z4, p)) goto err;
992 if (!BN_mod_add_quick(tmp, tmp, Z4, p)) goto err;
993 if (!BN_mod_sub_quick(rh, rh, tmp, p)) goto err;
994 if (!field_mul(group, rh, rh, &point->X, ctx)) goto err;
995 }
996 else
997 {
998 if (!field_mul(group, tmp, Z4, &group->a, ctx)) goto err;
999 if (!BN_mod_add_quick(rh, rh, tmp, p)) goto err;
1000 if (!field_mul(group, rh, rh, &point->X, ctx)) goto err;
1001 }
1002
1003 /* rh := rh + b*Z^6 */
1004 if (!field_mul(group, tmp, &group->b, Z6, ctx)) goto err;
1005 if (!BN_mod_add_quick(rh, rh, tmp, p)) goto err;
1006 }
1007 else
1008 {
1009 /* point->Z_is_one */
1010
1011 /* rh := (rh + a)*X */
1012 if (!BN_mod_add_quick(rh, rh, &group->a, p)) goto err;
1013 if (!field_mul(group, rh, rh, &point->X, ctx)) goto err;
1014 /* rh := rh + b */
1015 if (!BN_mod_add_quick(rh, rh, &group->b, p)) goto err;
1016 }
1017
1018 /* 'lh' := Y^2 */
1019 if (!field_sqr(group, tmp, &point->Y, ctx)) goto err;
1020
1021 ret = (0 == BN_ucmp(tmp, rh));
1022
1023 err:
1024 BN_CTX_end(ctx);
1025 if (new_ctx != NULL)
1026 BN_CTX_free(new_ctx);
1027 return ret;
1028 }
1029
1030
1031int ec_GFp_simple_cmp(const EC_GROUP *group, const EC_POINT *a, const EC_POINT *b, BN_CTX *ctx)
1032 {
1033 /* return values:
1034 * -1 error
1035 * 0 equal (in affine coordinates)
1036 * 1 not equal
1037 */
1038
1039 int (*field_mul)(const EC_GROUP *, BIGNUM *, const BIGNUM *, const BIGNUM *, BN_CTX *);
1040 int (*field_sqr)(const EC_GROUP *, BIGNUM *, const BIGNUM *, BN_CTX *);
1041 BN_CTX *new_ctx = NULL;
1042 BIGNUM *tmp1, *tmp2, *Za23, *Zb23;
1043 const BIGNUM *tmp1_, *tmp2_;
1044 int ret = -1;
1045
1046 if (EC_POINT_is_at_infinity(group, a))
1047 {
1048 return EC_POINT_is_at_infinity(group, b) ? 0 : 1;
1049 }
1050
1051 if (EC_POINT_is_at_infinity(group, b))
1052 return 1;
1053
1054 if (a->Z_is_one && b->Z_is_one)
1055 {
1056 return ((BN_cmp(&a->X, &b->X) == 0) && BN_cmp(&a->Y, &b->Y) == 0) ? 0 : 1;
1057 }
1058
1059 field_mul = group->meth->field_mul;
1060 field_sqr = group->meth->field_sqr;
1061
1062 if (ctx == NULL)
1063 {
1064 ctx = new_ctx = BN_CTX_new();
1065 if (ctx == NULL)
1066 return -1;
1067 }
1068
1069 BN_CTX_start(ctx);
1070 tmp1 = BN_CTX_get(ctx);
1071 tmp2 = BN_CTX_get(ctx);
1072 Za23 = BN_CTX_get(ctx);
1073 Zb23 = BN_CTX_get(ctx);
1074 if (Zb23 == NULL) goto end;
1075
1076 /* We have to decide whether
1077 * (X_a/Z_a^2, Y_a/Z_a^3) = (X_b/Z_b^2, Y_b/Z_b^3),
1078 * or equivalently, whether
1079 * (X_a*Z_b^2, Y_a*Z_b^3) = (X_b*Z_a^2, Y_b*Z_a^3).
1080 */
1081
1082 if (!b->Z_is_one)
1083 {
1084 if (!field_sqr(group, Zb23, &b->Z, ctx)) goto end;
1085 if (!field_mul(group, tmp1, &a->X, Zb23, ctx)) goto end;
1086 tmp1_ = tmp1;
1087 }
1088 else
1089 tmp1_ = &a->X;
1090 if (!a->Z_is_one)
1091 {
1092 if (!field_sqr(group, Za23, &a->Z, ctx)) goto end;
1093 if (!field_mul(group, tmp2, &b->X, Za23, ctx)) goto end;
1094 tmp2_ = tmp2;
1095 }
1096 else
1097 tmp2_ = &b->X;
1098
1099 /* compare X_a*Z_b^2 with X_b*Z_a^2 */
1100 if (BN_cmp(tmp1_, tmp2_) != 0)
1101 {
1102 ret = 1; /* points differ */
1103 goto end;
1104 }
1105
1106
1107 if (!b->Z_is_one)
1108 {
1109 if (!field_mul(group, Zb23, Zb23, &b->Z, ctx)) goto end;
1110 if (!field_mul(group, tmp1, &a->Y, Zb23, ctx)) goto end;
1111 /* tmp1_ = tmp1 */
1112 }
1113 else
1114 tmp1_ = &a->Y;
1115 if (!a->Z_is_one)
1116 {
1117 if (!field_mul(group, Za23, Za23, &a->Z, ctx)) goto end;
1118 if (!field_mul(group, tmp2, &b->Y, Za23, ctx)) goto end;
1119 /* tmp2_ = tmp2 */
1120 }
1121 else
1122 tmp2_ = &b->Y;
1123
1124 /* compare Y_a*Z_b^3 with Y_b*Z_a^3 */
1125 if (BN_cmp(tmp1_, tmp2_) != 0)
1126 {
1127 ret = 1; /* points differ */
1128 goto end;
1129 }
1130
1131 /* points are equal */
1132 ret = 0;
1133
1134 end:
1135 BN_CTX_end(ctx);
1136 if (new_ctx != NULL)
1137 BN_CTX_free(new_ctx);
1138 return ret;
1139 }
1140
1141
1142int ec_GFp_simple_make_affine(const EC_GROUP *group, EC_POINT *point, BN_CTX *ctx)
1143 {
1144 BN_CTX *new_ctx = NULL;
1145 BIGNUM *x, *y;
1146 int ret = 0;
1147
1148 if (point->Z_is_one || EC_POINT_is_at_infinity(group, point))
1149 return 1;
1150
1151 if (ctx == NULL)
1152 {
1153 ctx = new_ctx = BN_CTX_new();
1154 if (ctx == NULL)
1155 return 0;
1156 }
1157
1158 BN_CTX_start(ctx);
1159 x = BN_CTX_get(ctx);
1160 y = BN_CTX_get(ctx);
1161 if (y == NULL) goto err;
1162
1163 if (!EC_POINT_get_affine_coordinates_GFp(group, point, x, y, ctx)) goto err;
1164 if (!EC_POINT_set_affine_coordinates_GFp(group, point, x, y, ctx)) goto err;
1165 if (!point->Z_is_one)
1166 {
1167 ECerr(EC_F_EC_GFP_SIMPLE_MAKE_AFFINE, ERR_R_INTERNAL_ERROR);
1168 goto err;
1169 }
1170
1171 ret = 1;
1172
1173 err:
1174 BN_CTX_end(ctx);
1175 if (new_ctx != NULL)
1176 BN_CTX_free(new_ctx);
1177 return ret;
1178 }
1179
1180
1181int ec_GFp_simple_points_make_affine(const EC_GROUP *group, size_t num, EC_POINT *points[], BN_CTX *ctx)
1182 {
1183 BN_CTX *new_ctx = NULL;
1184 BIGNUM *tmp0, *tmp1;
1185 size_t pow2 = 0;
1186 BIGNUM **heap = NULL;
1187 size_t i;
1188 int ret = 0;
1189
1190 if (num == 0)
1191 return 1;
1192
1193 if (ctx == NULL)
1194 {
1195 ctx = new_ctx = BN_CTX_new();
1196 if (ctx == NULL)
1197 return 0;
1198 }
1199
1200 BN_CTX_start(ctx);
1201 tmp0 = BN_CTX_get(ctx);
1202 tmp1 = BN_CTX_get(ctx);
1203 if (tmp0 == NULL || tmp1 == NULL) goto err;
1204
1205 /* Before converting the individual points, compute inverses of all Z values.
1206 * Modular inversion is rather slow, but luckily we can do with a single
1207 * explicit inversion, plus about 3 multiplications per input value.
1208 */
1209
1210 pow2 = 1;
1211 while (num > pow2)
1212 pow2 <<= 1;
1213 /* Now pow2 is the smallest power of 2 satifsying pow2 >= num.
1214 * We need twice that. */
1215 pow2 <<= 1;
1216
1217 heap = OPENSSL_malloc(pow2 * sizeof heap[0]);
1218 if (heap == NULL) goto err;
1219
1220 /* The array is used as a binary tree, exactly as in heapsort:
1221 *
1222 * heap[1]
1223 * heap[2] heap[3]
1224 * heap[4] heap[5] heap[6] heap[7]
1225 * heap[8]heap[9] heap[10]heap[11] heap[12]heap[13] heap[14] heap[15]
1226 *
1227 * We put the Z's in the last line;
1228 * then we set each other node to the product of its two child-nodes (where
1229 * empty or 0 entries are treated as ones);
1230 * then we invert heap[1];
1231 * then we invert each other node by replacing it by the product of its
1232 * parent (after inversion) and its sibling (before inversion).
1233 */
1234 heap[0] = NULL;
1235 for (i = pow2/2 - 1; i > 0; i--)
1236 heap[i] = NULL;
1237 for (i = 0; i < num; i++)
1238 heap[pow2/2 + i] = &points[i]->Z;
1239 for (i = pow2/2 + num; i < pow2; i++)
1240 heap[i] = NULL;
1241
1242 /* set each node to the product of its children */
1243 for (i = pow2/2 - 1; i > 0; i--)
1244 {
1245 heap[i] = BN_new();
1246 if (heap[i] == NULL) goto err;
1247
1248 if (heap[2*i] != NULL)
1249 {
1250 if ((heap[2*i + 1] == NULL) || BN_is_zero(heap[2*i + 1]))
1251 {
1252 if (!BN_copy(heap[i], heap[2*i])) goto err;
1253 }
1254 else
1255 {
1256 if (BN_is_zero(heap[2*i]))
1257 {
1258 if (!BN_copy(heap[i], heap[2*i + 1])) goto err;
1259 }
1260 else
1261 {
1262 if (!group->meth->field_mul(group, heap[i],
1263 heap[2*i], heap[2*i + 1], ctx)) goto err;
1264 }
1265 }
1266 }
1267 }
1268
1269 /* invert heap[1] */
1270 if (!BN_is_zero(heap[1]))
1271 {
1272 if (!BN_mod_inverse(heap[1], heap[1], &group->field, ctx))
1273 {
1274 ECerr(EC_F_EC_GFP_SIMPLE_POINTS_MAKE_AFFINE, ERR_R_BN_LIB);
1275 goto err;
1276 }
1277 }
1278 if (group->meth->field_encode != 0)
1279 {
1280 /* in the Montgomery case, we just turned R*H (representing H)
1281 * into 1/(R*H), but we need R*(1/H) (representing 1/H);
1282 * i.e. we have need to multiply by the Montgomery factor twice */
1283 if (!group->meth->field_encode(group, heap[1], heap[1], ctx)) goto err;
1284 if (!group->meth->field_encode(group, heap[1], heap[1], ctx)) goto err;
1285 }
1286
1287 /* set other heap[i]'s to their inverses */
1288 for (i = 2; i < pow2/2 + num; i += 2)
1289 {
1290 /* i is even */
1291 if ((heap[i + 1] != NULL) && !BN_is_zero(heap[i + 1]))
1292 {
1293 if (!group->meth->field_mul(group, tmp0, heap[i/2], heap[i + 1], ctx)) goto err;
1294 if (!group->meth->field_mul(group, tmp1, heap[i/2], heap[i], ctx)) goto err;
1295 if (!BN_copy(heap[i], tmp0)) goto err;
1296 if (!BN_copy(heap[i + 1], tmp1)) goto err;
1297 }
1298 else
1299 {
1300 if (!BN_copy(heap[i], heap[i/2])) goto err;
1301 }
1302 }
1303
1304 /* we have replaced all non-zero Z's by their inverses, now fix up all the points */
1305 for (i = 0; i < num; i++)
1306 {
1307 EC_POINT *p = points[i];
1308
1309 if (!BN_is_zero(&p->Z))
1310 {
1311 /* turn (X, Y, 1/Z) into (X/Z^2, Y/Z^3, 1) */
1312
1313 if (!group->meth->field_sqr(group, tmp1, &p->Z, ctx)) goto err;
1314 if (!group->meth->field_mul(group, &p->X, &p->X, tmp1, ctx)) goto err;
1315
1316 if (!group->meth->field_mul(group, tmp1, tmp1, &p->Z, ctx)) goto err;
1317 if (!group->meth->field_mul(group, &p->Y, &p->Y, tmp1, ctx)) goto err;
1318
1319 if (group->meth->field_set_to_one != 0)
1320 {
1321 if (!group->meth->field_set_to_one(group, &p->Z, ctx)) goto err;
1322 }
1323 else
1324 {
1325 if (!BN_one(&p->Z)) goto err;
1326 }
1327 p->Z_is_one = 1;
1328 }
1329 }
1330
1331 ret = 1;
1332
1333 err:
1334 BN_CTX_end(ctx);
1335 if (new_ctx != NULL)
1336 BN_CTX_free(new_ctx);
1337 if (heap != NULL)
1338 {
1339 /* heap[pow2/2] .. heap[pow2-1] have not been allocated locally! */
1340 for (i = pow2/2 - 1; i > 0; i--)
1341 {
1342 if (heap[i] != NULL)
1343 BN_clear_free(heap[i]);
1344 }
1345 OPENSSL_free(heap);
1346 }
1347 return ret;
1348 }
1349
1350
1351int ec_GFp_simple_field_mul(const EC_GROUP *group, BIGNUM *r, const BIGNUM *a, const BIGNUM *b, BN_CTX *ctx)
1352 {
1353 return BN_mod_mul(r, a, b, &group->field, ctx);
1354 }
1355
1356
1357int ec_GFp_simple_field_sqr(const EC_GROUP *group, BIGNUM *r, const BIGNUM *a, BN_CTX *ctx)
1358 {
1359 return BN_mod_sqr(r, a, &group->field, ctx);
1360 }
generated by cgit v1.2.3-55-g6feb (git 2.39.1) at 2025-08-11 21:43:37 +0000