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[thirdparty/openssl.git] / crypto / ec / ecp_smpl.c
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f8fe20e0 1/* crypto/ec/ecp_smpl.c */
0f113f3e
MC		 2/*
3 * Includes code written by Lenka Fibikova <fibikova@exp-math.uni-essen.de>
4 * for the OpenSSL project. Includes code written by Bodo Moeller for the
5 * OpenSSL project.
6 */
f8fe20e0 7/* ====================================================================
af28dd6c 8 * Copyright (c) 1998-2002 The OpenSSL Project. All rights reserved.
f8fe20e0
BM		 9 *
10 * Redistribution and use in source and binary forms, with or without
11 * modification, are permitted provided that the following conditions
12 * are met:
13 *
14 * 1. Redistributions of source code must retain the above copyright
0f113f3e 15 * notice, this list of conditions and the following disclaimer.
f8fe20e0
BM		 16 *
17 * 2. Redistributions in binary form must reproduce the above copyright
18 * notice, this list of conditions and the following disclaimer in
19 * the documentation and/or other materials provided with the
20 * distribution.
21 *
22 * 3. All advertising materials mentioning features or use of this
23 * software must display the following acknowledgment:
24 * "This product includes software developed by the OpenSSL Project
25 * for use in the OpenSSL Toolkit. (http://www.openssl.org/)"
26 *
27 * 4. The names "OpenSSL Toolkit" and "OpenSSL Project" must not be used to
28 * endorse or promote products derived from this software without
29 * prior written permission. For written permission, please contact
30 * openssl-core@openssl.org.
31 *
32 * 5. Products derived from this software may not be called "OpenSSL"
33 * nor may "OpenSSL" appear in their names without prior written
34 * permission of the OpenSSL Project.
35 *
36 * 6. Redistributions of any form whatsoever must retain the following
37 * acknowledgment:
38 * "This product includes software developed by the OpenSSL Project
39 * for use in the OpenSSL Toolkit (http://www.openssl.org/)"
40 *
41 * THIS SOFTWARE IS PROVIDED BY THE OpenSSL PROJECT ``AS IS'' AND ANY
42 * EXPRESSED OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
43 * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR
44 * PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE OpenSSL PROJECT OR
45 * ITS CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL,
46 * SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT
47 * NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES;
48 * LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
49 * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT,
50 * STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE)
51 * ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED
52 * OF THE POSSIBILITY OF SUCH DAMAGE.
53 * ====================================================================
54 *
55 * This product includes cryptographic software written by Eric Young
56 * (eay@cryptsoft.com). This product includes software written by Tim
57 * Hudson (tjh@cryptsoft.com).
58 *
59 */
7793f30e
BM		 60/* ====================================================================
61 * Copyright 2002 Sun Microsystems, Inc. ALL RIGHTS RESERVED.
62 * Portions of this software developed by SUN MICROSYSTEMS, INC.,
63 * and contributed to the OpenSSL project.
64 */
f8fe20e0 65
60428dbf 66#include <openssl/err.h>
02cbedc3 67#include <openssl/symhacks.h>
60428dbf 68
f8fe20e0 69#include "ec_lcl.h"
0657bf9c 70
0657bf9c 71const EC_METHOD *EC_GFp_simple_method(void)
0f113f3e
MC		 72{
73 static const EC_METHOD ret = {
74 EC_FLAGS_DEFAULT_OCT,
75 NID_X9_62_prime_field,
76 ec_GFp_simple_group_init,
77 ec_GFp_simple_group_finish,
78 ec_GFp_simple_group_clear_finish,
79 ec_GFp_simple_group_copy,
80 ec_GFp_simple_group_set_curve,
81 ec_GFp_simple_group_get_curve,
82 ec_GFp_simple_group_get_degree,
83 ec_GFp_simple_group_check_discriminant,
84 ec_GFp_simple_point_init,
85 ec_GFp_simple_point_finish,
86 ec_GFp_simple_point_clear_finish,
87 ec_GFp_simple_point_copy,
88 ec_GFp_simple_point_set_to_infinity,
89 ec_GFp_simple_set_Jprojective_coordinates_GFp,
90 ec_GFp_simple_get_Jprojective_coordinates_GFp,
91 ec_GFp_simple_point_set_affine_coordinates,
92 ec_GFp_simple_point_get_affine_coordinates,
93 0, 0, 0,
94 ec_GFp_simple_add,
95 ec_GFp_simple_dbl,
96 ec_GFp_simple_invert,
97 ec_GFp_simple_is_at_infinity,
98 ec_GFp_simple_is_on_curve,
99 ec_GFp_simple_cmp,
100 ec_GFp_simple_make_affine,
101 ec_GFp_simple_points_make_affine,
102 0 /* mul */ ,
103 0 /* precompute_mult */ ,
104 0 /* have_precompute_mult */ ,
105 ec_GFp_simple_field_mul,
106 ec_GFp_simple_field_sqr,
107 0 /* field_div */ ,
108 0 /* field_encode */ ,
109 0 /* field_decode */ ,
110 0 /* field_set_to_one */
111 };
112
113 return &ret;
114}
60428dbf 115
3a83462d
MC		 116/*
117 * Most method functions in this file are designed to work with
922fa76e
BM		 118 * non-trivial representations of field elements if necessary
119 * (see ecp_mont.c): while standard modular addition and subtraction
120 * are used, the field_mul and field_sqr methods will be used for
121 * multiplication, and field_encode and field_decode (if defined)
122 * will be used for converting between representations.
3a83462d 123 *
922fa76e
BM		 124 * Functions ec_GFp_simple_points_make_affine() and
125 * ec_GFp_simple_point_get_affine_coordinates() specifically assume
126 * that if a non-trivial representation is used, it is a Montgomery
127 * representation (i.e. 'encoding' means multiplying by some factor R).
128 */
129
60428dbf 130int ec_GFp_simple_group_init(EC_GROUP *group)
0f113f3e
MC		 131{
132 group->field = BN_new();
133 group->a = BN_new();
134 group->b = BN_new();
135 if (!group->field || !group->a || !group->b) {
136 if (!group->field)
137 BN_free(group->field);
138 if (!group->a)
139 BN_free(group->a);
140 if (!group->b)
141 BN_free(group->b);
142 return 0;
143 }
144 group->a_is_minus3 = 0;
145 return 1;
146}
60428dbf 147
bb62a8b0 148void ec_GFp_simple_group_finish(EC_GROUP *group)
0f113f3e
MC		 149{
150 BN_free(group->field);
151 BN_free(group->a);
152 BN_free(group->b);
153}
bb62a8b0
BM		 154
155void ec_GFp_simple_group_clear_finish(EC_GROUP *group)
0f113f3e
MC		 156{
157 BN_clear_free(group->field);
158 BN_clear_free(group->a);
159 BN_clear_free(group->b);
160}
bb62a8b0
BM		 161
162int ec_GFp_simple_group_copy(EC_GROUP *dest, const EC_GROUP *src)
0f113f3e
MC		 163{
164 if (!BN_copy(dest->field, src->field))
165 return 0;
166 if (!BN_copy(dest->a, src->a))
167 return 0;
168 if (!BN_copy(dest->b, src->b))
169 return 0;
bb62a8b0 170
0f113f3e 171 dest->a_is_minus3 = src->a_is_minus3;
bb62a8b0 172
0f113f3e
MC		 173 return 1;
174}
bb62a8b0 175
35b73a1f 176int ec_GFp_simple_group_set_curve(EC_GROUP *group,
0f113f3e
MC		 177 const BIGNUM *p, const BIGNUM *a,
178 const BIGNUM *b, BN_CTX *ctx)
179{
180 int ret = 0;
181 BN_CTX *new_ctx = NULL;
182 BIGNUM *tmp_a;
183
184 /* p must be a prime > 3 */
185 if (BN_num_bits(p) <= 2 || !BN_is_odd(p)) {
186 ECerr(EC_F_EC_GFP_SIMPLE_GROUP_SET_CURVE, EC_R_INVALID_FIELD);
187 return 0;
188 }
189
190 if (ctx == NULL) {
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)
199 goto err;
200
201 /* group->field */
202 if (!BN_copy(group->field, p))
203 goto err;
204 BN_set_negative(group->field, 0);
205
206 /* group->a */
207 if (!BN_nnmod(tmp_a, a, p, ctx))
208 goto err;
209 if (group->meth->field_encode) {
210 if (!group->meth->field_encode(group, group->a, tmp_a, ctx))
211 goto err;
212 } else if (!BN_copy(group->a, tmp_a))
213 goto err;
214
215 /* group->b */
216 if (!BN_nnmod(group->b, b, p, ctx))
217 goto err;
218 if (group->meth->field_encode)
219 if (!group->meth->field_encode(group, group->b, group->b, ctx))
220 goto err;
221
222 /* group->a_is_minus3 */
223 if (!BN_add_word(tmp_a, 3))
224 goto err;
225 group->a_is_minus3 = (0 == BN_cmp(tmp_a, group->field));
226
227 ret = 1;
60428dbf
BM		 228
229 err:
0f113f3e
MC		 230 BN_CTX_end(ctx);
231 if (new_ctx != NULL)
232 BN_CTX_free(new_ctx);
233 return ret;
234}
235
236int ec_GFp_simple_group_get_curve(const EC_GROUP *group, BIGNUM *p, BIGNUM *a,
237 BIGNUM *b, BN_CTX *ctx)
238{
239 int ret = 0;
240 BN_CTX *new_ctx = NULL;
241
242 if (p != NULL) {
243 if (!BN_copy(p, group->field))
244 return 0;
245 }
246
247 if (a != NULL || b != NULL) {
248 if (group->meth->field_decode) {
249 if (ctx == NULL) {
250 ctx = new_ctx = BN_CTX_new();
251 if (ctx == NULL)
252 return 0;
253 }
254 if (a != NULL) {
255 if (!group->meth->field_decode(group, a, group->a, ctx))
256 goto err;
257 }
258 if (b != NULL) {
259 if (!group->meth->field_decode(group, b, group->b, ctx))
260 goto err;
261 }
262 } else {
263 if (a != NULL) {
264 if (!BN_copy(a, group->a))
265 goto err;
266 }
267 if (b != NULL) {
268 if (!BN_copy(b, group->b))
269 goto err;
270 }
271 }
272 }
273
274 ret = 1;
60428dbf 275
0f113f3e
MC		 276 err:
277 if (new_ctx)
278 BN_CTX_free(new_ctx);
279 return ret;
280}
60428dbf 281
7793f30e 282int ec_GFp_simple_group_get_degree(const EC_GROUP *group)
0f113f3e
MC		 283{
284 return BN_num_bits(group->field);
285}
7793f30e 286
17d6bb81 287int ec_GFp_simple_group_check_discriminant(const EC_GROUP *group, BN_CTX *ctx)
0f113f3e
MC		 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 ctx = new_ctx = BN_CTX_new();
296 if (ctx == NULL) {
297 ECerr(EC_F_EC_GFP_SIMPLE_GROUP_CHECK_DISCRIMINANT,
298 ERR_R_MALLOC_FAILURE);
299 goto err;
300 }
301 }
302 BN_CTX_start(ctx);
303 a = BN_CTX_get(ctx);
304 b = BN_CTX_get(ctx);
305 tmp_1 = BN_CTX_get(ctx);
306 tmp_2 = BN_CTX_get(ctx);
307 order = BN_CTX_get(ctx);
308 if (order == NULL)
309 goto err;
310
311 if (group->meth->field_decode) {
312 if (!group->meth->field_decode(group, a, group->a, ctx))
313 goto err;
314 if (!group->meth->field_decode(group, b, group->b, ctx))
315 goto err;
316 } else {
317 if (!BN_copy(a, group->a))
318 goto err;
319 if (!BN_copy(b, group->b))
320 goto err;
321 }
322
50e735f9
MC		 323 /*-
324 * check the discriminant:
325 * y^2 = x^3 + a*x + b is an elliptic curve <=> 4*a^3 + 27*b^2 != 0 (mod p)
326 * 0 =< a, b < p
327 */
0f113f3e
MC		 328 if (BN_is_zero(a)) {
329 if (BN_is_zero(b))
330 goto err;
331 } else if (!BN_is_zero(b)) {
332 if (!BN_mod_sqr(tmp_1, a, p, ctx))
333 goto err;
334 if (!BN_mod_mul(tmp_2, tmp_1, a, p, ctx))
335 goto err;
336 if (!BN_lshift(tmp_1, tmp_2, 2))
337 goto err;
338 /* tmp_1 = 4*a^3 */
339
340 if (!BN_mod_sqr(tmp_2, b, p, ctx))
341 goto err;
342 if (!BN_mul_word(tmp_2, 27))
343 goto err;
344 /* tmp_2 = 27*b^2 */
345
346 if (!BN_mod_add(a, tmp_1, tmp_2, p, ctx))
347 goto err;
348 if (BN_is_zero(a))
349 goto err;
350 }
351 ret = 1;
af28dd6c 352
0f113f3e
MC		 353 err:
354 if (ctx != NULL)
355 BN_CTX_end(ctx);
356 if (new_ctx != NULL)
357 BN_CTX_free(new_ctx);
358 return ret;
359}
af28dd6c 360
60428dbf 361int ec_GFp_simple_point_init(EC_POINT *point)
0f113f3e
MC		 362{
363 point->X = BN_new();
364 point->Y = BN_new();
365 point->Z = BN_new();
366 point->Z_is_one = 0;
367
368 if (!point->X || !point->Y || !point->Z) {
369 if (point->X)
370 BN_free(point->X);
371 if (point->Y)
372 BN_free(point->Y);
373 if (point->Z)
374 BN_free(point->Z);
375 return 0;
376 }
377 return 1;
378}
60428dbf
BM		 379
380void ec_GFp_simple_point_finish(EC_POINT *point)
0f113f3e
MC		 381{
382 BN_free(point->X);
383 BN_free(point->Y);
384 BN_free(point->Z);
385}
60428dbf
BM		 386
387void ec_GFp_simple_point_clear_finish(EC_POINT *point)
0f113f3e
MC		 388{
389 BN_clear_free(point->X);
390 BN_clear_free(point->Y);
391 BN_clear_free(point->Z);
392 point->Z_is_one = 0;
393}
60428dbf
BM		 394
395int ec_GFp_simple_point_copy(EC_POINT *dest, const EC_POINT *src)
0f113f3e
MC		 396{
397 if (!BN_copy(dest->X, src->X))
398 return 0;
399 if (!BN_copy(dest->Y, src->Y))
400 return 0;
401 if (!BN_copy(dest->Z, src->Z))
402 return 0;
403 dest->Z_is_one = src->Z_is_one;
404
405 return 1;
406}
407
408int ec_GFp_simple_point_set_to_infinity(const EC_GROUP *group,
409 EC_POINT *point)
410{
411 point->Z_is_one = 0;
412 BN_zero(point->Z);
413 return 1;
414}
415
416int ec_GFp_simple_set_Jprojective_coordinates_GFp(const EC_GROUP *group,
417 EC_POINT *point,
418 const BIGNUM *x,
419 const BIGNUM *y,
420 const BIGNUM *z,
421 BN_CTX *ctx)
422{
423 BN_CTX *new_ctx = NULL;
424 int ret = 0;
425
426 if (ctx == NULL) {
427 ctx = new_ctx = BN_CTX_new();
428 if (ctx == NULL)
429 return 0;
430 }
431
432 if (x != NULL) {
433 if (!BN_nnmod(point->X, x, group->field, ctx))
434 goto err;
435 if (group->meth->field_encode) {
436 if (!group->meth->field_encode(group, point->X, point->X, ctx))
437 goto err;
438 }
439 }
440
441 if (y != NULL) {
442 if (!BN_nnmod(point->Y, y, group->field, ctx))
443 goto err;
444 if (group->meth->field_encode) {
445 if (!group->meth->field_encode(group, point->Y, point->Y, ctx))
446 goto err;
447 }
448 }
449
450 if (z != NULL) {
451 int Z_is_one;
452
453 if (!BN_nnmod(point->Z, z, group->field, ctx))
454 goto err;
455 Z_is_one = BN_is_one(point->Z);
456 if (group->meth->field_encode) {
457 if (Z_is_one && (group->meth->field_set_to_one != 0)) {
458 if (!group->meth->field_set_to_one(group, point->Z, ctx))
459 goto err;
460 } else {
461 if (!group->
462 meth->field_encode(group, point->Z, point->Z, ctx))
463 goto err;
464 }
465 }
466 point->Z_is_one = Z_is_one;
467 }
468
469 ret = 1;
470
bb62a8b0 471 err:
0f113f3e
MC		 472 if (new_ctx != NULL)
473 BN_CTX_free(new_ctx);
474 return ret;
475}
476
477int ec_GFp_simple_get_Jprojective_coordinates_GFp(const EC_GROUP *group,
478 const EC_POINT *point,
479 BIGNUM *x, BIGNUM *y,
480 BIGNUM *z, BN_CTX *ctx)
481{
482 BN_CTX *new_ctx = NULL;
483 int ret = 0;
484
485 if (group->meth->field_decode != 0) {
486 if (ctx == NULL) {
487 ctx = new_ctx = BN_CTX_new();
488 if (ctx == NULL)
489 return 0;
490 }
491
492 if (x != NULL) {
493 if (!group->meth->field_decode(group, x, point->X, ctx))
494 goto err;
495 }
496 if (y != NULL) {
497 if (!group->meth->field_decode(group, y, point->Y, ctx))
498 goto err;
499 }
500 if (z != NULL) {
501 if (!group->meth->field_decode(group, z, point->Z, ctx))
502 goto err;
503 }
504 } else {
505 if (x != NULL) {
506 if (!BN_copy(x, point->X))
507 goto err;
508 }
509 if (y != NULL) {
510 if (!BN_copy(y, point->Y))
511 goto err;
512 }
513 if (z != NULL) {
514 if (!BN_copy(z, point->Z))
515 goto err;
516 }
517 }
518
519 ret = 1;
bb62a8b0 520
226cc7de 521 err:
0f113f3e
MC		 522 if (new_ctx != NULL)
523 BN_CTX_free(new_ctx);
524 return ret;
525}
526
527int ec_GFp_simple_point_set_affine_coordinates(const EC_GROUP *group,
528 EC_POINT *point,
529 const BIGNUM *x,
530 const BIGNUM *y, BN_CTX *ctx)
531{
532 if (x == NULL || y == NULL) {
533 /*
534 * unlike for projective coordinates, we do not tolerate this
535 */
536 ECerr(EC_F_EC_GFP_SIMPLE_POINT_SET_AFFINE_COORDINATES,
537 ERR_R_PASSED_NULL_PARAMETER);
538 return 0;
539 }
540
541 return EC_POINT_set_Jprojective_coordinates_GFp(group, point, x, y,
542 BN_value_one(), ctx);
543}
544
545int ec_GFp_simple_point_get_affine_coordinates(const EC_GROUP *group,
546 const EC_POINT *point,
547 BIGNUM *x, BIGNUM *y,
548 BN_CTX *ctx)
549{
550 BN_CTX *new_ctx = NULL;
551 BIGNUM *Z, *Z_1, *Z_2, *Z_3;
552 const BIGNUM *Z_;
553 int ret = 0;
554
555 if (EC_POINT_is_at_infinity(group, point)) {
556 ECerr(EC_F_EC_GFP_SIMPLE_POINT_GET_AFFINE_COORDINATES,
557 EC_R_POINT_AT_INFINITY);
558 return 0;
559 }
560
561 if (ctx == NULL) {
562 ctx = new_ctx = BN_CTX_new();
563 if (ctx == NULL)
564 return 0;
565 }
566
567 BN_CTX_start(ctx);
568 Z = BN_CTX_get(ctx);
569 Z_1 = BN_CTX_get(ctx);
570 Z_2 = BN_CTX_get(ctx);
571 Z_3 = BN_CTX_get(ctx);
572 if (Z_3 == NULL)
573 goto err;
574
575 /* transform (X, Y, Z) into (x, y) := (X/Z^2, Y/Z^3) */
576
577 if (group->meth->field_decode) {
578 if (!group->meth->field_decode(group, Z, point->Z, ctx))
579 goto err;
580 Z_ = Z;
581 } else {
582 Z_ = point->Z;
583 }
584
585 if (BN_is_one(Z_)) {
586 if (group->meth->field_decode) {
587 if (x != NULL) {
588 if (!group->meth->field_decode(group, x, point->X, ctx))
589 goto err;
590 }
591 if (y != NULL) {
592 if (!group->meth->field_decode(group, y, point->Y, ctx))
593 goto err;
594 }
595 } else {
596 if (x != NULL) {
597 if (!BN_copy(x, point->X))
598 goto err;
599 }
600 if (y != NULL) {
601 if (!BN_copy(y, point->Y))
602 goto err;
603 }
604 }
605 } else {
606 if (!BN_mod_inverse(Z_1, Z_, group->field, ctx)) {
607 ECerr(EC_F_EC_GFP_SIMPLE_POINT_GET_AFFINE_COORDINATES,
608 ERR_R_BN_LIB);
609 goto err;
610 }
611
612 if (group->meth->field_encode == 0) {
613 /* field_sqr works on standard representation */
614 if (!group->meth->field_sqr(group, Z_2, Z_1, ctx))
615 goto err;
616 } else {
617 if (!BN_mod_sqr(Z_2, Z_1, group->field, ctx))
618 goto err;
619 }
620
621 if (x != NULL) {
622 /*
623 * in the Montgomery case, field_mul will cancel out Montgomery
624 * factor in X:
625 */
626 if (!group->meth->field_mul(group, x, point->X, Z_2, ctx))
627 goto err;
628 }
629
630 if (y != NULL) {
631 if (group->meth->field_encode == 0) {
632 /*
633 * field_mul works on standard representation
634 */
635 if (!group->meth->field_mul(group, Z_3, Z_2, Z_1, ctx))
636 goto err;
637 } else {
638 if (!BN_mod_mul(Z_3, Z_2, Z_1, group->field, ctx))
639 goto err;
640 }
641
642 /*
643 * in the Montgomery case, field_mul will cancel out Montgomery
644 * factor in Y:
645 */
646 if (!group->meth->field_mul(group, y, point->Y, Z_3, ctx))
647 goto err;
648 }
649 }
650
651 ret = 1;
226cc7de
BM		 652
653 err:
0f113f3e
MC		 654 BN_CTX_end(ctx);
655 if (new_ctx != NULL)
656 BN_CTX_free(new_ctx);
657 return ret;
658}
659
660int ec_GFp_simple_add(const EC_GROUP *group, EC_POINT *r, const EC_POINT *a,
661 const EC_POINT *b, BN_CTX *ctx)
662{
663 int (*field_mul) (const EC_GROUP *, BIGNUM *, const BIGNUM *,
664 const BIGNUM *, BN_CTX *);
665 int (*field_sqr) (const EC_GROUP *, BIGNUM *, const BIGNUM *, BN_CTX *);
666 const BIGNUM *p;
667 BN_CTX *new_ctx = NULL;
668 BIGNUM *n0, *n1, *n2, *n3, *n4, *n5, *n6;
669 int ret = 0;
670
671 if (a == b)
672 return EC_POINT_dbl(group, r, a, ctx);
673 if (EC_POINT_is_at_infinity(group, a))
674 return EC_POINT_copy(r, b);
675 if (EC_POINT_is_at_infinity(group, b))
676 return EC_POINT_copy(r, a);
677
678 field_mul = group->meth->field_mul;
679 field_sqr = group->meth->field_sqr;
680 p = group->field;
681
682 if (ctx == NULL) {
683 ctx = new_ctx = BN_CTX_new();
684 if (ctx == NULL)
685 return 0;
686 }
687
688 BN_CTX_start(ctx);
689 n0 = BN_CTX_get(ctx);
690 n1 = BN_CTX_get(ctx);
691 n2 = BN_CTX_get(ctx);
692 n3 = BN_CTX_get(ctx);
693 n4 = BN_CTX_get(ctx);
694 n5 = BN_CTX_get(ctx);
695 n6 = BN_CTX_get(ctx);
696 if (n6 == NULL)
697 goto end;
698
699 /*
700 * Note that in this function we must not read components of 'a' or 'b'
701 * once we have written the corresponding components of 'r'. ('r' might
702 * be one of 'a' or 'b'.)
703 */
704
705 /* n1, n2 */
706 if (b->Z_is_one) {
707 if (!BN_copy(n1, a->X))
708 goto end;
709 if (!BN_copy(n2, a->Y))
710 goto end;
711 /* n1 = X_a */
712 /* n2 = Y_a */
713 } else {
714 if (!field_sqr(group, n0, b->Z, ctx))
715 goto end;
716 if (!field_mul(group, n1, a->X, n0, ctx))
717 goto end;
718 /* n1 = X_a * Z_b^2 */
719
720 if (!field_mul(group, n0, n0, b->Z, ctx))
721 goto end;
722 if (!field_mul(group, n2, a->Y, n0, ctx))
723 goto end;
724 /* n2 = Y_a * Z_b^3 */
725 }
726
727 /* n3, n4 */
728 if (a->Z_is_one) {
729 if (!BN_copy(n3, b->X))
730 goto end;
731 if (!BN_copy(n4, b->Y))
732 goto end;
733 /* n3 = X_b */
734 /* n4 = Y_b */
735 } else {
736 if (!field_sqr(group, n0, a->Z, ctx))
737 goto end;
738 if (!field_mul(group, n3, b->X, n0, ctx))
739 goto end;
740 /* n3 = X_b * Z_a^2 */
741
742 if (!field_mul(group, n0, n0, a->Z, ctx))
743 goto end;
744 if (!field_mul(group, n4, b->Y, n0, ctx))
745 goto end;
746 /* n4 = Y_b * Z_a^3 */
747 }
748
749 /* n5, n6 */
750 if (!BN_mod_sub_quick(n5, n1, n3, p))
751 goto end;
752 if (!BN_mod_sub_quick(n6, n2, n4, p))
753 goto end;
754 /* n5 = n1 - n3 */
755 /* n6 = n2 - n4 */
756
757 if (BN_is_zero(n5)) {
758 if (BN_is_zero(n6)) {
759 /* a is the same point as b */
760 BN_CTX_end(ctx);
761 ret = EC_POINT_dbl(group, r, a, ctx);
762 ctx = NULL;
763 goto end;
764 } else {
765 /* a is the inverse of b */
766 BN_zero(r->Z);
767 r->Z_is_one = 0;
768 ret = 1;
769 goto end;
770 }
771 }
772
773 /* 'n7', 'n8' */
774 if (!BN_mod_add_quick(n1, n1, n3, p))
775 goto end;
776 if (!BN_mod_add_quick(n2, n2, n4, p))
777 goto end;
778 /* 'n7' = n1 + n3 */
779 /* 'n8' = n2 + n4 */
780
781 /* Z_r */
782 if (a->Z_is_one && b->Z_is_one) {
783 if (!BN_copy(r->Z, n5))
784 goto end;
785 } else {
786 if (a->Z_is_one) {
787 if (!BN_copy(n0, b->Z))
788 goto end;
789 } else if (b->Z_is_one) {
790 if (!BN_copy(n0, a->Z))
791 goto end;
792 } else {
793 if (!field_mul(group, n0, a->Z, b->Z, ctx))
794 goto end;
795 }
796 if (!field_mul(group, r->Z, n0, n5, ctx))
797 goto end;
798 }
799 r->Z_is_one = 0;
800 /* Z_r = Z_a * Z_b * n5 */
801
802 /* X_r */
803 if (!field_sqr(group, n0, n6, ctx))
804 goto end;
805 if (!field_sqr(group, n4, n5, ctx))
806 goto end;
807 if (!field_mul(group, n3, n1, n4, ctx))
808 goto end;
809 if (!BN_mod_sub_quick(r->X, n0, n3, p))
810 goto end;
811 /* X_r = n6^2 - n5^2 * 'n7' */
812
813 /* 'n9' */
814 if (!BN_mod_lshift1_quick(n0, r->X, p))
815 goto end;
816 if (!BN_mod_sub_quick(n0, n3, n0, p))
817 goto end;
818 /* n9 = n5^2 * 'n7' - 2 * X_r */
819
820 /* Y_r */
821 if (!field_mul(group, n0, n0, n6, ctx))
822 goto end;
823 if (!field_mul(group, n5, n4, n5, ctx))
824 goto end; /* now n5 is n5^3 */
825 if (!field_mul(group, n1, n2, n5, ctx))
826 goto end;
827 if (!BN_mod_sub_quick(n0, n0, n1, p))
828 goto end;
829 if (BN_is_odd(n0))
830 if (!BN_add(n0, n0, p))
831 goto end;
832 /* now 0 <= n0 < 2*p, and n0 is even */
833 if (!BN_rshift1(r->Y, n0))
834 goto end;
835 /* Y_r = (n6 * 'n9' - 'n8' * 'n5^3') / 2 */
836
837 ret = 1;
60428dbf
BM		 838
839 end:
0f113f3e
MC		 840 if (ctx) /* otherwise we already called BN_CTX_end */
841 BN_CTX_end(ctx);
842 if (new_ctx != NULL)
843 BN_CTX_free(new_ctx);
844 return ret;
845}
846
847int ec_GFp_simple_dbl(const EC_GROUP *group, EC_POINT *r, const EC_POINT *a,
848 BN_CTX *ctx)
849{
850 int (*field_mul) (const EC_GROUP *, BIGNUM *, const BIGNUM *,
851 const BIGNUM *, BN_CTX *);
852 int (*field_sqr) (const EC_GROUP *, BIGNUM *, const BIGNUM *, BN_CTX *);
853 const BIGNUM *p;
854 BN_CTX *new_ctx = NULL;
855 BIGNUM *n0, *n1, *n2, *n3;
856 int ret = 0;
857
858 if (EC_POINT_is_at_infinity(group, a)) {
859 BN_zero(r->Z);
860 r->Z_is_one = 0;
861 return 1;
862 }
863
864 field_mul = group->meth->field_mul;
865 field_sqr = group->meth->field_sqr;
866 p = group->field;
867
868 if (ctx == NULL) {
869 ctx = new_ctx = BN_CTX_new();
870 if (ctx == NULL)
871 return 0;
872 }
873
874 BN_CTX_start(ctx);
875 n0 = BN_CTX_get(ctx);
876 n1 = BN_CTX_get(ctx);
877 n2 = BN_CTX_get(ctx);
878 n3 = BN_CTX_get(ctx);
879 if (n3 == NULL)
880 goto err;
881
882 /*
883 * Note that in this function we must not read components of 'a' once we
884 * have written the corresponding components of 'r'. ('r' might the same
885 * as 'a'.)
886 */
887
888 /* n1 */
889 if (a->Z_is_one) {
890 if (!field_sqr(group, n0, a->X, ctx))
891 goto err;
892 if (!BN_mod_lshift1_quick(n1, n0, p))
893 goto err;
894 if (!BN_mod_add_quick(n0, n0, n1, p))
895 goto err;
896 if (!BN_mod_add_quick(n1, n0, group->a, p))
897 goto err;
898 /* n1 = 3 * X_a^2 + a_curve */
899 } else if (group->a_is_minus3) {
900 if (!field_sqr(group, n1, a->Z, ctx))
901 goto err;
902 if (!BN_mod_add_quick(n0, a->X, n1, p))
903 goto err;
904 if (!BN_mod_sub_quick(n2, a->X, n1, p))
905 goto err;
906 if (!field_mul(group, n1, n0, n2, ctx))
907 goto err;
908 if (!BN_mod_lshift1_quick(n0, n1, p))
909 goto err;
910 if (!BN_mod_add_quick(n1, n0, n1, p))
911 goto err;
912 /*-
913 * n1 = 3 * (X_a + Z_a^2) * (X_a - Z_a^2)
914 * = 3 * X_a^2 - 3 * Z_a^4
915 */
916 } else {
917 if (!field_sqr(group, n0, a->X, ctx))
918 goto err;
919 if (!BN_mod_lshift1_quick(n1, n0, p))
920 goto err;
921 if (!BN_mod_add_quick(n0, n0, n1, p))
922 goto err;
923 if (!field_sqr(group, n1, a->Z, ctx))
924 goto err;
925 if (!field_sqr(group, n1, n1, ctx))
926 goto err;
927 if (!field_mul(group, n1, n1, group->a, ctx))
928 goto err;
929 if (!BN_mod_add_quick(n1, n1, n0, p))
930 goto err;
931 /* n1 = 3 * X_a^2 + a_curve * Z_a^4 */
932 }
933
934 /* Z_r */
935 if (a->Z_is_one) {
936 if (!BN_copy(n0, a->Y))
937 goto err;
938 } else {
939 if (!field_mul(group, n0, a->Y, a->Z, ctx))
940 goto err;
941 }
942 if (!BN_mod_lshift1_quick(r->Z, n0, p))
943 goto err;
944 r->Z_is_one = 0;
945 /* Z_r = 2 * Y_a * Z_a */
946
947 /* n2 */
948 if (!field_sqr(group, n3, a->Y, ctx))
949 goto err;
950 if (!field_mul(group, n2, a->X, n3, ctx))
951 goto err;
952 if (!BN_mod_lshift_quick(n2, n2, 2, p))
953 goto err;
954 /* n2 = 4 * X_a * Y_a^2 */
955
956 /* X_r */
957 if (!BN_mod_lshift1_quick(n0, n2, p))
958 goto err;
959 if (!field_sqr(group, r->X, n1, ctx))
960 goto err;
961 if (!BN_mod_sub_quick(r->X, r->X, n0, p))
962 goto err;
963 /* X_r = n1^2 - 2 * n2 */
964
965 /* n3 */
966 if (!field_sqr(group, n0, n3, ctx))
967 goto err;
968 if (!BN_mod_lshift_quick(n3, n0, 3, p))
969 goto err;
970 /* n3 = 8 * Y_a^4 */
971
972 /* Y_r */
973 if (!BN_mod_sub_quick(n0, n2, r->X, p))
974 goto err;
975 if (!field_mul(group, n0, n1, n0, ctx))
976 goto err;
977 if (!BN_mod_sub_quick(r->Y, n0, n3, p))
978 goto err;
979 /* Y_r = n1 * (n2 - X_r) - n3 */
980
981 ret = 1;
60428dbf
BM		 982
983 err:
0f113f3e
MC		 984 BN_CTX_end(ctx);
985 if (new_ctx != NULL)
986 BN_CTX_free(new_ctx);
987 return ret;
988}
60428dbf 989
bb62a8b0 990int ec_GFp_simple_invert(const EC_GROUP *group, EC_POINT *point, BN_CTX *ctx)
0f113f3e
MC		 991{
992 if (EC_POINT_is_at_infinity(group, point) || BN_is_zero(point->Y))
993 /* point is its own inverse */
994 return 1;
1d5bd6cf 995
0f113f3e
MC		 996 return BN_usub(point->Y, group->field, point->Y);
997}
1d5bd6cf 998
60428dbf 999int ec_GFp_simple_is_at_infinity(const EC_GROUP *group, const EC_POINT *point)
0f113f3e
MC		 1000{
1001 return BN_is_zero(point->Z);
1002}
1003
1004int ec_GFp_simple_is_on_curve(const EC_GROUP *group, const EC_POINT *point,
1005 BN_CTX *ctx)
1006{
1007 int (*field_mul) (const EC_GROUP *, BIGNUM *, const BIGNUM *,
1008 const BIGNUM *, BN_CTX *);
1009 int (*field_sqr) (const EC_GROUP *, BIGNUM *, const BIGNUM *, BN_CTX *);
1010 const BIGNUM *p;
1011 BN_CTX *new_ctx = NULL;
1012 BIGNUM *rh, *tmp, *Z4, *Z6;
1013 int ret = -1;
1014
1015 if (EC_POINT_is_at_infinity(group, point))
1016 return 1;
1017
1018 field_mul = group->meth->field_mul;
1019 field_sqr = group->meth->field_sqr;
1020 p = group->field;
1021
1022 if (ctx == NULL) {
1023 ctx = new_ctx = BN_CTX_new();
1024 if (ctx == NULL)
1025 return -1;
1026 }
1027
1028 BN_CTX_start(ctx);
1029 rh = BN_CTX_get(ctx);
1030 tmp = BN_CTX_get(ctx);
1031 Z4 = BN_CTX_get(ctx);
1032 Z6 = BN_CTX_get(ctx);
1033 if (Z6 == NULL)
1034 goto err;
1035
50e735f9
MC		 1036 /*-
1037 * We have a curve defined by a Weierstrass equation
1038 * y^2 = x^3 + a*x + b.
1039 * The point to consider is given in Jacobian projective coordinates
1040 * where (X, Y, Z) represents (x, y) = (X/Z^2, Y/Z^3).
1041 * Substituting this and multiplying by Z^6 transforms the above equation into
1042 * Y^2 = X^3 + a*X*Z^4 + b*Z^6.
1043 * To test this, we add up the right-hand side in 'rh'.
1044 */
0f113f3e
MC		 1045
1046 /* rh := X^2 */
1047 if (!field_sqr(group, rh, point->X, ctx))
1048 goto err;
1049
1050 if (!point->Z_is_one) {
1051 if (!field_sqr(group, tmp, point->Z, ctx))
1052 goto err;
1053 if (!field_sqr(group, Z4, tmp, ctx))
1054 goto err;
1055 if (!field_mul(group, Z6, Z4, tmp, ctx))
1056 goto err;
1057
1058 /* rh := (rh + a*Z^4)*X */
1059 if (group->a_is_minus3) {
1060 if (!BN_mod_lshift1_quick(tmp, Z4, p))
1061 goto err;
1062 if (!BN_mod_add_quick(tmp, tmp, Z4, p))
1063 goto err;
1064 if (!BN_mod_sub_quick(rh, rh, tmp, p))
1065 goto err;
1066 if (!field_mul(group, rh, rh, point->X, ctx))
1067 goto err;
1068 } else {
1069 if (!field_mul(group, tmp, Z4, group->a, ctx))
1070 goto err;
1071 if (!BN_mod_add_quick(rh, rh, tmp, p))
1072 goto err;
1073 if (!field_mul(group, rh, rh, point->X, ctx))
1074 goto err;
1075 }
1076
1077 /* rh := rh + b*Z^6 */
1078 if (!field_mul(group, tmp, group->b, Z6, ctx))
1079 goto err;
1080 if (!BN_mod_add_quick(rh, rh, tmp, p))
1081 goto err;
1082 } else {
1083 /* point->Z_is_one */
1084
1085 /* rh := (rh + a)*X */
1086 if (!BN_mod_add_quick(rh, rh, group->a, p))
1087 goto err;
1088 if (!field_mul(group, rh, rh, point->X, ctx))
1089 goto err;
1090 /* rh := rh + b */
1091 if (!BN_mod_add_quick(rh, rh, group->b, p))
1092 goto err;
1093 }
1094
1095 /* 'lh' := Y^2 */
1096 if (!field_sqr(group, tmp, point->Y, ctx))
1097 goto err;
1098
1099 ret = (0 == BN_ucmp(tmp, rh));
e869d4bd
BM		 1100
1101 err:
0f113f3e
MC		 1102 BN_CTX_end(ctx);
1103 if (new_ctx != NULL)
1104 BN_CTX_free(new_ctx);
1105 return ret;
1106}
1107
1108int ec_GFp_simple_cmp(const EC_GROUP *group, const EC_POINT *a,
1109 const EC_POINT *b, BN_CTX *ctx)
1110{
1111 /*-
1112 * return values:
1113 * -1 error
1114 * 0 equal (in affine coordinates)
1115 * 1 not equal
1116 */
1117
1118 int (*field_mul) (const EC_GROUP *, BIGNUM *, const BIGNUM *,
1119 const BIGNUM *, BN_CTX *);
1120 int (*field_sqr) (const EC_GROUP *, BIGNUM *, const BIGNUM *, BN_CTX *);
1121 BN_CTX *new_ctx = NULL;
1122 BIGNUM *tmp1, *tmp2, *Za23, *Zb23;
1123 const BIGNUM *tmp1_, *tmp2_;
1124 int ret = -1;
1125
1126 if (EC_POINT_is_at_infinity(group, a)) {
1127 return EC_POINT_is_at_infinity(group, b) ? 0 : 1;
1128 }
1129
1130 if (EC_POINT_is_at_infinity(group, b))
1131 return 1;
1132
1133 if (a->Z_is_one && b->Z_is_one) {
1134 return ((BN_cmp(a->X, b->X) == 0) && BN_cmp(a->Y, b->Y) == 0) ? 0 : 1;
1135 }
1136
1137 field_mul = group->meth->field_mul;
1138 field_sqr = group->meth->field_sqr;
1139
1140 if (ctx == NULL) {
1141 ctx = new_ctx = BN_CTX_new();
1142 if (ctx == NULL)
1143 return -1;
1144 }
1145
1146 BN_CTX_start(ctx);
1147 tmp1 = BN_CTX_get(ctx);
1148 tmp2 = BN_CTX_get(ctx);
1149 Za23 = BN_CTX_get(ctx);
1150 Zb23 = BN_CTX_get(ctx);
1151 if (Zb23 == NULL)
1152 goto end;
1153
50e735f9
MC		 1154 /*-
1155 * We have to decide whether
1156 * (X_a/Z_a^2, Y_a/Z_a^3) = (X_b/Z_b^2, Y_b/Z_b^3),
1157 * or equivalently, whether
1158 * (X_a*Z_b^2, Y_a*Z_b^3) = (X_b*Z_a^2, Y_b*Z_a^3).
1159 */
0f113f3e
MC		 1160
1161 if (!b->Z_is_one) {
1162 if (!field_sqr(group, Zb23, b->Z, ctx))
1163 goto end;
1164 if (!field_mul(group, tmp1, a->X, Zb23, ctx))
1165 goto end;
1166 tmp1_ = tmp1;
1167 } else
1168 tmp1_ = a->X;
1169 if (!a->Z_is_one) {
1170 if (!field_sqr(group, Za23, a->Z, ctx))
1171 goto end;
1172 if (!field_mul(group, tmp2, b->X, Za23, ctx))
1173 goto end;
1174 tmp2_ = tmp2;
1175 } else
1176 tmp2_ = b->X;
1177
1178 /* compare X_a*Z_b^2 with X_b*Z_a^2 */
1179 if (BN_cmp(tmp1_, tmp2_) != 0) {
1180 ret = 1; /* points differ */
1181 goto end;
1182 }
1183
1184 if (!b->Z_is_one) {
1185 if (!field_mul(group, Zb23, Zb23, b->Z, ctx))
1186 goto end;
1187 if (!field_mul(group, tmp1, a->Y, Zb23, ctx))
1188 goto end;
1189 /* tmp1_ = tmp1 */
1190 } else
1191 tmp1_ = a->Y;
1192 if (!a->Z_is_one) {
1193 if (!field_mul(group, Za23, Za23, a->Z, ctx))
1194 goto end;
1195 if (!field_mul(group, tmp2, b->Y, Za23, ctx))
1196 goto end;
1197 /* tmp2_ = tmp2 */
1198 } else
1199 tmp2_ = b->Y;
1200
1201 /* compare Y_a*Z_b^3 with Y_b*Z_a^3 */
1202 if (BN_cmp(tmp1_, tmp2_) != 0) {
1203 ret = 1; /* points differ */
1204 goto end;
1205 }
1206
1207 /* points are equal */
1208 ret = 0;
bb62a8b0
BM		 1209
1210 end:
0f113f3e
MC		 1211 BN_CTX_end(ctx);
1212 if (new_ctx != NULL)
1213 BN_CTX_free(new_ctx);
1214 return ret;
1215}
1216
1217int ec_GFp_simple_make_affine(const EC_GROUP *group, EC_POINT *point,
1218 BN_CTX *ctx)
1219{
1220 BN_CTX *new_ctx = NULL;
1221 BIGNUM *x, *y;
1222 int ret = 0;
1223
1224 if (point->Z_is_one || EC_POINT_is_at_infinity(group, point))
1225 return 1;
1226
1227 if (ctx == NULL) {
1228 ctx = new_ctx = BN_CTX_new();
1229 if (ctx == NULL)
1230 return 0;
1231 }
1232
1233 BN_CTX_start(ctx);
1234 x = BN_CTX_get(ctx);
1235 y = BN_CTX_get(ctx);
1236 if (y == NULL)
1237 goto err;
1238
1239 if (!EC_POINT_get_affine_coordinates_GFp(group, point, x, y, ctx))
1240 goto err;
1241 if (!EC_POINT_set_affine_coordinates_GFp(group, point, x, y, ctx))
1242 goto err;
1243 if (!point->Z_is_one) {
1244 ECerr(EC_F_EC_GFP_SIMPLE_MAKE_AFFINE, ERR_R_INTERNAL_ERROR);
1245 goto err;
1246 }
1247
1248 ret = 1;
e869d4bd 1249
226cc7de 1250 err:
0f113f3e
MC		 1251 BN_CTX_end(ctx);
1252 if (new_ctx != NULL)
1253 BN_CTX_free(new_ctx);
1254 return ret;
1255}
1256
1257int ec_GFp_simple_points_make_affine(const EC_GROUP *group, size_t num,
1258 EC_POINT *points[], BN_CTX *ctx)
1259{
1260 BN_CTX *new_ctx = NULL;
1261 BIGNUM *tmp, *tmp_Z;
1262 BIGNUM **prod_Z = NULL;
1263 size_t i;
1264 int ret = 0;
1265
1266 if (num == 0)
1267 return 1;
1268
1269 if (ctx == NULL) {
1270 ctx = new_ctx = BN_CTX_new();
1271 if (ctx == NULL)
1272 return 0;
1273 }
1274
1275 BN_CTX_start(ctx);
1276 tmp = BN_CTX_get(ctx);
1277 tmp_Z = BN_CTX_get(ctx);
1278 if (tmp == NULL || tmp_Z == NULL)
1279 goto err;
1280
1281 prod_Z = OPENSSL_malloc(num * sizeof prod_Z[0]);
1282 if (prod_Z == NULL)
1283 goto err;
1284 for (i = 0; i < num; i++) {
1285 prod_Z[i] = BN_new();
1286 if (prod_Z[i] == NULL)
1287 goto err;
1288 }
1289
1290 /*
1291 * Set each prod_Z[i] to the product of points[0]->Z .. points[i]->Z,
1292 * skipping any zero-valued inputs (pretend that they're 1).
1293 */
1294
1295 if (!BN_is_zero(points[0]->Z)) {
1296 if (!BN_copy(prod_Z[0], points[0]->Z))
1297 goto err;
1298 } else {
1299 if (group->meth->field_set_to_one != 0) {
1300 if (!group->meth->field_set_to_one(group, prod_Z[0], ctx))
1301 goto err;
1302 } else {
1303 if (!BN_one(prod_Z[0]))
1304 goto err;
1305 }
1306 }
1307
1308 for (i = 1; i < num; i++) {
1309 if (!BN_is_zero(points[i]->Z)) {
1310 if (!group->
1311 meth->field_mul(group, prod_Z[i], prod_Z[i - 1], points[i]->Z,
1312 ctx))
1313 goto err;
1314 } else {
1315 if (!BN_copy(prod_Z[i], prod_Z[i - 1]))
1316 goto err;
1317 }
1318 }
1319
1320 /*
1321 * Now use a single explicit inversion to replace every non-zero
1322 * points[i]->Z by its inverse.
1323 */
1324
1325 if (!BN_mod_inverse(tmp, prod_Z[num - 1], group->field, ctx)) {
1326 ECerr(EC_F_EC_GFP_SIMPLE_POINTS_MAKE_AFFINE, ERR_R_BN_LIB);
1327 goto err;
1328 }
1329 if (group->meth->field_encode != 0) {
1330 /*
1331 * In the Montgomery case, we just turned R*H (representing H) into
1332 * 1/(R*H), but we need R*(1/H) (representing 1/H); i.e. we need to
1333 * multiply by the Montgomery factor twice.
1334 */
1335 if (!group->meth->field_encode(group, tmp, tmp, ctx))
1336 goto err;
1337 if (!group->meth->field_encode(group, tmp, tmp, ctx))
1338 goto err;
1339 }
1340
1341 for (i = num - 1; i > 0; --i) {
1342 /*
1343 * Loop invariant: tmp is the product of the inverses of points[0]->Z
1344 * .. points[i]->Z (zero-valued inputs skipped).
1345 */
1346 if (!BN_is_zero(points[i]->Z)) {
1347 /*
1348 * Set tmp_Z to the inverse of points[i]->Z (as product of Z
1349 * inverses 0 .. i, Z values 0 .. i - 1).
1350 */
1351 if (!group->
1352 meth->field_mul(group, tmp_Z, prod_Z[i - 1], tmp, ctx))
1353 goto err;
1354 /*
1355 * Update tmp to satisfy the loop invariant for i - 1.
1356 */
1357 if (!group->meth->field_mul(group, tmp, tmp, points[i]->Z, ctx))
1358 goto err;
1359 /* Replace points[i]->Z by its inverse. */
1360 if (!BN_copy(points[i]->Z, tmp_Z))
1361 goto err;
1362 }
1363 }
1364
1365 if (!BN_is_zero(points[0]->Z)) {
1366 /* Replace points[0]->Z by its inverse. */
1367 if (!BN_copy(points[0]->Z, tmp))
1368 goto err;
1369 }
1370
1371 /* Finally, fix up the X and Y coordinates for all points. */
1372
1373 for (i = 0; i < num; i++) {
1374 EC_POINT *p = points[i];
1375
1376 if (!BN_is_zero(p->Z)) {
1377 /* turn (X, Y, 1/Z) into (X/Z^2, Y/Z^3, 1) */
1378
1379 if (!group->meth->field_sqr(group, tmp, p->Z, ctx))
1380 goto err;
1381 if (!group->meth->field_mul(group, p->X, p->X, tmp, ctx))
1382 goto err;
1383
1384 if (!group->meth->field_mul(group, tmp, tmp, p->Z, ctx))
1385 goto err;
1386 if (!group->meth->field_mul(group, p->Y, p->Y, tmp, ctx))
1387 goto err;
1388
1389 if (group->meth->field_set_to_one != 0) {
1390 if (!group->meth->field_set_to_one(group, p->Z, ctx))
1391 goto err;
1392 } else {
1393 if (!BN_one(p->Z))
1394 goto err;
1395 }
1396 p->Z_is_one = 1;
1397 }
1398 }
1399
1400 ret = 1;
0fe73d6c 1401
48fe4d62 1402 err:
0f113f3e
MC		 1403 BN_CTX_end(ctx);
1404 if (new_ctx != NULL)
1405 BN_CTX_free(new_ctx);
1406 if (prod_Z != NULL) {
1407 for (i = 0; i < num; i++) {
1408 if (prod_Z[i] == NULL)
1409 break;
1410 BN_clear_free(prod_Z[i]);
1411 }
1412 OPENSSL_free(prod_Z);
1413 }
1414 return ret;
1415}
1416
1417int ec_GFp_simple_field_mul(const EC_GROUP *group, BIGNUM *r, const BIGNUM *a,
1418 const BIGNUM *b, BN_CTX *ctx)
1419{
1420 return BN_mod_mul(r, a, b, group->field, ctx);
1421}
1422
1423int ec_GFp_simple_field_sqr(const EC_GROUP *group, BIGNUM *r, const BIGNUM *a,
1424 BN_CTX *ctx)
1425{
1426 return BN_mod_sqr(r, a, group->field, ctx);
1427}
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