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[thirdparty/openssl.git] / crypto / ec / ecp_smpl.c
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f8fe20e0 1/* crypto/ec/ecp_smpl.c */
60428dbf
BM		 2/* Includes code written by Lenka Fibikova <fibikova@exp-math.uni-essen.de>
3 * for the OpenSSL project. */
f8fe20e0
BM		 4/* ====================================================================
5 * Copyright (c) 1998-2001 The OpenSSL Project. All rights reserved.
6 *
7 * Redistribution and use in source and binary forms, with or without
8 * modification, are permitted provided that the following conditions
9 * are met:
10 *
11 * 1. Redistributions of source code must retain the above copyright
12 * notice, this list of conditions and the following disclaimer.
13 *
14 * 2. Redistributions in binary form must reproduce the above copyright
15 * notice, this list of conditions and the following disclaimer in
16 * the documentation and/or other materials provided with the
17 * distribution.
18 *
19 * 3. All advertising materials mentioning features or use of this
20 * software must display the following acknowledgment:
21 * "This product includes software developed by the OpenSSL Project
22 * for use in the OpenSSL Toolkit. (http://www.openssl.org/)"
23 *
24 * 4. The names "OpenSSL Toolkit" and "OpenSSL Project" must not be used to
25 * endorse or promote products derived from this software without
26 * prior written permission. For written permission, please contact
27 * openssl-core@openssl.org.
28 *
29 * 5. Products derived from this software may not be called "OpenSSL"
30 * nor may "OpenSSL" appear in their names without prior written
31 * permission of the OpenSSL Project.
32 *
33 * 6. Redistributions of any form whatsoever must retain the following
34 * acknowledgment:
35 * "This product includes software developed by the OpenSSL Project
36 * for use in the OpenSSL Toolkit (http://www.openssl.org/)"
37 *
38 * THIS SOFTWARE IS PROVIDED BY THE OpenSSL PROJECT ``AS IS'' AND ANY
39 * EXPRESSED OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
40 * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR
41 * PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE OpenSSL PROJECT OR
42 * ITS CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL,
43 * SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT
44 * NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES;
45 * LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
46 * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT,
47 * STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE)
48 * ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED
49 * OF THE POSSIBILITY OF SUCH DAMAGE.
50 * ====================================================================
51 *
52 * This product includes cryptographic software written by Eric Young
53 * (eay@cryptsoft.com). This product includes software written by Tim
54 * Hudson (tjh@cryptsoft.com).
55 *
56 */
57
60428dbf
BM		 58#include <openssl/err.h>
59
f8fe20e0 60#include "ec_lcl.h"
0657bf9c
BM		 61
62
63const EC_METHOD *EC_GFp_simple_method(void)
64 {
58fc6229
BM		 65 static const EC_METHOD ret = {
66 ec_GFp_simple_group_init,
58fc6229
BM		 67 ec_GFp_simple_group_finish,
68 ec_GFp_simple_group_clear_finish,
69 ec_GFp_simple_group_copy,
bb62a8b0
BM		 70 ec_GFp_simple_group_set_curve_GFp,
71 ec_GFp_simple_group_get_curve_GFp,
58fc6229 72 ec_GFp_simple_group_set_generator,
bb62a8b0
BM		 73 ec_GFp_simple_group_get0_generator,
74 ec_GFp_simple_group_get_order,
75 ec_GFp_simple_group_get_cofactor,
58fc6229
BM		 76 ec_GFp_simple_point_init,
77 ec_GFp_simple_point_finish,
78 ec_GFp_simple_point_clear_finish,
79 ec_GFp_simple_point_copy,
226cc7de 80 ec_GFp_simple_point_set_to_infinity,
1d5bd6cf
BM		 81 ec_GFp_simple_set_Jprojective_coordinates_GFp,
82 ec_GFp_simple_get_Jprojective_coordinates_GFp,
226cc7de
BM		 83 ec_GFp_simple_point_set_affine_coordinates_GFp,
84 ec_GFp_simple_point_get_affine_coordinates_GFp,
1d5bd6cf 85 ec_GFp_simple_set_compressed_coordinates_GFp,
58fc6229
BM		 86 ec_GFp_simple_point2oct,
87 ec_GFp_simple_oct2point,
88 ec_GFp_simple_add,
89 ec_GFp_simple_dbl,
1d5bd6cf 90 ec_GFp_simple_invert,
58fc6229
BM		 91 ec_GFp_simple_is_at_infinity,
92 ec_GFp_simple_is_on_curve,
1d5bd6cf 93 ec_GFp_simple_cmp,
58fc6229 94 ec_GFp_simple_make_affine,
48fe4d62 95 ec_GFp_simple_points_make_affine,
60428dbf 96 ec_GFp_simple_field_mul,
58fc6229
BM		 97 ec_GFp_simple_field_sqr,
98 0 /* field_encode */,
48fe4d62
BM		 99 0 /* field_decode */,
100 0 /* field_set_to_one */ };
0657bf9c
BM		 101
102 return &ret;
103 }
60428dbf
BM		 104
105
106int ec_GFp_simple_group_init(EC_GROUP *group)
107 {
108 BN_init(&group->field);
109 BN_init(&group->a);
110 BN_init(&group->b);
111 group->a_is_minus3 = 0;
112 group->generator = NULL;
113 BN_init(&group->order);
114 BN_init(&group->cofactor);
115 return 1;
116 }
117
118
bb62a8b0
BM		 119void ec_GFp_simple_group_finish(EC_GROUP *group)
120 {
121 BN_free(&group->field);
122 BN_free(&group->a);
123 BN_free(&group->b);
124 if (group->generator != NULL)
125 EC_POINT_free(group->generator);
126 BN_free(&group->order);
127 BN_free(&group->cofactor);
128 }
129
130
131void ec_GFp_simple_group_clear_finish(EC_GROUP *group)
132 {
133 BN_clear_free(&group->field);
134 BN_clear_free(&group->a);
135 BN_clear_free(&group->b);
136 if (group->generator != NULL)
137 {
138 EC_POINT_clear_free(group->generator);
139 group->generator = NULL;
140 }
141 BN_clear_free(&group->order);
142 BN_clear_free(&group->cofactor);
143 }
144
145
146int ec_GFp_simple_group_copy(EC_GROUP *dest, const EC_GROUP *src)
147 {
148 if (!BN_copy(&dest->field, &src->field)) return 0;
149 if (!BN_copy(&dest->a, &src->a)) return 0;
150 if (!BN_copy(&dest->b, &src->b)) return 0;
151
152 dest->a_is_minus3 = src->a_is_minus3;
153
154 if (src->generator != NULL)
155 {
156 if (dest->generator == NULL)
157 {
158 dest->generator = EC_POINT_new(dest);
159 if (dest->generator == NULL) return 0;
160 }
161 if (!EC_POINT_copy(dest->generator, src->generator)) return 0;
162 }
163 else
164 {
165 /* src->generator == NULL */
166 if (dest->generator != NULL)
167 {
168 EC_POINT_clear_free(dest->generator);
169 dest->generator = NULL;
170 }
171 }
172
173 if (!BN_copy(&dest->order, &src->order)) return 0;
174 if (!BN_copy(&dest->cofactor, &src->cofactor)) return 0;
175
176 return 1;
177 }
178
179
60428dbf
BM		 180int ec_GFp_simple_group_set_curve_GFp(EC_GROUP *group,
181 const BIGNUM *p, const BIGNUM *a, const BIGNUM *b, BN_CTX *ctx)
182 {
183 int ret = 0;
184 BN_CTX *new_ctx = NULL;
185 BIGNUM *tmp_a;
186
1d5bd6cf
BM		 187 /* p must be a prime > 3 */
188 if (BN_num_bits(p) <= 2 || !BN_is_odd(p))
189 {
190 ECerr(EC_F_EC_GFP_SIMPLE_GROUP_SET_CURVE_GFP, EC_R_INVALID_FIELD);
191 return 0;
192 }
193
60428dbf
BM		 194 if (ctx == NULL)
195 {
196 ctx = new_ctx = BN_CTX_new();
197 if (ctx == NULL)
198 return 0;
199 }
60428dbf 200
226cc7de 201 BN_CTX_start(ctx);
60428dbf
BM		 202 tmp_a = BN_CTX_get(ctx);
203 if (tmp_a == NULL) goto err;
204
205 /* group->field */
206 if (!BN_copy(&group->field, p)) goto err;
207 group->field.neg = 0;
208
209 /* group->a */
210 if (!BN_nnmod(tmp_a, a, p, ctx)) goto err;
211 if (group->meth->field_encode)
212 { if (!group->meth->field_encode(group, &group->a, tmp_a, ctx)) goto err; }
213 else
214 if (!BN_copy(&group->a, tmp_a)) goto err;
215
216 /* group->b */
217 if (!BN_nnmod(&group->b, b, p, ctx)) goto err;
218 if (group->meth->field_encode)
219 if (!group->meth->field_encode(group, &group->b, &group->b, ctx)) goto err;
220
221 /* group->a_is_minus3 */
222 if (!BN_add_word(tmp_a, 3)) goto err;
223 group->a_is_minus3 = (0 == BN_cmp(tmp_a, &group->field));
224
225 ret = 1;
226
227 err:
228 BN_CTX_end(ctx);
229 if (new_ctx != NULL)
230 BN_CTX_free(new_ctx);
231 return ret;
232 }
233
234
48fe4d62 235int ec_GFp_simple_group_get_curve_GFp(const EC_GROUP *group, BIGNUM *p, BIGNUM *a, BIGNUM *b, BN_CTX *ctx)
60428dbf 236 {
bb62a8b0
BM		 237 int ret = 0;
238 BN_CTX *new_ctx = NULL;
239
240 if (p != NULL)
60428dbf 241 {
bb62a8b0 242 if (!BN_copy(p, &group->field)) return 0;
60428dbf 243 }
60428dbf 244
bb62a8b0 245 if (a != NULL || b != NULL)
60428dbf 246 {
bb62a8b0 247 if (group->meth->field_decode)
60428dbf 248 {
bb62a8b0
BM		 249 if (ctx == NULL)
250 {
251 ctx = new_ctx = BN_CTX_new();
252 if (ctx == NULL)
253 return 0;
254 }
255 if (a != NULL)
256 {
257 if (!group->meth->field_decode(group, a, &group->a, ctx)) goto err;
258 }
259 if (b != NULL)
260 {
261 if (!group->meth->field_decode(group, b, &group->b, ctx)) goto err;
262 }
60428dbf 263 }
bb62a8b0 264 else
60428dbf 265 {
bb62a8b0
BM		 266 if (a != NULL)
267 {
268 if (!BN_copy(a, &group->a)) goto err;
269 }
270 if (b != NULL)
271 {
272 if (!BN_copy(b, &group->b)) goto err;
273 }
60428dbf
BM		 274 }
275 }
bb62a8b0
BM		 276
277 ret = 1;
278
279 err:
280 if (new_ctx)
281 BN_CTX_free(new_ctx);
282 return ret;
60428dbf
BM		 283 }
284
285
bb62a8b0 286
60428dbf
BM		 287int ec_GFp_simple_group_set_generator(EC_GROUP *group, const EC_POINT *generator,
288 const BIGNUM *order, const BIGNUM *cofactor)
289 {
48fe4d62 290 if (generator == NULL)
60428dbf
BM		 291 {
292 ECerr(EC_F_EC_GFP_SIMPLE_GROUP_SET_GENERATOR, ERR_R_PASSED_NULL_PARAMETER);
293 return 0 ;
294 }
295
296 if (group->generator == NULL)
297 {
298 group->generator = EC_POINT_new(group);
299 if (group->generator == NULL) return 0;
300 }
301 if (!EC_POINT_copy(group->generator, generator)) return 0;
302
303 if (order != NULL)
304 { if (!BN_copy(&group->order, order)) return 0; }
305 else
306 { if (!BN_zero(&group->order)) return 0; }
307
308 if (cofactor != NULL)
309 { if (!BN_copy(&group->cofactor, cofactor)) return 0; }
310 else
311 { if (!BN_zero(&group->cofactor)) return 0; }
312
313 return 1;
314 }
315
316
48fe4d62 317EC_POINT *ec_GFp_simple_group_get0_generator(const EC_GROUP *group)
bb62a8b0
BM		 318 {
319 return group->generator;
320 }
321
322
48fe4d62 323int ec_GFp_simple_group_get_order(const EC_GROUP *group, BIGNUM *order, BN_CTX *ctx)
bb62a8b0
BM		 324 {
325 if (!BN_copy(order, &group->order))
326 return 0;
327
328 return !BN_is_zero(&group->order);
329 }
330
331
48fe4d62 332int ec_GFp_simple_group_get_cofactor(const EC_GROUP *group, BIGNUM *cofactor, BN_CTX *ctx)
bb62a8b0
BM		 333 {
334 if (!BN_copy(cofactor, &group->cofactor))
335 return 0;
336
337 return !BN_is_zero(&group->cofactor);
338 }
60428dbf
BM		 339
340
341int ec_GFp_simple_point_init(EC_POINT *point)
342 {
343 BN_init(&point->X);
344 BN_init(&point->Y);
345 BN_init(&point->Z);
346 point->Z_is_one = 0;
347
348 return 1;
349 }
350
351
352void ec_GFp_simple_point_finish(EC_POINT *point)
353 {
354 BN_free(&point->X);
355 BN_free(&point->Y);
356 BN_free(&point->Z);
357 }
358
359
360void ec_GFp_simple_point_clear_finish(EC_POINT *point)
361 {
362 BN_clear_free(&point->X);
363 BN_clear_free(&point->Y);
364 BN_clear_free(&point->Z);
365 point->Z_is_one = 0;
366 }
367
368
369int ec_GFp_simple_point_copy(EC_POINT *dest, const EC_POINT *src)
370 {
371 if (!BN_copy(&dest->X, &src->X)) return 0;
372 if (!BN_copy(&dest->Y, &src->Y)) return 0;
373 if (!BN_copy(&dest->Z, &src->Z)) return 0;
374 dest->Z_is_one = src->Z_is_one;
375
376 return 1;
377 }
378
379
226cc7de
BM		 380int ec_GFp_simple_point_set_to_infinity(const EC_GROUP *group, EC_POINT *point)
381 {
382 point->Z_is_one = 0;
383 return (BN_zero(&point->Z));
384 }
385
386
1d5bd6cf 387int ec_GFp_simple_set_Jprojective_coordinates_GFp(const EC_GROUP *group, EC_POINT *point,
bb62a8b0
BM		 388 const BIGNUM *x, const BIGNUM *y, const BIGNUM *z, BN_CTX *ctx)
389 {
390 BN_CTX *new_ctx = NULL;
391 int ret = 0;
392
393 if (ctx == NULL)
394 {
395 ctx = new_ctx = BN_CTX_new();
396 if (ctx == NULL)
397 return 0;
398 }
1d5bd6cf 399
bb62a8b0
BM		 400 if (x != NULL)
401 {
402 if (!BN_nnmod(&point->X, x, &group->field, ctx)) goto err;
403 if (group->meth->field_encode)
404 {
405 if (!group->meth->field_encode(group, &point->X, &point->X, ctx)) goto err;
406 }
407 }
408
409 if (y != NULL)
410 {
411 if (!BN_nnmod(&point->Y, y, &group->field, ctx)) goto err;
412 if (group->meth->field_encode)
413 {
414 if (!group->meth->field_encode(group, &point->Y, &point->Y, ctx)) goto err;
415 }
416 }
417
418 if (z != NULL)
419 {
420 int Z_is_one;
1d5bd6cf 421
bb62a8b0
BM		 422 if (!BN_nnmod(&point->Z, z, &group->field, ctx)) goto err;
423 Z_is_one = BN_is_one(&point->Z);
424 if (group->meth->field_encode)
425 {
48fe4d62
BM		 426 if (Z_is_one && (group->meth->field_set_to_one != 0))
427 {
428 if (!group->meth->field_set_to_one(group, &point->Z, ctx)) goto err;
429 }
430 else
431 {
432 if (!group->meth->field_encode(group, &point->Z, &point->Z, ctx)) goto err;
433 }
bb62a8b0
BM		 434 }
435 point->Z_is_one = Z_is_one;
436 }
437
438 ret = 1;
439
440 err:
441 if (new_ctx != NULL)
442 BN_CTX_free(new_ctx);
443 return ret;
444 }
1d5bd6cf
BM		 445
446
bb62a8b0
BM		 447int ec_GFp_simple_get_Jprojective_coordinates_GFp(const EC_GROUP *group, const EC_POINT *point,
448 BIGNUM *x, BIGNUM *y, BIGNUM *z, BN_CTX *ctx)
226cc7de
BM		 449 {
450 BN_CTX *new_ctx = NULL;
451 int ret = 0;
bb62a8b0
BM		 452
453 if (group->meth->field_decode != 0)
226cc7de
BM		 454 {
455 if (ctx == NULL)
456 {
457 ctx = new_ctx = BN_CTX_new();
458 if (ctx == NULL)
459 return 0;
460 }
226cc7de 461
bb62a8b0
BM		 462 if (x != NULL)
463 {
464 if (!group->meth->field_decode(group, x, &point->X, ctx)) goto err;
465 }
466 if (y != NULL)
467 {
468 if (!group->meth->field_decode(group, y, &point->Y, ctx)) goto err;
469 }
470 if (z != NULL)
471 {
472 if (!group->meth->field_decode(group, z, &point->Z, ctx)) goto err;
473 }
474 }
475 else
476 {
477 if (x != NULL)
478 {
479 if (!BN_copy(x, &point->X)) goto err;
480 }
481 if (y != NULL)
482 {
483 if (!BN_copy(y, &point->Y)) goto err;
484 }
485 if (z != NULL)
486 {
487 if (!BN_copy(z, &point->Z)) goto err;
488 }
489 }
226cc7de 490
bb62a8b0
BM		 491 ret = 1;
492
226cc7de
BM		 493 err:
494 if (new_ctx != NULL)
495 BN_CTX_free(new_ctx);
496 return ret;
497 }
498
499
bb62a8b0
BM		 500int ec_GFp_simple_point_set_affine_coordinates_GFp(const EC_GROUP *group, EC_POINT *point,
501 const BIGNUM *x, const BIGNUM *y, BN_CTX *ctx)
502 {
503 if (x == NULL || y == NULL)
504 {
505 /* unlike for projective coordinates, we do not tolerate this */
506 ECerr(EC_F_EC_GFP_SIMPLE_POINT_SET_AFFINE_COORDINATES_GFP, ERR_R_PASSED_NULL_PARAMETER);
507 return 0;
508 }
509
510 return EC_POINT_set_Jprojective_coordinates_GFp(group, point, x, y, BN_value_one(), ctx);
511 }
512
513
226cc7de
BM		 514int ec_GFp_simple_point_get_affine_coordinates_GFp(const EC_GROUP *group, const EC_POINT *point,
515 BIGNUM *x, BIGNUM *y, BN_CTX *ctx)
516 {
517 BN_CTX *new_ctx = NULL;
518 BIGNUM *X, *Y, *Z, *Z_1, *Z_2, *Z_3;
519 const BIGNUM *X_, *Y_, *Z_;
520 int ret = 0;
521
522 if (EC_POINT_is_at_infinity(group, point))
523 {
524 ECerr(EC_F_EC_GFP_SIMPLE_POINT_GET_AFFINE_COORDINATES_GFP, EC_R_POINT_AT_INFINITY);
525 return 0;
526 }
527
528 if (ctx == NULL)
529 {
530 ctx = new_ctx = BN_CTX_new();
531 if (ctx == NULL)
532 return 0;
533 }
534
535 BN_CTX_start(ctx);
536 X = BN_CTX_get(ctx);
537 Y = BN_CTX_get(ctx);
538 Z = BN_CTX_get(ctx);
539 Z_1 = BN_CTX_get(ctx);
540 Z_2 = BN_CTX_get(ctx);
541 Z_3 = BN_CTX_get(ctx);
542 if (Z_3 == NULL) goto err;
543
544 /* transform (X, Y, Z) into (x, y) := (X/Z^2, Y/Z^3) */
545
546 if (group->meth->field_decode)
547 {
548 if (!group->meth->field_decode(group, X, &point->X, ctx)) goto err;
549 if (!group->meth->field_decode(group, Y, &point->Y, ctx)) goto err;
550 if (!group->meth->field_decode(group, Z, &point->Z, ctx)) goto err;
551 X_ = X; Y_ = Y; Z_ = Z;
552 }
553 else
554 {
555 X_ = &point->X;
556 Y_ = &point->Y;
557 Z_ = &point->Z;
558 }
559
560 if (BN_is_one(Z_))
561 {
1d5bd6cf
BM		 562 if (x != NULL)
563 {
564 if (!BN_copy(x, X_)) goto err;
565 }
566 if (y != NULL)
567 {
568 if (!BN_copy(y, Y_)) goto err;
569 }
226cc7de
BM		 570 }
571 else
572 {
573 if (!BN_mod_inverse(Z_1, Z_, &group->field, ctx))
574 {
575 ECerr(EC_F_EC_GFP_SIMPLE_POINT_GET_AFFINE_COORDINATES_GFP, ERR_R_BN_LIB);
576 goto err;
577 }
48fe4d62
BM		 578
579 if (group->meth->field_encode == 0)
580 {
581 /* field_sqr works on standard representation */
582 if (!group->meth->field_sqr(group, Z_2, Z_1, ctx)) goto err;
583 }
584 else
585 {
586 if (!BN_mod_sqr(Z_2, Z_1, &group->field, ctx)) goto err;
587 }
226cc7de 588
1d5bd6cf
BM		 589 if (x != NULL)
590 {
48fe4d62
BM		 591 if (group->meth->field_encode == 0)
592 {
593 /* field_mul works on standard representation */
594 if (!group->meth->field_mul(group, x, X_, Z_2, ctx)) goto err;
595 }
596 else
597 {
598 if (!BN_mod_mul(x, X_, Z_2, &group->field, ctx)) goto err;
599 }
1d5bd6cf
BM		 600 }
601
602 if (y != NULL)
603 {
48fe4d62
BM		 604 if (group->meth->field_encode == 0)
605 {
606 /* field_mul works on standard representation */
607 if (!group->meth->field_mul(group, Z_3, Z_2, Z_1, ctx)) goto err;
608 if (!group->meth->field_mul(group, y, Y_, Z_3, ctx)) goto err;
609
610 }
611 else
612 {
613 if (!BN_mod_mul(Z_3, Z_2, Z_1, &group->field, ctx)) goto err;
614 if (!BN_mod_mul(y, Y_, Z_3, &group->field, ctx)) goto err;
615 }
1d5bd6cf 616 }
226cc7de
BM		 617 }
618
619 ret = 1;
620
621 err:
622 BN_CTX_end(ctx);
623 if (new_ctx != NULL)
624 BN_CTX_free(new_ctx);
625 return ret;
626 }
627
628
1d5bd6cf 629int ec_GFp_simple_set_compressed_coordinates_GFp(const EC_GROUP *group, EC_POINT *point,
48fe4d62 630 const BIGNUM *x_, int y_bit, BN_CTX *ctx)
bb62a8b0
BM		 631 {
632 BN_CTX *new_ctx = NULL;
48fe4d62 633 BIGNUM *tmp1, *tmp2, *x, *y;
bb62a8b0
BM		 634 int ret = 0;
635
636 if (ctx == NULL)
637 {
638 ctx = new_ctx = BN_CTX_new();
639 if (ctx == NULL)
640 return 0;
641 }
642
643 y_bit = (y_bit != 0);
644
645 BN_CTX_start(ctx);
646 tmp1 = BN_CTX_get(ctx);
647 tmp2 = BN_CTX_get(ctx);
48fe4d62 648 x = BN_CTX_get(ctx);
bb62a8b0
BM		 649 y = BN_CTX_get(ctx);
650 if (y == NULL) goto err;
651
652 /* Recover y. We have a Weierstrass equation
653 * y^2 = x^3 + a*x + b,
654 * so y is one of the square roots of x^3 + a*x + b.
655 */
656
657 /* tmp1 := x^3 */
48fe4d62
BM		 658 if (!BN_nnmod(x, x_, &group->field,ctx)) goto err;
659 if (group->meth->field_decode == 0)
660 {
661 /* field_{sqr,mul} work on standard representation */
662 if (!group->meth->field_sqr(group, tmp2, x_, ctx)) goto err;
663 if (!group->meth->field_mul(group, tmp1, tmp2, x_, ctx)) goto err;
664 }
665 else
666 {
667 if (!BN_mod_sqr(tmp2, x_, &group->field, ctx)) goto err;
668 if (!BN_mod_mul(tmp1, tmp2, x_, &group->field, ctx)) goto err;
669 }
bb62a8b0
BM		 670
671 /* tmp1 := tmp1 + a*x */
672 if (group->a_is_minus3)
673 {
674 if (!BN_mod_lshift1_quick(tmp2, x, &group->field)) goto err;
675 if (!BN_mod_add_quick(tmp2, tmp2, x, &group->field)) goto err;
676 if (!BN_mod_sub_quick(tmp1, tmp1, tmp2, &group->field)) goto err;
677 }
678 else
679 {
156e8557
BM		 680 if (group->meth->field_decode)
681 {
682 if (!group->meth->field_decode(group, tmp2, &group->a, ctx)) goto err;
683 if (!BN_mod_mul(tmp2, tmp2, x, &group->field, ctx)) goto err;
684 }
685 else
686 {
48fe4d62
BM		 687 /* field_mul works on standard representation */
688 if (!group->meth->field_mul(group, tmp2, &group->a, x, ctx)) goto err;
156e8557
BM		 689 }
690
bb62a8b0
BM		 691 if (!BN_mod_add_quick(tmp1, tmp1, tmp2, &group->field)) goto err;
692 }
693
694 /* tmp1 := tmp1 + b */
156e8557
BM		 695 if (group->meth->field_decode)
696 {
697 if (!group->meth->field_decode(group, tmp2, &group->b, ctx)) goto err;
698 if (!BN_mod_add_quick(tmp1, tmp1, tmp2, &group->field)) goto err;
699 }
700 else
701 {
702 if (!BN_mod_add_quick(tmp1, tmp1, &group->b, &group->field)) goto err;
703 }
bb62a8b0
BM		 704
705 if (!BN_mod_sqrt(y, tmp1, &group->field, ctx))
706 {
48fe4d62
BM		 707 unsigned long err = ERR_peek_error();
708
709 if (ERR_GET_LIB(err) == ERR_LIB_BN && ERR_GET_REASON(err) == BN_R_NOT_A_SQUARE)
710 {
711 (void)ERR_get_error();
712 ECerr(EC_F_EC_GFP_SIMPLE_SET_COMPRESSED_COORDINATES_GFP, EC_R_INVALID_COMPRESSED_POINT);
713 }
714 else
715 ECerr(EC_F_EC_GFP_SIMPLE_SET_COMPRESSED_COORDINATES_GFP, ERR_R_BN_LIB);
bb62a8b0
BM		 716 goto err;
717 }
718 /* If tmp1 is not a square (i.e. there is no point on the curve with
719 * our x), then y now is a nonsense value too */
720
721 if (y_bit != BN_is_odd(y))
722 {
723 if (BN_is_zero(y))
724 {
725 int kron;
726
727 kron = BN_kronecker(x, &group->field, ctx);
728 if (kron == -2) goto err;
729
730 if (kron == 1)
731 ECerr(EC_F_EC_GFP_SIMPLE_SET_COMPRESSED_COORDINATES_GFP, EC_R_INVALID_COMPRESSION_BIT);
732 else
733 ECerr(EC_F_EC_GFP_SIMPLE_SET_COMPRESSED_COORDINATES_GFP, EC_R_INVALID_COMPRESSED_POINT);
734 goto err;
735 }
736 if (!BN_usub(y, &group->field, y)) goto err;
737 }
738 if (y_bit != BN_is_odd(y))
739 {
740 ECerr(EC_F_EC_GFP_SIMPLE_SET_COMPRESSED_COORDINATES_GFP, ERR_R_INTERNAL_ERROR);
741 goto err;
742 }
743
744 if (!EC_POINT_set_affine_coordinates_GFp(group, point, x, y, ctx)) goto err;
745
746 ret = 1;
747
748 err:
749 BN_CTX_end(ctx);
750 if (new_ctx != NULL)
751 BN_CTX_free(new_ctx);
752 return ret;
753 }
60428dbf
BM		 754
755
756size_t ec_GFp_simple_point2oct(const EC_GROUP *group, const EC_POINT *point, point_conversion_form_t form,
226cc7de
BM		 757 unsigned char *buf, size_t len, BN_CTX *ctx)
758 {
759 size_t ret;
760 BN_CTX *new_ctx = NULL;
761 int used_ctx = 0;
762 BIGNUM *x, *y;
763 size_t field_len, i, skip;
764
765 if ((form != POINT_CONVERSION_COMPRESSED)
766 && (form != POINT_CONVERSION_UNCOMPRESSED)
767 && (form != POINT_CONVERSION_HYBRID))
768 {
769 ECerr(EC_F_EC_GFP_SIMPLE_POINT2OCT, EC_R_INVALID_FORM);
770 goto err;
771 }
772
773 if (EC_POINT_is_at_infinity(group, point))
774 {
775 /* encodes to a single 0 octet */
776 if (buf != NULL)
777 {
778 if (len < 1)
779 {
780 ECerr(EC_F_EC_GFP_SIMPLE_POINT2OCT, EC_R_BUFFER_TOO_SMALL);
781 return 0;
782 }
783 buf[0] = 0;
784 }
785 return 1;
786 }
787
788
789 /* ret := required output buffer length */
790 field_len = BN_num_bytes(&group->field);
791 ret = (form == POINT_CONVERSION_COMPRESSED) ? 1 + field_len : 1 + 2*field_len;
792
793 /* if 'buf' is NULL, just return required length */
794 if (buf != NULL)
795 {
796 if (len < ret)
797 {
798 ECerr(EC_F_EC_GFP_SIMPLE_POINT2OCT, EC_R_BUFFER_TOO_SMALL);
799 goto err;
800 }
801
802 if (ctx == NULL)
803 {
804 ctx = new_ctx = BN_CTX_new();
805 if (ctx == NULL)
806 return 0;
807 }
808
809 BN_CTX_start(ctx);
810 used_ctx = 1;
811 x = BN_CTX_get(ctx);
812 y = BN_CTX_get(ctx);
813 if (y == NULL) goto err;
814
815 if (!EC_POINT_get_affine_coordinates_GFp(group, point, x, y, ctx)) goto err;
816
1d5bd6cf 817 if ((form == POINT_CONVERSION_COMPRESSED || form == POINT_CONVERSION_HYBRID) && BN_is_odd(y))
226cc7de
BM		 818 buf[0] = form + 1;
819 else
820 buf[0] = form;
821
822 i = 1;
823
824 skip = field_len - BN_num_bytes(x);
825 if (skip > field_len)
826 {
827 ECerr(EC_F_EC_GFP_SIMPLE_POINT2OCT, ERR_R_INTERNAL_ERROR);
828 goto err;
829 }
830 while (skip > 0)
831 {
832 buf[i++] = 0;
833 skip--;
834 }
835 skip = BN_bn2bin(x, buf + i);
836 i += skip;
837 if (i != 1 + field_len)
838 {
839 ECerr(EC_F_EC_GFP_SIMPLE_POINT2OCT, ERR_R_INTERNAL_ERROR);
840 goto err;
841 }
842
843 if (form == POINT_CONVERSION_UNCOMPRESSED || form == POINT_CONVERSION_HYBRID)
844 {
845 skip = field_len - BN_num_bytes(y);
846 if (skip > field_len)
847 {
848 ECerr(EC_F_EC_GFP_SIMPLE_POINT2OCT, ERR_R_INTERNAL_ERROR);
849 goto err;
850 }
851 while (skip > 0)
852 {
853 buf[i++] = 0;
854 skip--;
855 }
856 skip = BN_bn2bin(y, buf + i);
857 i += skip;
858 }
859
860 if (i != ret)
861 {
862 ECerr(EC_F_EC_GFP_SIMPLE_POINT2OCT, ERR_R_INTERNAL_ERROR);
863 goto err;
864 }
865 }
866
867 if (used_ctx)
868 BN_CTX_end(ctx);
869 if (new_ctx != NULL)
870 BN_CTX_free(new_ctx);
871 return ret;
872
873 err:
874 if (used_ctx)
875 BN_CTX_end(ctx);
876 if (new_ctx != NULL)
877 BN_CTX_free(new_ctx);
878 return 0;
879 }
60428dbf
BM		 880
881
882int ec_GFp_simple_oct2point(const EC_GROUP *group, EC_POINT *point,
226cc7de
BM		 883 const unsigned char *buf, size_t len, BN_CTX *ctx)
884 {
885 point_conversion_form_t form;
886 int y_bit;
887 BN_CTX *new_ctx = NULL;
888 BIGNUM *x, *y;
889 size_t field_len, enc_len;
890 int ret = 0;
891
1f0af2c0 892 if (len == 0)
226cc7de
BM		 893 {
894 ECerr(EC_F_EC_GFP_SIMPLE_OCT2POINT, EC_R_BUFFER_TOO_SMALL);
895 return 0;
896 }
897 form = buf[0];
898 y_bit = form & 1;
899 form = form & ~1;
900 if ((form != 0) && (form != POINT_CONVERSION_COMPRESSED)
901 && (form != POINT_CONVERSION_UNCOMPRESSED)
902 && (form != POINT_CONVERSION_HYBRID))
903 {
904 ECerr(EC_F_EC_GFP_SIMPLE_OCT2POINT, EC_R_INVALID_ENCODING);
905 return 0;
906 }
907 if ((form == 0 || form == POINT_CONVERSION_UNCOMPRESSED) && y_bit)
908 {
909 ECerr(EC_F_EC_GFP_SIMPLE_OCT2POINT, EC_R_INVALID_ENCODING);
910 return 0;
911 }
912
913 if (form == 0)
914 {
915 if (len != 1)
916 {
917 ECerr(EC_F_EC_GFP_SIMPLE_OCT2POINT, EC_R_INVALID_ENCODING);
918 return 0;
919 }
920
921 return EC_POINT_set_to_infinity(group, point);
922 }
923
924 field_len = BN_num_bytes(&group->field);
925 enc_len = (form == POINT_CONVERSION_COMPRESSED) ? 1 + field_len : 1 + 2*field_len;
926
927 if (len != enc_len)
928 {
929 ECerr(EC_F_EC_GFP_SIMPLE_OCT2POINT, EC_R_INVALID_ENCODING);
930 return 0;
931 }
932
933 if (ctx == NULL)
934 {
935 ctx = new_ctx = BN_CTX_new();
936 if (ctx == NULL)
937 return 0;
938 }
939
940 BN_CTX_start(ctx);
941 x = BN_CTX_get(ctx);
942 y = BN_CTX_get(ctx);
943 if (y == NULL) goto err;
944
945 if (!BN_bin2bn(buf + 1, field_len, x)) goto err;
946 if (BN_ucmp(x, &group->field) >= 0)
947 {
948 ECerr(EC_F_EC_GFP_SIMPLE_OCT2POINT, EC_R_INVALID_ENCODING);
949 goto err;
950 }
951
bb62a8b0
BM		 952 if (form == POINT_CONVERSION_COMPRESSED)
953 {
954 if (!EC_POINT_set_compressed_coordinates_GFp(group, point, x, y_bit, ctx)) goto err;
955 }
956 else
226cc7de
BM		 957 {
958 if (!BN_bin2bn(buf + 1 + field_len, field_len, y)) goto err;
959 if (BN_ucmp(y, &group->field) >= 0)
960 {
961 ECerr(EC_F_EC_GFP_SIMPLE_OCT2POINT, EC_R_INVALID_ENCODING);
962 goto err;
963 }
964 if (form == POINT_CONVERSION_HYBRID)
965 {
1d5bd6cf 966 if (y_bit != BN_is_odd(y))
226cc7de
BM		 967 {
968 ECerr(EC_F_EC_GFP_SIMPLE_OCT2POINT, EC_R_INVALID_ENCODING);
969 goto err;
970 }
971 }
226cc7de 972
bb62a8b0 973 if (!EC_POINT_set_affine_coordinates_GFp(group, point, x, y, ctx)) goto err;
226cc7de
BM		 974 }
975
226cc7de
BM		 976 if (!EC_POINT_is_on_curve(group, point, ctx)) /* test required by X9.62 */
977 {
978 ECerr(EC_F_EC_GFP_SIMPLE_OCT2POINT, EC_R_POINT_IS_NOT_ON_CURVE);
979 goto err;
980 }
981
982 ret = 1;
983
984 err:
985 BN_CTX_end(ctx);
986 if (new_ctx != NULL)
987 BN_CTX_free(new_ctx);
988 return ret;
989 }
60428dbf
BM		 990
991
992int ec_GFp_simple_add(const EC_GROUP *group, EC_POINT *r, const EC_POINT *a, const EC_POINT *b, BN_CTX *ctx)
993 {
994 int (*field_mul)(const EC_GROUP *, BIGNUM *, const BIGNUM *, const BIGNUM *, BN_CTX *);
995 int (*field_sqr)(const EC_GROUP *, BIGNUM *, const BIGNUM *, BN_CTX *);
996 const BIGNUM *p;
997 BN_CTX *new_ctx = NULL;
998 BIGNUM *n0, *n1, *n2, *n3, *n4, *n5, *n6;
999 int ret = 0;
1000
1001 if (a == b)
1002 return EC_POINT_dbl(group, r, a, ctx);
1003 if (EC_POINT_is_at_infinity(group, a))
1004 return EC_POINT_copy(r, b);
1005 if (EC_POINT_is_at_infinity(group, b))
1006 return EC_POINT_copy(r, a);
1007
1008 field_mul = group->meth->field_mul;
1009 field_sqr = group->meth->field_sqr;
1010 p = &group->field;
1011
1012 if (ctx == NULL)
1013 {
1014 ctx = new_ctx = BN_CTX_new();
1015 if (ctx == NULL)
1016 return 0;
1017 }
60428dbf 1018
226cc7de 1019 BN_CTX_start(ctx);
60428dbf
BM		 1020 n0 = BN_CTX_get(ctx);
1021 n1 = BN_CTX_get(ctx);
1022 n2 = BN_CTX_get(ctx);
1023 n3 = BN_CTX_get(ctx);
1024 n4 = BN_CTX_get(ctx);
1025 n5 = BN_CTX_get(ctx);
1026 n6 = BN_CTX_get(ctx);
1027 if (n6 == NULL) goto end;
1028
1d5bd6cf
BM		 1029 /* Note that in this function we must not read components of 'a' or 'b'
1030 * once we have written the corresponding components of 'r'.
1031 * ('r' might be one of 'a' or 'b'.)
1032 */
1033
60428dbf
BM		 1034 /* n1, n2 */
1035 if (b->Z_is_one)
1036 {
1037 if (!BN_copy(n1, &a->X)) goto end;
1038 if (!BN_copy(n2, &a->Y)) goto end;
1039 /* n1 = X_a */
1040 /* n2 = Y_a */
1041 }
1042 else
1043 {
1044 if (!field_sqr(group, n0, &b->Z, ctx)) goto end;
1045 if (!field_mul(group, n1, &a->X, n0, ctx)) goto end;
1046 /* n1 = X_a * Z_b^2 */
1047
1048 if (!field_mul(group, n0, n0, &b->Z, ctx)) goto end;
1049 if (!field_mul(group, n2, &a->Y, n0, ctx)) goto end;
1050 /* n2 = Y_a * Z_b^3 */
1051 }
1052
1053 /* n3, n4 */
1054 if (a->Z_is_one)
1055 {
1056 if (!BN_copy(n3, &b->X)) goto end;
1057 if (!BN_copy(n4, &b->Y)) goto end;
1058 /* n3 = X_b */
1059 /* n4 = Y_b */
1060 }
1061 else
1062 {
1063 if (!field_sqr(group, n0, &a->Z, ctx)) goto end;
1064 if (!field_mul(group, n3, &b->X, n0, ctx)) goto end;
1065 /* n3 = X_b * Z_a^2 */
1066
1067 if (!field_mul(group, n0, n0, &a->Z, ctx)) goto end;
1068 if (!field_mul(group, n4, &b->Y, n0, ctx)) goto end;
1069 /* n4 = Y_b * Z_a^3 */
1070 }
1071
1072 /* n5, n6 */
1073 if (!BN_mod_sub_quick(n5, n1, n3, p)) goto end;
1074 if (!BN_mod_sub_quick(n6, n2, n4, p)) goto end;
1075 /* n5 = n1 - n3 */
1076 /* n6 = n2 - n4 */
1077
1078 if (BN_is_zero(n5))
1079 {
1080 if (BN_is_zero(n6))
1081 {
1082 /* a is the same point as b */
1083 BN_CTX_end(ctx);
60428dbf 1084 ret = EC_POINT_dbl(group, r, a, ctx);
e869d4bd 1085 ctx = NULL;
60428dbf
BM		 1086 goto end;
1087 }
1088 else
1089 {
1090 /* a is the inverse of b */
1091 if (!BN_zero(&r->Z)) goto end;
1092 r->Z_is_one = 0;
1093 ret = 1;
1094 goto end;
1095 }
1096 }
1097
1098 /* 'n7', 'n8' */
1099 if (!BN_mod_add_quick(n1, n1, n3, p)) goto end;
1100 if (!BN_mod_add_quick(n2, n2, n4, p)) goto end;
1101 /* 'n7' = n1 + n3 */
1102 /* 'n8' = n2 + n4 */
1103
1104 /* Z_r */
1105 if (a->Z_is_one && b->Z_is_one)
1106 {
1107 if (!BN_copy(&r->Z, n5)) goto end;
1108 }
1109 else
1110 {
1111 if (a->Z_is_one)
1112 { if (!BN_copy(n0, &b->Z)) goto end; }
1113 else if (b->Z_is_one)
1114 { if (!BN_copy(n0, &a->Z)) goto end; }
1115 else
1116 { if (!field_mul(group, n0, &a->Z, &b->Z, ctx)) goto end; }
1117 if (!field_mul(group, &r->Z, n0, n5, ctx)) goto end;
1118 }
1119 r->Z_is_one = 0;
1120 /* Z_r = Z_a * Z_b * n5 */
1121
1122 /* X_r */
1123 if (!field_sqr(group, n0, n6, ctx)) goto end;
1124 if (!field_sqr(group, n4, n5, ctx)) goto end;
1125 if (!field_mul(group, n3, n1, n4, ctx)) goto end;
1126 if (!BN_mod_sub_quick(&r->X, n0, n3, p)) goto end;
1127 /* X_r = n6^2 - n5^2 * 'n7' */
1128
1129 /* 'n9' */
1130 if (!BN_mod_lshift1_quick(n0, &r->X, p)) goto end;
1131 if (!BN_mod_sub_quick(n0, n3, n0, p)) goto end;
1132 /* n9 = n5^2 * 'n7' - 2 * X_r */
1133
1134 /* Y_r */
1135 if (!field_mul(group, n0, n0, n6, ctx)) goto end;
1136 if (!field_mul(group, n5, n4, n5, ctx)) goto end; /* now n5 is n5^3 */
1137 if (!field_mul(group, n1, n2, n5, ctx)) goto end;
1138 if (!BN_mod_sub_quick(n0, n0, n1, p)) goto end;
1139 if (BN_is_odd(n0))
1140 if (!BN_add(n0, n0, p)) goto end;
1141 /* now 0 <= n0 < 2*p, and n0 is even */
1142 if (!BN_rshift1(&r->Y, n0)) goto end;
1143 /* Y_r = (n6 * 'n9' - 'n8' * 'n5^3') / 2 */
1144
1145 ret = 1;
1146
1147 end:
1148 if (ctx) /* otherwise we already called BN_CTX_end */
1149 BN_CTX_end(ctx);
1150 if (new_ctx != NULL)
1151 BN_CTX_free(new_ctx);
1152 return ret;
1153 }
1154
1155
1156int ec_GFp_simple_dbl(const EC_GROUP *group, EC_POINT *r, const EC_POINT *a, BN_CTX *ctx)
1157 {
1158 int (*field_mul)(const EC_GROUP *, BIGNUM *, const BIGNUM *, const BIGNUM *, BN_CTX *);
1159 int (*field_sqr)(const EC_GROUP *, BIGNUM *, const BIGNUM *, BN_CTX *);
1160 const BIGNUM *p;
1161 BN_CTX *new_ctx = NULL;
1162 BIGNUM *n0, *n1, *n2, *n3;
1163 int ret = 0;
1164
1165 if (EC_POINT_is_at_infinity(group, a))
1166 {
1167 if (!BN_zero(&r->Z)) return 0;
1168 r->Z_is_one = 0;
1169 return 1;
1170 }
1171
1172 field_mul = group->meth->field_mul;
1173 field_sqr = group->meth->field_sqr;
1174 p = &group->field;
1175
1176 if (ctx == NULL)
1177 {
1178 ctx = new_ctx = BN_CTX_new();
1179 if (ctx == NULL)
1180 return 0;
1181 }
60428dbf 1182
226cc7de 1183 BN_CTX_start(ctx);
60428dbf
BM		 1184 n0 = BN_CTX_get(ctx);
1185 n1 = BN_CTX_get(ctx);
1186 n2 = BN_CTX_get(ctx);
1187 n3 = BN_CTX_get(ctx);
1188 if (n3 == NULL) goto err;
1189
1d5bd6cf
BM		 1190 /* Note that in this function we must not read components of 'a'
1191 * once we have written the corresponding components of 'r'.
1192 * ('r' might the same as 'a'.)
1193 */
1194
60428dbf
BM		 1195 /* n1 */
1196 if (a->Z_is_one)
1197 {
1198 if (!field_sqr(group, n0, &a->X, ctx)) goto err;
1199 if (!BN_mod_lshift1_quick(n1, n0, p)) goto err;
1200 if (!BN_mod_add_quick(n0, n0, n1, p)) goto err;
1201 if (!BN_mod_add_quick(n1, n0, &group->a, p)) goto err;
1202 /* n1 = 3 * X_a^2 + a_curve */
1203 }
1204 else if (group->a_is_minus3)
1205 {
1206 if (!field_sqr(group, n1, &a->Z, ctx)) goto err;
1207 if (!BN_mod_add_quick(n0, &a->X, n1, p)) goto err;
1208 if (!BN_mod_sub_quick(n2, &a->X, n1, p)) goto err;
1209 if (!field_mul(group, n1, n0, n2, ctx)) goto err;
1210 if (!BN_mod_lshift1_quick(n0, n1, p)) goto err;
1211 if (!BN_mod_add_quick(n1, n0, n1, p)) goto err;
1212 /* n1 = 3 * (X_a + Z_a^2) * (X_a - Z_a^2)
1213 * = 3 * X_a^2 - 3 * Z_a^4 */
1214 }
1215 else
1216 {
1217 if (!field_sqr(group, n0, &a->X, ctx)) goto err;
1218 if (!BN_mod_lshift1_quick(n1, n0, p)) goto err;
1219 if (!BN_mod_add_quick(n0, n0, n1, p)) goto err;
1220 if (!field_sqr(group, n1, &a->Z, ctx)) goto err;
1221 if (!field_sqr(group, n1, n1, ctx)) goto err;
1222 if (!field_mul(group, n1, n1, &group->a, ctx)) goto err;
1223 if (!BN_mod_add_quick(n1, n1, n0, p)) goto err;
1224 /* n1 = 3 * X_a^2 + a_curve * Z_a^4 */
1225 }
1226
1227 /* Z_r */
1228 if (a->Z_is_one)
1229 {
1230 if (!BN_copy(n0, &a->Y)) goto err;
1231 }
1232 else
1233 {
1234 if (!field_mul(group, n0, &a->Y, &a->Z, ctx)) goto err;
1235 }
1236 if (!BN_mod_lshift1_quick(&r->Z, n0, p)) goto err;
1237 r->Z_is_one = 0;
1238 /* Z_r = 2 * Y_a * Z_a */
1239
1240 /* n2 */
1241 if (!field_sqr(group, n3, &a->Y, ctx)) goto err;
1242 if (!field_mul(group, n2, &a->X, n3, ctx)) goto err;
1243 if (!BN_mod_lshift_quick(n2, n2, 2, p)) goto err;
1244 /* n2 = 4 * X_a * Y_a^2 */
1245
1246 /* X_r */
1247 if (!BN_mod_lshift1_quick(n0, n2, p)) goto err;
1248 if (!field_sqr(group, &r->X, n1, ctx)) goto err;
1249 if (!BN_mod_sub_quick(&r->X, &r->X, n0, p)) goto err;
1250 /* X_r = n1^2 - 2 * n2 */
1251
1252 /* n3 */
1253 if (!field_sqr(group, n0, n3, ctx)) goto err;
1254 if (!BN_mod_lshift_quick(n3, n0, 3, p)) goto err;
1255 /* n3 = 8 * Y_a^4 */
1256
1257 /* Y_r */
1258 if (!BN_mod_sub_quick(n0, n2, &r->X, p)) goto err;
1259 if (!field_mul(group, n0, n1, n0, ctx)) goto err;
1260 if (!BN_mod_sub_quick(&r->Y, n0, n3, p)) goto err;
1261 /* Y_r = n1 * (n2 - X_r) - n3 */
1262
1263 ret = 1;
1264
1265 err:
1266 BN_CTX_end(ctx);
1267 if (new_ctx != NULL)
1268 BN_CTX_free(new_ctx);
1269 return ret;
1270 }
1271
1272
bb62a8b0
BM		 1273int ec_GFp_simple_invert(const EC_GROUP *group, EC_POINT *point, BN_CTX *ctx)
1274 {
1275 if (EC_POINT_is_at_infinity(group, point) || BN_is_zero(&point->Y))
1276 /* point is its own inverse */
1277 return 1;
1278
1279 return BN_usub(&point->Y, &group->field, &point->Y);
1280 }
1d5bd6cf
BM		 1281
1282
60428dbf
BM		 1283int ec_GFp_simple_is_at_infinity(const EC_GROUP *group, const EC_POINT *point)
1284 {
1285 return BN_is_zero(&point->Z);
1286 }
1287
1288
e869d4bd
BM		 1289int ec_GFp_simple_is_on_curve(const EC_GROUP *group, const EC_POINT *point, BN_CTX *ctx)
1290 {
1291 int (*field_mul)(const EC_GROUP *, BIGNUM *, const BIGNUM *, const BIGNUM *, BN_CTX *);
1292 int (*field_sqr)(const EC_GROUP *, BIGNUM *, const BIGNUM *, BN_CTX *);
1293 const BIGNUM *p;
1294 BN_CTX *new_ctx = NULL;
1295 BIGNUM *rh, *tmp1, *tmp2, *Z4, *Z6;
1296 int ret = -1;
60428dbf 1297
e869d4bd
BM		 1298 if (EC_POINT_is_at_infinity(group, point))
1299 return 1;
1300
1301 field_mul = group->meth->field_mul;
1302 field_sqr = group->meth->field_sqr;
1303 p = &group->field;
60428dbf 1304
e869d4bd
BM		 1305 if (ctx == NULL)
1306 {
1307 ctx = new_ctx = BN_CTX_new();
1308 if (ctx == NULL)
226cc7de 1309 return -1;
e869d4bd 1310 }
e869d4bd 1311
226cc7de 1312 BN_CTX_start(ctx);
e869d4bd
BM		 1313 rh = BN_CTX_get(ctx);
1314 tmp1 = BN_CTX_get(ctx);
1315 tmp2 = BN_CTX_get(ctx);
1316 Z4 = BN_CTX_get(ctx);
1317 Z6 = BN_CTX_get(ctx);
1318 if (Z6 == NULL) goto err;
1319
1320 /* We have a curve defined by a Weierstrass equation
1321 * y^2 = x^3 + a*x + b.
1322 * The point to consider is given in Jacobian projective coordinates
1323 * where (X, Y, Z) represents (x, y) = (X/Z^2, Y/Z^3).
1324 * Substituting this and multiplying by Z^6 transforms the above equation into
1325 * Y^2 = X^3 + a*X*Z^4 + b*Z^6.
1326 * To test this, we add up the right-hand side in 'rh'.
1327 */
1328
1329 /* rh := X^3 */
1330 if (!field_sqr(group, rh, &point->X, ctx)) goto err;
1331 if (!field_mul(group, rh, rh, &point->X, ctx)) goto err;
1332
1333 if (!point->Z_is_one)
1334 {
1335 if (!field_sqr(group, tmp1, &point->Z, ctx)) goto err;
1336 if (!field_sqr(group, Z4, tmp1, ctx)) goto err;
1337 if (!field_mul(group, Z6, Z4, tmp1, ctx)) goto err;
1338
1339 /* rh := rh + a*X*Z^4 */
1340 if (!field_mul(group, tmp1, &point->X, Z4, ctx)) goto err;
bb62a8b0 1341 if (group->a_is_minus3)
e869d4bd
BM		 1342 {
1343 if (!BN_mod_lshift1_quick(tmp2, tmp1, p)) goto err;
1344 if (!BN_mod_add_quick(tmp2, tmp2, tmp1, p)) goto err;
1345 if (!BN_mod_sub_quick(rh, rh, tmp2, p)) goto err;
1346 }
1347 else
1348 {
1349 if (!field_mul(group, tmp2, tmp1, &group->a, ctx)) goto err;
1350 if (!BN_mod_add_quick(rh, rh, tmp2, p)) goto err;
1351 }
1352
1353 /* rh := rh + b*Z^6 */
1354 if (!field_mul(group, tmp1, &group->b, Z6, ctx)) goto err;
1355 if (!BN_mod_add_quick(rh, rh, tmp1, p)) goto err;
1356 }
1357 else
1358 {
1359 /* point->Z_is_one */
1360
1361 /* rh := rh + a*X */
bb62a8b0 1362 if (group->a_is_minus3)
e869d4bd
BM		 1363 {
1364 if (!BN_mod_lshift1_quick(tmp2, &point->X, p)) goto err;
1365 if (!BN_mod_add_quick(tmp2, tmp2, &point->X, p)) goto err;
1366 if (!BN_mod_sub_quick(rh, rh, tmp2, p)) goto err;
1367 }
1368 else
1369 {
1370 if (!field_mul(group, tmp2, &point->X, &group->a, ctx)) goto err;
1371 if (!BN_mod_add_quick(rh, rh, tmp2, p)) goto err;
1372 }
1373
1374 /* rh := rh + b */
1375 if (!BN_mod_add_quick(rh, rh, &group->b, p)) goto err;
1376 }
1377
1378 /* 'lh' := Y^2 */
1379 if (!field_sqr(group, tmp1, &point->Y, ctx)) goto err;
1380
1381 ret = (0 == BN_cmp(tmp1, rh));
1382
1383 err:
1384 BN_CTX_end(ctx);
1385 if (new_ctx != NULL)
1386 BN_CTX_free(new_ctx);
1387 return ret;
1388 }
1389
1390
bb62a8b0
BM		 1391int ec_GFp_simple_cmp(const EC_GROUP *group, const EC_POINT *a, const EC_POINT *b, BN_CTX *ctx)
1392 {
1393 /* return values:
1394 * -1 error
1395 * 0 equal (in affine coordinates)
1396 * 1 not equal
1397 */
1398
1399 int (*field_mul)(const EC_GROUP *, BIGNUM *, const BIGNUM *, const BIGNUM *, BN_CTX *);
1400 int (*field_sqr)(const EC_GROUP *, BIGNUM *, const BIGNUM *, BN_CTX *);
1401 BN_CTX *new_ctx = NULL;
1402 BIGNUM *tmp1, *tmp2, *Za23, *Zb23;
1403 const BIGNUM *tmp1_, *tmp2_;
1404 int ret = -1;
1405
1406 if (EC_POINT_is_at_infinity(group, a))
1407 {
1408 return EC_POINT_is_at_infinity(group, b) ? 0 : 1;
1409 }
1410
1411 if (a->Z_is_one && b->Z_is_one)
1412 {
1413 return ((BN_cmp(&a->X, &b->X) == 0) && BN_cmp(&a->Y, &b->Y) == 0) ? 0 : 1;
1414 }
1415
1416 field_mul = group->meth->field_mul;
1417 field_sqr = group->meth->field_sqr;
1418
1419 if (ctx == NULL)
1420 {
1421 ctx = new_ctx = BN_CTX_new();
1422 if (ctx == NULL)
1423 return -1;
1424 }
1425
1426 BN_CTX_start(ctx);
1427 tmp1 = BN_CTX_get(ctx);
1428 tmp2 = BN_CTX_get(ctx);
1429 Za23 = BN_CTX_get(ctx);
1430 Zb23 = BN_CTX_get(ctx);
1431 if (Zb23 == NULL) goto end;
1432
1433 /* We have to decide whether
1434 * (X_a/Z_a^2, Y_a/Z_a^3) = (X_b/Z_b^2, Y_b/Z_b^3),
1435 * or equivalently, whether
1436 * (X_a*Z_b^2, Y_a*Z_b^3) = (X_b*Z_a^2, Y_b*Z_a^3).
1437 */
1438
1439 if (!b->Z_is_one)
1440 {
1441 if (!field_sqr(group, Zb23, &b->Z, ctx)) goto end;
1442 if (!field_mul(group, tmp1, &a->X, Zb23, ctx)) goto end;
1443 tmp1_ = tmp1;
1444 }
1445 else
1446 tmp1_ = &a->X;
1447 if (!a->Z_is_one)
1448 {
1449 if (!field_sqr(group, Za23, &a->Z, ctx)) goto end;
1450 if (!field_mul(group, tmp2, &b->X, Za23, ctx)) goto end;
1451 tmp2_ = tmp2;
1452 }
1453 else
1454 tmp2_ = &b->X;
1455
1456 /* compare X_a*Z_b^2 with X_b*Z_a^2 */
1457 if (BN_cmp(tmp1_, tmp2_) != 0)
1458 {
1459 ret = 1; /* points differ */
1460 goto end;
1461 }
1462
1463
1464 if (!b->Z_is_one)
1465 {
1466 if (!field_mul(group, Zb23, Zb23, &b->Z, ctx)) goto end;
1467 if (!field_mul(group, tmp1, &a->Y, Zb23, ctx)) goto end;
42909e39 1468 /* tmp1_ = tmp1 */
bb62a8b0 1469 }
42909e39
BM		 1470 else
1471 tmp1_ = &a->Y;
bb62a8b0
BM		 1472 if (!a->Z_is_one)
1473 {
1474 if (!field_mul(group, Za23, Za23, &a->Z, ctx)) goto end;
1475 if (!field_mul(group, tmp2, &b->Y, Za23, ctx)) goto end;
42909e39 1476 /* tmp2_ = tmp2 */
bb62a8b0 1477 }
42909e39
BM		 1478 else
1479 tmp2_ = &b->Y;
bb62a8b0
BM		 1480
1481 /* compare Y_a*Z_b^3 with Y_b*Z_a^3 */
1482 if (BN_cmp(tmp1_, tmp2_) != 0)
1483 {
1484 ret = 1; /* points differ */
1485 goto end;
1486 }
1487
1488 /* points are equal */
1489 ret = 0;
1490
1491 end:
1492 BN_CTX_end(ctx);
1493 if (new_ctx != NULL)
1494 BN_CTX_free(new_ctx);
1495 return ret;
1496 }
1d5bd6cf
BM		 1497
1498
e869d4bd
BM		 1499int ec_GFp_simple_make_affine(const EC_GROUP *group, EC_POINT *point, BN_CTX *ctx)
1500 {
1501 BN_CTX *new_ctx = NULL;
226cc7de 1502 BIGNUM *x, *y;
e869d4bd
BM		 1503 int ret = 0;
1504
1505 if (point->Z_is_one || EC_POINT_is_at_infinity(group, point))
1506 return 1;
1507
1508 if (ctx == NULL)
1509 {
1510 ctx = new_ctx = BN_CTX_new();
1511 if (ctx == NULL)
1512 return 0;
1513 }
e869d4bd 1514
226cc7de
BM		 1515 BN_CTX_start(ctx);
1516 x = BN_CTX_get(ctx);
1517 y = BN_CTX_get(ctx);
1518 if (y == NULL) goto err;
e869d4bd 1519
226cc7de
BM		 1520 if (!EC_POINT_get_affine_coordinates_GFp(group, point, x, y, ctx)) goto err;
1521 if (!EC_POINT_set_affine_coordinates_GFp(group, point, x, y, ctx)) goto err;
1522 if (!point->Z_is_one)
e869d4bd 1523 {
226cc7de
BM		 1524 ECerr(EC_F_EC_GFP_SIMPLE_MAKE_AFFINE, ERR_R_INTERNAL_ERROR);
1525 goto err;
e869d4bd 1526 }
e869d4bd 1527
e869d4bd
BM		 1528 ret = 1;
1529
226cc7de 1530 err:
e869d4bd
BM		 1531 BN_CTX_end(ctx);
1532 if (new_ctx != NULL)
1533 BN_CTX_free(new_ctx);
1534 return ret;
1535 }
60428dbf
BM		 1536
1537
48fe4d62
BM		 1538int ec_GFp_simple_points_make_affine(const EC_GROUP *group, size_t num, EC_POINT *points[], BN_CTX *ctx)
1539 {
1540 BN_CTX *new_ctx = NULL;
1541 BIGNUM *tmp0, *tmp1;
1542 size_t pow2 = 0;
1543 BIGNUM **heap = NULL;
1544 size_t i;
1545 int ret = 0;
1546
1547 if (num == 0)
1548 return 1;
1549
1550 if (ctx == NULL)
1551 {
1552 ctx = new_ctx = BN_CTX_new();
1553 if (ctx == NULL)
1554 return 0;
1555 }
1556
1557 BN_CTX_start(ctx);
1558 tmp0 = BN_CTX_get(ctx);
1559 tmp1 = BN_CTX_get(ctx);
1560 if (tmp0 == NULL || tmp1 == NULL) goto err;
1561
1562 /* Before converting the individual points, compute inverses of all Z values.
1563 * Modular inversion is rather slow, but luckily we can do with a single
1564 * explicit inversion, plus about 3 multiplications per input value.
1565 */
1566
1567 pow2 = 1;
1568 while (num > pow2)
1569 pow2 <<= 1;
1570 /* Now pow2 is the smallest power of 2 satifsying pow2 >= num.
1571 * We need twice that. */
1572 pow2 <<= 1;
1573
1574 heap = OPENSSL_malloc(pow2 * sizeof heap[0]);
1575 if (heap == NULL) goto err;
1576
1577 /* The array is used as a binary tree, exactly as in heapsort:
1578 *
1579 * heap[1]
1580 * heap[2] heap[3]
1581 * heap[4] heap[5] heap[6] heap[7]
1582 * heap[8]heap[9] heap[10]heap[11] heap[12]heap[13] heap[14] heap[15]
1583 *
1584 * We put the Z's in the last line;
1585 * then we set each other node to the product of its two child-nodes (where
1586 * empty or 0 entries are treated as ones);
1587 * then we invert heap[1];
1588 * then we invert each other node by replacing it by the product of its
1589 * parent (after inversion) and its sibling (before inversion).
1590 */
1591 heap[0] = NULL;
1592 for (i = pow2/2 - 1; i > 0; i--)
1593 heap[i] = NULL;
1594 for (i = 0; i < num; i++)
1595 heap[pow2/2 + i] = &points[i]->Z;
1596 for (i = pow2/2 + num; i < pow2; i++)
1597 heap[i] = NULL;
1598
1599 /* set each node to the product of its children */
1600 for (i = pow2/2 - 1; i > 0; i--)
1601 {
1602 heap[i] = BN_new();
1603 if (heap[i] == NULL) goto err;
1604
1605 if (heap[2*i] != NULL)
1606 {
1607 if ((heap[2*i + 1] == NULL) || BN_is_zero(heap[2*i + 1]))
1608 {
1609 if (!BN_copy(heap[i], heap[2*i])) goto err;
1610 }
1611 else
1612 {
1613 if (BN_is_zero(heap[2*i]))
1614 {
1615 if (!BN_copy(heap[i], heap[2*i + 1])) goto err;
1616 }
1617 else
1618 {
1619 if (!group->meth->field_mul(group, heap[i],
1620 heap[2*i], heap[2*i + 1], ctx)) goto err;
1621 }
1622 }
1623 }
1624 }
1625
1626 /* invert heap[1] */
1627 if (!BN_is_zero(heap[1]))
1628 {
1629 if (!BN_mod_inverse(heap[1], heap[1], &group->field, ctx))
1630 {
1631 ECerr(EC_F_EC_GFP_SIMPLE_POINTS_MAKE_AFFINE, ERR_R_BN_LIB);
1632 goto err;
1633 }
1634 }
1635 if (group->meth->field_encode != 0)
1636 {
1637 /* in the Montgomery case, we just turned R*H (representing H)
1638 * into 1/(R*H), but we need R*(1/H) (representing 1/H);
1639 * i.e. we have need to multiply by the Montgomery factor twice */
1640 if (!group->meth->field_encode(group, heap[1], heap[1], ctx)) goto err;
1641 if (!group->meth->field_encode(group, heap[1], heap[1], ctx)) goto err;
1642 }
1643
1644 /* set other heap[i]'s to their inverses */
1645 for (i = 2; i < pow2/2 + num; i += 2)
1646 {
1647 /* i is even */
1648 if ((heap[i + 1] != NULL) && !BN_is_zero(heap[i + 1]))
1649 {
1650 if (!group->meth->field_mul(group, tmp0, heap[i/2], heap[i + 1], ctx)) goto err;
1651 if (!group->meth->field_mul(group, tmp1, heap[i/2], heap[i], ctx)) goto err;
1652 if (!BN_copy(heap[i], tmp0)) goto err;
1653 if (!BN_copy(heap[i + 1], tmp1)) goto err;
1654 }
1655 else
1656 {
1657 if (!BN_copy(heap[i], heap[i/2])) goto err;
1658 }
1659 }
1660
1661 /* we have replaced all non-zero Z's by their inverses, now fix up all the points */
1662 for (i = 0; i < num; i++)
1663 {
1664 EC_POINT *p = points[i];
1665
1666 if (!BN_is_zero(&p->Z))
1667 {
1668 /* turn (X, Y, 1/Z) into (X/Z^2, Y/Z^3, 1) */
1669
1670 if (!group->meth->field_sqr(group, tmp1, &p->Z, ctx)) goto err;
1671 if (!group->meth->field_mul(group, &p->X, &p->X, tmp1, ctx)) goto err;
1672
1673 if (!group->meth->field_mul(group, tmp1, tmp1, &p->Z, ctx)) goto err;
1674 if (!group->meth->field_mul(group, &p->Y, &p->Y, tmp1, ctx)) goto err;
1675
1676 if (group->meth->field_set_to_one != 0)
1677 {
1678 if (!group->meth->field_set_to_one(group, &p->Z, ctx)) goto err;
1679 }
1680 else
1681 {
1682 if (!BN_one(&p->Z)) goto err;
1683 }
1684 p->Z_is_one = 1;
1685 }
1686 }
1687
1688 ret = 1;
1689
1690 err:
1691 BN_CTX_end(ctx);
1692 if (new_ctx != NULL)
1693 BN_CTX_free(new_ctx);
1694 if (heap != NULL)
1695 {
1696 /* heap[pow2/2] .. heap[pow2-1] have not been allocated locally! */
1697 for (i = pow2/2 - 1; i > 0; i--)
1698 {
1699 if (heap[i] != NULL)
1700 BN_clear_free(heap[i]);
1701 }
1702 OPENSSL_free(heap);
1703 }
1704 return ret;
1705 }
1706
1707
60428dbf
BM		 1708int ec_GFp_simple_field_mul(const EC_GROUP *group, BIGNUM *r, const BIGNUM *a, const BIGNUM *b, BN_CTX *ctx)
1709 {
1710 return BN_mod_mul(r, a, b, &group->field, ctx);
1711 }
1712
1713
1714int ec_GFp_simple_field_sqr(const EC_GROUP *group, BIGNUM *r, const BIGNUM *a, BN_CTX *ctx)
1715 {
1716 return BN_mod_sqr(r, a, &group->field, ctx);
1717 }
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