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New function EC_GROUP_check_discriminant().
[thirdparty/openssl.git] / crypto / ec / ecp_smpl.c
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 /* ====================================================================
5 * Copyright (c) 1998-2002 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
58 #include <openssl/err.h>
59
60 #include "ec_lcl.h"
61
62
63 const EC_METHOD *EC_GFp_simple_method(void)
64 {
65 static const EC_METHOD ret = {
66 ec_GFp_simple_group_init,
67 ec_GFp_simple_group_finish,
68 ec_GFp_simple_group_clear_finish,
69 ec_GFp_simple_group_copy,
70 ec_GFp_simple_group_set_curve_GFp,
71 ec_GFp_simple_group_get_curve_GFp,
72 ec_GFp_simple_group_set_generator,
73 ec_GFp_simple_group_get0_generator,
74 ec_GFp_simple_group_get_order,
75 ec_GFp_simple_group_get_cofactor,
76 ec_GFp_simple_group_check_discriminant,
77 ec_GFp_simple_point_init,
78 ec_GFp_simple_point_finish,
79 ec_GFp_simple_point_clear_finish,
80 ec_GFp_simple_point_copy,
81 ec_GFp_simple_point_set_to_infinity,
82 ec_GFp_simple_set_Jprojective_coordinates_GFp,
83 ec_GFp_simple_get_Jprojective_coordinates_GFp,
84 ec_GFp_simple_point_set_affine_coordinates_GFp,
85 ec_GFp_simple_point_get_affine_coordinates_GFp,
86 ec_GFp_simple_set_compressed_coordinates_GFp,
87 ec_GFp_simple_point2oct,
88 ec_GFp_simple_oct2point,
89 ec_GFp_simple_add,
90 ec_GFp_simple_dbl,
91 ec_GFp_simple_invert,
92 ec_GFp_simple_is_at_infinity,
93 ec_GFp_simple_is_on_curve,
94 ec_GFp_simple_cmp,
95 ec_GFp_simple_make_affine,
96 ec_GFp_simple_points_make_affine,
97 ec_GFp_simple_field_mul,
98 ec_GFp_simple_field_sqr,
99 0 /* field_encode */,
100 0 /* field_decode */,
101 0 /* field_set_to_one */ };
102
103 return &ret;
104 }
105
106
107 int ec_GFp_simple_group_init(EC_GROUP *group)
108 {
109 BN_init(&group->field);
110 BN_init(&group->a);
111 BN_init(&group->b);
112 group->a_is_minus3 = 0;
113 group->generator = NULL;
114 BN_init(&group->order);
115 BN_init(&group->cofactor);
116 return 1;
117 }
118
119
120 void ec_GFp_simple_group_finish(EC_GROUP *group)
121 {
122 BN_free(&group->field);
123 BN_free(&group->a);
124 BN_free(&group->b);
125 if (group->generator != NULL)
126 EC_POINT_free(group->generator);
127 BN_free(&group->order);
128 BN_free(&group->cofactor);
129 }
130
131
132 void ec_GFp_simple_group_clear_finish(EC_GROUP *group)
133 {
134 BN_clear_free(&group->field);
135 BN_clear_free(&group->a);
136 BN_clear_free(&group->b);
137 if (group->generator != NULL)
138 {
139 EC_POINT_clear_free(group->generator);
140 group->generator = NULL;
141 }
142 BN_clear_free(&group->order);
143 BN_clear_free(&group->cofactor);
144 }
145
146
147 int ec_GFp_simple_group_copy(EC_GROUP *dest, const EC_GROUP *src)
148 {
149 if (!BN_copy(&dest->field, &src->field)) return 0;
150 if (!BN_copy(&dest->a, &src->a)) return 0;
151 if (!BN_copy(&dest->b, &src->b)) return 0;
152
153 dest->a_is_minus3 = src->a_is_minus3;
154
155 if (src->generator != NULL)
156 {
157 if (dest->generator == NULL)
158 {
159 dest->generator = EC_POINT_new(dest);
160 if (dest->generator == NULL) return 0;
161 }
162 if (!EC_POINT_copy(dest->generator, src->generator)) return 0;
163 }
164 else
165 {
166 /* src->generator == NULL */
167 if (dest->generator != NULL)
168 {
169 EC_POINT_clear_free(dest->generator);
170 dest->generator = NULL;
171 }
172 }
173
174 if (!BN_copy(&dest->order, &src->order)) return 0;
175 if (!BN_copy(&dest->cofactor, &src->cofactor)) return 0;
176
177 return 1;
178 }
179
180
181 int ec_GFp_simple_group_set_curve_GFp(EC_GROUP *group,
182 const BIGNUM *p, const BIGNUM *a, const BIGNUM *b, BN_CTX *ctx)
183 {
184 int ret = 0;
185 BN_CTX *new_ctx = NULL;
186 BIGNUM *tmp_a;
187
188 /* p must be a prime > 3 */
189 if (BN_num_bits(p) <= 2 || !BN_is_odd(p))
190 {
191 ECerr(EC_F_EC_GFP_SIMPLE_GROUP_SET_CURVE_GFP, EC_R_INVALID_FIELD);
192 return 0;
193 }
194
195 if (ctx == NULL)
196 {
197 ctx = new_ctx = BN_CTX_new();
198 if (ctx == NULL)
199 return 0;
200 }
201
202 BN_CTX_start(ctx);
203 tmp_a = BN_CTX_get(ctx);
204 if (tmp_a == NULL) goto err;
205
206 /* group->field */
207 if (!BN_copy(&group->field, p)) goto err;
208 group->field.neg = 0;
209
210 /* group->a */
211 if (!BN_nnmod(tmp_a, a, p, ctx)) goto err;
212 if (group->meth->field_encode)
213 { if (!group->meth->field_encode(group, &group->a, tmp_a, ctx)) goto err; }
214 else
215 if (!BN_copy(&group->a, tmp_a)) goto err;
216
217 /* group->b */
218 if (!BN_nnmod(&group->b, b, p, ctx)) goto err;
219 if (group->meth->field_encode)
220 if (!group->meth->field_encode(group, &group->b, &group->b, ctx)) goto err;
221
222 /* group->a_is_minus3 */
223 if (!BN_add_word(tmp_a, 3)) goto err;
224 group->a_is_minus3 = (0 == BN_cmp(tmp_a, &group->field));
225
226 ret = 1;
227
228 err:
229 BN_CTX_end(ctx);
230 if (new_ctx != NULL)
231 BN_CTX_free(new_ctx);
232 return ret;
233 }
234
235
236 int ec_GFp_simple_group_get_curve_GFp(const EC_GROUP *group, BIGNUM *p, BIGNUM *a, BIGNUM *b, BN_CTX *ctx)
237 {
238 int ret = 0;
239 BN_CTX *new_ctx = NULL;
240
241 if (p != NULL)
242 {
243 if (!BN_copy(p, &group->field)) return 0;
244 }
245
246 if (a != NULL || b != NULL)
247 {
248 if (group->meth->field_decode)
249 {
250 if (ctx == NULL)
251 {
252 ctx = new_ctx = BN_CTX_new();
253 if (ctx == NULL)
254 return 0;
255 }
256 if (a != NULL)
257 {
258 if (!group->meth->field_decode(group, a, &group->a, ctx)) goto err;
259 }
260 if (b != NULL)
261 {
262 if (!group->meth->field_decode(group, b, &group->b, ctx)) goto err;
263 }
264 }
265 else
266 {
267 if (a != NULL)
268 {
269 if (!BN_copy(a, &group->a)) goto err;
270 }
271 if (b != NULL)
272 {
273 if (!BN_copy(b, &group->b)) goto err;
274 }
275 }
276 }
277
278 ret = 1;
279
280 err:
281 if (new_ctx)
282 BN_CTX_free(new_ctx);
283 return ret;
284 }
285
286
287
288 int ec_GFp_simple_group_set_generator(EC_GROUP *group, const EC_POINT *generator,
289 const BIGNUM *order, const BIGNUM *cofactor)
290 {
291 if (generator == NULL)
292 {
293 ECerr(EC_F_EC_GFP_SIMPLE_GROUP_SET_GENERATOR, ERR_R_PASSED_NULL_PARAMETER);
294 return 0 ;
295 }
296
297 if (group->generator == NULL)
298 {
299 group->generator = EC_POINT_new(group);
300 if (group->generator == NULL) return 0;
301 }
302 if (!EC_POINT_copy(group->generator, generator)) return 0;
303
304 if (order != NULL)
305 { if (!BN_copy(&group->order, order)) return 0; }
306 else
307 { if (!BN_zero(&group->order)) return 0; }
308
309 if (cofactor != NULL)
310 { if (!BN_copy(&group->cofactor, cofactor)) return 0; }
311 else
312 { if (!BN_zero(&group->cofactor)) return 0; }
313
314 return 1;
315 }
316
317
318 EC_POINT *ec_GFp_simple_group_get0_generator(const EC_GROUP *group)
319 {
320 return group->generator;
321 }
322
323
324 int ec_GFp_simple_group_get_order(const EC_GROUP *group, BIGNUM *order, BN_CTX *ctx)
325 {
326 if (!BN_copy(order, &group->order))
327 return 0;
328
329 return !BN_is_zero(&group->order);
330 }
331
332
333 int ec_GFp_simple_group_get_cofactor(const EC_GROUP *group, BIGNUM *cofactor, BN_CTX *ctx)
334 {
335 if (!BN_copy(cofactor, &group->cofactor))
336 return 0;
337
338 return !BN_is_zero(&group->cofactor);
339 }
340
341
342 int ec_GFp_simple_group_check_discriminant(const EC_GROUP *group, BN_CTX *ctx)
343 {
344 int ret = 0;
345 BIGNUM *a,*b,*order,*tmp_1,*tmp_2;
346 const BIGNUM *p = &group->field;
347 BN_CTX *new_ctx = NULL;
348
349 if (ctx == NULL)
350 {
351 ctx = new_ctx = BN_CTX_new();
352 if (ctx == NULL)
353 {
354 ECerr(EC_F_EC_GFP_SIMPLE_GROUP_CHECK_DISCRIMINANT, ERR_R_MALLOC_FAILURE);
355 goto err;
356 }
357 }
358 BN_CTX_start(ctx);
359 a = BN_CTX_get(ctx);
360 b = BN_CTX_get(ctx);
361 tmp_1 = BN_CTX_get(ctx);
362 tmp_2 = BN_CTX_get(ctx);
363 order = BN_CTX_get(ctx);
364 if (order == NULL) goto err;
365
366 if (group->meth->field_decode)
367 {
368 if (!group->meth->field_decode(group, a, &group->a, ctx)) goto err;
369 if (!group->meth->field_decode(group, b, &group->b, ctx)) goto err;
370 }
371 else
372 {
373 if (!BN_copy(a, &group->a)) goto err;
374 if (!BN_copy(b, &group->b)) goto err;
375 }
376
377 /* check the discriminant:
378 * y^2 = x^3 + a*x + b is an elliptic curve <=> 4*a^3 + 27*b^2 != 0 (mod p)
379 * 0 =< a, b < p */
380 if (BN_is_zero(a))
381 {
382 if (BN_is_zero(b)) goto err;
383 }
384 else if (!BN_is_zero(b))
385 {
386 if (!BN_mod_sqr(tmp_1, a, p, ctx)) goto err;
387 if (!BN_mod_mul(tmp_2, tmp_1, a, p, ctx)) goto err;
388 if (!BN_lshift(tmp_1, tmp_2, 2)) goto err;
389 /* tmp_1 = 4*a^3 */
390
391 if (!BN_mod_sqr(tmp_2, b, p, ctx)) goto err;
392 if (!BN_mul_word(tmp_2, 27)) goto err;
393 /* tmp_2 = 27*b^2 */
394
395 if (!BN_mod_add(a, tmp_1, tmp_2, p, ctx)) goto err;
396 if (BN_is_zero(a)) goto err;
397 }
398 ret = 1;
399
400 err:
401 BN_CTX_end(ctx);
402 if (new_ctx != NULL)
403 BN_CTX_free(new_ctx);
404 return ret;
405 }
406
407
408 int ec_GFp_simple_point_init(EC_POINT *point)
409 {
410 BN_init(&point->X);
411 BN_init(&point->Y);
412 BN_init(&point->Z);
413 point->Z_is_one = 0;
414
415 return 1;
416 }
417
418
419 void ec_GFp_simple_point_finish(EC_POINT *point)
420 {
421 BN_free(&point->X);
422 BN_free(&point->Y);
423 BN_free(&point->Z);
424 }
425
426
427 void ec_GFp_simple_point_clear_finish(EC_POINT *point)
428 {
429 BN_clear_free(&point->X);
430 BN_clear_free(&point->Y);
431 BN_clear_free(&point->Z);
432 point->Z_is_one = 0;
433 }
434
435
436 int ec_GFp_simple_point_copy(EC_POINT *dest, const EC_POINT *src)
437 {
438 if (!BN_copy(&dest->X, &src->X)) return 0;
439 if (!BN_copy(&dest->Y, &src->Y)) return 0;
440 if (!BN_copy(&dest->Z, &src->Z)) return 0;
441 dest->Z_is_one = src->Z_is_one;
442
443 return 1;
444 }
445
446
447 int ec_GFp_simple_point_set_to_infinity(const EC_GROUP *group, EC_POINT *point)
448 {
449 point->Z_is_one = 0;
450 return (BN_zero(&point->Z));
451 }
452
453
454 int ec_GFp_simple_set_Jprojective_coordinates_GFp(const EC_GROUP *group, EC_POINT *point,
455 const BIGNUM *x, const BIGNUM *y, const BIGNUM *z, BN_CTX *ctx)
456 {
457 BN_CTX *new_ctx = NULL;
458 int ret = 0;
459
460 if (ctx == NULL)
461 {
462 ctx = new_ctx = BN_CTX_new();
463 if (ctx == NULL)
464 return 0;
465 }
466
467 if (x != NULL)
468 {
469 if (!BN_nnmod(&point->X, x, &group->field, ctx)) goto err;
470 if (group->meth->field_encode)
471 {
472 if (!group->meth->field_encode(group, &point->X, &point->X, ctx)) goto err;
473 }
474 }
475
476 if (y != NULL)
477 {
478 if (!BN_nnmod(&point->Y, y, &group->field, ctx)) goto err;
479 if (group->meth->field_encode)
480 {
481 if (!group->meth->field_encode(group, &point->Y, &point->Y, ctx)) goto err;
482 }
483 }
484
485 if (z != NULL)
486 {
487 int Z_is_one;
488
489 if (!BN_nnmod(&point->Z, z, &group->field, ctx)) goto err;
490 Z_is_one = BN_is_one(&point->Z);
491 if (group->meth->field_encode)
492 {
493 if (Z_is_one && (group->meth->field_set_to_one != 0))
494 {
495 if (!group->meth->field_set_to_one(group, &point->Z, ctx)) goto err;
496 }
497 else
498 {
499 if (!group->meth->field_encode(group, &point->Z, &point->Z, ctx)) goto err;
500 }
501 }
502 point->Z_is_one = Z_is_one;
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
514 int ec_GFp_simple_get_Jprojective_coordinates_GFp(const EC_GROUP *group, const EC_POINT *point,
515 BIGNUM *x, BIGNUM *y, BIGNUM *z, BN_CTX *ctx)
516 {
517 BN_CTX *new_ctx = NULL;
518 int ret = 0;
519
520 if (group->meth->field_decode != 0)
521 {
522 if (ctx == NULL)
523 {
524 ctx = new_ctx = BN_CTX_new();
525 if (ctx == NULL)
526 return 0;
527 }
528
529 if (x != NULL)
530 {
531 if (!group->meth->field_decode(group, x, &point->X, ctx)) goto err;
532 }
533 if (y != NULL)
534 {
535 if (!group->meth->field_decode(group, y, &point->Y, ctx)) goto err;
536 }
537 if (z != NULL)
538 {
539 if (!group->meth->field_decode(group, z, &point->Z, ctx)) goto err;
540 }
541 }
542 else
543 {
544 if (x != NULL)
545 {
546 if (!BN_copy(x, &point->X)) goto err;
547 }
548 if (y != NULL)
549 {
550 if (!BN_copy(y, &point->Y)) goto err;
551 }
552 if (z != NULL)
553 {
554 if (!BN_copy(z, &point->Z)) goto err;
555 }
556 }
557
558 ret = 1;
559
560 err:
561 if (new_ctx != NULL)
562 BN_CTX_free(new_ctx);
563 return ret;
564 }
565
566
567 int ec_GFp_simple_point_set_affine_coordinates_GFp(const EC_GROUP *group, EC_POINT *point,
568 const BIGNUM *x, const BIGNUM *y, BN_CTX *ctx)
569 {
570 if (x == NULL || y == NULL)
571 {
572 /* unlike for projective coordinates, we do not tolerate this */
573 ECerr(EC_F_EC_GFP_SIMPLE_POINT_SET_AFFINE_COORDINATES_GFP, ERR_R_PASSED_NULL_PARAMETER);
574 return 0;
575 }
576
577 return EC_POINT_set_Jprojective_coordinates_GFp(group, point, x, y, BN_value_one(), ctx);
578 }
579
580
581 int ec_GFp_simple_point_get_affine_coordinates_GFp(const EC_GROUP *group, const EC_POINT *point,
582 BIGNUM *x, BIGNUM *y, BN_CTX *ctx)
583 {
584 BN_CTX *new_ctx = NULL;
585 BIGNUM *X, *Y, *Z, *Z_1, *Z_2, *Z_3;
586 const BIGNUM *X_, *Y_, *Z_;
587 int ret = 0;
588
589 if (EC_POINT_is_at_infinity(group, point))
590 {
591 ECerr(EC_F_EC_GFP_SIMPLE_POINT_GET_AFFINE_COORDINATES_GFP, EC_R_POINT_AT_INFINITY);
592 return 0;
593 }
594
595 if (ctx == NULL)
596 {
597 ctx = new_ctx = BN_CTX_new();
598 if (ctx == NULL)
599 return 0;
600 }
601
602 BN_CTX_start(ctx);
603 X = BN_CTX_get(ctx);
604 Y = BN_CTX_get(ctx);
605 Z = BN_CTX_get(ctx);
606 Z_1 = BN_CTX_get(ctx);
607 Z_2 = BN_CTX_get(ctx);
608 Z_3 = BN_CTX_get(ctx);
609 if (Z_3 == NULL) goto err;
610
611 /* transform (X, Y, Z) into (x, y) := (X/Z^2, Y/Z^3) */
612
613 if (group->meth->field_decode)
614 {
615 if (!group->meth->field_decode(group, X, &point->X, ctx)) goto err;
616 if (!group->meth->field_decode(group, Y, &point->Y, ctx)) goto err;
617 if (!group->meth->field_decode(group, Z, &point->Z, ctx)) goto err;
618 X_ = X; Y_ = Y; Z_ = Z;
619 }
620 else
621 {
622 X_ = &point->X;
623 Y_ = &point->Y;
624 Z_ = &point->Z;
625 }
626
627 if (BN_is_one(Z_))
628 {
629 if (x != NULL)
630 {
631 if (!BN_copy(x, X_)) goto err;
632 }
633 if (y != NULL)
634 {
635 if (!BN_copy(y, Y_)) goto err;
636 }
637 }
638 else
639 {
640 if (!BN_mod_inverse(Z_1, Z_, &group->field, ctx))
641 {
642 ECerr(EC_F_EC_GFP_SIMPLE_POINT_GET_AFFINE_COORDINATES_GFP, ERR_R_BN_LIB);
643 goto err;
644 }
645
646 if (group->meth->field_encode == 0)
647 {
648 /* field_sqr works on standard representation */
649 if (!group->meth->field_sqr(group, Z_2, Z_1, ctx)) goto err;
650 }
651 else
652 {
653 if (!BN_mod_sqr(Z_2, Z_1, &group->field, ctx)) goto err;
654 }
655
656 if (x != NULL)
657 {
658 if (group->meth->field_encode == 0)
659 {
660 /* field_mul works on standard representation */
661 if (!group->meth->field_mul(group, x, X_, Z_2, ctx)) goto err;
662 }
663 else
664 {
665 if (!BN_mod_mul(x, X_, Z_2, &group->field, ctx)) goto err;
666 }
667 }
668
669 if (y != NULL)
670 {
671 if (group->meth->field_encode == 0)
672 {
673 /* field_mul works on standard representation */
674 if (!group->meth->field_mul(group, Z_3, Z_2, Z_1, ctx)) goto err;
675 if (!group->meth->field_mul(group, y, Y_, Z_3, ctx)) goto err;
676
677 }
678 else
679 {
680 if (!BN_mod_mul(Z_3, Z_2, Z_1, &group->field, ctx)) goto err;
681 if (!BN_mod_mul(y, Y_, Z_3, &group->field, ctx)) goto err;
682 }
683 }
684 }
685
686 ret = 1;
687
688 err:
689 BN_CTX_end(ctx);
690 if (new_ctx != NULL)
691 BN_CTX_free(new_ctx);
692 return ret;
693 }
694
695
696 int ec_GFp_simple_set_compressed_coordinates_GFp(const EC_GROUP *group, EC_POINT *point,
697 const BIGNUM *x_, int y_bit, BN_CTX *ctx)
698 {
699 BN_CTX *new_ctx = NULL;
700 BIGNUM *tmp1, *tmp2, *x, *y;
701 int ret = 0;
702
703 if (ctx == NULL)
704 {
705 ctx = new_ctx = BN_CTX_new();
706 if (ctx == NULL)
707 return 0;
708 }
709
710 y_bit = (y_bit != 0);
711
712 BN_CTX_start(ctx);
713 tmp1 = BN_CTX_get(ctx);
714 tmp2 = BN_CTX_get(ctx);
715 x = BN_CTX_get(ctx);
716 y = BN_CTX_get(ctx);
717 if (y == NULL) goto err;
718
719 /* Recover y. We have a Weierstrass equation
720 * y^2 = x^3 + a*x + b,
721 * so y is one of the square roots of x^3 + a*x + b.
722 */
723
724 /* tmp1 := x^3 */
725 if (!BN_nnmod(x, x_, &group->field,ctx)) goto err;
726 if (group->meth->field_decode == 0)
727 {
728 /* field_{sqr,mul} work on standard representation */
729 if (!group->meth->field_sqr(group, tmp2, x_, ctx)) goto err;
730 if (!group->meth->field_mul(group, tmp1, tmp2, x_, ctx)) goto err;
731 }
732 else
733 {
734 if (!BN_mod_sqr(tmp2, x_, &group->field, ctx)) goto err;
735 if (!BN_mod_mul(tmp1, tmp2, x_, &group->field, ctx)) goto err;
736 }
737
738 /* tmp1 := tmp1 + a*x */
739 if (group->a_is_minus3)
740 {
741 if (!BN_mod_lshift1_quick(tmp2, x, &group->field)) goto err;
742 if (!BN_mod_add_quick(tmp2, tmp2, x, &group->field)) goto err;
743 if (!BN_mod_sub_quick(tmp1, tmp1, tmp2, &group->field)) goto err;
744 }
745 else
746 {
747 if (group->meth->field_decode)
748 {
749 if (!group->meth->field_decode(group, tmp2, &group->a, ctx)) goto err;
750 if (!BN_mod_mul(tmp2, tmp2, x, &group->field, ctx)) goto err;
751 }
752 else
753 {
754 /* field_mul works on standard representation */
755 if (!group->meth->field_mul(group, tmp2, &group->a, x, ctx)) goto err;
756 }
757
758 if (!BN_mod_add_quick(tmp1, tmp1, tmp2, &group->field)) goto err;
759 }
760
761 /* tmp1 := tmp1 + b */
762 if (group->meth->field_decode)
763 {
764 if (!group->meth->field_decode(group, tmp2, &group->b, ctx)) goto err;
765 if (!BN_mod_add_quick(tmp1, tmp1, tmp2, &group->field)) goto err;
766 }
767 else
768 {
769 if (!BN_mod_add_quick(tmp1, tmp1, &group->b, &group->field)) goto err;
770 }
771
772 if (!BN_mod_sqrt(y, tmp1, &group->field, ctx))
773 {
774 unsigned long err = ERR_peek_error();
775
776 if (ERR_GET_LIB(err) == ERR_LIB_BN && ERR_GET_REASON(err) == BN_R_NOT_A_SQUARE)
777 {
778 (void)ERR_get_error();
779 ECerr(EC_F_EC_GFP_SIMPLE_SET_COMPRESSED_COORDINATES_GFP, EC_R_INVALID_COMPRESSED_POINT);
780 }
781 else
782 ECerr(EC_F_EC_GFP_SIMPLE_SET_COMPRESSED_COORDINATES_GFP, ERR_R_BN_LIB);
783 goto err;
784 }
785 /* If tmp1 is not a square (i.e. there is no point on the curve with
786 * our x), then y now is a nonsense value too */
787
788 if (y_bit != BN_is_odd(y))
789 {
790 if (BN_is_zero(y))
791 {
792 int kron;
793
794 kron = BN_kronecker(x, &group->field, ctx);
795 if (kron == -2) goto err;
796
797 if (kron == 1)
798 ECerr(EC_F_EC_GFP_SIMPLE_SET_COMPRESSED_COORDINATES_GFP, EC_R_INVALID_COMPRESSION_BIT);
799 else
800 ECerr(EC_F_EC_GFP_SIMPLE_SET_COMPRESSED_COORDINATES_GFP, EC_R_INVALID_COMPRESSED_POINT);
801 goto err;
802 }
803 if (!BN_usub(y, &group->field, y)) goto err;
804 }
805 if (y_bit != BN_is_odd(y))
806 {
807 ECerr(EC_F_EC_GFP_SIMPLE_SET_COMPRESSED_COORDINATES_GFP, ERR_R_INTERNAL_ERROR);
808 goto err;
809 }
810
811 if (!EC_POINT_set_affine_coordinates_GFp(group, point, x, y, ctx)) goto err;
812
813 ret = 1;
814
815 err:
816 BN_CTX_end(ctx);
817 if (new_ctx != NULL)
818 BN_CTX_free(new_ctx);
819 return ret;
820 }
821
822
823 size_t ec_GFp_simple_point2oct(const EC_GROUP *group, const EC_POINT *point, point_conversion_form_t form,
824 unsigned char *buf, size_t len, BN_CTX *ctx)
825 {
826 size_t ret;
827 BN_CTX *new_ctx = NULL;
828 int used_ctx = 0;
829 BIGNUM *x, *y;
830 size_t field_len, i, skip;
831
832 if ((form != POINT_CONVERSION_COMPRESSED)
833 && (form != POINT_CONVERSION_UNCOMPRESSED)
834 && (form != POINT_CONVERSION_HYBRID))
835 {
836 ECerr(EC_F_EC_GFP_SIMPLE_POINT2OCT, EC_R_INVALID_FORM);
837 goto err;
838 }
839
840 if (EC_POINT_is_at_infinity(group, point))
841 {
842 /* encodes to a single 0 octet */
843 if (buf != NULL)
844 {
845 if (len < 1)
846 {
847 ECerr(EC_F_EC_GFP_SIMPLE_POINT2OCT, EC_R_BUFFER_TOO_SMALL);
848 return 0;
849 }
850 buf[0] = 0;
851 }
852 return 1;
853 }
854
855
856 /* ret := required output buffer length */
857 field_len = BN_num_bytes(&group->field);
858 ret = (form == POINT_CONVERSION_COMPRESSED) ? 1 + field_len : 1 + 2*field_len;
859
860 /* if 'buf' is NULL, just return required length */
861 if (buf != NULL)
862 {
863 if (len < ret)
864 {
865 ECerr(EC_F_EC_GFP_SIMPLE_POINT2OCT, EC_R_BUFFER_TOO_SMALL);
866 goto err;
867 }
868
869 if (ctx == NULL)
870 {
871 ctx = new_ctx = BN_CTX_new();
872 if (ctx == NULL)
873 return 0;
874 }
875
876 BN_CTX_start(ctx);
877 used_ctx = 1;
878 x = BN_CTX_get(ctx);
879 y = BN_CTX_get(ctx);
880 if (y == NULL) goto err;
881
882 if (!EC_POINT_get_affine_coordinates_GFp(group, point, x, y, ctx)) goto err;
883
884 if ((form == POINT_CONVERSION_COMPRESSED || form == POINT_CONVERSION_HYBRID) && BN_is_odd(y))
885 buf[0] = form + 1;
886 else
887 buf[0] = form;
888
889 i = 1;
890
891 skip = field_len - BN_num_bytes(x);
892 if (skip > field_len)
893 {
894 ECerr(EC_F_EC_GFP_SIMPLE_POINT2OCT, ERR_R_INTERNAL_ERROR);
895 goto err;
896 }
897 while (skip > 0)
898 {
899 buf[i++] = 0;
900 skip--;
901 }
902 skip = BN_bn2bin(x, buf + i);
903 i += skip;
904 if (i != 1 + field_len)
905 {
906 ECerr(EC_F_EC_GFP_SIMPLE_POINT2OCT, ERR_R_INTERNAL_ERROR);
907 goto err;
908 }
909
910 if (form == POINT_CONVERSION_UNCOMPRESSED || form == POINT_CONVERSION_HYBRID)
911 {
912 skip = field_len - BN_num_bytes(y);
913 if (skip > field_len)
914 {
915 ECerr(EC_F_EC_GFP_SIMPLE_POINT2OCT, ERR_R_INTERNAL_ERROR);
916 goto err;
917 }
918 while (skip > 0)
919 {
920 buf[i++] = 0;
921 skip--;
922 }
923 skip = BN_bn2bin(y, buf + i);
924 i += skip;
925 }
926
927 if (i != ret)
928 {
929 ECerr(EC_F_EC_GFP_SIMPLE_POINT2OCT, ERR_R_INTERNAL_ERROR);
930 goto err;
931 }
932 }
933
934 if (used_ctx)
935 BN_CTX_end(ctx);
936 if (new_ctx != NULL)
937 BN_CTX_free(new_ctx);
938 return ret;
939
940 err:
941 if (used_ctx)
942 BN_CTX_end(ctx);
943 if (new_ctx != NULL)
944 BN_CTX_free(new_ctx);
945 return 0;
946 }
947
948
949 int ec_GFp_simple_oct2point(const EC_GROUP *group, EC_POINT *point,
950 const unsigned char *buf, size_t len, BN_CTX *ctx)
951 {
952 point_conversion_form_t form;
953 int y_bit;
954 BN_CTX *new_ctx = NULL;
955 BIGNUM *x, *y;
956 size_t field_len, enc_len;
957 int ret = 0;
958
959 if (len == 0)
960 {
961 ECerr(EC_F_EC_GFP_SIMPLE_OCT2POINT, EC_R_BUFFER_TOO_SMALL);
962 return 0;
963 }
964 form = buf[0];
965 y_bit = form & 1;
966 form = form & ~1;
967 if ((form != 0) && (form != POINT_CONVERSION_COMPRESSED)
968 && (form != POINT_CONVERSION_UNCOMPRESSED)
969 && (form != POINT_CONVERSION_HYBRID))
970 {
971 ECerr(EC_F_EC_GFP_SIMPLE_OCT2POINT, EC_R_INVALID_ENCODING);
972 return 0;
973 }
974 if ((form == 0 || form == POINT_CONVERSION_UNCOMPRESSED) && y_bit)
975 {
976 ECerr(EC_F_EC_GFP_SIMPLE_OCT2POINT, EC_R_INVALID_ENCODING);
977 return 0;
978 }
979
980 if (form == 0)
981 {
982 if (len != 1)
983 {
984 ECerr(EC_F_EC_GFP_SIMPLE_OCT2POINT, EC_R_INVALID_ENCODING);
985 return 0;
986 }
987
988 return EC_POINT_set_to_infinity(group, point);
989 }
990
991 field_len = BN_num_bytes(&group->field);
992 enc_len = (form == POINT_CONVERSION_COMPRESSED) ? 1 + field_len : 1 + 2*field_len;
993
994 if (len != enc_len)
995 {
996 ECerr(EC_F_EC_GFP_SIMPLE_OCT2POINT, EC_R_INVALID_ENCODING);
997 return 0;
998 }
999
1000 if (ctx == NULL)
1001 {
1002 ctx = new_ctx = BN_CTX_new();
1003 if (ctx == NULL)
1004 return 0;
1005 }
1006
1007 BN_CTX_start(ctx);
1008 x = BN_CTX_get(ctx);
1009 y = BN_CTX_get(ctx);
1010 if (y == NULL) goto err;
1011
1012 if (!BN_bin2bn(buf + 1, field_len, x)) goto err;
1013 if (BN_ucmp(x, &group->field) >= 0)
1014 {
1015 ECerr(EC_F_EC_GFP_SIMPLE_OCT2POINT, EC_R_INVALID_ENCODING);
1016 goto err;
1017 }
1018
1019 if (form == POINT_CONVERSION_COMPRESSED)
1020 {
1021 if (!EC_POINT_set_compressed_coordinates_GFp(group, point, x, y_bit, ctx)) goto err;
1022 }
1023 else
1024 {
1025 if (!BN_bin2bn(buf + 1 + field_len, field_len, y)) goto err;
1026 if (BN_ucmp(y, &group->field) >= 0)
1027 {
1028 ECerr(EC_F_EC_GFP_SIMPLE_OCT2POINT, EC_R_INVALID_ENCODING);
1029 goto err;
1030 }
1031 if (form == POINT_CONVERSION_HYBRID)
1032 {
1033 if (y_bit != BN_is_odd(y))
1034 {
1035 ECerr(EC_F_EC_GFP_SIMPLE_OCT2POINT, EC_R_INVALID_ENCODING);
1036 goto err;
1037 }
1038 }
1039
1040 if (!EC_POINT_set_affine_coordinates_GFp(group, point, x, y, ctx)) goto err;
1041 }
1042
1043 if (!EC_POINT_is_on_curve(group, point, ctx)) /* test required by X9.62 */
1044 {
1045 ECerr(EC_F_EC_GFP_SIMPLE_OCT2POINT, EC_R_POINT_IS_NOT_ON_CURVE);
1046 goto err;
1047 }
1048
1049 ret = 1;
1050
1051 err:
1052 BN_CTX_end(ctx);
1053 if (new_ctx != NULL)
1054 BN_CTX_free(new_ctx);
1055 return ret;
1056 }
1057
1058
1059 int ec_GFp_simple_add(const EC_GROUP *group, EC_POINT *r, const EC_POINT *a, const EC_POINT *b, BN_CTX *ctx)
1060 {
1061 int (*field_mul)(const EC_GROUP *, BIGNUM *, const BIGNUM *, const BIGNUM *, BN_CTX *);
1062 int (*field_sqr)(const EC_GROUP *, BIGNUM *, const BIGNUM *, BN_CTX *);
1063 const BIGNUM *p;
1064 BN_CTX *new_ctx = NULL;
1065 BIGNUM *n0, *n1, *n2, *n3, *n4, *n5, *n6;
1066 int ret = 0;
1067
1068 if (a == b)
1069 return EC_POINT_dbl(group, r, a, ctx);
1070 if (EC_POINT_is_at_infinity(group, a))
1071 return EC_POINT_copy(r, b);
1072 if (EC_POINT_is_at_infinity(group, b))
1073 return EC_POINT_copy(r, a);
1074
1075 field_mul = group->meth->field_mul;
1076 field_sqr = group->meth->field_sqr;
1077 p = &group->field;
1078
1079 if (ctx == NULL)
1080 {
1081 ctx = new_ctx = BN_CTX_new();
1082 if (ctx == NULL)
1083 return 0;
1084 }
1085
1086 BN_CTX_start(ctx);
1087 n0 = BN_CTX_get(ctx);
1088 n1 = BN_CTX_get(ctx);
1089 n2 = BN_CTX_get(ctx);
1090 n3 = BN_CTX_get(ctx);
1091 n4 = BN_CTX_get(ctx);
1092 n5 = BN_CTX_get(ctx);
1093 n6 = BN_CTX_get(ctx);
1094 if (n6 == NULL) goto end;
1095
1096 /* Note that in this function we must not read components of 'a' or 'b'
1097 * once we have written the corresponding components of 'r'.
1098 * ('r' might be one of 'a' or 'b'.)
1099 */
1100
1101 /* n1, n2 */
1102 if (b->Z_is_one)
1103 {
1104 if (!BN_copy(n1, &a->X)) goto end;
1105 if (!BN_copy(n2, &a->Y)) goto end;
1106 /* n1 = X_a */
1107 /* n2 = Y_a */
1108 }
1109 else
1110 {
1111 if (!field_sqr(group, n0, &b->Z, ctx)) goto end;
1112 if (!field_mul(group, n1, &a->X, n0, ctx)) goto end;
1113 /* n1 = X_a * Z_b^2 */
1114
1115 if (!field_mul(group, n0, n0, &b->Z, ctx)) goto end;
1116 if (!field_mul(group, n2, &a->Y, n0, ctx)) goto end;
1117 /* n2 = Y_a * Z_b^3 */
1118 }
1119
1120 /* n3, n4 */
1121 if (a->Z_is_one)
1122 {
1123 if (!BN_copy(n3, &b->X)) goto end;
1124 if (!BN_copy(n4, &b->Y)) goto end;
1125 /* n3 = X_b */
1126 /* n4 = Y_b */
1127 }
1128 else
1129 {
1130 if (!field_sqr(group, n0, &a->Z, ctx)) goto end;
1131 if (!field_mul(group, n3, &b->X, n0, ctx)) goto end;
1132 /* n3 = X_b * Z_a^2 */
1133
1134 if (!field_mul(group, n0, n0, &a->Z, ctx)) goto end;
1135 if (!field_mul(group, n4, &b->Y, n0, ctx)) goto end;
1136 /* n4 = Y_b * Z_a^3 */
1137 }
1138
1139 /* n5, n6 */
1140 if (!BN_mod_sub_quick(n5, n1, n3, p)) goto end;
1141 if (!BN_mod_sub_quick(n6, n2, n4, p)) goto end;
1142 /* n5 = n1 - n3 */
1143 /* n6 = n2 - n4 */
1144
1145 if (BN_is_zero(n5))
1146 {
1147 if (BN_is_zero(n6))
1148 {
1149 /* a is the same point as b */
1150 BN_CTX_end(ctx);
1151 ret = EC_POINT_dbl(group, r, a, ctx);
1152 ctx = NULL;
1153 goto end;
1154 }
1155 else
1156 {
1157 /* a is the inverse of b */
1158 if (!BN_zero(&r->Z)) goto end;
1159 r->Z_is_one = 0;
1160 ret = 1;
1161 goto end;
1162 }
1163 }
1164
1165 /* 'n7', 'n8' */
1166 if (!BN_mod_add_quick(n1, n1, n3, p)) goto end;
1167 if (!BN_mod_add_quick(n2, n2, n4, p)) goto end;
1168 /* 'n7' = n1 + n3 */
1169 /* 'n8' = n2 + n4 */
1170
1171 /* Z_r */
1172 if (a->Z_is_one && b->Z_is_one)
1173 {
1174 if (!BN_copy(&r->Z, n5)) goto end;
1175 }
1176 else
1177 {
1178 if (a->Z_is_one)
1179 { if (!BN_copy(n0, &b->Z)) goto end; }
1180 else if (b->Z_is_one)
1181 { if (!BN_copy(n0, &a->Z)) goto end; }
1182 else
1183 { if (!field_mul(group, n0, &a->Z, &b->Z, ctx)) goto end; }
1184 if (!field_mul(group, &r->Z, n0, n5, ctx)) goto end;
1185 }
1186 r->Z_is_one = 0;
1187 /* Z_r = Z_a * Z_b * n5 */
1188
1189 /* X_r */
1190 if (!field_sqr(group, n0, n6, ctx)) goto end;
1191 if (!field_sqr(group, n4, n5, ctx)) goto end;
1192 if (!field_mul(group, n3, n1, n4, ctx)) goto end;
1193 if (!BN_mod_sub_quick(&r->X, n0, n3, p)) goto end;
1194 /* X_r = n6^2 - n5^2 * 'n7' */
1195
1196 /* 'n9' */
1197 if (!BN_mod_lshift1_quick(n0, &r->X, p)) goto end;
1198 if (!BN_mod_sub_quick(n0, n3, n0, p)) goto end;
1199 /* n9 = n5^2 * 'n7' - 2 * X_r */
1200
1201 /* Y_r */
1202 if (!field_mul(group, n0, n0, n6, ctx)) goto end;
1203 if (!field_mul(group, n5, n4, n5, ctx)) goto end; /* now n5 is n5^3 */
1204 if (!field_mul(group, n1, n2, n5, ctx)) goto end;
1205 if (!BN_mod_sub_quick(n0, n0, n1, p)) goto end;
1206 if (BN_is_odd(n0))
1207 if (!BN_add(n0, n0, p)) goto end;
1208 /* now 0 <= n0 < 2*p, and n0 is even */
1209 if (!BN_rshift1(&r->Y, n0)) goto end;
1210 /* Y_r = (n6 * 'n9' - 'n8' * 'n5^3') / 2 */
1211
1212 ret = 1;
1213
1214 end:
1215 if (ctx) /* otherwise we already called BN_CTX_end */
1216 BN_CTX_end(ctx);
1217 if (new_ctx != NULL)
1218 BN_CTX_free(new_ctx);
1219 return ret;
1220 }
1221
1222
1223 int ec_GFp_simple_dbl(const EC_GROUP *group, EC_POINT *r, const EC_POINT *a, BN_CTX *ctx)
1224 {
1225 int (*field_mul)(const EC_GROUP *, BIGNUM *, const BIGNUM *, const BIGNUM *, BN_CTX *);
1226 int (*field_sqr)(const EC_GROUP *, BIGNUM *, const BIGNUM *, BN_CTX *);
1227 const BIGNUM *p;
1228 BN_CTX *new_ctx = NULL;
1229 BIGNUM *n0, *n1, *n2, *n3;
1230 int ret = 0;
1231
1232 if (EC_POINT_is_at_infinity(group, a))
1233 {
1234 if (!BN_zero(&r->Z)) return 0;
1235 r->Z_is_one = 0;
1236 return 1;
1237 }
1238
1239 field_mul = group->meth->field_mul;
1240 field_sqr = group->meth->field_sqr;
1241 p = &group->field;
1242
1243 if (ctx == NULL)
1244 {
1245 ctx = new_ctx = BN_CTX_new();
1246 if (ctx == NULL)
1247 return 0;
1248 }
1249
1250 BN_CTX_start(ctx);
1251 n0 = BN_CTX_get(ctx);
1252 n1 = BN_CTX_get(ctx);
1253 n2 = BN_CTX_get(ctx);
1254 n3 = BN_CTX_get(ctx);
1255 if (n3 == NULL) goto err;
1256
1257 /* Note that in this function we must not read components of 'a'
1258 * once we have written the corresponding components of 'r'.
1259 * ('r' might the same as 'a'.)
1260 */
1261
1262 /* n1 */
1263 if (a->Z_is_one)
1264 {
1265 if (!field_sqr(group, n0, &a->X, ctx)) goto err;
1266 if (!BN_mod_lshift1_quick(n1, n0, p)) goto err;
1267 if (!BN_mod_add_quick(n0, n0, n1, p)) goto err;
1268 if (!BN_mod_add_quick(n1, n0, &group->a, p)) goto err;
1269 /* n1 = 3 * X_a^2 + a_curve */
1270 }
1271 else if (group->a_is_minus3)
1272 {
1273 if (!field_sqr(group, n1, &a->Z, ctx)) goto err;
1274 if (!BN_mod_add_quick(n0, &a->X, n1, p)) goto err;
1275 if (!BN_mod_sub_quick(n2, &a->X, n1, p)) goto err;
1276 if (!field_mul(group, n1, n0, n2, ctx)) goto err;
1277 if (!BN_mod_lshift1_quick(n0, n1, p)) goto err;
1278 if (!BN_mod_add_quick(n1, n0, n1, p)) goto err;
1279 /* n1 = 3 * (X_a + Z_a^2) * (X_a - Z_a^2)
1280 * = 3 * X_a^2 - 3 * Z_a^4 */
1281 }
1282 else
1283 {
1284 if (!field_sqr(group, n0, &a->X, ctx)) goto err;
1285 if (!BN_mod_lshift1_quick(n1, n0, p)) goto err;
1286 if (!BN_mod_add_quick(n0, n0, n1, p)) goto err;
1287 if (!field_sqr(group, n1, &a->Z, ctx)) goto err;
1288 if (!field_sqr(group, n1, n1, ctx)) goto err;
1289 if (!field_mul(group, n1, n1, &group->a, ctx)) goto err;
1290 if (!BN_mod_add_quick(n1, n1, n0, p)) goto err;
1291 /* n1 = 3 * X_a^2 + a_curve * Z_a^4 */
1292 }
1293
1294 /* Z_r */
1295 if (a->Z_is_one)
1296 {
1297 if (!BN_copy(n0, &a->Y)) goto err;
1298 }
1299 else
1300 {
1301 if (!field_mul(group, n0, &a->Y, &a->Z, ctx)) goto err;
1302 }
1303 if (!BN_mod_lshift1_quick(&r->Z, n0, p)) goto err;
1304 r->Z_is_one = 0;
1305 /* Z_r = 2 * Y_a * Z_a */
1306
1307 /* n2 */
1308 if (!field_sqr(group, n3, &a->Y, ctx)) goto err;
1309 if (!field_mul(group, n2, &a->X, n3, ctx)) goto err;
1310 if (!BN_mod_lshift_quick(n2, n2, 2, p)) goto err;
1311 /* n2 = 4 * X_a * Y_a^2 */
1312
1313 /* X_r */
1314 if (!BN_mod_lshift1_quick(n0, n2, p)) goto err;
1315 if (!field_sqr(group, &r->X, n1, ctx)) goto err;
1316 if (!BN_mod_sub_quick(&r->X, &r->X, n0, p)) goto err;
1317 /* X_r = n1^2 - 2 * n2 */
1318
1319 /* n3 */
1320 if (!field_sqr(group, n0, n3, ctx)) goto err;
1321 if (!BN_mod_lshift_quick(n3, n0, 3, p)) goto err;
1322 /* n3 = 8 * Y_a^4 */
1323
1324 /* Y_r */
1325 if (!BN_mod_sub_quick(n0, n2, &r->X, p)) goto err;
1326 if (!field_mul(group, n0, n1, n0, ctx)) goto err;
1327 if (!BN_mod_sub_quick(&r->Y, n0, n3, p)) goto err;
1328 /* Y_r = n1 * (n2 - X_r) - n3 */
1329
1330 ret = 1;
1331
1332 err:
1333 BN_CTX_end(ctx);
1334 if (new_ctx != NULL)
1335 BN_CTX_free(new_ctx);
1336 return ret;
1337 }
1338
1339
1340 int ec_GFp_simple_invert(const EC_GROUP *group, EC_POINT *point, BN_CTX *ctx)
1341 {
1342 if (EC_POINT_is_at_infinity(group, point) || BN_is_zero(&point->Y))
1343 /* point is its own inverse */
1344 return 1;
1345
1346 return BN_usub(&point->Y, &group->field, &point->Y);
1347 }
1348
1349
1350 int ec_GFp_simple_is_at_infinity(const EC_GROUP *group, const EC_POINT *point)
1351 {
1352 return BN_is_zero(&point->Z);
1353 }
1354
1355
1356 int ec_GFp_simple_is_on_curve(const EC_GROUP *group, const EC_POINT *point, BN_CTX *ctx)
1357 {
1358 int (*field_mul)(const EC_GROUP *, BIGNUM *, const BIGNUM *, const BIGNUM *, BN_CTX *);
1359 int (*field_sqr)(const EC_GROUP *, BIGNUM *, const BIGNUM *, BN_CTX *);
1360 const BIGNUM *p;
1361 BN_CTX *new_ctx = NULL;
1362 BIGNUM *rh, *tmp1, *tmp2, *Z4, *Z6;
1363 int ret = -1;
1364
1365 if (EC_POINT_is_at_infinity(group, point))
1366 return 1;
1367
1368 field_mul = group->meth->field_mul;
1369 field_sqr = group->meth->field_sqr;
1370 p = &group->field;
1371
1372 if (ctx == NULL)
1373 {
1374 ctx = new_ctx = BN_CTX_new();
1375 if (ctx == NULL)
1376 return -1;
1377 }
1378
1379 BN_CTX_start(ctx);
1380 rh = BN_CTX_get(ctx);
1381 tmp1 = BN_CTX_get(ctx);
1382 tmp2 = BN_CTX_get(ctx);
1383 Z4 = BN_CTX_get(ctx);
1384 Z6 = BN_CTX_get(ctx);
1385 if (Z6 == NULL) goto err;
1386
1387 /* We have a curve defined by a Weierstrass equation
1388 * y^2 = x^3 + a*x + b.
1389 * The point to consider is given in Jacobian projective coordinates
1390 * where (X, Y, Z) represents (x, y) = (X/Z^2, Y/Z^3).
1391 * Substituting this and multiplying by Z^6 transforms the above equation into
1392 * Y^2 = X^3 + a*X*Z^4 + b*Z^6.
1393 * To test this, we add up the right-hand side in 'rh'.
1394 */
1395
1396 /* rh := X^3 */
1397 if (!field_sqr(group, rh, &point->X, ctx)) goto err;
1398 if (!field_mul(group, rh, rh, &point->X, ctx)) goto err;
1399
1400 if (!point->Z_is_one)
1401 {
1402 if (!field_sqr(group, tmp1, &point->Z, ctx)) goto err;
1403 if (!field_sqr(group, Z4, tmp1, ctx)) goto err;
1404 if (!field_mul(group, Z6, Z4, tmp1, ctx)) goto err;
1405
1406 /* rh := rh + a*X*Z^4 */
1407 if (!field_mul(group, tmp1, &point->X, Z4, ctx)) goto err;
1408 if (group->a_is_minus3)
1409 {
1410 if (!BN_mod_lshift1_quick(tmp2, tmp1, p)) goto err;
1411 if (!BN_mod_add_quick(tmp2, tmp2, tmp1, p)) goto err;
1412 if (!BN_mod_sub_quick(rh, rh, tmp2, p)) goto err;
1413 }
1414 else
1415 {
1416 if (!field_mul(group, tmp2, tmp1, &group->a, ctx)) goto err;
1417 if (!BN_mod_add_quick(rh, rh, tmp2, p)) goto err;
1418 }
1419
1420 /* rh := rh + b*Z^6 */
1421 if (!field_mul(group, tmp1, &group->b, Z6, ctx)) goto err;
1422 if (!BN_mod_add_quick(rh, rh, tmp1, p)) goto err;
1423 }
1424 else
1425 {
1426 /* point->Z_is_one */
1427
1428 /* rh := rh + a*X */
1429 if (group->a_is_minus3)
1430 {
1431 if (!BN_mod_lshift1_quick(tmp2, &point->X, p)) goto err;
1432 if (!BN_mod_add_quick(tmp2, tmp2, &point->X, p)) goto err;
1433 if (!BN_mod_sub_quick(rh, rh, tmp2, p)) goto err;
1434 }
1435 else
1436 {
1437 if (!field_mul(group, tmp2, &point->X, &group->a, ctx)) goto err;
1438 if (!BN_mod_add_quick(rh, rh, tmp2, p)) goto err;
1439 }
1440
1441 /* rh := rh + b */
1442 if (!BN_mod_add_quick(rh, rh, &group->b, p)) goto err;
1443 }
1444
1445 /* 'lh' := Y^2 */
1446 if (!field_sqr(group, tmp1, &point->Y, ctx)) goto err;
1447
1448 ret = (0 == BN_cmp(tmp1, rh));
1449
1450 err:
1451 BN_CTX_end(ctx);
1452 if (new_ctx != NULL)
1453 BN_CTX_free(new_ctx);
1454 return ret;
1455 }
1456
1457
1458 int ec_GFp_simple_cmp(const EC_GROUP *group, const EC_POINT *a, const EC_POINT *b, BN_CTX *ctx)
1459 {
1460 /* return values:
1461 * -1 error
1462 * 0 equal (in affine coordinates)
1463 * 1 not equal
1464 */
1465
1466 int (*field_mul)(const EC_GROUP *, BIGNUM *, const BIGNUM *, const BIGNUM *, BN_CTX *);
1467 int (*field_sqr)(const EC_GROUP *, BIGNUM *, const BIGNUM *, BN_CTX *);
1468 BN_CTX *new_ctx = NULL;
1469 BIGNUM *tmp1, *tmp2, *Za23, *Zb23;
1470 const BIGNUM *tmp1_, *tmp2_;
1471 int ret = -1;
1472
1473 if (EC_POINT_is_at_infinity(group, a))
1474 {
1475 return EC_POINT_is_at_infinity(group, b) ? 0 : 1;
1476 }
1477
1478 if (a->Z_is_one && b->Z_is_one)
1479 {
1480 return ((BN_cmp(&a->X, &b->X) == 0) && BN_cmp(&a->Y, &b->Y) == 0) ? 0 : 1;
1481 }
1482
1483 field_mul = group->meth->field_mul;
1484 field_sqr = group->meth->field_sqr;
1485
1486 if (ctx == NULL)
1487 {
1488 ctx = new_ctx = BN_CTX_new();
1489 if (ctx == NULL)
1490 return -1;
1491 }
1492
1493 BN_CTX_start(ctx);
1494 tmp1 = BN_CTX_get(ctx);
1495 tmp2 = BN_CTX_get(ctx);
1496 Za23 = BN_CTX_get(ctx);
1497 Zb23 = BN_CTX_get(ctx);
1498 if (Zb23 == NULL) goto end;
1499
1500 /* We have to decide whether
1501 * (X_a/Z_a^2, Y_a/Z_a^3) = (X_b/Z_b^2, Y_b/Z_b^3),
1502 * or equivalently, whether
1503 * (X_a*Z_b^2, Y_a*Z_b^3) = (X_b*Z_a^2, Y_b*Z_a^3).
1504 */
1505
1506 if (!b->Z_is_one)
1507 {
1508 if (!field_sqr(group, Zb23, &b->Z, ctx)) goto end;
1509 if (!field_mul(group, tmp1, &a->X, Zb23, ctx)) goto end;
1510 tmp1_ = tmp1;
1511 }
1512 else
1513 tmp1_ = &a->X;
1514 if (!a->Z_is_one)
1515 {
1516 if (!field_sqr(group, Za23, &a->Z, ctx)) goto end;
1517 if (!field_mul(group, tmp2, &b->X, Za23, ctx)) goto end;
1518 tmp2_ = tmp2;
1519 }
1520 else
1521 tmp2_ = &b->X;
1522
1523 /* compare X_a*Z_b^2 with X_b*Z_a^2 */
1524 if (BN_cmp(tmp1_, tmp2_) != 0)
1525 {
1526 ret = 1; /* points differ */
1527 goto end;
1528 }
1529
1530
1531 if (!b->Z_is_one)
1532 {
1533 if (!field_mul(group, Zb23, Zb23, &b->Z, ctx)) goto end;
1534 if (!field_mul(group, tmp1, &a->Y, Zb23, ctx)) goto end;
1535 /* tmp1_ = tmp1 */
1536 }
1537 else
1538 tmp1_ = &a->Y;
1539 if (!a->Z_is_one)
1540 {
1541 if (!field_mul(group, Za23, Za23, &a->Z, ctx)) goto end;
1542 if (!field_mul(group, tmp2, &b->Y, Za23, ctx)) goto end;
1543 /* tmp2_ = tmp2 */
1544 }
1545 else
1546 tmp2_ = &b->Y;
1547
1548 /* compare Y_a*Z_b^3 with Y_b*Z_a^3 */
1549 if (BN_cmp(tmp1_, tmp2_) != 0)
1550 {
1551 ret = 1; /* points differ */
1552 goto end;
1553 }
1554
1555 /* points are equal */
1556 ret = 0;
1557
1558 end:
1559 BN_CTX_end(ctx);
1560 if (new_ctx != NULL)
1561 BN_CTX_free(new_ctx);
1562 return ret;
1563 }
1564
1565
1566 int ec_GFp_simple_make_affine(const EC_GROUP *group, EC_POINT *point, BN_CTX *ctx)
1567 {
1568 BN_CTX *new_ctx = NULL;
1569 BIGNUM *x, *y;
1570 int ret = 0;
1571
1572 if (point->Z_is_one || EC_POINT_is_at_infinity(group, point))
1573 return 1;
1574
1575 if (ctx == NULL)
1576 {
1577 ctx = new_ctx = BN_CTX_new();
1578 if (ctx == NULL)
1579 return 0;
1580 }
1581
1582 BN_CTX_start(ctx);
1583 x = BN_CTX_get(ctx);
1584 y = BN_CTX_get(ctx);
1585 if (y == NULL) goto err;
1586
1587 if (!EC_POINT_get_affine_coordinates_GFp(group, point, x, y, ctx)) goto err;
1588 if (!EC_POINT_set_affine_coordinates_GFp(group, point, x, y, ctx)) goto err;
1589 if (!point->Z_is_one)
1590 {
1591 ECerr(EC_F_EC_GFP_SIMPLE_MAKE_AFFINE, ERR_R_INTERNAL_ERROR);
1592 goto err;
1593 }
1594
1595 ret = 1;
1596
1597 err:
1598 BN_CTX_end(ctx);
1599 if (new_ctx != NULL)
1600 BN_CTX_free(new_ctx);
1601 return ret;
1602 }
1603
1604
1605 int ec_GFp_simple_points_make_affine(const EC_GROUP *group, size_t num, EC_POINT *points[], BN_CTX *ctx)
1606 {
1607 BN_CTX *new_ctx = NULL;
1608 BIGNUM *tmp0, *tmp1;
1609 size_t pow2 = 0;
1610 BIGNUM **heap = NULL;
1611 size_t i;
1612 int ret = 0;
1613
1614 if (num == 0)
1615 return 1;
1616
1617 if (ctx == NULL)
1618 {
1619 ctx = new_ctx = BN_CTX_new();
1620 if (ctx == NULL)
1621 return 0;
1622 }
1623
1624 BN_CTX_start(ctx);
1625 tmp0 = BN_CTX_get(ctx);
1626 tmp1 = BN_CTX_get(ctx);
1627 if (tmp0 == NULL || tmp1 == NULL) goto err;
1628
1629 /* Before converting the individual points, compute inverses of all Z values.
1630 * Modular inversion is rather slow, but luckily we can do with a single
1631 * explicit inversion, plus about 3 multiplications per input value.
1632 */
1633
1634 pow2 = 1;
1635 while (num > pow2)
1636 pow2 <<= 1;
1637 /* Now pow2 is the smallest power of 2 satifsying pow2 >= num.
1638 * We need twice that. */
1639 pow2 <<= 1;
1640
1641 heap = OPENSSL_malloc(pow2 * sizeof heap[0]);
1642 if (heap == NULL) goto err;
1643
1644 /* The array is used as a binary tree, exactly as in heapsort:
1645 *
1646 * heap[1]
1647 * heap[2] heap[3]
1648 * heap[4] heap[5] heap[6] heap[7]
1649 * heap[8]heap[9] heap[10]heap[11] heap[12]heap[13] heap[14] heap[15]
1650 *
1651 * We put the Z's in the last line;
1652 * then we set each other node to the product of its two child-nodes (where
1653 * empty or 0 entries are treated as ones);
1654 * then we invert heap[1];
1655 * then we invert each other node by replacing it by the product of its
1656 * parent (after inversion) and its sibling (before inversion).
1657 */
1658 heap[0] = NULL;
1659 for (i = pow2/2 - 1; i > 0; i--)
1660 heap[i] = NULL;
1661 for (i = 0; i < num; i++)
1662 heap[pow2/2 + i] = &points[i]->Z;
1663 for (i = pow2/2 + num; i < pow2; i++)
1664 heap[i] = NULL;
1665
1666 /* set each node to the product of its children */
1667 for (i = pow2/2 - 1; i > 0; i--)
1668 {
1669 heap[i] = BN_new();
1670 if (heap[i] == NULL) goto err;
1671
1672 if (heap[2*i] != NULL)
1673 {
1674 if ((heap[2*i + 1] == NULL) || BN_is_zero(heap[2*i + 1]))
1675 {
1676 if (!BN_copy(heap[i], heap[2*i])) goto err;
1677 }
1678 else
1679 {
1680 if (BN_is_zero(heap[2*i]))
1681 {
1682 if (!BN_copy(heap[i], heap[2*i + 1])) goto err;
1683 }
1684 else
1685 {
1686 if (!group->meth->field_mul(group, heap[i],
1687 heap[2*i], heap[2*i + 1], ctx)) goto err;
1688 }
1689 }
1690 }
1691 }
1692
1693 /* invert heap[1] */
1694 if (!BN_is_zero(heap[1]))
1695 {
1696 if (!BN_mod_inverse(heap[1], heap[1], &group->field, ctx))
1697 {
1698 ECerr(EC_F_EC_GFP_SIMPLE_POINTS_MAKE_AFFINE, ERR_R_BN_LIB);
1699 goto err;
1700 }
1701 }
1702 if (group->meth->field_encode != 0)
1703 {
1704 /* in the Montgomery case, we just turned R*H (representing H)
1705 * into 1/(R*H), but we need R*(1/H) (representing 1/H);
1706 * i.e. we have need to multiply by the Montgomery factor twice */
1707 if (!group->meth->field_encode(group, heap[1], heap[1], ctx)) goto err;
1708 if (!group->meth->field_encode(group, heap[1], heap[1], ctx)) goto err;
1709 }
1710
1711 /* set other heap[i]'s to their inverses */
1712 for (i = 2; i < pow2/2 + num; i += 2)
1713 {
1714 /* i is even */
1715 if ((heap[i + 1] != NULL) && !BN_is_zero(heap[i + 1]))
1716 {
1717 if (!group->meth->field_mul(group, tmp0, heap[i/2], heap[i + 1], ctx)) goto err;
1718 if (!group->meth->field_mul(group, tmp1, heap[i/2], heap[i], ctx)) goto err;
1719 if (!BN_copy(heap[i], tmp0)) goto err;
1720 if (!BN_copy(heap[i + 1], tmp1)) goto err;
1721 }
1722 else
1723 {
1724 if (!BN_copy(heap[i], heap[i/2])) goto err;
1725 }
1726 }
1727
1728 /* we have replaced all non-zero Z's by their inverses, now fix up all the points */
1729 for (i = 0; i < num; i++)
1730 {
1731 EC_POINT *p = points[i];
1732
1733 if (!BN_is_zero(&p->Z))
1734 {
1735 /* turn (X, Y, 1/Z) into (X/Z^2, Y/Z^3, 1) */
1736
1737 if (!group->meth->field_sqr(group, tmp1, &p->Z, ctx)) goto err;
1738 if (!group->meth->field_mul(group, &p->X, &p->X, tmp1, ctx)) goto err;
1739
1740 if (!group->meth->field_mul(group, tmp1, tmp1, &p->Z, ctx)) goto err;
1741 if (!group->meth->field_mul(group, &p->Y, &p->Y, tmp1, ctx)) goto err;
1742
1743 if (group->meth->field_set_to_one != 0)
1744 {
1745 if (!group->meth->field_set_to_one(group, &p->Z, ctx)) goto err;
1746 }
1747 else
1748 {
1749 if (!BN_one(&p->Z)) goto err;
1750 }
1751 p->Z_is_one = 1;
1752 }
1753 }
1754
1755 ret = 1;
1756
1757 err:
1758 BN_CTX_end(ctx);
1759 if (new_ctx != NULL)
1760 BN_CTX_free(new_ctx);
1761 if (heap != NULL)
1762 {
1763 /* heap[pow2/2] .. heap[pow2-1] have not been allocated locally! */
1764 for (i = pow2/2 - 1; i > 0; i--)
1765 {
1766 if (heap[i] != NULL)
1767 BN_clear_free(heap[i]);
1768 }
1769 OPENSSL_free(heap);
1770 }
1771 return ret;
1772 }
1773
1774
1775 int ec_GFp_simple_field_mul(const EC_GROUP *group, BIGNUM *r, const BIGNUM *a, const BIGNUM *b, BN_CTX *ctx)
1776 {
1777 return BN_mod_mul(r, a, b, &group->field, ctx);
1778 }
1779
1780
1781 int ec_GFp_simple_field_sqr(const EC_GROUP *group, BIGNUM *r, const BIGNUM *a, BN_CTX *ctx)
1782 {
1783 return BN_mod_sqr(r, a, &group->field, ctx);
1784 }
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