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source: vbox/trunk/src/libs/openssl-1.1.0g/crypto/ec/ecp_smpl.c@ 69881

Last change on this file since 69881 was 69881, checked in by vboxsync, 7 years ago

Update OpenSSL to 1.1.0g.
bugref:8070: src/libs maintenance
  • Property svn:eol-style set to native
File size: 36.4 KB
Line 
1/*
2 * Copyright 2001-2016 The OpenSSL Project Authors. All Rights Reserved.
3 *
4 * Licensed under the OpenSSL license (the "License"). You may not use
5 * this file except in compliance with the License. You can obtain a copy
6 * in the file LICENSE in the source distribution or at
7 * https://www.openssl.org/source/license.html
8 */
9
10/* ====================================================================
11 * Copyright 2002 Sun Microsystems, Inc. ALL RIGHTS RESERVED.
12 * Portions of this software developed by SUN MICROSYSTEMS, INC.,
13 * and contributed to the OpenSSL project.
14 */
15
16#include <openssl/err.h>
17#include <openssl/symhacks.h>
18
19#include "ec_lcl.h"
20
21const EC_METHOD *EC_GFp_simple_method(void)
22{
23 static const EC_METHOD ret = {
24 EC_FLAGS_DEFAULT_OCT,
25 NID_X9_62_prime_field,
26 ec_GFp_simple_group_init,
27 ec_GFp_simple_group_finish,
28 ec_GFp_simple_group_clear_finish,
29 ec_GFp_simple_group_copy,
30 ec_GFp_simple_group_set_curve,
31 ec_GFp_simple_group_get_curve,
32 ec_GFp_simple_group_get_degree,
33 ec_group_simple_order_bits,
34 ec_GFp_simple_group_check_discriminant,
35 ec_GFp_simple_point_init,
36 ec_GFp_simple_point_finish,
37 ec_GFp_simple_point_clear_finish,
38 ec_GFp_simple_point_copy,
39 ec_GFp_simple_point_set_to_infinity,
40 ec_GFp_simple_set_Jprojective_coordinates_GFp,
41 ec_GFp_simple_get_Jprojective_coordinates_GFp,
42 ec_GFp_simple_point_set_affine_coordinates,
43 ec_GFp_simple_point_get_affine_coordinates,
44 0, 0, 0,
45 ec_GFp_simple_add,
46 ec_GFp_simple_dbl,
47 ec_GFp_simple_invert,
48 ec_GFp_simple_is_at_infinity,
49 ec_GFp_simple_is_on_curve,
50 ec_GFp_simple_cmp,
51 ec_GFp_simple_make_affine,
52 ec_GFp_simple_points_make_affine,
53 0 /* mul */ ,
54 0 /* precompute_mult */ ,
55 0 /* have_precompute_mult */ ,
56 ec_GFp_simple_field_mul,
57 ec_GFp_simple_field_sqr,
58 0 /* field_div */ ,
59 0 /* field_encode */ ,
60 0 /* field_decode */ ,
61 0, /* field_set_to_one */
62 ec_key_simple_priv2oct,
63 ec_key_simple_oct2priv,
64 0, /* set private */
65 ec_key_simple_generate_key,
66 ec_key_simple_check_key,
67 ec_key_simple_generate_public_key,
68 0, /* keycopy */
69 0, /* keyfinish */
70 ecdh_simple_compute_key
71 };
72
73 return &ret;
74}
75
76/*
77 * Most method functions in this file are designed to work with
78 * non-trivial representations of field elements if necessary
79 * (see ecp_mont.c): while standard modular addition and subtraction
80 * are used, the field_mul and field_sqr methods will be used for
81 * multiplication, and field_encode and field_decode (if defined)
82 * will be used for converting between representations.
83 *
84 * Functions ec_GFp_simple_points_make_affine() and
85 * ec_GFp_simple_point_get_affine_coordinates() specifically assume
86 * that if a non-trivial representation is used, it is a Montgomery
87 * representation (i.e. 'encoding' means multiplying by some factor R).
88 */
89
90int ec_GFp_simple_group_init(EC_GROUP *group)
91{
92 group->field = BN_new();
93 group->a = BN_new();
94 group->b = BN_new();
95 if (group->field == NULL || group->a == NULL || group->b == NULL) {
96 BN_free(group->field);
97 BN_free(group->a);
98 BN_free(group->b);
99 return 0;
100 }
101 group->a_is_minus3 = 0;
102 return 1;
103}
104
105void ec_GFp_simple_group_finish(EC_GROUP *group)
106{
107 BN_free(group->field);
108 BN_free(group->a);
109 BN_free(group->b);
110}
111
112void ec_GFp_simple_group_clear_finish(EC_GROUP *group)
113{
114 BN_clear_free(group->field);
115 BN_clear_free(group->a);
116 BN_clear_free(group->b);
117}
118
119int ec_GFp_simple_group_copy(EC_GROUP *dest, const EC_GROUP *src)
120{
121 if (!BN_copy(dest->field, src->field))
122 return 0;
123 if (!BN_copy(dest->a, src->a))
124 return 0;
125 if (!BN_copy(dest->b, src->b))
126 return 0;
127
128 dest->a_is_minus3 = src->a_is_minus3;
129
130 return 1;
131}
132
133int ec_GFp_simple_group_set_curve(EC_GROUP *group,
134 const BIGNUM *p, const BIGNUM *a,
135 const BIGNUM *b, BN_CTX *ctx)
136{
137 int ret = 0;
138 BN_CTX *new_ctx = NULL;
139 BIGNUM *tmp_a;
140
141 /* p must be a prime > 3 */
142 if (BN_num_bits(p) <= 2 || !BN_is_odd(p)) {
143 ECerr(EC_F_EC_GFP_SIMPLE_GROUP_SET_CURVE, EC_R_INVALID_FIELD);
144 return 0;
145 }
146
147 if (ctx == NULL) {
148 ctx = new_ctx = BN_CTX_new();
149 if (ctx == NULL)
150 return 0;
151 }
152
153 BN_CTX_start(ctx);
154 tmp_a = BN_CTX_get(ctx);
155 if (tmp_a == NULL)
156 goto err;
157
158 /* group->field */
159 if (!BN_copy(group->field, p))
160 goto err;
161 BN_set_negative(group->field, 0);
162
163 /* group->a */
164 if (!BN_nnmod(tmp_a, a, p, ctx))
165 goto err;
166 if (group->meth->field_encode) {
167 if (!group->meth->field_encode(group, group->a, tmp_a, ctx))
168 goto err;
169 } else if (!BN_copy(group->a, tmp_a))
170 goto err;
171
172 /* group->b */
173 if (!BN_nnmod(group->b, b, p, ctx))
174 goto err;
175 if (group->meth->field_encode)
176 if (!group->meth->field_encode(group, group->b, group->b, ctx))
177 goto err;
178
179 /* group->a_is_minus3 */
180 if (!BN_add_word(tmp_a, 3))
181 goto err;
182 group->a_is_minus3 = (0 == BN_cmp(tmp_a, group->field));
183
184 ret = 1;
185
186 err:
187 BN_CTX_end(ctx);
188 BN_CTX_free(new_ctx);
189 return ret;
190}
191
192int ec_GFp_simple_group_get_curve(const EC_GROUP *group, BIGNUM *p, BIGNUM *a,
193 BIGNUM *b, BN_CTX *ctx)
194{
195 int ret = 0;
196 BN_CTX *new_ctx = NULL;
197
198 if (p != NULL) {
199 if (!BN_copy(p, group->field))
200 return 0;
201 }
202
203 if (a != NULL || b != NULL) {
204 if (group->meth->field_decode) {
205 if (ctx == NULL) {
206 ctx = new_ctx = BN_CTX_new();
207 if (ctx == NULL)
208 return 0;
209 }
210 if (a != NULL) {
211 if (!group->meth->field_decode(group, a, group->a, ctx))
212 goto err;
213 }
214 if (b != NULL) {
215 if (!group->meth->field_decode(group, b, group->b, ctx))
216 goto err;
217 }
218 } else {
219 if (a != NULL) {
220 if (!BN_copy(a, group->a))
221 goto err;
222 }
223 if (b != NULL) {
224 if (!BN_copy(b, group->b))
225 goto err;
226 }
227 }
228 }
229
230 ret = 1;
231
232 err:
233 BN_CTX_free(new_ctx);
234 return ret;
235}
236
237int ec_GFp_simple_group_get_degree(const EC_GROUP *group)
238{
239 return BN_num_bits(group->field);
240}
241
242int ec_GFp_simple_group_check_discriminant(const EC_GROUP *group, BN_CTX *ctx)
243{
244 int ret = 0;
245 BIGNUM *a, *b, *order, *tmp_1, *tmp_2;
246 const BIGNUM *p = group->field;
247 BN_CTX *new_ctx = NULL;
248
249 if (ctx == NULL) {
250 ctx = new_ctx = BN_CTX_new();
251 if (ctx == NULL) {
252 ECerr(EC_F_EC_GFP_SIMPLE_GROUP_CHECK_DISCRIMINANT,
253 ERR_R_MALLOC_FAILURE);
254 goto err;
255 }
256 }
257 BN_CTX_start(ctx);
258 a = BN_CTX_get(ctx);
259 b = BN_CTX_get(ctx);
260 tmp_1 = BN_CTX_get(ctx);
261 tmp_2 = BN_CTX_get(ctx);
262 order = BN_CTX_get(ctx);
263 if (order == NULL)
264 goto err;
265
266 if (group->meth->field_decode) {
267 if (!group->meth->field_decode(group, a, group->a, ctx))
268 goto err;
269 if (!group->meth->field_decode(group, b, group->b, ctx))
270 goto err;
271 } else {
272 if (!BN_copy(a, group->a))
273 goto err;
274 if (!BN_copy(b, group->b))
275 goto err;
276 }
277
278 /*-
279 * check the discriminant:
280 * y^2 = x^3 + a*x + b is an elliptic curve <=> 4*a^3 + 27*b^2 != 0 (mod p)
281 * 0 =< a, b < p
282 */
283 if (BN_is_zero(a)) {
284 if (BN_is_zero(b))
285 goto err;
286 } else if (!BN_is_zero(b)) {
287 if (!BN_mod_sqr(tmp_1, a, p, ctx))
288 goto err;
289 if (!BN_mod_mul(tmp_2, tmp_1, a, p, ctx))
290 goto err;
291 if (!BN_lshift(tmp_1, tmp_2, 2))
292 goto err;
293 /* tmp_1 = 4*a^3 */
294
295 if (!BN_mod_sqr(tmp_2, b, p, ctx))
296 goto err;
297 if (!BN_mul_word(tmp_2, 27))
298 goto err;
299 /* tmp_2 = 27*b^2 */
300
301 if (!BN_mod_add(a, tmp_1, tmp_2, p, ctx))
302 goto err;
303 if (BN_is_zero(a))
304 goto err;
305 }
306 ret = 1;
307
308 err:
309 if (ctx != NULL)
310 BN_CTX_end(ctx);
311 BN_CTX_free(new_ctx);
312 return ret;
313}
314
315int ec_GFp_simple_point_init(EC_POINT *point)
316{
317 point->X = BN_new();
318 point->Y = BN_new();
319 point->Z = BN_new();
320 point->Z_is_one = 0;
321
322 if (point->X == NULL || point->Y == NULL || point->Z == NULL) {
323 BN_free(point->X);
324 BN_free(point->Y);
325 BN_free(point->Z);
326 return 0;
327 }
328 return 1;
329}
330
331void ec_GFp_simple_point_finish(EC_POINT *point)
332{
333 BN_free(point->X);
334 BN_free(point->Y);
335 BN_free(point->Z);
336}
337
338void ec_GFp_simple_point_clear_finish(EC_POINT *point)
339{
340 BN_clear_free(point->X);
341 BN_clear_free(point->Y);
342 BN_clear_free(point->Z);
343 point->Z_is_one = 0;
344}
345
346int ec_GFp_simple_point_copy(EC_POINT *dest, const EC_POINT *src)
347{
348 if (!BN_copy(dest->X, src->X))
349 return 0;
350 if (!BN_copy(dest->Y, src->Y))
351 return 0;
352 if (!BN_copy(dest->Z, src->Z))
353 return 0;
354 dest->Z_is_one = src->Z_is_one;
355
356 return 1;
357}
358
359int ec_GFp_simple_point_set_to_infinity(const EC_GROUP *group,
360 EC_POINT *point)
361{
362 point->Z_is_one = 0;
363 BN_zero(point->Z);
364 return 1;
365}
366
367int ec_GFp_simple_set_Jprojective_coordinates_GFp(const EC_GROUP *group,
368 EC_POINT *point,
369 const BIGNUM *x,
370 const BIGNUM *y,
371 const BIGNUM *z,
372 BN_CTX *ctx)
373{
374 BN_CTX *new_ctx = NULL;
375 int ret = 0;
376
377 if (ctx == NULL) {
378 ctx = new_ctx = BN_CTX_new();
379 if (ctx == NULL)
380 return 0;
381 }
382
383 if (x != NULL) {
384 if (!BN_nnmod(point->X, x, group->field, ctx))
385 goto err;
386 if (group->meth->field_encode) {
387 if (!group->meth->field_encode(group, point->X, point->X, ctx))
388 goto err;
389 }
390 }
391
392 if (y != NULL) {
393 if (!BN_nnmod(point->Y, y, group->field, ctx))
394 goto err;
395 if (group->meth->field_encode) {
396 if (!group->meth->field_encode(group, point->Y, point->Y, ctx))
397 goto err;
398 }
399 }
400
401 if (z != NULL) {
402 int Z_is_one;
403
404 if (!BN_nnmod(point->Z, z, group->field, ctx))
405 goto err;
406 Z_is_one = BN_is_one(point->Z);
407 if (group->meth->field_encode) {
408 if (Z_is_one && (group->meth->field_set_to_one != 0)) {
409 if (!group->meth->field_set_to_one(group, point->Z, ctx))
410 goto err;
411 } else {
412 if (!group->
413 meth->field_encode(group, point->Z, point->Z, ctx))
414 goto err;
415 }
416 }
417 point->Z_is_one = Z_is_one;
418 }
419
420 ret = 1;
421
422 err:
423 BN_CTX_free(new_ctx);
424 return ret;
425}
426
427int ec_GFp_simple_get_Jprojective_coordinates_GFp(const EC_GROUP *group,
428 const EC_POINT *point,
429 BIGNUM *x, BIGNUM *y,
430 BIGNUM *z, BN_CTX *ctx)
431{
432 BN_CTX *new_ctx = NULL;
433 int ret = 0;
434
435 if (group->meth->field_decode != 0) {
436 if (ctx == NULL) {
437 ctx = new_ctx = BN_CTX_new();
438 if (ctx == NULL)
439 return 0;
440 }
441
442 if (x != NULL) {
443 if (!group->meth->field_decode(group, x, point->X, ctx))
444 goto err;
445 }
446 if (y != NULL) {
447 if (!group->meth->field_decode(group, y, point->Y, ctx))
448 goto err;
449 }
450 if (z != NULL) {
451 if (!group->meth->field_decode(group, z, point->Z, ctx))
452 goto err;
453 }
454 } else {
455 if (x != NULL) {
456 if (!BN_copy(x, point->X))
457 goto err;
458 }
459 if (y != NULL) {
460 if (!BN_copy(y, point->Y))
461 goto err;
462 }
463 if (z != NULL) {
464 if (!BN_copy(z, point->Z))
465 goto err;
466 }
467 }
468
469 ret = 1;
470
471 err:
472 BN_CTX_free(new_ctx);
473 return ret;
474}
475
476int ec_GFp_simple_point_set_affine_coordinates(const EC_GROUP *group,
477 EC_POINT *point,
478 const BIGNUM *x,
479 const BIGNUM *y, BN_CTX *ctx)
480{
481 if (x == NULL || y == NULL) {
482 /*
483 * unlike for projective coordinates, we do not tolerate this
484 */
485 ECerr(EC_F_EC_GFP_SIMPLE_POINT_SET_AFFINE_COORDINATES,
486 ERR_R_PASSED_NULL_PARAMETER);
487 return 0;
488 }
489
490 return EC_POINT_set_Jprojective_coordinates_GFp(group, point, x, y,
491 BN_value_one(), ctx);
492}
493
494int ec_GFp_simple_point_get_affine_coordinates(const EC_GROUP *group,
495 const EC_POINT *point,
496 BIGNUM *x, BIGNUM *y,
497 BN_CTX *ctx)
498{
499 BN_CTX *new_ctx = NULL;
500 BIGNUM *Z, *Z_1, *Z_2, *Z_3;
501 const BIGNUM *Z_;
502 int ret = 0;
503
504 if (EC_POINT_is_at_infinity(group, point)) {
505 ECerr(EC_F_EC_GFP_SIMPLE_POINT_GET_AFFINE_COORDINATES,
506 EC_R_POINT_AT_INFINITY);
507 return 0;
508 }
509
510 if (ctx == NULL) {
511 ctx = new_ctx = BN_CTX_new();
512 if (ctx == NULL)
513 return 0;
514 }
515
516 BN_CTX_start(ctx);
517 Z = BN_CTX_get(ctx);
518 Z_1 = BN_CTX_get(ctx);
519 Z_2 = BN_CTX_get(ctx);
520 Z_3 = BN_CTX_get(ctx);
521 if (Z_3 == NULL)
522 goto err;
523
524 /* transform (X, Y, Z) into (x, y) := (X/Z^2, Y/Z^3) */
525
526 if (group->meth->field_decode) {
527 if (!group->meth->field_decode(group, Z, point->Z, ctx))
528 goto err;
529 Z_ = Z;
530 } else {
531 Z_ = point->Z;
532 }
533
534 if (BN_is_one(Z_)) {
535 if (group->meth->field_decode) {
536 if (x != NULL) {
537 if (!group->meth->field_decode(group, x, point->X, ctx))
538 goto err;
539 }
540 if (y != NULL) {
541 if (!group->meth->field_decode(group, y, point->Y, ctx))
542 goto err;
543 }
544 } else {
545 if (x != NULL) {
546 if (!BN_copy(x, point->X))
547 goto err;
548 }
549 if (y != NULL) {
550 if (!BN_copy(y, point->Y))
551 goto err;
552 }
553 }
554 } else {
555 if (!BN_mod_inverse(Z_1, Z_, group->field, ctx)) {
556 ECerr(EC_F_EC_GFP_SIMPLE_POINT_GET_AFFINE_COORDINATES,
557 ERR_R_BN_LIB);
558 goto err;
559 }
560
561 if (group->meth->field_encode == 0) {
562 /* field_sqr works on standard representation */
563 if (!group->meth->field_sqr(group, Z_2, Z_1, ctx))
564 goto err;
565 } else {
566 if (!BN_mod_sqr(Z_2, Z_1, group->field, ctx))
567 goto err;
568 }
569
570 if (x != NULL) {
571 /*
572 * in the Montgomery case, field_mul will cancel out Montgomery
573 * factor in X:
574 */
575 if (!group->meth->field_mul(group, x, point->X, Z_2, ctx))
576 goto err;
577 }
578
579 if (y != NULL) {
580 if (group->meth->field_encode == 0) {
581 /*
582 * field_mul works on standard representation
583 */
584 if (!group->meth->field_mul(group, Z_3, Z_2, Z_1, ctx))
585 goto err;
586 } else {
587 if (!BN_mod_mul(Z_3, Z_2, Z_1, group->field, ctx))
588 goto err;
589 }
590
591 /*
592 * in the Montgomery case, field_mul will cancel out Montgomery
593 * factor in Y:
594 */
595 if (!group->meth->field_mul(group, y, point->Y, Z_3, ctx))
596 goto err;
597 }
598 }
599
600 ret = 1;
601
602 err:
603 BN_CTX_end(ctx);
604 BN_CTX_free(new_ctx);
605 return ret;
606}
607
608int ec_GFp_simple_add(const EC_GROUP *group, EC_POINT *r, const EC_POINT *a,
609 const EC_POINT *b, BN_CTX *ctx)
610{
611 int (*field_mul) (const EC_GROUP *, BIGNUM *, const BIGNUM *,
612 const BIGNUM *, BN_CTX *);
613 int (*field_sqr) (const EC_GROUP *, BIGNUM *, const BIGNUM *, BN_CTX *);
614 const BIGNUM *p;
615 BN_CTX *new_ctx = NULL;
616 BIGNUM *n0, *n1, *n2, *n3, *n4, *n5, *n6;
617 int ret = 0;
618
619 if (a == b)
620 return EC_POINT_dbl(group, r, a, ctx);
621 if (EC_POINT_is_at_infinity(group, a))
622 return EC_POINT_copy(r, b);
623 if (EC_POINT_is_at_infinity(group, b))
624 return EC_POINT_copy(r, a);
625
626 field_mul = group->meth->field_mul;
627 field_sqr = group->meth->field_sqr;
628 p = group->field;
629
630 if (ctx == NULL) {
631 ctx = new_ctx = BN_CTX_new();
632 if (ctx == NULL)
633 return 0;
634 }
635
636 BN_CTX_start(ctx);
637 n0 = BN_CTX_get(ctx);
638 n1 = BN_CTX_get(ctx);
639 n2 = BN_CTX_get(ctx);
640 n3 = BN_CTX_get(ctx);
641 n4 = BN_CTX_get(ctx);
642 n5 = BN_CTX_get(ctx);
643 n6 = BN_CTX_get(ctx);
644 if (n6 == NULL)
645 goto end;
646
647 /*
648 * Note that in this function we must not read components of 'a' or 'b'
649 * once we have written the corresponding components of 'r'. ('r' might
650 * be one of 'a' or 'b'.)
651 */
652
653 /* n1, n2 */
654 if (b->Z_is_one) {
655 if (!BN_copy(n1, a->X))
656 goto end;
657 if (!BN_copy(n2, a->Y))
658 goto end;
659 /* n1 = X_a */
660 /* n2 = Y_a */
661 } else {
662 if (!field_sqr(group, n0, b->Z, ctx))
663 goto end;
664 if (!field_mul(group, n1, a->X, n0, ctx))
665 goto end;
666 /* n1 = X_a * Z_b^2 */
667
668 if (!field_mul(group, n0, n0, b->Z, ctx))
669 goto end;
670 if (!field_mul(group, n2, a->Y, n0, ctx))
671 goto end;
672 /* n2 = Y_a * Z_b^3 */
673 }
674
675 /* n3, n4 */
676 if (a->Z_is_one) {
677 if (!BN_copy(n3, b->X))
678 goto end;
679 if (!BN_copy(n4, b->Y))
680 goto end;
681 /* n3 = X_b */
682 /* n4 = Y_b */
683 } else {
684 if (!field_sqr(group, n0, a->Z, ctx))
685 goto end;
686 if (!field_mul(group, n3, b->X, n0, ctx))
687 goto end;
688 /* n3 = X_b * Z_a^2 */
689
690 if (!field_mul(group, n0, n0, a->Z, ctx))
691 goto end;
692 if (!field_mul(group, n4, b->Y, n0, ctx))
693 goto end;
694 /* n4 = Y_b * Z_a^3 */
695 }
696
697 /* n5, n6 */
698 if (!BN_mod_sub_quick(n5, n1, n3, p))
699 goto end;
700 if (!BN_mod_sub_quick(n6, n2, n4, p))
701 goto end;
702 /* n5 = n1 - n3 */
703 /* n6 = n2 - n4 */
704
705 if (BN_is_zero(n5)) {
706 if (BN_is_zero(n6)) {
707 /* a is the same point as b */
708 BN_CTX_end(ctx);
709 ret = EC_POINT_dbl(group, r, a, ctx);
710 ctx = NULL;
711 goto end;
712 } else {
713 /* a is the inverse of b */
714 BN_zero(r->Z);
715 r->Z_is_one = 0;
716 ret = 1;
717 goto end;
718 }
719 }
720
721 /* 'n7', 'n8' */
722 if (!BN_mod_add_quick(n1, n1, n3, p))
723 goto end;
724 if (!BN_mod_add_quick(n2, n2, n4, p))
725 goto end;
726 /* 'n7' = n1 + n3 */
727 /* 'n8' = n2 + n4 */
728
729 /* Z_r */
730 if (a->Z_is_one && b->Z_is_one) {
731 if (!BN_copy(r->Z, n5))
732 goto end;
733 } else {
734 if (a->Z_is_one) {
735 if (!BN_copy(n0, b->Z))
736 goto end;
737 } else if (b->Z_is_one) {
738 if (!BN_copy(n0, a->Z))
739 goto end;
740 } else {
741 if (!field_mul(group, n0, a->Z, b->Z, ctx))
742 goto end;
743 }
744 if (!field_mul(group, r->Z, n0, n5, ctx))
745 goto end;
746 }
747 r->Z_is_one = 0;
748 /* Z_r = Z_a * Z_b * n5 */
749
750 /* X_r */
751 if (!field_sqr(group, n0, n6, ctx))
752 goto end;
753 if (!field_sqr(group, n4, n5, ctx))
754 goto end;
755 if (!field_mul(group, n3, n1, n4, ctx))
756 goto end;
757 if (!BN_mod_sub_quick(r->X, n0, n3, p))
758 goto end;
759 /* X_r = n6^2 - n5^2 * 'n7' */
760
761 /* 'n9' */
762 if (!BN_mod_lshift1_quick(n0, r->X, p))
763 goto end;
764 if (!BN_mod_sub_quick(n0, n3, n0, p))
765 goto end;
766 /* n9 = n5^2 * 'n7' - 2 * X_r */
767
768 /* Y_r */
769 if (!field_mul(group, n0, n0, n6, ctx))
770 goto end;
771 if (!field_mul(group, n5, n4, n5, ctx))
772 goto end; /* now n5 is n5^3 */
773 if (!field_mul(group, n1, n2, n5, ctx))
774 goto end;
775 if (!BN_mod_sub_quick(n0, n0, n1, p))
776 goto end;
777 if (BN_is_odd(n0))
778 if (!BN_add(n0, n0, p))
779 goto end;
780 /* now 0 <= n0 < 2*p, and n0 is even */
781 if (!BN_rshift1(r->Y, n0))
782 goto end;
783 /* Y_r = (n6 * 'n9' - 'n8' * 'n5^3') / 2 */
784
785 ret = 1;
786
787 end:
788 if (ctx) /* otherwise we already called BN_CTX_end */
789 BN_CTX_end(ctx);
790 BN_CTX_free(new_ctx);
791 return ret;
792}
793
794int ec_GFp_simple_dbl(const EC_GROUP *group, EC_POINT *r, const EC_POINT *a,
795 BN_CTX *ctx)
796{
797 int (*field_mul) (const EC_GROUP *, BIGNUM *, const BIGNUM *,
798 const BIGNUM *, BN_CTX *);
799 int (*field_sqr) (const EC_GROUP *, BIGNUM *, const BIGNUM *, BN_CTX *);
800 const BIGNUM *p;
801 BN_CTX *new_ctx = NULL;
802 BIGNUM *n0, *n1, *n2, *n3;
803 int ret = 0;
804
805 if (EC_POINT_is_at_infinity(group, a)) {
806 BN_zero(r->Z);
807 r->Z_is_one = 0;
808 return 1;
809 }
810
811 field_mul = group->meth->field_mul;
812 field_sqr = group->meth->field_sqr;
813 p = group->field;
814
815 if (ctx == NULL) {
816 ctx = new_ctx = BN_CTX_new();
817 if (ctx == NULL)
818 return 0;
819 }
820
821 BN_CTX_start(ctx);
822 n0 = BN_CTX_get(ctx);
823 n1 = BN_CTX_get(ctx);
824 n2 = BN_CTX_get(ctx);
825 n3 = BN_CTX_get(ctx);
826 if (n3 == NULL)
827 goto err;
828
829 /*
830 * Note that in this function we must not read components of 'a' once we
831 * have written the corresponding components of 'r'. ('r' might the same
832 * as 'a'.)
833 */
834
835 /* n1 */
836 if (a->Z_is_one) {
837 if (!field_sqr(group, n0, a->X, ctx))
838 goto err;
839 if (!BN_mod_lshift1_quick(n1, n0, p))
840 goto err;
841 if (!BN_mod_add_quick(n0, n0, n1, p))
842 goto err;
843 if (!BN_mod_add_quick(n1, n0, group->a, p))
844 goto err;
845 /* n1 = 3 * X_a^2 + a_curve */
846 } else if (group->a_is_minus3) {
847 if (!field_sqr(group, n1, a->Z, ctx))
848 goto err;
849 if (!BN_mod_add_quick(n0, a->X, n1, p))
850 goto err;
851 if (!BN_mod_sub_quick(n2, a->X, n1, p))
852 goto err;
853 if (!field_mul(group, n1, n0, n2, ctx))
854 goto err;
855 if (!BN_mod_lshift1_quick(n0, n1, p))
856 goto err;
857 if (!BN_mod_add_quick(n1, n0, n1, p))
858 goto err;
859 /*-
860 * n1 = 3 * (X_a + Z_a^2) * (X_a - Z_a^2)
861 * = 3 * X_a^2 - 3 * Z_a^4
862 */
863 } else {
864 if (!field_sqr(group, n0, a->X, ctx))
865 goto err;
866 if (!BN_mod_lshift1_quick(n1, n0, p))
867 goto err;
868 if (!BN_mod_add_quick(n0, n0, n1, p))
869 goto err;
870 if (!field_sqr(group, n1, a->Z, ctx))
871 goto err;
872 if (!field_sqr(group, n1, n1, ctx))
873 goto err;
874 if (!field_mul(group, n1, n1, group->a, ctx))
875 goto err;
876 if (!BN_mod_add_quick(n1, n1, n0, p))
877 goto err;
878 /* n1 = 3 * X_a^2 + a_curve * Z_a^4 */
879 }
880
881 /* Z_r */
882 if (a->Z_is_one) {
883 if (!BN_copy(n0, a->Y))
884 goto err;
885 } else {
886 if (!field_mul(group, n0, a->Y, a->Z, ctx))
887 goto err;
888 }
889 if (!BN_mod_lshift1_quick(r->Z, n0, p))
890 goto err;
891 r->Z_is_one = 0;
892 /* Z_r = 2 * Y_a * Z_a */
893
894 /* n2 */
895 if (!field_sqr(group, n3, a->Y, ctx))
896 goto err;
897 if (!field_mul(group, n2, a->X, n3, ctx))
898 goto err;
899 if (!BN_mod_lshift_quick(n2, n2, 2, p))
900 goto err;
901 /* n2 = 4 * X_a * Y_a^2 */
902
903 /* X_r */
904 if (!BN_mod_lshift1_quick(n0, n2, p))
905 goto err;
906 if (!field_sqr(group, r->X, n1, ctx))
907 goto err;
908 if (!BN_mod_sub_quick(r->X, r->X, n0, p))
909 goto err;
910 /* X_r = n1^2 - 2 * n2 */
911
912 /* n3 */
913 if (!field_sqr(group, n0, n3, ctx))
914 goto err;
915 if (!BN_mod_lshift_quick(n3, n0, 3, p))
916 goto err;
917 /* n3 = 8 * Y_a^4 */
918
919 /* Y_r */
920 if (!BN_mod_sub_quick(n0, n2, r->X, p))
921 goto err;
922 if (!field_mul(group, n0, n1, n0, ctx))
923 goto err;
924 if (!BN_mod_sub_quick(r->Y, n0, n3, p))
925 goto err;
926 /* Y_r = n1 * (n2 - X_r) - n3 */
927
928 ret = 1;
929
930 err:
931 BN_CTX_end(ctx);
932 BN_CTX_free(new_ctx);
933 return ret;
934}
935
936int ec_GFp_simple_invert(const EC_GROUP *group, EC_POINT *point, BN_CTX *ctx)
937{
938 if (EC_POINT_is_at_infinity(group, point) || BN_is_zero(point->Y))
939 /* point is its own inverse */
940 return 1;
941
942 return BN_usub(point->Y, group->field, point->Y);
943}
944
945int ec_GFp_simple_is_at_infinity(const EC_GROUP *group, const EC_POINT *point)
946{
947 return BN_is_zero(point->Z);
948}
949
950int ec_GFp_simple_is_on_curve(const EC_GROUP *group, const EC_POINT *point,
951 BN_CTX *ctx)
952{
953 int (*field_mul) (const EC_GROUP *, BIGNUM *, const BIGNUM *,
954 const BIGNUM *, BN_CTX *);
955 int (*field_sqr) (const EC_GROUP *, BIGNUM *, const BIGNUM *, BN_CTX *);
956 const BIGNUM *p;
957 BN_CTX *new_ctx = NULL;
958 BIGNUM *rh, *tmp, *Z4, *Z6;
959 int ret = -1;
960
961 if (EC_POINT_is_at_infinity(group, point))
962 return 1;
963
964 field_mul = group->meth->field_mul;
965 field_sqr = group->meth->field_sqr;
966 p = group->field;
967
968 if (ctx == NULL) {
969 ctx = new_ctx = BN_CTX_new();
970 if (ctx == NULL)
971 return -1;
972 }
973
974 BN_CTX_start(ctx);
975 rh = BN_CTX_get(ctx);
976 tmp = BN_CTX_get(ctx);
977 Z4 = BN_CTX_get(ctx);
978 Z6 = BN_CTX_get(ctx);
979 if (Z6 == NULL)
980 goto err;
981
982 /*-
983 * We have a curve defined by a Weierstrass equation
984 * y^2 = x^3 + a*x + b.
985 * The point to consider is given in Jacobian projective coordinates
986 * where (X, Y, Z) represents (x, y) = (X/Z^2, Y/Z^3).
987 * Substituting this and multiplying by Z^6 transforms the above equation into
988 * Y^2 = X^3 + a*X*Z^4 + b*Z^6.
989 * To test this, we add up the right-hand side in 'rh'.
990 */
991
992 /* rh := X^2 */
993 if (!field_sqr(group, rh, point->X, ctx))
994 goto err;
995
996 if (!point->Z_is_one) {
997 if (!field_sqr(group, tmp, point->Z, ctx))
998 goto err;
999 if (!field_sqr(group, Z4, tmp, ctx))
1000 goto err;
1001 if (!field_mul(group, Z6, Z4, tmp, ctx))
1002 goto err;
1003
1004 /* rh := (rh + a*Z^4)*X */
1005 if (group->a_is_minus3) {
1006 if (!BN_mod_lshift1_quick(tmp, Z4, p))
1007 goto err;
1008 if (!BN_mod_add_quick(tmp, tmp, Z4, p))
1009 goto err;
1010 if (!BN_mod_sub_quick(rh, rh, tmp, p))
1011 goto err;
1012 if (!field_mul(group, rh, rh, point->X, ctx))
1013 goto err;
1014 } else {
1015 if (!field_mul(group, tmp, Z4, group->a, ctx))
1016 goto err;
1017 if (!BN_mod_add_quick(rh, rh, tmp, p))
1018 goto err;
1019 if (!field_mul(group, rh, rh, point->X, ctx))
1020 goto err;
1021 }
1022
1023 /* rh := rh + b*Z^6 */
1024 if (!field_mul(group, tmp, group->b, Z6, ctx))
1025 goto err;
1026 if (!BN_mod_add_quick(rh, rh, tmp, p))
1027 goto err;
1028 } else {
1029 /* point->Z_is_one */
1030
1031 /* rh := (rh + a)*X */
1032 if (!BN_mod_add_quick(rh, rh, group->a, p))
1033 goto err;
1034 if (!field_mul(group, rh, rh, point->X, ctx))
1035 goto err;
1036 /* rh := rh + b */
1037 if (!BN_mod_add_quick(rh, rh, group->b, p))
1038 goto err;
1039 }
1040
1041 /* 'lh' := Y^2 */
1042 if (!field_sqr(group, tmp, point->Y, ctx))
1043 goto err;
1044
1045 ret = (0 == BN_ucmp(tmp, rh));
1046
1047 err:
1048 BN_CTX_end(ctx);
1049 BN_CTX_free(new_ctx);
1050 return ret;
1051}
1052
1053int ec_GFp_simple_cmp(const EC_GROUP *group, const EC_POINT *a,
1054 const EC_POINT *b, BN_CTX *ctx)
1055{
1056 /*-
1057 * return values:
1058 * -1 error
1059 * 0 equal (in affine coordinates)
1060 * 1 not equal
1061 */
1062
1063 int (*field_mul) (const EC_GROUP *, BIGNUM *, const BIGNUM *,
1064 const BIGNUM *, BN_CTX *);
1065 int (*field_sqr) (const EC_GROUP *, BIGNUM *, const BIGNUM *, BN_CTX *);
1066 BN_CTX *new_ctx = NULL;
1067 BIGNUM *tmp1, *tmp2, *Za23, *Zb23;
1068 const BIGNUM *tmp1_, *tmp2_;
1069 int ret = -1;
1070
1071 if (EC_POINT_is_at_infinity(group, a)) {
1072 return EC_POINT_is_at_infinity(group, b) ? 0 : 1;
1073 }
1074
1075 if (EC_POINT_is_at_infinity(group, b))
1076 return 1;
1077
1078 if (a->Z_is_one && b->Z_is_one) {
1079 return ((BN_cmp(a->X, b->X) == 0) && BN_cmp(a->Y, b->Y) == 0) ? 0 : 1;
1080 }
1081
1082 field_mul = group->meth->field_mul;
1083 field_sqr = group->meth->field_sqr;
1084
1085 if (ctx == NULL) {
1086 ctx = new_ctx = BN_CTX_new();
1087 if (ctx == NULL)
1088 return -1;
1089 }
1090
1091 BN_CTX_start(ctx);
1092 tmp1 = BN_CTX_get(ctx);
1093 tmp2 = BN_CTX_get(ctx);
1094 Za23 = BN_CTX_get(ctx);
1095 Zb23 = BN_CTX_get(ctx);
1096 if (Zb23 == NULL)
1097 goto end;
1098
1099 /*-
1100 * We have to decide whether
1101 * (X_a/Z_a^2, Y_a/Z_a^3) = (X_b/Z_b^2, Y_b/Z_b^3),
1102 * or equivalently, whether
1103 * (X_a*Z_b^2, Y_a*Z_b^3) = (X_b*Z_a^2, Y_b*Z_a^3).
1104 */
1105
1106 if (!b->Z_is_one) {
1107 if (!field_sqr(group, Zb23, b->Z, ctx))
1108 goto end;
1109 if (!field_mul(group, tmp1, a->X, Zb23, ctx))
1110 goto end;
1111 tmp1_ = tmp1;
1112 } else
1113 tmp1_ = a->X;
1114 if (!a->Z_is_one) {
1115 if (!field_sqr(group, Za23, a->Z, ctx))
1116 goto end;
1117 if (!field_mul(group, tmp2, b->X, Za23, ctx))
1118 goto end;
1119 tmp2_ = tmp2;
1120 } else
1121 tmp2_ = b->X;
1122
1123 /* compare X_a*Z_b^2 with X_b*Z_a^2 */
1124 if (BN_cmp(tmp1_, tmp2_) != 0) {
1125 ret = 1; /* points differ */
1126 goto end;
1127 }
1128
1129 if (!b->Z_is_one) {
1130 if (!field_mul(group, Zb23, Zb23, b->Z, ctx))
1131 goto end;
1132 if (!field_mul(group, tmp1, a->Y, Zb23, ctx))
1133 goto end;
1134 /* tmp1_ = tmp1 */
1135 } else
1136 tmp1_ = a->Y;
1137 if (!a->Z_is_one) {
1138 if (!field_mul(group, Za23, Za23, a->Z, ctx))
1139 goto end;
1140 if (!field_mul(group, tmp2, b->Y, Za23, ctx))
1141 goto end;
1142 /* tmp2_ = tmp2 */
1143 } else
1144 tmp2_ = b->Y;
1145
1146 /* compare Y_a*Z_b^3 with Y_b*Z_a^3 */
1147 if (BN_cmp(tmp1_, tmp2_) != 0) {
1148 ret = 1; /* points differ */
1149 goto end;
1150 }
1151
1152 /* points are equal */
1153 ret = 0;
1154
1155 end:
1156 BN_CTX_end(ctx);
1157 BN_CTX_free(new_ctx);
1158 return ret;
1159}
1160
1161int ec_GFp_simple_make_affine(const EC_GROUP *group, EC_POINT *point,
1162 BN_CTX *ctx)
1163{
1164 BN_CTX *new_ctx = NULL;
1165 BIGNUM *x, *y;
1166 int ret = 0;
1167
1168 if (point->Z_is_one || EC_POINT_is_at_infinity(group, point))
1169 return 1;
1170
1171 if (ctx == NULL) {
1172 ctx = new_ctx = BN_CTX_new();
1173 if (ctx == NULL)
1174 return 0;
1175 }
1176
1177 BN_CTX_start(ctx);
1178 x = BN_CTX_get(ctx);
1179 y = BN_CTX_get(ctx);
1180 if (y == NULL)
1181 goto err;
1182
1183 if (!EC_POINT_get_affine_coordinates_GFp(group, point, x, y, ctx))
1184 goto err;
1185 if (!EC_POINT_set_affine_coordinates_GFp(group, point, x, y, ctx))
1186 goto err;
1187 if (!point->Z_is_one) {
1188 ECerr(EC_F_EC_GFP_SIMPLE_MAKE_AFFINE, ERR_R_INTERNAL_ERROR);
1189 goto err;
1190 }
1191
1192 ret = 1;
1193
1194 err:
1195 BN_CTX_end(ctx);
1196 BN_CTX_free(new_ctx);
1197 return ret;
1198}
1199
1200int ec_GFp_simple_points_make_affine(const EC_GROUP *group, size_t num,
1201 EC_POINT *points[], BN_CTX *ctx)
1202{
1203 BN_CTX *new_ctx = NULL;
1204 BIGNUM *tmp, *tmp_Z;
1205 BIGNUM **prod_Z = NULL;
1206 size_t i;
1207 int ret = 0;
1208
1209 if (num == 0)
1210 return 1;
1211
1212 if (ctx == NULL) {
1213 ctx = new_ctx = BN_CTX_new();
1214 if (ctx == NULL)
1215 return 0;
1216 }
1217
1218 BN_CTX_start(ctx);
1219 tmp = BN_CTX_get(ctx);
1220 tmp_Z = BN_CTX_get(ctx);
1221 if (tmp == NULL || tmp_Z == NULL)
1222 goto err;
1223
1224 prod_Z = OPENSSL_malloc(num * sizeof prod_Z[0]);
1225 if (prod_Z == NULL)
1226 goto err;
1227 for (i = 0; i < num; i++) {
1228 prod_Z[i] = BN_new();
1229 if (prod_Z[i] == NULL)
1230 goto err;
1231 }
1232
1233 /*
1234 * Set each prod_Z[i] to the product of points[0]->Z .. points[i]->Z,
1235 * skipping any zero-valued inputs (pretend that they're 1).
1236 */
1237
1238 if (!BN_is_zero(points[0]->Z)) {
1239 if (!BN_copy(prod_Z[0], points[0]->Z))
1240 goto err;
1241 } else {
1242 if (group->meth->field_set_to_one != 0) {
1243 if (!group->meth->field_set_to_one(group, prod_Z[0], ctx))
1244 goto err;
1245 } else {
1246 if (!BN_one(prod_Z[0]))
1247 goto err;
1248 }
1249 }
1250
1251 for (i = 1; i < num; i++) {
1252 if (!BN_is_zero(points[i]->Z)) {
1253 if (!group->
1254 meth->field_mul(group, prod_Z[i], prod_Z[i - 1], points[i]->Z,
1255 ctx))
1256 goto err;
1257 } else {
1258 if (!BN_copy(prod_Z[i], prod_Z[i - 1]))
1259 goto err;
1260 }
1261 }
1262
1263 /*
1264 * Now use a single explicit inversion to replace every non-zero
1265 * points[i]->Z by its inverse.
1266 */
1267
1268 if (!BN_mod_inverse(tmp, prod_Z[num - 1], group->field, ctx)) {
1269 ECerr(EC_F_EC_GFP_SIMPLE_POINTS_MAKE_AFFINE, ERR_R_BN_LIB);
1270 goto err;
1271 }
1272 if (group->meth->field_encode != 0) {
1273 /*
1274 * In the Montgomery case, we just turned R*H (representing H) into
1275 * 1/(R*H), but we need R*(1/H) (representing 1/H); i.e. we need to
1276 * multiply by the Montgomery factor twice.
1277 */
1278 if (!group->meth->field_encode(group, tmp, tmp, ctx))
1279 goto err;
1280 if (!group->meth->field_encode(group, tmp, tmp, ctx))
1281 goto err;
1282 }
1283
1284 for (i = num - 1; i > 0; --i) {
1285 /*
1286 * Loop invariant: tmp is the product of the inverses of points[0]->Z
1287 * .. points[i]->Z (zero-valued inputs skipped).
1288 */
1289 if (!BN_is_zero(points[i]->Z)) {
1290 /*
1291 * Set tmp_Z to the inverse of points[i]->Z (as product of Z
1292 * inverses 0 .. i, Z values 0 .. i - 1).
1293 */
1294 if (!group->
1295 meth->field_mul(group, tmp_Z, prod_Z[i - 1], tmp, ctx))
1296 goto err;
1297 /*
1298 * Update tmp to satisfy the loop invariant for i - 1.
1299 */
1300 if (!group->meth->field_mul(group, tmp, tmp, points[i]->Z, ctx))
1301 goto err;
1302 /* Replace points[i]->Z by its inverse. */
1303 if (!BN_copy(points[i]->Z, tmp_Z))
1304 goto err;
1305 }
1306 }
1307
1308 if (!BN_is_zero(points[0]->Z)) {
1309 /* Replace points[0]->Z by its inverse. */
1310 if (!BN_copy(points[0]->Z, tmp))
1311 goto err;
1312 }
1313
1314 /* Finally, fix up the X and Y coordinates for all points. */
1315
1316 for (i = 0; i < num; i++) {
1317 EC_POINT *p = points[i];
1318
1319 if (!BN_is_zero(p->Z)) {
1320 /* turn (X, Y, 1/Z) into (X/Z^2, Y/Z^3, 1) */
1321
1322 if (!group->meth->field_sqr(group, tmp, p->Z, ctx))
1323 goto err;
1324 if (!group->meth->field_mul(group, p->X, p->X, tmp, ctx))
1325 goto err;
1326
1327 if (!group->meth->field_mul(group, tmp, tmp, p->Z, ctx))
1328 goto err;
1329 if (!group->meth->field_mul(group, p->Y, p->Y, tmp, ctx))
1330 goto err;
1331
1332 if (group->meth->field_set_to_one != 0) {
1333 if (!group->meth->field_set_to_one(group, p->Z, ctx))
1334 goto err;
1335 } else {
1336 if (!BN_one(p->Z))
1337 goto err;
1338 }
1339 p->Z_is_one = 1;
1340 }
1341 }
1342
1343 ret = 1;
1344
1345 err:
1346 BN_CTX_end(ctx);
1347 BN_CTX_free(new_ctx);
1348 if (prod_Z != NULL) {
1349 for (i = 0; i < num; i++) {
1350 if (prod_Z[i] == NULL)
1351 break;
1352 BN_clear_free(prod_Z[i]);
1353 }
1354 OPENSSL_free(prod_Z);
1355 }
1356 return ret;
1357}
1358
1359int ec_GFp_simple_field_mul(const EC_GROUP *group, BIGNUM *r, const BIGNUM *a,
1360 const BIGNUM *b, BN_CTX *ctx)
1361{
1362 return BN_mod_mul(r, a, b, group->field, ctx);
1363}
1364
1365int ec_GFp_simple_field_sqr(const EC_GROUP *group, BIGNUM *r, const BIGNUM *a,
1366 BN_CTX *ctx)
1367{
1368 return BN_mod_sqr(r, a, group->field, ctx);
1369}
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