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[thirdparty/openssl.git] / crypto / ec / ecp_smpl.c
1 /*
2 * Copyright 2001-2018 The OpenSSL Project Authors. All Rights Reserved.
3 * Copyright (c) 2002, Oracle and/or its affiliates. All rights reserved
4 *
5 * Licensed under the Apache License 2.0 (the "License"). You may not use
6 * this file except in compliance with the License. You can obtain a copy
7 * in the file LICENSE in the source distribution or at
8 * https://www.openssl.org/source/license.html
9 */
10
11 #include <openssl/err.h>
12 #include <openssl/symhacks.h>
13
14 #include "ec_lcl.h"
15
16 const EC_METHOD *EC_GFp_simple_method(void)
17 {
18 static const EC_METHOD ret = {
19 EC_FLAGS_DEFAULT_OCT,
20 NID_X9_62_prime_field,
21 ec_GFp_simple_group_init,
22 ec_GFp_simple_group_finish,
23 ec_GFp_simple_group_clear_finish,
24 ec_GFp_simple_group_copy,
25 ec_GFp_simple_group_set_curve,
26 ec_GFp_simple_group_get_curve,
27 ec_GFp_simple_group_get_degree,
28 ec_group_simple_order_bits,
29 ec_GFp_simple_group_check_discriminant,
30 ec_GFp_simple_point_init,
31 ec_GFp_simple_point_finish,
32 ec_GFp_simple_point_clear_finish,
33 ec_GFp_simple_point_copy,
34 ec_GFp_simple_point_set_to_infinity,
35 ec_GFp_simple_set_Jprojective_coordinates_GFp,
36 ec_GFp_simple_get_Jprojective_coordinates_GFp,
37 ec_GFp_simple_point_set_affine_coordinates,
38 ec_GFp_simple_point_get_affine_coordinates,
39 0, 0, 0,
40 ec_GFp_simple_add,
41 ec_GFp_simple_dbl,
42 ec_GFp_simple_invert,
43 ec_GFp_simple_is_at_infinity,
44 ec_GFp_simple_is_on_curve,
45 ec_GFp_simple_cmp,
46 ec_GFp_simple_make_affine,
47 ec_GFp_simple_points_make_affine,
48 0 /* mul */ ,
49 0 /* precompute_mult */ ,
50 0 /* have_precompute_mult */ ,
51 ec_GFp_simple_field_mul,
52 ec_GFp_simple_field_sqr,
53 0 /* field_div */ ,
54 ec_GFp_simple_field_inv,
55 0 /* field_encode */ ,
56 0 /* field_decode */ ,
57 0, /* field_set_to_one */
58 ec_key_simple_priv2oct,
59 ec_key_simple_oct2priv,
60 0, /* set private */
61 ec_key_simple_generate_key,
62 ec_key_simple_check_key,
63 ec_key_simple_generate_public_key,
64 0, /* keycopy */
65 0, /* keyfinish */
66 ecdh_simple_compute_key,
67 0, /* field_inverse_mod_ord */
68 ec_GFp_simple_blind_coordinates,
69 ec_GFp_simple_ladder_pre,
70 ec_GFp_simple_ladder_step,
71 ec_GFp_simple_ladder_post
72 };
73
74 return &ret;
75 }
76
77 /*
78 * Most method functions in this file are designed to work with
79 * non-trivial representations of field elements if necessary
80 * (see ecp_mont.c): while standard modular addition and subtraction
81 * are used, the field_mul and field_sqr methods will be used for
82 * multiplication, and field_encode and field_decode (if defined)
83 * will be used for converting between representations.
84 *
85 * Functions ec_GFp_simple_points_make_affine() and
86 * ec_GFp_simple_point_get_affine_coordinates() specifically assume
87 * that if a non-trivial representation is used, it is a Montgomery
88 * representation (i.e. 'encoding' means multiplying by some factor R).
89 */
90
91 int ec_GFp_simple_group_init(EC_GROUP *group)
92 {
93 group->field = BN_new();
94 group->a = BN_new();
95 group->b = BN_new();
96 if (group->field == NULL || group->a == NULL || group->b == NULL) {
97 BN_free(group->field);
98 BN_free(group->a);
99 BN_free(group->b);
100 return 0;
101 }
102 group->a_is_minus3 = 0;
103 return 1;
104 }
105
106 void ec_GFp_simple_group_finish(EC_GROUP *group)
107 {
108 BN_free(group->field);
109 BN_free(group->a);
110 BN_free(group->b);
111 }
112
113 void ec_GFp_simple_group_clear_finish(EC_GROUP *group)
114 {
115 BN_clear_free(group->field);
116 BN_clear_free(group->a);
117 BN_clear_free(group->b);
118 }
119
120 int ec_GFp_simple_group_copy(EC_GROUP *dest, const EC_GROUP *src)
121 {
122 if (!BN_copy(dest->field, src->field))
123 return 0;
124 if (!BN_copy(dest->a, src->a))
125 return 0;
126 if (!BN_copy(dest->b, src->b))
127 return 0;
128
129 dest->a_is_minus3 = src->a_is_minus3;
130
131 return 1;
132 }
133
134 int ec_GFp_simple_group_set_curve(EC_GROUP *group,
135 const BIGNUM *p, const BIGNUM *a,
136 const BIGNUM *b, BN_CTX *ctx)
137 {
138 int ret = 0;
139 BN_CTX *new_ctx = NULL;
140 BIGNUM *tmp_a;
141
142 /* p must be a prime > 3 */
143 if (BN_num_bits(p) <= 2 || !BN_is_odd(p)) {
144 ECerr(EC_F_EC_GFP_SIMPLE_GROUP_SET_CURVE, EC_R_INVALID_FIELD);
145 return 0;
146 }
147
148 if (ctx == NULL) {
149 ctx = new_ctx = BN_CTX_new();
150 if (ctx == NULL)
151 return 0;
152 }
153
154 BN_CTX_start(ctx);
155 tmp_a = BN_CTX_get(ctx);
156 if (tmp_a == NULL)
157 goto err;
158
159 /* group->field */
160 if (!BN_copy(group->field, p))
161 goto err;
162 BN_set_negative(group->field, 0);
163
164 /* group->a */
165 if (!BN_nnmod(tmp_a, a, p, ctx))
166 goto err;
167 if (group->meth->field_encode) {
168 if (!group->meth->field_encode(group, group->a, tmp_a, ctx))
169 goto err;
170 } else if (!BN_copy(group->a, tmp_a))
171 goto err;
172
173 /* group->b */
174 if (!BN_nnmod(group->b, b, p, ctx))
175 goto err;
176 if (group->meth->field_encode)
177 if (!group->meth->field_encode(group, group->b, group->b, ctx))
178 goto err;
179
180 /* group->a_is_minus3 */
181 if (!BN_add_word(tmp_a, 3))
182 goto err;
183 group->a_is_minus3 = (0 == BN_cmp(tmp_a, group->field));
184
185 ret = 1;
186
187 err:
188 BN_CTX_end(ctx);
189 BN_CTX_free(new_ctx);
190 return ret;
191 }
192
193 int ec_GFp_simple_group_get_curve(const EC_GROUP *group, BIGNUM *p, BIGNUM *a,
194 BIGNUM *b, BN_CTX *ctx)
195 {
196 int ret = 0;
197 BN_CTX *new_ctx = NULL;
198
199 if (p != NULL) {
200 if (!BN_copy(p, group->field))
201 return 0;
202 }
203
204 if (a != NULL || b != NULL) {
205 if (group->meth->field_decode) {
206 if (ctx == NULL) {
207 ctx = new_ctx = BN_CTX_new();
208 if (ctx == NULL)
209 return 0;
210 }
211 if (a != NULL) {
212 if (!group->meth->field_decode(group, a, group->a, ctx))
213 goto err;
214 }
215 if (b != NULL) {
216 if (!group->meth->field_decode(group, b, group->b, ctx))
217 goto err;
218 }
219 } else {
220 if (a != NULL) {
221 if (!BN_copy(a, group->a))
222 goto err;
223 }
224 if (b != NULL) {
225 if (!BN_copy(b, group->b))
226 goto err;
227 }
228 }
229 }
230
231 ret = 1;
232
233 err:
234 BN_CTX_free(new_ctx);
235 return ret;
236 }
237
238 int ec_GFp_simple_group_get_degree(const EC_GROUP *group)
239 {
240 return BN_num_bits(group->field);
241 }
242
243 int ec_GFp_simple_group_check_discriminant(const EC_GROUP *group, BN_CTX *ctx)
244 {
245 int ret = 0;
246 BIGNUM *a, *b, *order, *tmp_1, *tmp_2;
247 const BIGNUM *p = group->field;
248 BN_CTX *new_ctx = NULL;
249
250 if (ctx == NULL) {
251 ctx = new_ctx = BN_CTX_new();
252 if (ctx == NULL) {
253 ECerr(EC_F_EC_GFP_SIMPLE_GROUP_CHECK_DISCRIMINANT,
254 ERR_R_MALLOC_FAILURE);
255 goto err;
256 }
257 }
258 BN_CTX_start(ctx);
259 a = BN_CTX_get(ctx);
260 b = BN_CTX_get(ctx);
261 tmp_1 = BN_CTX_get(ctx);
262 tmp_2 = BN_CTX_get(ctx);
263 order = BN_CTX_get(ctx);
264 if (order == NULL)
265 goto err;
266
267 if (group->meth->field_decode) {
268 if (!group->meth->field_decode(group, a, group->a, ctx))
269 goto err;
270 if (!group->meth->field_decode(group, b, group->b, ctx))
271 goto err;
272 } else {
273 if (!BN_copy(a, group->a))
274 goto err;
275 if (!BN_copy(b, group->b))
276 goto err;
277 }
278
279 /*-
280 * check the discriminant:
281 * y^2 = x^3 + a*x + b is an elliptic curve <=> 4*a^3 + 27*b^2 != 0 (mod p)
282 * 0 =< a, b < p
283 */
284 if (BN_is_zero(a)) {
285 if (BN_is_zero(b))
286 goto err;
287 } else if (!BN_is_zero(b)) {
288 if (!BN_mod_sqr(tmp_1, a, p, ctx))
289 goto err;
290 if (!BN_mod_mul(tmp_2, tmp_1, a, p, ctx))
291 goto err;
292 if (!BN_lshift(tmp_1, tmp_2, 2))
293 goto err;
294 /* tmp_1 = 4*a^3 */
295
296 if (!BN_mod_sqr(tmp_2, b, p, ctx))
297 goto err;
298 if (!BN_mul_word(tmp_2, 27))
299 goto err;
300 /* tmp_2 = 27*b^2 */
301
302 if (!BN_mod_add(a, tmp_1, tmp_2, p, ctx))
303 goto err;
304 if (BN_is_zero(a))
305 goto err;
306 }
307 ret = 1;
308
309 err:
310 BN_CTX_end(ctx);
311 BN_CTX_free(new_ctx);
312 return ret;
313 }
314
315 int 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
331 void 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
338 void 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
346 int 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 dest->curve_name = src->curve_name;
356
357 return 1;
358 }
359
360 int ec_GFp_simple_point_set_to_infinity(const EC_GROUP *group,
361 EC_POINT *point)
362 {
363 point->Z_is_one = 0;
364 BN_zero(point->Z);
365 return 1;
366 }
367
368 int ec_GFp_simple_set_Jprojective_coordinates_GFp(const EC_GROUP *group,
369 EC_POINT *point,
370 const BIGNUM *x,
371 const BIGNUM *y,
372 const BIGNUM *z,
373 BN_CTX *ctx)
374 {
375 BN_CTX *new_ctx = NULL;
376 int ret = 0;
377
378 if (ctx == NULL) {
379 ctx = new_ctx = BN_CTX_new();
380 if (ctx == NULL)
381 return 0;
382 }
383
384 if (x != NULL) {
385 if (!BN_nnmod(point->X, x, group->field, ctx))
386 goto err;
387 if (group->meth->field_encode) {
388 if (!group->meth->field_encode(group, point->X, point->X, ctx))
389 goto err;
390 }
391 }
392
393 if (y != NULL) {
394 if (!BN_nnmod(point->Y, y, group->field, ctx))
395 goto err;
396 if (group->meth->field_encode) {
397 if (!group->meth->field_encode(group, point->Y, point->Y, ctx))
398 goto err;
399 }
400 }
401
402 if (z != NULL) {
403 int Z_is_one;
404
405 if (!BN_nnmod(point->Z, z, group->field, ctx))
406 goto err;
407 Z_is_one = BN_is_one(point->Z);
408 if (group->meth->field_encode) {
409 if (Z_is_one && (group->meth->field_set_to_one != 0)) {
410 if (!group->meth->field_set_to_one(group, point->Z, ctx))
411 goto err;
412 } else {
413 if (!group->
414 meth->field_encode(group, point->Z, point->Z, ctx))
415 goto err;
416 }
417 }
418 point->Z_is_one = Z_is_one;
419 }
420
421 ret = 1;
422
423 err:
424 BN_CTX_free(new_ctx);
425 return ret;
426 }
427
428 int ec_GFp_simple_get_Jprojective_coordinates_GFp(const EC_GROUP *group,
429 const EC_POINT *point,
430 BIGNUM *x, BIGNUM *y,
431 BIGNUM *z, BN_CTX *ctx)
432 {
433 BN_CTX *new_ctx = NULL;
434 int ret = 0;
435
436 if (group->meth->field_decode != 0) {
437 if (ctx == NULL) {
438 ctx = new_ctx = BN_CTX_new();
439 if (ctx == NULL)
440 return 0;
441 }
442
443 if (x != NULL) {
444 if (!group->meth->field_decode(group, x, point->X, ctx))
445 goto err;
446 }
447 if (y != NULL) {
448 if (!group->meth->field_decode(group, y, point->Y, ctx))
449 goto err;
450 }
451 if (z != NULL) {
452 if (!group->meth->field_decode(group, z, point->Z, ctx))
453 goto err;
454 }
455 } else {
456 if (x != NULL) {
457 if (!BN_copy(x, point->X))
458 goto err;
459 }
460 if (y != NULL) {
461 if (!BN_copy(y, point->Y))
462 goto err;
463 }
464 if (z != NULL) {
465 if (!BN_copy(z, point->Z))
466 goto err;
467 }
468 }
469
470 ret = 1;
471
472 err:
473 BN_CTX_free(new_ctx);
474 return ret;
475 }
476
477 int ec_GFp_simple_point_set_affine_coordinates(const EC_GROUP *group,
478 EC_POINT *point,
479 const BIGNUM *x,
480 const BIGNUM *y, BN_CTX *ctx)
481 {
482 if (x == NULL || y == NULL) {
483 /*
484 * unlike for projective coordinates, we do not tolerate this
485 */
486 ECerr(EC_F_EC_GFP_SIMPLE_POINT_SET_AFFINE_COORDINATES,
487 ERR_R_PASSED_NULL_PARAMETER);
488 return 0;
489 }
490
491 return EC_POINT_set_Jprojective_coordinates_GFp(group, point, x, y,
492 BN_value_one(), ctx);
493 }
494
495 int ec_GFp_simple_point_get_affine_coordinates(const EC_GROUP *group,
496 const EC_POINT *point,
497 BIGNUM *x, BIGNUM *y,
498 BN_CTX *ctx)
499 {
500 BN_CTX *new_ctx = NULL;
501 BIGNUM *Z, *Z_1, *Z_2, *Z_3;
502 const BIGNUM *Z_;
503 int ret = 0;
504
505 if (EC_POINT_is_at_infinity(group, point)) {
506 ECerr(EC_F_EC_GFP_SIMPLE_POINT_GET_AFFINE_COORDINATES,
507 EC_R_POINT_AT_INFINITY);
508 return 0;
509 }
510
511 if (ctx == NULL) {
512 ctx = new_ctx = BN_CTX_new();
513 if (ctx == NULL)
514 return 0;
515 }
516
517 BN_CTX_start(ctx);
518 Z = BN_CTX_get(ctx);
519 Z_1 = BN_CTX_get(ctx);
520 Z_2 = BN_CTX_get(ctx);
521 Z_3 = BN_CTX_get(ctx);
522 if (Z_3 == NULL)
523 goto err;
524
525 /* transform (X, Y, Z) into (x, y) := (X/Z^2, Y/Z^3) */
526
527 if (group->meth->field_decode) {
528 if (!group->meth->field_decode(group, Z, point->Z, ctx))
529 goto err;
530 Z_ = Z;
531 } else {
532 Z_ = point->Z;
533 }
534
535 if (BN_is_one(Z_)) {
536 if (group->meth->field_decode) {
537 if (x != NULL) {
538 if (!group->meth->field_decode(group, x, point->X, ctx))
539 goto err;
540 }
541 if (y != NULL) {
542 if (!group->meth->field_decode(group, y, point->Y, ctx))
543 goto err;
544 }
545 } else {
546 if (x != NULL) {
547 if (!BN_copy(x, point->X))
548 goto err;
549 }
550 if (y != NULL) {
551 if (!BN_copy(y, point->Y))
552 goto err;
553 }
554 }
555 } else {
556 if (!group->meth->field_inv(group, Z_1, Z_, ctx)) {
557 ECerr(EC_F_EC_GFP_SIMPLE_POINT_GET_AFFINE_COORDINATES,
558 ERR_R_BN_LIB);
559 goto err;
560 }
561
562 if (group->meth->field_encode == 0) {
563 /* field_sqr works on standard representation */
564 if (!group->meth->field_sqr(group, Z_2, Z_1, ctx))
565 goto err;
566 } else {
567 if (!BN_mod_sqr(Z_2, Z_1, group->field, ctx))
568 goto err;
569 }
570
571 if (x != NULL) {
572 /*
573 * in the Montgomery case, field_mul will cancel out Montgomery
574 * factor in X:
575 */
576 if (!group->meth->field_mul(group, x, point->X, Z_2, ctx))
577 goto err;
578 }
579
580 if (y != NULL) {
581 if (group->meth->field_encode == 0) {
582 /*
583 * field_mul works on standard representation
584 */
585 if (!group->meth->field_mul(group, Z_3, Z_2, Z_1, ctx))
586 goto err;
587 } else {
588 if (!BN_mod_mul(Z_3, Z_2, Z_1, group->field, ctx))
589 goto err;
590 }
591
592 /*
593 * in the Montgomery case, field_mul will cancel out Montgomery
594 * factor in Y:
595 */
596 if (!group->meth->field_mul(group, y, point->Y, Z_3, ctx))
597 goto err;
598 }
599 }
600
601 ret = 1;
602
603 err:
604 BN_CTX_end(ctx);
605 BN_CTX_free(new_ctx);
606 return ret;
607 }
608
609 int ec_GFp_simple_add(const EC_GROUP *group, EC_POINT *r, const EC_POINT *a,
610 const EC_POINT *b, BN_CTX *ctx)
611 {
612 int (*field_mul) (const EC_GROUP *, BIGNUM *, const BIGNUM *,
613 const BIGNUM *, BN_CTX *);
614 int (*field_sqr) (const EC_GROUP *, BIGNUM *, const BIGNUM *, BN_CTX *);
615 const BIGNUM *p;
616 BN_CTX *new_ctx = NULL;
617 BIGNUM *n0, *n1, *n2, *n3, *n4, *n5, *n6;
618 int ret = 0;
619
620 if (a == b)
621 return EC_POINT_dbl(group, r, a, ctx);
622 if (EC_POINT_is_at_infinity(group, a))
623 return EC_POINT_copy(r, b);
624 if (EC_POINT_is_at_infinity(group, b))
625 return EC_POINT_copy(r, a);
626
627 field_mul = group->meth->field_mul;
628 field_sqr = group->meth->field_sqr;
629 p = group->field;
630
631 if (ctx == NULL) {
632 ctx = new_ctx = BN_CTX_new();
633 if (ctx == NULL)
634 return 0;
635 }
636
637 BN_CTX_start(ctx);
638 n0 = BN_CTX_get(ctx);
639 n1 = BN_CTX_get(ctx);
640 n2 = BN_CTX_get(ctx);
641 n3 = BN_CTX_get(ctx);
642 n4 = BN_CTX_get(ctx);
643 n5 = BN_CTX_get(ctx);
644 n6 = BN_CTX_get(ctx);
645 if (n6 == NULL)
646 goto end;
647
648 /*
649 * Note that in this function we must not read components of 'a' or 'b'
650 * once we have written the corresponding components of 'r'. ('r' might
651 * be one of 'a' or 'b'.)
652 */
653
654 /* n1, n2 */
655 if (b->Z_is_one) {
656 if (!BN_copy(n1, a->X))
657 goto end;
658 if (!BN_copy(n2, a->Y))
659 goto end;
660 /* n1 = X_a */
661 /* n2 = Y_a */
662 } else {
663 if (!field_sqr(group, n0, b->Z, ctx))
664 goto end;
665 if (!field_mul(group, n1, a->X, n0, ctx))
666 goto end;
667 /* n1 = X_a * Z_b^2 */
668
669 if (!field_mul(group, n0, n0, b->Z, ctx))
670 goto end;
671 if (!field_mul(group, n2, a->Y, n0, ctx))
672 goto end;
673 /* n2 = Y_a * Z_b^3 */
674 }
675
676 /* n3, n4 */
677 if (a->Z_is_one) {
678 if (!BN_copy(n3, b->X))
679 goto end;
680 if (!BN_copy(n4, b->Y))
681 goto end;
682 /* n3 = X_b */
683 /* n4 = Y_b */
684 } else {
685 if (!field_sqr(group, n0, a->Z, ctx))
686 goto end;
687 if (!field_mul(group, n3, b->X, n0, ctx))
688 goto end;
689 /* n3 = X_b * Z_a^2 */
690
691 if (!field_mul(group, n0, n0, a->Z, ctx))
692 goto end;
693 if (!field_mul(group, n4, b->Y, n0, ctx))
694 goto end;
695 /* n4 = Y_b * Z_a^3 */
696 }
697
698 /* n5, n6 */
699 if (!BN_mod_sub_quick(n5, n1, n3, p))
700 goto end;
701 if (!BN_mod_sub_quick(n6, n2, n4, p))
702 goto end;
703 /* n5 = n1 - n3 */
704 /* n6 = n2 - n4 */
705
706 if (BN_is_zero(n5)) {
707 if (BN_is_zero(n6)) {
708 /* a is the same point as b */
709 BN_CTX_end(ctx);
710 ret = EC_POINT_dbl(group, r, a, ctx);
711 ctx = NULL;
712 goto end;
713 } else {
714 /* a is the inverse of b */
715 BN_zero(r->Z);
716 r->Z_is_one = 0;
717 ret = 1;
718 goto end;
719 }
720 }
721
722 /* 'n7', 'n8' */
723 if (!BN_mod_add_quick(n1, n1, n3, p))
724 goto end;
725 if (!BN_mod_add_quick(n2, n2, n4, p))
726 goto end;
727 /* 'n7' = n1 + n3 */
728 /* 'n8' = n2 + n4 */
729
730 /* Z_r */
731 if (a->Z_is_one && b->Z_is_one) {
732 if (!BN_copy(r->Z, n5))
733 goto end;
734 } else {
735 if (a->Z_is_one) {
736 if (!BN_copy(n0, b->Z))
737 goto end;
738 } else if (b->Z_is_one) {
739 if (!BN_copy(n0, a->Z))
740 goto end;
741 } else {
742 if (!field_mul(group, n0, a->Z, b->Z, ctx))
743 goto end;
744 }
745 if (!field_mul(group, r->Z, n0, n5, ctx))
746 goto end;
747 }
748 r->Z_is_one = 0;
749 /* Z_r = Z_a * Z_b * n5 */
750
751 /* X_r */
752 if (!field_sqr(group, n0, n6, ctx))
753 goto end;
754 if (!field_sqr(group, n4, n5, ctx))
755 goto end;
756 if (!field_mul(group, n3, n1, n4, ctx))
757 goto end;
758 if (!BN_mod_sub_quick(r->X, n0, n3, p))
759 goto end;
760 /* X_r = n6^2 - n5^2 * 'n7' */
761
762 /* 'n9' */
763 if (!BN_mod_lshift1_quick(n0, r->X, p))
764 goto end;
765 if (!BN_mod_sub_quick(n0, n3, n0, p))
766 goto end;
767 /* n9 = n5^2 * 'n7' - 2 * X_r */
768
769 /* Y_r */
770 if (!field_mul(group, n0, n0, n6, ctx))
771 goto end;
772 if (!field_mul(group, n5, n4, n5, ctx))
773 goto end; /* now n5 is n5^3 */
774 if (!field_mul(group, n1, n2, n5, ctx))
775 goto end;
776 if (!BN_mod_sub_quick(n0, n0, n1, p))
777 goto end;
778 if (BN_is_odd(n0))
779 if (!BN_add(n0, n0, p))
780 goto end;
781 /* now 0 <= n0 < 2*p, and n0 is even */
782 if (!BN_rshift1(r->Y, n0))
783 goto end;
784 /* Y_r = (n6 * 'n9' - 'n8' * 'n5^3') / 2 */
785
786 ret = 1;
787
788 end:
789 BN_CTX_end(ctx);
790 BN_CTX_free(new_ctx);
791 return ret;
792 }
793
794 int 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
936 int 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
945 int ec_GFp_simple_is_at_infinity(const EC_GROUP *group, const EC_POINT *point)
946 {
947 return BN_is_zero(point->Z);
948 }
949
950 int 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
1053 int 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
1161 int 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(group, point, x, y, ctx))
1184 goto err;
1185 if (!EC_POINT_set_affine_coordinates(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
1200 int 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_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 (!group->meth->field_inv(group, tmp, prod_Z[num - 1], 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
1359 int 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
1365 int 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 }
1370
1371 /*-
1372 * Computes the multiplicative inverse of a in GF(p), storing the result in r.
1373 * If a is zero (or equivalent), you'll get a EC_R_CANNOT_INVERT error.
1374 * Since we don't have a Mont structure here, SCA hardening is with blinding.
1375 */
1376 int ec_GFp_simple_field_inv(const EC_GROUP *group, BIGNUM *r, const BIGNUM *a,
1377 BN_CTX *ctx)
1378 {
1379 BIGNUM *e = NULL;
1380 BN_CTX *new_ctx = NULL;
1381 int ret = 0;
1382
1383 if (ctx == NULL && (ctx = new_ctx = BN_CTX_secure_new()) == NULL)
1384 return 0;
1385
1386 BN_CTX_start(ctx);
1387 if ((e = BN_CTX_get(ctx)) == NULL)
1388 goto err;
1389
1390 do {
1391 if (!BN_priv_rand_range(e, group->field))
1392 goto err;
1393 } while (BN_is_zero(e));
1394
1395 /* r := a * e */
1396 if (!group->meth->field_mul(group, r, a, e, ctx))
1397 goto err;
1398 /* r := 1/(a * e) */
1399 if (!BN_mod_inverse(r, r, group->field, ctx)) {
1400 ECerr(EC_F_EC_GFP_SIMPLE_FIELD_INV, EC_R_CANNOT_INVERT);
1401 goto err;
1402 }
1403 /* r := e/(a * e) = 1/a */
1404 if (!group->meth->field_mul(group, r, r, e, ctx))
1405 goto err;
1406
1407 ret = 1;
1408
1409 err:
1410 BN_CTX_end(ctx);
1411 BN_CTX_free(new_ctx);
1412 return ret;
1413 }
1414
1415 /*-
1416 * Apply randomization of EC point projective coordinates:
1417 *
1418 * (X, Y ,Z ) = (lambda^2*X, lambda^3*Y, lambda*Z)
1419 * lambda = [1,group->field)
1420 *
1421 */
1422 int ec_GFp_simple_blind_coordinates(const EC_GROUP *group, EC_POINT *p,
1423 BN_CTX *ctx)
1424 {
1425 int ret = 0;
1426 BIGNUM *lambda = NULL;
1427 BIGNUM *temp = NULL;
1428
1429 BN_CTX_start(ctx);
1430 lambda = BN_CTX_get(ctx);
1431 temp = BN_CTX_get(ctx);
1432 if (temp == NULL) {
1433 ECerr(EC_F_EC_GFP_SIMPLE_BLIND_COORDINATES, ERR_R_MALLOC_FAILURE);
1434 goto err;
1435 }
1436
1437 /* make sure lambda is not zero */
1438 do {
1439 if (!BN_priv_rand_range(lambda, group->field)) {
1440 ECerr(EC_F_EC_GFP_SIMPLE_BLIND_COORDINATES, ERR_R_BN_LIB);
1441 goto err;
1442 }
1443 } while (BN_is_zero(lambda));
1444
1445 /* if field_encode defined convert between representations */
1446 if (group->meth->field_encode != NULL
1447 && !group->meth->field_encode(group, lambda, lambda, ctx))
1448 goto err;
1449 if (!group->meth->field_mul(group, p->Z, p->Z, lambda, ctx))
1450 goto err;
1451 if (!group->meth->field_sqr(group, temp, lambda, ctx))
1452 goto err;
1453 if (!group->meth->field_mul(group, p->X, p->X, temp, ctx))
1454 goto err;
1455 if (!group->meth->field_mul(group, temp, temp, lambda, ctx))
1456 goto err;
1457 if (!group->meth->field_mul(group, p->Y, p->Y, temp, ctx))
1458 goto err;
1459 p->Z_is_one = 0;
1460
1461 ret = 1;
1462
1463 err:
1464 BN_CTX_end(ctx);
1465 return ret;
1466 }
1467
1468 /*-
1469 * Set s := p, r := 2p.
1470 *
1471 * For doubling we use Formula 3 from Izu-Takagi "A fast parallel elliptic curve
1472 * multiplication resistant against side channel attacks" appendix, as described
1473 * at
1474 * https://hyperelliptic.org/EFD/g1p/auto-shortw-xz.html#doubling-dbl-2002-it-2
1475 *
1476 * The input point p will be in randomized Jacobian projective coords:
1477 * x = X/Z**2, y=Y/Z**3
1478 *
1479 * The output points p, s, and r are converted to standard (homogeneous)
1480 * projective coords:
1481 * x = X/Z, y=Y/Z
1482 */
1483 int ec_GFp_simple_ladder_pre(const EC_GROUP *group,
1484 EC_POINT *r, EC_POINT *s,
1485 EC_POINT *p, BN_CTX *ctx)
1486 {
1487 BIGNUM *t1, *t2, *t3, *t4, *t5, *t6 = NULL;
1488
1489 t1 = r->Z;
1490 t2 = r->Y;
1491 t3 = s->X;
1492 t4 = r->X;
1493 t5 = s->Y;
1494 t6 = s->Z;
1495
1496 /* convert p: (X,Y,Z) -> (XZ,Y,Z**3) */
1497 if (!group->meth->field_mul(group, p->X, p->X, p->Z, ctx)
1498 || !group->meth->field_sqr(group, t1, p->Z, ctx)
1499 || !group->meth->field_mul(group, p->Z, p->Z, t1, ctx)
1500 /* r := 2p */
1501 || !group->meth->field_sqr(group, t2, p->X, ctx)
1502 || !group->meth->field_sqr(group, t3, p->Z, ctx)
1503 || !group->meth->field_mul(group, t4, t3, group->a, ctx)
1504 || !BN_mod_sub_quick(t5, t2, t4, group->field)
1505 || !BN_mod_add_quick(t2, t2, t4, group->field)
1506 || !group->meth->field_sqr(group, t5, t5, ctx)
1507 || !group->meth->field_mul(group, t6, t3, group->b, ctx)
1508 || !group->meth->field_mul(group, t1, p->X, p->Z, ctx)
1509 || !group->meth->field_mul(group, t4, t1, t6, ctx)
1510 || !BN_mod_lshift_quick(t4, t4, 3, group->field)
1511 /* r->X coord output */
1512 || !BN_mod_sub_quick(r->X, t5, t4, group->field)
1513 || !group->meth->field_mul(group, t1, t1, t2, ctx)
1514 || !group->meth->field_mul(group, t2, t3, t6, ctx)
1515 || !BN_mod_add_quick(t1, t1, t2, group->field)
1516 /* r->Z coord output */
1517 || !BN_mod_lshift_quick(r->Z, t1, 2, group->field)
1518 || !EC_POINT_copy(s, p))
1519 return 0;
1520
1521 r->Z_is_one = 0;
1522 s->Z_is_one = 0;
1523 p->Z_is_one = 0;
1524
1525 return 1;
1526 }
1527
1528 /*-
1529 * Differential addition-and-doubling using Eq. (9) and (10) from Izu-Takagi
1530 * "A fast parallel elliptic curve multiplication resistant against side channel
1531 * attacks", as described at
1532 * https://hyperelliptic.org/EFD/g1p/auto-shortw-xz.html#ladder-ladd-2002-it-4
1533 */
1534 int ec_GFp_simple_ladder_step(const EC_GROUP *group,
1535 EC_POINT *r, EC_POINT *s,
1536 EC_POINT *p, BN_CTX *ctx)
1537 {
1538 int ret = 0;
1539 BIGNUM *t0, *t1, *t2, *t3, *t4, *t5, *t6, *t7 = NULL;
1540
1541 BN_CTX_start(ctx);
1542 t0 = BN_CTX_get(ctx);
1543 t1 = BN_CTX_get(ctx);
1544 t2 = BN_CTX_get(ctx);
1545 t3 = BN_CTX_get(ctx);
1546 t4 = BN_CTX_get(ctx);
1547 t5 = BN_CTX_get(ctx);
1548 t6 = BN_CTX_get(ctx);
1549 t7 = BN_CTX_get(ctx);
1550
1551 if (t7 == NULL
1552 || !group->meth->field_mul(group, t0, r->X, s->X, ctx)
1553 || !group->meth->field_mul(group, t1, r->Z, s->Z, ctx)
1554 || !group->meth->field_mul(group, t2, r->X, s->Z, ctx)
1555 || !group->meth->field_mul(group, t3, r->Z, s->X, ctx)
1556 || !group->meth->field_mul(group, t4, group->a, t1, ctx)
1557 || !BN_mod_add_quick(t0, t0, t4, group->field)
1558 || !BN_mod_add_quick(t4, t3, t2, group->field)
1559 || !group->meth->field_mul(group, t0, t4, t0, ctx)
1560 || !group->meth->field_sqr(group, t1, t1, ctx)
1561 || !BN_mod_lshift_quick(t7, group->b, 2, group->field)
1562 || !group->meth->field_mul(group, t1, t7, t1, ctx)
1563 || !BN_mod_lshift1_quick(t0, t0, group->field)
1564 || !BN_mod_add_quick(t0, t1, t0, group->field)
1565 || !BN_mod_sub_quick(t1, t2, t3, group->field)
1566 || !group->meth->field_sqr(group, t1, t1, ctx)
1567 || !group->meth->field_mul(group, t3, t1, p->X, ctx)
1568 || !group->meth->field_mul(group, t0, p->Z, t0, ctx)
1569 /* s->X coord output */
1570 || !BN_mod_sub_quick(s->X, t0, t3, group->field)
1571 /* s->Z coord output */
1572 || !group->meth->field_mul(group, s->Z, p->Z, t1, ctx)
1573 || !group->meth->field_sqr(group, t3, r->X, ctx)
1574 || !group->meth->field_sqr(group, t2, r->Z, ctx)
1575 || !group->meth->field_mul(group, t4, t2, group->a, ctx)
1576 || !BN_mod_add_quick(t5, r->X, r->Z, group->field)
1577 || !group->meth->field_sqr(group, t5, t5, ctx)
1578 || !BN_mod_sub_quick(t5, t5, t3, group->field)
1579 || !BN_mod_sub_quick(t5, t5, t2, group->field)
1580 || !BN_mod_sub_quick(t6, t3, t4, group->field)
1581 || !group->meth->field_sqr(group, t6, t6, ctx)
1582 || !group->meth->field_mul(group, t0, t2, t5, ctx)
1583 || !group->meth->field_mul(group, t0, t7, t0, ctx)
1584 /* r->X coord output */
1585 || !BN_mod_sub_quick(r->X, t6, t0, group->field)
1586 || !BN_mod_add_quick(t6, t3, t4, group->field)
1587 || !group->meth->field_sqr(group, t3, t2, ctx)
1588 || !group->meth->field_mul(group, t7, t3, t7, ctx)
1589 || !group->meth->field_mul(group, t5, t5, t6, ctx)
1590 || !BN_mod_lshift1_quick(t5, t5, group->field)
1591 /* r->Z coord output */
1592 || !BN_mod_add_quick(r->Z, t7, t5, group->field))
1593 goto err;
1594
1595 ret = 1;
1596
1597 err:
1598 BN_CTX_end(ctx);
1599 return ret;
1600 }
1601
1602 /*-
1603 * Recovers the y-coordinate of r using Eq. (8) from Brier-Joye, "Weierstrass
1604 * Elliptic Curves and Side-Channel Attacks", modified to work in projective
1605 * coordinates and return r in Jacobian projective coordinates.
1606 *
1607 * X4 = two*Y1*X2*Z3*Z2*Z1;
1608 * Y4 = two*b*Z3*SQR(Z2*Z1) + Z3*(a*Z2*Z1+X1*X2)*(X1*Z2+X2*Z1) - X3*SQR(X1*Z2-X2*Z1);
1609 * Z4 = two*Y1*Z3*SQR(Z2)*Z1;
1610 *
1611 * Z4 != 0 because:
1612 * - Z1==0 implies p is at infinity, which would have caused an early exit in
1613 * the caller;
1614 * - Z2==0 implies r is at infinity (handled by the BN_is_zero(r->Z) branch);
1615 * - Z3==0 implies s is at infinity (handled by the BN_is_zero(s->Z) branch);
1616 * - Y1==0 implies p has order 2, so either r or s are infinity and handled by
1617 * one of the BN_is_zero(...) branches.
1618 */
1619 int ec_GFp_simple_ladder_post(const EC_GROUP *group,
1620 EC_POINT *r, EC_POINT *s,
1621 EC_POINT *p, BN_CTX *ctx)
1622 {
1623 int ret = 0;
1624 BIGNUM *t0, *t1, *t2, *t3, *t4, *t5, *t6 = NULL;
1625
1626 if (BN_is_zero(r->Z))
1627 return EC_POINT_set_to_infinity(group, r);
1628
1629 if (BN_is_zero(s->Z)) {
1630 /* (X,Y,Z) -> (XZ,YZ**2,Z) */
1631 if (!group->meth->field_mul(group, r->X, p->X, p->Z, ctx)
1632 || !group->meth->field_sqr(group, r->Z, p->Z, ctx)
1633 || !group->meth->field_mul(group, r->Y, p->Y, r->Z, ctx)
1634 || !BN_copy(r->Z, p->Z)
1635 || !EC_POINT_invert(group, r, ctx))
1636 return 0;
1637 return 1;
1638 }
1639
1640 BN_CTX_start(ctx);
1641 t0 = BN_CTX_get(ctx);
1642 t1 = BN_CTX_get(ctx);
1643 t2 = BN_CTX_get(ctx);
1644 t3 = BN_CTX_get(ctx);
1645 t4 = BN_CTX_get(ctx);
1646 t5 = BN_CTX_get(ctx);
1647 t6 = BN_CTX_get(ctx);
1648
1649 if (t6 == NULL
1650 || !BN_mod_lshift1_quick(t0, p->Y, group->field)
1651 || !group->meth->field_mul(group, t1, r->X, p->Z, ctx)
1652 || !group->meth->field_mul(group, t2, r->Z, s->Z, ctx)
1653 || !group->meth->field_mul(group, t2, t1, t2, ctx)
1654 || !group->meth->field_mul(group, t3, t2, t0, ctx)
1655 || !group->meth->field_mul(group, t2, r->Z, p->Z, ctx)
1656 || !group->meth->field_sqr(group, t4, t2, ctx)
1657 || !BN_mod_lshift1_quick(t5, group->b, group->field)
1658 || !group->meth->field_mul(group, t4, t4, t5, ctx)
1659 || !group->meth->field_mul(group, t6, t2, group->a, ctx)
1660 || !group->meth->field_mul(group, t5, r->X, p->X, ctx)
1661 || !BN_mod_add_quick(t5, t6, t5, group->field)
1662 || !group->meth->field_mul(group, t6, r->Z, p->X, ctx)
1663 || !BN_mod_add_quick(t2, t6, t1, group->field)
1664 || !group->meth->field_mul(group, t5, t5, t2, ctx)
1665 || !BN_mod_sub_quick(t6, t6, t1, group->field)
1666 || !group->meth->field_sqr(group, t6, t6, ctx)
1667 || !group->meth->field_mul(group, t6, t6, s->X, ctx)
1668 || !BN_mod_add_quick(t4, t5, t4, group->field)
1669 || !group->meth->field_mul(group, t4, t4, s->Z, ctx)
1670 || !BN_mod_sub_quick(t4, t4, t6, group->field)
1671 || !group->meth->field_sqr(group, t5, r->Z, ctx)
1672 || !group->meth->field_mul(group, r->Z, p->Z, s->Z, ctx)
1673 || !group->meth->field_mul(group, r->Z, t5, r->Z, ctx)
1674 || !group->meth->field_mul(group, r->Z, r->Z, t0, ctx)
1675 /* t3 := X, t4 := Y */
1676 /* (X,Y,Z) -> (XZ,YZ**2,Z) */
1677 || !group->meth->field_mul(group, r->X, t3, r->Z, ctx)
1678 || !group->meth->field_sqr(group, t3, r->Z, ctx)
1679 || !group->meth->field_mul(group, r->Y, t4, t3, ctx))
1680 goto err;
1681
1682 ret = 1;
1683
1684 err:
1685 BN_CTX_end(ctx);
1686 return ret;
1687 }
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