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_local.h"
15
16const 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 ecdsa_simple_sign_setup,
68 ecdsa_simple_sign_sig,
69 ecdsa_simple_verify_sig,
70 0, /* field_inverse_mod_ord */
71 ec_GFp_simple_blind_coordinates,
72 ec_GFp_simple_ladder_pre,
73 ec_GFp_simple_ladder_step,
74 ec_GFp_simple_ladder_post
75 };
76
77 return &ret;
78}
79
80/*
81 * Most method functions in this file are designed to work with
82 * non-trivial representations of field elements if necessary
83 * (see ecp_mont.c): while standard modular addition and subtraction
84 * are used, the field_mul and field_sqr methods will be used for
85 * multiplication, and field_encode and field_decode (if defined)
86 * will be used for converting between representations.
87 *
88 * Functions ec_GFp_simple_points_make_affine() and
89 * ec_GFp_simple_point_get_affine_coordinates() specifically assume
90 * that if a non-trivial representation is used, it is a Montgomery
91 * representation (i.e. 'encoding' means multiplying by some factor R).
92 */
93
94int ec_GFp_simple_group_init(EC_GROUP *group)
95{
96 group->field = BN_new();
97 group->a = BN_new();
98 group->b = BN_new();
99 if (group->field == NULL || group->a == NULL || group->b == NULL) {
100 BN_free(group->field);
101 BN_free(group->a);
102 BN_free(group->b);
103 return 0;
104 }
105 group->a_is_minus3 = 0;
106 return 1;
107}
108
109void ec_GFp_simple_group_finish(EC_GROUP *group)
110{
111 BN_free(group->field);
112 BN_free(group->a);
113 BN_free(group->b);
114}
115
116void ec_GFp_simple_group_clear_finish(EC_GROUP *group)
117{
118 BN_clear_free(group->field);
119 BN_clear_free(group->a);
120 BN_clear_free(group->b);
121}
122
123int ec_GFp_simple_group_copy(EC_GROUP *dest, const EC_GROUP *src)
124{
125 if (!BN_copy(dest->field, src->field))
126 return 0;
127 if (!BN_copy(dest->a, src->a))
128 return 0;
129 if (!BN_copy(dest->b, src->b))
130 return 0;
131
132 dest->a_is_minus3 = src->a_is_minus3;
133
134 return 1;
135}
136
137int ec_GFp_simple_group_set_curve(EC_GROUP *group,
138 const BIGNUM *p, const BIGNUM *a,
139 const BIGNUM *b, BN_CTX *ctx)
140{
141 int ret = 0;
142 BN_CTX *new_ctx = NULL;
143 BIGNUM *tmp_a;
144
145 /* p must be a prime > 3 */
146 if (BN_num_bits(p) <= 2 || !BN_is_odd(p)) {
147 ECerr(EC_F_EC_GFP_SIMPLE_GROUP_SET_CURVE, EC_R_INVALID_FIELD);
148 return 0;
149 }
150
151 if (ctx == NULL) {
152 ctx = new_ctx = BN_CTX_new_ex(group->libctx);
153 if (ctx == NULL)
154 return 0;
155 }
156
157 BN_CTX_start(ctx);
158 tmp_a = BN_CTX_get(ctx);
159 if (tmp_a == NULL)
160 goto err;
161
162 /* group->field */
163 if (!BN_copy(group->field, p))
164 goto err;
165 BN_set_negative(group->field, 0);
166
167 /* group->a */
168 if (!BN_nnmod(tmp_a, a, p, ctx))
169 goto err;
170 if (group->meth->field_encode) {
171 if (!group->meth->field_encode(group, group->a, tmp_a, ctx))
172 goto err;
173 } else if (!BN_copy(group->a, tmp_a))
174 goto err;
175
176 /* group->b */
177 if (!BN_nnmod(group->b, b, p, ctx))
178 goto err;
179 if (group->meth->field_encode)
180 if (!group->meth->field_encode(group, group->b, group->b, ctx))
181 goto err;
182
183 /* group->a_is_minus3 */
184 if (!BN_add_word(tmp_a, 3))
185 goto err;
186 group->a_is_minus3 = (0 == BN_cmp(tmp_a, group->field));
187
188 ret = 1;
189
190 err:
191 BN_CTX_end(ctx);
192 BN_CTX_free(new_ctx);
193 return ret;
194}
195
196int ec_GFp_simple_group_get_curve(const EC_GROUP *group, BIGNUM *p, BIGNUM *a,
197 BIGNUM *b, BN_CTX *ctx)
198{
199 int ret = 0;
200 BN_CTX *new_ctx = NULL;
201
202 if (p != NULL) {
203 if (!BN_copy(p, group->field))
204 return 0;
205 }
206
207 if (a != NULL || b != NULL) {
208 if (group->meth->field_decode) {
209 if (ctx == NULL) {
210 ctx = new_ctx = BN_CTX_new_ex(group->libctx);
211 if (ctx == NULL)
212 return 0;
213 }
214 if (a != NULL) {
215 if (!group->meth->field_decode(group, a, group->a, ctx))
216 goto err;
217 }
218 if (b != NULL) {
219 if (!group->meth->field_decode(group, b, group->b, ctx))
220 goto err;
221 }
222 } else {
223 if (a != NULL) {
224 if (!BN_copy(a, group->a))
225 goto err;
226 }
227 if (b != NULL) {
228 if (!BN_copy(b, group->b))
229 goto err;
230 }
231 }
232 }
233
234 ret = 1;
235
236 err:
237 BN_CTX_free(new_ctx);
238 return ret;
239}
240
241int ec_GFp_simple_group_get_degree(const EC_GROUP *group)
242{
243 return BN_num_bits(group->field);
244}
245
246int ec_GFp_simple_group_check_discriminant(const EC_GROUP *group, BN_CTX *ctx)
247{
248 int ret = 0;
249 BIGNUM *a, *b, *order, *tmp_1, *tmp_2;
250 const BIGNUM *p = group->field;
251 BN_CTX *new_ctx = NULL;
252
253 if (ctx == NULL) {
254 ctx = new_ctx = BN_CTX_new_ex(group->libctx);
255 if (ctx == NULL) {
256 ECerr(EC_F_EC_GFP_SIMPLE_GROUP_CHECK_DISCRIMINANT,
257 ERR_R_MALLOC_FAILURE);
258 goto err;
259 }
260 }
261 BN_CTX_start(ctx);
262 a = BN_CTX_get(ctx);
263 b = BN_CTX_get(ctx);
264 tmp_1 = BN_CTX_get(ctx);
265 tmp_2 = BN_CTX_get(ctx);
266 order = BN_CTX_get(ctx);
267 if (order == NULL)
268 goto err;
269
270 if (group->meth->field_decode) {
271 if (!group->meth->field_decode(group, a, group->a, ctx))
272 goto err;
273 if (!group->meth->field_decode(group, b, group->b, ctx))
274 goto err;
275 } else {
276 if (!BN_copy(a, group->a))
277 goto err;
278 if (!BN_copy(b, group->b))
279 goto err;
280 }
281
282 /*-
283 * check the discriminant:
284 * y^2 = x^3 + a*x + b is an elliptic curve <=> 4*a^3 + 27*b^2 != 0 (mod p)
285 * 0 =< a, b < p
286 */
287 if (BN_is_zero(a)) {
288 if (BN_is_zero(b))
289 goto err;
290 } else if (!BN_is_zero(b)) {
291 if (!BN_mod_sqr(tmp_1, a, p, ctx))
292 goto err;
293 if (!BN_mod_mul(tmp_2, tmp_1, a, p, ctx))
294 goto err;
295 if (!BN_lshift(tmp_1, tmp_2, 2))
296 goto err;
297 /* tmp_1 = 4*a^3 */
298
299 if (!BN_mod_sqr(tmp_2, b, p, ctx))
300 goto err;
301 if (!BN_mul_word(tmp_2, 27))
302 goto err;
303 /* tmp_2 = 27*b^2 */
304
305 if (!BN_mod_add(a, tmp_1, tmp_2, p, ctx))
306 goto err;
307 if (BN_is_zero(a))
308 goto err;
309 }
310 ret = 1;
311
312 err:
313 BN_CTX_end(ctx);
314 BN_CTX_free(new_ctx);
315 return ret;
316}
317
318int ec_GFp_simple_point_init(EC_POINT *point)
319{
320 point->X = BN_new();
321 point->Y = BN_new();
322 point->Z = BN_new();
323 point->Z_is_one = 0;
324
325 if (point->X == NULL || point->Y == NULL || point->Z == NULL) {
326 BN_free(point->X);
327 BN_free(point->Y);
328 BN_free(point->Z);
329 return 0;
330 }
331 return 1;
332}
333
334void ec_GFp_simple_point_finish(EC_POINT *point)
335{
336 BN_free(point->X);
337 BN_free(point->Y);
338 BN_free(point->Z);
339}
340
341void ec_GFp_simple_point_clear_finish(EC_POINT *point)
342{
343 BN_clear_free(point->X);
344 BN_clear_free(point->Y);
345 BN_clear_free(point->Z);
346 point->Z_is_one = 0;
347}
348
349int ec_GFp_simple_point_copy(EC_POINT *dest, const EC_POINT *src)
350{
351 if (!BN_copy(dest->X, src->X))
352 return 0;
353 if (!BN_copy(dest->Y, src->Y))
354 return 0;
355 if (!BN_copy(dest->Z, src->Z))
356 return 0;
357 dest->Z_is_one = src->Z_is_one;
358 dest->curve_name = src->curve_name;
359
360 return 1;
361}
362
363int ec_GFp_simple_point_set_to_infinity(const EC_GROUP *group,
364 EC_POINT *point)
365{
366 point->Z_is_one = 0;
367 BN_zero(point->Z);
368 return 1;
369}
370
371int ec_GFp_simple_set_Jprojective_coordinates_GFp(const EC_GROUP *group,
372 EC_POINT *point,
373 const BIGNUM *x,
374 const BIGNUM *y,
375 const BIGNUM *z,
376 BN_CTX *ctx)
377{
378 BN_CTX *new_ctx = NULL;
379 int ret = 0;
380
381 if (ctx == NULL) {
382 ctx = new_ctx = BN_CTX_new_ex(group->libctx);
383 if (ctx == NULL)
384 return 0;
385 }
386
387 if (x != NULL) {
388 if (!BN_nnmod(point->X, x, group->field, ctx))
389 goto err;
390 if (group->meth->field_encode) {
391 if (!group->meth->field_encode(group, point->X, point->X, ctx))
392 goto err;
393 }
394 }
395
396 if (y != NULL) {
397 if (!BN_nnmod(point->Y, y, group->field, ctx))
398 goto err;
399 if (group->meth->field_encode) {
400 if (!group->meth->field_encode(group, point->Y, point->Y, ctx))
401 goto err;
402 }
403 }
404
405 if (z != NULL) {
406 int Z_is_one;
407
408 if (!BN_nnmod(point->Z, z, group->field, ctx))
409 goto err;
410 Z_is_one = BN_is_one(point->Z);
411 if (group->meth->field_encode) {
412 if (Z_is_one && (group->meth->field_set_to_one != 0)) {
413 if (!group->meth->field_set_to_one(group, point->Z, ctx))
414 goto err;
415 } else {
416 if (!group->
417 meth->field_encode(group, point->Z, point->Z, ctx))
418 goto err;
419 }
420 }
421 point->Z_is_one = Z_is_one;
422 }
423
424 ret = 1;
425
426 err:
427 BN_CTX_free(new_ctx);
428 return ret;
429}
430
431int ec_GFp_simple_get_Jprojective_coordinates_GFp(const EC_GROUP *group,
432 const EC_POINT *point,
433 BIGNUM *x, BIGNUM *y,
434 BIGNUM *z, BN_CTX *ctx)
435{
436 BN_CTX *new_ctx = NULL;
437 int ret = 0;
438
439 if (group->meth->field_decode != 0) {
440 if (ctx == NULL) {
441 ctx = new_ctx = BN_CTX_new_ex(group->libctx);
442 if (ctx == NULL)
443 return 0;
444 }
445
446 if (x != NULL) {
447 if (!group->meth->field_decode(group, x, point->X, ctx))
448 goto err;
449 }
450 if (y != NULL) {
451 if (!group->meth->field_decode(group, y, point->Y, ctx))
452 goto err;
453 }
454 if (z != NULL) {
455 if (!group->meth->field_decode(group, z, point->Z, ctx))
456 goto err;
457 }
458 } else {
459 if (x != NULL) {
460 if (!BN_copy(x, point->X))
461 goto err;
462 }
463 if (y != NULL) {
464 if (!BN_copy(y, point->Y))
465 goto err;
466 }
467 if (z != NULL) {
468 if (!BN_copy(z, point->Z))
469 goto err;
470 }
471 }
472
473 ret = 1;
474
475 err:
476 BN_CTX_free(new_ctx);
477 return ret;
478}
479
480int ec_GFp_simple_point_set_affine_coordinates(const EC_GROUP *group,
481 EC_POINT *point,
482 const BIGNUM *x,
483 const BIGNUM *y, BN_CTX *ctx)
484{
485 if (x == NULL || y == NULL) {
486 /*
487 * unlike for projective coordinates, we do not tolerate this
488 */
489 ECerr(EC_F_EC_GFP_SIMPLE_POINT_SET_AFFINE_COORDINATES,
490 ERR_R_PASSED_NULL_PARAMETER);
491 return 0;
492 }
493
494 return EC_POINT_set_Jprojective_coordinates_GFp(group, point, x, y,
495 BN_value_one(), ctx);
496}
497
498int ec_GFp_simple_point_get_affine_coordinates(const EC_GROUP *group,
499 const EC_POINT *point,
500 BIGNUM *x, BIGNUM *y,
501 BN_CTX *ctx)
502{
503 BN_CTX *new_ctx = NULL;
504 BIGNUM *Z, *Z_1, *Z_2, *Z_3;
505 const BIGNUM *Z_;
506 int ret = 0;
507
508 if (EC_POINT_is_at_infinity(group, point)) {
509 ECerr(EC_F_EC_GFP_SIMPLE_POINT_GET_AFFINE_COORDINATES,
510 EC_R_POINT_AT_INFINITY);
511 return 0;
512 }
513
514 if (ctx == NULL) {
515 ctx = new_ctx = BN_CTX_new_ex(group->libctx);
516 if (ctx == NULL)
517 return 0;
518 }
519
520 BN_CTX_start(ctx);
521 Z = BN_CTX_get(ctx);
522 Z_1 = BN_CTX_get(ctx);
523 Z_2 = BN_CTX_get(ctx);
524 Z_3 = BN_CTX_get(ctx);
525 if (Z_3 == NULL)
526 goto err;
527
528 /* transform (X, Y, Z) into (x, y) := (X/Z^2, Y/Z^3) */
529
530 if (group->meth->field_decode) {
531 if (!group->meth->field_decode(group, Z, point->Z, ctx))
532 goto err;
533 Z_ = Z;
534 } else {
535 Z_ = point->Z;
536 }
537
538 if (BN_is_one(Z_)) {
539 if (group->meth->field_decode) {
540 if (x != NULL) {
541 if (!group->meth->field_decode(group, x, point->X, ctx))
542 goto err;
543 }
544 if (y != NULL) {
545 if (!group->meth->field_decode(group, y, point->Y, ctx))
546 goto err;
547 }
548 } else {
549 if (x != NULL) {
550 if (!BN_copy(x, point->X))
551 goto err;
552 }
553 if (y != NULL) {
554 if (!BN_copy(y, point->Y))
555 goto err;
556 }
557 }
558 } else {
559 if (!group->meth->field_inv(group, Z_1, Z_, ctx)) {
560 ECerr(EC_F_EC_GFP_SIMPLE_POINT_GET_AFFINE_COORDINATES,
561 ERR_R_BN_LIB);
562 goto err;
563 }
564
565 if (group->meth->field_encode == 0) {
566 /* field_sqr works on standard representation */
567 if (!group->meth->field_sqr(group, Z_2, Z_1, ctx))
568 goto err;
569 } else {
570 if (!BN_mod_sqr(Z_2, Z_1, group->field, ctx))
571 goto err;
572 }
573
574 if (x != NULL) {
575 /*
576 * in the Montgomery case, field_mul will cancel out Montgomery
577 * factor in X:
578 */
579 if (!group->meth->field_mul(group, x, point->X, Z_2, ctx))
580 goto err;
581 }
582
583 if (y != NULL) {
584 if (group->meth->field_encode == 0) {
585 /*
586 * field_mul works on standard representation
587 */
588 if (!group->meth->field_mul(group, Z_3, Z_2, Z_1, ctx))
589 goto err;
590 } else {
591 if (!BN_mod_mul(Z_3, Z_2, Z_1, group->field, ctx))
592 goto err;
593 }
594
595 /*
596 * in the Montgomery case, field_mul will cancel out Montgomery
597 * factor in Y:
598 */
599 if (!group->meth->field_mul(group, y, point->Y, Z_3, ctx))
600 goto err;
601 }
602 }
603
604 ret = 1;
605
606 err:
607 BN_CTX_end(ctx);
608 BN_CTX_free(new_ctx);
609 return ret;
610}
611
612int ec_GFp_simple_add(const EC_GROUP *group, EC_POINT *r, const EC_POINT *a,
613 const EC_POINT *b, BN_CTX *ctx)
614{
615 int (*field_mul) (const EC_GROUP *, BIGNUM *, const BIGNUM *,
616 const BIGNUM *, BN_CTX *);
617 int (*field_sqr) (const EC_GROUP *, BIGNUM *, const BIGNUM *, BN_CTX *);
618 const BIGNUM *p;
619 BN_CTX *new_ctx = NULL;
620 BIGNUM *n0, *n1, *n2, *n3, *n4, *n5, *n6;
621 int ret = 0;
622
623 if (a == b)
624 return EC_POINT_dbl(group, r, a, ctx);
625 if (EC_POINT_is_at_infinity(group, a))
626 return EC_POINT_copy(r, b);
627 if (EC_POINT_is_at_infinity(group, b))
628 return EC_POINT_copy(r, a);
629
630 field_mul = group->meth->field_mul;
631 field_sqr = group->meth->field_sqr;
632 p = group->field;
633
634 if (ctx == NULL) {
635 ctx = new_ctx = BN_CTX_new_ex(group->libctx);
636 if (ctx == NULL)
637 return 0;
638 }
639
640 BN_CTX_start(ctx);
641 n0 = BN_CTX_get(ctx);
642 n1 = BN_CTX_get(ctx);
643 n2 = BN_CTX_get(ctx);
644 n3 = BN_CTX_get(ctx);
645 n4 = BN_CTX_get(ctx);
646 n5 = BN_CTX_get(ctx);
647 n6 = BN_CTX_get(ctx);
648 if (n6 == NULL)
649 goto end;
650
651 /*
652 * Note that in this function we must not read components of 'a' or 'b'
653 * once we have written the corresponding components of 'r'. ('r' might
654 * be one of 'a' or 'b'.)
655 */
656
657 /* n1, n2 */
658 if (b->Z_is_one) {
659 if (!BN_copy(n1, a->X))
660 goto end;
661 if (!BN_copy(n2, a->Y))
662 goto end;
663 /* n1 = X_a */
664 /* n2 = Y_a */
665 } else {
666 if (!field_sqr(group, n0, b->Z, ctx))
667 goto end;
668 if (!field_mul(group, n1, a->X, n0, ctx))
669 goto end;
670 /* n1 = X_a * Z_b^2 */
671
672 if (!field_mul(group, n0, n0, b->Z, ctx))
673 goto end;
674 if (!field_mul(group, n2, a->Y, n0, ctx))
675 goto end;
676 /* n2 = Y_a * Z_b^3 */
677 }
678
679 /* n3, n4 */
680 if (a->Z_is_one) {
681 if (!BN_copy(n3, b->X))
682 goto end;
683 if (!BN_copy(n4, b->Y))
684 goto end;
685 /* n3 = X_b */
686 /* n4 = Y_b */
687 } else {
688 if (!field_sqr(group, n0, a->Z, ctx))
689 goto end;
690 if (!field_mul(group, n3, b->X, n0, ctx))
691 goto end;
692 /* n3 = X_b * Z_a^2 */
693
694 if (!field_mul(group, n0, n0, a->Z, ctx))
695 goto end;
696 if (!field_mul(group, n4, b->Y, n0, ctx))
697 goto end;
698 /* n4 = Y_b * Z_a^3 */
699 }
700
701 /* n5, n6 */
702 if (!BN_mod_sub_quick(n5, n1, n3, p))
703 goto end;
704 if (!BN_mod_sub_quick(n6, n2, n4, p))
705 goto end;
706 /* n5 = n1 - n3 */
707 /* n6 = n2 - n4 */
708
709 if (BN_is_zero(n5)) {
710 if (BN_is_zero(n6)) {
711 /* a is the same point as b */
712 BN_CTX_end(ctx);
713 ret = EC_POINT_dbl(group, r, a, ctx);
714 ctx = NULL;
715 goto end;
716 } else {
717 /* a is the inverse of b */
718 BN_zero(r->Z);
719 r->Z_is_one = 0;
720 ret = 1;
721 goto end;
722 }
723 }
724
725 /* 'n7', 'n8' */
726 if (!BN_mod_add_quick(n1, n1, n3, p))
727 goto end;
728 if (!BN_mod_add_quick(n2, n2, n4, p))
729 goto end;
730 /* 'n7' = n1 + n3 */
731 /* 'n8' = n2 + n4 */
732
733 /* Z_r */
734 if (a->Z_is_one && b->Z_is_one) {
735 if (!BN_copy(r->Z, n5))
736 goto end;
737 } else {
738 if (a->Z_is_one) {
739 if (!BN_copy(n0, b->Z))
740 goto end;
741 } else if (b->Z_is_one) {
742 if (!BN_copy(n0, a->Z))
743 goto end;
744 } else {
745 if (!field_mul(group, n0, a->Z, b->Z, ctx))
746 goto end;
747 }
748 if (!field_mul(group, r->Z, n0, n5, ctx))
749 goto end;
750 }
751 r->Z_is_one = 0;
752 /* Z_r = Z_a * Z_b * n5 */
753
754 /* X_r */
755 if (!field_sqr(group, n0, n6, ctx))
756 goto end;
757 if (!field_sqr(group, n4, n5, ctx))
758 goto end;
759 if (!field_mul(group, n3, n1, n4, ctx))
760 goto end;
761 if (!BN_mod_sub_quick(r->X, n0, n3, p))
762 goto end;
763 /* X_r = n6^2 - n5^2 * 'n7' */
764
765 /* 'n9' */
766 if (!BN_mod_lshift1_quick(n0, r->X, p))
767 goto end;
768 if (!BN_mod_sub_quick(n0, n3, n0, p))
769 goto end;
770 /* n9 = n5^2 * 'n7' - 2 * X_r */
771
772 /* Y_r */
773 if (!field_mul(group, n0, n0, n6, ctx))
774 goto end;
775 if (!field_mul(group, n5, n4, n5, ctx))
776 goto end; /* now n5 is n5^3 */
777 if (!field_mul(group, n1, n2, n5, ctx))
778 goto end;
779 if (!BN_mod_sub_quick(n0, n0, n1, p))
780 goto end;
781 if (BN_is_odd(n0))
782 if (!BN_add(n0, n0, p))
783 goto end;
784 /* now 0 <= n0 < 2*p, and n0 is even */
785 if (!BN_rshift1(r->Y, n0))
786 goto end;
787 /* Y_r = (n6 * 'n9' - 'n8' * 'n5^3') / 2 */
788
789 ret = 1;
790
791 end:
792 BN_CTX_end(ctx);
793 BN_CTX_free(new_ctx);
794 return ret;
795}
796
797int ec_GFp_simple_dbl(const EC_GROUP *group, EC_POINT *r, const EC_POINT *a,
798 BN_CTX *ctx)
799{
800 int (*field_mul) (const EC_GROUP *, BIGNUM *, const BIGNUM *,
801 const BIGNUM *, BN_CTX *);
802 int (*field_sqr) (const EC_GROUP *, BIGNUM *, const BIGNUM *, BN_CTX *);
803 const BIGNUM *p;
804 BN_CTX *new_ctx = NULL;
805 BIGNUM *n0, *n1, *n2, *n3;
806 int ret = 0;
807
808 if (EC_POINT_is_at_infinity(group, a)) {
809 BN_zero(r->Z);
810 r->Z_is_one = 0;
811 return 1;
812 }
813
814 field_mul = group->meth->field_mul;
815 field_sqr = group->meth->field_sqr;
816 p = group->field;
817
818 if (ctx == NULL) {
819 ctx = new_ctx = BN_CTX_new_ex(group->libctx);
820 if (ctx == NULL)
821 return 0;
822 }
823
824 BN_CTX_start(ctx);
825 n0 = BN_CTX_get(ctx);
826 n1 = BN_CTX_get(ctx);
827 n2 = BN_CTX_get(ctx);
828 n3 = BN_CTX_get(ctx);
829 if (n3 == NULL)
830 goto err;
831
832 /*
833 * Note that in this function we must not read components of 'a' once we
834 * have written the corresponding components of 'r'. ('r' might the same
835 * as 'a'.)
836 */
837
838 /* n1 */
839 if (a->Z_is_one) {
840 if (!field_sqr(group, n0, a->X, ctx))
841 goto err;
842 if (!BN_mod_lshift1_quick(n1, n0, p))
843 goto err;
844 if (!BN_mod_add_quick(n0, n0, n1, p))
845 goto err;
846 if (!BN_mod_add_quick(n1, n0, group->a, p))
847 goto err;
848 /* n1 = 3 * X_a^2 + a_curve */
849 } else if (group->a_is_minus3) {
850 if (!field_sqr(group, n1, a->Z, ctx))
851 goto err;
852 if (!BN_mod_add_quick(n0, a->X, n1, p))
853 goto err;
854 if (!BN_mod_sub_quick(n2, a->X, n1, p))
855 goto err;
856 if (!field_mul(group, n1, n0, n2, ctx))
857 goto err;
858 if (!BN_mod_lshift1_quick(n0, n1, p))
859 goto err;
860 if (!BN_mod_add_quick(n1, n0, n1, p))
861 goto err;
862 /*-
863 * n1 = 3 * (X_a + Z_a^2) * (X_a - Z_a^2)
864 * = 3 * X_a^2 - 3 * Z_a^4
865 */
866 } else {
867 if (!field_sqr(group, n0, a->X, ctx))
868 goto err;
869 if (!BN_mod_lshift1_quick(n1, n0, p))
870 goto err;
871 if (!BN_mod_add_quick(n0, n0, n1, p))
872 goto err;
873 if (!field_sqr(group, n1, a->Z, ctx))
874 goto err;
875 if (!field_sqr(group, n1, n1, ctx))
876 goto err;
877 if (!field_mul(group, n1, n1, group->a, ctx))
878 goto err;
879 if (!BN_mod_add_quick(n1, n1, n0, p))
880 goto err;
881 /* n1 = 3 * X_a^2 + a_curve * Z_a^4 */
882 }
883
884 /* Z_r */
885 if (a->Z_is_one) {
886 if (!BN_copy(n0, a->Y))
887 goto err;
888 } else {
889 if (!field_mul(group, n0, a->Y, a->Z, ctx))
890 goto err;
891 }
892 if (!BN_mod_lshift1_quick(r->Z, n0, p))
893 goto err;
894 r->Z_is_one = 0;
895 /* Z_r = 2 * Y_a * Z_a */
896
897 /* n2 */
898 if (!field_sqr(group, n3, a->Y, ctx))
899 goto err;
900 if (!field_mul(group, n2, a->X, n3, ctx))
901 goto err;
902 if (!BN_mod_lshift_quick(n2, n2, 2, p))
903 goto err;
904 /* n2 = 4 * X_a * Y_a^2 */
905
906 /* X_r */
907 if (!BN_mod_lshift1_quick(n0, n2, p))
908 goto err;
909 if (!field_sqr(group, r->X, n1, ctx))
910 goto err;
911 if (!BN_mod_sub_quick(r->X, r->X, n0, p))
912 goto err;
913 /* X_r = n1^2 - 2 * n2 */
914
915 /* n3 */
916 if (!field_sqr(group, n0, n3, ctx))
917 goto err;
918 if (!BN_mod_lshift_quick(n3, n0, 3, p))
919 goto err;
920 /* n3 = 8 * Y_a^4 */
921
922 /* Y_r */
923 if (!BN_mod_sub_quick(n0, n2, r->X, p))
924 goto err;
925 if (!field_mul(group, n0, n1, n0, ctx))
926 goto err;
927 if (!BN_mod_sub_quick(r->Y, n0, n3, p))
928 goto err;
929 /* Y_r = n1 * (n2 - X_r) - n3 */
930
931 ret = 1;
932
933 err:
934 BN_CTX_end(ctx);
935 BN_CTX_free(new_ctx);
936 return ret;
937}
938
939int ec_GFp_simple_invert(const EC_GROUP *group, EC_POINT *point, BN_CTX *ctx)
940{
941 if (EC_POINT_is_at_infinity(group, point) || BN_is_zero(point->Y))
942 /* point is its own inverse */
943 return 1;
944
945 return BN_usub(point->Y, group->field, point->Y);
946}
947
948int ec_GFp_simple_is_at_infinity(const EC_GROUP *group, const EC_POINT *point)
949{
950 return BN_is_zero(point->Z);
951}
952
953int ec_GFp_simple_is_on_curve(const EC_GROUP *group, const EC_POINT *point,
954 BN_CTX *ctx)
955{
956 int (*field_mul) (const EC_GROUP *, BIGNUM *, const BIGNUM *,
957 const BIGNUM *, BN_CTX *);
958 int (*field_sqr) (const EC_GROUP *, BIGNUM *, const BIGNUM *, BN_CTX *);
959 const BIGNUM *p;
960 BN_CTX *new_ctx = NULL;
961 BIGNUM *rh, *tmp, *Z4, *Z6;
962 int ret = -1;
963
964 if (EC_POINT_is_at_infinity(group, point))
965 return 1;
966
967 field_mul = group->meth->field_mul;
968 field_sqr = group->meth->field_sqr;
969 p = group->field;
970
971 if (ctx == NULL) {
972 ctx = new_ctx = BN_CTX_new_ex(group->libctx);
973 if (ctx == NULL)
974 return -1;
975 }
976
977 BN_CTX_start(ctx);
978 rh = BN_CTX_get(ctx);
979 tmp = BN_CTX_get(ctx);
980 Z4 = BN_CTX_get(ctx);
981 Z6 = BN_CTX_get(ctx);
982 if (Z6 == NULL)
983 goto err;
984
985 /*-
986 * We have a curve defined by a Weierstrass equation
987 * y^2 = x^3 + a*x + b.
988 * The point to consider is given in Jacobian projective coordinates
989 * where (X, Y, Z) represents (x, y) = (X/Z^2, Y/Z^3).
990 * Substituting this and multiplying by Z^6 transforms the above equation into
991 * Y^2 = X^3 + a*X*Z^4 + b*Z^6.
992 * To test this, we add up the right-hand side in 'rh'.
993 */
994
995 /* rh := X^2 */
996 if (!field_sqr(group, rh, point->X, ctx))
997 goto err;
998
999 if (!point->Z_is_one) {
1000 if (!field_sqr(group, tmp, point->Z, ctx))
1001 goto err;
1002 if (!field_sqr(group, Z4, tmp, ctx))
1003 goto err;
1004 if (!field_mul(group, Z6, Z4, tmp, ctx))
1005 goto err;
1006
1007 /* rh := (rh + a*Z^4)*X */
1008 if (group->a_is_minus3) {
1009 if (!BN_mod_lshift1_quick(tmp, Z4, p))
1010 goto err;
1011 if (!BN_mod_add_quick(tmp, tmp, Z4, p))
1012 goto err;
1013 if (!BN_mod_sub_quick(rh, rh, tmp, p))
1014 goto err;
1015 if (!field_mul(group, rh, rh, point->X, ctx))
1016 goto err;
1017 } else {
1018 if (!field_mul(group, tmp, Z4, group->a, ctx))
1019 goto err;
1020 if (!BN_mod_add_quick(rh, rh, tmp, p))
1021 goto err;
1022 if (!field_mul(group, rh, rh, point->X, ctx))
1023 goto err;
1024 }
1025
1026 /* rh := rh + b*Z^6 */
1027 if (!field_mul(group, tmp, group->b, Z6, ctx))
1028 goto err;
1029 if (!BN_mod_add_quick(rh, rh, tmp, p))
1030 goto err;
1031 } else {
1032 /* point->Z_is_one */
1033
1034 /* rh := (rh + a)*X */
1035 if (!BN_mod_add_quick(rh, rh, group->a, p))
1036 goto err;
1037 if (!field_mul(group, rh, rh, point->X, ctx))
1038 goto err;
1039 /* rh := rh + b */
1040 if (!BN_mod_add_quick(rh, rh, group->b, p))
1041 goto err;
1042 }
1043
1044 /* 'lh' := Y^2 */
1045 if (!field_sqr(group, tmp, point->Y, ctx))
1046 goto err;
1047
1048 ret = (0 == BN_ucmp(tmp, rh));
1049
1050 err:
1051 BN_CTX_end(ctx);
1052 BN_CTX_free(new_ctx);
1053 return ret;
1054}
1055
1056int ec_GFp_simple_cmp(const EC_GROUP *group, const EC_POINT *a,
1057 const EC_POINT *b, BN_CTX *ctx)
1058{
1059 /*-
1060 * return values:
1061 * -1 error
1062 * 0 equal (in affine coordinates)
1063 * 1 not equal
1064 */
1065
1066 int (*field_mul) (const EC_GROUP *, BIGNUM *, const BIGNUM *,
1067 const BIGNUM *, BN_CTX *);
1068 int (*field_sqr) (const EC_GROUP *, BIGNUM *, const BIGNUM *, BN_CTX *);
1069 BN_CTX *new_ctx = NULL;
1070 BIGNUM *tmp1, *tmp2, *Za23, *Zb23;
1071 const BIGNUM *tmp1_, *tmp2_;
1072 int ret = -1;
1073
1074 if (EC_POINT_is_at_infinity(group, a)) {
1075 return EC_POINT_is_at_infinity(group, b) ? 0 : 1;
1076 }
1077
1078 if (EC_POINT_is_at_infinity(group, b))
1079 return 1;
1080
1081 if (a->Z_is_one && b->Z_is_one) {
1082 return ((BN_cmp(a->X, b->X) == 0) && BN_cmp(a->Y, b->Y) == 0) ? 0 : 1;
1083 }
1084
1085 field_mul = group->meth->field_mul;
1086 field_sqr = group->meth->field_sqr;
1087
1088 if (ctx == NULL) {
1089 ctx = new_ctx = BN_CTX_new_ex(group->libctx);
1090 if (ctx == NULL)
1091 return -1;
1092 }
1093
1094 BN_CTX_start(ctx);
1095 tmp1 = BN_CTX_get(ctx);
1096 tmp2 = BN_CTX_get(ctx);
1097 Za23 = BN_CTX_get(ctx);
1098 Zb23 = BN_CTX_get(ctx);
1099 if (Zb23 == NULL)
1100 goto end;
1101
1102 /*-
1103 * We have to decide whether
1104 * (X_a/Z_a^2, Y_a/Z_a^3) = (X_b/Z_b^2, Y_b/Z_b^3),
1105 * or equivalently, whether
1106 * (X_a*Z_b^2, Y_a*Z_b^3) = (X_b*Z_a^2, Y_b*Z_a^3).
1107 */
1108
1109 if (!b->Z_is_one) {
1110 if (!field_sqr(group, Zb23, b->Z, ctx))
1111 goto end;
1112 if (!field_mul(group, tmp1, a->X, Zb23, ctx))
1113 goto end;
1114 tmp1_ = tmp1;
1115 } else
1116 tmp1_ = a->X;
1117 if (!a->Z_is_one) {
1118 if (!field_sqr(group, Za23, a->Z, ctx))
1119 goto end;
1120 if (!field_mul(group, tmp2, b->X, Za23, ctx))
1121 goto end;
1122 tmp2_ = tmp2;
1123 } else
1124 tmp2_ = b->X;
1125
1126 /* compare X_a*Z_b^2 with X_b*Z_a^2 */
1127 if (BN_cmp(tmp1_, tmp2_) != 0) {
1128 ret = 1; /* points differ */
1129 goto end;
1130 }
1131
1132 if (!b->Z_is_one) {
1133 if (!field_mul(group, Zb23, Zb23, b->Z, ctx))
1134 goto end;
1135 if (!field_mul(group, tmp1, a->Y, Zb23, ctx))
1136 goto end;
1137 /* tmp1_ = tmp1 */
1138 } else
1139 tmp1_ = a->Y;
1140 if (!a->Z_is_one) {
1141 if (!field_mul(group, Za23, Za23, a->Z, ctx))
1142 goto end;
1143 if (!field_mul(group, tmp2, b->Y, Za23, ctx))
1144 goto end;
1145 /* tmp2_ = tmp2 */
1146 } else
1147 tmp2_ = b->Y;
1148
1149 /* compare Y_a*Z_b^3 with Y_b*Z_a^3 */
1150 if (BN_cmp(tmp1_, tmp2_) != 0) {
1151 ret = 1; /* points differ */
1152 goto end;
1153 }
1154
1155 /* points are equal */
1156 ret = 0;
1157
1158 end:
1159 BN_CTX_end(ctx);
1160 BN_CTX_free(new_ctx);
1161 return ret;
1162}
1163
1164int ec_GFp_simple_make_affine(const EC_GROUP *group, EC_POINT *point,
1165 BN_CTX *ctx)
1166{
1167 BN_CTX *new_ctx = NULL;
1168 BIGNUM *x, *y;
1169 int ret = 0;
1170
1171 if (point->Z_is_one || EC_POINT_is_at_infinity(group, point))
1172 return 1;
1173
1174 if (ctx == NULL) {
1175 ctx = new_ctx = BN_CTX_new_ex(group->libctx);
1176 if (ctx == NULL)
1177 return 0;
1178 }
1179
1180 BN_CTX_start(ctx);
1181 x = BN_CTX_get(ctx);
1182 y = BN_CTX_get(ctx);
1183 if (y == NULL)
1184 goto err;
1185
1186 if (!EC_POINT_get_affine_coordinates(group, point, x, y, ctx))
1187 goto err;
1188 if (!EC_POINT_set_affine_coordinates(group, point, x, y, ctx))
1189 goto err;
1190 if (!point->Z_is_one) {
1191 ECerr(EC_F_EC_GFP_SIMPLE_MAKE_AFFINE, ERR_R_INTERNAL_ERROR);
1192 goto err;
1193 }
1194
1195 ret = 1;
1196
1197 err:
1198 BN_CTX_end(ctx);
1199 BN_CTX_free(new_ctx);
1200 return ret;
1201}
1202
1203int ec_GFp_simple_points_make_affine(const EC_GROUP *group, size_t num,
1204 EC_POINT *points[], BN_CTX *ctx)
1205{
1206 BN_CTX *new_ctx = NULL;
1207 BIGNUM *tmp, *tmp_Z;
1208 BIGNUM **prod_Z = NULL;
1209 size_t i;
1210 int ret = 0;
1211
1212 if (num == 0)
1213 return 1;
1214
1215 if (ctx == NULL) {
1216 ctx = new_ctx = BN_CTX_new_ex(group->libctx);
1217 if (ctx == NULL)
1218 return 0;
1219 }
1220
1221 BN_CTX_start(ctx);
1222 tmp = BN_CTX_get(ctx);
1223 tmp_Z = BN_CTX_get(ctx);
1224 if (tmp_Z == NULL)
1225 goto err;
1226
1227 prod_Z = OPENSSL_malloc(num * sizeof(prod_Z[0]));
1228 if (prod_Z == NULL)
1229 goto err;
1230 for (i = 0; i < num; i++) {
1231 prod_Z[i] = BN_new();
1232 if (prod_Z[i] == NULL)
1233 goto err;
1234 }
1235
1236 /*
1237 * Set each prod_Z[i] to the product of points[0]->Z .. points[i]->Z,
1238 * skipping any zero-valued inputs (pretend that they're 1).
1239 */
1240
1241 if (!BN_is_zero(points[0]->Z)) {
1242 if (!BN_copy(prod_Z[0], points[0]->Z))
1243 goto err;
1244 } else {
1245 if (group->meth->field_set_to_one != 0) {
1246 if (!group->meth->field_set_to_one(group, prod_Z[0], ctx))
1247 goto err;
1248 } else {
1249 if (!BN_one(prod_Z[0]))
1250 goto err;
1251 }
1252 }
1253
1254 for (i = 1; i < num; i++) {
1255 if (!BN_is_zero(points[i]->Z)) {
1256 if (!group->
1257 meth->field_mul(group, prod_Z[i], prod_Z[i - 1], points[i]->Z,
1258 ctx))
1259 goto err;
1260 } else {
1261 if (!BN_copy(prod_Z[i], prod_Z[i - 1]))
1262 goto err;
1263 }
1264 }
1265
1266 /*
1267 * Now use a single explicit inversion to replace every non-zero
1268 * points[i]->Z by its inverse.
1269 */
1270
1271 if (!group->meth->field_inv(group, tmp, prod_Z[num - 1], ctx)) {
1272 ECerr(EC_F_EC_GFP_SIMPLE_POINTS_MAKE_AFFINE, ERR_R_BN_LIB);
1273 goto err;
1274 }
1275 if (group->meth->field_encode != 0) {
1276 /*
1277 * In the Montgomery case, we just turned R*H (representing H) into
1278 * 1/(R*H), but we need R*(1/H) (representing 1/H); i.e. we need to
1279 * multiply by the Montgomery factor twice.
1280 */
1281 if (!group->meth->field_encode(group, tmp, tmp, ctx))
1282 goto err;
1283 if (!group->meth->field_encode(group, tmp, tmp, ctx))
1284 goto err;
1285 }
1286
1287 for (i = num - 1; i > 0; --i) {
1288 /*
1289 * Loop invariant: tmp is the product of the inverses of points[0]->Z
1290 * .. points[i]->Z (zero-valued inputs skipped).
1291 */
1292 if (!BN_is_zero(points[i]->Z)) {
1293 /*
1294 * Set tmp_Z to the inverse of points[i]->Z (as product of Z
1295 * inverses 0 .. i, Z values 0 .. i - 1).
1296 */
1297 if (!group->
1298 meth->field_mul(group, tmp_Z, prod_Z[i - 1], tmp, ctx))
1299 goto err;
1300 /*
1301 * Update tmp to satisfy the loop invariant for i - 1.
1302 */
1303 if (!group->meth->field_mul(group, tmp, tmp, points[i]->Z, ctx))
1304 goto err;
1305 /* Replace points[i]->Z by its inverse. */
1306 if (!BN_copy(points[i]->Z, tmp_Z))
1307 goto err;
1308 }
1309 }
1310
1311 if (!BN_is_zero(points[0]->Z)) {
1312 /* Replace points[0]->Z by its inverse. */
1313 if (!BN_copy(points[0]->Z, tmp))
1314 goto err;
1315 }
1316
1317 /* Finally, fix up the X and Y coordinates for all points. */
1318
1319 for (i = 0; i < num; i++) {
1320 EC_POINT *p = points[i];
1321
1322 if (!BN_is_zero(p->Z)) {
1323 /* turn (X, Y, 1/Z) into (X/Z^2, Y/Z^3, 1) */
1324
1325 if (!group->meth->field_sqr(group, tmp, p->Z, ctx))
1326 goto err;
1327 if (!group->meth->field_mul(group, p->X, p->X, tmp, ctx))
1328 goto err;
1329
1330 if (!group->meth->field_mul(group, tmp, tmp, p->Z, ctx))
1331 goto err;
1332 if (!group->meth->field_mul(group, p->Y, p->Y, tmp, ctx))
1333 goto err;
1334
1335 if (group->meth->field_set_to_one != 0) {
1336 if (!group->meth->field_set_to_one(group, p->Z, ctx))
1337 goto err;
1338 } else {
1339 if (!BN_one(p->Z))
1340 goto err;
1341 }
1342 p->Z_is_one = 1;
1343 }
1344 }
1345
1346 ret = 1;
1347
1348 err:
1349 BN_CTX_end(ctx);
1350 BN_CTX_free(new_ctx);
1351 if (prod_Z != NULL) {
1352 for (i = 0; i < num; i++) {
1353 if (prod_Z[i] == NULL)
1354 break;
1355 BN_clear_free(prod_Z[i]);
1356 }
1357 OPENSSL_free(prod_Z);
1358 }
1359 return ret;
1360}
1361
1362int ec_GFp_simple_field_mul(const EC_GROUP *group, BIGNUM *r, const BIGNUM *a,
1363 const BIGNUM *b, BN_CTX *ctx)
1364{
1365 return BN_mod_mul(r, a, b, group->field, ctx);
1366}
1367
1368int ec_GFp_simple_field_sqr(const EC_GROUP *group, BIGNUM *r, const BIGNUM *a,
1369 BN_CTX *ctx)
1370{
1371 return BN_mod_sqr(r, a, group->field, ctx);
1372}
1373
1374/*-
1375 * Computes the multiplicative inverse of a in GF(p), storing the result in r.
1376 * If a is zero (or equivalent), you'll get a EC_R_CANNOT_INVERT error.
1377 * Since we don't have a Mont structure here, SCA hardening is with blinding.
1378 */
1379int ec_GFp_simple_field_inv(const EC_GROUP *group, BIGNUM *r, const BIGNUM *a,
1380 BN_CTX *ctx)
1381{
1382 BIGNUM *e = NULL;
1383 BN_CTX *new_ctx = NULL;
1384 int ret = 0;
1385
1386 if (ctx == NULL
1387 && (ctx = new_ctx = BN_CTX_secure_new_ex(group->libctx)) == NULL)
1388 return 0;
1389
1390 BN_CTX_start(ctx);
1391 if ((e = BN_CTX_get(ctx)) == NULL)
1392 goto err;
1393
1394 do {
1395 if (!BN_priv_rand_range_ex(e, group->field, ctx))
1396 goto err;
1397 } while (BN_is_zero(e));
1398
1399 /* r := a * e */
1400 if (!group->meth->field_mul(group, r, a, e, ctx))
1401 goto err;
1402 /* r := 1/(a * e) */
1403 if (!BN_mod_inverse(r, r, group->field, ctx)) {
1404 ECerr(EC_F_EC_GFP_SIMPLE_FIELD_INV, EC_R_CANNOT_INVERT);
1405 goto err;
1406 }
1407 /* r := e/(a * e) = 1/a */
1408 if (!group->meth->field_mul(group, r, r, e, ctx))
1409 goto err;
1410
1411 ret = 1;
1412
1413 err:
1414 BN_CTX_end(ctx);
1415 BN_CTX_free(new_ctx);
1416 return ret;
1417}
1418
1419/*-
1420 * Apply randomization of EC point projective coordinates:
1421 *
1422 * (X, Y ,Z ) = (lambda^2*X, lambda^3*Y, lambda*Z)
1423 * lambda = [1,group->field)
1424 *
1425 */
1426int ec_GFp_simple_blind_coordinates(const EC_GROUP *group, EC_POINT *p,
1427 BN_CTX *ctx)
1428{
1429 int ret = 0;
1430 BIGNUM *lambda = NULL;
1431 BIGNUM *temp = NULL;
1432
1433 BN_CTX_start(ctx);
1434 lambda = BN_CTX_get(ctx);
1435 temp = BN_CTX_get(ctx);
1436 if (temp == NULL) {
1437 ECerr(EC_F_EC_GFP_SIMPLE_BLIND_COORDINATES, ERR_R_MALLOC_FAILURE);
1438 goto err;
1439 }
1440
1441 /* make sure lambda is not zero */
1442 do {
1443 if (!BN_priv_rand_range_ex(lambda, group->field, ctx)) {
1444 ECerr(EC_F_EC_GFP_SIMPLE_BLIND_COORDINATES, ERR_R_BN_LIB);
1445 goto err;
1446 }
1447 } while (BN_is_zero(lambda));
1448
1449 /* if field_encode defined convert between representations */
1450 if (group->meth->field_encode != NULL
1451 && !group->meth->field_encode(group, lambda, lambda, ctx))
1452 goto err;
1453 if (!group->meth->field_mul(group, p->Z, p->Z, lambda, ctx))
1454 goto err;
1455 if (!group->meth->field_sqr(group, temp, lambda, ctx))
1456 goto err;
1457 if (!group->meth->field_mul(group, p->X, p->X, temp, ctx))
1458 goto err;
1459 if (!group->meth->field_mul(group, temp, temp, lambda, ctx))
1460 goto err;
1461 if (!group->meth->field_mul(group, p->Y, p->Y, temp, ctx))
1462 goto err;
1463 p->Z_is_one = 0;
1464
1465 ret = 1;
1466
1467 err:
1468 BN_CTX_end(ctx);
1469 return ret;
1470}
1471
1472/*-
1473 * Set s := p, r := 2p.
1474 *
1475 * For doubling we use Formula 3 from Izu-Takagi "A fast parallel elliptic curve
1476 * multiplication resistant against side channel attacks" appendix, as described
1477 * at
1478 * https://hyperelliptic.org/EFD/g1p/auto-shortw-xz.html#doubling-dbl-2002-it-2
1479 *
1480 * The input point p will be in randomized Jacobian projective coords:
1481 * x = X/Z**2, y=Y/Z**3
1482 *
1483 * The output points p, s, and r are converted to standard (homogeneous)
1484 * projective coords:
1485 * x = X/Z, y=Y/Z
1486 */
1487int ec_GFp_simple_ladder_pre(const EC_GROUP *group,
1488 EC_POINT *r, EC_POINT *s,
1489 EC_POINT *p, BN_CTX *ctx)
1490{
1491 BIGNUM *t1, *t2, *t3, *t4, *t5, *t6 = NULL;
1492
1493 t1 = r->Z;
1494 t2 = r->Y;
1495 t3 = s->X;
1496 t4 = r->X;
1497 t5 = s->Y;
1498 t6 = s->Z;
1499
1500 /* convert p: (X,Y,Z) -> (XZ,Y,Z**3) */
1501 if (!group->meth->field_mul(group, p->X, p->X, p->Z, ctx)
1502 || !group->meth->field_sqr(group, t1, p->Z, ctx)
1503 || !group->meth->field_mul(group, p->Z, p->Z, t1, ctx)
1504 /* r := 2p */
1505 || !group->meth->field_sqr(group, t2, p->X, ctx)
1506 || !group->meth->field_sqr(group, t3, p->Z, ctx)
1507 || !group->meth->field_mul(group, t4, t3, group->a, ctx)
1508 || !BN_mod_sub_quick(t5, t2, t4, group->field)
1509 || !BN_mod_add_quick(t2, t2, t4, group->field)
1510 || !group->meth->field_sqr(group, t5, t5, ctx)
1511 || !group->meth->field_mul(group, t6, t3, group->b, ctx)
1512 || !group->meth->field_mul(group, t1, p->X, p->Z, ctx)
1513 || !group->meth->field_mul(group, t4, t1, t6, ctx)
1514 || !BN_mod_lshift_quick(t4, t4, 3, group->field)
1515 /* r->X coord output */
1516 || !BN_mod_sub_quick(r->X, t5, t4, group->field)
1517 || !group->meth->field_mul(group, t1, t1, t2, ctx)
1518 || !group->meth->field_mul(group, t2, t3, t6, ctx)
1519 || !BN_mod_add_quick(t1, t1, t2, group->field)
1520 /* r->Z coord output */
1521 || !BN_mod_lshift_quick(r->Z, t1, 2, group->field)
1522 || !EC_POINT_copy(s, p))
1523 return 0;
1524
1525 r->Z_is_one = 0;
1526 s->Z_is_one = 0;
1527 p->Z_is_one = 0;
1528
1529 return 1;
1530}
1531
1532/*-
1533 * Differential addition-and-doubling using Eq. (9) and (10) from Izu-Takagi
1534 * "A fast parallel elliptic curve multiplication resistant against side channel
1535 * attacks", as described at
1536 * https://hyperelliptic.org/EFD/g1p/auto-shortw-xz.html#ladder-ladd-2002-it-4
1537 */
1538int ec_GFp_simple_ladder_step(const EC_GROUP *group,
1539 EC_POINT *r, EC_POINT *s,
1540 EC_POINT *p, BN_CTX *ctx)
1541{
1542 int ret = 0;
1543 BIGNUM *t0, *t1, *t2, *t3, *t4, *t5, *t6, *t7 = NULL;
1544
1545 BN_CTX_start(ctx);
1546 t0 = BN_CTX_get(ctx);
1547 t1 = BN_CTX_get(ctx);
1548 t2 = BN_CTX_get(ctx);
1549 t3 = BN_CTX_get(ctx);
1550 t4 = BN_CTX_get(ctx);
1551 t5 = BN_CTX_get(ctx);
1552 t6 = BN_CTX_get(ctx);
1553 t7 = BN_CTX_get(ctx);
1554
1555 if (t7 == NULL
1556 || !group->meth->field_mul(group, t0, r->X, s->X, ctx)
1557 || !group->meth->field_mul(group, t1, r->Z, s->Z, ctx)
1558 || !group->meth->field_mul(group, t2, r->X, s->Z, ctx)
1559 || !group->meth->field_mul(group, t3, r->Z, s->X, ctx)
1560 || !group->meth->field_mul(group, t4, group->a, t1, ctx)
1561 || !BN_mod_add_quick(t0, t0, t4, group->field)
1562 || !BN_mod_add_quick(t4, t3, t2, group->field)
1563 || !group->meth->field_mul(group, t0, t4, t0, ctx)
1564 || !group->meth->field_sqr(group, t1, t1, ctx)
1565 || !BN_mod_lshift_quick(t7, group->b, 2, group->field)
1566 || !group->meth->field_mul(group, t1, t7, t1, ctx)
1567 || !BN_mod_lshift1_quick(t0, t0, group->field)
1568 || !BN_mod_add_quick(t0, t1, t0, group->field)
1569 || !BN_mod_sub_quick(t1, t2, t3, group->field)
1570 || !group->meth->field_sqr(group, t1, t1, ctx)
1571 || !group->meth->field_mul(group, t3, t1, p->X, ctx)
1572 || !group->meth->field_mul(group, t0, p->Z, t0, ctx)
1573 /* s->X coord output */
1574 || !BN_mod_sub_quick(s->X, t0, t3, group->field)
1575 /* s->Z coord output */
1576 || !group->meth->field_mul(group, s->Z, p->Z, t1, ctx)
1577 || !group->meth->field_sqr(group, t3, r->X, ctx)
1578 || !group->meth->field_sqr(group, t2, r->Z, ctx)
1579 || !group->meth->field_mul(group, t4, t2, group->a, ctx)
1580 || !BN_mod_add_quick(t5, r->X, r->Z, group->field)
1581 || !group->meth->field_sqr(group, t5, t5, ctx)
1582 || !BN_mod_sub_quick(t5, t5, t3, group->field)
1583 || !BN_mod_sub_quick(t5, t5, t2, group->field)
1584 || !BN_mod_sub_quick(t6, t3, t4, group->field)
1585 || !group->meth->field_sqr(group, t6, t6, ctx)
1586 || !group->meth->field_mul(group, t0, t2, t5, ctx)
1587 || !group->meth->field_mul(group, t0, t7, t0, ctx)
1588 /* r->X coord output */
1589 || !BN_mod_sub_quick(r->X, t6, t0, group->field)
1590 || !BN_mod_add_quick(t6, t3, t4, group->field)
1591 || !group->meth->field_sqr(group, t3, t2, ctx)
1592 || !group->meth->field_mul(group, t7, t3, t7, ctx)
1593 || !group->meth->field_mul(group, t5, t5, t6, ctx)
1594 || !BN_mod_lshift1_quick(t5, t5, group->field)
1595 /* r->Z coord output */
1596 || !BN_mod_add_quick(r->Z, t7, t5, group->field))
1597 goto err;
1598
1599 ret = 1;
1600
1601 err:
1602 BN_CTX_end(ctx);
1603 return ret;
1604}
1605
1606/*-
1607 * Recovers the y-coordinate of r using Eq. (8) from Brier-Joye, "Weierstrass
1608 * Elliptic Curves and Side-Channel Attacks", modified to work in projective
1609 * coordinates and return r in Jacobian projective coordinates.
1610 *
1611 * X4 = two*Y1*X2*Z3*Z2*Z1;
1612 * Y4 = two*b*Z3*SQR(Z2*Z1) + Z3*(a*Z2*Z1+X1*X2)*(X1*Z2+X2*Z1) - X3*SQR(X1*Z2-X2*Z1);
1613 * Z4 = two*Y1*Z3*SQR(Z2)*Z1;
1614 *
1615 * Z4 != 0 because:
1616 * - Z1==0 implies p is at infinity, which would have caused an early exit in
1617 * the caller;
1618 * - Z2==0 implies r is at infinity (handled by the BN_is_zero(r->Z) branch);
1619 * - Z3==0 implies s is at infinity (handled by the BN_is_zero(s->Z) branch);
1620 * - Y1==0 implies p has order 2, so either r or s are infinity and handled by
1621 * one of the BN_is_zero(...) branches.
1622 */
1623int ec_GFp_simple_ladder_post(const EC_GROUP *group,
1624 EC_POINT *r, EC_POINT *s,
1625 EC_POINT *p, BN_CTX *ctx)
1626{
1627 int ret = 0;
1628 BIGNUM *t0, *t1, *t2, *t3, *t4, *t5, *t6 = NULL;
1629
1630 if (BN_is_zero(r->Z))
1631 return EC_POINT_set_to_infinity(group, r);
1632
1633 if (BN_is_zero(s->Z)) {
1634 /* (X,Y,Z) -> (XZ,YZ**2,Z) */
1635 if (!group->meth->field_mul(group, r->X, p->X, p->Z, ctx)
1636 || !group->meth->field_sqr(group, r->Z, p->Z, ctx)
1637 || !group->meth->field_mul(group, r->Y, p->Y, r->Z, ctx)
1638 || !BN_copy(r->Z, p->Z)
1639 || !EC_POINT_invert(group, r, ctx))
1640 return 0;
1641 return 1;
1642 }
1643
1644 BN_CTX_start(ctx);
1645 t0 = BN_CTX_get(ctx);
1646 t1 = BN_CTX_get(ctx);
1647 t2 = BN_CTX_get(ctx);
1648 t3 = BN_CTX_get(ctx);
1649 t4 = BN_CTX_get(ctx);
1650 t5 = BN_CTX_get(ctx);
1651 t6 = BN_CTX_get(ctx);
1652
1653 if (t6 == NULL
1654 || !BN_mod_lshift1_quick(t0, p->Y, group->field)
1655 || !group->meth->field_mul(group, t1, r->X, p->Z, ctx)
1656 || !group->meth->field_mul(group, t2, r->Z, s->Z, ctx)
1657 || !group->meth->field_mul(group, t2, t1, t2, ctx)
1658 || !group->meth->field_mul(group, t3, t2, t0, ctx)
1659 || !group->meth->field_mul(group, t2, r->Z, p->Z, ctx)
1660 || !group->meth->field_sqr(group, t4, t2, ctx)
1661 || !BN_mod_lshift1_quick(t5, group->b, group->field)
1662 || !group->meth->field_mul(group, t4, t4, t5, ctx)
1663 || !group->meth->field_mul(group, t6, t2, group->a, ctx)
1664 || !group->meth->field_mul(group, t5, r->X, p->X, ctx)
1665 || !BN_mod_add_quick(t5, t6, t5, group->field)
1666 || !group->meth->field_mul(group, t6, r->Z, p->X, ctx)
1667 || !BN_mod_add_quick(t2, t6, t1, group->field)
1668 || !group->meth->field_mul(group, t5, t5, t2, ctx)
1669 || !BN_mod_sub_quick(t6, t6, t1, group->field)
1670 || !group->meth->field_sqr(group, t6, t6, ctx)
1671 || !group->meth->field_mul(group, t6, t6, s->X, ctx)
1672 || !BN_mod_add_quick(t4, t5, t4, group->field)
1673 || !group->meth->field_mul(group, t4, t4, s->Z, ctx)
1674 || !BN_mod_sub_quick(t4, t4, t6, group->field)
1675 || !group->meth->field_sqr(group, t5, r->Z, ctx)
1676 || !group->meth->field_mul(group, r->Z, p->Z, s->Z, ctx)
1677 || !group->meth->field_mul(group, r->Z, t5, r->Z, ctx)
1678 || !group->meth->field_mul(group, r->Z, r->Z, t0, ctx)
1679 /* t3 := X, t4 := Y */
1680 /* (X,Y,Z) -> (XZ,YZ**2,Z) */
1681 || !group->meth->field_mul(group, r->X, t3, r->Z, ctx)
1682 || !group->meth->field_sqr(group, t3, r->Z, ctx)
1683 || !group->meth->field_mul(group, r->Y, t4, t3, ctx))
1684 goto err;
1685
1686 ret = 1;
1687
1688 err:
1689 BN_CTX_end(ctx);
1690 return ret;
1691}
1692