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source: vbox/trunk/src/libs/openssl-3.1.3/crypto/ec/ecp_smpl.c@ 101665

Last change on this file since 101665 was 101211, checked in by vboxsync, 14 months ago

openssl-3.1.3: Applied and adjusted our OpenSSL changes to 3.1.2. bugref:10527
File size: 48.9 KB
Line 
1/*
2 * Copyright 2001-2022 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/*
12 * ECDSA low-level APIs are deprecated for public use, but still ok for
13 * internal use.
14 */
15#include "internal/deprecated.h"
16
17#include <openssl/err.h>
18#include <openssl/symhacks.h>
19
20#include "ec_local.h"
21
22const EC_METHOD *EC_GFp_simple_method(void)
23{
24 static const EC_METHOD ret = {
25 EC_FLAGS_DEFAULT_OCT,
26 NID_X9_62_prime_field,
27 ossl_ec_GFp_simple_group_init,
28 ossl_ec_GFp_simple_group_finish,
29 ossl_ec_GFp_simple_group_clear_finish,
30 ossl_ec_GFp_simple_group_copy,
31 ossl_ec_GFp_simple_group_set_curve,
32 ossl_ec_GFp_simple_group_get_curve,
33 ossl_ec_GFp_simple_group_get_degree,
34 ossl_ec_group_simple_order_bits,
35 ossl_ec_GFp_simple_group_check_discriminant,
36 ossl_ec_GFp_simple_point_init,
37 ossl_ec_GFp_simple_point_finish,
38 ossl_ec_GFp_simple_point_clear_finish,
39 ossl_ec_GFp_simple_point_copy,
40 ossl_ec_GFp_simple_point_set_to_infinity,
41 ossl_ec_GFp_simple_point_set_affine_coordinates,
42 ossl_ec_GFp_simple_point_get_affine_coordinates,
43 0, 0, 0,
44 ossl_ec_GFp_simple_add,
45 ossl_ec_GFp_simple_dbl,
46 ossl_ec_GFp_simple_invert,
47 ossl_ec_GFp_simple_is_at_infinity,
48 ossl_ec_GFp_simple_is_on_curve,
49 ossl_ec_GFp_simple_cmp,
50 ossl_ec_GFp_simple_make_affine,
51 ossl_ec_GFp_simple_points_make_affine,
52 0 /* mul */ ,
53 0 /* precompute_mult */ ,
54 0 /* have_precompute_mult */ ,
55 ossl_ec_GFp_simple_field_mul,
56 ossl_ec_GFp_simple_field_sqr,
57 0 /* field_div */ ,
58 ossl_ec_GFp_simple_field_inv,
59 0 /* field_encode */ ,
60 0 /* field_decode */ ,
61 0, /* field_set_to_one */
62 ossl_ec_key_simple_priv2oct,
63 ossl_ec_key_simple_oct2priv,
64 0, /* set private */
65 ossl_ec_key_simple_generate_key,
66 ossl_ec_key_simple_check_key,
67 ossl_ec_key_simple_generate_public_key,
68 0, /* keycopy */
69 0, /* keyfinish */
70 ossl_ecdh_simple_compute_key,
71 ossl_ecdsa_simple_sign_setup,
72 ossl_ecdsa_simple_sign_sig,
73 ossl_ecdsa_simple_verify_sig,
74 0, /* field_inverse_mod_ord */
75 ossl_ec_GFp_simple_blind_coordinates,
76 ossl_ec_GFp_simple_ladder_pre,
77 ossl_ec_GFp_simple_ladder_step,
78 ossl_ec_GFp_simple_ladder_post
79 };
80
81 return &ret;
82}
83
84/*
85 * Most method functions in this file are designed to work with
86 * non-trivial representations of field elements if necessary
87 * (see ecp_mont.c): while standard modular addition and subtraction
88 * are used, the field_mul and field_sqr methods will be used for
89 * multiplication, and field_encode and field_decode (if defined)
90 * will be used for converting between representations.
91 *
92 * Functions ec_GFp_simple_points_make_affine() and
93 * ec_GFp_simple_point_get_affine_coordinates() specifically assume
94 * that if a non-trivial representation is used, it is a Montgomery
95 * representation (i.e. 'encoding' means multiplying by some factor R).
96 */
97
98int ossl_ec_GFp_simple_group_init(EC_GROUP *group)
99{
100 group->field = BN_new();
101 group->a = BN_new();
102 group->b = BN_new();
103 if (group->field == NULL || group->a == NULL || group->b == NULL) {
104 BN_free(group->field);
105 BN_free(group->a);
106 BN_free(group->b);
107 return 0;
108 }
109 group->a_is_minus3 = 0;
110 return 1;
111}
112
113void ossl_ec_GFp_simple_group_finish(EC_GROUP *group)
114{
115 BN_free(group->field);
116 BN_free(group->a);
117 BN_free(group->b);
118}
119
120void ossl_ec_GFp_simple_group_clear_finish(EC_GROUP *group)
121{
122 BN_clear_free(group->field);
123 BN_clear_free(group->a);
124 BN_clear_free(group->b);
125}
126
127int ossl_ec_GFp_simple_group_copy(EC_GROUP *dest, const EC_GROUP *src)
128{
129 if (!BN_copy(dest->field, src->field))
130 return 0;
131 if (!BN_copy(dest->a, src->a))
132 return 0;
133 if (!BN_copy(dest->b, src->b))
134 return 0;
135
136 dest->a_is_minus3 = src->a_is_minus3;
137
138 return 1;
139}
140
141int ossl_ec_GFp_simple_group_set_curve(EC_GROUP *group,
142 const BIGNUM *p, const BIGNUM *a,
143 const BIGNUM *b, BN_CTX *ctx)
144{
145 int ret = 0;
146 BN_CTX *new_ctx = NULL;
147 BIGNUM *tmp_a;
148
149 /* p must be a prime > 3 */
150 if (BN_num_bits(p) <= 2 || !BN_is_odd(p)) {
151 ERR_raise(ERR_LIB_EC, EC_R_INVALID_FIELD);
152 return 0;
153 }
154
155 if (ctx == NULL) {
156 ctx = new_ctx = BN_CTX_new_ex(group->libctx);
157 if (ctx == NULL)
158 return 0;
159 }
160
161 BN_CTX_start(ctx);
162 tmp_a = BN_CTX_get(ctx);
163 if (tmp_a == NULL)
164 goto err;
165
166 /* group->field */
167 if (!BN_copy(group->field, p))
168 goto err;
169 BN_set_negative(group->field, 0);
170
171 /* group->a */
172 if (!BN_nnmod(tmp_a, a, p, ctx))
173 goto err;
174 if (group->meth->field_encode != NULL) {
175 if (!group->meth->field_encode(group, group->a, tmp_a, ctx))
176 goto err;
177 } else if (!BN_copy(group->a, tmp_a))
178 goto err;
179
180 /* group->b */
181 if (!BN_nnmod(group->b, b, p, ctx))
182 goto err;
183 if (group->meth->field_encode != NULL)
184 if (!group->meth->field_encode(group, group->b, group->b, ctx))
185 goto err;
186
187 /* group->a_is_minus3 */
188 if (!BN_add_word(tmp_a, 3))
189 goto err;
190 group->a_is_minus3 = (0 == BN_cmp(tmp_a, group->field));
191
192 ret = 1;
193
194 err:
195 BN_CTX_end(ctx);
196 BN_CTX_free(new_ctx);
197 return ret;
198}
199
200int ossl_ec_GFp_simple_group_get_curve(const EC_GROUP *group, BIGNUM *p,
201 BIGNUM *a, BIGNUM *b, BN_CTX *ctx)
202{
203 int ret = 0;
204 BN_CTX *new_ctx = NULL;
205
206 if (p != NULL) {
207 if (!BN_copy(p, group->field))
208 return 0;
209 }
210
211 if (a != NULL || b != NULL) {
212 if (group->meth->field_decode != NULL) {
213 if (ctx == NULL) {
214 ctx = new_ctx = BN_CTX_new_ex(group->libctx);
215 if (ctx == NULL)
216 return 0;
217 }
218 if (a != NULL) {
219 if (!group->meth->field_decode(group, a, group->a, ctx))
220 goto err;
221 }
222 if (b != NULL) {
223 if (!group->meth->field_decode(group, b, group->b, ctx))
224 goto err;
225 }
226 } else {
227 if (a != NULL) {
228 if (!BN_copy(a, group->a))
229 goto err;
230 }
231 if (b != NULL) {
232 if (!BN_copy(b, group->b))
233 goto err;
234 }
235 }
236 }
237
238 ret = 1;
239
240 err:
241 BN_CTX_free(new_ctx);
242 return ret;
243}
244
245int ossl_ec_GFp_simple_group_get_degree(const EC_GROUP *group)
246{
247 return BN_num_bits(group->field);
248}
249
250int ossl_ec_GFp_simple_group_check_discriminant(const EC_GROUP *group,
251 BN_CTX *ctx)
252{
253 int ret = 0;
254 BIGNUM *a, *b, *order, *tmp_1, *tmp_2;
255 const BIGNUM *p = group->field;
256 BN_CTX *new_ctx = NULL;
257
258 if (ctx == NULL) {
259 ctx = new_ctx = BN_CTX_new_ex(group->libctx);
260 if (ctx == NULL) {
261 ERR_raise(ERR_LIB_EC, ERR_R_MALLOC_FAILURE);
262 goto err;
263 }
264 }
265 BN_CTX_start(ctx);
266 a = BN_CTX_get(ctx);
267 b = BN_CTX_get(ctx);
268 tmp_1 = BN_CTX_get(ctx);
269 tmp_2 = BN_CTX_get(ctx);
270 order = BN_CTX_get(ctx);
271 if (order == NULL)
272 goto err;
273
274 if (group->meth->field_decode != NULL) {
275 if (!group->meth->field_decode(group, a, group->a, ctx))
276 goto err;
277 if (!group->meth->field_decode(group, b, group->b, ctx))
278 goto err;
279 } else {
280 if (!BN_copy(a, group->a))
281 goto err;
282 if (!BN_copy(b, group->b))
283 goto err;
284 }
285
286 /*-
287 * check the discriminant:
288 * y^2 = x^3 + a*x + b is an elliptic curve <=> 4*a^3 + 27*b^2 != 0 (mod p)
289 * 0 =< a, b < p
290 */
291 if (BN_is_zero(a)) {
292 if (BN_is_zero(b))
293 goto err;
294 } else if (!BN_is_zero(b)) {
295 if (!BN_mod_sqr(tmp_1, a, p, ctx))
296 goto err;
297 if (!BN_mod_mul(tmp_2, tmp_1, a, p, ctx))
298 goto err;
299 if (!BN_lshift(tmp_1, tmp_2, 2))
300 goto err;
301 /* tmp_1 = 4*a^3 */
302
303 if (!BN_mod_sqr(tmp_2, b, p, ctx))
304 goto err;
305 if (!BN_mul_word(tmp_2, 27))
306 goto err;
307 /* tmp_2 = 27*b^2 */
308
309 if (!BN_mod_add(a, tmp_1, tmp_2, p, ctx))
310 goto err;
311 if (BN_is_zero(a))
312 goto err;
313 }
314 ret = 1;
315
316 err:
317 BN_CTX_end(ctx);
318 BN_CTX_free(new_ctx);
319 return ret;
320}
321
322int ossl_ec_GFp_simple_point_init(EC_POINT *point)
323{
324 point->X = BN_new();
325 point->Y = BN_new();
326 point->Z = BN_new();
327 point->Z_is_one = 0;
328
329 if (point->X == NULL || point->Y == NULL || point->Z == NULL) {
330 BN_free(point->X);
331 BN_free(point->Y);
332 BN_free(point->Z);
333 return 0;
334 }
335 return 1;
336}
337
338void ossl_ec_GFp_simple_point_finish(EC_POINT *point)
339{
340 BN_free(point->X);
341 BN_free(point->Y);
342 BN_free(point->Z);
343}
344
345void ossl_ec_GFp_simple_point_clear_finish(EC_POINT *point)
346{
347 BN_clear_free(point->X);
348 BN_clear_free(point->Y);
349 BN_clear_free(point->Z);
350 point->Z_is_one = 0;
351}
352
353int ossl_ec_GFp_simple_point_copy(EC_POINT *dest, const EC_POINT *src)
354{
355 if (!BN_copy(dest->X, src->X))
356 return 0;
357 if (!BN_copy(dest->Y, src->Y))
358 return 0;
359 if (!BN_copy(dest->Z, src->Z))
360 return 0;
361 dest->Z_is_one = src->Z_is_one;
362 dest->curve_name = src->curve_name;
363
364 return 1;
365}
366
367int ossl_ec_GFp_simple_point_set_to_infinity(const EC_GROUP *group,
368 EC_POINT *point)
369{
370 point->Z_is_one = 0;
371 BN_zero(point->Z);
372 return 1;
373}
374
375int ossl_ec_GFp_simple_set_Jprojective_coordinates_GFp(const EC_GROUP *group,
376 EC_POINT *point,
377 const BIGNUM *x,
378 const BIGNUM *y,
379 const BIGNUM *z,
380 BN_CTX *ctx)
381{
382 BN_CTX *new_ctx = NULL;
383 int ret = 0;
384
385 if (ctx == NULL) {
386 ctx = new_ctx = BN_CTX_new_ex(group->libctx);
387 if (ctx == NULL)
388 return 0;
389 }
390
391 if (x != NULL) {
392 if (!BN_nnmod(point->X, x, group->field, ctx))
393 goto err;
394 if (group->meth->field_encode) {
395 if (!group->meth->field_encode(group, point->X, point->X, ctx))
396 goto err;
397 }
398 }
399
400 if (y != NULL) {
401 if (!BN_nnmod(point->Y, y, group->field, ctx))
402 goto err;
403 if (group->meth->field_encode) {
404 if (!group->meth->field_encode(group, point->Y, point->Y, ctx))
405 goto err;
406 }
407 }
408
409 if (z != NULL) {
410 int Z_is_one;
411
412 if (!BN_nnmod(point->Z, z, group->field, ctx))
413 goto err;
414 Z_is_one = BN_is_one(point->Z);
415 if (group->meth->field_encode) {
416 if (Z_is_one && (group->meth->field_set_to_one != 0)) {
417 if (!group->meth->field_set_to_one(group, point->Z, ctx))
418 goto err;
419 } else {
420 if (!group->
421 meth->field_encode(group, point->Z, point->Z, ctx))
422 goto err;
423 }
424 }
425 point->Z_is_one = Z_is_one;
426 }
427
428 ret = 1;
429
430 err:
431 BN_CTX_free(new_ctx);
432 return ret;
433}
434
435int ossl_ec_GFp_simple_get_Jprojective_coordinates_GFp(const EC_GROUP *group,
436 const EC_POINT *point,
437 BIGNUM *x, BIGNUM *y,
438 BIGNUM *z, BN_CTX *ctx)
439{
440 BN_CTX *new_ctx = NULL;
441 int ret = 0;
442
443 if (group->meth->field_decode != NULL) {
444 if (ctx == NULL) {
445 ctx = new_ctx = BN_CTX_new_ex(group->libctx);
446 if (ctx == NULL)
447 return 0;
448 }
449
450 if (x != NULL) {
451 if (!group->meth->field_decode(group, x, point->X, ctx))
452 goto err;
453 }
454 if (y != NULL) {
455 if (!group->meth->field_decode(group, y, point->Y, ctx))
456 goto err;
457 }
458 if (z != NULL) {
459 if (!group->meth->field_decode(group, z, point->Z, ctx))
460 goto err;
461 }
462 } else {
463 if (x != NULL) {
464 if (!BN_copy(x, point->X))
465 goto err;
466 }
467 if (y != NULL) {
468 if (!BN_copy(y, point->Y))
469 goto err;
470 }
471 if (z != NULL) {
472 if (!BN_copy(z, point->Z))
473 goto err;
474 }
475 }
476
477 ret = 1;
478
479 err:
480 BN_CTX_free(new_ctx);
481 return ret;
482}
483
484int ossl_ec_GFp_simple_point_set_affine_coordinates(const EC_GROUP *group,
485 EC_POINT *point,
486 const BIGNUM *x,
487 const BIGNUM *y, BN_CTX *ctx)
488{
489 if (x == NULL || y == NULL) {
490 /*
491 * unlike for projective coordinates, we do not tolerate this
492 */
493 ERR_raise(ERR_LIB_EC, ERR_R_PASSED_NULL_PARAMETER);
494 return 0;
495 }
496
497 return EC_POINT_set_Jprojective_coordinates_GFp(group, point, x, y,
498 BN_value_one(), ctx);
499}
500
501int ossl_ec_GFp_simple_point_get_affine_coordinates(const EC_GROUP *group,
502 const EC_POINT *point,
503 BIGNUM *x, BIGNUM *y,
504 BN_CTX *ctx)
505{
506 BN_CTX *new_ctx = NULL;
507 BIGNUM *Z, *Z_1, *Z_2, *Z_3;
508 const BIGNUM *Z_;
509 int ret = 0;
510
511 if (EC_POINT_is_at_infinity(group, point)) {
512 ERR_raise(ERR_LIB_EC, EC_R_POINT_AT_INFINITY);
513 return 0;
514 }
515
516 if (ctx == NULL) {
517 ctx = new_ctx = BN_CTX_new_ex(group->libctx);
518 if (ctx == NULL)
519 return 0;
520 }
521
522 BN_CTX_start(ctx);
523 Z = BN_CTX_get(ctx);
524 Z_1 = BN_CTX_get(ctx);
525 Z_2 = BN_CTX_get(ctx);
526 Z_3 = BN_CTX_get(ctx);
527 if (Z_3 == NULL)
528 goto err;
529
530 /* transform (X, Y, Z) into (x, y) := (X/Z^2, Y/Z^3) */
531
532 if (group->meth->field_decode != NULL) {
533 if (!group->meth->field_decode(group, Z, point->Z, ctx))
534 goto err;
535 Z_ = Z;
536 } else {
537 Z_ = point->Z;
538 }
539
540 if (BN_is_one(Z_)) {
541 if (group->meth->field_decode != NULL) {
542 if (x != NULL) {
543 if (!group->meth->field_decode(group, x, point->X, ctx))
544 goto err;
545 }
546 if (y != NULL) {
547 if (!group->meth->field_decode(group, y, point->Y, ctx))
548 goto err;
549 }
550 } else {
551 if (x != NULL) {
552 if (!BN_copy(x, point->X))
553 goto err;
554 }
555 if (y != NULL) {
556 if (!BN_copy(y, point->Y))
557 goto err;
558 }
559 }
560 } else {
561 if (!group->meth->field_inv(group, Z_1, Z_, ctx)) {
562 ERR_raise(ERR_LIB_EC, ERR_R_BN_LIB);
563 goto err;
564 }
565
566 if (group->meth->field_encode == NULL) {
567 /* field_sqr works on standard representation */
568 if (!group->meth->field_sqr(group, Z_2, Z_1, ctx))
569 goto err;
570 } else {
571 if (!BN_mod_sqr(Z_2, Z_1, group->field, ctx))
572 goto err;
573 }
574
575 if (x != NULL) {
576 /*
577 * in the Montgomery case, field_mul will cancel out Montgomery
578 * factor in X:
579 */
580 if (!group->meth->field_mul(group, x, point->X, Z_2, ctx))
581 goto err;
582 }
583
584 if (y != NULL) {
585 if (group->meth->field_encode == NULL) {
586 /*
587 * field_mul works on standard representation
588 */
589 if (!group->meth->field_mul(group, Z_3, Z_2, Z_1, ctx))
590 goto err;
591 } else {
592 if (!BN_mod_mul(Z_3, Z_2, Z_1, group->field, ctx))
593 goto err;
594 }
595
596 /*
597 * in the Montgomery case, field_mul will cancel out Montgomery
598 * factor in Y:
599 */
600 if (!group->meth->field_mul(group, y, point->Y, Z_3, ctx))
601 goto err;
602 }
603 }
604
605 ret = 1;
606
607 err:
608 BN_CTX_end(ctx);
609 BN_CTX_free(new_ctx);
610 return ret;
611}
612
613int ossl_ec_GFp_simple_add(const EC_GROUP *group, EC_POINT *r, const EC_POINT *a,
614 const EC_POINT *b, BN_CTX *ctx)
615{
616 int (*field_mul) (const EC_GROUP *, BIGNUM *, const BIGNUM *,
617 const BIGNUM *, BN_CTX *);
618 int (*field_sqr) (const EC_GROUP *, BIGNUM *, const BIGNUM *, BN_CTX *);
619 const BIGNUM *p;
620 BN_CTX *new_ctx = NULL;
621 BIGNUM *n0, *n1, *n2, *n3, *n4, *n5, *n6;
622 int ret = 0;
623
624 if (a == b)
625 return EC_POINT_dbl(group, r, a, ctx);
626 if (EC_POINT_is_at_infinity(group, a))
627 return EC_POINT_copy(r, b);
628 if (EC_POINT_is_at_infinity(group, b))
629 return EC_POINT_copy(r, a);
630
631 field_mul = group->meth->field_mul;
632 field_sqr = group->meth->field_sqr;
633 p = group->field;
634
635 if (ctx == NULL) {
636 ctx = new_ctx = BN_CTX_new_ex(group->libctx);
637 if (ctx == NULL)
638 return 0;
639 }
640
641 BN_CTX_start(ctx);
642 n0 = BN_CTX_get(ctx);
643 n1 = BN_CTX_get(ctx);
644 n2 = BN_CTX_get(ctx);
645 n3 = BN_CTX_get(ctx);
646 n4 = BN_CTX_get(ctx);
647 n5 = BN_CTX_get(ctx);
648 n6 = BN_CTX_get(ctx);
649 if (n6 == NULL)
650 goto end;
651
652 /*
653 * Note that in this function we must not read components of 'a' or 'b'
654 * once we have written the corresponding components of 'r'. ('r' might
655 * be one of 'a' or 'b'.)
656 */
657
658 /* n1, n2 */
659 if (b->Z_is_one) {
660 if (!BN_copy(n1, a->X))
661 goto end;
662 if (!BN_copy(n2, a->Y))
663 goto end;
664 /* n1 = X_a */
665 /* n2 = Y_a */
666 } else {
667 if (!field_sqr(group, n0, b->Z, ctx))
668 goto end;
669 if (!field_mul(group, n1, a->X, n0, ctx))
670 goto end;
671 /* n1 = X_a * Z_b^2 */
672
673 if (!field_mul(group, n0, n0, b->Z, ctx))
674 goto end;
675 if (!field_mul(group, n2, a->Y, n0, ctx))
676 goto end;
677 /* n2 = Y_a * Z_b^3 */
678 }
679
680 /* n3, n4 */
681 if (a->Z_is_one) {
682 if (!BN_copy(n3, b->X))
683 goto end;
684 if (!BN_copy(n4, b->Y))
685 goto end;
686 /* n3 = X_b */
687 /* n4 = Y_b */
688 } else {
689 if (!field_sqr(group, n0, a->Z, ctx))
690 goto end;
691 if (!field_mul(group, n3, b->X, n0, ctx))
692 goto end;
693 /* n3 = X_b * Z_a^2 */
694
695 if (!field_mul(group, n0, n0, a->Z, ctx))
696 goto end;
697 if (!field_mul(group, n4, b->Y, n0, ctx))
698 goto end;
699 /* n4 = Y_b * Z_a^3 */
700 }
701
702 /* n5, n6 */
703 if (!BN_mod_sub_quick(n5, n1, n3, p))
704 goto end;
705 if (!BN_mod_sub_quick(n6, n2, n4, p))
706 goto end;
707 /* n5 = n1 - n3 */
708 /* n6 = n2 - n4 */
709
710 if (BN_is_zero(n5)) {
711 if (BN_is_zero(n6)) {
712 /* a is the same point as b */
713 BN_CTX_end(ctx);
714 ret = EC_POINT_dbl(group, r, a, ctx);
715 ctx = NULL;
716 goto end;
717 } else {
718 /* a is the inverse of b */
719 BN_zero(r->Z);
720 r->Z_is_one = 0;
721 ret = 1;
722 goto end;
723 }
724 }
725
726 /* 'n7', 'n8' */
727 if (!BN_mod_add_quick(n1, n1, n3, p))
728 goto end;
729 if (!BN_mod_add_quick(n2, n2, n4, p))
730 goto end;
731 /* 'n7' = n1 + n3 */
732 /* 'n8' = n2 + n4 */
733
734 /* Z_r */
735 if (a->Z_is_one && b->Z_is_one) {
736 if (!BN_copy(r->Z, n5))
737 goto end;
738 } else {
739 if (a->Z_is_one) {
740 if (!BN_copy(n0, b->Z))
741 goto end;
742 } else if (b->Z_is_one) {
743 if (!BN_copy(n0, a->Z))
744 goto end;
745 } else {
746 if (!field_mul(group, n0, a->Z, b->Z, ctx))
747 goto end;
748 }
749 if (!field_mul(group, r->Z, n0, n5, ctx))
750 goto end;
751 }
752 r->Z_is_one = 0;
753 /* Z_r = Z_a * Z_b * n5 */
754
755 /* X_r */
756 if (!field_sqr(group, n0, n6, ctx))
757 goto end;
758 if (!field_sqr(group, n4, n5, ctx))
759 goto end;
760 if (!field_mul(group, n3, n1, n4, ctx))
761 goto end;
762 if (!BN_mod_sub_quick(r->X, n0, n3, p))
763 goto end;
764 /* X_r = n6^2 - n5^2 * 'n7' */
765
766 /* 'n9' */
767 if (!BN_mod_lshift1_quick(n0, r->X, p))
768 goto end;
769 if (!BN_mod_sub_quick(n0, n3, n0, p))
770 goto end;
771 /* n9 = n5^2 * 'n7' - 2 * X_r */
772
773 /* Y_r */
774 if (!field_mul(group, n0, n0, n6, ctx))
775 goto end;
776 if (!field_mul(group, n5, n4, n5, ctx))
777 goto end; /* now n5 is n5^3 */
778 if (!field_mul(group, n1, n2, n5, ctx))
779 goto end;
780 if (!BN_mod_sub_quick(n0, n0, n1, p))
781 goto end;
782 if (BN_is_odd(n0))
783 if (!BN_add(n0, n0, p))
784 goto end;
785 /* now 0 <= n0 < 2*p, and n0 is even */
786 if (!BN_rshift1(r->Y, n0))
787 goto end;
788 /* Y_r = (n6 * 'n9' - 'n8' * 'n5^3') / 2 */
789
790 ret = 1;
791
792 end:
793 BN_CTX_end(ctx);
794 BN_CTX_free(new_ctx);
795 return ret;
796}
797
798int ossl_ec_GFp_simple_dbl(const EC_GROUP *group, EC_POINT *r, const EC_POINT *a,
799 BN_CTX *ctx)
800{
801 int (*field_mul) (const EC_GROUP *, BIGNUM *, const BIGNUM *,
802 const BIGNUM *, BN_CTX *);
803 int (*field_sqr) (const EC_GROUP *, BIGNUM *, const BIGNUM *, BN_CTX *);
804 const BIGNUM *p;
805 BN_CTX *new_ctx = NULL;
806 BIGNUM *n0, *n1, *n2, *n3;
807 int ret = 0;
808
809 if (EC_POINT_is_at_infinity(group, a)) {
810 BN_zero(r->Z);
811 r->Z_is_one = 0;
812 return 1;
813 }
814
815 field_mul = group->meth->field_mul;
816 field_sqr = group->meth->field_sqr;
817 p = group->field;
818
819 if (ctx == NULL) {
820 ctx = new_ctx = BN_CTX_new_ex(group->libctx);
821 if (ctx == NULL)
822 return 0;
823 }
824
825 BN_CTX_start(ctx);
826 n0 = BN_CTX_get(ctx);
827 n1 = BN_CTX_get(ctx);
828 n2 = BN_CTX_get(ctx);
829 n3 = BN_CTX_get(ctx);
830 if (n3 == NULL)
831 goto err;
832
833 /*
834 * Note that in this function we must not read components of 'a' once we
835 * have written the corresponding components of 'r'. ('r' might the same
836 * as 'a'.)
837 */
838
839 /* n1 */
840 if (a->Z_is_one) {
841 if (!field_sqr(group, n0, a->X, ctx))
842 goto err;
843 if (!BN_mod_lshift1_quick(n1, n0, p))
844 goto err;
845 if (!BN_mod_add_quick(n0, n0, n1, p))
846 goto err;
847 if (!BN_mod_add_quick(n1, n0, group->a, p))
848 goto err;
849 /* n1 = 3 * X_a^2 + a_curve */
850 } else if (group->a_is_minus3) {
851 if (!field_sqr(group, n1, a->Z, ctx))
852 goto err;
853 if (!BN_mod_add_quick(n0, a->X, n1, p))
854 goto err;
855 if (!BN_mod_sub_quick(n2, a->X, n1, p))
856 goto err;
857 if (!field_mul(group, n1, n0, n2, ctx))
858 goto err;
859 if (!BN_mod_lshift1_quick(n0, n1, p))
860 goto err;
861 if (!BN_mod_add_quick(n1, n0, n1, p))
862 goto err;
863 /*-
864 * n1 = 3 * (X_a + Z_a^2) * (X_a - Z_a^2)
865 * = 3 * X_a^2 - 3 * Z_a^4
866 */
867 } else {
868 if (!field_sqr(group, n0, a->X, ctx))
869 goto err;
870 if (!BN_mod_lshift1_quick(n1, n0, p))
871 goto err;
872 if (!BN_mod_add_quick(n0, n0, n1, p))
873 goto err;
874 if (!field_sqr(group, n1, a->Z, ctx))
875 goto err;
876 if (!field_sqr(group, n1, n1, ctx))
877 goto err;
878 if (!field_mul(group, n1, n1, group->a, ctx))
879 goto err;
880 if (!BN_mod_add_quick(n1, n1, n0, p))
881 goto err;
882 /* n1 = 3 * X_a^2 + a_curve * Z_a^4 */
883 }
884
885 /* Z_r */
886 if (a->Z_is_one) {
887 if (!BN_copy(n0, a->Y))
888 goto err;
889 } else {
890 if (!field_mul(group, n0, a->Y, a->Z, ctx))
891 goto err;
892 }
893 if (!BN_mod_lshift1_quick(r->Z, n0, p))
894 goto err;
895 r->Z_is_one = 0;
896 /* Z_r = 2 * Y_a * Z_a */
897
898 /* n2 */
899 if (!field_sqr(group, n3, a->Y, ctx))
900 goto err;
901 if (!field_mul(group, n2, a->X, n3, ctx))
902 goto err;
903 if (!BN_mod_lshift_quick(n2, n2, 2, p))
904 goto err;
905 /* n2 = 4 * X_a * Y_a^2 */
906
907 /* X_r */
908 if (!BN_mod_lshift1_quick(n0, n2, p))
909 goto err;
910 if (!field_sqr(group, r->X, n1, ctx))
911 goto err;
912 if (!BN_mod_sub_quick(r->X, r->X, n0, p))
913 goto err;
914 /* X_r = n1^2 - 2 * n2 */
915
916 /* n3 */
917 if (!field_sqr(group, n0, n3, ctx))
918 goto err;
919 if (!BN_mod_lshift_quick(n3, n0, 3, p))
920 goto err;
921 /* n3 = 8 * Y_a^4 */
922
923 /* Y_r */
924 if (!BN_mod_sub_quick(n0, n2, r->X, p))
925 goto err;
926 if (!field_mul(group, n0, n1, n0, ctx))
927 goto err;
928 if (!BN_mod_sub_quick(r->Y, n0, n3, p))
929 goto err;
930 /* Y_r = n1 * (n2 - X_r) - n3 */
931
932 ret = 1;
933
934 err:
935 BN_CTX_end(ctx);
936 BN_CTX_free(new_ctx);
937 return ret;
938}
939
940int ossl_ec_GFp_simple_invert(const EC_GROUP *group, EC_POINT *point,
941 BN_CTX *ctx)
942{
943 if (EC_POINT_is_at_infinity(group, point) || BN_is_zero(point->Y))
944 /* point is its own inverse */
945 return 1;
946
947 return BN_usub(point->Y, group->field, point->Y);
948}
949
950int ossl_ec_GFp_simple_is_at_infinity(const EC_GROUP *group,
951 const EC_POINT *point)
952{
953 return BN_is_zero(point->Z);
954}
955
956int ossl_ec_GFp_simple_is_on_curve(const EC_GROUP *group, const EC_POINT *point,
957 BN_CTX *ctx)
958{
959 int (*field_mul) (const EC_GROUP *, BIGNUM *, const BIGNUM *,
960 const BIGNUM *, BN_CTX *);
961 int (*field_sqr) (const EC_GROUP *, BIGNUM *, const BIGNUM *, BN_CTX *);
962 const BIGNUM *p;
963 BN_CTX *new_ctx = NULL;
964 BIGNUM *rh, *tmp, *Z4, *Z6;
965 int ret = -1;
966
967 if (EC_POINT_is_at_infinity(group, point))
968 return 1;
969
970 field_mul = group->meth->field_mul;
971 field_sqr = group->meth->field_sqr;
972 p = group->field;
973
974 if (ctx == NULL) {
975 ctx = new_ctx = BN_CTX_new_ex(group->libctx);
976 if (ctx == NULL)
977 return -1;
978 }
979
980 BN_CTX_start(ctx);
981 rh = BN_CTX_get(ctx);
982 tmp = BN_CTX_get(ctx);
983 Z4 = BN_CTX_get(ctx);
984 Z6 = BN_CTX_get(ctx);
985 if (Z6 == NULL)
986 goto err;
987
988 /*-
989 * We have a curve defined by a Weierstrass equation
990 * y^2 = x^3 + a*x + b.
991 * The point to consider is given in Jacobian projective coordinates
992 * where (X, Y, Z) represents (x, y) = (X/Z^2, Y/Z^3).
993 * Substituting this and multiplying by Z^6 transforms the above equation into
994 * Y^2 = X^3 + a*X*Z^4 + b*Z^6.
995 * To test this, we add up the right-hand side in 'rh'.
996 */
997
998 /* rh := X^2 */
999 if (!field_sqr(group, rh, point->X, ctx))
1000 goto err;
1001
1002 if (!point->Z_is_one) {
1003 if (!field_sqr(group, tmp, point->Z, ctx))
1004 goto err;
1005 if (!field_sqr(group, Z4, tmp, ctx))
1006 goto err;
1007 if (!field_mul(group, Z6, Z4, tmp, ctx))
1008 goto err;
1009
1010 /* rh := (rh + a*Z^4)*X */
1011 if (group->a_is_minus3) {
1012 if (!BN_mod_lshift1_quick(tmp, Z4, p))
1013 goto err;
1014 if (!BN_mod_add_quick(tmp, tmp, Z4, p))
1015 goto err;
1016 if (!BN_mod_sub_quick(rh, rh, tmp, p))
1017 goto err;
1018 if (!field_mul(group, rh, rh, point->X, ctx))
1019 goto err;
1020 } else {
1021 if (!field_mul(group, tmp, Z4, group->a, ctx))
1022 goto err;
1023 if (!BN_mod_add_quick(rh, rh, tmp, p))
1024 goto err;
1025 if (!field_mul(group, rh, rh, point->X, ctx))
1026 goto err;
1027 }
1028
1029 /* rh := rh + b*Z^6 */
1030 if (!field_mul(group, tmp, group->b, Z6, ctx))
1031 goto err;
1032 if (!BN_mod_add_quick(rh, rh, tmp, p))
1033 goto err;
1034 } else {
1035 /* point->Z_is_one */
1036
1037 /* rh := (rh + a)*X */
1038 if (!BN_mod_add_quick(rh, rh, group->a, p))
1039 goto err;
1040 if (!field_mul(group, rh, rh, point->X, ctx))
1041 goto err;
1042 /* rh := rh + b */
1043 if (!BN_mod_add_quick(rh, rh, group->b, p))
1044 goto err;
1045 }
1046
1047 /* 'lh' := Y^2 */
1048 if (!field_sqr(group, tmp, point->Y, ctx))
1049 goto err;
1050
1051 ret = (0 == BN_ucmp(tmp, rh));
1052
1053 err:
1054 BN_CTX_end(ctx);
1055 BN_CTX_free(new_ctx);
1056 return ret;
1057}
1058
1059int ossl_ec_GFp_simple_cmp(const EC_GROUP *group, const EC_POINT *a,
1060 const EC_POINT *b, BN_CTX *ctx)
1061{
1062 /*-
1063 * return values:
1064 * -1 error
1065 * 0 equal (in affine coordinates)
1066 * 1 not equal
1067 */
1068
1069 int (*field_mul) (const EC_GROUP *, BIGNUM *, const BIGNUM *,
1070 const BIGNUM *, BN_CTX *);
1071 int (*field_sqr) (const EC_GROUP *, BIGNUM *, const BIGNUM *, BN_CTX *);
1072 BN_CTX *new_ctx = NULL;
1073 BIGNUM *tmp1, *tmp2, *Za23, *Zb23;
1074 const BIGNUM *tmp1_, *tmp2_;
1075 int ret = -1;
1076
1077 if (EC_POINT_is_at_infinity(group, a)) {
1078 return EC_POINT_is_at_infinity(group, b) ? 0 : 1;
1079 }
1080
1081 if (EC_POINT_is_at_infinity(group, b))
1082 return 1;
1083
1084 if (a->Z_is_one && b->Z_is_one) {
1085 return ((BN_cmp(a->X, b->X) == 0) && BN_cmp(a->Y, b->Y) == 0) ? 0 : 1;
1086 }
1087
1088 field_mul = group->meth->field_mul;
1089 field_sqr = group->meth->field_sqr;
1090
1091 if (ctx == NULL) {
1092 ctx = new_ctx = BN_CTX_new_ex(group->libctx);
1093 if (ctx == NULL)
1094 return -1;
1095 }
1096
1097 BN_CTX_start(ctx);
1098 tmp1 = BN_CTX_get(ctx);
1099 tmp2 = BN_CTX_get(ctx);
1100 Za23 = BN_CTX_get(ctx);
1101 Zb23 = BN_CTX_get(ctx);
1102 if (Zb23 == NULL)
1103 goto end;
1104
1105 /*-
1106 * We have to decide whether
1107 * (X_a/Z_a^2, Y_a/Z_a^3) = (X_b/Z_b^2, Y_b/Z_b^3),
1108 * or equivalently, whether
1109 * (X_a*Z_b^2, Y_a*Z_b^3) = (X_b*Z_a^2, Y_b*Z_a^3).
1110 */
1111
1112 if (!b->Z_is_one) {
1113 if (!field_sqr(group, Zb23, b->Z, ctx))
1114 goto end;
1115 if (!field_mul(group, tmp1, a->X, Zb23, ctx))
1116 goto end;
1117 tmp1_ = tmp1;
1118 } else
1119 tmp1_ = a->X;
1120 if (!a->Z_is_one) {
1121 if (!field_sqr(group, Za23, a->Z, ctx))
1122 goto end;
1123 if (!field_mul(group, tmp2, b->X, Za23, ctx))
1124 goto end;
1125 tmp2_ = tmp2;
1126 } else
1127 tmp2_ = b->X;
1128
1129 /* compare X_a*Z_b^2 with X_b*Z_a^2 */
1130 if (BN_cmp(tmp1_, tmp2_) != 0) {
1131 ret = 1; /* points differ */
1132 goto end;
1133 }
1134
1135 if (!b->Z_is_one) {
1136 if (!field_mul(group, Zb23, Zb23, b->Z, ctx))
1137 goto end;
1138 if (!field_mul(group, tmp1, a->Y, Zb23, ctx))
1139 goto end;
1140 /* tmp1_ = tmp1 */
1141 } else
1142 tmp1_ = a->Y;
1143 if (!a->Z_is_one) {
1144 if (!field_mul(group, Za23, Za23, a->Z, ctx))
1145 goto end;
1146 if (!field_mul(group, tmp2, b->Y, Za23, ctx))
1147 goto end;
1148 /* tmp2_ = tmp2 */
1149 } else
1150 tmp2_ = b->Y;
1151
1152 /* compare Y_a*Z_b^3 with Y_b*Z_a^3 */
1153 if (BN_cmp(tmp1_, tmp2_) != 0) {
1154 ret = 1; /* points differ */
1155 goto end;
1156 }
1157
1158 /* points are equal */
1159 ret = 0;
1160
1161 end:
1162 BN_CTX_end(ctx);
1163 BN_CTX_free(new_ctx);
1164 return ret;
1165}
1166
1167int ossl_ec_GFp_simple_make_affine(const EC_GROUP *group, EC_POINT *point,
1168 BN_CTX *ctx)
1169{
1170 BN_CTX *new_ctx = NULL;
1171 BIGNUM *x, *y;
1172 int ret = 0;
1173
1174 if (point->Z_is_one || EC_POINT_is_at_infinity(group, point))
1175 return 1;
1176
1177 if (ctx == NULL) {
1178 ctx = new_ctx = BN_CTX_new_ex(group->libctx);
1179 if (ctx == NULL)
1180 return 0;
1181 }
1182
1183 BN_CTX_start(ctx);
1184 x = BN_CTX_get(ctx);
1185 y = BN_CTX_get(ctx);
1186 if (y == NULL)
1187 goto err;
1188
1189 if (!EC_POINT_get_affine_coordinates(group, point, x, y, ctx))
1190 goto err;
1191 if (!EC_POINT_set_affine_coordinates(group, point, x, y, ctx))
1192 goto err;
1193 if (!point->Z_is_one) {
1194 ERR_raise(ERR_LIB_EC, ERR_R_INTERNAL_ERROR);
1195 goto err;
1196 }
1197
1198 ret = 1;
1199
1200 err:
1201 BN_CTX_end(ctx);
1202 BN_CTX_free(new_ctx);
1203 return ret;
1204}
1205
1206int ossl_ec_GFp_simple_points_make_affine(const EC_GROUP *group, size_t num,
1207 EC_POINT *points[], BN_CTX *ctx)
1208{
1209 BN_CTX *new_ctx = NULL;
1210 BIGNUM *tmp, *tmp_Z;
1211 BIGNUM **prod_Z = NULL;
1212 size_t i;
1213 int ret = 0;
1214
1215 if (num == 0)
1216 return 1;
1217
1218 if (ctx == NULL) {
1219 ctx = new_ctx = BN_CTX_new_ex(group->libctx);
1220 if (ctx == NULL)
1221 return 0;
1222 }
1223
1224 BN_CTX_start(ctx);
1225 tmp = BN_CTX_get(ctx);
1226 tmp_Z = BN_CTX_get(ctx);
1227 if (tmp_Z == NULL)
1228 goto err;
1229
1230 prod_Z = OPENSSL_malloc(num * sizeof(prod_Z[0]));
1231 if (prod_Z == NULL)
1232 goto err;
1233 for (i = 0; i < num; i++) {
1234 prod_Z[i] = BN_new();
1235 if (prod_Z[i] == NULL)
1236 goto err;
1237 }
1238
1239 /*
1240 * Set each prod_Z[i] to the product of points[0]->Z .. points[i]->Z,
1241 * skipping any zero-valued inputs (pretend that they're 1).
1242 */
1243
1244 if (!BN_is_zero(points[0]->Z)) {
1245 if (!BN_copy(prod_Z[0], points[0]->Z))
1246 goto err;
1247 } else {
1248 if (group->meth->field_set_to_one != 0) {
1249 if (!group->meth->field_set_to_one(group, prod_Z[0], ctx))
1250 goto err;
1251 } else {
1252 if (!BN_one(prod_Z[0]))
1253 goto err;
1254 }
1255 }
1256
1257 for (i = 1; i < num; i++) {
1258 if (!BN_is_zero(points[i]->Z)) {
1259 if (!group->
1260 meth->field_mul(group, prod_Z[i], prod_Z[i - 1], points[i]->Z,
1261 ctx))
1262 goto err;
1263 } else {
1264 if (!BN_copy(prod_Z[i], prod_Z[i - 1]))
1265 goto err;
1266 }
1267 }
1268
1269 /*
1270 * Now use a single explicit inversion to replace every non-zero
1271 * points[i]->Z by its inverse.
1272 */
1273
1274 if (!group->meth->field_inv(group, tmp, prod_Z[num - 1], ctx)) {
1275 ERR_raise(ERR_LIB_EC, ERR_R_BN_LIB);
1276 goto err;
1277 }
1278 if (group->meth->field_encode != NULL) {
1279 /*
1280 * In the Montgomery case, we just turned R*H (representing H) into
1281 * 1/(R*H), but we need R*(1/H) (representing 1/H); i.e. we need to
1282 * multiply by the Montgomery factor twice.
1283 */
1284 if (!group->meth->field_encode(group, tmp, tmp, ctx))
1285 goto err;
1286 if (!group->meth->field_encode(group, tmp, tmp, ctx))
1287 goto err;
1288 }
1289
1290 for (i = num - 1; i > 0; --i) {
1291 /*
1292 * Loop invariant: tmp is the product of the inverses of points[0]->Z
1293 * .. points[i]->Z (zero-valued inputs skipped).
1294 */
1295 if (!BN_is_zero(points[i]->Z)) {
1296 /*
1297 * Set tmp_Z to the inverse of points[i]->Z (as product of Z
1298 * inverses 0 .. i, Z values 0 .. i - 1).
1299 */
1300 if (!group->
1301 meth->field_mul(group, tmp_Z, prod_Z[i - 1], tmp, ctx))
1302 goto err;
1303 /*
1304 * Update tmp to satisfy the loop invariant for i - 1.
1305 */
1306 if (!group->meth->field_mul(group, tmp, tmp, points[i]->Z, ctx))
1307 goto err;
1308 /* Replace points[i]->Z by its inverse. */
1309 if (!BN_copy(points[i]->Z, tmp_Z))
1310 goto err;
1311 }
1312 }
1313
1314 if (!BN_is_zero(points[0]->Z)) {
1315 /* Replace points[0]->Z by its inverse. */
1316 if (!BN_copy(points[0]->Z, tmp))
1317 goto err;
1318 }
1319
1320 /* Finally, fix up the X and Y coordinates for all points. */
1321
1322 for (i = 0; i < num; i++) {
1323 EC_POINT *p = points[i];
1324
1325 if (!BN_is_zero(p->Z)) {
1326 /* turn (X, Y, 1/Z) into (X/Z^2, Y/Z^3, 1) */
1327
1328 if (!group->meth->field_sqr(group, tmp, p->Z, ctx))
1329 goto err;
1330 if (!group->meth->field_mul(group, p->X, p->X, tmp, ctx))
1331 goto err;
1332
1333 if (!group->meth->field_mul(group, tmp, tmp, p->Z, ctx))
1334 goto err;
1335 if (!group->meth->field_mul(group, p->Y, p->Y, tmp, ctx))
1336 goto err;
1337
1338 if (group->meth->field_set_to_one != 0) {
1339 if (!group->meth->field_set_to_one(group, p->Z, ctx))
1340 goto err;
1341 } else {
1342 if (!BN_one(p->Z))
1343 goto err;
1344 }
1345 p->Z_is_one = 1;
1346 }
1347 }
1348
1349 ret = 1;
1350
1351 err:
1352 BN_CTX_end(ctx);
1353 BN_CTX_free(new_ctx);
1354 if (prod_Z != NULL) {
1355 for (i = 0; i < num; i++) {
1356 if (prod_Z[i] == NULL)
1357 break;
1358 BN_clear_free(prod_Z[i]);
1359 }
1360 OPENSSL_free(prod_Z);
1361 }
1362 return ret;
1363}
1364
1365int ossl_ec_GFp_simple_field_mul(const EC_GROUP *group, BIGNUM *r, const BIGNUM *a,
1366 const BIGNUM *b, BN_CTX *ctx)
1367{
1368 return BN_mod_mul(r, a, b, group->field, ctx);
1369}
1370
1371int ossl_ec_GFp_simple_field_sqr(const EC_GROUP *group, BIGNUM *r, const BIGNUM *a,
1372 BN_CTX *ctx)
1373{
1374 return BN_mod_sqr(r, a, group->field, ctx);
1375}
1376
1377/*-
1378 * Computes the multiplicative inverse of a in GF(p), storing the result in r.
1379 * If a is zero (or equivalent), you'll get an EC_R_CANNOT_INVERT error.
1380 * Since we don't have a Mont structure here, SCA hardening is with blinding.
1381 * NB: "a" must be in _decoded_ form. (i.e. field_decode must precede.)
1382 */
1383int ossl_ec_GFp_simple_field_inv(const EC_GROUP *group, BIGNUM *r,
1384 const BIGNUM *a, BN_CTX *ctx)
1385{
1386 BIGNUM *e = NULL;
1387 BN_CTX *new_ctx = NULL;
1388 int ret = 0;
1389
1390 if (ctx == NULL
1391 && (ctx = new_ctx = BN_CTX_secure_new_ex(group->libctx)) == NULL)
1392 return 0;
1393
1394 BN_CTX_start(ctx);
1395 if ((e = BN_CTX_get(ctx)) == NULL)
1396 goto err;
1397
1398 do {
1399 if (!BN_priv_rand_range_ex(e, group->field, 0, ctx))
1400 goto err;
1401 } while (BN_is_zero(e));
1402
1403 /* r := a * e */
1404 if (!group->meth->field_mul(group, r, a, e, ctx))
1405 goto err;
1406 /* r := 1/(a * e) */
1407 if (!BN_mod_inverse(r, r, group->field, ctx)) {
1408 ERR_raise(ERR_LIB_EC, EC_R_CANNOT_INVERT);
1409 goto err;
1410 }
1411 /* r := e/(a * e) = 1/a */
1412 if (!group->meth->field_mul(group, r, r, e, ctx))
1413 goto err;
1414
1415 ret = 1;
1416
1417 err:
1418 BN_CTX_end(ctx);
1419 BN_CTX_free(new_ctx);
1420 return ret;
1421}
1422
1423/*-
1424 * Apply randomization of EC point projective coordinates:
1425 *
1426 * (X, Y ,Z ) = (lambda^2*X, lambda^3*Y, lambda*Z)
1427 * lambda = [1,group->field)
1428 *
1429 */
1430int ossl_ec_GFp_simple_blind_coordinates(const EC_GROUP *group, EC_POINT *p,
1431 BN_CTX *ctx)
1432{
1433 int ret = 0;
1434 BIGNUM *lambda = NULL;
1435 BIGNUM *temp = NULL;
1436
1437 BN_CTX_start(ctx);
1438 lambda = BN_CTX_get(ctx);
1439 temp = BN_CTX_get(ctx);
1440 if (temp == NULL) {
1441 ERR_raise(ERR_LIB_EC, ERR_R_MALLOC_FAILURE);
1442 goto end;
1443 }
1444
1445 /*-
1446 * Make sure lambda is not zero.
1447 * If the RNG fails, we cannot blind but nevertheless want
1448 * code to continue smoothly and not clobber the error stack.
1449 */
1450 do {
1451 ERR_set_mark();
1452 ret = BN_priv_rand_range_ex(lambda, group->field, 0, ctx);
1453 ERR_pop_to_mark();
1454 if (ret == 0) {
1455 ret = 1;
1456 goto end;
1457 }
1458 } while (BN_is_zero(lambda));
1459
1460 /* if field_encode defined convert between representations */
1461 if ((group->meth->field_encode != NULL
1462 && !group->meth->field_encode(group, lambda, lambda, ctx))
1463 || !group->meth->field_mul(group, p->Z, p->Z, lambda, ctx)
1464 || !group->meth->field_sqr(group, temp, lambda, ctx)
1465 || !group->meth->field_mul(group, p->X, p->X, temp, ctx)
1466 || !group->meth->field_mul(group, temp, temp, lambda, ctx)
1467 || !group->meth->field_mul(group, p->Y, p->Y, temp, ctx))
1468 goto end;
1469
1470 p->Z_is_one = 0;
1471 ret = 1;
1472
1473 end:
1474 BN_CTX_end(ctx);
1475 return ret;
1476}
1477
1478/*-
1479 * Input:
1480 * - p: affine coordinates
1481 *
1482 * Output:
1483 * - s := p, r := 2p: blinded projective (homogeneous) coordinates
1484 *
1485 * For doubling we use Formula 3 from Izu-Takagi "A fast parallel elliptic curve
1486 * multiplication resistant against side channel attacks" appendix, described at
1487 * https://hyperelliptic.org/EFD/g1p/auto-shortw-xz.html#doubling-dbl-2002-it-2
1488 * simplified for Z1=1.
1489 *
1490 * Blinding uses the equivalence relation (\lambda X, \lambda Y, \lambda Z)
1491 * for any non-zero \lambda that holds for projective (homogeneous) coords.
1492 */
1493int ossl_ec_GFp_simple_ladder_pre(const EC_GROUP *group,
1494 EC_POINT *r, EC_POINT *s,
1495 EC_POINT *p, BN_CTX *ctx)
1496{
1497 BIGNUM *t1, *t2, *t3, *t4, *t5 = NULL;
1498
1499 t1 = s->Z;
1500 t2 = r->Z;
1501 t3 = s->X;
1502 t4 = r->X;
1503 t5 = s->Y;
1504
1505 if (!p->Z_is_one /* r := 2p */
1506 || !group->meth->field_sqr(group, t3, p->X, ctx)
1507 || !BN_mod_sub_quick(t4, t3, group->a, group->field)
1508 || !group->meth->field_sqr(group, t4, t4, ctx)
1509 || !group->meth->field_mul(group, t5, p->X, group->b, ctx)
1510 || !BN_mod_lshift_quick(t5, t5, 3, group->field)
1511 /* r->X coord output */
1512 || !BN_mod_sub_quick(r->X, t4, t5, group->field)
1513 || !BN_mod_add_quick(t1, t3, group->a, group->field)
1514 || !group->meth->field_mul(group, t2, p->X, t1, ctx)
1515 || !BN_mod_add_quick(t2, group->b, t2, group->field)
1516 /* r->Z coord output */
1517 || !BN_mod_lshift_quick(r->Z, t2, 2, group->field))
1518 return 0;
1519
1520 /* make sure lambda (r->Y here for storage) is not zero */
1521 do {
1522 if (!BN_priv_rand_range_ex(r->Y, group->field, 0, ctx))
1523 return 0;
1524 } while (BN_is_zero(r->Y));
1525
1526 /* make sure lambda (s->Z here for storage) is not zero */
1527 do {
1528 if (!BN_priv_rand_range_ex(s->Z, group->field, 0, ctx))
1529 return 0;
1530 } while (BN_is_zero(s->Z));
1531
1532 /* if field_encode defined convert between representations */
1533 if (group->meth->field_encode != NULL
1534 && (!group->meth->field_encode(group, r->Y, r->Y, ctx)
1535 || !group->meth->field_encode(group, s->Z, s->Z, ctx)))
1536 return 0;
1537
1538 /* blind r and s independently */
1539 if (!group->meth->field_mul(group, r->Z, r->Z, r->Y, ctx)
1540 || !group->meth->field_mul(group, r->X, r->X, r->Y, ctx)
1541 || !group->meth->field_mul(group, s->X, p->X, s->Z, ctx)) /* s := p */
1542 return 0;
1543
1544 r->Z_is_one = 0;
1545 s->Z_is_one = 0;
1546
1547 return 1;
1548}
1549
1550/*-
1551 * Input:
1552 * - s, r: projective (homogeneous) coordinates
1553 * - p: affine coordinates
1554 *
1555 * Output:
1556 * - s := r + s, r := 2r: projective (homogeneous) coordinates
1557 *
1558 * Differential addition-and-doubling using Eq. (9) and (10) from Izu-Takagi
1559 * "A fast parallel elliptic curve multiplication resistant against side channel
1560 * attacks", as described at
1561 * https://hyperelliptic.org/EFD/g1p/auto-shortw-xz.html#ladder-mladd-2002-it-4
1562 */
1563int ossl_ec_GFp_simple_ladder_step(const EC_GROUP *group,
1564 EC_POINT *r, EC_POINT *s,
1565 EC_POINT *p, BN_CTX *ctx)
1566{
1567 int ret = 0;
1568 BIGNUM *t0, *t1, *t2, *t3, *t4, *t5, *t6 = NULL;
1569
1570 BN_CTX_start(ctx);
1571 t0 = BN_CTX_get(ctx);
1572 t1 = BN_CTX_get(ctx);
1573 t2 = BN_CTX_get(ctx);
1574 t3 = BN_CTX_get(ctx);
1575 t4 = BN_CTX_get(ctx);
1576 t5 = BN_CTX_get(ctx);
1577 t6 = BN_CTX_get(ctx);
1578
1579 if (t6 == NULL
1580 || !group->meth->field_mul(group, t6, r->X, s->X, ctx)
1581 || !group->meth->field_mul(group, t0, r->Z, s->Z, ctx)
1582 || !group->meth->field_mul(group, t4, r->X, s->Z, ctx)
1583 || !group->meth->field_mul(group, t3, r->Z, s->X, ctx)
1584 || !group->meth->field_mul(group, t5, group->a, t0, ctx)
1585 || !BN_mod_add_quick(t5, t6, t5, group->field)
1586 || !BN_mod_add_quick(t6, t3, t4, group->field)
1587 || !group->meth->field_mul(group, t5, t6, t5, ctx)
1588 || !group->meth->field_sqr(group, t0, t0, ctx)
1589 || !BN_mod_lshift_quick(t2, group->b, 2, group->field)
1590 || !group->meth->field_mul(group, t0, t2, t0, ctx)
1591 || !BN_mod_lshift1_quick(t5, t5, group->field)
1592 || !BN_mod_sub_quick(t3, t4, t3, group->field)
1593 /* s->Z coord output */
1594 || !group->meth->field_sqr(group, s->Z, t3, ctx)
1595 || !group->meth->field_mul(group, t4, s->Z, p->X, ctx)
1596 || !BN_mod_add_quick(t0, t0, t5, group->field)
1597 /* s->X coord output */
1598 || !BN_mod_sub_quick(s->X, t0, t4, group->field)
1599 || !group->meth->field_sqr(group, t4, r->X, ctx)
1600 || !group->meth->field_sqr(group, t5, r->Z, ctx)
1601 || !group->meth->field_mul(group, t6, t5, group->a, ctx)
1602 || !BN_mod_add_quick(t1, r->X, r->Z, group->field)
1603 || !group->meth->field_sqr(group, t1, t1, ctx)
1604 || !BN_mod_sub_quick(t1, t1, t4, group->field)
1605 || !BN_mod_sub_quick(t1, t1, t5, group->field)
1606 || !BN_mod_sub_quick(t3, t4, t6, group->field)
1607 || !group->meth->field_sqr(group, t3, t3, ctx)
1608 || !group->meth->field_mul(group, t0, t5, t1, ctx)
1609 || !group->meth->field_mul(group, t0, t2, t0, ctx)
1610 /* r->X coord output */
1611 || !BN_mod_sub_quick(r->X, t3, t0, group->field)
1612 || !BN_mod_add_quick(t3, t4, t6, group->field)
1613 || !group->meth->field_sqr(group, t4, t5, ctx)
1614 || !group->meth->field_mul(group, t4, t4, t2, ctx)
1615 || !group->meth->field_mul(group, t1, t1, t3, ctx)
1616 || !BN_mod_lshift1_quick(t1, t1, group->field)
1617 /* r->Z coord output */
1618 || !BN_mod_add_quick(r->Z, t4, t1, group->field))
1619 goto err;
1620
1621 ret = 1;
1622
1623 err:
1624 BN_CTX_end(ctx);
1625 return ret;
1626}
1627
1628/*-
1629 * Input:
1630 * - s, r: projective (homogeneous) coordinates
1631 * - p: affine coordinates
1632 *
1633 * Output:
1634 * - r := (x,y): affine coordinates
1635 *
1636 * Recovers the y-coordinate of r using Eq. (8) from Brier-Joye, "Weierstrass
1637 * Elliptic Curves and Side-Channel Attacks", modified to work in mixed
1638 * projective coords, i.e. p is affine and (r,s) in projective (homogeneous)
1639 * coords, and return r in affine coordinates.
1640 *
1641 * X4 = two*Y1*X2*Z3*Z2;
1642 * Y4 = two*b*Z3*SQR(Z2) + Z3*(a*Z2+X1*X2)*(X1*Z2+X2) - X3*SQR(X1*Z2-X2);
1643 * Z4 = two*Y1*Z3*SQR(Z2);
1644 *
1645 * Z4 != 0 because:
1646 * - Z2==0 implies r is at infinity (handled by the BN_is_zero(r->Z) branch);
1647 * - Z3==0 implies s is at infinity (handled by the BN_is_zero(s->Z) branch);
1648 * - Y1==0 implies p has order 2, so either r or s are infinity and handled by
1649 * one of the BN_is_zero(...) branches.
1650 */
1651int ossl_ec_GFp_simple_ladder_post(const EC_GROUP *group,
1652 EC_POINT *r, EC_POINT *s,
1653 EC_POINT *p, BN_CTX *ctx)
1654{
1655 int ret = 0;
1656 BIGNUM *t0, *t1, *t2, *t3, *t4, *t5, *t6 = NULL;
1657
1658 if (BN_is_zero(r->Z))
1659 return EC_POINT_set_to_infinity(group, r);
1660
1661 if (BN_is_zero(s->Z)) {
1662 if (!EC_POINT_copy(r, p)
1663 || !EC_POINT_invert(group, r, ctx))
1664 return 0;
1665 return 1;
1666 }
1667
1668 BN_CTX_start(ctx);
1669 t0 = BN_CTX_get(ctx);
1670 t1 = BN_CTX_get(ctx);
1671 t2 = BN_CTX_get(ctx);
1672 t3 = BN_CTX_get(ctx);
1673 t4 = BN_CTX_get(ctx);
1674 t5 = BN_CTX_get(ctx);
1675 t6 = BN_CTX_get(ctx);
1676
1677 if (t6 == NULL
1678 || !BN_mod_lshift1_quick(t4, p->Y, group->field)
1679 || !group->meth->field_mul(group, t6, r->X, t4, ctx)
1680 || !group->meth->field_mul(group, t6, s->Z, t6, ctx)
1681 || !group->meth->field_mul(group, t5, r->Z, t6, ctx)
1682 || !BN_mod_lshift1_quick(t1, group->b, group->field)
1683 || !group->meth->field_mul(group, t1, s->Z, t1, ctx)
1684 || !group->meth->field_sqr(group, t3, r->Z, ctx)
1685 || !group->meth->field_mul(group, t2, t3, t1, ctx)
1686 || !group->meth->field_mul(group, t6, r->Z, group->a, ctx)
1687 || !group->meth->field_mul(group, t1, p->X, r->X, ctx)
1688 || !BN_mod_add_quick(t1, t1, t6, group->field)
1689 || !group->meth->field_mul(group, t1, s->Z, t1, ctx)
1690 || !group->meth->field_mul(group, t0, p->X, r->Z, ctx)
1691 || !BN_mod_add_quick(t6, r->X, t0, group->field)
1692 || !group->meth->field_mul(group, t6, t6, t1, ctx)
1693 || !BN_mod_add_quick(t6, t6, t2, group->field)
1694 || !BN_mod_sub_quick(t0, t0, r->X, group->field)
1695 || !group->meth->field_sqr(group, t0, t0, ctx)
1696 || !group->meth->field_mul(group, t0, t0, s->X, ctx)
1697 || !BN_mod_sub_quick(t0, t6, t0, group->field)
1698 || !group->meth->field_mul(group, t1, s->Z, t4, ctx)
1699 || !group->meth->field_mul(group, t1, t3, t1, ctx)
1700 || (group->meth->field_decode != NULL
1701 && !group->meth->field_decode(group, t1, t1, ctx))
1702 || !group->meth->field_inv(group, t1, t1, ctx)
1703 || (group->meth->field_encode != NULL
1704 && !group->meth->field_encode(group, t1, t1, ctx))
1705 || !group->meth->field_mul(group, r->X, t5, t1, ctx)
1706 || !group->meth->field_mul(group, r->Y, t0, t1, ctx))
1707 goto err;
1708
1709 if (group->meth->field_set_to_one != NULL) {
1710 if (!group->meth->field_set_to_one(group, r->Z, ctx))
1711 goto err;
1712 } else {
1713 if (!BN_one(r->Z))
1714 goto err;
1715 }
1716
1717 r->Z_is_one = 1;
1718 ret = 1;
1719
1720 err:
1721 BN_CTX_end(ctx);
1722 return ret;
1723}
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