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 | |
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 | 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 | |
94 | int 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 | |
109 | void 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 | |
116 | void 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 | |
123 | int 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 | |
137 | int 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 | |
196 | int 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 | |
241 | int ec_GFp_simple_group_get_degree(const EC_GROUP *group) |
242 | { |
243 | return BN_num_bits(group->field); |
244 | } |
245 | |
246 | int 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 | |
318 | int 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 | |
334 | void 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 | |
341 | void 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 | |
349 | int 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 | |
363 | int 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 | |
371 | int 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 | |
431 | int 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 | |
480 | int 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 | |
498 | int 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 | |
612 | int 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 | |
797 | int 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 | |
939 | int 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 | |
948 | int ec_GFp_simple_is_at_infinity(const EC_GROUP *group, const EC_POINT *point) |
949 | { |
950 | return BN_is_zero(point->Z); |
951 | } |
952 | |
953 | int 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 | |
1056 | int 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 | |
1164 | int 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 | |
1203 | int 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 | |
1362 | int 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 | |
1368 | int 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 | */ |
1379 | int 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 | */ |
1426 | int 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 | */ |
1487 | int 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 | */ |
1538 | int 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 | */ |
1623 | int 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 | |