File: | src/lib/libcrypto/ec/ecp_smpl.c |
Warning: | line 1381, column 16 Access to field 'Z_is_one' results in a dereference of a null pointer (loaded from variable 'p') |
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1 | /* $OpenBSD: ecp_smpl.c,v 1.33 2021/09/08 17:29:21 tb Exp $ */ | |||
2 | /* Includes code written by Lenka Fibikova <fibikova@exp-math.uni-essen.de> | |||
3 | * for the OpenSSL project. | |||
4 | * Includes code written by Bodo Moeller for the OpenSSL project. | |||
5 | */ | |||
6 | /* ==================================================================== | |||
7 | * Copyright (c) 1998-2002 The OpenSSL Project. All rights reserved. | |||
8 | * | |||
9 | * Redistribution and use in source and binary forms, with or without | |||
10 | * modification, are permitted provided that the following conditions | |||
11 | * are met: | |||
12 | * | |||
13 | * 1. Redistributions of source code must retain the above copyright | |||
14 | * notice, this list of conditions and the following disclaimer. | |||
15 | * | |||
16 | * 2. Redistributions in binary form must reproduce the above copyright | |||
17 | * notice, this list of conditions and the following disclaimer in | |||
18 | * the documentation and/or other materials provided with the | |||
19 | * distribution. | |||
20 | * | |||
21 | * 3. All advertising materials mentioning features or use of this | |||
22 | * software must display the following acknowledgment: | |||
23 | * "This product includes software developed by the OpenSSL Project | |||
24 | * for use in the OpenSSL Toolkit. (http://www.openssl.org/)" | |||
25 | * | |||
26 | * 4. The names "OpenSSL Toolkit" and "OpenSSL Project" must not be used to | |||
27 | * endorse or promote products derived from this software without | |||
28 | * prior written permission. For written permission, please contact | |||
29 | * openssl-core@openssl.org. | |||
30 | * | |||
31 | * 5. Products derived from this software may not be called "OpenSSL" | |||
32 | * nor may "OpenSSL" appear in their names without prior written | |||
33 | * permission of the OpenSSL Project. | |||
34 | * | |||
35 | * 6. Redistributions of any form whatsoever must retain the following | |||
36 | * acknowledgment: | |||
37 | * "This product includes software developed by the OpenSSL Project | |||
38 | * for use in the OpenSSL Toolkit (http://www.openssl.org/)" | |||
39 | * | |||
40 | * THIS SOFTWARE IS PROVIDED BY THE OpenSSL PROJECT ``AS IS'' AND ANY | |||
41 | * EXPRESSED OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE | |||
42 | * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR | |||
43 | * PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE OpenSSL PROJECT OR | |||
44 | * ITS CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, | |||
45 | * SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT | |||
46 | * NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; | |||
47 | * LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) | |||
48 | * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, | |||
49 | * STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) | |||
50 | * ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED | |||
51 | * OF THE POSSIBILITY OF SUCH DAMAGE. | |||
52 | * ==================================================================== | |||
53 | * | |||
54 | * This product includes cryptographic software written by Eric Young | |||
55 | * (eay@cryptsoft.com). This product includes software written by Tim | |||
56 | * Hudson (tjh@cryptsoft.com). | |||
57 | * | |||
58 | */ | |||
59 | /* ==================================================================== | |||
60 | * Copyright 2002 Sun Microsystems, Inc. ALL RIGHTS RESERVED. | |||
61 | * Portions of this software developed by SUN MICROSYSTEMS, INC., | |||
62 | * and contributed to the OpenSSL project. | |||
63 | */ | |||
64 | ||||
65 | #include <openssl/err.h> | |||
66 | ||||
67 | #include "bn_lcl.h" | |||
68 | #include "ec_lcl.h" | |||
69 | ||||
70 | const EC_METHOD * | |||
71 | EC_GFp_simple_method(void) | |||
72 | { | |||
73 | static const EC_METHOD ret = { | |||
74 | .flags = EC_FLAGS_DEFAULT_OCT0x1, | |||
75 | .field_type = NID_X9_62_prime_field406, | |||
76 | .group_init = ec_GFp_simple_group_init, | |||
77 | .group_finish = ec_GFp_simple_group_finish, | |||
78 | .group_clear_finish = ec_GFp_simple_group_clear_finish, | |||
79 | .group_copy = ec_GFp_simple_group_copy, | |||
80 | .group_set_curve = ec_GFp_simple_group_set_curve, | |||
81 | .group_get_curve = ec_GFp_simple_group_get_curve, | |||
82 | .group_get_degree = ec_GFp_simple_group_get_degree, | |||
83 | .group_order_bits = ec_group_simple_order_bits, | |||
84 | .group_check_discriminant = | |||
85 | ec_GFp_simple_group_check_discriminant, | |||
86 | .point_init = ec_GFp_simple_point_init, | |||
87 | .point_finish = ec_GFp_simple_point_finish, | |||
88 | .point_clear_finish = ec_GFp_simple_point_clear_finish, | |||
89 | .point_copy = ec_GFp_simple_point_copy, | |||
90 | .point_set_to_infinity = ec_GFp_simple_point_set_to_infinity, | |||
91 | .point_set_Jprojective_coordinates = | |||
92 | ec_GFp_simple_set_Jprojective_coordinates, | |||
93 | .point_get_Jprojective_coordinates = | |||
94 | ec_GFp_simple_get_Jprojective_coordinates, | |||
95 | .point_set_affine_coordinates = | |||
96 | ec_GFp_simple_point_set_affine_coordinates, | |||
97 | .point_get_affine_coordinates = | |||
98 | ec_GFp_simple_point_get_affine_coordinates, | |||
99 | .add = ec_GFp_simple_add, | |||
100 | .dbl = ec_GFp_simple_dbl, | |||
101 | .invert = ec_GFp_simple_invert, | |||
102 | .is_at_infinity = ec_GFp_simple_is_at_infinity, | |||
103 | .is_on_curve = ec_GFp_simple_is_on_curve, | |||
104 | .point_cmp = ec_GFp_simple_cmp, | |||
105 | .make_affine = ec_GFp_simple_make_affine, | |||
106 | .points_make_affine = ec_GFp_simple_points_make_affine, | |||
107 | .mul_generator_ct = ec_GFp_simple_mul_generator_ct, | |||
108 | .mul_single_ct = ec_GFp_simple_mul_single_ct, | |||
109 | .mul_double_nonct = ec_GFp_simple_mul_double_nonct, | |||
110 | .field_mul = ec_GFp_simple_field_mul, | |||
111 | .field_sqr = ec_GFp_simple_field_sqr, | |||
112 | .blind_coordinates = ec_GFp_simple_blind_coordinates, | |||
113 | }; | |||
114 | ||||
115 | return &ret; | |||
116 | } | |||
117 | ||||
118 | ||||
119 | /* Most method functions in this file are designed to work with | |||
120 | * non-trivial representations of field elements if necessary | |||
121 | * (see ecp_mont.c): while standard modular addition and subtraction | |||
122 | * are used, the field_mul and field_sqr methods will be used for | |||
123 | * multiplication, and field_encode and field_decode (if defined) | |||
124 | * will be used for converting between representations. | |||
125 | ||||
126 | * Functions ec_GFp_simple_points_make_affine() and | |||
127 | * ec_GFp_simple_point_get_affine_coordinates() specifically assume | |||
128 | * that if a non-trivial representation is used, it is a Montgomery | |||
129 | * representation (i.e. 'encoding' means multiplying by some factor R). | |||
130 | */ | |||
131 | ||||
132 | ||||
133 | int | |||
134 | ec_GFp_simple_group_init(EC_GROUP * group) | |||
135 | { | |||
136 | BN_init(&group->field); | |||
137 | BN_init(&group->a); | |||
138 | BN_init(&group->b); | |||
139 | group->a_is_minus3 = 0; | |||
140 | return 1; | |||
141 | } | |||
142 | ||||
143 | ||||
144 | void | |||
145 | ec_GFp_simple_group_finish(EC_GROUP * group) | |||
146 | { | |||
147 | BN_free(&group->field); | |||
148 | BN_free(&group->a); | |||
149 | BN_free(&group->b); | |||
150 | } | |||
151 | ||||
152 | ||||
153 | void | |||
154 | ec_GFp_simple_group_clear_finish(EC_GROUP * group) | |||
155 | { | |||
156 | BN_clear_free(&group->field); | |||
157 | BN_clear_free(&group->a); | |||
158 | BN_clear_free(&group->b); | |||
159 | } | |||
160 | ||||
161 | ||||
162 | int | |||
163 | ec_GFp_simple_group_copy(EC_GROUP * dest, const EC_GROUP * src) | |||
164 | { | |||
165 | if (!BN_copy(&dest->field, &src->field)) | |||
166 | return 0; | |||
167 | if (!BN_copy(&dest->a, &src->a)) | |||
168 | return 0; | |||
169 | if (!BN_copy(&dest->b, &src->b)) | |||
170 | return 0; | |||
171 | ||||
172 | dest->a_is_minus3 = src->a_is_minus3; | |||
173 | ||||
174 | return 1; | |||
175 | } | |||
176 | ||||
177 | ||||
178 | int | |||
179 | ec_GFp_simple_group_set_curve(EC_GROUP * group, | |||
180 | const BIGNUM * p, const BIGNUM * a, const BIGNUM * b, BN_CTX * ctx) | |||
181 | { | |||
182 | int ret = 0; | |||
183 | BN_CTX *new_ctx = NULL((void *)0); | |||
184 | BIGNUM *tmp_a; | |||
185 | ||||
186 | /* p must be a prime > 3 */ | |||
187 | if (BN_num_bits(p) <= 2 || !BN_is_odd(p)) { | |||
188 | ECerror(EC_R_INVALID_FIELD)ERR_put_error(16,(0xfff),(103),"/usr/src/lib/libcrypto/ec/ecp_smpl.c" ,188); | |||
189 | return 0; | |||
190 | } | |||
191 | if (ctx == NULL((void *)0)) { | |||
192 | ctx = new_ctx = BN_CTX_new(); | |||
193 | if (ctx == NULL((void *)0)) | |||
194 | return 0; | |||
195 | } | |||
196 | BN_CTX_start(ctx); | |||
197 | if ((tmp_a = BN_CTX_get(ctx)) == NULL((void *)0)) | |||
198 | goto err; | |||
199 | ||||
200 | /* group->field */ | |||
201 | if (!BN_copy(&group->field, p)) | |||
202 | goto err; | |||
203 | BN_set_negative(&group->field, 0); | |||
204 | ||||
205 | /* group->a */ | |||
206 | if (!BN_nnmod(tmp_a, a, p, ctx)) | |||
207 | goto err; | |||
208 | if (group->meth->field_encode) { | |||
209 | if (!group->meth->field_encode(group, &group->a, tmp_a, ctx)) | |||
210 | goto err; | |||
211 | } else if (!BN_copy(&group->a, tmp_a)) | |||
212 | goto err; | |||
213 | ||||
214 | /* group->b */ | |||
215 | if (!BN_nnmod(&group->b, b, p, ctx)) | |||
216 | goto err; | |||
217 | if (group->meth->field_encode) | |||
218 | if (!group->meth->field_encode(group, &group->b, &group->b, ctx)) | |||
219 | goto err; | |||
220 | ||||
221 | /* group->a_is_minus3 */ | |||
222 | if (!BN_add_word(tmp_a, 3)) | |||
223 | goto err; | |||
224 | group->a_is_minus3 = (0 == BN_cmp(tmp_a, &group->field)); | |||
225 | ||||
226 | ret = 1; | |||
227 | ||||
228 | err: | |||
229 | BN_CTX_end(ctx); | |||
230 | BN_CTX_free(new_ctx); | |||
231 | return ret; | |||
232 | } | |||
233 | ||||
234 | ||||
235 | int | |||
236 | ec_GFp_simple_group_get_curve(const EC_GROUP * group, BIGNUM * p, BIGNUM * a, BIGNUM * b, BN_CTX * ctx) | |||
237 | { | |||
238 | int ret = 0; | |||
239 | BN_CTX *new_ctx = NULL((void *)0); | |||
240 | ||||
241 | if (p != NULL((void *)0)) { | |||
242 | if (!BN_copy(p, &group->field)) | |||
243 | return 0; | |||
244 | } | |||
245 | if (a != NULL((void *)0) || b != NULL((void *)0)) { | |||
246 | if (group->meth->field_decode) { | |||
247 | if (ctx == NULL((void *)0)) { | |||
248 | ctx = new_ctx = BN_CTX_new(); | |||
249 | if (ctx == NULL((void *)0)) | |||
250 | return 0; | |||
251 | } | |||
252 | if (a != NULL((void *)0)) { | |||
253 | if (!group->meth->field_decode(group, a, &group->a, ctx)) | |||
254 | goto err; | |||
255 | } | |||
256 | if (b != NULL((void *)0)) { | |||
257 | if (!group->meth->field_decode(group, b, &group->b, ctx)) | |||
258 | goto err; | |||
259 | } | |||
260 | } else { | |||
261 | if (a != NULL((void *)0)) { | |||
262 | if (!BN_copy(a, &group->a)) | |||
263 | goto err; | |||
264 | } | |||
265 | if (b != NULL((void *)0)) { | |||
266 | if (!BN_copy(b, &group->b)) | |||
267 | goto err; | |||
268 | } | |||
269 | } | |||
270 | } | |||
271 | ret = 1; | |||
272 | ||||
273 | err: | |||
274 | BN_CTX_free(new_ctx); | |||
275 | return ret; | |||
276 | } | |||
277 | ||||
278 | ||||
279 | int | |||
280 | ec_GFp_simple_group_get_degree(const EC_GROUP * group) | |||
281 | { | |||
282 | return BN_num_bits(&group->field); | |||
283 | } | |||
284 | ||||
285 | ||||
286 | int | |||
287 | ec_GFp_simple_group_check_discriminant(const EC_GROUP * group, BN_CTX * ctx) | |||
288 | { | |||
289 | int ret = 0; | |||
290 | BIGNUM *a, *b, *order, *tmp_1, *tmp_2; | |||
291 | const BIGNUM *p = &group->field; | |||
292 | BN_CTX *new_ctx = NULL((void *)0); | |||
293 | ||||
294 | if (ctx == NULL((void *)0)) { | |||
295 | ctx = new_ctx = BN_CTX_new(); | |||
296 | if (ctx == NULL((void *)0)) { | |||
297 | ECerror(ERR_R_MALLOC_FAILURE)ERR_put_error(16,(0xfff),((1|64)),"/usr/src/lib/libcrypto/ec/ecp_smpl.c" ,297); | |||
298 | goto err; | |||
299 | } | |||
300 | } | |||
301 | BN_CTX_start(ctx); | |||
302 | if ((a = BN_CTX_get(ctx)) == NULL((void *)0)) | |||
303 | goto err; | |||
304 | if ((b = BN_CTX_get(ctx)) == NULL((void *)0)) | |||
305 | goto err; | |||
306 | if ((tmp_1 = BN_CTX_get(ctx)) == NULL((void *)0)) | |||
307 | goto err; | |||
308 | if ((tmp_2 = BN_CTX_get(ctx)) == NULL((void *)0)) | |||
309 | goto err; | |||
310 | if ((order = BN_CTX_get(ctx)) == NULL((void *)0)) | |||
311 | goto err; | |||
312 | ||||
313 | if (group->meth->field_decode) { | |||
314 | if (!group->meth->field_decode(group, a, &group->a, ctx)) | |||
315 | goto err; | |||
316 | if (!group->meth->field_decode(group, b, &group->b, ctx)) | |||
317 | goto err; | |||
318 | } else { | |||
319 | if (!BN_copy(a, &group->a)) | |||
320 | goto err; | |||
321 | if (!BN_copy(b, &group->b)) | |||
322 | goto err; | |||
323 | } | |||
324 | ||||
325 | /* | |||
326 | * check the discriminant: y^2 = x^3 + a*x + b is an elliptic curve | |||
327 | * <=> 4*a^3 + 27*b^2 != 0 (mod p) 0 =< a, b < p | |||
328 | */ | |||
329 | if (BN_is_zero(a)) { | |||
330 | if (BN_is_zero(b)) | |||
331 | goto err; | |||
332 | } else if (!BN_is_zero(b)) { | |||
333 | if (!BN_mod_sqr(tmp_1, a, p, ctx)) | |||
334 | goto err; | |||
335 | if (!BN_mod_mul(tmp_2, tmp_1, a, p, ctx)) | |||
336 | goto err; | |||
337 | if (!BN_lshift(tmp_1, tmp_2, 2)) | |||
338 | goto err; | |||
339 | /* tmp_1 = 4*a^3 */ | |||
340 | ||||
341 | if (!BN_mod_sqr(tmp_2, b, p, ctx)) | |||
342 | goto err; | |||
343 | if (!BN_mul_word(tmp_2, 27)) | |||
344 | goto err; | |||
345 | /* tmp_2 = 27*b^2 */ | |||
346 | ||||
347 | if (!BN_mod_add(a, tmp_1, tmp_2, p, ctx)) | |||
348 | goto err; | |||
349 | if (BN_is_zero(a)) | |||
350 | goto err; | |||
351 | } | |||
352 | ret = 1; | |||
353 | ||||
354 | err: | |||
355 | if (ctx != NULL((void *)0)) | |||
356 | BN_CTX_end(ctx); | |||
357 | BN_CTX_free(new_ctx); | |||
358 | return ret; | |||
359 | } | |||
360 | ||||
361 | ||||
362 | int | |||
363 | ec_GFp_simple_point_init(EC_POINT * point) | |||
364 | { | |||
365 | BN_init(&point->X); | |||
366 | BN_init(&point->Y); | |||
367 | BN_init(&point->Z); | |||
368 | point->Z_is_one = 0; | |||
369 | ||||
370 | return 1; | |||
371 | } | |||
372 | ||||
373 | ||||
374 | void | |||
375 | ec_GFp_simple_point_finish(EC_POINT * point) | |||
376 | { | |||
377 | BN_free(&point->X); | |||
378 | BN_free(&point->Y); | |||
379 | BN_free(&point->Z); | |||
380 | } | |||
381 | ||||
382 | ||||
383 | void | |||
384 | ec_GFp_simple_point_clear_finish(EC_POINT * point) | |||
385 | { | |||
386 | BN_clear_free(&point->X); | |||
387 | BN_clear_free(&point->Y); | |||
388 | BN_clear_free(&point->Z); | |||
389 | point->Z_is_one = 0; | |||
390 | } | |||
391 | ||||
392 | ||||
393 | int | |||
394 | ec_GFp_simple_point_copy(EC_POINT * dest, const EC_POINT * src) | |||
395 | { | |||
396 | if (!BN_copy(&dest->X, &src->X)) | |||
397 | return 0; | |||
398 | if (!BN_copy(&dest->Y, &src->Y)) | |||
399 | return 0; | |||
400 | if (!BN_copy(&dest->Z, &src->Z)) | |||
401 | return 0; | |||
402 | dest->Z_is_one = src->Z_is_one; | |||
403 | ||||
404 | return 1; | |||
405 | } | |||
406 | ||||
407 | ||||
408 | int | |||
409 | ec_GFp_simple_point_set_to_infinity(const EC_GROUP * group, EC_POINT * point) | |||
410 | { | |||
411 | point->Z_is_one = 0; | |||
412 | BN_zero(&point->Z)(BN_set_word((&point->Z),0)); | |||
413 | return 1; | |||
414 | } | |||
415 | ||||
416 | ||||
417 | int | |||
418 | ec_GFp_simple_set_Jprojective_coordinates(const EC_GROUP *group, | |||
419 | EC_POINT *point, const BIGNUM *x, const BIGNUM *y, const BIGNUM *z, | |||
420 | BN_CTX *ctx) | |||
421 | { | |||
422 | BN_CTX *new_ctx = NULL((void *)0); | |||
423 | int ret = 0; | |||
424 | ||||
425 | if (ctx == NULL((void *)0)) { | |||
426 | ctx = new_ctx = BN_CTX_new(); | |||
427 | if (ctx == NULL((void *)0)) | |||
428 | return 0; | |||
429 | } | |||
430 | if (x != NULL((void *)0)) { | |||
431 | if (!BN_nnmod(&point->X, x, &group->field, ctx)) | |||
432 | goto err; | |||
433 | if (group->meth->field_encode) { | |||
434 | if (!group->meth->field_encode(group, &point->X, &point->X, ctx)) | |||
435 | goto err; | |||
436 | } | |||
437 | } | |||
438 | if (y != NULL((void *)0)) { | |||
439 | if (!BN_nnmod(&point->Y, y, &group->field, ctx)) | |||
440 | goto err; | |||
441 | if (group->meth->field_encode) { | |||
442 | if (!group->meth->field_encode(group, &point->Y, &point->Y, ctx)) | |||
443 | goto err; | |||
444 | } | |||
445 | } | |||
446 | if (z != NULL((void *)0)) { | |||
447 | int Z_is_one; | |||
448 | ||||
449 | if (!BN_nnmod(&point->Z, z, &group->field, ctx)) | |||
450 | goto err; | |||
451 | Z_is_one = BN_is_one(&point->Z); | |||
452 | if (group->meth->field_encode) { | |||
453 | if (Z_is_one && (group->meth->field_set_to_one != 0)) { | |||
454 | if (!group->meth->field_set_to_one(group, &point->Z, ctx)) | |||
455 | goto err; | |||
456 | } else { | |||
457 | if (!group->meth->field_encode(group, &point->Z, &point->Z, ctx)) | |||
458 | goto err; | |||
459 | } | |||
460 | } | |||
461 | point->Z_is_one = Z_is_one; | |||
462 | } | |||
463 | ret = 1; | |||
464 | ||||
465 | err: | |||
466 | BN_CTX_free(new_ctx); | |||
467 | return ret; | |||
468 | } | |||
469 | ||||
470 | int | |||
471 | ec_GFp_simple_get_Jprojective_coordinates(const EC_GROUP *group, | |||
472 | const EC_POINT *point, BIGNUM *x, BIGNUM *y, BIGNUM *z, BN_CTX *ctx) | |||
473 | { | |||
474 | BN_CTX *new_ctx = NULL((void *)0); | |||
475 | int ret = 0; | |||
476 | ||||
477 | if (group->meth->field_decode != 0) { | |||
478 | if (ctx == NULL((void *)0)) { | |||
479 | ctx = new_ctx = BN_CTX_new(); | |||
480 | if (ctx == NULL((void *)0)) | |||
481 | return 0; | |||
482 | } | |||
483 | if (x != NULL((void *)0)) { | |||
484 | if (!group->meth->field_decode(group, x, &point->X, ctx)) | |||
485 | goto err; | |||
486 | } | |||
487 | if (y != NULL((void *)0)) { | |||
488 | if (!group->meth->field_decode(group, y, &point->Y, ctx)) | |||
489 | goto err; | |||
490 | } | |||
491 | if (z != NULL((void *)0)) { | |||
492 | if (!group->meth->field_decode(group, z, &point->Z, ctx)) | |||
493 | goto err; | |||
494 | } | |||
495 | } else { | |||
496 | if (x != NULL((void *)0)) { | |||
497 | if (!BN_copy(x, &point->X)) | |||
498 | goto err; | |||
499 | } | |||
500 | if (y != NULL((void *)0)) { | |||
501 | if (!BN_copy(y, &point->Y)) | |||
502 | goto err; | |||
503 | } | |||
504 | if (z != NULL((void *)0)) { | |||
505 | if (!BN_copy(z, &point->Z)) | |||
506 | goto err; | |||
507 | } | |||
508 | } | |||
509 | ||||
510 | ret = 1; | |||
511 | ||||
512 | err: | |||
513 | BN_CTX_free(new_ctx); | |||
514 | return ret; | |||
515 | } | |||
516 | ||||
517 | int | |||
518 | ec_GFp_simple_point_set_affine_coordinates(const EC_GROUP * group, EC_POINT * point, | |||
519 | const BIGNUM * x, const BIGNUM * y, BN_CTX * ctx) | |||
520 | { | |||
521 | if (x == NULL((void *)0) || y == NULL((void *)0)) { | |||
522 | /* unlike for projective coordinates, we do not tolerate this */ | |||
523 | ECerror(ERR_R_PASSED_NULL_PARAMETER)ERR_put_error(16,(0xfff),((3|64)),"/usr/src/lib/libcrypto/ec/ecp_smpl.c" ,523); | |||
524 | return 0; | |||
525 | } | |||
526 | return EC_POINT_set_Jprojective_coordinates(group, point, x, y, | |||
527 | BN_value_one(), ctx); | |||
528 | } | |||
529 | ||||
530 | int | |||
531 | ec_GFp_simple_point_get_affine_coordinates(const EC_GROUP * group, const EC_POINT * point, | |||
532 | BIGNUM * x, BIGNUM * y, BN_CTX * ctx) | |||
533 | { | |||
534 | BN_CTX *new_ctx = NULL((void *)0); | |||
535 | BIGNUM *Z, *Z_1, *Z_2, *Z_3; | |||
536 | const BIGNUM *Z_; | |||
537 | int ret = 0; | |||
538 | ||||
539 | if (EC_POINT_is_at_infinity(group, point) > 0) { | |||
540 | ECerror(EC_R_POINT_AT_INFINITY)ERR_put_error(16,(0xfff),(106),"/usr/src/lib/libcrypto/ec/ecp_smpl.c" ,540); | |||
541 | return 0; | |||
542 | } | |||
543 | if (ctx == NULL((void *)0)) { | |||
544 | ctx = new_ctx = BN_CTX_new(); | |||
545 | if (ctx == NULL((void *)0)) | |||
546 | return 0; | |||
547 | } | |||
548 | BN_CTX_start(ctx); | |||
549 | if ((Z = BN_CTX_get(ctx)) == NULL((void *)0)) | |||
550 | goto err; | |||
551 | if ((Z_1 = BN_CTX_get(ctx)) == NULL((void *)0)) | |||
552 | goto err; | |||
553 | if ((Z_2 = BN_CTX_get(ctx)) == NULL((void *)0)) | |||
554 | goto err; | |||
555 | if ((Z_3 = BN_CTX_get(ctx)) == NULL((void *)0)) | |||
556 | goto err; | |||
557 | ||||
558 | /* transform (X, Y, Z) into (x, y) := (X/Z^2, Y/Z^3) */ | |||
559 | ||||
560 | if (group->meth->field_decode) { | |||
561 | if (!group->meth->field_decode(group, Z, &point->Z, ctx)) | |||
562 | goto err; | |||
563 | Z_ = Z; | |||
564 | } else { | |||
565 | Z_ = &point->Z; | |||
566 | } | |||
567 | ||||
568 | if (BN_is_one(Z_)) { | |||
569 | if (group->meth->field_decode) { | |||
570 | if (x != NULL((void *)0)) { | |||
571 | if (!group->meth->field_decode(group, x, &point->X, ctx)) | |||
572 | goto err; | |||
573 | } | |||
574 | if (y != NULL((void *)0)) { | |||
575 | if (!group->meth->field_decode(group, y, &point->Y, ctx)) | |||
576 | goto err; | |||
577 | } | |||
578 | } else { | |||
579 | if (x != NULL((void *)0)) { | |||
580 | if (!BN_copy(x, &point->X)) | |||
581 | goto err; | |||
582 | } | |||
583 | if (y != NULL((void *)0)) { | |||
584 | if (!BN_copy(y, &point->Y)) | |||
585 | goto err; | |||
586 | } | |||
587 | } | |||
588 | } else { | |||
589 | if (!BN_mod_inverse_ct(Z_1, Z_, &group->field, ctx)) { | |||
590 | ECerror(ERR_R_BN_LIB)ERR_put_error(16,(0xfff),(3),"/usr/src/lib/libcrypto/ec/ecp_smpl.c" ,590); | |||
591 | goto err; | |||
592 | } | |||
593 | if (group->meth->field_encode == 0) { | |||
594 | /* field_sqr works on standard representation */ | |||
595 | if (!group->meth->field_sqr(group, Z_2, Z_1, ctx)) | |||
596 | goto err; | |||
597 | } else { | |||
598 | if (!BN_mod_sqr(Z_2, Z_1, &group->field, ctx)) | |||
599 | goto err; | |||
600 | } | |||
601 | ||||
602 | if (x != NULL((void *)0)) { | |||
603 | /* | |||
604 | * in the Montgomery case, field_mul will cancel out | |||
605 | * Montgomery factor in X: | |||
606 | */ | |||
607 | if (!group->meth->field_mul(group, x, &point->X, Z_2, ctx)) | |||
608 | goto err; | |||
609 | } | |||
610 | if (y != NULL((void *)0)) { | |||
611 | if (group->meth->field_encode == 0) { | |||
612 | /* field_mul works on standard representation */ | |||
613 | if (!group->meth->field_mul(group, Z_3, Z_2, Z_1, ctx)) | |||
614 | goto err; | |||
615 | } else { | |||
616 | if (!BN_mod_mul(Z_3, Z_2, Z_1, &group->field, ctx)) | |||
617 | goto err; | |||
618 | } | |||
619 | ||||
620 | /* | |||
621 | * in the Montgomery case, field_mul will cancel out | |||
622 | * Montgomery factor in Y: | |||
623 | */ | |||
624 | if (!group->meth->field_mul(group, y, &point->Y, Z_3, ctx)) | |||
625 | goto err; | |||
626 | } | |||
627 | } | |||
628 | ||||
629 | ret = 1; | |||
630 | ||||
631 | err: | |||
632 | BN_CTX_end(ctx); | |||
633 | BN_CTX_free(new_ctx); | |||
634 | return ret; | |||
635 | } | |||
636 | ||||
637 | int | |||
638 | ec_GFp_simple_add(const EC_GROUP * group, EC_POINT * r, const EC_POINT * a, const EC_POINT * b, BN_CTX * ctx) | |||
639 | { | |||
640 | int (*field_mul) (const EC_GROUP *, BIGNUM *, const BIGNUM *, const BIGNUM *, BN_CTX *); | |||
641 | int (*field_sqr) (const EC_GROUP *, BIGNUM *, const BIGNUM *, BN_CTX *); | |||
642 | const BIGNUM *p; | |||
643 | BN_CTX *new_ctx = NULL((void *)0); | |||
644 | BIGNUM *n0, *n1, *n2, *n3, *n4, *n5, *n6; | |||
645 | int ret = 0; | |||
646 | ||||
647 | if (a == b) | |||
648 | return EC_POINT_dbl(group, r, a, ctx); | |||
649 | if (EC_POINT_is_at_infinity(group, a) > 0) | |||
650 | return EC_POINT_copy(r, b); | |||
651 | if (EC_POINT_is_at_infinity(group, b) > 0) | |||
652 | return EC_POINT_copy(r, a); | |||
653 | ||||
654 | field_mul = group->meth->field_mul; | |||
655 | field_sqr = group->meth->field_sqr; | |||
656 | p = &group->field; | |||
657 | ||||
658 | if (ctx == NULL((void *)0)) { | |||
659 | ctx = new_ctx = BN_CTX_new(); | |||
660 | if (ctx == NULL((void *)0)) | |||
661 | return 0; | |||
662 | } | |||
663 | BN_CTX_start(ctx); | |||
664 | if ((n0 = BN_CTX_get(ctx)) == NULL((void *)0)) | |||
665 | goto end; | |||
666 | if ((n1 = BN_CTX_get(ctx)) == NULL((void *)0)) | |||
667 | goto end; | |||
668 | if ((n2 = BN_CTX_get(ctx)) == NULL((void *)0)) | |||
669 | goto end; | |||
670 | if ((n3 = BN_CTX_get(ctx)) == NULL((void *)0)) | |||
671 | goto end; | |||
672 | if ((n4 = BN_CTX_get(ctx)) == NULL((void *)0)) | |||
673 | goto end; | |||
674 | if ((n5 = BN_CTX_get(ctx)) == NULL((void *)0)) | |||
675 | goto end; | |||
676 | if ((n6 = BN_CTX_get(ctx)) == NULL((void *)0)) | |||
677 | goto end; | |||
678 | ||||
679 | /* | |||
680 | * Note that in this function we must not read components of 'a' or | |||
681 | * 'b' once we have written the corresponding components of 'r'. ('r' | |||
682 | * might be one of 'a' or 'b'.) | |||
683 | */ | |||
684 | ||||
685 | /* n1, n2 */ | |||
686 | if (b->Z_is_one) { | |||
687 | if (!BN_copy(n1, &a->X)) | |||
688 | goto end; | |||
689 | if (!BN_copy(n2, &a->Y)) | |||
690 | goto end; | |||
691 | /* n1 = X_a */ | |||
692 | /* n2 = Y_a */ | |||
693 | } else { | |||
694 | if (!field_sqr(group, n0, &b->Z, ctx)) | |||
695 | goto end; | |||
696 | if (!field_mul(group, n1, &a->X, n0, ctx)) | |||
697 | goto end; | |||
698 | /* n1 = X_a * Z_b^2 */ | |||
699 | ||||
700 | if (!field_mul(group, n0, n0, &b->Z, ctx)) | |||
701 | goto end; | |||
702 | if (!field_mul(group, n2, &a->Y, n0, ctx)) | |||
703 | goto end; | |||
704 | /* n2 = Y_a * Z_b^3 */ | |||
705 | } | |||
706 | ||||
707 | /* n3, n4 */ | |||
708 | if (a->Z_is_one) { | |||
709 | if (!BN_copy(n3, &b->X)) | |||
710 | goto end; | |||
711 | if (!BN_copy(n4, &b->Y)) | |||
712 | goto end; | |||
713 | /* n3 = X_b */ | |||
714 | /* n4 = Y_b */ | |||
715 | } else { | |||
716 | if (!field_sqr(group, n0, &a->Z, ctx)) | |||
717 | goto end; | |||
718 | if (!field_mul(group, n3, &b->X, n0, ctx)) | |||
719 | goto end; | |||
720 | /* n3 = X_b * Z_a^2 */ | |||
721 | ||||
722 | if (!field_mul(group, n0, n0, &a->Z, ctx)) | |||
723 | goto end; | |||
724 | if (!field_mul(group, n4, &b->Y, n0, ctx)) | |||
725 | goto end; | |||
726 | /* n4 = Y_b * Z_a^3 */ | |||
727 | } | |||
728 | ||||
729 | /* n5, n6 */ | |||
730 | if (!BN_mod_sub_quick(n5, n1, n3, p)) | |||
731 | goto end; | |||
732 | if (!BN_mod_sub_quick(n6, n2, n4, p)) | |||
733 | goto end; | |||
734 | /* n5 = n1 - n3 */ | |||
735 | /* n6 = n2 - n4 */ | |||
736 | ||||
737 | if (BN_is_zero(n5)) { | |||
738 | if (BN_is_zero(n6)) { | |||
739 | /* a is the same point as b */ | |||
740 | BN_CTX_end(ctx); | |||
741 | ret = EC_POINT_dbl(group, r, a, ctx); | |||
742 | ctx = NULL((void *)0); | |||
743 | goto end; | |||
744 | } else { | |||
745 | /* a is the inverse of b */ | |||
746 | BN_zero(&r->Z)(BN_set_word((&r->Z),0)); | |||
747 | r->Z_is_one = 0; | |||
748 | ret = 1; | |||
749 | goto end; | |||
750 | } | |||
751 | } | |||
752 | /* 'n7', 'n8' */ | |||
753 | if (!BN_mod_add_quick(n1, n1, n3, p)) | |||
754 | goto end; | |||
755 | if (!BN_mod_add_quick(n2, n2, n4, p)) | |||
756 | goto end; | |||
757 | /* 'n7' = n1 + n3 */ | |||
758 | /* 'n8' = n2 + n4 */ | |||
759 | ||||
760 | /* Z_r */ | |||
761 | if (a->Z_is_one && b->Z_is_one) { | |||
762 | if (!BN_copy(&r->Z, n5)) | |||
763 | goto end; | |||
764 | } else { | |||
765 | if (a->Z_is_one) { | |||
766 | if (!BN_copy(n0, &b->Z)) | |||
767 | goto end; | |||
768 | } else if (b->Z_is_one) { | |||
769 | if (!BN_copy(n0, &a->Z)) | |||
770 | goto end; | |||
771 | } else { | |||
772 | if (!field_mul(group, n0, &a->Z, &b->Z, ctx)) | |||
773 | goto end; | |||
774 | } | |||
775 | if (!field_mul(group, &r->Z, n0, n5, ctx)) | |||
776 | goto end; | |||
777 | } | |||
778 | r->Z_is_one = 0; | |||
779 | /* Z_r = Z_a * Z_b * n5 */ | |||
780 | ||||
781 | /* X_r */ | |||
782 | if (!field_sqr(group, n0, n6, ctx)) | |||
783 | goto end; | |||
784 | if (!field_sqr(group, n4, n5, ctx)) | |||
785 | goto end; | |||
786 | if (!field_mul(group, n3, n1, n4, ctx)) | |||
787 | goto end; | |||
788 | if (!BN_mod_sub_quick(&r->X, n0, n3, p)) | |||
789 | goto end; | |||
790 | /* X_r = n6^2 - n5^2 * 'n7' */ | |||
791 | ||||
792 | /* 'n9' */ | |||
793 | if (!BN_mod_lshift1_quick(n0, &r->X, p)) | |||
794 | goto end; | |||
795 | if (!BN_mod_sub_quick(n0, n3, n0, p)) | |||
796 | goto end; | |||
797 | /* n9 = n5^2 * 'n7' - 2 * X_r */ | |||
798 | ||||
799 | /* Y_r */ | |||
800 | if (!field_mul(group, n0, n0, n6, ctx)) | |||
801 | goto end; | |||
802 | if (!field_mul(group, n5, n4, n5, ctx)) | |||
803 | goto end; /* now n5 is n5^3 */ | |||
804 | if (!field_mul(group, n1, n2, n5, ctx)) | |||
805 | goto end; | |||
806 | if (!BN_mod_sub_quick(n0, n0, n1, p)) | |||
807 | goto end; | |||
808 | if (BN_is_odd(n0)) | |||
809 | if (!BN_add(n0, n0, p)) | |||
810 | goto end; | |||
811 | /* now 0 <= n0 < 2*p, and n0 is even */ | |||
812 | if (!BN_rshift1(&r->Y, n0)) | |||
813 | goto end; | |||
814 | /* Y_r = (n6 * 'n9' - 'n8' * 'n5^3') / 2 */ | |||
815 | ||||
816 | ret = 1; | |||
817 | ||||
818 | end: | |||
819 | if (ctx) /* otherwise we already called BN_CTX_end */ | |||
820 | BN_CTX_end(ctx); | |||
821 | BN_CTX_free(new_ctx); | |||
822 | return ret; | |||
823 | } | |||
824 | ||||
825 | ||||
826 | int | |||
827 | ec_GFp_simple_dbl(const EC_GROUP * group, EC_POINT * r, const EC_POINT * a, BN_CTX * ctx) | |||
828 | { | |||
829 | int (*field_mul) (const EC_GROUP *, BIGNUM *, const BIGNUM *, const BIGNUM *, BN_CTX *); | |||
830 | int (*field_sqr) (const EC_GROUP *, BIGNUM *, const BIGNUM *, BN_CTX *); | |||
831 | const BIGNUM *p; | |||
832 | BN_CTX *new_ctx = NULL((void *)0); | |||
833 | BIGNUM *n0, *n1, *n2, *n3; | |||
834 | int ret = 0; | |||
835 | ||||
836 | if (EC_POINT_is_at_infinity(group, a) > 0) { | |||
837 | BN_zero(&r->Z)(BN_set_word((&r->Z),0)); | |||
838 | r->Z_is_one = 0; | |||
839 | return 1; | |||
840 | } | |||
841 | field_mul = group->meth->field_mul; | |||
842 | field_sqr = group->meth->field_sqr; | |||
843 | p = &group->field; | |||
844 | ||||
845 | if (ctx == NULL((void *)0)) { | |||
846 | ctx = new_ctx = BN_CTX_new(); | |||
847 | if (ctx == NULL((void *)0)) | |||
848 | return 0; | |||
849 | } | |||
850 | BN_CTX_start(ctx); | |||
851 | if ((n0 = BN_CTX_get(ctx)) == NULL((void *)0)) | |||
852 | goto err; | |||
853 | if ((n1 = BN_CTX_get(ctx)) == NULL((void *)0)) | |||
854 | goto err; | |||
855 | if ((n2 = BN_CTX_get(ctx)) == NULL((void *)0)) | |||
856 | goto err; | |||
857 | if ((n3 = BN_CTX_get(ctx)) == NULL((void *)0)) | |||
858 | goto err; | |||
859 | ||||
860 | /* | |||
861 | * Note that in this function we must not read components of 'a' once | |||
862 | * we have written the corresponding components of 'r'. ('r' might | |||
863 | * the same as 'a'.) | |||
864 | */ | |||
865 | ||||
866 | /* n1 */ | |||
867 | if (a->Z_is_one) { | |||
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 (!BN_mod_add_quick(n1, n0, &group->a, p)) | |||
875 | goto err; | |||
876 | /* n1 = 3 * X_a^2 + a_curve */ | |||
877 | } else if (group->a_is_minus3) { | |||
878 | if (!field_sqr(group, n1, &a->Z, ctx)) | |||
879 | goto err; | |||
880 | if (!BN_mod_add_quick(n0, &a->X, n1, p)) | |||
881 | goto err; | |||
882 | if (!BN_mod_sub_quick(n2, &a->X, n1, p)) | |||
883 | goto err; | |||
884 | if (!field_mul(group, n1, n0, n2, ctx)) | |||
885 | goto err; | |||
886 | if (!BN_mod_lshift1_quick(n0, n1, p)) | |||
887 | goto err; | |||
888 | if (!BN_mod_add_quick(n1, n0, n1, p)) | |||
889 | goto err; | |||
890 | /* | |||
891 | * n1 = 3 * (X_a + Z_a^2) * (X_a - Z_a^2) = 3 * X_a^2 - 3 * | |||
892 | * Z_a^4 | |||
893 | */ | |||
894 | } else { | |||
895 | if (!field_sqr(group, n0, &a->X, ctx)) | |||
896 | goto err; | |||
897 | if (!BN_mod_lshift1_quick(n1, n0, p)) | |||
898 | goto err; | |||
899 | if (!BN_mod_add_quick(n0, n0, n1, p)) | |||
900 | goto err; | |||
901 | if (!field_sqr(group, n1, &a->Z, ctx)) | |||
902 | goto err; | |||
903 | if (!field_sqr(group, n1, n1, ctx)) | |||
904 | goto err; | |||
905 | if (!field_mul(group, n1, n1, &group->a, ctx)) | |||
906 | goto err; | |||
907 | if (!BN_mod_add_quick(n1, n1, n0, p)) | |||
908 | goto err; | |||
909 | /* n1 = 3 * X_a^2 + a_curve * Z_a^4 */ | |||
910 | } | |||
911 | ||||
912 | /* Z_r */ | |||
913 | if (a->Z_is_one) { | |||
914 | if (!BN_copy(n0, &a->Y)) | |||
915 | goto err; | |||
916 | } else { | |||
917 | if (!field_mul(group, n0, &a->Y, &a->Z, ctx)) | |||
918 | goto err; | |||
919 | } | |||
920 | if (!BN_mod_lshift1_quick(&r->Z, n0, p)) | |||
921 | goto err; | |||
922 | r->Z_is_one = 0; | |||
923 | /* Z_r = 2 * Y_a * Z_a */ | |||
924 | ||||
925 | /* n2 */ | |||
926 | if (!field_sqr(group, n3, &a->Y, ctx)) | |||
927 | goto err; | |||
928 | if (!field_mul(group, n2, &a->X, n3, ctx)) | |||
929 | goto err; | |||
930 | if (!BN_mod_lshift_quick(n2, n2, 2, p)) | |||
931 | goto err; | |||
932 | /* n2 = 4 * X_a * Y_a^2 */ | |||
933 | ||||
934 | /* X_r */ | |||
935 | if (!BN_mod_lshift1_quick(n0, n2, p)) | |||
936 | goto err; | |||
937 | if (!field_sqr(group, &r->X, n1, ctx)) | |||
938 | goto err; | |||
939 | if (!BN_mod_sub_quick(&r->X, &r->X, n0, p)) | |||
940 | goto err; | |||
941 | /* X_r = n1^2 - 2 * n2 */ | |||
942 | ||||
943 | /* n3 */ | |||
944 | if (!field_sqr(group, n0, n3, ctx)) | |||
945 | goto err; | |||
946 | if (!BN_mod_lshift_quick(n3, n0, 3, p)) | |||
947 | goto err; | |||
948 | /* n3 = 8 * Y_a^4 */ | |||
949 | ||||
950 | /* Y_r */ | |||
951 | if (!BN_mod_sub_quick(n0, n2, &r->X, p)) | |||
952 | goto err; | |||
953 | if (!field_mul(group, n0, n1, n0, ctx)) | |||
954 | goto err; | |||
955 | if (!BN_mod_sub_quick(&r->Y, n0, n3, p)) | |||
956 | goto err; | |||
957 | /* Y_r = n1 * (n2 - X_r) - n3 */ | |||
958 | ||||
959 | ret = 1; | |||
960 | ||||
961 | err: | |||
962 | BN_CTX_end(ctx); | |||
963 | BN_CTX_free(new_ctx); | |||
964 | return ret; | |||
965 | } | |||
966 | ||||
967 | ||||
968 | int | |||
969 | ec_GFp_simple_invert(const EC_GROUP * group, EC_POINT * point, BN_CTX * ctx) | |||
970 | { | |||
971 | if (EC_POINT_is_at_infinity(group, point) > 0 || BN_is_zero(&point->Y)) | |||
972 | /* point is its own inverse */ | |||
973 | return 1; | |||
974 | ||||
975 | return BN_usub(&point->Y, &group->field, &point->Y); | |||
976 | } | |||
977 | ||||
978 | ||||
979 | int | |||
980 | ec_GFp_simple_is_at_infinity(const EC_GROUP * group, const EC_POINT * point) | |||
981 | { | |||
982 | return BN_is_zero(&point->Z); | |||
983 | } | |||
984 | ||||
985 | ||||
986 | int | |||
987 | ec_GFp_simple_is_on_curve(const EC_GROUP * group, const EC_POINT * point, BN_CTX * ctx) | |||
988 | { | |||
989 | int (*field_mul) (const EC_GROUP *, BIGNUM *, const BIGNUM *, const BIGNUM *, BN_CTX *); | |||
990 | int (*field_sqr) (const EC_GROUP *, BIGNUM *, const BIGNUM *, BN_CTX *); | |||
991 | const BIGNUM *p; | |||
992 | BN_CTX *new_ctx = NULL((void *)0); | |||
993 | BIGNUM *rh, *tmp, *Z4, *Z6; | |||
994 | int ret = -1; | |||
995 | ||||
996 | if (EC_POINT_is_at_infinity(group, point) > 0) | |||
997 | return 1; | |||
998 | ||||
999 | field_mul = group->meth->field_mul; | |||
1000 | field_sqr = group->meth->field_sqr; | |||
1001 | p = &group->field; | |||
1002 | ||||
1003 | if (ctx == NULL((void *)0)) { | |||
1004 | ctx = new_ctx = BN_CTX_new(); | |||
1005 | if (ctx == NULL((void *)0)) | |||
1006 | return -1; | |||
1007 | } | |||
1008 | BN_CTX_start(ctx); | |||
1009 | if ((rh = BN_CTX_get(ctx)) == NULL((void *)0)) | |||
1010 | goto err; | |||
1011 | if ((tmp = BN_CTX_get(ctx)) == NULL((void *)0)) | |||
1012 | goto err; | |||
1013 | if ((Z4 = BN_CTX_get(ctx)) == NULL((void *)0)) | |||
1014 | goto err; | |||
1015 | if ((Z6 = BN_CTX_get(ctx)) == NULL((void *)0)) | |||
1016 | goto err; | |||
1017 | ||||
1018 | /* | |||
1019 | * We have a curve defined by a Weierstrass equation y^2 = x^3 + a*x | |||
1020 | * + b. The point to consider is given in Jacobian projective | |||
1021 | * coordinates where (X, Y, Z) represents (x, y) = (X/Z^2, Y/Z^3). | |||
1022 | * Substituting this and multiplying by Z^6 transforms the above | |||
1023 | * equation into Y^2 = X^3 + a*X*Z^4 + b*Z^6. To test this, we add up | |||
1024 | * the right-hand side in 'rh'. | |||
1025 | */ | |||
1026 | ||||
1027 | /* rh := X^2 */ | |||
1028 | if (!field_sqr(group, rh, &point->X, ctx)) | |||
1029 | goto err; | |||
1030 | ||||
1031 | if (!point->Z_is_one) { | |||
1032 | if (!field_sqr(group, tmp, &point->Z, ctx)) | |||
1033 | goto err; | |||
1034 | if (!field_sqr(group, Z4, tmp, ctx)) | |||
1035 | goto err; | |||
1036 | if (!field_mul(group, Z6, Z4, tmp, ctx)) | |||
1037 | goto err; | |||
1038 | ||||
1039 | /* rh := (rh + a*Z^4)*X */ | |||
1040 | if (group->a_is_minus3) { | |||
1041 | if (!BN_mod_lshift1_quick(tmp, Z4, p)) | |||
1042 | goto err; | |||
1043 | if (!BN_mod_add_quick(tmp, tmp, Z4, p)) | |||
1044 | goto err; | |||
1045 | if (!BN_mod_sub_quick(rh, rh, tmp, p)) | |||
1046 | goto err; | |||
1047 | if (!field_mul(group, rh, rh, &point->X, ctx)) | |||
1048 | goto err; | |||
1049 | } else { | |||
1050 | if (!field_mul(group, tmp, Z4, &group->a, ctx)) | |||
1051 | goto err; | |||
1052 | if (!BN_mod_add_quick(rh, rh, tmp, p)) | |||
1053 | goto err; | |||
1054 | if (!field_mul(group, rh, rh, &point->X, ctx)) | |||
1055 | goto err; | |||
1056 | } | |||
1057 | ||||
1058 | /* rh := rh + b*Z^6 */ | |||
1059 | if (!field_mul(group, tmp, &group->b, Z6, ctx)) | |||
1060 | goto err; | |||
1061 | if (!BN_mod_add_quick(rh, rh, tmp, p)) | |||
1062 | goto err; | |||
1063 | } else { | |||
1064 | /* point->Z_is_one */ | |||
1065 | ||||
1066 | /* rh := (rh + a)*X */ | |||
1067 | if (!BN_mod_add_quick(rh, rh, &group->a, p)) | |||
1068 | goto err; | |||
1069 | if (!field_mul(group, rh, rh, &point->X, ctx)) | |||
1070 | goto err; | |||
1071 | /* rh := rh + b */ | |||
1072 | if (!BN_mod_add_quick(rh, rh, &group->b, p)) | |||
1073 | goto err; | |||
1074 | } | |||
1075 | ||||
1076 | /* 'lh' := Y^2 */ | |||
1077 | if (!field_sqr(group, tmp, &point->Y, ctx)) | |||
1078 | goto err; | |||
1079 | ||||
1080 | ret = (0 == BN_ucmp(tmp, rh)); | |||
1081 | ||||
1082 | err: | |||
1083 | BN_CTX_end(ctx); | |||
1084 | BN_CTX_free(new_ctx); | |||
1085 | return ret; | |||
1086 | } | |||
1087 | ||||
1088 | ||||
1089 | int | |||
1090 | ec_GFp_simple_cmp(const EC_GROUP * group, const EC_POINT * a, const EC_POINT * b, BN_CTX * ctx) | |||
1091 | { | |||
1092 | /* | |||
1093 | * return values: -1 error 0 equal (in affine coordinates) 1 | |||
1094 | * not equal | |||
1095 | */ | |||
1096 | ||||
1097 | int (*field_mul) (const EC_GROUP *, BIGNUM *, const BIGNUM *, const BIGNUM *, BN_CTX *); | |||
1098 | int (*field_sqr) (const EC_GROUP *, BIGNUM *, const BIGNUM *, BN_CTX *); | |||
1099 | BN_CTX *new_ctx = NULL((void *)0); | |||
1100 | BIGNUM *tmp1, *tmp2, *Za23, *Zb23; | |||
1101 | const BIGNUM *tmp1_, *tmp2_; | |||
1102 | int ret = -1; | |||
1103 | ||||
1104 | if (EC_POINT_is_at_infinity(group, a) > 0) { | |||
1105 | return EC_POINT_is_at_infinity(group, b) > 0 ? 0 : 1; | |||
1106 | } | |||
1107 | if (EC_POINT_is_at_infinity(group, b) > 0) | |||
1108 | return 1; | |||
1109 | ||||
1110 | if (a->Z_is_one && b->Z_is_one) { | |||
1111 | return ((BN_cmp(&a->X, &b->X) == 0) && BN_cmp(&a->Y, &b->Y) == 0) ? 0 : 1; | |||
1112 | } | |||
1113 | field_mul = group->meth->field_mul; | |||
1114 | field_sqr = group->meth->field_sqr; | |||
1115 | ||||
1116 | if (ctx == NULL((void *)0)) { | |||
1117 | ctx = new_ctx = BN_CTX_new(); | |||
1118 | if (ctx == NULL((void *)0)) | |||
1119 | return -1; | |||
1120 | } | |||
1121 | BN_CTX_start(ctx); | |||
1122 | if ((tmp1 = BN_CTX_get(ctx)) == NULL((void *)0)) | |||
1123 | goto end; | |||
1124 | if ((tmp2 = BN_CTX_get(ctx)) == NULL((void *)0)) | |||
1125 | goto end; | |||
1126 | if ((Za23 = BN_CTX_get(ctx)) == NULL((void *)0)) | |||
1127 | goto end; | |||
1128 | if ((Zb23 = BN_CTX_get(ctx)) == NULL((void *)0)) | |||
1129 | goto end; | |||
1130 | ||||
1131 | /* | |||
1132 | * We have to decide whether (X_a/Z_a^2, Y_a/Z_a^3) = (X_b/Z_b^2, | |||
1133 | * Y_b/Z_b^3), or equivalently, whether (X_a*Z_b^2, Y_a*Z_b^3) = | |||
1134 | * (X_b*Z_a^2, Y_b*Z_a^3). | |||
1135 | */ | |||
1136 | ||||
1137 | if (!b->Z_is_one) { | |||
1138 | if (!field_sqr(group, Zb23, &b->Z, ctx)) | |||
1139 | goto end; | |||
1140 | if (!field_mul(group, tmp1, &a->X, Zb23, ctx)) | |||
1141 | goto end; | |||
1142 | tmp1_ = tmp1; | |||
1143 | } else | |||
1144 | tmp1_ = &a->X; | |||
1145 | if (!a->Z_is_one) { | |||
1146 | if (!field_sqr(group, Za23, &a->Z, ctx)) | |||
1147 | goto end; | |||
1148 | if (!field_mul(group, tmp2, &b->X, Za23, ctx)) | |||
1149 | goto end; | |||
1150 | tmp2_ = tmp2; | |||
1151 | } else | |||
1152 | tmp2_ = &b->X; | |||
1153 | ||||
1154 | /* compare X_a*Z_b^2 with X_b*Z_a^2 */ | |||
1155 | if (BN_cmp(tmp1_, tmp2_) != 0) { | |||
1156 | ret = 1; /* points differ */ | |||
1157 | goto end; | |||
1158 | } | |||
1159 | if (!b->Z_is_one) { | |||
1160 | if (!field_mul(group, Zb23, Zb23, &b->Z, ctx)) | |||
1161 | goto end; | |||
1162 | if (!field_mul(group, tmp1, &a->Y, Zb23, ctx)) | |||
1163 | goto end; | |||
1164 | /* tmp1_ = tmp1 */ | |||
1165 | } else | |||
1166 | tmp1_ = &a->Y; | |||
1167 | if (!a->Z_is_one) { | |||
1168 | if (!field_mul(group, Za23, Za23, &a->Z, ctx)) | |||
1169 | goto end; | |||
1170 | if (!field_mul(group, tmp2, &b->Y, Za23, ctx)) | |||
1171 | goto end; | |||
1172 | /* tmp2_ = tmp2 */ | |||
1173 | } else | |||
1174 | tmp2_ = &b->Y; | |||
1175 | ||||
1176 | /* compare Y_a*Z_b^3 with Y_b*Z_a^3 */ | |||
1177 | if (BN_cmp(tmp1_, tmp2_) != 0) { | |||
1178 | ret = 1; /* points differ */ | |||
1179 | goto end; | |||
1180 | } | |||
1181 | /* points are equal */ | |||
1182 | ret = 0; | |||
1183 | ||||
1184 | end: | |||
1185 | BN_CTX_end(ctx); | |||
1186 | BN_CTX_free(new_ctx); | |||
1187 | return ret; | |||
1188 | } | |||
1189 | ||||
1190 | ||||
1191 | int | |||
1192 | ec_GFp_simple_make_affine(const EC_GROUP * group, EC_POINT * point, BN_CTX * ctx) | |||
1193 | { | |||
1194 | BN_CTX *new_ctx = NULL((void *)0); | |||
1195 | BIGNUM *x, *y; | |||
1196 | int ret = 0; | |||
1197 | ||||
1198 | if (point->Z_is_one || EC_POINT_is_at_infinity(group, point) > 0) | |||
1199 | return 1; | |||
1200 | ||||
1201 | if (ctx == NULL((void *)0)) { | |||
1202 | ctx = new_ctx = BN_CTX_new(); | |||
1203 | if (ctx == NULL((void *)0)) | |||
1204 | return 0; | |||
1205 | } | |||
1206 | BN_CTX_start(ctx); | |||
1207 | if ((x = BN_CTX_get(ctx)) == NULL((void *)0)) | |||
1208 | goto err; | |||
1209 | if ((y = BN_CTX_get(ctx)) == NULL((void *)0)) | |||
1210 | goto err; | |||
1211 | ||||
1212 | if (!EC_POINT_get_affine_coordinates(group, point, x, y, ctx)) | |||
1213 | goto err; | |||
1214 | if (!EC_POINT_set_affine_coordinates(group, point, x, y, ctx)) | |||
1215 | goto err; | |||
1216 | if (!point->Z_is_one) { | |||
1217 | ECerror(ERR_R_INTERNAL_ERROR)ERR_put_error(16,(0xfff),((4|64)),"/usr/src/lib/libcrypto/ec/ecp_smpl.c" ,1217); | |||
1218 | goto err; | |||
1219 | } | |||
1220 | ret = 1; | |||
1221 | ||||
1222 | err: | |||
1223 | BN_CTX_end(ctx); | |||
1224 | BN_CTX_free(new_ctx); | |||
1225 | return ret; | |||
1226 | } | |||
1227 | ||||
1228 | ||||
1229 | int | |||
1230 | ec_GFp_simple_points_make_affine(const EC_GROUP * group, size_t num, EC_POINT * points[], BN_CTX * ctx) | |||
1231 | { | |||
1232 | BN_CTX *new_ctx = NULL((void *)0); | |||
1233 | BIGNUM *tmp0, *tmp1; | |||
1234 | size_t pow2 = 0; | |||
1235 | BIGNUM **heap = NULL((void *)0); | |||
1236 | size_t i; | |||
1237 | int ret = 0; | |||
1238 | ||||
1239 | if (num == 0) | |||
| ||||
1240 | return 1; | |||
1241 | ||||
1242 | if (ctx == NULL((void *)0)) { | |||
1243 | ctx = new_ctx = BN_CTX_new(); | |||
1244 | if (ctx == NULL((void *)0)) | |||
1245 | return 0; | |||
1246 | } | |||
1247 | BN_CTX_start(ctx); | |||
1248 | if ((tmp0 = BN_CTX_get(ctx)) == NULL((void *)0)) | |||
1249 | goto err; | |||
1250 | if ((tmp1 = BN_CTX_get(ctx)) == NULL((void *)0)) | |||
1251 | goto err; | |||
1252 | ||||
1253 | /* | |||
1254 | * Before converting the individual points, compute inverses of all Z | |||
1255 | * values. Modular inversion is rather slow, but luckily we can do | |||
1256 | * with a single explicit inversion, plus about 3 multiplications per | |||
1257 | * input value. | |||
1258 | */ | |||
1259 | ||||
1260 | pow2 = 1; | |||
1261 | while (num > pow2) | |||
1262 | pow2 <<= 1; | |||
1263 | /* | |||
1264 | * Now pow2 is the smallest power of 2 satifsying pow2 >= num. We | |||
1265 | * need twice that. | |||
1266 | */ | |||
1267 | pow2 <<= 1; | |||
1268 | ||||
1269 | heap = reallocarray(NULL((void *)0), pow2, sizeof heap[0]); | |||
1270 | if (heap == NULL((void *)0)) | |||
1271 | goto err; | |||
1272 | ||||
1273 | /* | |||
1274 | * The array is used as a binary tree, exactly as in heapsort: | |||
1275 | * | |||
1276 | * heap[1] heap[2] heap[3] heap[4] heap[5] | |||
1277 | * heap[6] heap[7] heap[8]heap[9] heap[10]heap[11] | |||
1278 | * heap[12]heap[13] heap[14] heap[15] | |||
1279 | * | |||
1280 | * We put the Z's in the last line; then we set each other node to the | |||
1281 | * product of its two child-nodes (where empty or 0 entries are | |||
1282 | * treated as ones); then we invert heap[1]; then we invert each | |||
1283 | * other node by replacing it by the product of its parent (after | |||
1284 | * inversion) and its sibling (before inversion). | |||
1285 | */ | |||
1286 | heap[0] = NULL((void *)0); | |||
1287 | for (i = pow2 / 2 - 1; i > 0; i--) | |||
1288 | heap[i] = NULL((void *)0); | |||
1289 | for (i = 0; i < num; i++) | |||
1290 | heap[pow2 / 2 + i] = &points[i]->Z; | |||
1291 | for (i = pow2 / 2 + num; i < pow2; i++) | |||
1292 | heap[i] = NULL((void *)0); | |||
1293 | ||||
1294 | /* set each node to the product of its children */ | |||
1295 | for (i = pow2 / 2 - 1; i > 0; i--) { | |||
1296 | heap[i] = BN_new(); | |||
1297 | if (heap[i] == NULL((void *)0)) | |||
1298 | goto err; | |||
1299 | ||||
1300 | if (heap[2 * i] != NULL((void *)0)) { | |||
1301 | if ((heap[2 * i + 1] == NULL((void *)0)) || BN_is_zero(heap[2 * i + 1])) { | |||
1302 | if (!BN_copy(heap[i], heap[2 * i])) | |||
1303 | goto err; | |||
1304 | } else { | |||
1305 | if (BN_is_zero(heap[2 * i])) { | |||
1306 | if (!BN_copy(heap[i], heap[2 * i + 1])) | |||
1307 | goto err; | |||
1308 | } else { | |||
1309 | if (!group->meth->field_mul(group, heap[i], | |||
1310 | heap[2 * i], heap[2 * i + 1], ctx)) | |||
1311 | goto err; | |||
1312 | } | |||
1313 | } | |||
1314 | } | |||
1315 | } | |||
1316 | ||||
1317 | /* invert heap[1] */ | |||
1318 | if (!BN_is_zero(heap[1])) { | |||
1319 | if (!BN_mod_inverse_ct(heap[1], heap[1], &group->field, ctx)) { | |||
1320 | ECerror(ERR_R_BN_LIB)ERR_put_error(16,(0xfff),(3),"/usr/src/lib/libcrypto/ec/ecp_smpl.c" ,1320); | |||
1321 | goto err; | |||
1322 | } | |||
1323 | } | |||
1324 | if (group->meth->field_encode != 0) { | |||
1325 | /* | |||
1326 | * in the Montgomery case, we just turned R*H (representing | |||
1327 | * H) into 1/(R*H), but we need R*(1/H) (representing | |||
1328 | * 1/H); i.e. we have need to multiply by the Montgomery | |||
1329 | * factor twice | |||
1330 | */ | |||
1331 | if (!group->meth->field_encode(group, heap[1], heap[1], ctx)) | |||
1332 | goto err; | |||
1333 | if (!group->meth->field_encode(group, heap[1], heap[1], ctx)) | |||
1334 | goto err; | |||
1335 | } | |||
1336 | /* set other heap[i]'s to their inverses */ | |||
1337 | for (i = 2; i < pow2 / 2 + num; i += 2) { | |||
1338 | /* i is even */ | |||
1339 | if ((heap[i + 1] != NULL((void *)0)) && !BN_is_zero(heap[i + 1])) { | |||
1340 | if (!group->meth->field_mul(group, tmp0, heap[i / 2], heap[i + 1], ctx)) | |||
1341 | goto err; | |||
1342 | if (!group->meth->field_mul(group, tmp1, heap[i / 2], heap[i], ctx)) | |||
1343 | goto err; | |||
1344 | if (!BN_copy(heap[i], tmp0)) | |||
1345 | goto err; | |||
1346 | if (!BN_copy(heap[i + 1], tmp1)) | |||
1347 | goto err; | |||
1348 | } else { | |||
1349 | if (!BN_copy(heap[i], heap[i / 2])) | |||
1350 | goto err; | |||
1351 | } | |||
1352 | } | |||
1353 | ||||
1354 | /* | |||
1355 | * we have replaced all non-zero Z's by their inverses, now fix up | |||
1356 | * all the points | |||
1357 | */ | |||
1358 | for (i = 0; i < num; i++) { | |||
1359 | EC_POINT *p = points[i]; | |||
1360 | ||||
1361 | if (!BN_is_zero(&p->Z)) { | |||
1362 | /* turn (X, Y, 1/Z) into (X/Z^2, Y/Z^3, 1) */ | |||
1363 | ||||
1364 | if (!group->meth->field_sqr(group, tmp1, &p->Z, ctx)) | |||
1365 | goto err; | |||
1366 | if (!group->meth->field_mul(group, &p->X, &p->X, tmp1, ctx)) | |||
1367 | goto err; | |||
1368 | ||||
1369 | if (!group->meth->field_mul(group, tmp1, tmp1, &p->Z, ctx)) | |||
1370 | goto err; | |||
1371 | if (!group->meth->field_mul(group, &p->Y, &p->Y, tmp1, ctx)) | |||
1372 | goto err; | |||
1373 | ||||
1374 | if (group->meth->field_set_to_one != 0) { | |||
1375 | if (!group->meth->field_set_to_one(group, &p->Z, ctx)) | |||
1376 | goto err; | |||
1377 | } else { | |||
1378 | if (!BN_one(&p->Z)BN_set_word((&p->Z), 1)) | |||
1379 | goto err; | |||
1380 | } | |||
1381 | p->Z_is_one = 1; | |||
| ||||
1382 | } | |||
1383 | } | |||
1384 | ||||
1385 | ret = 1; | |||
1386 | ||||
1387 | err: | |||
1388 | BN_CTX_end(ctx); | |||
1389 | BN_CTX_free(new_ctx); | |||
1390 | if (heap != NULL((void *)0)) { | |||
1391 | /* | |||
1392 | * heap[pow2/2] .. heap[pow2-1] have not been allocated | |||
1393 | * locally! | |||
1394 | */ | |||
1395 | for (i = pow2 / 2 - 1; i > 0; i--) { | |||
1396 | BN_clear_free(heap[i]); | |||
1397 | } | |||
1398 | free(heap); | |||
1399 | } | |||
1400 | return ret; | |||
1401 | } | |||
1402 | ||||
1403 | ||||
1404 | int | |||
1405 | ec_GFp_simple_field_mul(const EC_GROUP * group, BIGNUM * r, const BIGNUM * a, const BIGNUM * b, BN_CTX * ctx) | |||
1406 | { | |||
1407 | return BN_mod_mul(r, a, b, &group->field, ctx); | |||
1408 | } | |||
1409 | ||||
1410 | int | |||
1411 | ec_GFp_simple_field_sqr(const EC_GROUP * group, BIGNUM * r, const BIGNUM * a, BN_CTX * ctx) | |||
1412 | { | |||
1413 | return BN_mod_sqr(r, a, &group->field, ctx); | |||
1414 | } | |||
1415 | ||||
1416 | /* | |||
1417 | * Apply randomization of EC point projective coordinates: | |||
1418 | * | |||
1419 | * (X, Y, Z) = (lambda^2 * X, lambda^3 * Y, lambda * Z) | |||
1420 | * | |||
1421 | * where lambda is in the interval [1, group->field). | |||
1422 | */ | |||
1423 | int | |||
1424 | ec_GFp_simple_blind_coordinates(const EC_GROUP *group, EC_POINT *p, BN_CTX *ctx) | |||
1425 | { | |||
1426 | BIGNUM *lambda = NULL((void *)0); | |||
1427 | BIGNUM *tmp = NULL((void *)0); | |||
1428 | int ret = 0; | |||
1429 | ||||
1430 | BN_CTX_start(ctx); | |||
1431 | if ((lambda = BN_CTX_get(ctx)) == NULL((void *)0)) | |||
1432 | goto err; | |||
1433 | if ((tmp = BN_CTX_get(ctx)) == NULL((void *)0)) | |||
1434 | goto err; | |||
1435 | ||||
1436 | /* Generate lambda in [1, group->field - 1] */ | |||
1437 | if (!bn_rand_interval(lambda, BN_value_one(), &group->field)) | |||
1438 | goto err; | |||
1439 | ||||
1440 | if (group->meth->field_encode != NULL((void *)0) && | |||
1441 | !group->meth->field_encode(group, lambda, lambda, ctx)) | |||
1442 | goto err; | |||
1443 | ||||
1444 | /* Z = lambda * Z */ | |||
1445 | if (!group->meth->field_mul(group, &p->Z, lambda, &p->Z, ctx)) | |||
1446 | goto err; | |||
1447 | ||||
1448 | /* tmp = lambda^2 */ | |||
1449 | if (!group->meth->field_sqr(group, tmp, lambda, ctx)) | |||
1450 | goto err; | |||
1451 | ||||
1452 | /* X = lambda^2 * X */ | |||
1453 | if (!group->meth->field_mul(group, &p->X, tmp, &p->X, ctx)) | |||
1454 | goto err; | |||
1455 | ||||
1456 | /* tmp = lambda^3 */ | |||
1457 | if (!group->meth->field_mul(group, tmp, tmp, lambda, ctx)) | |||
1458 | goto err; | |||
1459 | ||||
1460 | /* Y = lambda^3 * Y */ | |||
1461 | if (!group->meth->field_mul(group, &p->Y, tmp, &p->Y, ctx)) | |||
1462 | goto err; | |||
1463 | ||||
1464 | /* Disable optimized arithmetics after replacing Z by lambda * Z. */ | |||
1465 | p->Z_is_one = 0; | |||
1466 | ||||
1467 | ret = 1; | |||
1468 | ||||
1469 | err: | |||
1470 | BN_CTX_end(ctx); | |||
1471 | return ret; | |||
1472 | } | |||
1473 | ||||
1474 | ||||
1475 | #define EC_POINT_BN_set_flags(P, flags) do { \ | |||
1476 | BN_set_flags(&(P)->X, (flags)); \ | |||
1477 | BN_set_flags(&(P)->Y, (flags)); \ | |||
1478 | BN_set_flags(&(P)->Z, (flags)); \ | |||
1479 | } while(0) | |||
1480 | ||||
1481 | #define EC_POINT_CSWAP(c, a, b, w, t) do { \ | |||
1482 | if (!BN_swap_ct(c, &(a)->X, &(b)->X, w) || \ | |||
1483 | !BN_swap_ct(c, &(a)->Y, &(b)->Y, w) || \ | |||
1484 | !BN_swap_ct(c, &(a)->Z, &(b)->Z, w)) \ | |||
1485 | goto err; \ | |||
1486 | t = ((a)->Z_is_one ^ (b)->Z_is_one) & (c); \ | |||
1487 | (a)->Z_is_one ^= (t); \ | |||
1488 | (b)->Z_is_one ^= (t); \ | |||
1489 | } while(0) | |||
1490 | ||||
1491 | /* | |||
1492 | * This function computes (in constant time) a point multiplication over the | |||
1493 | * EC group. | |||
1494 | * | |||
1495 | * At a high level, it is Montgomery ladder with conditional swaps. | |||
1496 | * | |||
1497 | * It performs either a fixed point multiplication | |||
1498 | * (scalar * generator) | |||
1499 | * when point is NULL, or a variable point multiplication | |||
1500 | * (scalar * point) | |||
1501 | * when point is not NULL. | |||
1502 | * | |||
1503 | * scalar should be in the range [0,n) otherwise all constant time bets are off. | |||
1504 | * | |||
1505 | * NB: This says nothing about EC_POINT_add and EC_POINT_dbl, | |||
1506 | * which of course are not constant time themselves. | |||
1507 | * | |||
1508 | * The product is stored in r. | |||
1509 | * | |||
1510 | * Returns 1 on success, 0 otherwise. | |||
1511 | */ | |||
1512 | static int | |||
1513 | ec_GFp_simple_mul_ct(const EC_GROUP *group, EC_POINT *r, const BIGNUM *scalar, | |||
1514 | const EC_POINT *point, BN_CTX *ctx) | |||
1515 | { | |||
1516 | int i, cardinality_bits, group_top, kbit, pbit, Z_is_one; | |||
1517 | EC_POINT *s = NULL((void *)0); | |||
1518 | BIGNUM *k = NULL((void *)0); | |||
1519 | BIGNUM *lambda = NULL((void *)0); | |||
1520 | BIGNUM *cardinality = NULL((void *)0); | |||
1521 | BN_CTX *new_ctx = NULL((void *)0); | |||
1522 | int ret = 0; | |||
1523 | ||||
1524 | if (ctx == NULL((void *)0) && (ctx = new_ctx = BN_CTX_new()) == NULL((void *)0)) | |||
1525 | return 0; | |||
1526 | ||||
1527 | BN_CTX_start(ctx); | |||
1528 | ||||
1529 | if ((s = EC_POINT_new(group)) == NULL((void *)0)) | |||
1530 | goto err; | |||
1531 | ||||
1532 | if (point == NULL((void *)0)) { | |||
1533 | if (!EC_POINT_copy(s, group->generator)) | |||
1534 | goto err; | |||
1535 | } else { | |||
1536 | if (!EC_POINT_copy(s, point)) | |||
1537 | goto err; | |||
1538 | } | |||
1539 | ||||
1540 | EC_POINT_BN_set_flags(s, BN_FLG_CONSTTIME0x04); | |||
1541 | ||||
1542 | if ((cardinality = BN_CTX_get(ctx)) == NULL((void *)0)) | |||
1543 | goto err; | |||
1544 | if ((lambda = BN_CTX_get(ctx)) == NULL((void *)0)) | |||
1545 | goto err; | |||
1546 | if ((k = BN_CTX_get(ctx)) == NULL((void *)0)) | |||
1547 | goto err; | |||
1548 | if (!BN_mul(cardinality, &group->order, &group->cofactor, ctx)) | |||
1549 | goto err; | |||
1550 | ||||
1551 | /* | |||
1552 | * Group cardinalities are often on a word boundary. | |||
1553 | * So when we pad the scalar, some timing diff might | |||
1554 | * pop if it needs to be expanded due to carries. | |||
1555 | * So expand ahead of time. | |||
1556 | */ | |||
1557 | cardinality_bits = BN_num_bits(cardinality); | |||
1558 | group_top = cardinality->top; | |||
1559 | if ((bn_wexpand(k, group_top + 2)(((group_top + 2) <= (k)->dmax)?(k):bn_expand2((k),(group_top + 2))) == NULL((void *)0)) || | |||
1560 | (bn_wexpand(lambda, group_top + 2)(((group_top + 2) <= (lambda)->dmax)?(lambda):bn_expand2 ((lambda),(group_top + 2))) == NULL((void *)0))) | |||
1561 | goto err; | |||
1562 | ||||
1563 | if (!BN_copy(k, scalar)) | |||
1564 | goto err; | |||
1565 | ||||
1566 | BN_set_flags(k, BN_FLG_CONSTTIME0x04); | |||
1567 | ||||
1568 | if (BN_num_bits(k) > cardinality_bits || BN_is_negative(k)) { | |||
1569 | /* | |||
1570 | * This is an unusual input, and we don't guarantee | |||
1571 | * constant-timeness | |||
1572 | */ | |||
1573 | if (!BN_nnmod(k, k, cardinality, ctx)) | |||
1574 | goto err; | |||
1575 | } | |||
1576 | ||||
1577 | if (!BN_add(lambda, k, cardinality)) | |||
1578 | goto err; | |||
1579 | BN_set_flags(lambda, BN_FLG_CONSTTIME0x04); | |||
1580 | if (!BN_add(k, lambda, cardinality)) | |||
1581 | goto err; | |||
1582 | /* | |||
1583 | * lambda := scalar + cardinality | |||
1584 | * k := scalar + 2*cardinality | |||
1585 | */ | |||
1586 | kbit = BN_is_bit_set(lambda, cardinality_bits); | |||
1587 | if (!BN_swap_ct(kbit, k, lambda, group_top + 2)) | |||
1588 | goto err; | |||
1589 | ||||
1590 | group_top = group->field.top; | |||
1591 | if ((bn_wexpand(&s->X, group_top)(((group_top) <= (&s->X)->dmax)?(&s->X):bn_expand2 ((&s->X),(group_top))) == NULL((void *)0)) || | |||
1592 | (bn_wexpand(&s->Y, group_top)(((group_top) <= (&s->Y)->dmax)?(&s->Y):bn_expand2 ((&s->Y),(group_top))) == NULL((void *)0)) || | |||
1593 | (bn_wexpand(&s->Z, group_top)(((group_top) <= (&s->Z)->dmax)?(&s->Z):bn_expand2 ((&s->Z),(group_top))) == NULL((void *)0)) || | |||
1594 | (bn_wexpand(&r->X, group_top)(((group_top) <= (&r->X)->dmax)?(&r->X):bn_expand2 ((&r->X),(group_top))) == NULL((void *)0)) || | |||
1595 | (bn_wexpand(&r->Y, group_top)(((group_top) <= (&r->Y)->dmax)?(&r->Y):bn_expand2 ((&r->Y),(group_top))) == NULL((void *)0)) || | |||
1596 | (bn_wexpand(&r->Z, group_top)(((group_top) <= (&r->Z)->dmax)?(&r->Z):bn_expand2 ((&r->Z),(group_top))) == NULL((void *)0))) | |||
1597 | goto err; | |||
1598 | ||||
1599 | /* | |||
1600 | * Apply coordinate blinding for EC_POINT if the underlying EC_METHOD | |||
1601 | * implements it. | |||
1602 | */ | |||
1603 | if (!ec_point_blind_coordinates(group, s, ctx)) | |||
1604 | goto err; | |||
1605 | ||||
1606 | /* top bit is a 1, in a fixed pos */ | |||
1607 | if (!EC_POINT_copy(r, s)) | |||
1608 | goto err; | |||
1609 | ||||
1610 | EC_POINT_BN_set_flags(r, BN_FLG_CONSTTIME0x04); | |||
1611 | ||||
1612 | if (!EC_POINT_dbl(group, s, s, ctx)) | |||
1613 | goto err; | |||
1614 | ||||
1615 | pbit = 0; | |||
1616 | ||||
1617 | /* | |||
1618 | * The ladder step, with branches, is | |||
1619 | * | |||
1620 | * k[i] == 0: S = add(R, S), R = dbl(R) | |||
1621 | * k[i] == 1: R = add(S, R), S = dbl(S) | |||
1622 | * | |||
1623 | * Swapping R, S conditionally on k[i] leaves you with state | |||
1624 | * | |||
1625 | * k[i] == 0: T, U = R, S | |||
1626 | * k[i] == 1: T, U = S, R | |||
1627 | * | |||
1628 | * Then perform the ECC ops. | |||
1629 | * | |||
1630 | * U = add(T, U) | |||
1631 | * T = dbl(T) | |||
1632 | * | |||
1633 | * Which leaves you with state | |||
1634 | * | |||
1635 | * k[i] == 0: U = add(R, S), T = dbl(R) | |||
1636 | * k[i] == 1: U = add(S, R), T = dbl(S) | |||
1637 | * | |||
1638 | * Swapping T, U conditionally on k[i] leaves you with state | |||
1639 | * | |||
1640 | * k[i] == 0: R, S = T, U | |||
1641 | * k[i] == 1: R, S = U, T | |||
1642 | * | |||
1643 | * Which leaves you with state | |||
1644 | * | |||
1645 | * k[i] == 0: S = add(R, S), R = dbl(R) | |||
1646 | * k[i] == 1: R = add(S, R), S = dbl(S) | |||
1647 | * | |||
1648 | * So we get the same logic, but instead of a branch it's a | |||
1649 | * conditional swap, followed by ECC ops, then another conditional swap. | |||
1650 | * | |||
1651 | * Optimization: The end of iteration i and start of i-1 looks like | |||
1652 | * | |||
1653 | * ... | |||
1654 | * CSWAP(k[i], R, S) | |||
1655 | * ECC | |||
1656 | * CSWAP(k[i], R, S) | |||
1657 | * (next iteration) | |||
1658 | * CSWAP(k[i-1], R, S) | |||
1659 | * ECC | |||
1660 | * CSWAP(k[i-1], R, S) | |||
1661 | * ... | |||
1662 | * | |||
1663 | * So instead of two contiguous swaps, you can merge the condition | |||
1664 | * bits and do a single swap. | |||
1665 | * | |||
1666 | * k[i] k[i-1] Outcome | |||
1667 | * 0 0 No Swap | |||
1668 | * 0 1 Swap | |||
1669 | * 1 0 Swap | |||
1670 | * 1 1 No Swap | |||
1671 | * | |||
1672 | * This is XOR. pbit tracks the previous bit of k. | |||
1673 | */ | |||
1674 | ||||
1675 | for (i = cardinality_bits - 1; i >= 0; i--) { | |||
1676 | kbit = BN_is_bit_set(k, i) ^ pbit; | |||
1677 | EC_POINT_CSWAP(kbit, r, s, group_top, Z_is_one); | |||
1678 | if (!EC_POINT_add(group, s, r, s, ctx)) | |||
1679 | goto err; | |||
1680 | if (!EC_POINT_dbl(group, r, r, ctx)) | |||
1681 | goto err; | |||
1682 | /* | |||
1683 | * pbit logic merges this cswap with that of the | |||
1684 | * next iteration | |||
1685 | */ | |||
1686 | pbit ^= kbit; | |||
1687 | } | |||
1688 | /* one final cswap to move the right value into r */ | |||
1689 | EC_POINT_CSWAP(pbit, r, s, group_top, Z_is_one); | |||
1690 | ||||
1691 | ret = 1; | |||
1692 | ||||
1693 | err: | |||
1694 | EC_POINT_free(s); | |||
1695 | if (ctx != NULL((void *)0)) | |||
1696 | BN_CTX_end(ctx); | |||
1697 | BN_CTX_free(new_ctx); | |||
1698 | ||||
1699 | return ret; | |||
1700 | } | |||
1701 | ||||
1702 | #undef EC_POINT_BN_set_flags | |||
1703 | #undef EC_POINT_CSWAP | |||
1704 | ||||
1705 | int | |||
1706 | ec_GFp_simple_mul_generator_ct(const EC_GROUP *group, EC_POINT *r, | |||
1707 | const BIGNUM *scalar, BN_CTX *ctx) | |||
1708 | { | |||
1709 | return ec_GFp_simple_mul_ct(group, r, scalar, NULL((void *)0), ctx); | |||
1710 | } | |||
1711 | ||||
1712 | int | |||
1713 | ec_GFp_simple_mul_single_ct(const EC_GROUP *group, EC_POINT *r, | |||
1714 | const BIGNUM *scalar, const EC_POINT *point, BN_CTX *ctx) | |||
1715 | { | |||
1716 | return ec_GFp_simple_mul_ct(group, r, scalar, point, ctx); | |||
1717 | } | |||
1718 | ||||
1719 | int | |||
1720 | ec_GFp_simple_mul_double_nonct(const EC_GROUP *group, EC_POINT *r, | |||
1721 | const BIGNUM *g_scalar, const BIGNUM *p_scalar, const EC_POINT *point, | |||
1722 | BN_CTX *ctx) | |||
1723 | { | |||
1724 | return ec_wNAF_mul(group, r, g_scalar, 1, &point, &p_scalar, ctx); | |||
1725 | } |