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Commit | Line | Data |
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0f113f3e | 1 | /* |
e1e93f7a | 2 | * Copyright 2001-2022 The OpenSSL Project Authors. All Rights Reserved. |
aa8f3d76 | 3 | * Copyright (c) 2002, Oracle and/or its affiliates. All rights reserved |
f8fe20e0 | 4 | * |
a7f182b7 | 5 | * Licensed under the Apache License 2.0 (the "License"). You may not use |
aa6bb135 RS |
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 | |
f8fe20e0 | 9 | */ |
aa6bb135 | 10 | |
579422c8 | 11 | /* |
1567a821 | 12 | * ECDSA low-level APIs are deprecated for public use, but still ok for |
579422c8 P |
13 | * internal use. |
14 | */ | |
15 | #include "internal/deprecated.h" | |
16 | ||
60428dbf | 17 | #include <openssl/err.h> |
02cbedc3 | 18 | #include <openssl/symhacks.h> |
60428dbf | 19 | |
706457b7 | 20 | #include "ec_local.h" |
0657bf9c | 21 | |
0657bf9c | 22 | const EC_METHOD *EC_GFp_simple_method(void) |
0f113f3e MC |
23 | { |
24 | static const EC_METHOD ret = { | |
25 | EC_FLAGS_DEFAULT_OCT, | |
26 | NID_X9_62_prime_field, | |
32ab57cb SL |
27 | ossl_ec_GFp_simple_group_init, |
28 | ossl_ec_GFp_simple_group_finish, | |
29 | ossl_ec_GFp_simple_group_clear_finish, | |
30 | ossl_ec_GFp_simple_group_copy, | |
31 | ossl_ec_GFp_simple_group_set_curve, | |
32 | ossl_ec_GFp_simple_group_get_curve, | |
33 | ossl_ec_GFp_simple_group_get_degree, | |
34 | ossl_ec_group_simple_order_bits, | |
35 | ossl_ec_GFp_simple_group_check_discriminant, | |
36 | ossl_ec_GFp_simple_point_init, | |
37 | ossl_ec_GFp_simple_point_finish, | |
38 | ossl_ec_GFp_simple_point_clear_finish, | |
39 | ossl_ec_GFp_simple_point_copy, | |
40 | ossl_ec_GFp_simple_point_set_to_infinity, | |
41 | ossl_ec_GFp_simple_point_set_affine_coordinates, | |
42 | ossl_ec_GFp_simple_point_get_affine_coordinates, | |
0f113f3e | 43 | 0, 0, 0, |
32ab57cb SL |
44 | ossl_ec_GFp_simple_add, |
45 | ossl_ec_GFp_simple_dbl, | |
46 | ossl_ec_GFp_simple_invert, | |
47 | ossl_ec_GFp_simple_is_at_infinity, | |
48 | ossl_ec_GFp_simple_is_on_curve, | |
49 | ossl_ec_GFp_simple_cmp, | |
50 | ossl_ec_GFp_simple_make_affine, | |
51 | ossl_ec_GFp_simple_points_make_affine, | |
0f113f3e MC |
52 | 0 /* mul */ , |
53 | 0 /* precompute_mult */ , | |
54 | 0 /* have_precompute_mult */ , | |
32ab57cb SL |
55 | ossl_ec_GFp_simple_field_mul, |
56 | ossl_ec_GFp_simple_field_sqr, | |
0f113f3e | 57 | 0 /* field_div */ , |
32ab57cb | 58 | ossl_ec_GFp_simple_field_inv, |
0f113f3e MC |
59 | 0 /* field_encode */ , |
60 | 0 /* field_decode */ , | |
9ff9bccc | 61 | 0, /* field_set_to_one */ |
32ab57cb SL |
62 | ossl_ec_key_simple_priv2oct, |
63 | ossl_ec_key_simple_oct2priv, | |
9ff9bccc | 64 | 0, /* set private */ |
32ab57cb SL |
65 | ossl_ec_key_simple_generate_key, |
66 | ossl_ec_key_simple_check_key, | |
67 | ossl_ec_key_simple_generate_public_key, | |
9ff9bccc DSH |
68 | 0, /* keycopy */ |
69 | 0, /* keyfinish */ | |
32ab57cb SL |
70 | ossl_ecdh_simple_compute_key, |
71 | ossl_ecdsa_simple_sign_setup, | |
72 | ossl_ecdsa_simple_sign_sig, | |
73 | ossl_ecdsa_simple_verify_sig, | |
f667820c | 74 | 0, /* field_inverse_mod_ord */ |
32ab57cb SL |
75 | ossl_ec_GFp_simple_blind_coordinates, |
76 | ossl_ec_GFp_simple_ladder_pre, | |
77 | ossl_ec_GFp_simple_ladder_step, | |
78 | ossl_ec_GFp_simple_ladder_post | |
0f113f3e MC |
79 | }; |
80 | ||
81 | return &ret; | |
82 | } | |
60428dbf | 83 | |
3a83462d MC |
84 | /* |
85 | * Most method functions in this file are designed to work with | |
922fa76e BM |
86 | * non-trivial representations of field elements if necessary |
87 | * (see ecp_mont.c): while standard modular addition and subtraction | |
88 | * are used, the field_mul and field_sqr methods will be used for | |
89 | * multiplication, and field_encode and field_decode (if defined) | |
90 | * will be used for converting between representations. | |
3a83462d | 91 | * |
922fa76e BM |
92 | * Functions ec_GFp_simple_points_make_affine() and |
93 | * ec_GFp_simple_point_get_affine_coordinates() specifically assume | |
94 | * that if a non-trivial representation is used, it is a Montgomery | |
95 | * representation (i.e. 'encoding' means multiplying by some factor R). | |
96 | */ | |
97 | ||
32ab57cb | 98 | int ossl_ec_GFp_simple_group_init(EC_GROUP *group) |
0f113f3e MC |
99 | { |
100 | group->field = BN_new(); | |
101 | group->a = BN_new(); | |
102 | group->b = BN_new(); | |
90945fa3 | 103 | if (group->field == NULL || group->a == NULL || group->b == NULL) { |
a3853772 RS |
104 | BN_free(group->field); |
105 | BN_free(group->a); | |
106 | BN_free(group->b); | |
0f113f3e MC |
107 | return 0; |
108 | } | |
109 | group->a_is_minus3 = 0; | |
110 | return 1; | |
111 | } | |
60428dbf | 112 | |
32ab57cb | 113 | void ossl_ec_GFp_simple_group_finish(EC_GROUP *group) |
0f113f3e MC |
114 | { |
115 | BN_free(group->field); | |
116 | BN_free(group->a); | |
117 | BN_free(group->b); | |
118 | } | |
bb62a8b0 | 119 | |
32ab57cb | 120 | void ossl_ec_GFp_simple_group_clear_finish(EC_GROUP *group) |
0f113f3e MC |
121 | { |
122 | BN_clear_free(group->field); | |
123 | BN_clear_free(group->a); | |
124 | BN_clear_free(group->b); | |
125 | } | |
bb62a8b0 | 126 | |
32ab57cb | 127 | int ossl_ec_GFp_simple_group_copy(EC_GROUP *dest, const EC_GROUP *src) |
0f113f3e MC |
128 | { |
129 | if (!BN_copy(dest->field, src->field)) | |
130 | return 0; | |
131 | if (!BN_copy(dest->a, src->a)) | |
132 | return 0; | |
133 | if (!BN_copy(dest->b, src->b)) | |
134 | return 0; | |
bb62a8b0 | 135 | |
0f113f3e | 136 | dest->a_is_minus3 = src->a_is_minus3; |
bb62a8b0 | 137 | |
0f113f3e MC |
138 | return 1; |
139 | } | |
bb62a8b0 | 140 | |
32ab57cb SL |
141 | int ossl_ec_GFp_simple_group_set_curve(EC_GROUP *group, |
142 | const BIGNUM *p, const BIGNUM *a, | |
143 | const BIGNUM *b, BN_CTX *ctx) | |
0f113f3e MC |
144 | { |
145 | int ret = 0; | |
146 | BN_CTX *new_ctx = NULL; | |
147 | BIGNUM *tmp_a; | |
148 | ||
149 | /* p must be a prime > 3 */ | |
150 | if (BN_num_bits(p) <= 2 || !BN_is_odd(p)) { | |
9311d0c4 | 151 | ERR_raise(ERR_LIB_EC, EC_R_INVALID_FIELD); |
0f113f3e MC |
152 | return 0; |
153 | } | |
154 | ||
155 | if (ctx == NULL) { | |
a9612d6c | 156 | ctx = new_ctx = BN_CTX_new_ex(group->libctx); |
0f113f3e MC |
157 | if (ctx == NULL) |
158 | return 0; | |
159 | } | |
160 | ||
161 | BN_CTX_start(ctx); | |
162 | tmp_a = BN_CTX_get(ctx); | |
163 | if (tmp_a == NULL) | |
164 | goto err; | |
165 | ||
166 | /* group->field */ | |
167 | if (!BN_copy(group->field, p)) | |
168 | goto err; | |
169 | BN_set_negative(group->field, 0); | |
170 | ||
171 | /* group->a */ | |
172 | if (!BN_nnmod(tmp_a, a, p, ctx)) | |
173 | goto err; | |
e1e93f7a | 174 | if (group->meth->field_encode != NULL) { |
0f113f3e MC |
175 | if (!group->meth->field_encode(group, group->a, tmp_a, ctx)) |
176 | goto err; | |
177 | } else if (!BN_copy(group->a, tmp_a)) | |
178 | goto err; | |
179 | ||
180 | /* group->b */ | |
181 | if (!BN_nnmod(group->b, b, p, ctx)) | |
182 | goto err; | |
e1e93f7a | 183 | if (group->meth->field_encode != NULL) |
0f113f3e MC |
184 | if (!group->meth->field_encode(group, group->b, group->b, ctx)) |
185 | goto err; | |
186 | ||
187 | /* group->a_is_minus3 */ | |
188 | if (!BN_add_word(tmp_a, 3)) | |
189 | goto err; | |
190 | group->a_is_minus3 = (0 == BN_cmp(tmp_a, group->field)); | |
191 | ||
192 | ret = 1; | |
60428dbf BM |
193 | |
194 | err: | |
0f113f3e | 195 | BN_CTX_end(ctx); |
23a1d5e9 | 196 | BN_CTX_free(new_ctx); |
0f113f3e MC |
197 | return ret; |
198 | } | |
199 | ||
32ab57cb SL |
200 | int ossl_ec_GFp_simple_group_get_curve(const EC_GROUP *group, BIGNUM *p, |
201 | BIGNUM *a, BIGNUM *b, BN_CTX *ctx) | |
0f113f3e MC |
202 | { |
203 | int ret = 0; | |
204 | BN_CTX *new_ctx = NULL; | |
205 | ||
206 | if (p != NULL) { | |
207 | if (!BN_copy(p, group->field)) | |
208 | return 0; | |
209 | } | |
210 | ||
211 | if (a != NULL || b != NULL) { | |
e1e93f7a | 212 | if (group->meth->field_decode != NULL) { |
0f113f3e | 213 | if (ctx == NULL) { |
a9612d6c | 214 | ctx = new_ctx = BN_CTX_new_ex(group->libctx); |
0f113f3e MC |
215 | if (ctx == NULL) |
216 | return 0; | |
217 | } | |
218 | if (a != NULL) { | |
219 | if (!group->meth->field_decode(group, a, group->a, ctx)) | |
220 | goto err; | |
221 | } | |
222 | if (b != NULL) { | |
223 | if (!group->meth->field_decode(group, b, group->b, ctx)) | |
224 | goto err; | |
225 | } | |
226 | } else { | |
227 | if (a != NULL) { | |
228 | if (!BN_copy(a, group->a)) | |
229 | goto err; | |
230 | } | |
231 | if (b != NULL) { | |
232 | if (!BN_copy(b, group->b)) | |
233 | goto err; | |
234 | } | |
235 | } | |
236 | } | |
237 | ||
238 | ret = 1; | |
60428dbf | 239 | |
0f113f3e | 240 | err: |
23a1d5e9 | 241 | BN_CTX_free(new_ctx); |
0f113f3e MC |
242 | return ret; |
243 | } | |
60428dbf | 244 | |
32ab57cb | 245 | int ossl_ec_GFp_simple_group_get_degree(const EC_GROUP *group) |
0f113f3e MC |
246 | { |
247 | return BN_num_bits(group->field); | |
248 | } | |
7793f30e | 249 | |
32ab57cb SL |
250 | int ossl_ec_GFp_simple_group_check_discriminant(const EC_GROUP *group, |
251 | BN_CTX *ctx) | |
0f113f3e MC |
252 | { |
253 | int ret = 0; | |
254 | BIGNUM *a, *b, *order, *tmp_1, *tmp_2; | |
255 | const BIGNUM *p = group->field; | |
256 | BN_CTX *new_ctx = NULL; | |
257 | ||
258 | if (ctx == NULL) { | |
a9612d6c | 259 | ctx = new_ctx = BN_CTX_new_ex(group->libctx); |
0f113f3e | 260 | if (ctx == NULL) { |
e077455e | 261 | ERR_raise(ERR_LIB_EC, ERR_R_BN_LIB); |
0f113f3e MC |
262 | goto err; |
263 | } | |
264 | } | |
265 | BN_CTX_start(ctx); | |
266 | a = BN_CTX_get(ctx); | |
267 | b = BN_CTX_get(ctx); | |
268 | tmp_1 = BN_CTX_get(ctx); | |
269 | tmp_2 = BN_CTX_get(ctx); | |
270 | order = BN_CTX_get(ctx); | |
271 | if (order == NULL) | |
272 | goto err; | |
273 | ||
e1e93f7a | 274 | if (group->meth->field_decode != NULL) { |
0f113f3e MC |
275 | if (!group->meth->field_decode(group, a, group->a, ctx)) |
276 | goto err; | |
277 | if (!group->meth->field_decode(group, b, group->b, ctx)) | |
278 | goto err; | |
279 | } else { | |
280 | if (!BN_copy(a, group->a)) | |
281 | goto err; | |
282 | if (!BN_copy(b, group->b)) | |
283 | goto err; | |
284 | } | |
285 | ||
50e735f9 MC |
286 | /*- |
287 | * check the discriminant: | |
288 | * y^2 = x^3 + a*x + b is an elliptic curve <=> 4*a^3 + 27*b^2 != 0 (mod p) | |
289 | * 0 =< a, b < p | |
290 | */ | |
0f113f3e MC |
291 | if (BN_is_zero(a)) { |
292 | if (BN_is_zero(b)) | |
293 | goto err; | |
294 | } else if (!BN_is_zero(b)) { | |
295 | if (!BN_mod_sqr(tmp_1, a, p, ctx)) | |
296 | goto err; | |
297 | if (!BN_mod_mul(tmp_2, tmp_1, a, p, ctx)) | |
298 | goto err; | |
299 | if (!BN_lshift(tmp_1, tmp_2, 2)) | |
300 | goto err; | |
301 | /* tmp_1 = 4*a^3 */ | |
302 | ||
303 | if (!BN_mod_sqr(tmp_2, b, p, ctx)) | |
304 | goto err; | |
305 | if (!BN_mul_word(tmp_2, 27)) | |
306 | goto err; | |
307 | /* tmp_2 = 27*b^2 */ | |
308 | ||
309 | if (!BN_mod_add(a, tmp_1, tmp_2, p, ctx)) | |
310 | goto err; | |
311 | if (BN_is_zero(a)) | |
312 | goto err; | |
313 | } | |
314 | ret = 1; | |
af28dd6c | 315 | |
0f113f3e | 316 | err: |
ce1415ed | 317 | BN_CTX_end(ctx); |
23a1d5e9 | 318 | BN_CTX_free(new_ctx); |
0f113f3e MC |
319 | return ret; |
320 | } | |
af28dd6c | 321 | |
32ab57cb | 322 | int ossl_ec_GFp_simple_point_init(EC_POINT *point) |
0f113f3e MC |
323 | { |
324 | point->X = BN_new(); | |
325 | point->Y = BN_new(); | |
326 | point->Z = BN_new(); | |
327 | point->Z_is_one = 0; | |
328 | ||
90945fa3 | 329 | if (point->X == NULL || point->Y == NULL || point->Z == NULL) { |
23a1d5e9 RS |
330 | BN_free(point->X); |
331 | BN_free(point->Y); | |
332 | BN_free(point->Z); | |
0f113f3e MC |
333 | return 0; |
334 | } | |
335 | return 1; | |
336 | } | |
60428dbf | 337 | |
32ab57cb | 338 | void ossl_ec_GFp_simple_point_finish(EC_POINT *point) |
0f113f3e MC |
339 | { |
340 | BN_free(point->X); | |
341 | BN_free(point->Y); | |
342 | BN_free(point->Z); | |
343 | } | |
60428dbf | 344 | |
32ab57cb | 345 | void ossl_ec_GFp_simple_point_clear_finish(EC_POINT *point) |
0f113f3e MC |
346 | { |
347 | BN_clear_free(point->X); | |
348 | BN_clear_free(point->Y); | |
349 | BN_clear_free(point->Z); | |
350 | point->Z_is_one = 0; | |
351 | } | |
60428dbf | 352 | |
32ab57cb | 353 | int ossl_ec_GFp_simple_point_copy(EC_POINT *dest, const EC_POINT *src) |
0f113f3e MC |
354 | { |
355 | if (!BN_copy(dest->X, src->X)) | |
356 | return 0; | |
357 | if (!BN_copy(dest->Y, src->Y)) | |
358 | return 0; | |
359 | if (!BN_copy(dest->Z, src->Z)) | |
360 | return 0; | |
361 | dest->Z_is_one = src->Z_is_one; | |
b14e6015 | 362 | dest->curve_name = src->curve_name; |
0f113f3e MC |
363 | |
364 | return 1; | |
365 | } | |
366 | ||
32ab57cb SL |
367 | int ossl_ec_GFp_simple_point_set_to_infinity(const EC_GROUP *group, |
368 | EC_POINT *point) | |
0f113f3e MC |
369 | { |
370 | point->Z_is_one = 0; | |
371 | BN_zero(point->Z); | |
372 | return 1; | |
373 | } | |
374 | ||
32ab57cb SL |
375 | int ossl_ec_GFp_simple_set_Jprojective_coordinates_GFp(const EC_GROUP *group, |
376 | EC_POINT *point, | |
377 | const BIGNUM *x, | |
378 | const BIGNUM *y, | |
379 | const BIGNUM *z, | |
380 | BN_CTX *ctx) | |
0f113f3e MC |
381 | { |
382 | BN_CTX *new_ctx = NULL; | |
383 | int ret = 0; | |
384 | ||
385 | if (ctx == NULL) { | |
a9612d6c | 386 | ctx = new_ctx = BN_CTX_new_ex(group->libctx); |
0f113f3e MC |
387 | if (ctx == NULL) |
388 | return 0; | |
389 | } | |
390 | ||
391 | if (x != NULL) { | |
392 | if (!BN_nnmod(point->X, x, group->field, ctx)) | |
393 | goto err; | |
394 | if (group->meth->field_encode) { | |
395 | if (!group->meth->field_encode(group, point->X, point->X, ctx)) | |
396 | goto err; | |
397 | } | |
398 | } | |
399 | ||
400 | if (y != NULL) { | |
401 | if (!BN_nnmod(point->Y, y, group->field, ctx)) | |
402 | goto err; | |
403 | if (group->meth->field_encode) { | |
404 | if (!group->meth->field_encode(group, point->Y, point->Y, ctx)) | |
405 | goto err; | |
406 | } | |
407 | } | |
408 | ||
409 | if (z != NULL) { | |
410 | int Z_is_one; | |
411 | ||
412 | if (!BN_nnmod(point->Z, z, group->field, ctx)) | |
413 | goto err; | |
414 | Z_is_one = BN_is_one(point->Z); | |
415 | if (group->meth->field_encode) { | |
416 | if (Z_is_one && (group->meth->field_set_to_one != 0)) { | |
417 | if (!group->meth->field_set_to_one(group, point->Z, ctx)) | |
418 | goto err; | |
419 | } else { | |
420 | if (!group-> | |
421 | meth->field_encode(group, point->Z, point->Z, ctx)) | |
422 | goto err; | |
423 | } | |
424 | } | |
425 | point->Z_is_one = Z_is_one; | |
426 | } | |
427 | ||
428 | ret = 1; | |
429 | ||
bb62a8b0 | 430 | err: |
23a1d5e9 | 431 | BN_CTX_free(new_ctx); |
0f113f3e MC |
432 | return ret; |
433 | } | |
434 | ||
32ab57cb SL |
435 | int ossl_ec_GFp_simple_get_Jprojective_coordinates_GFp(const EC_GROUP *group, |
436 | const EC_POINT *point, | |
437 | BIGNUM *x, BIGNUM *y, | |
438 | BIGNUM *z, BN_CTX *ctx) | |
0f113f3e MC |
439 | { |
440 | BN_CTX *new_ctx = NULL; | |
441 | int ret = 0; | |
442 | ||
e1e93f7a | 443 | if (group->meth->field_decode != NULL) { |
0f113f3e | 444 | if (ctx == NULL) { |
a9612d6c | 445 | ctx = new_ctx = BN_CTX_new_ex(group->libctx); |
0f113f3e MC |
446 | if (ctx == NULL) |
447 | return 0; | |
448 | } | |
449 | ||
450 | if (x != NULL) { | |
451 | if (!group->meth->field_decode(group, x, point->X, ctx)) | |
452 | goto err; | |
453 | } | |
454 | if (y != NULL) { | |
455 | if (!group->meth->field_decode(group, y, point->Y, ctx)) | |
456 | goto err; | |
457 | } | |
458 | if (z != NULL) { | |
459 | if (!group->meth->field_decode(group, z, point->Z, ctx)) | |
460 | goto err; | |
461 | } | |
462 | } else { | |
463 | if (x != NULL) { | |
464 | if (!BN_copy(x, point->X)) | |
465 | goto err; | |
466 | } | |
467 | if (y != NULL) { | |
468 | if (!BN_copy(y, point->Y)) | |
469 | goto err; | |
470 | } | |
471 | if (z != NULL) { | |
472 | if (!BN_copy(z, point->Z)) | |
473 | goto err; | |
474 | } | |
475 | } | |
476 | ||
477 | ret = 1; | |
bb62a8b0 | 478 | |
226cc7de | 479 | err: |
23a1d5e9 | 480 | BN_CTX_free(new_ctx); |
0f113f3e MC |
481 | return ret; |
482 | } | |
483 | ||
32ab57cb SL |
484 | int ossl_ec_GFp_simple_point_set_affine_coordinates(const EC_GROUP *group, |
485 | EC_POINT *point, | |
486 | const BIGNUM *x, | |
487 | const BIGNUM *y, BN_CTX *ctx) | |
0f113f3e MC |
488 | { |
489 | if (x == NULL || y == NULL) { | |
490 | /* | |
491 | * unlike for projective coordinates, we do not tolerate this | |
492 | */ | |
9311d0c4 | 493 | ERR_raise(ERR_LIB_EC, ERR_R_PASSED_NULL_PARAMETER); |
0f113f3e MC |
494 | return 0; |
495 | } | |
496 | ||
497 | return EC_POINT_set_Jprojective_coordinates_GFp(group, point, x, y, | |
498 | BN_value_one(), ctx); | |
499 | } | |
500 | ||
32ab57cb SL |
501 | int ossl_ec_GFp_simple_point_get_affine_coordinates(const EC_GROUP *group, |
502 | const EC_POINT *point, | |
503 | BIGNUM *x, BIGNUM *y, | |
504 | BN_CTX *ctx) | |
0f113f3e MC |
505 | { |
506 | BN_CTX *new_ctx = NULL; | |
507 | BIGNUM *Z, *Z_1, *Z_2, *Z_3; | |
508 | const BIGNUM *Z_; | |
509 | int ret = 0; | |
510 | ||
511 | if (EC_POINT_is_at_infinity(group, point)) { | |
9311d0c4 | 512 | ERR_raise(ERR_LIB_EC, EC_R_POINT_AT_INFINITY); |
0f113f3e MC |
513 | return 0; |
514 | } | |
515 | ||
516 | if (ctx == NULL) { | |
a9612d6c | 517 | ctx = new_ctx = BN_CTX_new_ex(group->libctx); |
0f113f3e MC |
518 | if (ctx == NULL) |
519 | return 0; | |
520 | } | |
521 | ||
522 | BN_CTX_start(ctx); | |
523 | Z = BN_CTX_get(ctx); | |
524 | Z_1 = BN_CTX_get(ctx); | |
525 | Z_2 = BN_CTX_get(ctx); | |
526 | Z_3 = BN_CTX_get(ctx); | |
527 | if (Z_3 == NULL) | |
528 | goto err; | |
529 | ||
530 | /* transform (X, Y, Z) into (x, y) := (X/Z^2, Y/Z^3) */ | |
531 | ||
e1e93f7a | 532 | if (group->meth->field_decode != NULL) { |
0f113f3e MC |
533 | if (!group->meth->field_decode(group, Z, point->Z, ctx)) |
534 | goto err; | |
535 | Z_ = Z; | |
536 | } else { | |
537 | Z_ = point->Z; | |
538 | } | |
539 | ||
540 | if (BN_is_one(Z_)) { | |
e1e93f7a | 541 | if (group->meth->field_decode != NULL) { |
0f113f3e MC |
542 | if (x != NULL) { |
543 | if (!group->meth->field_decode(group, x, point->X, ctx)) | |
544 | goto err; | |
545 | } | |
546 | if (y != NULL) { | |
547 | if (!group->meth->field_decode(group, y, point->Y, ctx)) | |
548 | goto err; | |
549 | } | |
550 | } else { | |
551 | if (x != NULL) { | |
552 | if (!BN_copy(x, point->X)) | |
553 | goto err; | |
554 | } | |
555 | if (y != NULL) { | |
556 | if (!BN_copy(y, point->Y)) | |
557 | goto err; | |
558 | } | |
559 | } | |
560 | } else { | |
e0033efc | 561 | if (!group->meth->field_inv(group, Z_1, Z_, ctx)) { |
9311d0c4 | 562 | ERR_raise(ERR_LIB_EC, ERR_R_BN_LIB); |
0f113f3e MC |
563 | goto err; |
564 | } | |
565 | ||
e1e93f7a | 566 | if (group->meth->field_encode == NULL) { |
0f113f3e MC |
567 | /* field_sqr works on standard representation */ |
568 | if (!group->meth->field_sqr(group, Z_2, Z_1, ctx)) | |
569 | goto err; | |
570 | } else { | |
571 | if (!BN_mod_sqr(Z_2, Z_1, group->field, ctx)) | |
572 | goto err; | |
573 | } | |
574 | ||
575 | if (x != NULL) { | |
576 | /* | |
577 | * in the Montgomery case, field_mul will cancel out Montgomery | |
578 | * factor in X: | |
579 | */ | |
580 | if (!group->meth->field_mul(group, x, point->X, Z_2, ctx)) | |
581 | goto err; | |
582 | } | |
583 | ||
584 | if (y != NULL) { | |
e1e93f7a | 585 | if (group->meth->field_encode == NULL) { |
0f113f3e MC |
586 | /* |
587 | * field_mul works on standard representation | |
588 | */ | |
589 | if (!group->meth->field_mul(group, Z_3, Z_2, Z_1, ctx)) | |
590 | goto err; | |
591 | } else { | |
592 | if (!BN_mod_mul(Z_3, Z_2, Z_1, group->field, ctx)) | |
593 | goto err; | |
594 | } | |
595 | ||
596 | /* | |
597 | * in the Montgomery case, field_mul will cancel out Montgomery | |
598 | * factor in Y: | |
599 | */ | |
600 | if (!group->meth->field_mul(group, y, point->Y, Z_3, ctx)) | |
601 | goto err; | |
602 | } | |
603 | } | |
604 | ||
605 | ret = 1; | |
226cc7de BM |
606 | |
607 | err: | |
0f113f3e | 608 | BN_CTX_end(ctx); |
23a1d5e9 | 609 | BN_CTX_free(new_ctx); |
0f113f3e MC |
610 | return ret; |
611 | } | |
612 | ||
32ab57cb SL |
613 | int ossl_ec_GFp_simple_add(const EC_GROUP *group, EC_POINT *r, const EC_POINT *a, |
614 | const EC_POINT *b, BN_CTX *ctx) | |
0f113f3e MC |
615 | { |
616 | int (*field_mul) (const EC_GROUP *, BIGNUM *, const BIGNUM *, | |
617 | const BIGNUM *, BN_CTX *); | |
618 | int (*field_sqr) (const EC_GROUP *, BIGNUM *, const BIGNUM *, BN_CTX *); | |
619 | const BIGNUM *p; | |
620 | BN_CTX *new_ctx = NULL; | |
621 | BIGNUM *n0, *n1, *n2, *n3, *n4, *n5, *n6; | |
622 | int ret = 0; | |
623 | ||
624 | if (a == b) | |
625 | return EC_POINT_dbl(group, r, a, ctx); | |
626 | if (EC_POINT_is_at_infinity(group, a)) | |
627 | return EC_POINT_copy(r, b); | |
628 | if (EC_POINT_is_at_infinity(group, b)) | |
629 | return EC_POINT_copy(r, a); | |
630 | ||
631 | field_mul = group->meth->field_mul; | |
632 | field_sqr = group->meth->field_sqr; | |
633 | p = group->field; | |
634 | ||
635 | if (ctx == NULL) { | |
a9612d6c | 636 | ctx = new_ctx = BN_CTX_new_ex(group->libctx); |
0f113f3e MC |
637 | if (ctx == NULL) |
638 | return 0; | |
639 | } | |
640 | ||
641 | BN_CTX_start(ctx); | |
642 | n0 = BN_CTX_get(ctx); | |
643 | n1 = BN_CTX_get(ctx); | |
644 | n2 = BN_CTX_get(ctx); | |
645 | n3 = BN_CTX_get(ctx); | |
646 | n4 = BN_CTX_get(ctx); | |
647 | n5 = BN_CTX_get(ctx); | |
648 | n6 = BN_CTX_get(ctx); | |
649 | if (n6 == NULL) | |
650 | goto end; | |
651 | ||
652 | /* | |
653 | * Note that in this function we must not read components of 'a' or 'b' | |
654 | * once we have written the corresponding components of 'r'. ('r' might | |
655 | * be one of 'a' or 'b'.) | |
656 | */ | |
657 | ||
658 | /* n1, n2 */ | |
659 | if (b->Z_is_one) { | |
660 | if (!BN_copy(n1, a->X)) | |
661 | goto end; | |
662 | if (!BN_copy(n2, a->Y)) | |
663 | goto end; | |
664 | /* n1 = X_a */ | |
665 | /* n2 = Y_a */ | |
666 | } else { | |
667 | if (!field_sqr(group, n0, b->Z, ctx)) | |
668 | goto end; | |
669 | if (!field_mul(group, n1, a->X, n0, ctx)) | |
670 | goto end; | |
671 | /* n1 = X_a * Z_b^2 */ | |
672 | ||
673 | if (!field_mul(group, n0, n0, b->Z, ctx)) | |
674 | goto end; | |
675 | if (!field_mul(group, n2, a->Y, n0, ctx)) | |
676 | goto end; | |
677 | /* n2 = Y_a * Z_b^3 */ | |
678 | } | |
679 | ||
680 | /* n3, n4 */ | |
681 | if (a->Z_is_one) { | |
682 | if (!BN_copy(n3, b->X)) | |
683 | goto end; | |
684 | if (!BN_copy(n4, b->Y)) | |
685 | goto end; | |
686 | /* n3 = X_b */ | |
687 | /* n4 = Y_b */ | |
688 | } else { | |
689 | if (!field_sqr(group, n0, a->Z, ctx)) | |
690 | goto end; | |
691 | if (!field_mul(group, n3, b->X, n0, ctx)) | |
692 | goto end; | |
693 | /* n3 = X_b * Z_a^2 */ | |
694 | ||
695 | if (!field_mul(group, n0, n0, a->Z, ctx)) | |
696 | goto end; | |
697 | if (!field_mul(group, n4, b->Y, n0, ctx)) | |
698 | goto end; | |
699 | /* n4 = Y_b * Z_a^3 */ | |
700 | } | |
701 | ||
702 | /* n5, n6 */ | |
703 | if (!BN_mod_sub_quick(n5, n1, n3, p)) | |
704 | goto end; | |
705 | if (!BN_mod_sub_quick(n6, n2, n4, p)) | |
706 | goto end; | |
707 | /* n5 = n1 - n3 */ | |
708 | /* n6 = n2 - n4 */ | |
709 | ||
710 | if (BN_is_zero(n5)) { | |
711 | if (BN_is_zero(n6)) { | |
712 | /* a is the same point as b */ | |
713 | BN_CTX_end(ctx); | |
714 | ret = EC_POINT_dbl(group, r, a, ctx); | |
715 | ctx = NULL; | |
716 | goto end; | |
717 | } else { | |
718 | /* a is the inverse of b */ | |
719 | BN_zero(r->Z); | |
720 | r->Z_is_one = 0; | |
721 | ret = 1; | |
722 | goto end; | |
723 | } | |
724 | } | |
725 | ||
726 | /* 'n7', 'n8' */ | |
727 | if (!BN_mod_add_quick(n1, n1, n3, p)) | |
728 | goto end; | |
729 | if (!BN_mod_add_quick(n2, n2, n4, p)) | |
730 | goto end; | |
731 | /* 'n7' = n1 + n3 */ | |
732 | /* 'n8' = n2 + n4 */ | |
733 | ||
734 | /* Z_r */ | |
735 | if (a->Z_is_one && b->Z_is_one) { | |
736 | if (!BN_copy(r->Z, n5)) | |
737 | goto end; | |
738 | } else { | |
739 | if (a->Z_is_one) { | |
740 | if (!BN_copy(n0, b->Z)) | |
741 | goto end; | |
742 | } else if (b->Z_is_one) { | |
743 | if (!BN_copy(n0, a->Z)) | |
744 | goto end; | |
745 | } else { | |
746 | if (!field_mul(group, n0, a->Z, b->Z, ctx)) | |
747 | goto end; | |
748 | } | |
749 | if (!field_mul(group, r->Z, n0, n5, ctx)) | |
750 | goto end; | |
751 | } | |
752 | r->Z_is_one = 0; | |
753 | /* Z_r = Z_a * Z_b * n5 */ | |
754 | ||
755 | /* X_r */ | |
756 | if (!field_sqr(group, n0, n6, ctx)) | |
757 | goto end; | |
758 | if (!field_sqr(group, n4, n5, ctx)) | |
759 | goto end; | |
760 | if (!field_mul(group, n3, n1, n4, ctx)) | |
761 | goto end; | |
762 | if (!BN_mod_sub_quick(r->X, n0, n3, p)) | |
763 | goto end; | |
764 | /* X_r = n6^2 - n5^2 * 'n7' */ | |
765 | ||
766 | /* 'n9' */ | |
767 | if (!BN_mod_lshift1_quick(n0, r->X, p)) | |
768 | goto end; | |
769 | if (!BN_mod_sub_quick(n0, n3, n0, p)) | |
770 | goto end; | |
771 | /* n9 = n5^2 * 'n7' - 2 * X_r */ | |
772 | ||
773 | /* Y_r */ | |
774 | if (!field_mul(group, n0, n0, n6, ctx)) | |
775 | goto end; | |
776 | if (!field_mul(group, n5, n4, n5, ctx)) | |
777 | goto end; /* now n5 is n5^3 */ | |
778 | if (!field_mul(group, n1, n2, n5, ctx)) | |
779 | goto end; | |
780 | if (!BN_mod_sub_quick(n0, n0, n1, p)) | |
781 | goto end; | |
782 | if (BN_is_odd(n0)) | |
783 | if (!BN_add(n0, n0, p)) | |
784 | goto end; | |
785 | /* now 0 <= n0 < 2*p, and n0 is even */ | |
786 | if (!BN_rshift1(r->Y, n0)) | |
787 | goto end; | |
788 | /* Y_r = (n6 * 'n9' - 'n8' * 'n5^3') / 2 */ | |
789 | ||
790 | ret = 1; | |
60428dbf BM |
791 | |
792 | end: | |
ce1415ed | 793 | BN_CTX_end(ctx); |
23a1d5e9 | 794 | BN_CTX_free(new_ctx); |
0f113f3e MC |
795 | return ret; |
796 | } | |
797 | ||
32ab57cb SL |
798 | int ossl_ec_GFp_simple_dbl(const EC_GROUP *group, EC_POINT *r, const EC_POINT *a, |
799 | BN_CTX *ctx) | |
0f113f3e MC |
800 | { |
801 | int (*field_mul) (const EC_GROUP *, BIGNUM *, const BIGNUM *, | |
802 | const BIGNUM *, BN_CTX *); | |
803 | int (*field_sqr) (const EC_GROUP *, BIGNUM *, const BIGNUM *, BN_CTX *); | |
804 | const BIGNUM *p; | |
805 | BN_CTX *new_ctx = NULL; | |
806 | BIGNUM *n0, *n1, *n2, *n3; | |
807 | int ret = 0; | |
808 | ||
809 | if (EC_POINT_is_at_infinity(group, a)) { | |
810 | BN_zero(r->Z); | |
811 | r->Z_is_one = 0; | |
812 | return 1; | |
813 | } | |
814 | ||
815 | field_mul = group->meth->field_mul; | |
816 | field_sqr = group->meth->field_sqr; | |
817 | p = group->field; | |
818 | ||
819 | if (ctx == NULL) { | |
a9612d6c | 820 | ctx = new_ctx = BN_CTX_new_ex(group->libctx); |
0f113f3e MC |
821 | if (ctx == NULL) |
822 | return 0; | |
823 | } | |
824 | ||
825 | BN_CTX_start(ctx); | |
826 | n0 = BN_CTX_get(ctx); | |
827 | n1 = BN_CTX_get(ctx); | |
828 | n2 = BN_CTX_get(ctx); | |
829 | n3 = BN_CTX_get(ctx); | |
830 | if (n3 == NULL) | |
831 | goto err; | |
832 | ||
833 | /* | |
834 | * Note that in this function we must not read components of 'a' once we | |
835 | * have written the corresponding components of 'r'. ('r' might the same | |
836 | * as 'a'.) | |
837 | */ | |
838 | ||
839 | /* n1 */ | |
840 | if (a->Z_is_one) { | |
841 | if (!field_sqr(group, n0, a->X, ctx)) | |
842 | goto err; | |
843 | if (!BN_mod_lshift1_quick(n1, n0, p)) | |
844 | goto err; | |
845 | if (!BN_mod_add_quick(n0, n0, n1, p)) | |
846 | goto err; | |
847 | if (!BN_mod_add_quick(n1, n0, group->a, p)) | |
848 | goto err; | |
849 | /* n1 = 3 * X_a^2 + a_curve */ | |
850 | } else if (group->a_is_minus3) { | |
851 | if (!field_sqr(group, n1, a->Z, ctx)) | |
852 | goto err; | |
853 | if (!BN_mod_add_quick(n0, a->X, n1, p)) | |
854 | goto err; | |
855 | if (!BN_mod_sub_quick(n2, a->X, n1, p)) | |
856 | goto err; | |
857 | if (!field_mul(group, n1, n0, n2, ctx)) | |
858 | goto err; | |
859 | if (!BN_mod_lshift1_quick(n0, n1, p)) | |
860 | goto err; | |
861 | if (!BN_mod_add_quick(n1, n0, n1, p)) | |
862 | goto err; | |
35a1cc90 MC |
863 | /*- |
864 | * n1 = 3 * (X_a + Z_a^2) * (X_a - Z_a^2) | |
865 | * = 3 * X_a^2 - 3 * Z_a^4 | |
866 | */ | |
0f113f3e MC |
867 | } else { |
868 | if (!field_sqr(group, n0, a->X, ctx)) | |
869 | goto err; | |
870 | if (!BN_mod_lshift1_quick(n1, n0, p)) | |
871 | goto err; | |
872 | if (!BN_mod_add_quick(n0, n0, n1, p)) | |
873 | goto err; | |
874 | if (!field_sqr(group, n1, a->Z, ctx)) | |
875 | goto err; | |
876 | if (!field_sqr(group, n1, n1, ctx)) | |
877 | goto err; | |
878 | if (!field_mul(group, n1, n1, group->a, ctx)) | |
879 | goto err; | |
880 | if (!BN_mod_add_quick(n1, n1, n0, p)) | |
881 | goto err; | |
882 | /* n1 = 3 * X_a^2 + a_curve * Z_a^4 */ | |
883 | } | |
884 | ||
885 | /* Z_r */ | |
886 | if (a->Z_is_one) { | |
887 | if (!BN_copy(n0, a->Y)) | |
888 | goto err; | |
889 | } else { | |
890 | if (!field_mul(group, n0, a->Y, a->Z, ctx)) | |
891 | goto err; | |
892 | } | |
893 | if (!BN_mod_lshift1_quick(r->Z, n0, p)) | |
894 | goto err; | |
895 | r->Z_is_one = 0; | |
896 | /* Z_r = 2 * Y_a * Z_a */ | |
897 | ||
898 | /* n2 */ | |
899 | if (!field_sqr(group, n3, a->Y, ctx)) | |
900 | goto err; | |
901 | if (!field_mul(group, n2, a->X, n3, ctx)) | |
902 | goto err; | |
903 | if (!BN_mod_lshift_quick(n2, n2, 2, p)) | |
904 | goto err; | |
905 | /* n2 = 4 * X_a * Y_a^2 */ | |
906 | ||
907 | /* X_r */ | |
908 | if (!BN_mod_lshift1_quick(n0, n2, p)) | |
909 | goto err; | |
910 | if (!field_sqr(group, r->X, n1, ctx)) | |
911 | goto err; | |
912 | if (!BN_mod_sub_quick(r->X, r->X, n0, p)) | |
913 | goto err; | |
914 | /* X_r = n1^2 - 2 * n2 */ | |
915 | ||
916 | /* n3 */ | |
917 | if (!field_sqr(group, n0, n3, ctx)) | |
918 | goto err; | |
919 | if (!BN_mod_lshift_quick(n3, n0, 3, p)) | |
920 | goto err; | |
921 | /* n3 = 8 * Y_a^4 */ | |
922 | ||
923 | /* Y_r */ | |
924 | if (!BN_mod_sub_quick(n0, n2, r->X, p)) | |
925 | goto err; | |
926 | if (!field_mul(group, n0, n1, n0, ctx)) | |
927 | goto err; | |
928 | if (!BN_mod_sub_quick(r->Y, n0, n3, p)) | |
929 | goto err; | |
930 | /* Y_r = n1 * (n2 - X_r) - n3 */ | |
931 | ||
932 | ret = 1; | |
60428dbf BM |
933 | |
934 | err: | |
0f113f3e | 935 | BN_CTX_end(ctx); |
23a1d5e9 | 936 | BN_CTX_free(new_ctx); |
0f113f3e MC |
937 | return ret; |
938 | } | |
60428dbf | 939 | |
32ab57cb SL |
940 | int ossl_ec_GFp_simple_invert(const EC_GROUP *group, EC_POINT *point, |
941 | BN_CTX *ctx) | |
0f113f3e MC |
942 | { |
943 | if (EC_POINT_is_at_infinity(group, point) || BN_is_zero(point->Y)) | |
944 | /* point is its own inverse */ | |
945 | return 1; | |
1d5bd6cf | 946 | |
0f113f3e MC |
947 | return BN_usub(point->Y, group->field, point->Y); |
948 | } | |
1d5bd6cf | 949 | |
32ab57cb SL |
950 | int ossl_ec_GFp_simple_is_at_infinity(const EC_GROUP *group, |
951 | const EC_POINT *point) | |
0f113f3e MC |
952 | { |
953 | return BN_is_zero(point->Z); | |
954 | } | |
955 | ||
32ab57cb SL |
956 | int ossl_ec_GFp_simple_is_on_curve(const EC_GROUP *group, const EC_POINT *point, |
957 | BN_CTX *ctx) | |
0f113f3e MC |
958 | { |
959 | int (*field_mul) (const EC_GROUP *, BIGNUM *, const BIGNUM *, | |
960 | const BIGNUM *, BN_CTX *); | |
961 | int (*field_sqr) (const EC_GROUP *, BIGNUM *, const BIGNUM *, BN_CTX *); | |
962 | const BIGNUM *p; | |
963 | BN_CTX *new_ctx = NULL; | |
964 | BIGNUM *rh, *tmp, *Z4, *Z6; | |
965 | int ret = -1; | |
966 | ||
967 | if (EC_POINT_is_at_infinity(group, point)) | |
968 | return 1; | |
969 | ||
970 | field_mul = group->meth->field_mul; | |
971 | field_sqr = group->meth->field_sqr; | |
972 | p = group->field; | |
973 | ||
974 | if (ctx == NULL) { | |
a9612d6c | 975 | ctx = new_ctx = BN_CTX_new_ex(group->libctx); |
0f113f3e MC |
976 | if (ctx == NULL) |
977 | return -1; | |
978 | } | |
979 | ||
980 | BN_CTX_start(ctx); | |
981 | rh = BN_CTX_get(ctx); | |
982 | tmp = BN_CTX_get(ctx); | |
983 | Z4 = BN_CTX_get(ctx); | |
984 | Z6 = BN_CTX_get(ctx); | |
985 | if (Z6 == NULL) | |
986 | goto err; | |
987 | ||
35a1cc90 MC |
988 | /*- |
989 | * We have a curve defined by a Weierstrass equation | |
990 | * y^2 = x^3 + a*x + b. | |
991 | * The point to consider is given in Jacobian projective coordinates | |
992 | * where (X, Y, Z) represents (x, y) = (X/Z^2, Y/Z^3). | |
993 | * Substituting this and multiplying by Z^6 transforms the above equation into | |
994 | * Y^2 = X^3 + a*X*Z^4 + b*Z^6. | |
995 | * To test this, we add up the right-hand side in 'rh'. | |
996 | */ | |
0f113f3e MC |
997 | |
998 | /* rh := X^2 */ | |
999 | if (!field_sqr(group, rh, point->X, ctx)) | |
1000 | goto err; | |
1001 | ||
1002 | if (!point->Z_is_one) { | |
1003 | if (!field_sqr(group, tmp, point->Z, ctx)) | |
1004 | goto err; | |
1005 | if (!field_sqr(group, Z4, tmp, ctx)) | |
1006 | goto err; | |
1007 | if (!field_mul(group, Z6, Z4, tmp, ctx)) | |
1008 | goto err; | |
1009 | ||
1010 | /* rh := (rh + a*Z^4)*X */ | |
1011 | if (group->a_is_minus3) { | |
1012 | if (!BN_mod_lshift1_quick(tmp, Z4, p)) | |
1013 | goto err; | |
1014 | if (!BN_mod_add_quick(tmp, tmp, Z4, p)) | |
1015 | goto err; | |
1016 | if (!BN_mod_sub_quick(rh, rh, tmp, p)) | |
1017 | goto err; | |
1018 | if (!field_mul(group, rh, rh, point->X, ctx)) | |
1019 | goto err; | |
1020 | } else { | |
1021 | if (!field_mul(group, tmp, Z4, group->a, ctx)) | |
1022 | goto err; | |
1023 | if (!BN_mod_add_quick(rh, rh, tmp, p)) | |
1024 | goto err; | |
1025 | if (!field_mul(group, rh, rh, point->X, ctx)) | |
1026 | goto err; | |
1027 | } | |
1028 | ||
1029 | /* rh := rh + b*Z^6 */ | |
1030 | if (!field_mul(group, tmp, group->b, Z6, ctx)) | |
1031 | goto err; | |
1032 | if (!BN_mod_add_quick(rh, rh, tmp, p)) | |
1033 | goto err; | |
1034 | } else { | |
1035 | /* point->Z_is_one */ | |
1036 | ||
1037 | /* rh := (rh + a)*X */ | |
1038 | if (!BN_mod_add_quick(rh, rh, group->a, p)) | |
1039 | goto err; | |
1040 | if (!field_mul(group, rh, rh, point->X, ctx)) | |
1041 | goto err; | |
1042 | /* rh := rh + b */ | |
1043 | if (!BN_mod_add_quick(rh, rh, group->b, p)) | |
1044 | goto err; | |
1045 | } | |
1046 | ||
1047 | /* 'lh' := Y^2 */ | |
1048 | if (!field_sqr(group, tmp, point->Y, ctx)) | |
1049 | goto err; | |
1050 | ||
1051 | ret = (0 == BN_ucmp(tmp, rh)); | |
e869d4bd BM |
1052 | |
1053 | err: | |
0f113f3e | 1054 | BN_CTX_end(ctx); |
23a1d5e9 | 1055 | BN_CTX_free(new_ctx); |
0f113f3e MC |
1056 | return ret; |
1057 | } | |
1058 | ||
32ab57cb SL |
1059 | int ossl_ec_GFp_simple_cmp(const EC_GROUP *group, const EC_POINT *a, |
1060 | const EC_POINT *b, BN_CTX *ctx) | |
0f113f3e | 1061 | { |
35a1cc90 MC |
1062 | /*- |
1063 | * return values: | |
1064 | * -1 error | |
1065 | * 0 equal (in affine coordinates) | |
1066 | * 1 not equal | |
1067 | */ | |
0f113f3e MC |
1068 | |
1069 | int (*field_mul) (const EC_GROUP *, BIGNUM *, const BIGNUM *, | |
1070 | const BIGNUM *, BN_CTX *); | |
1071 | int (*field_sqr) (const EC_GROUP *, BIGNUM *, const BIGNUM *, BN_CTX *); | |
1072 | BN_CTX *new_ctx = NULL; | |
1073 | BIGNUM *tmp1, *tmp2, *Za23, *Zb23; | |
1074 | const BIGNUM *tmp1_, *tmp2_; | |
1075 | int ret = -1; | |
1076 | ||
1077 | if (EC_POINT_is_at_infinity(group, a)) { | |
1078 | return EC_POINT_is_at_infinity(group, b) ? 0 : 1; | |
1079 | } | |
1080 | ||
1081 | if (EC_POINT_is_at_infinity(group, b)) | |
1082 | return 1; | |
1083 | ||
1084 | if (a->Z_is_one && b->Z_is_one) { | |
1085 | return ((BN_cmp(a->X, b->X) == 0) && BN_cmp(a->Y, b->Y) == 0) ? 0 : 1; | |
1086 | } | |
1087 | ||
1088 | field_mul = group->meth->field_mul; | |
1089 | field_sqr = group->meth->field_sqr; | |
1090 | ||
1091 | if (ctx == NULL) { | |
a9612d6c | 1092 | ctx = new_ctx = BN_CTX_new_ex(group->libctx); |
0f113f3e MC |
1093 | if (ctx == NULL) |
1094 | return -1; | |
1095 | } | |
1096 | ||
1097 | BN_CTX_start(ctx); | |
1098 | tmp1 = BN_CTX_get(ctx); | |
1099 | tmp2 = BN_CTX_get(ctx); | |
1100 | Za23 = BN_CTX_get(ctx); | |
1101 | Zb23 = BN_CTX_get(ctx); | |
1102 | if (Zb23 == NULL) | |
1103 | goto end; | |
1104 | ||
35a1cc90 MC |
1105 | /*- |
1106 | * We have to decide whether | |
1107 | * (X_a/Z_a^2, Y_a/Z_a^3) = (X_b/Z_b^2, Y_b/Z_b^3), | |
1108 | * or equivalently, whether | |
1109 | * (X_a*Z_b^2, Y_a*Z_b^3) = (X_b*Z_a^2, Y_b*Z_a^3). | |
1110 | */ | |
0f113f3e MC |
1111 | |
1112 | if (!b->Z_is_one) { | |
1113 | if (!field_sqr(group, Zb23, b->Z, ctx)) | |
1114 | goto end; | |
1115 | if (!field_mul(group, tmp1, a->X, Zb23, ctx)) | |
1116 | goto end; | |
1117 | tmp1_ = tmp1; | |
1118 | } else | |
1119 | tmp1_ = a->X; | |
1120 | if (!a->Z_is_one) { | |
1121 | if (!field_sqr(group, Za23, a->Z, ctx)) | |
1122 | goto end; | |
1123 | if (!field_mul(group, tmp2, b->X, Za23, ctx)) | |
1124 | goto end; | |
1125 | tmp2_ = tmp2; | |
1126 | } else | |
1127 | tmp2_ = b->X; | |
1128 | ||
1129 | /* compare X_a*Z_b^2 with X_b*Z_a^2 */ | |
1130 | if (BN_cmp(tmp1_, tmp2_) != 0) { | |
1131 | ret = 1; /* points differ */ | |
1132 | goto end; | |
1133 | } | |
1134 | ||
1135 | if (!b->Z_is_one) { | |
1136 | if (!field_mul(group, Zb23, Zb23, b->Z, ctx)) | |
1137 | goto end; | |
1138 | if (!field_mul(group, tmp1, a->Y, Zb23, ctx)) | |
1139 | goto end; | |
1140 | /* tmp1_ = tmp1 */ | |
1141 | } else | |
1142 | tmp1_ = a->Y; | |
1143 | if (!a->Z_is_one) { | |
1144 | if (!field_mul(group, Za23, Za23, a->Z, ctx)) | |
1145 | goto end; | |
1146 | if (!field_mul(group, tmp2, b->Y, Za23, ctx)) | |
1147 | goto end; | |
1148 | /* tmp2_ = tmp2 */ | |
1149 | } else | |
1150 | tmp2_ = b->Y; | |
1151 | ||
1152 | /* compare Y_a*Z_b^3 with Y_b*Z_a^3 */ | |
1153 | if (BN_cmp(tmp1_, tmp2_) != 0) { | |
1154 | ret = 1; /* points differ */ | |
1155 | goto end; | |
1156 | } | |
1157 | ||
1158 | /* points are equal */ | |
1159 | ret = 0; | |
bb62a8b0 BM |
1160 | |
1161 | end: | |
0f113f3e | 1162 | BN_CTX_end(ctx); |
23a1d5e9 | 1163 | BN_CTX_free(new_ctx); |
0f113f3e MC |
1164 | return ret; |
1165 | } | |
1166 | ||
32ab57cb SL |
1167 | int ossl_ec_GFp_simple_make_affine(const EC_GROUP *group, EC_POINT *point, |
1168 | BN_CTX *ctx) | |
0f113f3e MC |
1169 | { |
1170 | BN_CTX *new_ctx = NULL; | |
1171 | BIGNUM *x, *y; | |
1172 | int ret = 0; | |
1173 | ||
1174 | if (point->Z_is_one || EC_POINT_is_at_infinity(group, point)) | |
1175 | return 1; | |
1176 | ||
1177 | if (ctx == NULL) { | |
a9612d6c | 1178 | ctx = new_ctx = BN_CTX_new_ex(group->libctx); |
0f113f3e MC |
1179 | if (ctx == NULL) |
1180 | return 0; | |
1181 | } | |
1182 | ||
1183 | BN_CTX_start(ctx); | |
1184 | x = BN_CTX_get(ctx); | |
1185 | y = BN_CTX_get(ctx); | |
1186 | if (y == NULL) | |
1187 | goto err; | |
1188 | ||
9cc570d4 | 1189 | if (!EC_POINT_get_affine_coordinates(group, point, x, y, ctx)) |
0f113f3e | 1190 | goto err; |
9cc570d4 | 1191 | if (!EC_POINT_set_affine_coordinates(group, point, x, y, ctx)) |
0f113f3e MC |
1192 | goto err; |
1193 | if (!point->Z_is_one) { | |
9311d0c4 | 1194 | ERR_raise(ERR_LIB_EC, ERR_R_INTERNAL_ERROR); |
0f113f3e MC |
1195 | goto err; |
1196 | } | |
1197 | ||
1198 | ret = 1; | |
e869d4bd | 1199 | |
226cc7de | 1200 | err: |
0f113f3e | 1201 | BN_CTX_end(ctx); |
23a1d5e9 | 1202 | BN_CTX_free(new_ctx); |
0f113f3e MC |
1203 | return ret; |
1204 | } | |
1205 | ||
32ab57cb SL |
1206 | int ossl_ec_GFp_simple_points_make_affine(const EC_GROUP *group, size_t num, |
1207 | EC_POINT *points[], BN_CTX *ctx) | |
0f113f3e MC |
1208 | { |
1209 | BN_CTX *new_ctx = NULL; | |
1210 | BIGNUM *tmp, *tmp_Z; | |
1211 | BIGNUM **prod_Z = NULL; | |
1212 | size_t i; | |
1213 | int ret = 0; | |
1214 | ||
1215 | if (num == 0) | |
1216 | return 1; | |
1217 | ||
1218 | if (ctx == NULL) { | |
a9612d6c | 1219 | ctx = new_ctx = BN_CTX_new_ex(group->libctx); |
0f113f3e MC |
1220 | if (ctx == NULL) |
1221 | return 0; | |
1222 | } | |
1223 | ||
1224 | BN_CTX_start(ctx); | |
1225 | tmp = BN_CTX_get(ctx); | |
1226 | tmp_Z = BN_CTX_get(ctx); | |
edea42c6 | 1227 | if (tmp_Z == NULL) |
0f113f3e MC |
1228 | goto err; |
1229 | ||
cbe29648 | 1230 | prod_Z = OPENSSL_malloc(num * sizeof(prod_Z[0])); |
0f113f3e MC |
1231 | if (prod_Z == NULL) |
1232 | goto err; | |
1233 | for (i = 0; i < num; i++) { | |
1234 | prod_Z[i] = BN_new(); | |
1235 | if (prod_Z[i] == NULL) | |
1236 | goto err; | |
1237 | } | |
1238 | ||
1239 | /* | |
1240 | * Set each prod_Z[i] to the product of points[0]->Z .. points[i]->Z, | |
1241 | * skipping any zero-valued inputs (pretend that they're 1). | |
1242 | */ | |
1243 | ||
1244 | if (!BN_is_zero(points[0]->Z)) { | |
1245 | if (!BN_copy(prod_Z[0], points[0]->Z)) | |
1246 | goto err; | |
1247 | } else { | |
1248 | if (group->meth->field_set_to_one != 0) { | |
1249 | if (!group->meth->field_set_to_one(group, prod_Z[0], ctx)) | |
1250 | goto err; | |
1251 | } else { | |
1252 | if (!BN_one(prod_Z[0])) | |
1253 | goto err; | |
1254 | } | |
1255 | } | |
1256 | ||
1257 | for (i = 1; i < num; i++) { | |
1258 | if (!BN_is_zero(points[i]->Z)) { | |
1259 | if (!group-> | |
1260 | meth->field_mul(group, prod_Z[i], prod_Z[i - 1], points[i]->Z, | |
1261 | ctx)) | |
1262 | goto err; | |
1263 | } else { | |
1264 | if (!BN_copy(prod_Z[i], prod_Z[i - 1])) | |
1265 | goto err; | |
1266 | } | |
1267 | } | |
1268 | ||
1269 | /* | |
1270 | * Now use a single explicit inversion to replace every non-zero | |
1271 | * points[i]->Z by its inverse. | |
1272 | */ | |
1273 | ||
e0033efc | 1274 | if (!group->meth->field_inv(group, tmp, prod_Z[num - 1], ctx)) { |
9311d0c4 | 1275 | ERR_raise(ERR_LIB_EC, ERR_R_BN_LIB); |
0f113f3e MC |
1276 | goto err; |
1277 | } | |
e1e93f7a | 1278 | if (group->meth->field_encode != NULL) { |
0f113f3e MC |
1279 | /* |
1280 | * In the Montgomery case, we just turned R*H (representing H) into | |
1281 | * 1/(R*H), but we need R*(1/H) (representing 1/H); i.e. we need to | |
1282 | * multiply by the Montgomery factor twice. | |
1283 | */ | |
1284 | if (!group->meth->field_encode(group, tmp, tmp, ctx)) | |
1285 | goto err; | |
1286 | if (!group->meth->field_encode(group, tmp, tmp, ctx)) | |
1287 | goto err; | |
1288 | } | |
1289 | ||
1290 | for (i = num - 1; i > 0; --i) { | |
1291 | /* | |
1292 | * Loop invariant: tmp is the product of the inverses of points[0]->Z | |
1293 | * .. points[i]->Z (zero-valued inputs skipped). | |
1294 | */ | |
1295 | if (!BN_is_zero(points[i]->Z)) { | |
1296 | /* | |
1297 | * Set tmp_Z to the inverse of points[i]->Z (as product of Z | |
1298 | * inverses 0 .. i, Z values 0 .. i - 1). | |
1299 | */ | |
1300 | if (!group-> | |
1301 | meth->field_mul(group, tmp_Z, prod_Z[i - 1], tmp, ctx)) | |
1302 | goto err; | |
1303 | /* | |
1304 | * Update tmp to satisfy the loop invariant for i - 1. | |
1305 | */ | |
1306 | if (!group->meth->field_mul(group, tmp, tmp, points[i]->Z, ctx)) | |
1307 | goto err; | |
1308 | /* Replace points[i]->Z by its inverse. */ | |
1309 | if (!BN_copy(points[i]->Z, tmp_Z)) | |
1310 | goto err; | |
1311 | } | |
1312 | } | |
1313 | ||
1314 | if (!BN_is_zero(points[0]->Z)) { | |
1315 | /* Replace points[0]->Z by its inverse. */ | |
1316 | if (!BN_copy(points[0]->Z, tmp)) | |
1317 | goto err; | |
1318 | } | |
1319 | ||
1320 | /* Finally, fix up the X and Y coordinates for all points. */ | |
1321 | ||
1322 | for (i = 0; i < num; i++) { | |
1323 | EC_POINT *p = points[i]; | |
1324 | ||
1325 | if (!BN_is_zero(p->Z)) { | |
1326 | /* turn (X, Y, 1/Z) into (X/Z^2, Y/Z^3, 1) */ | |
1327 | ||
1328 | if (!group->meth->field_sqr(group, tmp, p->Z, ctx)) | |
1329 | goto err; | |
1330 | if (!group->meth->field_mul(group, p->X, p->X, tmp, ctx)) | |
1331 | goto err; | |
1332 | ||
1333 | if (!group->meth->field_mul(group, tmp, tmp, p->Z, ctx)) | |
1334 | goto err; | |
1335 | if (!group->meth->field_mul(group, p->Y, p->Y, tmp, ctx)) | |
1336 | goto err; | |
1337 | ||
1338 | if (group->meth->field_set_to_one != 0) { | |
1339 | if (!group->meth->field_set_to_one(group, p->Z, ctx)) | |
1340 | goto err; | |
1341 | } else { | |
1342 | if (!BN_one(p->Z)) | |
1343 | goto err; | |
1344 | } | |
1345 | p->Z_is_one = 1; | |
1346 | } | |
1347 | } | |
1348 | ||
1349 | ret = 1; | |
0fe73d6c | 1350 | |
48fe4d62 | 1351 | err: |
0f113f3e | 1352 | BN_CTX_end(ctx); |
23a1d5e9 | 1353 | BN_CTX_free(new_ctx); |
0f113f3e MC |
1354 | if (prod_Z != NULL) { |
1355 | for (i = 0; i < num; i++) { | |
1356 | if (prod_Z[i] == NULL) | |
1357 | break; | |
1358 | BN_clear_free(prod_Z[i]); | |
1359 | } | |
1360 | OPENSSL_free(prod_Z); | |
1361 | } | |
1362 | return ret; | |
1363 | } | |
1364 | ||
32ab57cb SL |
1365 | int ossl_ec_GFp_simple_field_mul(const EC_GROUP *group, BIGNUM *r, const BIGNUM *a, |
1366 | const BIGNUM *b, BN_CTX *ctx) | |
0f113f3e MC |
1367 | { |
1368 | return BN_mod_mul(r, a, b, group->field, ctx); | |
1369 | } | |
1370 | ||
32ab57cb SL |
1371 | int ossl_ec_GFp_simple_field_sqr(const EC_GROUP *group, BIGNUM *r, const BIGNUM *a, |
1372 | BN_CTX *ctx) | |
0f113f3e MC |
1373 | { |
1374 | return BN_mod_sqr(r, a, group->field, ctx); | |
1375 | } | |
f667820c | 1376 | |
e0033efc BB |
1377 | /*- |
1378 | * Computes the multiplicative inverse of a in GF(p), storing the result in r. | |
1567a821 | 1379 | * If a is zero (or equivalent), you'll get an EC_R_CANNOT_INVERT error. |
e0033efc | 1380 | * Since we don't have a Mont structure here, SCA hardening is with blinding. |
a4a93bbf | 1381 | * NB: "a" must be in _decoded_ form. (i.e. field_decode must precede.) |
e0033efc | 1382 | */ |
32ab57cb SL |
1383 | int ossl_ec_GFp_simple_field_inv(const EC_GROUP *group, BIGNUM *r, |
1384 | const BIGNUM *a, BN_CTX *ctx) | |
e0033efc BB |
1385 | { |
1386 | BIGNUM *e = NULL; | |
1387 | BN_CTX *new_ctx = NULL; | |
1388 | int ret = 0; | |
1389 | ||
a9612d6c MC |
1390 | if (ctx == NULL |
1391 | && (ctx = new_ctx = BN_CTX_secure_new_ex(group->libctx)) == NULL) | |
e0033efc BB |
1392 | return 0; |
1393 | ||
1394 | BN_CTX_start(ctx); | |
1395 | if ((e = BN_CTX_get(ctx)) == NULL) | |
1396 | goto err; | |
1397 | ||
1398 | do { | |
5cbd2ea3 | 1399 | if (!BN_priv_rand_range_ex(e, group->field, 0, ctx)) |
e0033efc BB |
1400 | goto err; |
1401 | } while (BN_is_zero(e)); | |
1402 | ||
1403 | /* r := a * e */ | |
1404 | if (!group->meth->field_mul(group, r, a, e, ctx)) | |
1405 | goto err; | |
1406 | /* r := 1/(a * e) */ | |
1407 | if (!BN_mod_inverse(r, r, group->field, ctx)) { | |
9311d0c4 | 1408 | ERR_raise(ERR_LIB_EC, EC_R_CANNOT_INVERT); |
e0033efc BB |
1409 | goto err; |
1410 | } | |
1411 | /* r := e/(a * e) = 1/a */ | |
1412 | if (!group->meth->field_mul(group, r, r, e, ctx)) | |
1413 | goto err; | |
1414 | ||
1415 | ret = 1; | |
1416 | ||
1417 | err: | |
1418 | BN_CTX_end(ctx); | |
1419 | BN_CTX_free(new_ctx); | |
1420 | return ret; | |
1421 | } | |
1422 | ||
f667820c SH |
1423 | /*- |
1424 | * Apply randomization of EC point projective coordinates: | |
1425 | * | |
1287dabd | 1426 | * (X, Y, Z) = (lambda^2*X, lambda^3*Y, lambda*Z) |
1427 | * lambda = [1, group->field) | |
f667820c SH |
1428 | * |
1429 | */ | |
32ab57cb SL |
1430 | int ossl_ec_GFp_simple_blind_coordinates(const EC_GROUP *group, EC_POINT *p, |
1431 | BN_CTX *ctx) | |
f667820c SH |
1432 | { |
1433 | int ret = 0; | |
1434 | BIGNUM *lambda = NULL; | |
1435 | BIGNUM *temp = NULL; | |
1436 | ||
1437 | BN_CTX_start(ctx); | |
1438 | lambda = BN_CTX_get(ctx); | |
1439 | temp = BN_CTX_get(ctx); | |
1440 | if (temp == NULL) { | |
e077455e | 1441 | ERR_raise(ERR_LIB_EC, ERR_R_BN_LIB); |
c61ced5e | 1442 | goto end; |
f667820c SH |
1443 | } |
1444 | ||
c61ced5e BB |
1445 | /*- |
1446 | * Make sure lambda is not zero. | |
1447 | * If the RNG fails, we cannot blind but nevertheless want | |
1448 | * code to continue smoothly and not clobber the error stack. | |
1449 | */ | |
f667820c | 1450 | do { |
c61ced5e | 1451 | ERR_set_mark(); |
5cbd2ea3 | 1452 | ret = BN_priv_rand_range_ex(lambda, group->field, 0, ctx); |
c61ced5e BB |
1453 | ERR_pop_to_mark(); |
1454 | if (ret == 0) { | |
1455 | ret = 1; | |
1456 | goto end; | |
f667820c SH |
1457 | } |
1458 | } while (BN_is_zero(lambda)); | |
1459 | ||
1460 | /* if field_encode defined convert between representations */ | |
c61ced5e BB |
1461 | if ((group->meth->field_encode != NULL |
1462 | && !group->meth->field_encode(group, lambda, lambda, ctx)) | |
1463 | || !group->meth->field_mul(group, p->Z, p->Z, lambda, ctx) | |
1464 | || !group->meth->field_sqr(group, temp, lambda, ctx) | |
1465 | || !group->meth->field_mul(group, p->X, p->X, temp, ctx) | |
1466 | || !group->meth->field_mul(group, temp, temp, lambda, ctx) | |
1467 | || !group->meth->field_mul(group, p->Y, p->Y, temp, ctx)) | |
1468 | goto end; | |
f667820c | 1469 | |
c61ced5e | 1470 | p->Z_is_one = 0; |
f667820c SH |
1471 | ret = 1; |
1472 | ||
c61ced5e | 1473 | end: |
9d91530d BB |
1474 | BN_CTX_end(ctx); |
1475 | return ret; | |
1476 | } | |
1477 | ||
1478 | /*- | |
a4a93bbf BB |
1479 | * Input: |
1480 | * - p: affine coordinates | |
1481 | * | |
1482 | * Output: | |
1483 | * - s := p, r := 2p: blinded projective (homogeneous) coordinates | |
9d91530d BB |
1484 | * |
1485 | * For doubling we use Formula 3 from Izu-Takagi "A fast parallel elliptic curve | |
a4a93bbf | 1486 | * multiplication resistant against side channel attacks" appendix, described at |
9d91530d | 1487 | * https://hyperelliptic.org/EFD/g1p/auto-shortw-xz.html#doubling-dbl-2002-it-2 |
a4a93bbf | 1488 | * simplified for Z1=1. |
9d91530d | 1489 | * |
a4a93bbf BB |
1490 | * Blinding uses the equivalence relation (\lambda X, \lambda Y, \lambda Z) |
1491 | * for any non-zero \lambda that holds for projective (homogeneous) coords. | |
9d91530d | 1492 | */ |
32ab57cb SL |
1493 | int ossl_ec_GFp_simple_ladder_pre(const EC_GROUP *group, |
1494 | EC_POINT *r, EC_POINT *s, | |
1495 | EC_POINT *p, BN_CTX *ctx) | |
9d91530d | 1496 | { |
a4a93bbf | 1497 | BIGNUM *t1, *t2, *t3, *t4, *t5 = NULL; |
9d91530d | 1498 | |
a4a93bbf BB |
1499 | t1 = s->Z; |
1500 | t2 = r->Z; | |
9d91530d BB |
1501 | t3 = s->X; |
1502 | t4 = r->X; | |
1503 | t5 = s->Y; | |
a4a93bbf BB |
1504 | |
1505 | if (!p->Z_is_one /* r := 2p */ | |
1506 | || !group->meth->field_sqr(group, t3, p->X, ctx) | |
1507 | || !BN_mod_sub_quick(t4, t3, group->a, group->field) | |
1508 | || !group->meth->field_sqr(group, t4, t4, ctx) | |
1509 | || !group->meth->field_mul(group, t5, p->X, group->b, ctx) | |
1510 | || !BN_mod_lshift_quick(t5, t5, 3, group->field) | |
9d91530d | 1511 | /* r->X coord output */ |
a4a93bbf BB |
1512 | || !BN_mod_sub_quick(r->X, t4, t5, group->field) |
1513 | || !BN_mod_add_quick(t1, t3, group->a, group->field) | |
1514 | || !group->meth->field_mul(group, t2, p->X, t1, ctx) | |
1515 | || !BN_mod_add_quick(t2, group->b, t2, group->field) | |
9d91530d | 1516 | /* r->Z coord output */ |
a4a93bbf BB |
1517 | || !BN_mod_lshift_quick(r->Z, t2, 2, group->field)) |
1518 | return 0; | |
1519 | ||
1520 | /* make sure lambda (r->Y here for storage) is not zero */ | |
1521 | do { | |
5cbd2ea3 | 1522 | if (!BN_priv_rand_range_ex(r->Y, group->field, 0, ctx)) |
a4a93bbf BB |
1523 | return 0; |
1524 | } while (BN_is_zero(r->Y)); | |
1525 | ||
1526 | /* make sure lambda (s->Z here for storage) is not zero */ | |
1527 | do { | |
5cbd2ea3 | 1528 | if (!BN_priv_rand_range_ex(s->Z, group->field, 0, ctx)) |
a4a93bbf BB |
1529 | return 0; |
1530 | } while (BN_is_zero(s->Z)); | |
1531 | ||
1532 | /* if field_encode defined convert between representations */ | |
1533 | if (group->meth->field_encode != NULL | |
1534 | && (!group->meth->field_encode(group, r->Y, r->Y, ctx) | |
1535 | || !group->meth->field_encode(group, s->Z, s->Z, ctx))) | |
1536 | return 0; | |
1537 | ||
1538 | /* blind r and s independently */ | |
1539 | if (!group->meth->field_mul(group, r->Z, r->Z, r->Y, ctx) | |
1540 | || !group->meth->field_mul(group, r->X, r->X, r->Y, ctx) | |
1541 | || !group->meth->field_mul(group, s->X, p->X, s->Z, ctx)) /* s := p */ | |
9d91530d BB |
1542 | return 0; |
1543 | ||
1544 | r->Z_is_one = 0; | |
1545 | s->Z_is_one = 0; | |
9d91530d BB |
1546 | |
1547 | return 1; | |
1548 | } | |
1549 | ||
1550 | /*- | |
a4a93bbf BB |
1551 | * Input: |
1552 | * - s, r: projective (homogeneous) coordinates | |
1553 | * - p: affine coordinates | |
1554 | * | |
1555 | * Output: | |
1556 | * - s := r + s, r := 2r: projective (homogeneous) coordinates | |
1557 | * | |
1558 | * Differential addition-and-doubling using Eq. (9) and (10) from Izu-Takagi | |
9d91530d BB |
1559 | * "A fast parallel elliptic curve multiplication resistant against side channel |
1560 | * attacks", as described at | |
a4a93bbf | 1561 | * https://hyperelliptic.org/EFD/g1p/auto-shortw-xz.html#ladder-mladd-2002-it-4 |
9d91530d | 1562 | */ |
32ab57cb SL |
1563 | int ossl_ec_GFp_simple_ladder_step(const EC_GROUP *group, |
1564 | EC_POINT *r, EC_POINT *s, | |
1565 | EC_POINT *p, BN_CTX *ctx) | |
9d91530d BB |
1566 | { |
1567 | int ret = 0; | |
a4a93bbf | 1568 | BIGNUM *t0, *t1, *t2, *t3, *t4, *t5, *t6 = NULL; |
9d91530d BB |
1569 | |
1570 | BN_CTX_start(ctx); | |
1571 | t0 = BN_CTX_get(ctx); | |
1572 | t1 = BN_CTX_get(ctx); | |
1573 | t2 = BN_CTX_get(ctx); | |
1574 | t3 = BN_CTX_get(ctx); | |
1575 | t4 = BN_CTX_get(ctx); | |
1576 | t5 = BN_CTX_get(ctx); | |
1577 | t6 = BN_CTX_get(ctx); | |
9d91530d | 1578 | |
a4a93bbf BB |
1579 | if (t6 == NULL |
1580 | || !group->meth->field_mul(group, t6, r->X, s->X, ctx) | |
1581 | || !group->meth->field_mul(group, t0, r->Z, s->Z, ctx) | |
1582 | || !group->meth->field_mul(group, t4, r->X, s->Z, ctx) | |
9d91530d | 1583 | || !group->meth->field_mul(group, t3, r->Z, s->X, ctx) |
a4a93bbf BB |
1584 | || !group->meth->field_mul(group, t5, group->a, t0, ctx) |
1585 | || !BN_mod_add_quick(t5, t6, t5, group->field) | |
5d92b853 | 1586 | || !BN_mod_add_quick(t6, t3, t4, group->field) |
a4a93bbf BB |
1587 | || !group->meth->field_mul(group, t5, t6, t5, ctx) |
1588 | || !group->meth->field_sqr(group, t0, t0, ctx) | |
1589 | || !BN_mod_lshift_quick(t2, group->b, 2, group->field) | |
1590 | || !group->meth->field_mul(group, t0, t2, t0, ctx) | |
5d92b853 | 1591 | || !BN_mod_lshift1_quick(t5, t5, group->field) |
a4a93bbf BB |
1592 | || !BN_mod_sub_quick(t3, t4, t3, group->field) |
1593 | /* s->Z coord output */ | |
1594 | || !group->meth->field_sqr(group, s->Z, t3, ctx) | |
1595 | || !group->meth->field_mul(group, t4, s->Z, p->X, ctx) | |
1596 | || !BN_mod_add_quick(t0, t0, t5, group->field) | |
1597 | /* s->X coord output */ | |
1598 | || !BN_mod_sub_quick(s->X, t0, t4, group->field) | |
1599 | || !group->meth->field_sqr(group, t4, r->X, ctx) | |
1600 | || !group->meth->field_sqr(group, t5, r->Z, ctx) | |
1601 | || !group->meth->field_mul(group, t6, t5, group->a, ctx) | |
1602 | || !BN_mod_add_quick(t1, r->X, r->Z, group->field) | |
1603 | || !group->meth->field_sqr(group, t1, t1, ctx) | |
1604 | || !BN_mod_sub_quick(t1, t1, t4, group->field) | |
1605 | || !BN_mod_sub_quick(t1, t1, t5, group->field) | |
1606 | || !BN_mod_sub_quick(t3, t4, t6, group->field) | |
1607 | || !group->meth->field_sqr(group, t3, t3, ctx) | |
1608 | || !group->meth->field_mul(group, t0, t5, t1, ctx) | |
1609 | || !group->meth->field_mul(group, t0, t2, t0, ctx) | |
1610 | /* r->X coord output */ | |
1611 | || !BN_mod_sub_quick(r->X, t3, t0, group->field) | |
1612 | || !BN_mod_add_quick(t3, t4, t6, group->field) | |
1613 | || !group->meth->field_sqr(group, t4, t5, ctx) | |
1614 | || !group->meth->field_mul(group, t4, t4, t2, ctx) | |
1615 | || !group->meth->field_mul(group, t1, t1, t3, ctx) | |
1616 | || !BN_mod_lshift1_quick(t1, t1, group->field) | |
9d91530d | 1617 | /* r->Z coord output */ |
a4a93bbf | 1618 | || !BN_mod_add_quick(r->Z, t4, t1, group->field)) |
9d91530d BB |
1619 | goto err; |
1620 | ||
1621 | ret = 1; | |
1622 | ||
1623 | err: | |
1624 | BN_CTX_end(ctx); | |
1625 | return ret; | |
1626 | } | |
1627 | ||
1628 | /*- | |
a4a93bbf BB |
1629 | * Input: |
1630 | * - s, r: projective (homogeneous) coordinates | |
1631 | * - p: affine coordinates | |
1632 | * | |
1633 | * Output: | |
1634 | * - r := (x,y): affine coordinates | |
1635 | * | |
9d91530d | 1636 | * Recovers the y-coordinate of r using Eq. (8) from Brier-Joye, "Weierstrass |
a4a93bbf BB |
1637 | * Elliptic Curves and Side-Channel Attacks", modified to work in mixed |
1638 | * projective coords, i.e. p is affine and (r,s) in projective (homogeneous) | |
1639 | * coords, and return r in affine coordinates. | |
9d91530d | 1640 | * |
a4a93bbf BB |
1641 | * X4 = two*Y1*X2*Z3*Z2; |
1642 | * Y4 = two*b*Z3*SQR(Z2) + Z3*(a*Z2+X1*X2)*(X1*Z2+X2) - X3*SQR(X1*Z2-X2); | |
1643 | * Z4 = two*Y1*Z3*SQR(Z2); | |
9d91530d BB |
1644 | * |
1645 | * Z4 != 0 because: | |
9d91530d BB |
1646 | * - Z2==0 implies r is at infinity (handled by the BN_is_zero(r->Z) branch); |
1647 | * - Z3==0 implies s is at infinity (handled by the BN_is_zero(s->Z) branch); | |
1648 | * - Y1==0 implies p has order 2, so either r or s are infinity and handled by | |
1649 | * one of the BN_is_zero(...) branches. | |
1650 | */ | |
32ab57cb SL |
1651 | int ossl_ec_GFp_simple_ladder_post(const EC_GROUP *group, |
1652 | EC_POINT *r, EC_POINT *s, | |
1653 | EC_POINT *p, BN_CTX *ctx) | |
9d91530d BB |
1654 | { |
1655 | int ret = 0; | |
1656 | BIGNUM *t0, *t1, *t2, *t3, *t4, *t5, *t6 = NULL; | |
1657 | ||
1658 | if (BN_is_zero(r->Z)) | |
1659 | return EC_POINT_set_to_infinity(group, r); | |
1660 | ||
1661 | if (BN_is_zero(s->Z)) { | |
a4a93bbf | 1662 | if (!EC_POINT_copy(r, p) |
9d91530d BB |
1663 | || !EC_POINT_invert(group, r, ctx)) |
1664 | return 0; | |
1665 | return 1; | |
1666 | } | |
1667 | ||
1668 | BN_CTX_start(ctx); | |
1669 | t0 = BN_CTX_get(ctx); | |
1670 | t1 = BN_CTX_get(ctx); | |
1671 | t2 = BN_CTX_get(ctx); | |
1672 | t3 = BN_CTX_get(ctx); | |
1673 | t4 = BN_CTX_get(ctx); | |
1674 | t5 = BN_CTX_get(ctx); | |
1675 | t6 = BN_CTX_get(ctx); | |
1676 | ||
1677 | if (t6 == NULL | |
a4a93bbf BB |
1678 | || !BN_mod_lshift1_quick(t4, p->Y, group->field) |
1679 | || !group->meth->field_mul(group, t6, r->X, t4, ctx) | |
1680 | || !group->meth->field_mul(group, t6, s->Z, t6, ctx) | |
1681 | || !group->meth->field_mul(group, t5, r->Z, t6, ctx) | |
1682 | || !BN_mod_lshift1_quick(t1, group->b, group->field) | |
1683 | || !group->meth->field_mul(group, t1, s->Z, t1, ctx) | |
9d91530d | 1684 | || !group->meth->field_sqr(group, t3, r->Z, ctx) |
a4a93bbf BB |
1685 | || !group->meth->field_mul(group, t2, t3, t1, ctx) |
1686 | || !group->meth->field_mul(group, t6, r->Z, group->a, ctx) | |
1687 | || !group->meth->field_mul(group, t1, p->X, r->X, ctx) | |
1688 | || !BN_mod_add_quick(t1, t1, t6, group->field) | |
1689 | || !group->meth->field_mul(group, t1, s->Z, t1, ctx) | |
1690 | || !group->meth->field_mul(group, t0, p->X, r->Z, ctx) | |
1691 | || !BN_mod_add_quick(t6, r->X, t0, group->field) | |
1692 | || !group->meth->field_mul(group, t6, t6, t1, ctx) | |
1693 | || !BN_mod_add_quick(t6, t6, t2, group->field) | |
1694 | || !BN_mod_sub_quick(t0, t0, r->X, group->field) | |
1695 | || !group->meth->field_sqr(group, t0, t0, ctx) | |
1696 | || !group->meth->field_mul(group, t0, t0, s->X, ctx) | |
1697 | || !BN_mod_sub_quick(t0, t6, t0, group->field) | |
1698 | || !group->meth->field_mul(group, t1, s->Z, t4, ctx) | |
1699 | || !group->meth->field_mul(group, t1, t3, t1, ctx) | |
1700 | || (group->meth->field_decode != NULL | |
1701 | && !group->meth->field_decode(group, t1, t1, ctx)) | |
1702 | || !group->meth->field_inv(group, t1, t1, ctx) | |
1703 | || (group->meth->field_encode != NULL | |
1704 | && !group->meth->field_encode(group, t1, t1, ctx)) | |
1705 | || !group->meth->field_mul(group, r->X, t5, t1, ctx) | |
1706 | || !group->meth->field_mul(group, r->Y, t0, t1, ctx)) | |
9d91530d BB |
1707 | goto err; |
1708 | ||
a4a93bbf BB |
1709 | if (group->meth->field_set_to_one != NULL) { |
1710 | if (!group->meth->field_set_to_one(group, r->Z, ctx)) | |
1711 | goto err; | |
1712 | } else { | |
1713 | if (!BN_one(r->Z)) | |
1714 | goto err; | |
1715 | } | |
1716 | ||
1717 | r->Z_is_one = 1; | |
9d91530d BB |
1718 | ret = 1; |
1719 | ||
1720 | err: | |
1721 | BN_CTX_end(ctx); | |
1722 | return ret; | |
f667820c | 1723 | } |