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Commit | Line | Data |
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4f22f405 | 1 | /* |
33388b44 | 2 | * Copyright 2002-2020 The OpenSSL Project Authors. All Rights Reserved. |
aa8f3d76 | 3 | * Copyright (c) 2002, Oracle and/or its affiliates. All rights reserved |
4f22f405 | 4 | * |
a7f182b7 | 5 | * Licensed under the Apache License 2.0 (the "License"). You may not use |
4f22f405 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 | |
9 | */ | |
10 | ||
579422c8 P |
11 | /* |
12 | * ECDSA low level APIs are deprecated for public use, but still ok for | |
13 | * internal use. | |
14 | */ | |
15 | #include "internal/deprecated.h" | |
16 | ||
7793f30e BM |
17 | #include <openssl/err.h> |
18 | ||
25f2138b | 19 | #include "crypto/bn.h" |
706457b7 | 20 | #include "ec_local.h" |
7793f30e | 21 | |
b3310161 DSH |
22 | #ifndef OPENSSL_NO_EC2M |
23 | ||
0f113f3e MC |
24 | /* |
25 | * Initialize a GF(2^m)-based EC_GROUP structure. Note that all other members | |
26 | * are handled by EC_GROUP_new. | |
7793f30e BM |
27 | */ |
28 | int ec_GF2m_simple_group_init(EC_GROUP *group) | |
0f113f3e MC |
29 | { |
30 | group->field = BN_new(); | |
31 | group->a = BN_new(); | |
32 | group->b = BN_new(); | |
33 | ||
90945fa3 | 34 | if (group->field == NULL || group->a == NULL || group->b == NULL) { |
23a1d5e9 RS |
35 | BN_free(group->field); |
36 | BN_free(group->a); | |
37 | BN_free(group->b); | |
0f113f3e MC |
38 | return 0; |
39 | } | |
40 | return 1; | |
41 | } | |
42 | ||
43 | /* | |
44 | * Free a GF(2^m)-based EC_GROUP structure. Note that all other members are | |
45 | * handled by EC_GROUP_free. | |
7793f30e BM |
46 | */ |
47 | void ec_GF2m_simple_group_finish(EC_GROUP *group) | |
0f113f3e MC |
48 | { |
49 | BN_free(group->field); | |
50 | BN_free(group->a); | |
51 | BN_free(group->b); | |
52 | } | |
53 | ||
54 | /* | |
55 | * Clear and free a GF(2^m)-based EC_GROUP structure. Note that all other | |
56 | * members are handled by EC_GROUP_clear_free. | |
7793f30e BM |
57 | */ |
58 | void ec_GF2m_simple_group_clear_finish(EC_GROUP *group) | |
0f113f3e MC |
59 | { |
60 | BN_clear_free(group->field); | |
61 | BN_clear_free(group->a); | |
62 | BN_clear_free(group->b); | |
63 | group->poly[0] = 0; | |
64 | group->poly[1] = 0; | |
65 | group->poly[2] = 0; | |
66 | group->poly[3] = 0; | |
67 | group->poly[4] = 0; | |
68 | group->poly[5] = -1; | |
69 | } | |
70 | ||
71 | /* | |
72 | * Copy a GF(2^m)-based EC_GROUP structure. Note that all other members are | |
73 | * handled by EC_GROUP_copy. | |
7793f30e BM |
74 | */ |
75 | int ec_GF2m_simple_group_copy(EC_GROUP *dest, const EC_GROUP *src) | |
0f113f3e MC |
76 | { |
77 | if (!BN_copy(dest->field, src->field)) | |
78 | return 0; | |
79 | if (!BN_copy(dest->a, src->a)) | |
80 | return 0; | |
81 | if (!BN_copy(dest->b, src->b)) | |
82 | return 0; | |
83 | dest->poly[0] = src->poly[0]; | |
84 | dest->poly[1] = src->poly[1]; | |
85 | dest->poly[2] = src->poly[2]; | |
86 | dest->poly[3] = src->poly[3]; | |
87 | dest->poly[4] = src->poly[4]; | |
88 | dest->poly[5] = src->poly[5]; | |
89 | if (bn_wexpand(dest->a, (int)(dest->poly[0] + BN_BITS2 - 1) / BN_BITS2) == | |
90 | NULL) | |
91 | return 0; | |
92 | if (bn_wexpand(dest->b, (int)(dest->poly[0] + BN_BITS2 - 1) / BN_BITS2) == | |
93 | NULL) | |
94 | return 0; | |
95 | bn_set_all_zero(dest->a); | |
96 | bn_set_all_zero(dest->b); | |
97 | return 1; | |
98 | } | |
7793f30e BM |
99 | |
100 | /* Set the curve parameters of an EC_GROUP structure. */ | |
35b73a1f | 101 | int ec_GF2m_simple_group_set_curve(EC_GROUP *group, |
0f113f3e MC |
102 | const BIGNUM *p, const BIGNUM *a, |
103 | const BIGNUM *b, BN_CTX *ctx) | |
104 | { | |
105 | int ret = 0, i; | |
106 | ||
107 | /* group->field */ | |
108 | if (!BN_copy(group->field, p)) | |
109 | goto err; | |
110 | i = BN_GF2m_poly2arr(group->field, group->poly, 6) - 1; | |
111 | if ((i != 5) && (i != 3)) { | |
112 | ECerr(EC_F_EC_GF2M_SIMPLE_GROUP_SET_CURVE, EC_R_UNSUPPORTED_FIELD); | |
113 | goto err; | |
114 | } | |
115 | ||
116 | /* group->a */ | |
117 | if (!BN_GF2m_mod_arr(group->a, a, group->poly)) | |
118 | goto err; | |
119 | if (bn_wexpand(group->a, (int)(group->poly[0] + BN_BITS2 - 1) / BN_BITS2) | |
120 | == NULL) | |
121 | goto err; | |
122 | bn_set_all_zero(group->a); | |
123 | ||
124 | /* group->b */ | |
125 | if (!BN_GF2m_mod_arr(group->b, b, group->poly)) | |
126 | goto err; | |
127 | if (bn_wexpand(group->b, (int)(group->poly[0] + BN_BITS2 - 1) / BN_BITS2) | |
128 | == NULL) | |
129 | goto err; | |
130 | bn_set_all_zero(group->b); | |
131 | ||
132 | ret = 1; | |
133 | err: | |
134 | return ret; | |
135 | } | |
136 | ||
137 | /* | |
138 | * Get the curve parameters of an EC_GROUP structure. If p, a, or b are NULL | |
139 | * then there values will not be set but the method will return with success. | |
7793f30e | 140 | */ |
0f113f3e MC |
141 | int ec_GF2m_simple_group_get_curve(const EC_GROUP *group, BIGNUM *p, |
142 | BIGNUM *a, BIGNUM *b, BN_CTX *ctx) | |
143 | { | |
144 | int ret = 0; | |
145 | ||
146 | if (p != NULL) { | |
147 | if (!BN_copy(p, group->field)) | |
148 | return 0; | |
149 | } | |
150 | ||
151 | if (a != NULL) { | |
152 | if (!BN_copy(a, group->a)) | |
153 | goto err; | |
154 | } | |
7793f30e | 155 | |
0f113f3e MC |
156 | if (b != NULL) { |
157 | if (!BN_copy(b, group->b)) | |
158 | goto err; | |
159 | } | |
7793f30e | 160 | |
0f113f3e MC |
161 | ret = 1; |
162 | ||
163 | err: | |
164 | return ret; | |
165 | } | |
166 | ||
167 | /* | |
168 | * Gets the degree of the field. For a curve over GF(2^m) this is the value | |
169 | * m. | |
170 | */ | |
171 | int ec_GF2m_simple_group_get_degree(const EC_GROUP *group) | |
172 | { | |
173 | return BN_num_bits(group->field) - 1; | |
174 | } | |
175 | ||
176 | /* | |
177 | * Checks the discriminant of the curve. y^2 + x*y = x^3 + a*x^2 + b is an | |
178 | * elliptic curve <=> b != 0 (mod p) | |
7793f30e | 179 | */ |
0f113f3e MC |
180 | int ec_GF2m_simple_group_check_discriminant(const EC_GROUP *group, |
181 | BN_CTX *ctx) | |
182 | { | |
183 | int ret = 0; | |
184 | BIGNUM *b; | |
f844f9eb | 185 | #ifndef FIPS_MODULE |
0f113f3e MC |
186 | BN_CTX *new_ctx = NULL; |
187 | ||
188 | if (ctx == NULL) { | |
189 | ctx = new_ctx = BN_CTX_new(); | |
190 | if (ctx == NULL) { | |
191 | ECerr(EC_F_EC_GF2M_SIMPLE_GROUP_CHECK_DISCRIMINANT, | |
192 | ERR_R_MALLOC_FAILURE); | |
193 | goto err; | |
194 | } | |
195 | } | |
a9612d6c | 196 | #endif |
0f113f3e MC |
197 | BN_CTX_start(ctx); |
198 | b = BN_CTX_get(ctx); | |
199 | if (b == NULL) | |
200 | goto err; | |
201 | ||
202 | if (!BN_GF2m_mod_arr(b, group->b, group->poly)) | |
203 | goto err; | |
204 | ||
205 | /* | |
206 | * check the discriminant: y^2 + x*y = x^3 + a*x^2 + b is an elliptic | |
207 | * curve <=> b != 0 (mod p) | |
208 | */ | |
209 | if (BN_is_zero(b)) | |
210 | goto err; | |
211 | ||
212 | ret = 1; | |
7793f30e | 213 | |
0f113f3e | 214 | err: |
ce1415ed | 215 | BN_CTX_end(ctx); |
f844f9eb | 216 | #ifndef FIPS_MODULE |
23a1d5e9 | 217 | BN_CTX_free(new_ctx); |
a9612d6c | 218 | #endif |
0f113f3e MC |
219 | return ret; |
220 | } | |
7793f30e BM |
221 | |
222 | /* Initializes an EC_POINT. */ | |
223 | int ec_GF2m_simple_point_init(EC_POINT *point) | |
0f113f3e MC |
224 | { |
225 | point->X = BN_new(); | |
226 | point->Y = BN_new(); | |
227 | point->Z = BN_new(); | |
228 | ||
90945fa3 | 229 | if (point->X == NULL || point->Y == NULL || point->Z == NULL) { |
23a1d5e9 RS |
230 | BN_free(point->X); |
231 | BN_free(point->Y); | |
232 | BN_free(point->Z); | |
0f113f3e MC |
233 | return 0; |
234 | } | |
235 | return 1; | |
236 | } | |
7793f30e BM |
237 | |
238 | /* Frees an EC_POINT. */ | |
239 | void ec_GF2m_simple_point_finish(EC_POINT *point) | |
0f113f3e MC |
240 | { |
241 | BN_free(point->X); | |
242 | BN_free(point->Y); | |
243 | BN_free(point->Z); | |
244 | } | |
7793f30e BM |
245 | |
246 | /* Clears and frees an EC_POINT. */ | |
247 | void ec_GF2m_simple_point_clear_finish(EC_POINT *point) | |
0f113f3e MC |
248 | { |
249 | BN_clear_free(point->X); | |
250 | BN_clear_free(point->Y); | |
251 | BN_clear_free(point->Z); | |
252 | point->Z_is_one = 0; | |
253 | } | |
254 | ||
255 | /* | |
256 | * Copy the contents of one EC_POINT into another. Assumes dest is | |
257 | * initialized. | |
7793f30e | 258 | */ |
0f113f3e MC |
259 | int ec_GF2m_simple_point_copy(EC_POINT *dest, const EC_POINT *src) |
260 | { | |
261 | if (!BN_copy(dest->X, src->X)) | |
262 | return 0; | |
263 | if (!BN_copy(dest->Y, src->Y)) | |
264 | return 0; | |
265 | if (!BN_copy(dest->Z, src->Z)) | |
266 | return 0; | |
267 | dest->Z_is_one = src->Z_is_one; | |
b14e6015 | 268 | dest->curve_name = src->curve_name; |
0f113f3e MC |
269 | |
270 | return 1; | |
271 | } | |
272 | ||
273 | /* | |
274 | * Set an EC_POINT to the point at infinity. A point at infinity is | |
275 | * represented by having Z=0. | |
7793f30e | 276 | */ |
0f113f3e MC |
277 | int ec_GF2m_simple_point_set_to_infinity(const EC_GROUP *group, |
278 | EC_POINT *point) | |
279 | { | |
280 | point->Z_is_one = 0; | |
281 | BN_zero(point->Z); | |
282 | return 1; | |
283 | } | |
284 | ||
285 | /* | |
286 | * Set the coordinates of an EC_POINT using affine coordinates. Note that | |
287 | * the simple implementation only uses affine coordinates. | |
7793f30e | 288 | */ |
0f113f3e MC |
289 | int ec_GF2m_simple_point_set_affine_coordinates(const EC_GROUP *group, |
290 | EC_POINT *point, | |
291 | const BIGNUM *x, | |
292 | const BIGNUM *y, BN_CTX *ctx) | |
293 | { | |
294 | int ret = 0; | |
295 | if (x == NULL || y == NULL) { | |
296 | ECerr(EC_F_EC_GF2M_SIMPLE_POINT_SET_AFFINE_COORDINATES, | |
297 | ERR_R_PASSED_NULL_PARAMETER); | |
298 | return 0; | |
299 | } | |
300 | ||
301 | if (!BN_copy(point->X, x)) | |
302 | goto err; | |
303 | BN_set_negative(point->X, 0); | |
304 | if (!BN_copy(point->Y, y)) | |
305 | goto err; | |
306 | BN_set_negative(point->Y, 0); | |
307 | if (!BN_copy(point->Z, BN_value_one())) | |
308 | goto err; | |
309 | BN_set_negative(point->Z, 0); | |
310 | point->Z_is_one = 1; | |
311 | ret = 1; | |
312 | ||
7793f30e | 313 | err: |
0f113f3e MC |
314 | return ret; |
315 | } | |
7793f30e | 316 | |
0f113f3e MC |
317 | /* |
318 | * Gets the affine coordinates of an EC_POINT. Note that the simple | |
319 | * implementation only uses affine coordinates. | |
7793f30e | 320 | */ |
0f113f3e MC |
321 | int ec_GF2m_simple_point_get_affine_coordinates(const EC_GROUP *group, |
322 | const EC_POINT *point, | |
323 | BIGNUM *x, BIGNUM *y, | |
324 | BN_CTX *ctx) | |
325 | { | |
326 | int ret = 0; | |
327 | ||
328 | if (EC_POINT_is_at_infinity(group, point)) { | |
329 | ECerr(EC_F_EC_GF2M_SIMPLE_POINT_GET_AFFINE_COORDINATES, | |
330 | EC_R_POINT_AT_INFINITY); | |
331 | return 0; | |
332 | } | |
333 | ||
334 | if (BN_cmp(point->Z, BN_value_one())) { | |
335 | ECerr(EC_F_EC_GF2M_SIMPLE_POINT_GET_AFFINE_COORDINATES, | |
336 | ERR_R_SHOULD_NOT_HAVE_BEEN_CALLED); | |
337 | return 0; | |
338 | } | |
339 | if (x != NULL) { | |
340 | if (!BN_copy(x, point->X)) | |
341 | goto err; | |
342 | BN_set_negative(x, 0); | |
343 | } | |
344 | if (y != NULL) { | |
345 | if (!BN_copy(y, point->Y)) | |
346 | goto err; | |
347 | BN_set_negative(y, 0); | |
348 | } | |
349 | ret = 1; | |
7793f30e BM |
350 | |
351 | err: | |
0f113f3e MC |
352 | return ret; |
353 | } | |
7793f30e | 354 | |
0f113f3e MC |
355 | /* |
356 | * Computes a + b and stores the result in r. r could be a or b, a could be | |
357 | * b. Uses algorithm A.10.2 of IEEE P1363. | |
7793f30e | 358 | */ |
0f113f3e MC |
359 | int ec_GF2m_simple_add(const EC_GROUP *group, EC_POINT *r, const EC_POINT *a, |
360 | const EC_POINT *b, BN_CTX *ctx) | |
361 | { | |
0f113f3e MC |
362 | BIGNUM *x0, *y0, *x1, *y1, *x2, *y2, *s, *t; |
363 | int ret = 0; | |
f844f9eb | 364 | #ifndef FIPS_MODULE |
a9612d6c MC |
365 | BN_CTX *new_ctx = NULL; |
366 | #endif | |
0f113f3e MC |
367 | |
368 | if (EC_POINT_is_at_infinity(group, a)) { | |
369 | if (!EC_POINT_copy(r, b)) | |
370 | return 0; | |
371 | return 1; | |
372 | } | |
373 | ||
374 | if (EC_POINT_is_at_infinity(group, b)) { | |
375 | if (!EC_POINT_copy(r, a)) | |
376 | return 0; | |
377 | return 1; | |
378 | } | |
379 | ||
f844f9eb | 380 | #ifndef FIPS_MODULE |
0f113f3e MC |
381 | if (ctx == NULL) { |
382 | ctx = new_ctx = BN_CTX_new(); | |
383 | if (ctx == NULL) | |
384 | return 0; | |
385 | } | |
a9612d6c | 386 | #endif |
0f113f3e MC |
387 | |
388 | BN_CTX_start(ctx); | |
389 | x0 = BN_CTX_get(ctx); | |
390 | y0 = BN_CTX_get(ctx); | |
391 | x1 = BN_CTX_get(ctx); | |
392 | y1 = BN_CTX_get(ctx); | |
393 | x2 = BN_CTX_get(ctx); | |
394 | y2 = BN_CTX_get(ctx); | |
395 | s = BN_CTX_get(ctx); | |
396 | t = BN_CTX_get(ctx); | |
397 | if (t == NULL) | |
398 | goto err; | |
399 | ||
400 | if (a->Z_is_one) { | |
401 | if (!BN_copy(x0, a->X)) | |
402 | goto err; | |
403 | if (!BN_copy(y0, a->Y)) | |
404 | goto err; | |
405 | } else { | |
9cc570d4 | 406 | if (!EC_POINT_get_affine_coordinates(group, a, x0, y0, ctx)) |
0f113f3e MC |
407 | goto err; |
408 | } | |
409 | if (b->Z_is_one) { | |
410 | if (!BN_copy(x1, b->X)) | |
411 | goto err; | |
412 | if (!BN_copy(y1, b->Y)) | |
413 | goto err; | |
414 | } else { | |
9cc570d4 | 415 | if (!EC_POINT_get_affine_coordinates(group, b, x1, y1, ctx)) |
0f113f3e MC |
416 | goto err; |
417 | } | |
418 | ||
419 | if (BN_GF2m_cmp(x0, x1)) { | |
420 | if (!BN_GF2m_add(t, x0, x1)) | |
421 | goto err; | |
422 | if (!BN_GF2m_add(s, y0, y1)) | |
423 | goto err; | |
424 | if (!group->meth->field_div(group, s, s, t, ctx)) | |
425 | goto err; | |
426 | if (!group->meth->field_sqr(group, x2, s, ctx)) | |
427 | goto err; | |
428 | if (!BN_GF2m_add(x2, x2, group->a)) | |
429 | goto err; | |
430 | if (!BN_GF2m_add(x2, x2, s)) | |
431 | goto err; | |
432 | if (!BN_GF2m_add(x2, x2, t)) | |
433 | goto err; | |
434 | } else { | |
435 | if (BN_GF2m_cmp(y0, y1) || BN_is_zero(x1)) { | |
436 | if (!EC_POINT_set_to_infinity(group, r)) | |
437 | goto err; | |
438 | ret = 1; | |
439 | goto err; | |
440 | } | |
441 | if (!group->meth->field_div(group, s, y1, x1, ctx)) | |
442 | goto err; | |
443 | if (!BN_GF2m_add(s, s, x1)) | |
444 | goto err; | |
445 | ||
446 | if (!group->meth->field_sqr(group, x2, s, ctx)) | |
447 | goto err; | |
448 | if (!BN_GF2m_add(x2, x2, s)) | |
449 | goto err; | |
450 | if (!BN_GF2m_add(x2, x2, group->a)) | |
451 | goto err; | |
452 | } | |
453 | ||
454 | if (!BN_GF2m_add(y2, x1, x2)) | |
455 | goto err; | |
456 | if (!group->meth->field_mul(group, y2, y2, s, ctx)) | |
457 | goto err; | |
458 | if (!BN_GF2m_add(y2, y2, x2)) | |
459 | goto err; | |
460 | if (!BN_GF2m_add(y2, y2, y1)) | |
461 | goto err; | |
462 | ||
9cc570d4 | 463 | if (!EC_POINT_set_affine_coordinates(group, r, x2, y2, ctx)) |
0f113f3e MC |
464 | goto err; |
465 | ||
466 | ret = 1; | |
7793f30e | 467 | |
0f113f3e MC |
468 | err: |
469 | BN_CTX_end(ctx); | |
f844f9eb | 470 | #ifndef FIPS_MODULE |
23a1d5e9 | 471 | BN_CTX_free(new_ctx); |
a9612d6c | 472 | #endif |
0f113f3e MC |
473 | return ret; |
474 | } | |
475 | ||
476 | /* | |
477 | * Computes 2 * a and stores the result in r. r could be a. Uses algorithm | |
478 | * A.10.2 of IEEE P1363. | |
479 | */ | |
480 | int ec_GF2m_simple_dbl(const EC_GROUP *group, EC_POINT *r, const EC_POINT *a, | |
481 | BN_CTX *ctx) | |
482 | { | |
483 | return ec_GF2m_simple_add(group, r, a, a, ctx); | |
484 | } | |
7793f30e BM |
485 | |
486 | int ec_GF2m_simple_invert(const EC_GROUP *group, EC_POINT *point, BN_CTX *ctx) | |
0f113f3e MC |
487 | { |
488 | if (EC_POINT_is_at_infinity(group, point) || BN_is_zero(point->Y)) | |
489 | /* point is its own inverse */ | |
490 | return 1; | |
7793f30e | 491 | |
0f113f3e MC |
492 | if (!EC_POINT_make_affine(group, point, ctx)) |
493 | return 0; | |
494 | return BN_GF2m_add(point->Y, point->X, point->Y); | |
495 | } | |
7793f30e BM |
496 | |
497 | /* Indicates whether the given point is the point at infinity. */ | |
0f113f3e MC |
498 | int ec_GF2m_simple_is_at_infinity(const EC_GROUP *group, |
499 | const EC_POINT *point) | |
500 | { | |
501 | return BN_is_zero(point->Z); | |
502 | } | |
7793f30e | 503 | |
23a22b4c MC |
504 | /*- |
505 | * Determines whether the given EC_POINT is an actual point on the curve defined | |
7793f30e BM |
506 | * in the EC_GROUP. A point is valid if it satisfies the Weierstrass equation: |
507 | * y^2 + x*y = x^3 + a*x^2 + b. | |
508 | */ | |
0f113f3e MC |
509 | int ec_GF2m_simple_is_on_curve(const EC_GROUP *group, const EC_POINT *point, |
510 | BN_CTX *ctx) | |
511 | { | |
512 | int ret = -1; | |
0f113f3e MC |
513 | BIGNUM *lh, *y2; |
514 | int (*field_mul) (const EC_GROUP *, BIGNUM *, const BIGNUM *, | |
515 | const BIGNUM *, BN_CTX *); | |
516 | int (*field_sqr) (const EC_GROUP *, BIGNUM *, const BIGNUM *, BN_CTX *); | |
f844f9eb | 517 | #ifndef FIPS_MODULE |
a9612d6c MC |
518 | BN_CTX *new_ctx = NULL; |
519 | #endif | |
0f113f3e MC |
520 | |
521 | if (EC_POINT_is_at_infinity(group, point)) | |
522 | return 1; | |
523 | ||
524 | field_mul = group->meth->field_mul; | |
525 | field_sqr = group->meth->field_sqr; | |
526 | ||
527 | /* only support affine coordinates */ | |
528 | if (!point->Z_is_one) | |
529 | return -1; | |
530 | ||
f844f9eb | 531 | #ifndef FIPS_MODULE |
0f113f3e MC |
532 | if (ctx == NULL) { |
533 | ctx = new_ctx = BN_CTX_new(); | |
534 | if (ctx == NULL) | |
535 | return -1; | |
536 | } | |
a9612d6c | 537 | #endif |
0f113f3e MC |
538 | |
539 | BN_CTX_start(ctx); | |
540 | y2 = BN_CTX_get(ctx); | |
541 | lh = BN_CTX_get(ctx); | |
542 | if (lh == NULL) | |
543 | goto err; | |
544 | ||
50e735f9 MC |
545 | /*- |
546 | * We have a curve defined by a Weierstrass equation | |
547 | * y^2 + x*y = x^3 + a*x^2 + b. | |
548 | * <=> x^3 + a*x^2 + x*y + b + y^2 = 0 | |
549 | * <=> ((x + a) * x + y ) * x + b + y^2 = 0 | |
550 | */ | |
0f113f3e MC |
551 | if (!BN_GF2m_add(lh, point->X, group->a)) |
552 | goto err; | |
553 | if (!field_mul(group, lh, lh, point->X, ctx)) | |
554 | goto err; | |
555 | if (!BN_GF2m_add(lh, lh, point->Y)) | |
556 | goto err; | |
557 | if (!field_mul(group, lh, lh, point->X, ctx)) | |
558 | goto err; | |
559 | if (!BN_GF2m_add(lh, lh, group->b)) | |
560 | goto err; | |
561 | if (!field_sqr(group, y2, point->Y, ctx)) | |
562 | goto err; | |
563 | if (!BN_GF2m_add(lh, lh, y2)) | |
564 | goto err; | |
565 | ret = BN_is_zero(lh); | |
a0fda2cf | 566 | |
7793f30e | 567 | err: |
a0fda2cf | 568 | BN_CTX_end(ctx); |
f844f9eb | 569 | #ifndef FIPS_MODULE |
23a1d5e9 | 570 | BN_CTX_free(new_ctx); |
a9612d6c | 571 | #endif |
0f113f3e MC |
572 | return ret; |
573 | } | |
7793f30e | 574 | |
1d97c843 TH |
575 | /*- |
576 | * Indicates whether two points are equal. | |
7793f30e BM |
577 | * Return values: |
578 | * -1 error | |
579 | * 0 equal (in affine coordinates) | |
580 | * 1 not equal | |
581 | */ | |
0f113f3e MC |
582 | int ec_GF2m_simple_cmp(const EC_GROUP *group, const EC_POINT *a, |
583 | const EC_POINT *b, BN_CTX *ctx) | |
584 | { | |
585 | BIGNUM *aX, *aY, *bX, *bY; | |
0f113f3e | 586 | int ret = -1; |
f844f9eb | 587 | #ifndef FIPS_MODULE |
a9612d6c MC |
588 | BN_CTX *new_ctx = NULL; |
589 | #endif | |
0f113f3e MC |
590 | |
591 | if (EC_POINT_is_at_infinity(group, a)) { | |
592 | return EC_POINT_is_at_infinity(group, b) ? 0 : 1; | |
593 | } | |
594 | ||
595 | if (EC_POINT_is_at_infinity(group, b)) | |
596 | return 1; | |
597 | ||
598 | if (a->Z_is_one && b->Z_is_one) { | |
599 | return ((BN_cmp(a->X, b->X) == 0) && BN_cmp(a->Y, b->Y) == 0) ? 0 : 1; | |
600 | } | |
601 | ||
f844f9eb | 602 | #ifndef FIPS_MODULE |
0f113f3e MC |
603 | if (ctx == NULL) { |
604 | ctx = new_ctx = BN_CTX_new(); | |
605 | if (ctx == NULL) | |
606 | return -1; | |
607 | } | |
a9612d6c | 608 | #endif |
0f113f3e MC |
609 | |
610 | BN_CTX_start(ctx); | |
611 | aX = BN_CTX_get(ctx); | |
612 | aY = BN_CTX_get(ctx); | |
613 | bX = BN_CTX_get(ctx); | |
614 | bY = BN_CTX_get(ctx); | |
615 | if (bY == NULL) | |
616 | goto err; | |
617 | ||
9cc570d4 | 618 | if (!EC_POINT_get_affine_coordinates(group, a, aX, aY, ctx)) |
0f113f3e | 619 | goto err; |
9cc570d4 | 620 | if (!EC_POINT_get_affine_coordinates(group, b, bX, bY, ctx)) |
0f113f3e MC |
621 | goto err; |
622 | ret = ((BN_cmp(aX, bX) == 0) && BN_cmp(aY, bY) == 0) ? 0 : 1; | |
7793f30e | 623 | |
0f113f3e | 624 | err: |
a0fda2cf | 625 | BN_CTX_end(ctx); |
f844f9eb | 626 | #ifndef FIPS_MODULE |
23a1d5e9 | 627 | BN_CTX_free(new_ctx); |
a9612d6c | 628 | #endif |
0f113f3e MC |
629 | return ret; |
630 | } | |
7793f30e BM |
631 | |
632 | /* Forces the given EC_POINT to internally use affine coordinates. */ | |
0f113f3e MC |
633 | int ec_GF2m_simple_make_affine(const EC_GROUP *group, EC_POINT *point, |
634 | BN_CTX *ctx) | |
635 | { | |
0f113f3e MC |
636 | BIGNUM *x, *y; |
637 | int ret = 0; | |
f844f9eb | 638 | #ifndef FIPS_MODULE |
a9612d6c MC |
639 | BN_CTX *new_ctx = NULL; |
640 | #endif | |
0f113f3e MC |
641 | |
642 | if (point->Z_is_one || EC_POINT_is_at_infinity(group, point)) | |
643 | return 1; | |
644 | ||
f844f9eb | 645 | #ifndef FIPS_MODULE |
0f113f3e MC |
646 | if (ctx == NULL) { |
647 | ctx = new_ctx = BN_CTX_new(); | |
648 | if (ctx == NULL) | |
649 | return 0; | |
650 | } | |
a9612d6c | 651 | #endif |
0f113f3e MC |
652 | |
653 | BN_CTX_start(ctx); | |
654 | x = BN_CTX_get(ctx); | |
655 | y = BN_CTX_get(ctx); | |
656 | if (y == NULL) | |
657 | goto err; | |
658 | ||
9cc570d4 | 659 | if (!EC_POINT_get_affine_coordinates(group, point, x, y, ctx)) |
0f113f3e MC |
660 | goto err; |
661 | if (!BN_copy(point->X, x)) | |
662 | goto err; | |
663 | if (!BN_copy(point->Y, y)) | |
664 | goto err; | |
665 | if (!BN_one(point->Z)) | |
666 | goto err; | |
dd67493c | 667 | point->Z_is_one = 1; |
0f113f3e MC |
668 | |
669 | ret = 1; | |
670 | ||
671 | err: | |
a0fda2cf | 672 | BN_CTX_end(ctx); |
f844f9eb | 673 | #ifndef FIPS_MODULE |
23a1d5e9 | 674 | BN_CTX_free(new_ctx); |
a9612d6c | 675 | #endif |
0f113f3e MC |
676 | return ret; |
677 | } | |
678 | ||
679 | /* | |
680 | * Forces each of the EC_POINTs in the given array to use affine coordinates. | |
681 | */ | |
682 | int ec_GF2m_simple_points_make_affine(const EC_GROUP *group, size_t num, | |
683 | EC_POINT *points[], BN_CTX *ctx) | |
684 | { | |
685 | size_t i; | |
7793f30e | 686 | |
0f113f3e MC |
687 | for (i = 0; i < num; i++) { |
688 | if (!group->meth->make_affine(group, points[i], ctx)) | |
689 | return 0; | |
690 | } | |
7793f30e | 691 | |
0f113f3e MC |
692 | return 1; |
693 | } | |
7793f30e | 694 | |
0f113f3e MC |
695 | /* Wrapper to simple binary polynomial field multiplication implementation. */ |
696 | int ec_GF2m_simple_field_mul(const EC_GROUP *group, BIGNUM *r, | |
697 | const BIGNUM *a, const BIGNUM *b, BN_CTX *ctx) | |
698 | { | |
699 | return BN_GF2m_mod_mul_arr(r, a, b, group->poly, ctx); | |
700 | } | |
7793f30e BM |
701 | |
702 | /* Wrapper to simple binary polynomial field squaring implementation. */ | |
0f113f3e MC |
703 | int ec_GF2m_simple_field_sqr(const EC_GROUP *group, BIGNUM *r, |
704 | const BIGNUM *a, BN_CTX *ctx) | |
705 | { | |
706 | return BN_GF2m_mod_sqr_arr(r, a, group->poly, ctx); | |
707 | } | |
7793f30e BM |
708 | |
709 | /* Wrapper to simple binary polynomial field division implementation. */ | |
0f113f3e MC |
710 | int ec_GF2m_simple_field_div(const EC_GROUP *group, BIGNUM *r, |
711 | const BIGNUM *a, const BIGNUM *b, BN_CTX *ctx) | |
712 | { | |
713 | return BN_GF2m_mod_div(r, a, b, group->field, ctx); | |
714 | } | |
b3310161 | 715 | |
f45846f5 NT |
716 | /*- |
717 | * Lopez-Dahab ladder, pre step. | |
718 | * See e.g. "Guide to ECC" Alg 3.40. | |
719 | * Modified to blind s and r independently. | |
720 | * s:= p, r := 2p | |
721 | */ | |
722 | static | |
723 | int ec_GF2m_simple_ladder_pre(const EC_GROUP *group, | |
724 | EC_POINT *r, EC_POINT *s, | |
725 | EC_POINT *p, BN_CTX *ctx) | |
726 | { | |
727 | /* if p is not affine, something is wrong */ | |
728 | if (p->Z_is_one == 0) | |
729 | return 0; | |
730 | ||
731 | /* s blinding: make sure lambda (s->Z here) is not zero */ | |
732 | do { | |
a9612d6c MC |
733 | if (!BN_priv_rand_ex(s->Z, BN_num_bits(group->field) - 1, |
734 | BN_RAND_TOP_ANY, BN_RAND_BOTTOM_ANY, ctx)) { | |
f45846f5 NT |
735 | ECerr(EC_F_EC_GF2M_SIMPLE_LADDER_PRE, ERR_R_BN_LIB); |
736 | return 0; | |
737 | } | |
738 | } while (BN_is_zero(s->Z)); | |
739 | ||
740 | /* if field_encode defined convert between representations */ | |
741 | if ((group->meth->field_encode != NULL | |
742 | && !group->meth->field_encode(group, s->Z, s->Z, ctx)) | |
743 | || !group->meth->field_mul(group, s->X, p->X, s->Z, ctx)) | |
744 | return 0; | |
745 | ||
746 | /* r blinding: make sure lambda (r->Y here for storage) is not zero */ | |
747 | do { | |
a9612d6c MC |
748 | if (!BN_priv_rand_ex(r->Y, BN_num_bits(group->field) - 1, |
749 | BN_RAND_TOP_ANY, BN_RAND_BOTTOM_ANY, ctx)) { | |
f45846f5 NT |
750 | ECerr(EC_F_EC_GF2M_SIMPLE_LADDER_PRE, ERR_R_BN_LIB); |
751 | return 0; | |
752 | } | |
753 | } while (BN_is_zero(r->Y)); | |
754 | ||
755 | if ((group->meth->field_encode != NULL | |
756 | && !group->meth->field_encode(group, r->Y, r->Y, ctx)) | |
757 | || !group->meth->field_sqr(group, r->Z, p->X, ctx) | |
758 | || !group->meth->field_sqr(group, r->X, r->Z, ctx) | |
759 | || !BN_GF2m_add(r->X, r->X, group->b) | |
760 | || !group->meth->field_mul(group, r->Z, r->Z, r->Y, ctx) | |
761 | || !group->meth->field_mul(group, r->X, r->X, r->Y, ctx)) | |
762 | return 0; | |
763 | ||
764 | s->Z_is_one = 0; | |
765 | r->Z_is_one = 0; | |
766 | ||
767 | return 1; | |
768 | } | |
769 | ||
770 | /*- | |
771 | * Ladder step: differential addition-and-doubling, mixed Lopez-Dahab coords. | |
772 | * http://www.hyperelliptic.org/EFD/g12o/auto-code/shortw/xz/ladder/mladd-2003-s.op3 | |
773 | * s := r + s, r := 2r | |
774 | */ | |
775 | static | |
776 | int ec_GF2m_simple_ladder_step(const EC_GROUP *group, | |
777 | EC_POINT *r, EC_POINT *s, | |
778 | EC_POINT *p, BN_CTX *ctx) | |
779 | { | |
780 | if (!group->meth->field_mul(group, r->Y, r->Z, s->X, ctx) | |
781 | || !group->meth->field_mul(group, s->X, r->X, s->Z, ctx) | |
782 | || !group->meth->field_sqr(group, s->Y, r->Z, ctx) | |
783 | || !group->meth->field_sqr(group, r->Z, r->X, ctx) | |
784 | || !BN_GF2m_add(s->Z, r->Y, s->X) | |
785 | || !group->meth->field_sqr(group, s->Z, s->Z, ctx) | |
786 | || !group->meth->field_mul(group, s->X, r->Y, s->X, ctx) | |
787 | || !group->meth->field_mul(group, r->Y, s->Z, p->X, ctx) | |
788 | || !BN_GF2m_add(s->X, s->X, r->Y) | |
789 | || !group->meth->field_sqr(group, r->Y, r->Z, ctx) | |
790 | || !group->meth->field_mul(group, r->Z, r->Z, s->Y, ctx) | |
791 | || !group->meth->field_sqr(group, s->Y, s->Y, ctx) | |
792 | || !group->meth->field_mul(group, s->Y, s->Y, group->b, ctx) | |
793 | || !BN_GF2m_add(r->X, r->Y, s->Y)) | |
794 | return 0; | |
795 | ||
796 | return 1; | |
797 | } | |
798 | ||
799 | /*- | |
800 | * Recover affine (x,y) result from Lopez-Dahab r and s, affine p. | |
801 | * See e.g. "Fast Multiplication on Elliptic Curves over GF(2**m) | |
802 | * without Precomputation" (Lopez and Dahab, CHES 1999), | |
803 | * Appendix Alg Mxy. | |
804 | */ | |
805 | static | |
806 | int ec_GF2m_simple_ladder_post(const EC_GROUP *group, | |
807 | EC_POINT *r, EC_POINT *s, | |
808 | EC_POINT *p, BN_CTX *ctx) | |
809 | { | |
810 | int ret = 0; | |
811 | BIGNUM *t0, *t1, *t2 = NULL; | |
812 | ||
813 | if (BN_is_zero(r->Z)) | |
814 | return EC_POINT_set_to_infinity(group, r); | |
815 | ||
816 | if (BN_is_zero(s->Z)) { | |
817 | if (!EC_POINT_copy(r, p) | |
818 | || !EC_POINT_invert(group, r, ctx)) { | |
819 | ECerr(EC_F_EC_GF2M_SIMPLE_LADDER_POST, ERR_R_EC_LIB); | |
820 | return 0; | |
821 | } | |
822 | return 1; | |
823 | } | |
824 | ||
825 | BN_CTX_start(ctx); | |
826 | t0 = BN_CTX_get(ctx); | |
827 | t1 = BN_CTX_get(ctx); | |
828 | t2 = BN_CTX_get(ctx); | |
829 | if (t2 == NULL) { | |
830 | ECerr(EC_F_EC_GF2M_SIMPLE_LADDER_POST, ERR_R_MALLOC_FAILURE); | |
831 | goto err; | |
832 | } | |
833 | ||
834 | if (!group->meth->field_mul(group, t0, r->Z, s->Z, ctx) | |
835 | || !group->meth->field_mul(group, t1, p->X, r->Z, ctx) | |
836 | || !BN_GF2m_add(t1, r->X, t1) | |
837 | || !group->meth->field_mul(group, t2, p->X, s->Z, ctx) | |
838 | || !group->meth->field_mul(group, r->Z, r->X, t2, ctx) | |
839 | || !BN_GF2m_add(t2, t2, s->X) | |
840 | || !group->meth->field_mul(group, t1, t1, t2, ctx) | |
841 | || !group->meth->field_sqr(group, t2, p->X, ctx) | |
842 | || !BN_GF2m_add(t2, p->Y, t2) | |
843 | || !group->meth->field_mul(group, t2, t2, t0, ctx) | |
844 | || !BN_GF2m_add(t1, t2, t1) | |
845 | || !group->meth->field_mul(group, t2, p->X, t0, ctx) | |
e0033efc | 846 | || !group->meth->field_inv(group, t2, t2, ctx) |
f45846f5 NT |
847 | || !group->meth->field_mul(group, t1, t1, t2, ctx) |
848 | || !group->meth->field_mul(group, r->X, r->Z, t2, ctx) | |
849 | || !BN_GF2m_add(t2, p->X, r->X) | |
850 | || !group->meth->field_mul(group, t2, t2, t1, ctx) | |
851 | || !BN_GF2m_add(r->Y, p->Y, t2) | |
852 | || !BN_one(r->Z)) | |
853 | goto err; | |
854 | ||
855 | r->Z_is_one = 1; | |
856 | ||
857 | /* GF(2^m) field elements should always have BIGNUM::neg = 0 */ | |
858 | BN_set_negative(r->X, 0); | |
859 | BN_set_negative(r->Y, 0); | |
860 | ||
861 | ret = 1; | |
862 | ||
863 | err: | |
864 | BN_CTX_end(ctx); | |
865 | return ret; | |
866 | } | |
867 | ||
01ad66f8 NT |
868 | static |
869 | int ec_GF2m_simple_points_mul(const EC_GROUP *group, EC_POINT *r, | |
870 | const BIGNUM *scalar, size_t num, | |
871 | const EC_POINT *points[], | |
872 | const BIGNUM *scalars[], | |
873 | BN_CTX *ctx) | |
874 | { | |
875 | int ret = 0; | |
876 | EC_POINT *t = NULL; | |
877 | ||
878 | /*- | |
879 | * We limit use of the ladder only to the following cases: | |
880 | * - r := scalar * G | |
881 | * Fixed point mul: scalar != NULL && num == 0; | |
882 | * - r := scalars[0] * points[0] | |
883 | * Variable point mul: scalar == NULL && num == 1; | |
884 | * - r := scalar * G + scalars[0] * points[0] | |
885 | * used, e.g., in ECDSA verification: scalar != NULL && num == 1 | |
886 | * | |
887 | * In any other case (num > 1) we use the default wNAF implementation. | |
888 | * | |
889 | * We also let the default implementation handle degenerate cases like group | |
890 | * order or cofactor set to 0. | |
891 | */ | |
892 | if (num > 1 || BN_is_zero(group->order) || BN_is_zero(group->cofactor)) | |
893 | return ec_wNAF_mul(group, r, scalar, num, points, scalars, ctx); | |
894 | ||
895 | if (scalar != NULL && num == 0) | |
896 | /* Fixed point multiplication */ | |
897 | return ec_scalar_mul_ladder(group, r, scalar, NULL, ctx); | |
898 | ||
899 | if (scalar == NULL && num == 1) | |
900 | /* Variable point multiplication */ | |
901 | return ec_scalar_mul_ladder(group, r, scalars[0], points[0], ctx); | |
902 | ||
903 | /*- | |
904 | * Double point multiplication: | |
905 | * r := scalar * G + scalars[0] * points[0] | |
906 | */ | |
907 | ||
908 | if ((t = EC_POINT_new(group)) == NULL) { | |
909 | ECerr(EC_F_EC_GF2M_SIMPLE_POINTS_MUL, ERR_R_MALLOC_FAILURE); | |
910 | return 0; | |
911 | } | |
912 | ||
913 | if (!ec_scalar_mul_ladder(group, t, scalar, NULL, ctx) | |
914 | || !ec_scalar_mul_ladder(group, r, scalars[0], points[0], ctx) | |
915 | || !EC_POINT_add(group, r, t, r, ctx)) | |
916 | goto err; | |
917 | ||
918 | ret = 1; | |
919 | ||
920 | err: | |
921 | EC_POINT_free(t); | |
922 | return ret; | |
923 | } | |
924 | ||
e0033efc BB |
925 | /*- |
926 | * Computes the multiplicative inverse of a in GF(2^m), storing the result in r. | |
927 | * If a is zero (or equivalent), you'll get a EC_R_CANNOT_INVERT error. | |
928 | * SCA hardening is with blinding: BN_GF2m_mod_inv does that. | |
929 | */ | |
930 | static int ec_GF2m_simple_field_inv(const EC_GROUP *group, BIGNUM *r, | |
931 | const BIGNUM *a, BN_CTX *ctx) | |
932 | { | |
933 | int ret; | |
934 | ||
935 | if (!(ret = BN_GF2m_mod_inv(r, a, group->field, ctx))) | |
936 | ECerr(EC_F_EC_GF2M_SIMPLE_FIELD_INV, EC_R_CANNOT_INVERT); | |
937 | return ret; | |
938 | } | |
939 | ||
f45846f5 NT |
940 | const EC_METHOD *EC_GF2m_simple_method(void) |
941 | { | |
942 | static const EC_METHOD ret = { | |
943 | EC_FLAGS_DEFAULT_OCT, | |
944 | NID_X9_62_characteristic_two_field, | |
945 | ec_GF2m_simple_group_init, | |
946 | ec_GF2m_simple_group_finish, | |
947 | ec_GF2m_simple_group_clear_finish, | |
948 | ec_GF2m_simple_group_copy, | |
949 | ec_GF2m_simple_group_set_curve, | |
950 | ec_GF2m_simple_group_get_curve, | |
951 | ec_GF2m_simple_group_get_degree, | |
952 | ec_group_simple_order_bits, | |
953 | ec_GF2m_simple_group_check_discriminant, | |
954 | ec_GF2m_simple_point_init, | |
955 | ec_GF2m_simple_point_finish, | |
956 | ec_GF2m_simple_point_clear_finish, | |
957 | ec_GF2m_simple_point_copy, | |
958 | ec_GF2m_simple_point_set_to_infinity, | |
f45846f5 NT |
959 | ec_GF2m_simple_point_set_affine_coordinates, |
960 | ec_GF2m_simple_point_get_affine_coordinates, | |
961 | 0, /* point_set_compressed_coordinates */ | |
962 | 0, /* point2oct */ | |
963 | 0, /* oct2point */ | |
964 | ec_GF2m_simple_add, | |
965 | ec_GF2m_simple_dbl, | |
966 | ec_GF2m_simple_invert, | |
967 | ec_GF2m_simple_is_at_infinity, | |
968 | ec_GF2m_simple_is_on_curve, | |
969 | ec_GF2m_simple_cmp, | |
970 | ec_GF2m_simple_make_affine, | |
971 | ec_GF2m_simple_points_make_affine, | |
01ad66f8 | 972 | ec_GF2m_simple_points_mul, |
f45846f5 NT |
973 | 0, /* precompute_mult */ |
974 | 0, /* have_precompute_mult */ | |
975 | ec_GF2m_simple_field_mul, | |
976 | ec_GF2m_simple_field_sqr, | |
977 | ec_GF2m_simple_field_div, | |
e0033efc | 978 | ec_GF2m_simple_field_inv, |
f45846f5 NT |
979 | 0, /* field_encode */ |
980 | 0, /* field_decode */ | |
981 | 0, /* field_set_to_one */ | |
982 | ec_key_simple_priv2oct, | |
983 | ec_key_simple_oct2priv, | |
984 | 0, /* set private */ | |
985 | ec_key_simple_generate_key, | |
986 | ec_key_simple_check_key, | |
987 | ec_key_simple_generate_public_key, | |
988 | 0, /* keycopy */ | |
989 | 0, /* keyfinish */ | |
990 | ecdh_simple_compute_key, | |
9bf682f6 PS |
991 | ecdsa_simple_sign_setup, |
992 | ecdsa_simple_sign_sig, | |
993 | ecdsa_simple_verify_sig, | |
f45846f5 NT |
994 | 0, /* field_inverse_mod_ord */ |
995 | 0, /* blind_coordinates */ | |
996 | ec_GF2m_simple_ladder_pre, | |
997 | ec_GF2m_simple_ladder_step, | |
998 | ec_GF2m_simple_ladder_post | |
999 | }; | |
1000 | ||
1001 | return &ret; | |
1002 | } | |
1003 | ||
b3310161 | 1004 | #endif |