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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 | 27 | */ |
32ab57cb | 28 | int ossl_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 | 46 | */ |
32ab57cb | 47 | void ossl_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 | 57 | */ |
32ab57cb | 58 | void ossl_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 | 74 | */ |
32ab57cb | 75 | int ossl_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. */ | |
32ab57cb SL |
101 | int ossl_ec_GF2m_simple_group_set_curve(EC_GROUP *group, |
102 | const BIGNUM *p, const BIGNUM *a, | |
103 | const BIGNUM *b, BN_CTX *ctx) | |
0f113f3e MC |
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)) { | |
9311d0c4 | 112 | ERR_raise(ERR_LIB_EC, EC_R_UNSUPPORTED_FIELD); |
0f113f3e MC |
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 | */ |
32ab57cb SL |
141 | int ossl_ec_GF2m_simple_group_get_curve(const EC_GROUP *group, BIGNUM *p, |
142 | BIGNUM *a, BIGNUM *b, BN_CTX *ctx) | |
0f113f3e MC |
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 | */ | |
32ab57cb | 171 | int ossl_ec_GF2m_simple_group_get_degree(const EC_GROUP *group) |
0f113f3e MC |
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 | */ |
32ab57cb SL |
180 | int ossl_ec_GF2m_simple_group_check_discriminant(const EC_GROUP *group, |
181 | BN_CTX *ctx) | |
0f113f3e MC |
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) { | |
9311d0c4 | 191 | ERR_raise(ERR_LIB_EC, ERR_R_MALLOC_FAILURE); |
0f113f3e MC |
192 | goto err; |
193 | } | |
194 | } | |
a9612d6c | 195 | #endif |
0f113f3e MC |
196 | BN_CTX_start(ctx); |
197 | b = BN_CTX_get(ctx); | |
198 | if (b == NULL) | |
199 | goto err; | |
200 | ||
201 | if (!BN_GF2m_mod_arr(b, group->b, group->poly)) | |
202 | goto err; | |
203 | ||
204 | /* | |
205 | * check the discriminant: y^2 + x*y = x^3 + a*x^2 + b is an elliptic | |
206 | * curve <=> b != 0 (mod p) | |
207 | */ | |
208 | if (BN_is_zero(b)) | |
209 | goto err; | |
210 | ||
211 | ret = 1; | |
7793f30e | 212 | |
0f113f3e | 213 | err: |
ce1415ed | 214 | BN_CTX_end(ctx); |
f844f9eb | 215 | #ifndef FIPS_MODULE |
23a1d5e9 | 216 | BN_CTX_free(new_ctx); |
a9612d6c | 217 | #endif |
0f113f3e MC |
218 | return ret; |
219 | } | |
7793f30e BM |
220 | |
221 | /* Initializes an EC_POINT. */ | |
32ab57cb | 222 | int ossl_ec_GF2m_simple_point_init(EC_POINT *point) |
0f113f3e MC |
223 | { |
224 | point->X = BN_new(); | |
225 | point->Y = BN_new(); | |
226 | point->Z = BN_new(); | |
227 | ||
90945fa3 | 228 | if (point->X == NULL || point->Y == NULL || point->Z == NULL) { |
23a1d5e9 RS |
229 | BN_free(point->X); |
230 | BN_free(point->Y); | |
231 | BN_free(point->Z); | |
0f113f3e MC |
232 | return 0; |
233 | } | |
234 | return 1; | |
235 | } | |
7793f30e BM |
236 | |
237 | /* Frees an EC_POINT. */ | |
32ab57cb | 238 | void ossl_ec_GF2m_simple_point_finish(EC_POINT *point) |
0f113f3e MC |
239 | { |
240 | BN_free(point->X); | |
241 | BN_free(point->Y); | |
242 | BN_free(point->Z); | |
243 | } | |
7793f30e BM |
244 | |
245 | /* Clears and frees an EC_POINT. */ | |
32ab57cb | 246 | void ossl_ec_GF2m_simple_point_clear_finish(EC_POINT *point) |
0f113f3e MC |
247 | { |
248 | BN_clear_free(point->X); | |
249 | BN_clear_free(point->Y); | |
250 | BN_clear_free(point->Z); | |
251 | point->Z_is_one = 0; | |
252 | } | |
253 | ||
254 | /* | |
255 | * Copy the contents of one EC_POINT into another. Assumes dest is | |
256 | * initialized. | |
7793f30e | 257 | */ |
32ab57cb | 258 | int ossl_ec_GF2m_simple_point_copy(EC_POINT *dest, const EC_POINT *src) |
0f113f3e MC |
259 | { |
260 | if (!BN_copy(dest->X, src->X)) | |
261 | return 0; | |
262 | if (!BN_copy(dest->Y, src->Y)) | |
263 | return 0; | |
264 | if (!BN_copy(dest->Z, src->Z)) | |
265 | return 0; | |
266 | dest->Z_is_one = src->Z_is_one; | |
b14e6015 | 267 | dest->curve_name = src->curve_name; |
0f113f3e MC |
268 | |
269 | return 1; | |
270 | } | |
271 | ||
272 | /* | |
273 | * Set an EC_POINT to the point at infinity. A point at infinity is | |
274 | * represented by having Z=0. | |
7793f30e | 275 | */ |
32ab57cb SL |
276 | int ossl_ec_GF2m_simple_point_set_to_infinity(const EC_GROUP *group, |
277 | EC_POINT *point) | |
0f113f3e MC |
278 | { |
279 | point->Z_is_one = 0; | |
280 | BN_zero(point->Z); | |
281 | return 1; | |
282 | } | |
283 | ||
284 | /* | |
285 | * Set the coordinates of an EC_POINT using affine coordinates. Note that | |
286 | * the simple implementation only uses affine coordinates. | |
7793f30e | 287 | */ |
32ab57cb SL |
288 | int ossl_ec_GF2m_simple_point_set_affine_coordinates(const EC_GROUP *group, |
289 | EC_POINT *point, | |
290 | const BIGNUM *x, | |
291 | const BIGNUM *y, | |
292 | BN_CTX *ctx) | |
0f113f3e MC |
293 | { |
294 | int ret = 0; | |
295 | if (x == NULL || y == NULL) { | |
9311d0c4 | 296 | ERR_raise(ERR_LIB_EC, ERR_R_PASSED_NULL_PARAMETER); |
0f113f3e MC |
297 | return 0; |
298 | } | |
299 | ||
300 | if (!BN_copy(point->X, x)) | |
301 | goto err; | |
302 | BN_set_negative(point->X, 0); | |
303 | if (!BN_copy(point->Y, y)) | |
304 | goto err; | |
305 | BN_set_negative(point->Y, 0); | |
306 | if (!BN_copy(point->Z, BN_value_one())) | |
307 | goto err; | |
308 | BN_set_negative(point->Z, 0); | |
309 | point->Z_is_one = 1; | |
310 | ret = 1; | |
311 | ||
7793f30e | 312 | err: |
0f113f3e MC |
313 | return ret; |
314 | } | |
7793f30e | 315 | |
0f113f3e MC |
316 | /* |
317 | * Gets the affine coordinates of an EC_POINT. Note that the simple | |
318 | * implementation only uses affine coordinates. | |
7793f30e | 319 | */ |
32ab57cb SL |
320 | int ossl_ec_GF2m_simple_point_get_affine_coordinates(const EC_GROUP *group, |
321 | const EC_POINT *point, | |
322 | BIGNUM *x, BIGNUM *y, | |
323 | BN_CTX *ctx) | |
0f113f3e MC |
324 | { |
325 | int ret = 0; | |
326 | ||
327 | if (EC_POINT_is_at_infinity(group, point)) { | |
9311d0c4 | 328 | ERR_raise(ERR_LIB_EC, EC_R_POINT_AT_INFINITY); |
0f113f3e MC |
329 | return 0; |
330 | } | |
331 | ||
332 | if (BN_cmp(point->Z, BN_value_one())) { | |
9311d0c4 | 333 | ERR_raise(ERR_LIB_EC, ERR_R_SHOULD_NOT_HAVE_BEEN_CALLED); |
0f113f3e MC |
334 | return 0; |
335 | } | |
336 | if (x != NULL) { | |
337 | if (!BN_copy(x, point->X)) | |
338 | goto err; | |
339 | BN_set_negative(x, 0); | |
340 | } | |
341 | if (y != NULL) { | |
342 | if (!BN_copy(y, point->Y)) | |
343 | goto err; | |
344 | BN_set_negative(y, 0); | |
345 | } | |
346 | ret = 1; | |
7793f30e BM |
347 | |
348 | err: | |
0f113f3e MC |
349 | return ret; |
350 | } | |
7793f30e | 351 | |
0f113f3e MC |
352 | /* |
353 | * Computes a + b and stores the result in r. r could be a or b, a could be | |
354 | * b. Uses algorithm A.10.2 of IEEE P1363. | |
7793f30e | 355 | */ |
32ab57cb SL |
356 | int ossl_ec_GF2m_simple_add(const EC_GROUP *group, EC_POINT *r, |
357 | const EC_POINT *a, const EC_POINT *b, BN_CTX *ctx) | |
0f113f3e | 358 | { |
0f113f3e MC |
359 | BIGNUM *x0, *y0, *x1, *y1, *x2, *y2, *s, *t; |
360 | int ret = 0; | |
f844f9eb | 361 | #ifndef FIPS_MODULE |
a9612d6c MC |
362 | BN_CTX *new_ctx = NULL; |
363 | #endif | |
0f113f3e MC |
364 | |
365 | if (EC_POINT_is_at_infinity(group, a)) { | |
366 | if (!EC_POINT_copy(r, b)) | |
367 | return 0; | |
368 | return 1; | |
369 | } | |
370 | ||
371 | if (EC_POINT_is_at_infinity(group, b)) { | |
372 | if (!EC_POINT_copy(r, a)) | |
373 | return 0; | |
374 | return 1; | |
375 | } | |
376 | ||
f844f9eb | 377 | #ifndef FIPS_MODULE |
0f113f3e MC |
378 | if (ctx == NULL) { |
379 | ctx = new_ctx = BN_CTX_new(); | |
380 | if (ctx == NULL) | |
381 | return 0; | |
382 | } | |
a9612d6c | 383 | #endif |
0f113f3e MC |
384 | |
385 | BN_CTX_start(ctx); | |
386 | x0 = BN_CTX_get(ctx); | |
387 | y0 = BN_CTX_get(ctx); | |
388 | x1 = BN_CTX_get(ctx); | |
389 | y1 = BN_CTX_get(ctx); | |
390 | x2 = BN_CTX_get(ctx); | |
391 | y2 = BN_CTX_get(ctx); | |
392 | s = BN_CTX_get(ctx); | |
393 | t = BN_CTX_get(ctx); | |
394 | if (t == NULL) | |
395 | goto err; | |
396 | ||
397 | if (a->Z_is_one) { | |
398 | if (!BN_copy(x0, a->X)) | |
399 | goto err; | |
400 | if (!BN_copy(y0, a->Y)) | |
401 | goto err; | |
402 | } else { | |
9cc570d4 | 403 | if (!EC_POINT_get_affine_coordinates(group, a, x0, y0, ctx)) |
0f113f3e MC |
404 | goto err; |
405 | } | |
406 | if (b->Z_is_one) { | |
407 | if (!BN_copy(x1, b->X)) | |
408 | goto err; | |
409 | if (!BN_copy(y1, b->Y)) | |
410 | goto err; | |
411 | } else { | |
9cc570d4 | 412 | if (!EC_POINT_get_affine_coordinates(group, b, x1, y1, ctx)) |
0f113f3e MC |
413 | goto err; |
414 | } | |
415 | ||
416 | if (BN_GF2m_cmp(x0, x1)) { | |
417 | if (!BN_GF2m_add(t, x0, x1)) | |
418 | goto err; | |
419 | if (!BN_GF2m_add(s, y0, y1)) | |
420 | goto err; | |
421 | if (!group->meth->field_div(group, s, s, t, ctx)) | |
422 | goto err; | |
423 | if (!group->meth->field_sqr(group, x2, s, ctx)) | |
424 | goto err; | |
425 | if (!BN_GF2m_add(x2, x2, group->a)) | |
426 | goto err; | |
427 | if (!BN_GF2m_add(x2, x2, s)) | |
428 | goto err; | |
429 | if (!BN_GF2m_add(x2, x2, t)) | |
430 | goto err; | |
431 | } else { | |
432 | if (BN_GF2m_cmp(y0, y1) || BN_is_zero(x1)) { | |
433 | if (!EC_POINT_set_to_infinity(group, r)) | |
434 | goto err; | |
435 | ret = 1; | |
436 | goto err; | |
437 | } | |
438 | if (!group->meth->field_div(group, s, y1, x1, ctx)) | |
439 | goto err; | |
440 | if (!BN_GF2m_add(s, s, x1)) | |
441 | goto err; | |
442 | ||
443 | if (!group->meth->field_sqr(group, x2, s, ctx)) | |
444 | goto err; | |
445 | if (!BN_GF2m_add(x2, x2, s)) | |
446 | goto err; | |
447 | if (!BN_GF2m_add(x2, x2, group->a)) | |
448 | goto err; | |
449 | } | |
450 | ||
451 | if (!BN_GF2m_add(y2, x1, x2)) | |
452 | goto err; | |
453 | if (!group->meth->field_mul(group, y2, y2, s, ctx)) | |
454 | goto err; | |
455 | if (!BN_GF2m_add(y2, y2, x2)) | |
456 | goto err; | |
457 | if (!BN_GF2m_add(y2, y2, y1)) | |
458 | goto err; | |
459 | ||
9cc570d4 | 460 | if (!EC_POINT_set_affine_coordinates(group, r, x2, y2, ctx)) |
0f113f3e MC |
461 | goto err; |
462 | ||
463 | ret = 1; | |
7793f30e | 464 | |
0f113f3e MC |
465 | err: |
466 | BN_CTX_end(ctx); | |
f844f9eb | 467 | #ifndef FIPS_MODULE |
23a1d5e9 | 468 | BN_CTX_free(new_ctx); |
a9612d6c | 469 | #endif |
0f113f3e MC |
470 | return ret; |
471 | } | |
472 | ||
473 | /* | |
474 | * Computes 2 * a and stores the result in r. r could be a. Uses algorithm | |
475 | * A.10.2 of IEEE P1363. | |
476 | */ | |
32ab57cb SL |
477 | int ossl_ec_GF2m_simple_dbl(const EC_GROUP *group, EC_POINT *r, |
478 | const EC_POINT *a, BN_CTX *ctx) | |
0f113f3e | 479 | { |
32ab57cb | 480 | return ossl_ec_GF2m_simple_add(group, r, a, a, ctx); |
0f113f3e | 481 | } |
7793f30e | 482 | |
32ab57cb SL |
483 | int ossl_ec_GF2m_simple_invert(const EC_GROUP *group, EC_POINT *point, |
484 | BN_CTX *ctx) | |
0f113f3e MC |
485 | { |
486 | if (EC_POINT_is_at_infinity(group, point) || BN_is_zero(point->Y)) | |
487 | /* point is its own inverse */ | |
488 | return 1; | |
7793f30e | 489 | |
c2f2db9b BB |
490 | if (group->meth->make_affine == NULL |
491 | || !group->meth->make_affine(group, point, ctx)) | |
0f113f3e MC |
492 | return 0; |
493 | return BN_GF2m_add(point->Y, point->X, point->Y); | |
494 | } | |
7793f30e BM |
495 | |
496 | /* Indicates whether the given point is the point at infinity. */ | |
32ab57cb SL |
497 | int ossl_ec_GF2m_simple_is_at_infinity(const EC_GROUP *group, |
498 | const EC_POINT *point) | |
0f113f3e MC |
499 | { |
500 | return BN_is_zero(point->Z); | |
501 | } | |
7793f30e | 502 | |
23a22b4c MC |
503 | /*- |
504 | * Determines whether the given EC_POINT is an actual point on the curve defined | |
7793f30e BM |
505 | * in the EC_GROUP. A point is valid if it satisfies the Weierstrass equation: |
506 | * y^2 + x*y = x^3 + a*x^2 + b. | |
507 | */ | |
32ab57cb SL |
508 | int ossl_ec_GF2m_simple_is_on_curve(const EC_GROUP *group, const EC_POINT *point, |
509 | BN_CTX *ctx) | |
0f113f3e MC |
510 | { |
511 | int ret = -1; | |
0f113f3e MC |
512 | BIGNUM *lh, *y2; |
513 | int (*field_mul) (const EC_GROUP *, BIGNUM *, const BIGNUM *, | |
514 | const BIGNUM *, BN_CTX *); | |
515 | int (*field_sqr) (const EC_GROUP *, BIGNUM *, const BIGNUM *, BN_CTX *); | |
f844f9eb | 516 | #ifndef FIPS_MODULE |
a9612d6c MC |
517 | BN_CTX *new_ctx = NULL; |
518 | #endif | |
0f113f3e MC |
519 | |
520 | if (EC_POINT_is_at_infinity(group, point)) | |
521 | return 1; | |
522 | ||
523 | field_mul = group->meth->field_mul; | |
524 | field_sqr = group->meth->field_sqr; | |
525 | ||
526 | /* only support affine coordinates */ | |
527 | if (!point->Z_is_one) | |
528 | return -1; | |
529 | ||
f844f9eb | 530 | #ifndef FIPS_MODULE |
0f113f3e MC |
531 | if (ctx == NULL) { |
532 | ctx = new_ctx = BN_CTX_new(); | |
533 | if (ctx == NULL) | |
534 | return -1; | |
535 | } | |
a9612d6c | 536 | #endif |
0f113f3e MC |
537 | |
538 | BN_CTX_start(ctx); | |
539 | y2 = BN_CTX_get(ctx); | |
540 | lh = BN_CTX_get(ctx); | |
541 | if (lh == NULL) | |
542 | goto err; | |
543 | ||
50e735f9 MC |
544 | /*- |
545 | * We have a curve defined by a Weierstrass equation | |
546 | * y^2 + x*y = x^3 + a*x^2 + b. | |
547 | * <=> x^3 + a*x^2 + x*y + b + y^2 = 0 | |
548 | * <=> ((x + a) * x + y ) * x + b + y^2 = 0 | |
549 | */ | |
0f113f3e MC |
550 | if (!BN_GF2m_add(lh, point->X, group->a)) |
551 | goto err; | |
552 | if (!field_mul(group, lh, lh, point->X, ctx)) | |
553 | goto err; | |
554 | if (!BN_GF2m_add(lh, lh, point->Y)) | |
555 | goto err; | |
556 | if (!field_mul(group, lh, lh, point->X, ctx)) | |
557 | goto err; | |
558 | if (!BN_GF2m_add(lh, lh, group->b)) | |
559 | goto err; | |
560 | if (!field_sqr(group, y2, point->Y, ctx)) | |
561 | goto err; | |
562 | if (!BN_GF2m_add(lh, lh, y2)) | |
563 | goto err; | |
564 | ret = BN_is_zero(lh); | |
a0fda2cf | 565 | |
7793f30e | 566 | err: |
a0fda2cf | 567 | BN_CTX_end(ctx); |
f844f9eb | 568 | #ifndef FIPS_MODULE |
23a1d5e9 | 569 | BN_CTX_free(new_ctx); |
a9612d6c | 570 | #endif |
0f113f3e MC |
571 | return ret; |
572 | } | |
7793f30e | 573 | |
1d97c843 TH |
574 | /*- |
575 | * Indicates whether two points are equal. | |
7793f30e BM |
576 | * Return values: |
577 | * -1 error | |
578 | * 0 equal (in affine coordinates) | |
579 | * 1 not equal | |
580 | */ | |
32ab57cb SL |
581 | int ossl_ec_GF2m_simple_cmp(const EC_GROUP *group, const EC_POINT *a, |
582 | const EC_POINT *b, BN_CTX *ctx) | |
0f113f3e MC |
583 | { |
584 | BIGNUM *aX, *aY, *bX, *bY; | |
0f113f3e | 585 | int ret = -1; |
f844f9eb | 586 | #ifndef FIPS_MODULE |
a9612d6c MC |
587 | BN_CTX *new_ctx = NULL; |
588 | #endif | |
0f113f3e MC |
589 | |
590 | if (EC_POINT_is_at_infinity(group, a)) { | |
591 | return EC_POINT_is_at_infinity(group, b) ? 0 : 1; | |
592 | } | |
593 | ||
594 | if (EC_POINT_is_at_infinity(group, b)) | |
595 | return 1; | |
596 | ||
597 | if (a->Z_is_one && b->Z_is_one) { | |
598 | return ((BN_cmp(a->X, b->X) == 0) && BN_cmp(a->Y, b->Y) == 0) ? 0 : 1; | |
599 | } | |
600 | ||
f844f9eb | 601 | #ifndef FIPS_MODULE |
0f113f3e MC |
602 | if (ctx == NULL) { |
603 | ctx = new_ctx = BN_CTX_new(); | |
604 | if (ctx == NULL) | |
605 | return -1; | |
606 | } | |
a9612d6c | 607 | #endif |
0f113f3e MC |
608 | |
609 | BN_CTX_start(ctx); | |
610 | aX = BN_CTX_get(ctx); | |
611 | aY = BN_CTX_get(ctx); | |
612 | bX = BN_CTX_get(ctx); | |
613 | bY = BN_CTX_get(ctx); | |
614 | if (bY == NULL) | |
615 | goto err; | |
616 | ||
9cc570d4 | 617 | if (!EC_POINT_get_affine_coordinates(group, a, aX, aY, ctx)) |
0f113f3e | 618 | goto err; |
9cc570d4 | 619 | if (!EC_POINT_get_affine_coordinates(group, b, bX, bY, ctx)) |
0f113f3e MC |
620 | goto err; |
621 | ret = ((BN_cmp(aX, bX) == 0) && BN_cmp(aY, bY) == 0) ? 0 : 1; | |
7793f30e | 622 | |
0f113f3e | 623 | err: |
a0fda2cf | 624 | BN_CTX_end(ctx); |
f844f9eb | 625 | #ifndef FIPS_MODULE |
23a1d5e9 | 626 | BN_CTX_free(new_ctx); |
a9612d6c | 627 | #endif |
0f113f3e MC |
628 | return ret; |
629 | } | |
7793f30e BM |
630 | |
631 | /* Forces the given EC_POINT to internally use affine coordinates. */ | |
32ab57cb SL |
632 | int ossl_ec_GF2m_simple_make_affine(const EC_GROUP *group, EC_POINT *point, |
633 | BN_CTX *ctx) | |
0f113f3e | 634 | { |
0f113f3e MC |
635 | BIGNUM *x, *y; |
636 | int ret = 0; | |
f844f9eb | 637 | #ifndef FIPS_MODULE |
a9612d6c MC |
638 | BN_CTX *new_ctx = NULL; |
639 | #endif | |
0f113f3e MC |
640 | |
641 | if (point->Z_is_one || EC_POINT_is_at_infinity(group, point)) | |
642 | return 1; | |
643 | ||
f844f9eb | 644 | #ifndef FIPS_MODULE |
0f113f3e MC |
645 | if (ctx == NULL) { |
646 | ctx = new_ctx = BN_CTX_new(); | |
647 | if (ctx == NULL) | |
648 | return 0; | |
649 | } | |
a9612d6c | 650 | #endif |
0f113f3e MC |
651 | |
652 | BN_CTX_start(ctx); | |
653 | x = BN_CTX_get(ctx); | |
654 | y = BN_CTX_get(ctx); | |
655 | if (y == NULL) | |
656 | goto err; | |
657 | ||
9cc570d4 | 658 | if (!EC_POINT_get_affine_coordinates(group, point, x, y, ctx)) |
0f113f3e MC |
659 | goto err; |
660 | if (!BN_copy(point->X, x)) | |
661 | goto err; | |
662 | if (!BN_copy(point->Y, y)) | |
663 | goto err; | |
664 | if (!BN_one(point->Z)) | |
665 | goto err; | |
dd67493c | 666 | point->Z_is_one = 1; |
0f113f3e MC |
667 | |
668 | ret = 1; | |
669 | ||
670 | err: | |
a0fda2cf | 671 | BN_CTX_end(ctx); |
f844f9eb | 672 | #ifndef FIPS_MODULE |
23a1d5e9 | 673 | BN_CTX_free(new_ctx); |
a9612d6c | 674 | #endif |
0f113f3e MC |
675 | return ret; |
676 | } | |
677 | ||
678 | /* | |
679 | * Forces each of the EC_POINTs in the given array to use affine coordinates. | |
680 | */ | |
32ab57cb SL |
681 | int ossl_ec_GF2m_simple_points_make_affine(const EC_GROUP *group, size_t num, |
682 | EC_POINT *points[], BN_CTX *ctx) | |
0f113f3e MC |
683 | { |
684 | size_t i; | |
7793f30e | 685 | |
0f113f3e MC |
686 | for (i = 0; i < num; i++) { |
687 | if (!group->meth->make_affine(group, points[i], ctx)) | |
688 | return 0; | |
689 | } | |
7793f30e | 690 | |
0f113f3e MC |
691 | return 1; |
692 | } | |
7793f30e | 693 | |
0f113f3e | 694 | /* Wrapper to simple binary polynomial field multiplication implementation. */ |
32ab57cb SL |
695 | int ossl_ec_GF2m_simple_field_mul(const EC_GROUP *group, BIGNUM *r, |
696 | const BIGNUM *a, const BIGNUM *b, BN_CTX *ctx) | |
0f113f3e MC |
697 | { |
698 | return BN_GF2m_mod_mul_arr(r, a, b, group->poly, ctx); | |
699 | } | |
7793f30e BM |
700 | |
701 | /* Wrapper to simple binary polynomial field squaring implementation. */ | |
32ab57cb SL |
702 | int ossl_ec_GF2m_simple_field_sqr(const EC_GROUP *group, BIGNUM *r, |
703 | const BIGNUM *a, BN_CTX *ctx) | |
0f113f3e MC |
704 | { |
705 | return BN_GF2m_mod_sqr_arr(r, a, group->poly, ctx); | |
706 | } | |
7793f30e BM |
707 | |
708 | /* Wrapper to simple binary polynomial field division implementation. */ | |
32ab57cb SL |
709 | int ossl_ec_GF2m_simple_field_div(const EC_GROUP *group, BIGNUM *r, |
710 | const BIGNUM *a, const BIGNUM *b, BN_CTX *ctx) | |
0f113f3e MC |
711 | { |
712 | return BN_GF2m_mod_div(r, a, b, group->field, ctx); | |
713 | } | |
b3310161 | 714 | |
f45846f5 NT |
715 | /*- |
716 | * Lopez-Dahab ladder, pre step. | |
717 | * See e.g. "Guide to ECC" Alg 3.40. | |
718 | * Modified to blind s and r independently. | |
719 | * s:= p, r := 2p | |
720 | */ | |
721 | static | |
722 | int ec_GF2m_simple_ladder_pre(const EC_GROUP *group, | |
723 | EC_POINT *r, EC_POINT *s, | |
724 | EC_POINT *p, BN_CTX *ctx) | |
725 | { | |
726 | /* if p is not affine, something is wrong */ | |
727 | if (p->Z_is_one == 0) | |
728 | return 0; | |
729 | ||
730 | /* s blinding: make sure lambda (s->Z here) is not zero */ | |
731 | do { | |
a9612d6c MC |
732 | if (!BN_priv_rand_ex(s->Z, BN_num_bits(group->field) - 1, |
733 | BN_RAND_TOP_ANY, BN_RAND_BOTTOM_ANY, ctx)) { | |
9311d0c4 | 734 | ERR_raise(ERR_LIB_EC, ERR_R_BN_LIB); |
f45846f5 NT |
735 | return 0; |
736 | } | |
737 | } while (BN_is_zero(s->Z)); | |
738 | ||
739 | /* if field_encode defined convert between representations */ | |
740 | if ((group->meth->field_encode != NULL | |
741 | && !group->meth->field_encode(group, s->Z, s->Z, ctx)) | |
742 | || !group->meth->field_mul(group, s->X, p->X, s->Z, ctx)) | |
743 | return 0; | |
744 | ||
745 | /* r blinding: make sure lambda (r->Y here for storage) is not zero */ | |
746 | do { | |
a9612d6c MC |
747 | if (!BN_priv_rand_ex(r->Y, BN_num_bits(group->field) - 1, |
748 | BN_RAND_TOP_ANY, BN_RAND_BOTTOM_ANY, ctx)) { | |
9311d0c4 | 749 | ERR_raise(ERR_LIB_EC, ERR_R_BN_LIB); |
f45846f5 NT |
750 | return 0; |
751 | } | |
752 | } while (BN_is_zero(r->Y)); | |
753 | ||
754 | if ((group->meth->field_encode != NULL | |
755 | && !group->meth->field_encode(group, r->Y, r->Y, ctx)) | |
756 | || !group->meth->field_sqr(group, r->Z, p->X, ctx) | |
757 | || !group->meth->field_sqr(group, r->X, r->Z, ctx) | |
758 | || !BN_GF2m_add(r->X, r->X, group->b) | |
759 | || !group->meth->field_mul(group, r->Z, r->Z, r->Y, ctx) | |
760 | || !group->meth->field_mul(group, r->X, r->X, r->Y, ctx)) | |
761 | return 0; | |
762 | ||
763 | s->Z_is_one = 0; | |
764 | r->Z_is_one = 0; | |
765 | ||
766 | return 1; | |
767 | } | |
768 | ||
769 | /*- | |
770 | * Ladder step: differential addition-and-doubling, mixed Lopez-Dahab coords. | |
771 | * http://www.hyperelliptic.org/EFD/g12o/auto-code/shortw/xz/ladder/mladd-2003-s.op3 | |
772 | * s := r + s, r := 2r | |
773 | */ | |
774 | static | |
775 | int ec_GF2m_simple_ladder_step(const EC_GROUP *group, | |
776 | EC_POINT *r, EC_POINT *s, | |
777 | EC_POINT *p, BN_CTX *ctx) | |
778 | { | |
779 | if (!group->meth->field_mul(group, r->Y, r->Z, s->X, ctx) | |
780 | || !group->meth->field_mul(group, s->X, r->X, s->Z, ctx) | |
781 | || !group->meth->field_sqr(group, s->Y, r->Z, ctx) | |
782 | || !group->meth->field_sqr(group, r->Z, r->X, ctx) | |
783 | || !BN_GF2m_add(s->Z, r->Y, s->X) | |
784 | || !group->meth->field_sqr(group, s->Z, s->Z, ctx) | |
785 | || !group->meth->field_mul(group, s->X, r->Y, s->X, ctx) | |
786 | || !group->meth->field_mul(group, r->Y, s->Z, p->X, ctx) | |
787 | || !BN_GF2m_add(s->X, s->X, r->Y) | |
788 | || !group->meth->field_sqr(group, r->Y, r->Z, ctx) | |
789 | || !group->meth->field_mul(group, r->Z, r->Z, s->Y, ctx) | |
790 | || !group->meth->field_sqr(group, s->Y, s->Y, ctx) | |
791 | || !group->meth->field_mul(group, s->Y, s->Y, group->b, ctx) | |
792 | || !BN_GF2m_add(r->X, r->Y, s->Y)) | |
793 | return 0; | |
794 | ||
795 | return 1; | |
796 | } | |
797 | ||
798 | /*- | |
799 | * Recover affine (x,y) result from Lopez-Dahab r and s, affine p. | |
800 | * See e.g. "Fast Multiplication on Elliptic Curves over GF(2**m) | |
801 | * without Precomputation" (Lopez and Dahab, CHES 1999), | |
802 | * Appendix Alg Mxy. | |
803 | */ | |
804 | static | |
805 | int ec_GF2m_simple_ladder_post(const EC_GROUP *group, | |
806 | EC_POINT *r, EC_POINT *s, | |
807 | EC_POINT *p, BN_CTX *ctx) | |
808 | { | |
809 | int ret = 0; | |
810 | BIGNUM *t0, *t1, *t2 = NULL; | |
811 | ||
812 | if (BN_is_zero(r->Z)) | |
813 | return EC_POINT_set_to_infinity(group, r); | |
814 | ||
815 | if (BN_is_zero(s->Z)) { | |
816 | if (!EC_POINT_copy(r, p) | |
817 | || !EC_POINT_invert(group, r, ctx)) { | |
9311d0c4 | 818 | ERR_raise(ERR_LIB_EC, ERR_R_EC_LIB); |
f45846f5 NT |
819 | return 0; |
820 | } | |
821 | return 1; | |
822 | } | |
823 | ||
824 | BN_CTX_start(ctx); | |
825 | t0 = BN_CTX_get(ctx); | |
826 | t1 = BN_CTX_get(ctx); | |
827 | t2 = BN_CTX_get(ctx); | |
828 | if (t2 == NULL) { | |
9311d0c4 | 829 | ERR_raise(ERR_LIB_EC, ERR_R_MALLOC_FAILURE); |
f45846f5 NT |
830 | goto err; |
831 | } | |
832 | ||
833 | if (!group->meth->field_mul(group, t0, r->Z, s->Z, ctx) | |
834 | || !group->meth->field_mul(group, t1, p->X, r->Z, ctx) | |
835 | || !BN_GF2m_add(t1, r->X, t1) | |
836 | || !group->meth->field_mul(group, t2, p->X, s->Z, ctx) | |
837 | || !group->meth->field_mul(group, r->Z, r->X, t2, ctx) | |
838 | || !BN_GF2m_add(t2, t2, s->X) | |
839 | || !group->meth->field_mul(group, t1, t1, t2, ctx) | |
840 | || !group->meth->field_sqr(group, t2, p->X, ctx) | |
841 | || !BN_GF2m_add(t2, p->Y, t2) | |
842 | || !group->meth->field_mul(group, t2, t2, t0, ctx) | |
843 | || !BN_GF2m_add(t1, t2, t1) | |
844 | || !group->meth->field_mul(group, t2, p->X, t0, ctx) | |
e0033efc | 845 | || !group->meth->field_inv(group, t2, t2, ctx) |
f45846f5 NT |
846 | || !group->meth->field_mul(group, t1, t1, t2, ctx) |
847 | || !group->meth->field_mul(group, r->X, r->Z, t2, ctx) | |
848 | || !BN_GF2m_add(t2, p->X, r->X) | |
849 | || !group->meth->field_mul(group, t2, t2, t1, ctx) | |
850 | || !BN_GF2m_add(r->Y, p->Y, t2) | |
851 | || !BN_one(r->Z)) | |
852 | goto err; | |
853 | ||
854 | r->Z_is_one = 1; | |
855 | ||
856 | /* GF(2^m) field elements should always have BIGNUM::neg = 0 */ | |
857 | BN_set_negative(r->X, 0); | |
858 | BN_set_negative(r->Y, 0); | |
859 | ||
860 | ret = 1; | |
861 | ||
862 | err: | |
863 | BN_CTX_end(ctx); | |
864 | return ret; | |
865 | } | |
866 | ||
01ad66f8 NT |
867 | static |
868 | int ec_GF2m_simple_points_mul(const EC_GROUP *group, EC_POINT *r, | |
869 | const BIGNUM *scalar, size_t num, | |
870 | const EC_POINT *points[], | |
871 | const BIGNUM *scalars[], | |
872 | BN_CTX *ctx) | |
873 | { | |
874 | int ret = 0; | |
875 | EC_POINT *t = NULL; | |
876 | ||
877 | /*- | |
878 | * We limit use of the ladder only to the following cases: | |
879 | * - r := scalar * G | |
880 | * Fixed point mul: scalar != NULL && num == 0; | |
881 | * - r := scalars[0] * points[0] | |
882 | * Variable point mul: scalar == NULL && num == 1; | |
883 | * - r := scalar * G + scalars[0] * points[0] | |
884 | * used, e.g., in ECDSA verification: scalar != NULL && num == 1 | |
885 | * | |
886 | * In any other case (num > 1) we use the default wNAF implementation. | |
887 | * | |
888 | * We also let the default implementation handle degenerate cases like group | |
889 | * order or cofactor set to 0. | |
890 | */ | |
891 | if (num > 1 || BN_is_zero(group->order) || BN_is_zero(group->cofactor)) | |
32ab57cb | 892 | return ossl_ec_wNAF_mul(group, r, scalar, num, points, scalars, ctx); |
01ad66f8 NT |
893 | |
894 | if (scalar != NULL && num == 0) | |
895 | /* Fixed point multiplication */ | |
32ab57cb | 896 | return ossl_ec_scalar_mul_ladder(group, r, scalar, NULL, ctx); |
01ad66f8 NT |
897 | |
898 | if (scalar == NULL && num == 1) | |
899 | /* Variable point multiplication */ | |
32ab57cb | 900 | return ossl_ec_scalar_mul_ladder(group, r, scalars[0], points[0], ctx); |
01ad66f8 NT |
901 | |
902 | /*- | |
903 | * Double point multiplication: | |
904 | * r := scalar * G + scalars[0] * points[0] | |
905 | */ | |
906 | ||
907 | if ((t = EC_POINT_new(group)) == NULL) { | |
9311d0c4 | 908 | ERR_raise(ERR_LIB_EC, ERR_R_MALLOC_FAILURE); |
01ad66f8 NT |
909 | return 0; |
910 | } | |
911 | ||
32ab57cb SL |
912 | if (!ossl_ec_scalar_mul_ladder(group, t, scalar, NULL, ctx) |
913 | || !ossl_ec_scalar_mul_ladder(group, r, scalars[0], points[0], ctx) | |
01ad66f8 NT |
914 | || !EC_POINT_add(group, r, t, r, ctx)) |
915 | goto err; | |
916 | ||
917 | ret = 1; | |
918 | ||
919 | err: | |
920 | EC_POINT_free(t); | |
921 | return ret; | |
922 | } | |
923 | ||
e0033efc BB |
924 | /*- |
925 | * Computes the multiplicative inverse of a in GF(2^m), storing the result in r. | |
926 | * If a is zero (or equivalent), you'll get a EC_R_CANNOT_INVERT error. | |
927 | * SCA hardening is with blinding: BN_GF2m_mod_inv does that. | |
928 | */ | |
929 | static int ec_GF2m_simple_field_inv(const EC_GROUP *group, BIGNUM *r, | |
930 | const BIGNUM *a, BN_CTX *ctx) | |
931 | { | |
932 | int ret; | |
933 | ||
934 | if (!(ret = BN_GF2m_mod_inv(r, a, group->field, ctx))) | |
9311d0c4 | 935 | ERR_raise(ERR_LIB_EC, EC_R_CANNOT_INVERT); |
e0033efc BB |
936 | return ret; |
937 | } | |
938 | ||
f45846f5 NT |
939 | const EC_METHOD *EC_GF2m_simple_method(void) |
940 | { | |
941 | static const EC_METHOD ret = { | |
942 | EC_FLAGS_DEFAULT_OCT, | |
943 | NID_X9_62_characteristic_two_field, | |
32ab57cb SL |
944 | ossl_ec_GF2m_simple_group_init, |
945 | ossl_ec_GF2m_simple_group_finish, | |
946 | ossl_ec_GF2m_simple_group_clear_finish, | |
947 | ossl_ec_GF2m_simple_group_copy, | |
948 | ossl_ec_GF2m_simple_group_set_curve, | |
949 | ossl_ec_GF2m_simple_group_get_curve, | |
950 | ossl_ec_GF2m_simple_group_get_degree, | |
951 | ossl_ec_group_simple_order_bits, | |
952 | ossl_ec_GF2m_simple_group_check_discriminant, | |
953 | ossl_ec_GF2m_simple_point_init, | |
954 | ossl_ec_GF2m_simple_point_finish, | |
955 | ossl_ec_GF2m_simple_point_clear_finish, | |
956 | ossl_ec_GF2m_simple_point_copy, | |
957 | ossl_ec_GF2m_simple_point_set_to_infinity, | |
958 | ossl_ec_GF2m_simple_point_set_affine_coordinates, | |
959 | ossl_ec_GF2m_simple_point_get_affine_coordinates, | |
f45846f5 NT |
960 | 0, /* point_set_compressed_coordinates */ |
961 | 0, /* point2oct */ | |
962 | 0, /* oct2point */ | |
32ab57cb SL |
963 | ossl_ec_GF2m_simple_add, |
964 | ossl_ec_GF2m_simple_dbl, | |
965 | ossl_ec_GF2m_simple_invert, | |
966 | ossl_ec_GF2m_simple_is_at_infinity, | |
967 | ossl_ec_GF2m_simple_is_on_curve, | |
968 | ossl_ec_GF2m_simple_cmp, | |
969 | ossl_ec_GF2m_simple_make_affine, | |
970 | ossl_ec_GF2m_simple_points_make_affine, | |
01ad66f8 | 971 | ec_GF2m_simple_points_mul, |
f45846f5 NT |
972 | 0, /* precompute_mult */ |
973 | 0, /* have_precompute_mult */ | |
32ab57cb SL |
974 | ossl_ec_GF2m_simple_field_mul, |
975 | ossl_ec_GF2m_simple_field_sqr, | |
976 | ossl_ec_GF2m_simple_field_div, | |
e0033efc | 977 | ec_GF2m_simple_field_inv, |
f45846f5 NT |
978 | 0, /* field_encode */ |
979 | 0, /* field_decode */ | |
980 | 0, /* field_set_to_one */ | |
32ab57cb SL |
981 | ossl_ec_key_simple_priv2oct, |
982 | ossl_ec_key_simple_oct2priv, | |
f45846f5 | 983 | 0, /* set private */ |
32ab57cb SL |
984 | ossl_ec_key_simple_generate_key, |
985 | ossl_ec_key_simple_check_key, | |
986 | ossl_ec_key_simple_generate_public_key, | |
f45846f5 NT |
987 | 0, /* keycopy */ |
988 | 0, /* keyfinish */ | |
32ab57cb SL |
989 | ossl_ecdh_simple_compute_key, |
990 | ossl_ecdsa_simple_sign_setup, | |
991 | ossl_ecdsa_simple_sign_sig, | |
992 | ossl_ecdsa_simple_verify_sig, | |
f45846f5 NT |
993 | 0, /* field_inverse_mod_ord */ |
994 | 0, /* blind_coordinates */ | |
995 | ec_GF2m_simple_ladder_pre, | |
996 | ec_GF2m_simple_ladder_step, | |
997 | ec_GF2m_simple_ladder_post | |
998 | }; | |
999 | ||
1000 | return &ret; | |
1001 | } | |
1002 | ||
b3310161 | 1003 | #endif |