ec2_smpl.c 19 KB

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  1. /* crypto/ec/ec2_smpl.c */
  2. /* ====================================================================
  3. * Copyright 2002 Sun Microsystems, Inc. ALL RIGHTS RESERVED.
  4. *
  5. * The Elliptic Curve Public-Key Crypto Library (ECC Code) included
  6. * herein is developed by SUN MICROSYSTEMS, INC., and is contributed
  7. * to the OpenSSL project.
  8. *
  9. * The ECC Code is licensed pursuant to the OpenSSL open source
  10. * license provided below.
  11. *
  12. * The software is originally written by Sheueling Chang Shantz and
  13. * Douglas Stebila of Sun Microsystems Laboratories.
  14. *
  15. */
  16. /* ====================================================================
  17. * Copyright (c) 1998-2005 The OpenSSL Project. All rights reserved.
  18. *
  19. * Redistribution and use in source and binary forms, with or without
  20. * modification, are permitted provided that the following conditions
  21. * are met:
  22. *
  23. * 1. Redistributions of source code must retain the above copyright
  24. * notice, this list of conditions and the following disclaimer.
  25. *
  26. * 2. Redistributions in binary form must reproduce the above copyright
  27. * notice, this list of conditions and the following disclaimer in
  28. * the documentation and/or other materials provided with the
  29. * distribution.
  30. *
  31. * 3. All advertising materials mentioning features or use of this
  32. * software must display the following acknowledgment:
  33. * "This product includes software developed by the OpenSSL Project
  34. * for use in the OpenSSL Toolkit. (http://www.openssl.org/)"
  35. *
  36. * 4. The names "OpenSSL Toolkit" and "OpenSSL Project" must not be used to
  37. * endorse or promote products derived from this software without
  38. * prior written permission. For written permission, please contact
  39. * openssl-core@openssl.org.
  40. *
  41. * 5. Products derived from this software may not be called "OpenSSL"
  42. * nor may "OpenSSL" appear in their names without prior written
  43. * permission of the OpenSSL Project.
  44. *
  45. * 6. Redistributions of any form whatsoever must retain the following
  46. * acknowledgment:
  47. * "This product includes software developed by the OpenSSL Project
  48. * for use in the OpenSSL Toolkit (http://www.openssl.org/)"
  49. *
  50. * THIS SOFTWARE IS PROVIDED BY THE OpenSSL PROJECT ``AS IS'' AND ANY
  51. * EXPRESSED OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
  52. * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR
  53. * PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE OpenSSL PROJECT OR
  54. * ITS CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL,
  55. * SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT
  56. * NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES;
  57. * LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
  58. * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT,
  59. * STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE)
  60. * ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED
  61. * OF THE POSSIBILITY OF SUCH DAMAGE.
  62. * ====================================================================
  63. *
  64. * This product includes cryptographic software written by Eric Young
  65. * (eay@cryptsoft.com). This product includes software written by Tim
  66. * Hudson (tjh@cryptsoft.com).
  67. *
  68. */
  69. #define OPENSSL_FIPSAPI
  70. #include <openssl/err.h>
  71. #include "ec_lcl.h"
  72. #ifndef OPENSSL_NO_EC2M
  73. const EC_METHOD *EC_GF2m_simple_method(void)
  74. {
  75. static const EC_METHOD ret = {
  76. EC_FLAGS_DEFAULT_OCT,
  77. NID_X9_62_characteristic_two_field,
  78. ec_GF2m_simple_group_init,
  79. ec_GF2m_simple_group_finish,
  80. ec_GF2m_simple_group_clear_finish,
  81. ec_GF2m_simple_group_copy,
  82. ec_GF2m_simple_group_set_curve,
  83. ec_GF2m_simple_group_get_curve,
  84. ec_GF2m_simple_group_get_degree,
  85. ec_GF2m_simple_group_check_discriminant,
  86. ec_GF2m_simple_point_init,
  87. ec_GF2m_simple_point_finish,
  88. ec_GF2m_simple_point_clear_finish,
  89. ec_GF2m_simple_point_copy,
  90. ec_GF2m_simple_point_set_to_infinity,
  91. 0 /* set_Jprojective_coordinates_GFp */,
  92. 0 /* get_Jprojective_coordinates_GFp */,
  93. ec_GF2m_simple_point_set_affine_coordinates,
  94. ec_GF2m_simple_point_get_affine_coordinates,
  95. 0,0,0,
  96. ec_GF2m_simple_add,
  97. ec_GF2m_simple_dbl,
  98. ec_GF2m_simple_invert,
  99. ec_GF2m_simple_is_at_infinity,
  100. ec_GF2m_simple_is_on_curve,
  101. ec_GF2m_simple_cmp,
  102. ec_GF2m_simple_make_affine,
  103. ec_GF2m_simple_points_make_affine,
  104. /* the following three method functions are defined in ec2_mult.c */
  105. ec_GF2m_simple_mul,
  106. ec_GF2m_precompute_mult,
  107. ec_GF2m_have_precompute_mult,
  108. ec_GF2m_simple_field_mul,
  109. ec_GF2m_simple_field_sqr,
  110. ec_GF2m_simple_field_div,
  111. 0 /* field_encode */,
  112. 0 /* field_decode */,
  113. 0 /* field_set_to_one */ };
  114. return &ret;
  115. }
  116. /* Initialize a GF(2^m)-based EC_GROUP structure.
  117. * Note that all other members are handled by EC_GROUP_new.
  118. */
  119. int ec_GF2m_simple_group_init(EC_GROUP *group)
  120. {
  121. BN_init(&group->field);
  122. BN_init(&group->a);
  123. BN_init(&group->b);
  124. return 1;
  125. }
  126. /* Free a GF(2^m)-based EC_GROUP structure.
  127. * Note that all other members are handled by EC_GROUP_free.
  128. */
  129. void ec_GF2m_simple_group_finish(EC_GROUP *group)
  130. {
  131. BN_free(&group->field);
  132. BN_free(&group->a);
  133. BN_free(&group->b);
  134. }
  135. /* Clear and free a GF(2^m)-based EC_GROUP structure.
  136. * Note that all other members are handled by EC_GROUP_clear_free.
  137. */
  138. void ec_GF2m_simple_group_clear_finish(EC_GROUP *group)
  139. {
  140. BN_clear_free(&group->field);
  141. BN_clear_free(&group->a);
  142. BN_clear_free(&group->b);
  143. group->poly[0] = 0;
  144. group->poly[1] = 0;
  145. group->poly[2] = 0;
  146. group->poly[3] = 0;
  147. group->poly[4] = 0;
  148. group->poly[5] = -1;
  149. }
  150. /* Copy a GF(2^m)-based EC_GROUP structure.
  151. * Note that all other members are handled by EC_GROUP_copy.
  152. */
  153. int ec_GF2m_simple_group_copy(EC_GROUP *dest, const EC_GROUP *src)
  154. {
  155. int i;
  156. if (!BN_copy(&dest->field, &src->field)) return 0;
  157. if (!BN_copy(&dest->a, &src->a)) return 0;
  158. if (!BN_copy(&dest->b, &src->b)) return 0;
  159. dest->poly[0] = src->poly[0];
  160. dest->poly[1] = src->poly[1];
  161. dest->poly[2] = src->poly[2];
  162. dest->poly[3] = src->poly[3];
  163. dest->poly[4] = src->poly[4];
  164. dest->poly[5] = src->poly[5];
  165. if (bn_wexpand(&dest->a, (int)(dest->poly[0] + BN_BITS2 - 1) / BN_BITS2) == NULL) return 0;
  166. if (bn_wexpand(&dest->b, (int)(dest->poly[0] + BN_BITS2 - 1) / BN_BITS2) == NULL) return 0;
  167. for (i = dest->a.top; i < dest->a.dmax; i++) dest->a.d[i] = 0;
  168. for (i = dest->b.top; i < dest->b.dmax; i++) dest->b.d[i] = 0;
  169. return 1;
  170. }
  171. /* Set the curve parameters of an EC_GROUP structure. */
  172. int ec_GF2m_simple_group_set_curve(EC_GROUP *group,
  173. const BIGNUM *p, const BIGNUM *a, const BIGNUM *b, BN_CTX *ctx)
  174. {
  175. int ret = 0, i;
  176. /* group->field */
  177. if (!BN_copy(&group->field, p)) goto err;
  178. i = BN_GF2m_poly2arr(&group->field, group->poly, 6) - 1;
  179. if ((i != 5) && (i != 3))
  180. {
  181. ECerr(EC_F_EC_GF2M_SIMPLE_GROUP_SET_CURVE, EC_R_UNSUPPORTED_FIELD);
  182. goto err;
  183. }
  184. /* group->a */
  185. if (!BN_GF2m_mod_arr(&group->a, a, group->poly)) goto err;
  186. if(bn_wexpand(&group->a, (int)(group->poly[0] + BN_BITS2 - 1) / BN_BITS2) == NULL) goto err;
  187. for (i = group->a.top; i < group->a.dmax; i++) group->a.d[i] = 0;
  188. /* group->b */
  189. if (!BN_GF2m_mod_arr(&group->b, b, group->poly)) goto err;
  190. if(bn_wexpand(&group->b, (int)(group->poly[0] + BN_BITS2 - 1) / BN_BITS2) == NULL) goto err;
  191. for (i = group->b.top; i < group->b.dmax; i++) group->b.d[i] = 0;
  192. ret = 1;
  193. err:
  194. return ret;
  195. }
  196. /* Get the curve parameters of an EC_GROUP structure.
  197. * If p, a, or b are NULL then there values will not be set but the method will return with success.
  198. */
  199. int ec_GF2m_simple_group_get_curve(const EC_GROUP *group, BIGNUM *p, BIGNUM *a, BIGNUM *b, BN_CTX *ctx)
  200. {
  201. int ret = 0;
  202. if (p != NULL)
  203. {
  204. if (!BN_copy(p, &group->field)) return 0;
  205. }
  206. if (a != NULL)
  207. {
  208. if (!BN_copy(a, &group->a)) goto err;
  209. }
  210. if (b != NULL)
  211. {
  212. if (!BN_copy(b, &group->b)) goto err;
  213. }
  214. ret = 1;
  215. err:
  216. return ret;
  217. }
  218. /* Gets the degree of the field. For a curve over GF(2^m) this is the value m. */
  219. int ec_GF2m_simple_group_get_degree(const EC_GROUP *group)
  220. {
  221. return BN_num_bits(&group->field)-1;
  222. }
  223. /* Checks the discriminant of the curve.
  224. * y^2 + x*y = x^3 + a*x^2 + b is an elliptic curve <=> b != 0 (mod p)
  225. */
  226. int ec_GF2m_simple_group_check_discriminant(const EC_GROUP *group, BN_CTX *ctx)
  227. {
  228. int ret = 0;
  229. BIGNUM *b;
  230. BN_CTX *new_ctx = NULL;
  231. if (ctx == NULL)
  232. {
  233. ctx = new_ctx = BN_CTX_new();
  234. if (ctx == NULL)
  235. {
  236. ECerr(EC_F_EC_GF2M_SIMPLE_GROUP_CHECK_DISCRIMINANT, ERR_R_MALLOC_FAILURE);
  237. goto err;
  238. }
  239. }
  240. BN_CTX_start(ctx);
  241. b = BN_CTX_get(ctx);
  242. if (b == NULL) goto err;
  243. if (!BN_GF2m_mod_arr(b, &group->b, group->poly)) goto err;
  244. /* check the discriminant:
  245. * y^2 + x*y = x^3 + a*x^2 + b is an elliptic curve <=> b != 0 (mod p)
  246. */
  247. if (BN_is_zero(b)) goto err;
  248. ret = 1;
  249. err:
  250. if (ctx != NULL)
  251. BN_CTX_end(ctx);
  252. if (new_ctx != NULL)
  253. BN_CTX_free(new_ctx);
  254. return ret;
  255. }
  256. /* Initializes an EC_POINT. */
  257. int ec_GF2m_simple_point_init(EC_POINT *point)
  258. {
  259. BN_init(&point->X);
  260. BN_init(&point->Y);
  261. BN_init(&point->Z);
  262. return 1;
  263. }
  264. /* Frees an EC_POINT. */
  265. void ec_GF2m_simple_point_finish(EC_POINT *point)
  266. {
  267. BN_free(&point->X);
  268. BN_free(&point->Y);
  269. BN_free(&point->Z);
  270. }
  271. /* Clears and frees an EC_POINT. */
  272. void ec_GF2m_simple_point_clear_finish(EC_POINT *point)
  273. {
  274. BN_clear_free(&point->X);
  275. BN_clear_free(&point->Y);
  276. BN_clear_free(&point->Z);
  277. point->Z_is_one = 0;
  278. }
  279. /* Copy the contents of one EC_POINT into another. Assumes dest is initialized. */
  280. int ec_GF2m_simple_point_copy(EC_POINT *dest, const EC_POINT *src)
  281. {
  282. if (!BN_copy(&dest->X, &src->X)) return 0;
  283. if (!BN_copy(&dest->Y, &src->Y)) return 0;
  284. if (!BN_copy(&dest->Z, &src->Z)) return 0;
  285. dest->Z_is_one = src->Z_is_one;
  286. return 1;
  287. }
  288. /* Set an EC_POINT to the point at infinity.
  289. * A point at infinity is represented by having Z=0.
  290. */
  291. int ec_GF2m_simple_point_set_to_infinity(const EC_GROUP *group, EC_POINT *point)
  292. {
  293. point->Z_is_one = 0;
  294. BN_zero(&point->Z);
  295. return 1;
  296. }
  297. /* Set the coordinates of an EC_POINT using affine coordinates.
  298. * Note that the simple implementation only uses affine coordinates.
  299. */
  300. int ec_GF2m_simple_point_set_affine_coordinates(const EC_GROUP *group, EC_POINT *point,
  301. const BIGNUM *x, const BIGNUM *y, BN_CTX *ctx)
  302. {
  303. int ret = 0;
  304. if (x == NULL || y == NULL)
  305. {
  306. ECerr(EC_F_EC_GF2M_SIMPLE_POINT_SET_AFFINE_COORDINATES, ERR_R_PASSED_NULL_PARAMETER);
  307. return 0;
  308. }
  309. if (!BN_copy(&point->X, x)) goto err;
  310. BN_set_negative(&point->X, 0);
  311. if (!BN_copy(&point->Y, y)) goto err;
  312. BN_set_negative(&point->Y, 0);
  313. if (!BN_copy(&point->Z, BN_value_one())) goto err;
  314. BN_set_negative(&point->Z, 0);
  315. point->Z_is_one = 1;
  316. ret = 1;
  317. err:
  318. return ret;
  319. }
  320. /* Gets the affine coordinates of an EC_POINT.
  321. * Note that the simple implementation only uses affine coordinates.
  322. */
  323. int ec_GF2m_simple_point_get_affine_coordinates(const EC_GROUP *group, const EC_POINT *point,
  324. BIGNUM *x, BIGNUM *y, BN_CTX *ctx)
  325. {
  326. int ret = 0;
  327. if (EC_POINT_is_at_infinity(group, point))
  328. {
  329. ECerr(EC_F_EC_GF2M_SIMPLE_POINT_GET_AFFINE_COORDINATES, EC_R_POINT_AT_INFINITY);
  330. return 0;
  331. }
  332. if (BN_cmp(&point->Z, BN_value_one()))
  333. {
  334. ECerr(EC_F_EC_GF2M_SIMPLE_POINT_GET_AFFINE_COORDINATES, ERR_R_SHOULD_NOT_HAVE_BEEN_CALLED);
  335. return 0;
  336. }
  337. if (x != NULL)
  338. {
  339. if (!BN_copy(x, &point->X)) goto err;
  340. BN_set_negative(x, 0);
  341. }
  342. if (y != NULL)
  343. {
  344. if (!BN_copy(y, &point->Y)) goto err;
  345. BN_set_negative(y, 0);
  346. }
  347. ret = 1;
  348. err:
  349. return ret;
  350. }
  351. /* Computes a + b and stores the result in r. r could be a or b, a could be b.
  352. * Uses algorithm A.10.2 of IEEE P1363.
  353. */
  354. int ec_GF2m_simple_add(const EC_GROUP *group, EC_POINT *r, const EC_POINT *a, const EC_POINT *b, BN_CTX *ctx)
  355. {
  356. BN_CTX *new_ctx = NULL;
  357. BIGNUM *x0, *y0, *x1, *y1, *x2, *y2, *s, *t;
  358. int ret = 0;
  359. if (EC_POINT_is_at_infinity(group, a))
  360. {
  361. if (!EC_POINT_copy(r, b)) return 0;
  362. return 1;
  363. }
  364. if (EC_POINT_is_at_infinity(group, b))
  365. {
  366. if (!EC_POINT_copy(r, a)) return 0;
  367. return 1;
  368. }
  369. if (ctx == NULL)
  370. {
  371. ctx = new_ctx = BN_CTX_new();
  372. if (ctx == NULL)
  373. return 0;
  374. }
  375. BN_CTX_start(ctx);
  376. x0 = BN_CTX_get(ctx);
  377. y0 = BN_CTX_get(ctx);
  378. x1 = BN_CTX_get(ctx);
  379. y1 = BN_CTX_get(ctx);
  380. x2 = BN_CTX_get(ctx);
  381. y2 = BN_CTX_get(ctx);
  382. s = BN_CTX_get(ctx);
  383. t = BN_CTX_get(ctx);
  384. if (t == NULL) goto err;
  385. if (a->Z_is_one)
  386. {
  387. if (!BN_copy(x0, &a->X)) goto err;
  388. if (!BN_copy(y0, &a->Y)) goto err;
  389. }
  390. else
  391. {
  392. if (!EC_POINT_get_affine_coordinates_GF2m(group, a, x0, y0, ctx)) goto err;
  393. }
  394. if (b->Z_is_one)
  395. {
  396. if (!BN_copy(x1, &b->X)) goto err;
  397. if (!BN_copy(y1, &b->Y)) goto err;
  398. }
  399. else
  400. {
  401. if (!EC_POINT_get_affine_coordinates_GF2m(group, b, x1, y1, ctx)) goto err;
  402. }
  403. if (BN_GF2m_cmp(x0, x1))
  404. {
  405. if (!BN_GF2m_add(t, x0, x1)) goto err;
  406. if (!BN_GF2m_add(s, y0, y1)) goto err;
  407. if (!group->meth->field_div(group, s, s, t, ctx)) goto err;
  408. if (!group->meth->field_sqr(group, x2, s, ctx)) goto err;
  409. if (!BN_GF2m_add(x2, x2, &group->a)) goto err;
  410. if (!BN_GF2m_add(x2, x2, s)) goto err;
  411. if (!BN_GF2m_add(x2, x2, t)) goto err;
  412. }
  413. else
  414. {
  415. if (BN_GF2m_cmp(y0, y1) || BN_is_zero(x1))
  416. {
  417. if (!EC_POINT_set_to_infinity(group, r)) goto err;
  418. ret = 1;
  419. goto err;
  420. }
  421. if (!group->meth->field_div(group, s, y1, x1, ctx)) goto err;
  422. if (!BN_GF2m_add(s, s, x1)) goto err;
  423. if (!group->meth->field_sqr(group, x2, s, ctx)) goto err;
  424. if (!BN_GF2m_add(x2, x2, s)) goto err;
  425. if (!BN_GF2m_add(x2, x2, &group->a)) goto err;
  426. }
  427. if (!BN_GF2m_add(y2, x1, x2)) goto err;
  428. if (!group->meth->field_mul(group, y2, y2, s, ctx)) goto err;
  429. if (!BN_GF2m_add(y2, y2, x2)) goto err;
  430. if (!BN_GF2m_add(y2, y2, y1)) goto err;
  431. if (!EC_POINT_set_affine_coordinates_GF2m(group, r, x2, y2, ctx)) goto err;
  432. ret = 1;
  433. err:
  434. BN_CTX_end(ctx);
  435. if (new_ctx != NULL)
  436. BN_CTX_free(new_ctx);
  437. return ret;
  438. }
  439. /* Computes 2 * a and stores the result in r. r could be a.
  440. * Uses algorithm A.10.2 of IEEE P1363.
  441. */
  442. int ec_GF2m_simple_dbl(const EC_GROUP *group, EC_POINT *r, const EC_POINT *a, BN_CTX *ctx)
  443. {
  444. return ec_GF2m_simple_add(group, r, a, a, ctx);
  445. }
  446. int ec_GF2m_simple_invert(const EC_GROUP *group, EC_POINT *point, BN_CTX *ctx)
  447. {
  448. if (EC_POINT_is_at_infinity(group, point) || BN_is_zero(&point->Y))
  449. /* point is its own inverse */
  450. return 1;
  451. if (!EC_POINT_make_affine(group, point, ctx)) return 0;
  452. return BN_GF2m_add(&point->Y, &point->X, &point->Y);
  453. }
  454. /* Indicates whether the given point is the point at infinity. */
  455. int ec_GF2m_simple_is_at_infinity(const EC_GROUP *group, const EC_POINT *point)
  456. {
  457. return BN_is_zero(&point->Z);
  458. }
  459. /* Determines whether the given EC_POINT is an actual point on the curve defined
  460. * in the EC_GROUP. A point is valid if it satisfies the Weierstrass equation:
  461. * y^2 + x*y = x^3 + a*x^2 + b.
  462. */
  463. int ec_GF2m_simple_is_on_curve(const EC_GROUP *group, const EC_POINT *point, BN_CTX *ctx)
  464. {
  465. int ret = -1;
  466. BN_CTX *new_ctx = NULL;
  467. BIGNUM *lh, *y2;
  468. int (*field_mul)(const EC_GROUP *, BIGNUM *, const BIGNUM *, const BIGNUM *, BN_CTX *);
  469. int (*field_sqr)(const EC_GROUP *, BIGNUM *, const BIGNUM *, BN_CTX *);
  470. if (EC_POINT_is_at_infinity(group, point))
  471. return 1;
  472. field_mul = group->meth->field_mul;
  473. field_sqr = group->meth->field_sqr;
  474. /* only support affine coordinates */
  475. if (!point->Z_is_one) goto err;
  476. if (ctx == NULL)
  477. {
  478. ctx = new_ctx = BN_CTX_new();
  479. if (ctx == NULL)
  480. return -1;
  481. }
  482. BN_CTX_start(ctx);
  483. y2 = BN_CTX_get(ctx);
  484. lh = BN_CTX_get(ctx);
  485. if (lh == NULL) goto err;
  486. /* We have a curve defined by a Weierstrass equation
  487. * y^2 + x*y = x^3 + a*x^2 + b.
  488. * <=> x^3 + a*x^2 + x*y + b + y^2 = 0
  489. * <=> ((x + a) * x + y ) * x + b + y^2 = 0
  490. */
  491. if (!BN_GF2m_add(lh, &point->X, &group->a)) goto err;
  492. if (!field_mul(group, lh, lh, &point->X, ctx)) goto err;
  493. if (!BN_GF2m_add(lh, lh, &point->Y)) goto err;
  494. if (!field_mul(group, lh, lh, &point->X, ctx)) goto err;
  495. if (!BN_GF2m_add(lh, lh, &group->b)) goto err;
  496. if (!field_sqr(group, y2, &point->Y, ctx)) goto err;
  497. if (!BN_GF2m_add(lh, lh, y2)) goto err;
  498. ret = BN_is_zero(lh);
  499. err:
  500. if (ctx) BN_CTX_end(ctx);
  501. if (new_ctx) BN_CTX_free(new_ctx);
  502. return ret;
  503. }
  504. /* Indicates whether two points are equal.
  505. * Return values:
  506. * -1 error
  507. * 0 equal (in affine coordinates)
  508. * 1 not equal
  509. */
  510. int ec_GF2m_simple_cmp(const EC_GROUP *group, const EC_POINT *a, const EC_POINT *b, BN_CTX *ctx)
  511. {
  512. BIGNUM *aX, *aY, *bX, *bY;
  513. BN_CTX *new_ctx = NULL;
  514. int ret = -1;
  515. if (EC_POINT_is_at_infinity(group, a))
  516. {
  517. return EC_POINT_is_at_infinity(group, b) ? 0 : 1;
  518. }
  519. if (EC_POINT_is_at_infinity(group, b))
  520. return 1;
  521. if (a->Z_is_one && b->Z_is_one)
  522. {
  523. return ((BN_cmp(&a->X, &b->X) == 0) && BN_cmp(&a->Y, &b->Y) == 0) ? 0 : 1;
  524. }
  525. if (ctx == NULL)
  526. {
  527. ctx = new_ctx = BN_CTX_new();
  528. if (ctx == NULL)
  529. return -1;
  530. }
  531. BN_CTX_start(ctx);
  532. aX = BN_CTX_get(ctx);
  533. aY = BN_CTX_get(ctx);
  534. bX = BN_CTX_get(ctx);
  535. bY = BN_CTX_get(ctx);
  536. if (bY == NULL) goto err;
  537. if (!EC_POINT_get_affine_coordinates_GF2m(group, a, aX, aY, ctx)) goto err;
  538. if (!EC_POINT_get_affine_coordinates_GF2m(group, b, bX, bY, ctx)) goto err;
  539. ret = ((BN_cmp(aX, bX) == 0) && BN_cmp(aY, bY) == 0) ? 0 : 1;
  540. err:
  541. if (ctx) BN_CTX_end(ctx);
  542. if (new_ctx) BN_CTX_free(new_ctx);
  543. return ret;
  544. }
  545. /* Forces the given EC_POINT to internally use affine coordinates. */
  546. int ec_GF2m_simple_make_affine(const EC_GROUP *group, EC_POINT *point, BN_CTX *ctx)
  547. {
  548. BN_CTX *new_ctx = NULL;
  549. BIGNUM *x, *y;
  550. int ret = 0;
  551. if (point->Z_is_one || EC_POINT_is_at_infinity(group, point))
  552. return 1;
  553. if (ctx == NULL)
  554. {
  555. ctx = new_ctx = BN_CTX_new();
  556. if (ctx == NULL)
  557. return 0;
  558. }
  559. BN_CTX_start(ctx);
  560. x = BN_CTX_get(ctx);
  561. y = BN_CTX_get(ctx);
  562. if (y == NULL) goto err;
  563. if (!EC_POINT_get_affine_coordinates_GF2m(group, point, x, y, ctx)) goto err;
  564. if (!BN_copy(&point->X, x)) goto err;
  565. if (!BN_copy(&point->Y, y)) goto err;
  566. if (!BN_one(&point->Z)) goto err;
  567. ret = 1;
  568. err:
  569. if (ctx) BN_CTX_end(ctx);
  570. if (new_ctx) BN_CTX_free(new_ctx);
  571. return ret;
  572. }
  573. /* Forces each of the EC_POINTs in the given array to use affine coordinates. */
  574. int ec_GF2m_simple_points_make_affine(const EC_GROUP *group, size_t num, EC_POINT *points[], BN_CTX *ctx)
  575. {
  576. size_t i;
  577. for (i = 0; i < num; i++)
  578. {
  579. if (!group->meth->make_affine(group, points[i], ctx)) return 0;
  580. }
  581. return 1;
  582. }
  583. /* Wrapper to simple binary polynomial field multiplication implementation. */
  584. int ec_GF2m_simple_field_mul(const EC_GROUP *group, BIGNUM *r, const BIGNUM *a, const BIGNUM *b, BN_CTX *ctx)
  585. {
  586. return BN_GF2m_mod_mul_arr(r, a, b, group->poly, ctx);
  587. }
  588. /* Wrapper to simple binary polynomial field squaring implementation. */
  589. int ec_GF2m_simple_field_sqr(const EC_GROUP *group, BIGNUM *r, const BIGNUM *a, BN_CTX *ctx)
  590. {
  591. return BN_GF2m_mod_sqr_arr(r, a, group->poly, ctx);
  592. }
  593. /* Wrapper to simple binary polynomial field division implementation. */
  594. int ec_GF2m_simple_field_div(const EC_GROUP *group, BIGNUM *r, const BIGNUM *a, const BIGNUM *b, BN_CTX *ctx)
  595. {
  596. return BN_GF2m_mod_div(r, a, b, &group->field, ctx);
  597. }
  598. #endif