ec2_mult.c 12 KB

123456789101112131415161718192021222324252627282930313233343536373839404142434445464748495051525354555657585960616263646566676869707172737475767778798081828384858687888990919293949596979899100101102103104105106107108109110111112113114115116117118119120121122123124125126127128129130131132133134135136137138139140141142143144145146147148149150151152153154155156157158159160161162163164165166167168169170171172173174175176177178179180181182183184185186187188189190191192193194195196197198199200201202203204205206207208209210211212213214215216217218219220221222223224225226227228229230231232233234235236237238239240241242243244245246247248249250251252253254255256257258259260261262263264265266267268269270271272273274275276277278279280281282283284285286287288289290291292293294295296297298299300301302303304305306307308309310311312313314315316317318319320321322323324325326327328329330331332333334335336337338339340341342343344345346347348349350351352353354355356357358359360361362363364365366367368369370371372373374375376377378379380
  1. /* crypto/ec/ec2_mult.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) 1998-2003 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. #include <openssl/err.h>
  70. #include "ec_lcl.h"
  71. /* Compute the x-coordinate x/z for the point 2*(x/z) in Montgomery projective
  72. * coordinates.
  73. * Uses algorithm Mdouble in appendix of
  74. * Lopez, J. and Dahab, R. "Fast multiplication on elliptic curves over
  75. * GF(2^m) without precomputation" (CHES '99, LNCS 1717).
  76. * modified to not require precomputation of c=b^{2^{m-1}}.
  77. */
  78. static int gf2m_Mdouble(const EC_GROUP *group, BIGNUM *x, BIGNUM *z, BN_CTX *ctx)
  79. {
  80. BIGNUM *t1;
  81. int ret = 0;
  82. /* Since Mdouble is static we can guarantee that ctx != NULL. */
  83. BN_CTX_start(ctx);
  84. t1 = BN_CTX_get(ctx);
  85. if (t1 == NULL) goto err;
  86. if (!group->meth->field_sqr(group, x, x, ctx)) goto err;
  87. if (!group->meth->field_sqr(group, t1, z, ctx)) goto err;
  88. if (!group->meth->field_mul(group, z, x, t1, ctx)) goto err;
  89. if (!group->meth->field_sqr(group, x, x, ctx)) goto err;
  90. if (!group->meth->field_sqr(group, t1, t1, ctx)) goto err;
  91. if (!group->meth->field_mul(group, t1, &group->b, t1, ctx)) goto err;
  92. if (!BN_GF2m_add(x, x, t1)) goto err;
  93. ret = 1;
  94. err:
  95. BN_CTX_end(ctx);
  96. return ret;
  97. }
  98. /* Compute the x-coordinate x1/z1 for the point (x1/z1)+(x2/x2) in Montgomery
  99. * projective coordinates.
  100. * Uses algorithm Madd in appendix of
  101. * Lopez, J. and Dahab, R. "Fast multiplication on elliptic curves over
  102. * GF(2^m) without precomputation" (CHES '99, LNCS 1717).
  103. */
  104. static int gf2m_Madd(const EC_GROUP *group, const BIGNUM *x, BIGNUM *x1, BIGNUM *z1,
  105. const BIGNUM *x2, const BIGNUM *z2, BN_CTX *ctx)
  106. {
  107. BIGNUM *t1, *t2;
  108. int ret = 0;
  109. /* Since Madd is static we can guarantee that ctx != NULL. */
  110. BN_CTX_start(ctx);
  111. t1 = BN_CTX_get(ctx);
  112. t2 = BN_CTX_get(ctx);
  113. if (t2 == NULL) goto err;
  114. if (!BN_copy(t1, x)) goto err;
  115. if (!group->meth->field_mul(group, x1, x1, z2, ctx)) goto err;
  116. if (!group->meth->field_mul(group, z1, z1, x2, ctx)) goto err;
  117. if (!group->meth->field_mul(group, t2, x1, z1, ctx)) goto err;
  118. if (!BN_GF2m_add(z1, z1, x1)) goto err;
  119. if (!group->meth->field_sqr(group, z1, z1, ctx)) goto err;
  120. if (!group->meth->field_mul(group, x1, z1, t1, ctx)) goto err;
  121. if (!BN_GF2m_add(x1, x1, t2)) goto err;
  122. ret = 1;
  123. err:
  124. BN_CTX_end(ctx);
  125. return ret;
  126. }
  127. /* Compute the x, y affine coordinates from the point (x1, z1) (x2, z2)
  128. * using Montgomery point multiplication algorithm Mxy() in appendix of
  129. * Lopez, J. and Dahab, R. "Fast multiplication on elliptic curves over
  130. * GF(2^m) without precomputation" (CHES '99, LNCS 1717).
  131. * Returns:
  132. * 0 on error
  133. * 1 if return value should be the point at infinity
  134. * 2 otherwise
  135. */
  136. static int gf2m_Mxy(const EC_GROUP *group, const BIGNUM *x, const BIGNUM *y, BIGNUM *x1,
  137. BIGNUM *z1, BIGNUM *x2, BIGNUM *z2, BN_CTX *ctx)
  138. {
  139. BIGNUM *t3, *t4, *t5;
  140. int ret = 0;
  141. if (BN_is_zero(z1))
  142. {
  143. BN_zero(x2);
  144. BN_zero(z2);
  145. return 1;
  146. }
  147. if (BN_is_zero(z2))
  148. {
  149. if (!BN_copy(x2, x)) return 0;
  150. if (!BN_GF2m_add(z2, x, y)) return 0;
  151. return 2;
  152. }
  153. /* Since Mxy is static we can guarantee that ctx != NULL. */
  154. BN_CTX_start(ctx);
  155. t3 = BN_CTX_get(ctx);
  156. t4 = BN_CTX_get(ctx);
  157. t5 = BN_CTX_get(ctx);
  158. if (t5 == NULL) goto err;
  159. if (!BN_one(t5)) goto err;
  160. if (!group->meth->field_mul(group, t3, z1, z2, ctx)) goto err;
  161. if (!group->meth->field_mul(group, z1, z1, x, ctx)) goto err;
  162. if (!BN_GF2m_add(z1, z1, x1)) goto err;
  163. if (!group->meth->field_mul(group, z2, z2, x, ctx)) goto err;
  164. if (!group->meth->field_mul(group, x1, z2, x1, ctx)) goto err;
  165. if (!BN_GF2m_add(z2, z2, x2)) goto err;
  166. if (!group->meth->field_mul(group, z2, z2, z1, ctx)) goto err;
  167. if (!group->meth->field_sqr(group, t4, x, ctx)) goto err;
  168. if (!BN_GF2m_add(t4, t4, y)) goto err;
  169. if (!group->meth->field_mul(group, t4, t4, t3, ctx)) goto err;
  170. if (!BN_GF2m_add(t4, t4, z2)) goto err;
  171. if (!group->meth->field_mul(group, t3, t3, x, ctx)) goto err;
  172. if (!group->meth->field_div(group, t3, t5, t3, ctx)) goto err;
  173. if (!group->meth->field_mul(group, t4, t3, t4, ctx)) goto err;
  174. if (!group->meth->field_mul(group, x2, x1, t3, ctx)) goto err;
  175. if (!BN_GF2m_add(z2, x2, x)) goto err;
  176. if (!group->meth->field_mul(group, z2, z2, t4, ctx)) goto err;
  177. if (!BN_GF2m_add(z2, z2, y)) goto err;
  178. ret = 2;
  179. err:
  180. BN_CTX_end(ctx);
  181. return ret;
  182. }
  183. /* Computes scalar*point and stores the result in r.
  184. * point can not equal r.
  185. * Uses algorithm 2P of
  186. * Lopez, J. and Dahab, R. "Fast multiplication on elliptic curves over
  187. * GF(2^m) without precomputation" (CHES '99, LNCS 1717).
  188. */
  189. static int ec_GF2m_montgomery_point_multiply(const EC_GROUP *group, EC_POINT *r, const BIGNUM *scalar,
  190. const EC_POINT *point, BN_CTX *ctx)
  191. {
  192. BIGNUM *x1, *x2, *z1, *z2;
  193. int ret = 0, i, j;
  194. BN_ULONG mask;
  195. if (r == point)
  196. {
  197. ECerr(EC_F_EC_GF2M_MONTGOMERY_POINT_MULTIPLY, EC_R_INVALID_ARGUMENT);
  198. return 0;
  199. }
  200. /* if result should be point at infinity */
  201. if ((scalar == NULL) || BN_is_zero(scalar) || (point == NULL) ||
  202. EC_POINT_is_at_infinity(group, point))
  203. {
  204. return EC_POINT_set_to_infinity(group, r);
  205. }
  206. /* only support affine coordinates */
  207. if (!point->Z_is_one) return 0;
  208. /* Since point_multiply is static we can guarantee that ctx != NULL. */
  209. BN_CTX_start(ctx);
  210. x1 = BN_CTX_get(ctx);
  211. z1 = BN_CTX_get(ctx);
  212. if (z1 == NULL) goto err;
  213. x2 = &r->X;
  214. z2 = &r->Y;
  215. if (!BN_GF2m_mod_arr(x1, &point->X, group->poly)) goto err; /* x1 = x */
  216. if (!BN_one(z1)) goto err; /* z1 = 1 */
  217. if (!group->meth->field_sqr(group, z2, x1, ctx)) goto err; /* z2 = x1^2 = x^2 */
  218. if (!group->meth->field_sqr(group, x2, z2, ctx)) goto err;
  219. if (!BN_GF2m_add(x2, x2, &group->b)) goto err; /* x2 = x^4 + b */
  220. /* find top most bit and go one past it */
  221. i = scalar->top - 1; j = BN_BITS2 - 1;
  222. mask = BN_TBIT;
  223. while (!(scalar->d[i] & mask)) { mask >>= 1; j--; }
  224. mask >>= 1; j--;
  225. /* if top most bit was at word break, go to next word */
  226. if (!mask)
  227. {
  228. i--; j = BN_BITS2 - 1;
  229. mask = BN_TBIT;
  230. }
  231. for (; i >= 0; i--)
  232. {
  233. for (; j >= 0; j--)
  234. {
  235. if (scalar->d[i] & mask)
  236. {
  237. if (!gf2m_Madd(group, &point->X, x1, z1, x2, z2, ctx)) goto err;
  238. if (!gf2m_Mdouble(group, x2, z2, ctx)) goto err;
  239. }
  240. else
  241. {
  242. if (!gf2m_Madd(group, &point->X, x2, z2, x1, z1, ctx)) goto err;
  243. if (!gf2m_Mdouble(group, x1, z1, ctx)) goto err;
  244. }
  245. mask >>= 1;
  246. }
  247. j = BN_BITS2 - 1;
  248. mask = BN_TBIT;
  249. }
  250. /* convert out of "projective" coordinates */
  251. i = gf2m_Mxy(group, &point->X, &point->Y, x1, z1, x2, z2, ctx);
  252. if (i == 0) goto err;
  253. else if (i == 1)
  254. {
  255. if (!EC_POINT_set_to_infinity(group, r)) goto err;
  256. }
  257. else
  258. {
  259. if (!BN_one(&r->Z)) goto err;
  260. r->Z_is_one = 1;
  261. }
  262. /* GF(2^m) field elements should always have BIGNUM::neg = 0 */
  263. BN_set_negative(&r->X, 0);
  264. BN_set_negative(&r->Y, 0);
  265. ret = 1;
  266. err:
  267. BN_CTX_end(ctx);
  268. return ret;
  269. }
  270. /* Computes the sum
  271. * scalar*group->generator + scalars[0]*points[0] + ... + scalars[num-1]*points[num-1]
  272. * gracefully ignoring NULL scalar values.
  273. */
  274. int ec_GF2m_simple_mul(const EC_GROUP *group, EC_POINT *r, const BIGNUM *scalar,
  275. size_t num, const EC_POINT *points[], const BIGNUM *scalars[], BN_CTX *ctx)
  276. {
  277. BN_CTX *new_ctx = NULL;
  278. int ret = 0;
  279. size_t i;
  280. EC_POINT *p=NULL;
  281. if (ctx == NULL)
  282. {
  283. ctx = new_ctx = BN_CTX_new();
  284. if (ctx == NULL)
  285. return 0;
  286. }
  287. /* This implementation is more efficient than the wNAF implementation for 2
  288. * or fewer points. Use the ec_wNAF_mul implementation for 3 or more points,
  289. * or if we can perform a fast multiplication based on precomputation.
  290. */
  291. if ((scalar && (num > 1)) || (num > 2) || (num == 0 && EC_GROUP_have_precompute_mult(group)))
  292. {
  293. ret = ec_wNAF_mul(group, r, scalar, num, points, scalars, ctx);
  294. goto err;
  295. }
  296. if ((p = EC_POINT_new(group)) == NULL) goto err;
  297. if (!EC_POINT_set_to_infinity(group, r)) goto err;
  298. if (scalar)
  299. {
  300. if (!ec_GF2m_montgomery_point_multiply(group, p, scalar, group->generator, ctx)) goto err;
  301. if (BN_is_negative(scalar))
  302. if (!group->meth->invert(group, p, ctx)) goto err;
  303. if (!group->meth->add(group, r, r, p, ctx)) goto err;
  304. }
  305. for (i = 0; i < num; i++)
  306. {
  307. if (!ec_GF2m_montgomery_point_multiply(group, p, scalars[i], points[i], ctx)) goto err;
  308. if (BN_is_negative(scalars[i]))
  309. if (!group->meth->invert(group, p, ctx)) goto err;
  310. if (!group->meth->add(group, r, r, p, ctx)) goto err;
  311. }
  312. ret = 1;
  313. err:
  314. if (p) EC_POINT_free(p);
  315. if (new_ctx != NULL)
  316. BN_CTX_free(new_ctx);
  317. return ret;
  318. }
  319. /* Precomputation for point multiplication: fall back to wNAF methods
  320. * because ec_GF2m_simple_mul() uses ec_wNAF_mul() if appropriate */
  321. int ec_GF2m_precompute_mult(EC_GROUP *group, BN_CTX *ctx)
  322. {
  323. return ec_wNAF_precompute_mult(group, ctx);
  324. }
  325. int ec_GF2m_have_precompute_mult(const EC_GROUP *group)
  326. {
  327. return ec_wNAF_have_precompute_mult(group);
  328. }