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ec_lcl.h 18 KB

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  1. /* crypto/ec/ec_lcl.h */
  2. /*
  3. * Originally written by Bodo Moeller for the OpenSSL project.
  4. */
  5. /* ====================================================================
  6. * Copyright (c) 1998-2003 The OpenSSL Project. All rights reserved.
  7. *
  8. * Redistribution and use in source and binary forms, with or without
  9. * modification, are permitted provided that the following conditions
  10. * are met:
  11. *
  12. * 1. Redistributions of source code must retain the above copyright
  13. * notice, this list of conditions and the following disclaimer.
  14. *
  15. * 2. Redistributions in binary form must reproduce the above copyright
  16. * notice, this list of conditions and the following disclaimer in
  17. * the documentation and/or other materials provided with the
  18. * distribution.
  19. *
  20. * 3. All advertising materials mentioning features or use of this
  21. * software must display the following acknowledgment:
  22. * "This product includes software developed by the OpenSSL Project
  23. * for use in the OpenSSL Toolkit. (http://www.openssl.org/)"
  24. *
  25. * 4. The names "OpenSSL Toolkit" and "OpenSSL Project" must not be used to
  26. * endorse or promote products derived from this software without
  27. * prior written permission. For written permission, please contact
  28. * openssl-core@openssl.org.
  29. *
  30. * 5. Products derived from this software may not be called "OpenSSL"
  31. * nor may "OpenSSL" appear in their names without prior written
  32. * permission of the OpenSSL Project.
  33. *
  34. * 6. Redistributions of any form whatsoever must retain the following
  35. * acknowledgment:
  36. * "This product includes software developed by the OpenSSL Project
  37. * for use in the OpenSSL Toolkit (http://www.openssl.org/)"
  38. *
  39. * THIS SOFTWARE IS PROVIDED BY THE OpenSSL PROJECT ``AS IS'' AND ANY
  40. * EXPRESSED OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
  41. * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR
  42. * PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE OpenSSL PROJECT OR
  43. * ITS CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL,
  44. * SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT
  45. * NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES;
  46. * LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
  47. * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT,
  48. * STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE)
  49. * ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED
  50. * OF THE POSSIBILITY OF SUCH DAMAGE.
  51. * ====================================================================
  52. *
  53. * This product includes cryptographic software written by Eric Young
  54. * (eay@cryptsoft.com). This product includes software written by Tim
  55. * Hudson (tjh@cryptsoft.com).
  56. *
  57. */
  58. /* ====================================================================
  59. * Copyright 2002 Sun Microsystems, Inc. ALL RIGHTS RESERVED.
  60. *
  61. * Portions of the attached software ("Contribution") are developed by
  62. * SUN MICROSYSTEMS, INC., and are contributed to the OpenSSL project.
  63. *
  64. * The Contribution is licensed pursuant to the OpenSSL open source
  65. * license provided above.
  66. *
  67. * The elliptic curve binary polynomial software is originally written by
  68. * Sheueling Chang Shantz and Douglas Stebila of Sun Microsystems Laboratories.
  69. *
  70. */
  71. #include <stdlib.h>
  72. #include <openssl/obj_mac.h>
  73. #include <openssl/ec.h>
  74. #include <openssl/bn.h>
  75. #if defined(__SUNPRO_C)
  76. # if __SUNPRO_C >= 0x520
  77. # pragma error_messages (off,E_ARRAY_OF_INCOMPLETE_NONAME,E_ARRAY_OF_INCOMPLETE)
  78. # endif
  79. #endif
  80. /* Structure details are not part of the exported interface,
  81. * so all this may change in future versions. */
  82. struct ec_method_st {
  83. /* used by EC_METHOD_get_field_type: */
  84. int field_type; /* a NID */
  85. /* used by EC_GROUP_new, EC_GROUP_free, EC_GROUP_clear_free, EC_GROUP_copy: */
  86. int (*group_init)(EC_GROUP *);
  87. void (*group_finish)(EC_GROUP *);
  88. void (*group_clear_finish)(EC_GROUP *);
  89. int (*group_copy)(EC_GROUP *, const EC_GROUP *);
  90. /* used by EC_GROUP_set_curve_GFp, EC_GROUP_get_curve_GFp, */
  91. /* EC_GROUP_set_curve_GF2m, and EC_GROUP_get_curve_GF2m: */
  92. int (*group_set_curve)(EC_GROUP *, const BIGNUM *p, const BIGNUM *a, const BIGNUM *b, BN_CTX *);
  93. int (*group_get_curve)(const EC_GROUP *, BIGNUM *p, BIGNUM *a, BIGNUM *b, BN_CTX *);
  94. /* used by EC_GROUP_get_degree: */
  95. int (*group_get_degree)(const EC_GROUP *);
  96. /* used by EC_GROUP_check: */
  97. int (*group_check_discriminant)(const EC_GROUP *, BN_CTX *);
  98. /* used by EC_POINT_new, EC_POINT_free, EC_POINT_clear_free, EC_POINT_copy: */
  99. int (*point_init)(EC_POINT *);
  100. void (*point_finish)(EC_POINT *);
  101. void (*point_clear_finish)(EC_POINT *);
  102. int (*point_copy)(EC_POINT *, const EC_POINT *);
  103. /* used by EC_POINT_set_to_infinity,
  104. * EC_POINT_set_Jprojective_coordinates_GFp,
  105. * EC_POINT_get_Jprojective_coordinates_GFp,
  106. * EC_POINT_set_affine_coordinates_GFp, ..._GF2m,
  107. * EC_POINT_get_affine_coordinates_GFp, ..._GF2m,
  108. * EC_POINT_set_compressed_coordinates_GFp, ..._GF2m:
  109. */
  110. int (*point_set_to_infinity)(const EC_GROUP *, EC_POINT *);
  111. int (*point_set_Jprojective_coordinates_GFp)(const EC_GROUP *, EC_POINT *,
  112. const BIGNUM *x, const BIGNUM *y, const BIGNUM *z, BN_CTX *);
  113. int (*point_get_Jprojective_coordinates_GFp)(const EC_GROUP *, const EC_POINT *,
  114. BIGNUM *x, BIGNUM *y, BIGNUM *z, BN_CTX *);
  115. int (*point_set_affine_coordinates)(const EC_GROUP *, EC_POINT *,
  116. const BIGNUM *x, const BIGNUM *y, BN_CTX *);
  117. int (*point_get_affine_coordinates)(const EC_GROUP *, const EC_POINT *,
  118. BIGNUM *x, BIGNUM *y, BN_CTX *);
  119. int (*point_set_compressed_coordinates)(const EC_GROUP *, EC_POINT *,
  120. const BIGNUM *x, int y_bit, BN_CTX *);
  121. /* used by EC_POINT_point2oct, EC_POINT_oct2point: */
  122. size_t (*point2oct)(const EC_GROUP *, const EC_POINT *, point_conversion_form_t form,
  123. unsigned char *buf, size_t len, BN_CTX *);
  124. int (*oct2point)(const EC_GROUP *, EC_POINT *,
  125. const unsigned char *buf, size_t len, BN_CTX *);
  126. /* used by EC_POINT_add, EC_POINT_dbl, ECP_POINT_invert: */
  127. int (*add)(const EC_GROUP *, EC_POINT *r, const EC_POINT *a, const EC_POINT *b, BN_CTX *);
  128. int (*dbl)(const EC_GROUP *, EC_POINT *r, const EC_POINT *a, BN_CTX *);
  129. int (*invert)(const EC_GROUP *, EC_POINT *, BN_CTX *);
  130. /* used by EC_POINT_is_at_infinity, EC_POINT_is_on_curve, EC_POINT_cmp: */
  131. int (*is_at_infinity)(const EC_GROUP *, const EC_POINT *);
  132. int (*is_on_curve)(const EC_GROUP *, const EC_POINT *, BN_CTX *);
  133. int (*point_cmp)(const EC_GROUP *, const EC_POINT *a, const EC_POINT *b, BN_CTX *);
  134. /* used by EC_POINT_make_affine, EC_POINTs_make_affine: */
  135. int (*make_affine)(const EC_GROUP *, EC_POINT *, BN_CTX *);
  136. int (*points_make_affine)(const EC_GROUP *, size_t num, EC_POINT *[], BN_CTX *);
  137. /* used by EC_POINTs_mul, EC_POINT_mul, EC_POINT_precompute_mult, EC_POINT_have_precompute_mult
  138. * (default implementations are used if the 'mul' pointer is 0): */
  139. int (*mul)(const EC_GROUP *group, EC_POINT *r, const BIGNUM *scalar,
  140. size_t num, const EC_POINT *points[], const BIGNUM *scalars[], BN_CTX *);
  141. int (*precompute_mult)(EC_GROUP *group, BN_CTX *);
  142. int (*have_precompute_mult)(const EC_GROUP *group);
  143. /* internal functions */
  144. /* 'field_mul', 'field_sqr', and 'field_div' can be used by 'add' and 'dbl' so that
  145. * the same implementations of point operations can be used with different
  146. * optimized implementations of expensive field operations: */
  147. int (*field_mul)(const EC_GROUP *, BIGNUM *r, const BIGNUM *a, const BIGNUM *b, BN_CTX *);
  148. int (*field_sqr)(const EC_GROUP *, BIGNUM *r, const BIGNUM *a, BN_CTX *);
  149. int (*field_div)(const EC_GROUP *, BIGNUM *r, const BIGNUM *a, const BIGNUM *b, BN_CTX *);
  150. int (*field_encode)(const EC_GROUP *, BIGNUM *r, const BIGNUM *a, BN_CTX *); /* e.g. to Montgomery */
  151. int (*field_decode)(const EC_GROUP *, BIGNUM *r, const BIGNUM *a, BN_CTX *); /* e.g. from Montgomery */
  152. int (*field_set_to_one)(const EC_GROUP *, BIGNUM *r, BN_CTX *);
  153. } /* EC_METHOD */;
  154. typedef struct ec_extra_data_st {
  155. struct ec_extra_data_st *next;
  156. void *data;
  157. void *(*dup_func)(void *);
  158. void (*free_func)(void *);
  159. void (*clear_free_func)(void *);
  160. } EC_EXTRA_DATA; /* used in EC_GROUP */
  161. struct ec_group_st {
  162. const EC_METHOD *meth;
  163. EC_POINT *generator; /* optional */
  164. BIGNUM order, cofactor;
  165. int curve_name;/* optional NID for named curve */
  166. int asn1_flag; /* flag to control the asn1 encoding */
  167. point_conversion_form_t asn1_form;
  168. unsigned char *seed; /* optional seed for parameters (appears in ASN1) */
  169. size_t seed_len;
  170. EC_EXTRA_DATA *extra_data; /* linked list */
  171. /* The following members are handled by the method functions,
  172. * even if they appear generic */
  173. BIGNUM field; /* Field specification.
  174. * For curves over GF(p), this is the modulus;
  175. * for curves over GF(2^m), this is the
  176. * irreducible polynomial defining the field.
  177. */
  178. unsigned int poly[5]; /* Field specification for curves over GF(2^m).
  179. * The irreducible f(t) is then of the form:
  180. * t^poly[0] + t^poly[1] + ... + t^poly[k]
  181. * where m = poly[0] > poly[1] > ... > poly[k] = 0.
  182. */
  183. BIGNUM a, b; /* Curve coefficients.
  184. * (Here the assumption is that BIGNUMs can be used
  185. * or abused for all kinds of fields, not just GF(p).)
  186. * For characteristic > 3, the curve is defined
  187. * by a Weierstrass equation of the form
  188. * y^2 = x^3 + a*x + b.
  189. * For characteristic 2, the curve is defined by
  190. * an equation of the form
  191. * y^2 + x*y = x^3 + a*x^2 + b.
  192. */
  193. int a_is_minus3; /* enable optimized point arithmetics for special case */
  194. void *field_data1; /* method-specific (e.g., Montgomery structure) */
  195. void *field_data2; /* method-specific */
  196. int (*field_mod_func)(BIGNUM *, const BIGNUM *, const BIGNUM *, BN_CTX *); /* method-specific */
  197. } /* EC_GROUP */;
  198. struct ec_key_st {
  199. int version;
  200. EC_GROUP *group;
  201. EC_POINT *pub_key;
  202. BIGNUM *priv_key;
  203. unsigned int enc_flag;
  204. point_conversion_form_t conv_form;
  205. int references;
  206. EC_EXTRA_DATA *method_data;
  207. } /* EC_KEY */;
  208. /* Basically a 'mixin' for extra data, but available for EC_GROUPs/EC_KEYs only
  209. * (with visibility limited to 'package' level for now).
  210. * We use the function pointers as index for retrieval; this obviates
  211. * global ex_data-style index tables.
  212. */
  213. int EC_EX_DATA_set_data(EC_EXTRA_DATA **, void *data,
  214. void *(*dup_func)(void *), void (*free_func)(void *), void (*clear_free_func)(void *));
  215. void *EC_EX_DATA_get_data(const EC_EXTRA_DATA *,
  216. void *(*dup_func)(void *), void (*free_func)(void *), void (*clear_free_func)(void *));
  217. void EC_EX_DATA_free_data(EC_EXTRA_DATA **,
  218. void *(*dup_func)(void *), void (*free_func)(void *), void (*clear_free_func)(void *));
  219. void EC_EX_DATA_clear_free_data(EC_EXTRA_DATA **,
  220. void *(*dup_func)(void *), void (*free_func)(void *), void (*clear_free_func)(void *));
  221. void EC_EX_DATA_free_all_data(EC_EXTRA_DATA **);
  222. void EC_EX_DATA_clear_free_all_data(EC_EXTRA_DATA **);
  223. struct ec_point_st {
  224. const EC_METHOD *meth;
  225. /* All members except 'meth' are handled by the method functions,
  226. * even if they appear generic */
  227. BIGNUM X;
  228. BIGNUM Y;
  229. BIGNUM Z; /* Jacobian projective coordinates:
  230. * (X, Y, Z) represents (X/Z^2, Y/Z^3) if Z != 0 */
  231. int Z_is_one; /* enable optimized point arithmetics for special case */
  232. } /* EC_POINT */;
  233. /* method functions in ec_mult.c
  234. * (ec_lib.c uses these as defaults if group->method->mul is 0) */
  235. int ec_wNAF_mul(const EC_GROUP *group, EC_POINT *r, const BIGNUM *scalar,
  236. size_t num, const EC_POINT *points[], const BIGNUM *scalars[], BN_CTX *);
  237. int ec_wNAF_precompute_mult(EC_GROUP *group, BN_CTX *);
  238. int ec_wNAF_have_precompute_mult(const EC_GROUP *group);
  239. /* method functions in ecp_smpl.c */
  240. int ec_GFp_simple_group_init(EC_GROUP *);
  241. void ec_GFp_simple_group_finish(EC_GROUP *);
  242. void ec_GFp_simple_group_clear_finish(EC_GROUP *);
  243. int ec_GFp_simple_group_copy(EC_GROUP *, const EC_GROUP *);
  244. int ec_GFp_simple_group_set_curve(EC_GROUP *, const BIGNUM *p, const BIGNUM *a, const BIGNUM *b, BN_CTX *);
  245. int ec_GFp_simple_group_get_curve(const EC_GROUP *, BIGNUM *p, BIGNUM *a, BIGNUM *b, BN_CTX *);
  246. int ec_GFp_simple_group_get_degree(const EC_GROUP *);
  247. int ec_GFp_simple_group_check_discriminant(const EC_GROUP *, BN_CTX *);
  248. int ec_GFp_simple_point_init(EC_POINT *);
  249. void ec_GFp_simple_point_finish(EC_POINT *);
  250. void ec_GFp_simple_point_clear_finish(EC_POINT *);
  251. int ec_GFp_simple_point_copy(EC_POINT *, const EC_POINT *);
  252. int ec_GFp_simple_point_set_to_infinity(const EC_GROUP *, EC_POINT *);
  253. int ec_GFp_simple_set_Jprojective_coordinates_GFp(const EC_GROUP *, EC_POINT *,
  254. const BIGNUM *x, const BIGNUM *y, const BIGNUM *z, BN_CTX *);
  255. int ec_GFp_simple_get_Jprojective_coordinates_GFp(const EC_GROUP *, const EC_POINT *,
  256. BIGNUM *x, BIGNUM *y, BIGNUM *z, BN_CTX *);
  257. int ec_GFp_simple_point_set_affine_coordinates(const EC_GROUP *, EC_POINT *,
  258. const BIGNUM *x, const BIGNUM *y, BN_CTX *);
  259. int ec_GFp_simple_point_get_affine_coordinates(const EC_GROUP *, const EC_POINT *,
  260. BIGNUM *x, BIGNUM *y, BN_CTX *);
  261. int ec_GFp_simple_set_compressed_coordinates(const EC_GROUP *, EC_POINT *,
  262. const BIGNUM *x, int y_bit, BN_CTX *);
  263. size_t ec_GFp_simple_point2oct(const EC_GROUP *, const EC_POINT *, point_conversion_form_t form,
  264. unsigned char *buf, size_t len, BN_CTX *);
  265. int ec_GFp_simple_oct2point(const EC_GROUP *, EC_POINT *,
  266. const unsigned char *buf, size_t len, BN_CTX *);
  267. int ec_GFp_simple_add(const EC_GROUP *, EC_POINT *r, const EC_POINT *a, const EC_POINT *b, BN_CTX *);
  268. int ec_GFp_simple_dbl(const EC_GROUP *, EC_POINT *r, const EC_POINT *a, BN_CTX *);
  269. int ec_GFp_simple_invert(const EC_GROUP *, EC_POINT *, BN_CTX *);
  270. int ec_GFp_simple_is_at_infinity(const EC_GROUP *, const EC_POINT *);
  271. int ec_GFp_simple_is_on_curve(const EC_GROUP *, const EC_POINT *, BN_CTX *);
  272. int ec_GFp_simple_cmp(const EC_GROUP *, const EC_POINT *a, const EC_POINT *b, BN_CTX *);
  273. int ec_GFp_simple_make_affine(const EC_GROUP *, EC_POINT *, BN_CTX *);
  274. int ec_GFp_simple_points_make_affine(const EC_GROUP *, size_t num, EC_POINT *[], BN_CTX *);
  275. int ec_GFp_simple_field_mul(const EC_GROUP *, BIGNUM *r, const BIGNUM *a, const BIGNUM *b, BN_CTX *);
  276. int ec_GFp_simple_field_sqr(const EC_GROUP *, BIGNUM *r, const BIGNUM *a, BN_CTX *);
  277. /* method functions in ecp_mont.c */
  278. int ec_GFp_mont_group_init(EC_GROUP *);
  279. int ec_GFp_mont_group_set_curve(EC_GROUP *, const BIGNUM *p, const BIGNUM *a, const BIGNUM *b, BN_CTX *);
  280. void ec_GFp_mont_group_finish(EC_GROUP *);
  281. void ec_GFp_mont_group_clear_finish(EC_GROUP *);
  282. int ec_GFp_mont_group_copy(EC_GROUP *, const EC_GROUP *);
  283. int ec_GFp_mont_field_mul(const EC_GROUP *, BIGNUM *r, const BIGNUM *a, const BIGNUM *b, BN_CTX *);
  284. int ec_GFp_mont_field_sqr(const EC_GROUP *, BIGNUM *r, const BIGNUM *a, BN_CTX *);
  285. int ec_GFp_mont_field_encode(const EC_GROUP *, BIGNUM *r, const BIGNUM *a, BN_CTX *);
  286. int ec_GFp_mont_field_decode(const EC_GROUP *, BIGNUM *r, const BIGNUM *a, BN_CTX *);
  287. int ec_GFp_mont_field_set_to_one(const EC_GROUP *, BIGNUM *r, BN_CTX *);
  288. /* method functions in ecp_nist.c */
  289. int ec_GFp_nist_group_copy(EC_GROUP *dest, const EC_GROUP *src);
  290. int ec_GFp_nist_group_set_curve(EC_GROUP *, const BIGNUM *p, const BIGNUM *a, const BIGNUM *b, BN_CTX *);
  291. int ec_GFp_nist_field_mul(const EC_GROUP *, BIGNUM *r, const BIGNUM *a, const BIGNUM *b, BN_CTX *);
  292. int ec_GFp_nist_field_sqr(const EC_GROUP *, BIGNUM *r, const BIGNUM *a, BN_CTX *);
  293. /* method functions in ec2_smpl.c */
  294. int ec_GF2m_simple_group_init(EC_GROUP *);
  295. void ec_GF2m_simple_group_finish(EC_GROUP *);
  296. void ec_GF2m_simple_group_clear_finish(EC_GROUP *);
  297. int ec_GF2m_simple_group_copy(EC_GROUP *, const EC_GROUP *);
  298. int ec_GF2m_simple_group_set_curve(EC_GROUP *, const BIGNUM *p, const BIGNUM *a, const BIGNUM *b, BN_CTX *);
  299. int ec_GF2m_simple_group_get_curve(const EC_GROUP *, BIGNUM *p, BIGNUM *a, BIGNUM *b, BN_CTX *);
  300. int ec_GF2m_simple_group_get_degree(const EC_GROUP *);
  301. int ec_GF2m_simple_group_check_discriminant(const EC_GROUP *, BN_CTX *);
  302. int ec_GF2m_simple_point_init(EC_POINT *);
  303. void ec_GF2m_simple_point_finish(EC_POINT *);
  304. void ec_GF2m_simple_point_clear_finish(EC_POINT *);
  305. int ec_GF2m_simple_point_copy(EC_POINT *, const EC_POINT *);
  306. int ec_GF2m_simple_point_set_to_infinity(const EC_GROUP *, EC_POINT *);
  307. int ec_GF2m_simple_point_set_affine_coordinates(const EC_GROUP *, EC_POINT *,
  308. const BIGNUM *x, const BIGNUM *y, BN_CTX *);
  309. int ec_GF2m_simple_point_get_affine_coordinates(const EC_GROUP *, const EC_POINT *,
  310. BIGNUM *x, BIGNUM *y, BN_CTX *);
  311. int ec_GF2m_simple_set_compressed_coordinates(const EC_GROUP *, EC_POINT *,
  312. const BIGNUM *x, int y_bit, BN_CTX *);
  313. size_t ec_GF2m_simple_point2oct(const EC_GROUP *, const EC_POINT *, point_conversion_form_t form,
  314. unsigned char *buf, size_t len, BN_CTX *);
  315. int ec_GF2m_simple_oct2point(const EC_GROUP *, EC_POINT *,
  316. const unsigned char *buf, size_t len, BN_CTX *);
  317. int ec_GF2m_simple_add(const EC_GROUP *, EC_POINT *r, const EC_POINT *a, const EC_POINT *b, BN_CTX *);
  318. int ec_GF2m_simple_dbl(const EC_GROUP *, EC_POINT *r, const EC_POINT *a, BN_CTX *);
  319. int ec_GF2m_simple_invert(const EC_GROUP *, EC_POINT *, BN_CTX *);
  320. int ec_GF2m_simple_is_at_infinity(const EC_GROUP *, const EC_POINT *);
  321. int ec_GF2m_simple_is_on_curve(const EC_GROUP *, const EC_POINT *, BN_CTX *);
  322. int ec_GF2m_simple_cmp(const EC_GROUP *, const EC_POINT *a, const EC_POINT *b, BN_CTX *);
  323. int ec_GF2m_simple_make_affine(const EC_GROUP *, EC_POINT *, BN_CTX *);
  324. int ec_GF2m_simple_points_make_affine(const EC_GROUP *, size_t num, EC_POINT *[], BN_CTX *);
  325. int ec_GF2m_simple_field_mul(const EC_GROUP *, BIGNUM *r, const BIGNUM *a, const BIGNUM *b, BN_CTX *);
  326. int ec_GF2m_simple_field_sqr(const EC_GROUP *, BIGNUM *r, const BIGNUM *a, BN_CTX *);
  327. int ec_GF2m_simple_field_div(const EC_GROUP *, BIGNUM *r, const BIGNUM *a, const BIGNUM *b, BN_CTX *);
  328. /* method functions in ec2_mult.c */
  329. int ec_GF2m_simple_mul(const EC_GROUP *group, EC_POINT *r, const BIGNUM *scalar,
  330. size_t num, const EC_POINT *points[], const BIGNUM *scalars[], BN_CTX *);
  331. int ec_GF2m_precompute_mult(EC_GROUP *group, BN_CTX *ctx);
  332. int ec_GF2m_have_precompute_mult(const EC_GROUP *group);