ec_lcl.h revision 296465
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 72#include <stdlib.h> 73 74#include <openssl/obj_mac.h> 75#include <openssl/ec.h> 76#include <openssl/bn.h> 77 78#if defined(__SUNPRO_C) 79# if __SUNPRO_C >= 0x520 80# pragma error_messages (off,E_ARRAY_OF_INCOMPLETE_NONAME,E_ARRAY_OF_INCOMPLETE) 81# endif 82#endif 83 84/* 85 * Structure details are not part of the exported interface, so all this may 86 * change in future versions. 87 */ 88 89struct ec_method_st { 90 /* used by EC_METHOD_get_field_type: */ 91 int field_type; /* a NID */ 92 /* 93 * used by EC_GROUP_new, EC_GROUP_free, EC_GROUP_clear_free, 94 * EC_GROUP_copy: 95 */ 96 int (*group_init) (EC_GROUP *); 97 void (*group_finish) (EC_GROUP *); 98 void (*group_clear_finish) (EC_GROUP *); 99 int (*group_copy) (EC_GROUP *, const EC_GROUP *); 100 /* used by EC_GROUP_set_curve_GFp, EC_GROUP_get_curve_GFp, */ 101 /* EC_GROUP_set_curve_GF2m, and EC_GROUP_get_curve_GF2m: */ 102 int (*group_set_curve) (EC_GROUP *, const BIGNUM *p, const BIGNUM *a, 103 const BIGNUM *b, BN_CTX *); 104 int (*group_get_curve) (const EC_GROUP *, BIGNUM *p, BIGNUM *a, BIGNUM *b, 105 BN_CTX *); 106 /* used by EC_GROUP_get_degree: */ 107 int (*group_get_degree) (const EC_GROUP *); 108 /* used by EC_GROUP_check: */ 109 int (*group_check_discriminant) (const EC_GROUP *, BN_CTX *); 110 /* 111 * used by EC_POINT_new, EC_POINT_free, EC_POINT_clear_free, 112 * EC_POINT_copy: 113 */ 114 int (*point_init) (EC_POINT *); 115 void (*point_finish) (EC_POINT *); 116 void (*point_clear_finish) (EC_POINT *); 117 int (*point_copy) (EC_POINT *, const EC_POINT *); 118 /*- 119 * used by EC_POINT_set_to_infinity, 120 * EC_POINT_set_Jprojective_coordinates_GFp, 121 * EC_POINT_get_Jprojective_coordinates_GFp, 122 * EC_POINT_set_affine_coordinates_GFp, ..._GF2m, 123 * EC_POINT_get_affine_coordinates_GFp, ..._GF2m, 124 * EC_POINT_set_compressed_coordinates_GFp, ..._GF2m: 125 */ 126 int (*point_set_to_infinity) (const EC_GROUP *, EC_POINT *); 127 int (*point_set_Jprojective_coordinates_GFp) (const EC_GROUP *, 128 EC_POINT *, const BIGNUM *x, 129 const BIGNUM *y, 130 const BIGNUM *z, BN_CTX *); 131 int (*point_get_Jprojective_coordinates_GFp) (const EC_GROUP *, 132 const EC_POINT *, BIGNUM *x, 133 BIGNUM *y, BIGNUM *z, 134 BN_CTX *); 135 int (*point_set_affine_coordinates) (const EC_GROUP *, EC_POINT *, 136 const BIGNUM *x, const BIGNUM *y, 137 BN_CTX *); 138 int (*point_get_affine_coordinates) (const EC_GROUP *, const EC_POINT *, 139 BIGNUM *x, BIGNUM *y, BN_CTX *); 140 int (*point_set_compressed_coordinates) (const EC_GROUP *, EC_POINT *, 141 const BIGNUM *x, int y_bit, 142 BN_CTX *); 143 /* used by EC_POINT_point2oct, EC_POINT_oct2point: */ 144 size_t (*point2oct) (const EC_GROUP *, const EC_POINT *, 145 point_conversion_form_t form, unsigned char *buf, 146 size_t len, BN_CTX *); 147 int (*oct2point) (const EC_GROUP *, EC_POINT *, const unsigned char *buf, 148 size_t len, BN_CTX *); 149 /* used by EC_POINT_add, EC_POINT_dbl, ECP_POINT_invert: */ 150 int (*add) (const EC_GROUP *, EC_POINT *r, const EC_POINT *a, 151 const EC_POINT *b, BN_CTX *); 152 int (*dbl) (const EC_GROUP *, EC_POINT *r, const EC_POINT *a, BN_CTX *); 153 int (*invert) (const EC_GROUP *, EC_POINT *, BN_CTX *); 154 /* 155 * used by EC_POINT_is_at_infinity, EC_POINT_is_on_curve, EC_POINT_cmp: 156 */ 157 int (*is_at_infinity) (const EC_GROUP *, const EC_POINT *); 158 int (*is_on_curve) (const EC_GROUP *, const EC_POINT *, BN_CTX *); 159 int (*point_cmp) (const EC_GROUP *, const EC_POINT *a, const EC_POINT *b, 160 BN_CTX *); 161 /* used by EC_POINT_make_affine, EC_POINTs_make_affine: */ 162 int (*make_affine) (const EC_GROUP *, EC_POINT *, BN_CTX *); 163 int (*points_make_affine) (const EC_GROUP *, size_t num, EC_POINT *[], 164 BN_CTX *); 165 /* 166 * used by EC_POINTs_mul, EC_POINT_mul, EC_POINT_precompute_mult, 167 * EC_POINT_have_precompute_mult (default implementations are used if the 168 * 'mul' pointer is 0): 169 */ 170 int (*mul) (const EC_GROUP *group, EC_POINT *r, const BIGNUM *scalar, 171 size_t num, const EC_POINT *points[], const BIGNUM *scalars[], 172 BN_CTX *); 173 int (*precompute_mult) (EC_GROUP *group, BN_CTX *); 174 int (*have_precompute_mult) (const EC_GROUP *group); 175 /* internal functions */ 176 /* 177 * 'field_mul', 'field_sqr', and 'field_div' can be used by 'add' and 178 * 'dbl' so that the same implementations of point operations can be used 179 * with different optimized implementations of expensive field 180 * operations: 181 */ 182 int (*field_mul) (const EC_GROUP *, BIGNUM *r, const BIGNUM *a, 183 const BIGNUM *b, BN_CTX *); 184 int (*field_sqr) (const EC_GROUP *, BIGNUM *r, const BIGNUM *a, BN_CTX *); 185 int (*field_div) (const EC_GROUP *, BIGNUM *r, const BIGNUM *a, 186 const BIGNUM *b, BN_CTX *); 187 /* e.g. to Montgomery */ 188 int (*field_encode) (const EC_GROUP *, BIGNUM *r, const BIGNUM *a, 189 BN_CTX *); 190 /* e.g. from Montgomery */ 191 int (*field_decode) (const EC_GROUP *, BIGNUM *r, const BIGNUM *a, 192 BN_CTX *); 193 int (*field_set_to_one) (const EC_GROUP *, BIGNUM *r, BN_CTX *); 194} /* EC_METHOD */ ; 195 196typedef struct ec_extra_data_st { 197 struct ec_extra_data_st *next; 198 void *data; 199 void *(*dup_func) (void *); 200 void (*free_func) (void *); 201 void (*clear_free_func) (void *); 202} EC_EXTRA_DATA; /* used in EC_GROUP */ 203 204struct ec_group_st { 205 const EC_METHOD *meth; 206 EC_POINT *generator; /* optional */ 207 BIGNUM order, cofactor; 208 int curve_name; /* optional NID for named curve */ 209 int asn1_flag; /* flag to control the asn1 encoding */ 210 point_conversion_form_t asn1_form; 211 unsigned char *seed; /* optional seed for parameters (appears in 212 * ASN1) */ 213 size_t seed_len; 214 EC_EXTRA_DATA *extra_data; /* linked list */ 215 /* 216 * The following members are handled by the method functions, even if 217 * they appear generic 218 */ 219 /* 220 * Field specification. For curves over GF(p), this is the modulus; for 221 * curves over GF(2^m), this is the irreducible polynomial defining the 222 * field. 223 */ 224 BIGNUM field; 225 /* 226 * Field specification for curves over GF(2^m). The irreducible f(t) is 227 * then of the form: t^poly[0] + t^poly[1] + ... + t^poly[k] where m = 228 * poly[0] > poly[1] > ... > poly[k] = 0. 229 */ 230 unsigned int poly[5]; 231 /* 232 * Curve coefficients. (Here the assumption is that BIGNUMs can be used 233 * or abused for all kinds of fields, not just GF(p).) For characteristic 234 * > 3, the curve is defined by a Weierstrass equation of the form y^2 = 235 * x^3 + a*x + b. For characteristic 2, the curve is defined by an 236 * equation of the form y^2 + x*y = x^3 + a*x^2 + b. 237 */ 238 BIGNUM a, b; 239 /* enable optimized point arithmetics for special case */ 240 int a_is_minus3; 241 /* method-specific (e.g., Montgomery structure) */ 242 void *field_data1; 243 /* method-specific */ 244 void *field_data2; 245 /* method-specific */ 246 int (*field_mod_func) (BIGNUM *, const BIGNUM *, const BIGNUM *, 247 BN_CTX *); 248} /* EC_GROUP */ ; 249 250struct ec_key_st { 251 int version; 252 EC_GROUP *group; 253 EC_POINT *pub_key; 254 BIGNUM *priv_key; 255 unsigned int enc_flag; 256 point_conversion_form_t conv_form; 257 int references; 258 EC_EXTRA_DATA *method_data; 259} /* EC_KEY */ ; 260 261/* 262 * Basically a 'mixin' for extra data, but available for EC_GROUPs/EC_KEYs 263 * only (with visibility limited to 'package' level for now). We use the 264 * function pointers as index for retrieval; this obviates global 265 * ex_data-style index tables. 266 */ 267int EC_EX_DATA_set_data(EC_EXTRA_DATA **, void *data, 268 void *(*dup_func) (void *), 269 void (*free_func) (void *), 270 void (*clear_free_func) (void *)); 271void *EC_EX_DATA_get_data(const EC_EXTRA_DATA *, void *(*dup_func) (void *), 272 void (*free_func) (void *), 273 void (*clear_free_func) (void *)); 274void EC_EX_DATA_free_data(EC_EXTRA_DATA **, void *(*dup_func) (void *), 275 void (*free_func) (void *), 276 void (*clear_free_func) (void *)); 277void EC_EX_DATA_clear_free_data(EC_EXTRA_DATA **, void *(*dup_func) (void *), 278 void (*free_func) (void *), 279 void (*clear_free_func) (void *)); 280void EC_EX_DATA_free_all_data(EC_EXTRA_DATA **); 281void EC_EX_DATA_clear_free_all_data(EC_EXTRA_DATA **); 282 283struct ec_point_st { 284 const EC_METHOD *meth; 285 /* 286 * All members except 'meth' are handled by the method functions, even if 287 * they appear generic 288 */ 289 BIGNUM X; 290 BIGNUM Y; 291 BIGNUM Z; /* Jacobian projective coordinates: (X, Y, Z) 292 * represents (X/Z^2, Y/Z^3) if Z != 0 */ 293 int Z_is_one; /* enable optimized point arithmetics for 294 * special case */ 295} /* EC_POINT */ ; 296 297/* 298 * method functions in ec_mult.c (ec_lib.c uses these as defaults if 299 * group->method->mul is 0) 300 */ 301int ec_wNAF_mul(const EC_GROUP *group, EC_POINT *r, const BIGNUM *scalar, 302 size_t num, const EC_POINT *points[], const BIGNUM *scalars[], 303 BN_CTX *); 304int ec_wNAF_precompute_mult(EC_GROUP *group, BN_CTX *); 305int ec_wNAF_have_precompute_mult(const EC_GROUP *group); 306 307/* method functions in ecp_smpl.c */ 308int ec_GFp_simple_group_init(EC_GROUP *); 309void ec_GFp_simple_group_finish(EC_GROUP *); 310void ec_GFp_simple_group_clear_finish(EC_GROUP *); 311int ec_GFp_simple_group_copy(EC_GROUP *, const EC_GROUP *); 312int ec_GFp_simple_group_set_curve(EC_GROUP *, const BIGNUM *p, 313 const BIGNUM *a, const BIGNUM *b, BN_CTX *); 314int ec_GFp_simple_group_get_curve(const EC_GROUP *, BIGNUM *p, BIGNUM *a, 315 BIGNUM *b, BN_CTX *); 316int ec_GFp_simple_group_get_degree(const EC_GROUP *); 317int ec_GFp_simple_group_check_discriminant(const EC_GROUP *, BN_CTX *); 318int ec_GFp_simple_point_init(EC_POINT *); 319void ec_GFp_simple_point_finish(EC_POINT *); 320void ec_GFp_simple_point_clear_finish(EC_POINT *); 321int ec_GFp_simple_point_copy(EC_POINT *, const EC_POINT *); 322int ec_GFp_simple_point_set_to_infinity(const EC_GROUP *, EC_POINT *); 323int ec_GFp_simple_set_Jprojective_coordinates_GFp(const EC_GROUP *, 324 EC_POINT *, const BIGNUM *x, 325 const BIGNUM *y, 326 const BIGNUM *z, BN_CTX *); 327int ec_GFp_simple_get_Jprojective_coordinates_GFp(const EC_GROUP *, 328 const EC_POINT *, BIGNUM *x, 329 BIGNUM *y, BIGNUM *z, 330 BN_CTX *); 331int ec_GFp_simple_point_set_affine_coordinates(const EC_GROUP *, EC_POINT *, 332 const BIGNUM *x, 333 const BIGNUM *y, BN_CTX *); 334int ec_GFp_simple_point_get_affine_coordinates(const EC_GROUP *, 335 const EC_POINT *, BIGNUM *x, 336 BIGNUM *y, BN_CTX *); 337int ec_GFp_simple_set_compressed_coordinates(const EC_GROUP *, EC_POINT *, 338 const BIGNUM *x, int y_bit, 339 BN_CTX *); 340size_t ec_GFp_simple_point2oct(const EC_GROUP *, const EC_POINT *, 341 point_conversion_form_t form, 342 unsigned char *buf, size_t len, BN_CTX *); 343int ec_GFp_simple_oct2point(const EC_GROUP *, EC_POINT *, 344 const unsigned char *buf, size_t len, BN_CTX *); 345int ec_GFp_simple_add(const EC_GROUP *, EC_POINT *r, const EC_POINT *a, 346 const EC_POINT *b, BN_CTX *); 347int ec_GFp_simple_dbl(const EC_GROUP *, EC_POINT *r, const EC_POINT *a, 348 BN_CTX *); 349int ec_GFp_simple_invert(const EC_GROUP *, EC_POINT *, BN_CTX *); 350int ec_GFp_simple_is_at_infinity(const EC_GROUP *, const EC_POINT *); 351int ec_GFp_simple_is_on_curve(const EC_GROUP *, const EC_POINT *, BN_CTX *); 352int ec_GFp_simple_cmp(const EC_GROUP *, const EC_POINT *a, const EC_POINT *b, 353 BN_CTX *); 354int ec_GFp_simple_make_affine(const EC_GROUP *, EC_POINT *, BN_CTX *); 355int ec_GFp_simple_points_make_affine(const EC_GROUP *, size_t num, 356 EC_POINT *[], BN_CTX *); 357int ec_GFp_simple_field_mul(const EC_GROUP *, BIGNUM *r, const BIGNUM *a, 358 const BIGNUM *b, BN_CTX *); 359int ec_GFp_simple_field_sqr(const EC_GROUP *, BIGNUM *r, const BIGNUM *a, 360 BN_CTX *); 361 362/* method functions in ecp_mont.c */ 363int ec_GFp_mont_group_init(EC_GROUP *); 364int ec_GFp_mont_group_set_curve(EC_GROUP *, const BIGNUM *p, const BIGNUM *a, 365 const BIGNUM *b, BN_CTX *); 366void ec_GFp_mont_group_finish(EC_GROUP *); 367void ec_GFp_mont_group_clear_finish(EC_GROUP *); 368int ec_GFp_mont_group_copy(EC_GROUP *, const EC_GROUP *); 369int ec_GFp_mont_field_mul(const EC_GROUP *, BIGNUM *r, const BIGNUM *a, 370 const BIGNUM *b, BN_CTX *); 371int ec_GFp_mont_field_sqr(const EC_GROUP *, BIGNUM *r, const BIGNUM *a, 372 BN_CTX *); 373int ec_GFp_mont_field_encode(const EC_GROUP *, BIGNUM *r, const BIGNUM *a, 374 BN_CTX *); 375int ec_GFp_mont_field_decode(const EC_GROUP *, BIGNUM *r, const BIGNUM *a, 376 BN_CTX *); 377int ec_GFp_mont_field_set_to_one(const EC_GROUP *, BIGNUM *r, BN_CTX *); 378 379/* method functions in ecp_nist.c */ 380int ec_GFp_nist_group_copy(EC_GROUP *dest, const EC_GROUP *src); 381int ec_GFp_nist_group_set_curve(EC_GROUP *, const BIGNUM *p, const BIGNUM *a, 382 const BIGNUM *b, BN_CTX *); 383int ec_GFp_nist_field_mul(const EC_GROUP *, BIGNUM *r, const BIGNUM *a, 384 const BIGNUM *b, BN_CTX *); 385int ec_GFp_nist_field_sqr(const EC_GROUP *, BIGNUM *r, const BIGNUM *a, 386 BN_CTX *); 387 388/* method functions in ec2_smpl.c */ 389int ec_GF2m_simple_group_init(EC_GROUP *); 390void ec_GF2m_simple_group_finish(EC_GROUP *); 391void ec_GF2m_simple_group_clear_finish(EC_GROUP *); 392int ec_GF2m_simple_group_copy(EC_GROUP *, const EC_GROUP *); 393int ec_GF2m_simple_group_set_curve(EC_GROUP *, const BIGNUM *p, 394 const BIGNUM *a, const BIGNUM *b, 395 BN_CTX *); 396int ec_GF2m_simple_group_get_curve(const EC_GROUP *, BIGNUM *p, BIGNUM *a, 397 BIGNUM *b, BN_CTX *); 398int ec_GF2m_simple_group_get_degree(const EC_GROUP *); 399int ec_GF2m_simple_group_check_discriminant(const EC_GROUP *, BN_CTX *); 400int ec_GF2m_simple_point_init(EC_POINT *); 401void ec_GF2m_simple_point_finish(EC_POINT *); 402void ec_GF2m_simple_point_clear_finish(EC_POINT *); 403int ec_GF2m_simple_point_copy(EC_POINT *, const EC_POINT *); 404int ec_GF2m_simple_point_set_to_infinity(const EC_GROUP *, EC_POINT *); 405int ec_GF2m_simple_point_set_affine_coordinates(const EC_GROUP *, EC_POINT *, 406 const BIGNUM *x, 407 const BIGNUM *y, BN_CTX *); 408int ec_GF2m_simple_point_get_affine_coordinates(const EC_GROUP *, 409 const EC_POINT *, BIGNUM *x, 410 BIGNUM *y, BN_CTX *); 411int ec_GF2m_simple_set_compressed_coordinates(const EC_GROUP *, EC_POINT *, 412 const BIGNUM *x, int y_bit, 413 BN_CTX *); 414size_t ec_GF2m_simple_point2oct(const EC_GROUP *, const EC_POINT *, 415 point_conversion_form_t form, 416 unsigned char *buf, size_t len, BN_CTX *); 417int ec_GF2m_simple_oct2point(const EC_GROUP *, EC_POINT *, 418 const unsigned char *buf, size_t len, BN_CTX *); 419int ec_GF2m_simple_add(const EC_GROUP *, EC_POINT *r, const EC_POINT *a, 420 const EC_POINT *b, BN_CTX *); 421int ec_GF2m_simple_dbl(const EC_GROUP *, EC_POINT *r, const EC_POINT *a, 422 BN_CTX *); 423int ec_GF2m_simple_invert(const EC_GROUP *, EC_POINT *, BN_CTX *); 424int ec_GF2m_simple_is_at_infinity(const EC_GROUP *, const EC_POINT *); 425int ec_GF2m_simple_is_on_curve(const EC_GROUP *, const EC_POINT *, BN_CTX *); 426int ec_GF2m_simple_cmp(const EC_GROUP *, const EC_POINT *a, const EC_POINT *b, 427 BN_CTX *); 428int ec_GF2m_simple_make_affine(const EC_GROUP *, EC_POINT *, BN_CTX *); 429int ec_GF2m_simple_points_make_affine(const EC_GROUP *, size_t num, 430 EC_POINT *[], BN_CTX *); 431int ec_GF2m_simple_field_mul(const EC_GROUP *, BIGNUM *r, const BIGNUM *a, 432 const BIGNUM *b, BN_CTX *); 433int ec_GF2m_simple_field_sqr(const EC_GROUP *, BIGNUM *r, const BIGNUM *a, 434 BN_CTX *); 435int ec_GF2m_simple_field_div(const EC_GROUP *, BIGNUM *r, const BIGNUM *a, 436 const BIGNUM *b, BN_CTX *); 437 438/* method functions in ec2_mult.c */ 439int ec_GF2m_simple_mul(const EC_GROUP *group, EC_POINT *r, 440 const BIGNUM *scalar, size_t num, 441 const EC_POINT *points[], const BIGNUM *scalars[], 442 BN_CTX *); 443int ec_GF2m_precompute_mult(EC_GROUP *group, BN_CTX *ctx); 444int ec_GF2m_have_precompute_mult(const EC_GROUP *group); 445