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 73 #include <stdlib.h> 74 75 #include <openssl/obj_mac.h> 76 #include <openssl/ec.h> 77 #include <openssl/bn.h> 78 79 #if defined(__SUNPRO_C) 80 # if __SUNPRO_C >= 0x520 81 # pragma error_messages (off,E_ARRAY_OF_INCOMPLETE_NONAME,E_ARRAY_OF_INCOMPLETE) 82 # endif 83 #endif 84 85 /* Structure details are not part of the exported interface, 86 * so all this may change in future versions. */ 87 88 struct ec_method_st { 89 /* used by EC_METHOD_get_field_type: */ 90 int field_type; /* a NID */ 91 92 /* used by EC_GROUP_new, EC_GROUP_free, EC_GROUP_clear_free, EC_GROUP_copy: */ 93 int (*group_init)(EC_GROUP *); 94 void (*group_finish)(EC_GROUP *); 95 void (*group_clear_finish)(EC_GROUP *); 96 int (*group_copy)(EC_GROUP *, const EC_GROUP *); 97 98 /* used by EC_GROUP_set_curve_GFp, EC_GROUP_get_curve_GFp, */ 99 /* EC_GROUP_set_curve_GF2m, and EC_GROUP_get_curve_GF2m: */ 100 int (*group_set_curve)(EC_GROUP *, const BIGNUM *p, const BIGNUM *a, const BIGNUM *b, BN_CTX *); 101 int (*group_get_curve)(const EC_GROUP *, BIGNUM *p, BIGNUM *a, BIGNUM *b, BN_CTX *); 102 103 /* used by EC_GROUP_get_degree: */ 104 int (*group_get_degree)(const EC_GROUP *); 105 106 /* used by EC_GROUP_check: */ 107 int (*group_check_discriminant)(const EC_GROUP *, BN_CTX *); 108 109 /* used by EC_POINT_new, EC_POINT_free, EC_POINT_clear_free, EC_POINT_copy: */ 110 int (*point_init)(EC_POINT *); 111 void (*point_finish)(EC_POINT *); 112 void (*point_clear_finish)(EC_POINT *); 113 int (*point_copy)(EC_POINT *, const EC_POINT *); 114 115 /* used by EC_POINT_set_to_infinity, 116 * EC_POINT_set_Jprojective_coordinates_GFp, 117 * EC_POINT_get_Jprojective_coordinates_GFp, 118 * EC_POINT_set_affine_coordinates_GFp, ..._GF2m, 119 * EC_POINT_get_affine_coordinates_GFp, ..._GF2m, 120 * EC_POINT_set_compressed_coordinates_GFp, ..._GF2m: 121 */ 122 int (*point_set_to_infinity)(const EC_GROUP *, EC_POINT *); 123 int (*point_set_Jprojective_coordinates_GFp)(const EC_GROUP *, EC_POINT *, 124 const BIGNUM *x, const BIGNUM *y, const BIGNUM *z, BN_CTX *); 125 int (*point_get_Jprojective_coordinates_GFp)(const EC_GROUP *, const EC_POINT *, 126 BIGNUM *x, BIGNUM *y, BIGNUM *z, BN_CTX *); 127 int (*point_set_affine_coordinates)(const EC_GROUP *, EC_POINT *, 128 const BIGNUM *x, const BIGNUM *y, BN_CTX *); 129 int (*point_get_affine_coordinates)(const EC_GROUP *, const EC_POINT *, 130 BIGNUM *x, BIGNUM *y, BN_CTX *); 131 int (*point_set_compressed_coordinates)(const EC_GROUP *, EC_POINT *, 132 const BIGNUM *x, int y_bit, BN_CTX *); 133 134 /* used by EC_POINT_point2oct, EC_POINT_oct2point: */ 135 size_t (*point2oct)(const EC_GROUP *, const EC_POINT *, point_conversion_form_t form, 136 unsigned char *buf, size_t len, BN_CTX *); 137 int (*oct2point)(const EC_GROUP *, EC_POINT *, 138 const unsigned char *buf, size_t len, BN_CTX *); 139 140 /* used by EC_POINT_add, EC_POINT_dbl, ECP_POINT_invert: */ 141 int (*add)(const EC_GROUP *, EC_POINT *r, const EC_POINT *a, const EC_POINT *b, BN_CTX *); 142 int (*dbl)(const EC_GROUP *, EC_POINT *r, const EC_POINT *a, BN_CTX *); 143 int (*invert)(const EC_GROUP *, EC_POINT *, BN_CTX *); 144 145 /* used by EC_POINT_is_at_infinity, EC_POINT_is_on_curve, EC_POINT_cmp: */ 146 int (*is_at_infinity)(const EC_GROUP *, const EC_POINT *); 147 int (*is_on_curve)(const EC_GROUP *, const EC_POINT *, BN_CTX *); 148 int (*point_cmp)(const EC_GROUP *, const EC_POINT *a, const EC_POINT *b, BN_CTX *); 149 150 /* used by EC_POINT_make_affine, EC_POINTs_make_affine: */ 151 int (*make_affine)(const EC_GROUP *, EC_POINT *, BN_CTX *); 152 int (*points_make_affine)(const EC_GROUP *, size_t num, EC_POINT *[], BN_CTX *); 153 154 /* used by EC_POINTs_mul, EC_POINT_mul, EC_POINT_precompute_mult, EC_POINT_have_precompute_mult 155 * (default implementations are used if the 'mul' pointer is 0): */ 156 int (*mul)(const EC_GROUP *group, EC_POINT *r, const BIGNUM *scalar, 157 size_t num, const EC_POINT *points[], const BIGNUM *scalars[], BN_CTX *); 158 int (*precompute_mult)(EC_GROUP *group, BN_CTX *); 159 int (*have_precompute_mult)(const EC_GROUP *group); 160 161 162 /* internal functions */ 163 164 /* 'field_mul', 'field_sqr', and 'field_div' can be used by 'add' and 'dbl' so that 165 * the same implementations of point operations can be used with different 166 * optimized implementations of expensive field operations: */ 167 int (*field_mul)(const EC_GROUP *, BIGNUM *r, const BIGNUM *a, const BIGNUM *b, BN_CTX *); 168 int (*field_sqr)(const EC_GROUP *, BIGNUM *r, const BIGNUM *a, BN_CTX *); 169 int (*field_div)(const EC_GROUP *, BIGNUM *r, const BIGNUM *a, const BIGNUM *b, BN_CTX *); 170 171 int (*field_encode)(const EC_GROUP *, BIGNUM *r, const BIGNUM *a, BN_CTX *); /* e.g. to Montgomery */ 172 int (*field_decode)(const EC_GROUP *, BIGNUM *r, const BIGNUM *a, BN_CTX *); /* e.g. from Montgomery */ 173 int (*field_set_to_one)(const EC_GROUP *, BIGNUM *r, BN_CTX *); 174 } /* EC_METHOD */; 175 176 typedef struct ec_extra_data_st { 177 struct ec_extra_data_st *next; 178 void *data; 179 void *(*dup_func)(void *); 180 void (*free_func)(void *); 181 void (*clear_free_func)(void *); 182 } EC_EXTRA_DATA; /* used in EC_GROUP */ 183 184 struct ec_group_st { 185 const EC_METHOD *meth; 186 187 EC_POINT *generator; /* optional */ 188 BIGNUM order, cofactor; 189 190 int curve_name;/* optional NID for named curve */ 191 int asn1_flag; /* flag to control the asn1 encoding */ 192 point_conversion_form_t asn1_form; 193 194 unsigned char *seed; /* optional seed for parameters (appears in ASN1) */ 195 size_t seed_len; 196 197 EC_EXTRA_DATA *extra_data; /* linked list */ 198 199 /* The following members are handled by the method functions, 200 * even if they appear generic */ 201 202 BIGNUM field; /* Field specification. 203 * For curves over GF(p), this is the modulus; 204 * for curves over GF(2^m), this is the 205 * irreducible polynomial defining the field. 206 */ 207 208 int poly[6]; /* Field specification for curves over GF(2^m). 209 * The irreducible f(t) is then of the form: 210 * t^poly[0] + t^poly[1] + ... + t^poly[k] 211 * where m = poly[0] > poly[1] > ... > poly[k] = 0. 212 * The array is terminated with poly[k+1]=-1. 213 * All elliptic curve irreducibles have at most 5 214 * non-zero terms. 215 */ 216 217 BIGNUM a, b; /* Curve coefficients. 218 * (Here the assumption is that BIGNUMs can be used 219 * or abused for all kinds of fields, not just GF(p).) 220 * For characteristic > 3, the curve is defined 221 * by a Weierstrass equation of the form 222 * y^2 = x^3 + a*x + b. 223 * For characteristic 2, the curve is defined by 224 * an equation of the form 225 * y^2 + x*y = x^3 + a*x^2 + b. 226 */ 227 228 int a_is_minus3; /* enable optimized point arithmetics for special case */ 229 230 void *field_data1; /* method-specific (e.g., Montgomery structure) */ 231 void *field_data2; /* method-specific */ 232 int (*field_mod_func)(BIGNUM *, const BIGNUM *, const BIGNUM *, BN_CTX *); /* method-specific */ 233 } /* EC_GROUP */; 234 235 struct ec_key_st { 236 int version; 237 238 EC_GROUP *group; 239 240 EC_POINT *pub_key; 241 BIGNUM *priv_key; 242 243 unsigned int enc_flag; 244 point_conversion_form_t conv_form; 245 246 int references; 247 248 EC_EXTRA_DATA *method_data; 249 } /* EC_KEY */; 250 251 /* Basically a 'mixin' for extra data, but available for EC_GROUPs/EC_KEYs only 252 * (with visibility limited to 'package' level for now). 253 * We use the function pointers as index for retrieval; this obviates 254 * global ex_data-style index tables. 255 */ 256 int EC_EX_DATA_set_data(EC_EXTRA_DATA **, void *data, 257 void *(*dup_func)(void *), void (*free_func)(void *), void (*clear_free_func)(void *)); 258 void *EC_EX_DATA_get_data(const EC_EXTRA_DATA *, 259 void *(*dup_func)(void *), void (*free_func)(void *), void (*clear_free_func)(void *)); 260 void EC_EX_DATA_free_data(EC_EXTRA_DATA **, 261 void *(*dup_func)(void *), void (*free_func)(void *), void (*clear_free_func)(void *)); 262 void EC_EX_DATA_clear_free_data(EC_EXTRA_DATA **, 263 void *(*dup_func)(void *), void (*free_func)(void *), void (*clear_free_func)(void *)); 264 void EC_EX_DATA_free_all_data(EC_EXTRA_DATA **); 265 void EC_EX_DATA_clear_free_all_data(EC_EXTRA_DATA **); 266 267 268 269 struct ec_point_st { 270 const EC_METHOD *meth; 271 272 /* All members except 'meth' are handled by the method functions, 273 * even if they appear generic */ 274 275 BIGNUM X; 276 BIGNUM Y; 277 BIGNUM Z; /* Jacobian projective coordinates: 278 * (X, Y, Z) represents (X/Z^2, Y/Z^3) if Z != 0 */ 279 int Z_is_one; /* enable optimized point arithmetics for special case */ 280 } /* EC_POINT */; 281 282 283 284 /* method functions in ec_mult.c 285 * (ec_lib.c uses these as defaults if group->method->mul is 0) */ 286 int ec_wNAF_mul(const EC_GROUP *group, EC_POINT *r, const BIGNUM *scalar, 287 size_t num, const EC_POINT *points[], const BIGNUM *scalars[], BN_CTX *); 288 int ec_wNAF_precompute_mult(EC_GROUP *group, BN_CTX *); 289 int ec_wNAF_have_precompute_mult(const EC_GROUP *group); 290 291 292 /* method functions in ecp_smpl.c */ 293 int ec_GFp_simple_group_init(EC_GROUP *); 294 void ec_GFp_simple_group_finish(EC_GROUP *); 295 void ec_GFp_simple_group_clear_finish(EC_GROUP *); 296 int ec_GFp_simple_group_copy(EC_GROUP *, const EC_GROUP *); 297 int ec_GFp_simple_group_set_curve(EC_GROUP *, const BIGNUM *p, const BIGNUM *a, const BIGNUM *b, BN_CTX *); 298 int ec_GFp_simple_group_get_curve(const EC_GROUP *, BIGNUM *p, BIGNUM *a, BIGNUM *b, BN_CTX *); 299 int ec_GFp_simple_group_get_degree(const EC_GROUP *); 300 int ec_GFp_simple_group_check_discriminant(const EC_GROUP *, BN_CTX *); 301 int ec_GFp_simple_point_init(EC_POINT *); 302 void ec_GFp_simple_point_finish(EC_POINT *); 303 void ec_GFp_simple_point_clear_finish(EC_POINT *); 304 int ec_GFp_simple_point_copy(EC_POINT *, const EC_POINT *); 305 int ec_GFp_simple_point_set_to_infinity(const EC_GROUP *, EC_POINT *); 306 int ec_GFp_simple_set_Jprojective_coordinates_GFp(const EC_GROUP *, EC_POINT *, 307 const BIGNUM *x, const BIGNUM *y, const BIGNUM *z, BN_CTX *); 308 int ec_GFp_simple_get_Jprojective_coordinates_GFp(const EC_GROUP *, const EC_POINT *, 309 BIGNUM *x, BIGNUM *y, BIGNUM *z, BN_CTX *); 310 int ec_GFp_simple_point_set_affine_coordinates(const EC_GROUP *, EC_POINT *, 311 const BIGNUM *x, const BIGNUM *y, BN_CTX *); 312 int ec_GFp_simple_point_get_affine_coordinates(const EC_GROUP *, const EC_POINT *, 313 BIGNUM *x, BIGNUM *y, BN_CTX *); 314 int ec_GFp_simple_set_compressed_coordinates(const EC_GROUP *, EC_POINT *, 315 const BIGNUM *x, int y_bit, BN_CTX *); 316 size_t ec_GFp_simple_point2oct(const EC_GROUP *, const EC_POINT *, point_conversion_form_t form, 317 unsigned char *buf, size_t len, BN_CTX *); 318 int ec_GFp_simple_oct2point(const EC_GROUP *, EC_POINT *, 319 const unsigned char *buf, size_t len, BN_CTX *); 320 int ec_GFp_simple_add(const EC_GROUP *, EC_POINT *r, const EC_POINT *a, const EC_POINT *b, BN_CTX *); 321 int ec_GFp_simple_dbl(const EC_GROUP *, EC_POINT *r, const EC_POINT *a, BN_CTX *); 322 int ec_GFp_simple_invert(const EC_GROUP *, EC_POINT *, BN_CTX *); 323 int ec_GFp_simple_is_at_infinity(const EC_GROUP *, const EC_POINT *); 324 int ec_GFp_simple_is_on_curve(const EC_GROUP *, const EC_POINT *, BN_CTX *); 325 int ec_GFp_simple_cmp(const EC_GROUP *, const EC_POINT *a, const EC_POINT *b, BN_CTX *); 326 int ec_GFp_simple_make_affine(const EC_GROUP *, EC_POINT *, BN_CTX *); 327 int ec_GFp_simple_points_make_affine(const EC_GROUP *, size_t num, EC_POINT *[], BN_CTX *); 328 int ec_GFp_simple_field_mul(const EC_GROUP *, BIGNUM *r, const BIGNUM *a, const BIGNUM *b, BN_CTX *); 329 int ec_GFp_simple_field_sqr(const EC_GROUP *, BIGNUM *r, const BIGNUM *a, BN_CTX *); 330 331 332 /* method functions in ecp_mont.c */ 333 int ec_GFp_mont_group_init(EC_GROUP *); 334 int ec_GFp_mont_group_set_curve(EC_GROUP *, const BIGNUM *p, const BIGNUM *a, const BIGNUM *b, BN_CTX *); 335 void ec_GFp_mont_group_finish(EC_GROUP *); 336 void ec_GFp_mont_group_clear_finish(EC_GROUP *); 337 int ec_GFp_mont_group_copy(EC_GROUP *, const EC_GROUP *); 338 int ec_GFp_mont_field_mul(const EC_GROUP *, BIGNUM *r, const BIGNUM *a, const BIGNUM *b, BN_CTX *); 339 int ec_GFp_mont_field_sqr(const EC_GROUP *, BIGNUM *r, const BIGNUM *a, BN_CTX *); 340 int ec_GFp_mont_field_encode(const EC_GROUP *, BIGNUM *r, const BIGNUM *a, BN_CTX *); 341 int ec_GFp_mont_field_decode(const EC_GROUP *, BIGNUM *r, const BIGNUM *a, BN_CTX *); 342 int ec_GFp_mont_field_set_to_one(const EC_GROUP *, BIGNUM *r, BN_CTX *); 343 344 345 /* method functions in ecp_nist.c */ 346 int ec_GFp_nist_group_copy(EC_GROUP *dest, const EC_GROUP *src); 347 int ec_GFp_nist_group_set_curve(EC_GROUP *, const BIGNUM *p, const BIGNUM *a, const BIGNUM *b, BN_CTX *); 348 int ec_GFp_nist_field_mul(const EC_GROUP *, BIGNUM *r, const BIGNUM *a, const BIGNUM *b, BN_CTX *); 349 int ec_GFp_nist_field_sqr(const EC_GROUP *, BIGNUM *r, const BIGNUM *a, BN_CTX *); 350 351 352 /* method functions in ec2_smpl.c */ 353 int ec_GF2m_simple_group_init(EC_GROUP *); 354 void ec_GF2m_simple_group_finish(EC_GROUP *); 355 void ec_GF2m_simple_group_clear_finish(EC_GROUP *); 356 int ec_GF2m_simple_group_copy(EC_GROUP *, const EC_GROUP *); 357 int ec_GF2m_simple_group_set_curve(EC_GROUP *, const BIGNUM *p, const BIGNUM *a, const BIGNUM *b, BN_CTX *); 358 int ec_GF2m_simple_group_get_curve(const EC_GROUP *, BIGNUM *p, BIGNUM *a, BIGNUM *b, BN_CTX *); 359 int ec_GF2m_simple_group_get_degree(const EC_GROUP *); 360 int ec_GF2m_simple_group_check_discriminant(const EC_GROUP *, BN_CTX *); 361 int ec_GF2m_simple_point_init(EC_POINT *); 362 void ec_GF2m_simple_point_finish(EC_POINT *); 363 void ec_GF2m_simple_point_clear_finish(EC_POINT *); 364 int ec_GF2m_simple_point_copy(EC_POINT *, const EC_POINT *); 365 int ec_GF2m_simple_point_set_to_infinity(const EC_GROUP *, EC_POINT *); 366 int ec_GF2m_simple_point_set_affine_coordinates(const EC_GROUP *, EC_POINT *, 367 const BIGNUM *x, const BIGNUM *y, BN_CTX *); 368 int ec_GF2m_simple_point_get_affine_coordinates(const EC_GROUP *, const EC_POINT *, 369 BIGNUM *x, BIGNUM *y, BN_CTX *); 370 int ec_GF2m_simple_set_compressed_coordinates(const EC_GROUP *, EC_POINT *, 371 const BIGNUM *x, int y_bit, BN_CTX *); 372 size_t ec_GF2m_simple_point2oct(const EC_GROUP *, const EC_POINT *, point_conversion_form_t form, 373 unsigned char *buf, size_t len, BN_CTX *); 374 int ec_GF2m_simple_oct2point(const EC_GROUP *, EC_POINT *, 375 const unsigned char *buf, size_t len, BN_CTX *); 376 int ec_GF2m_simple_add(const EC_GROUP *, EC_POINT *r, const EC_POINT *a, const EC_POINT *b, BN_CTX *); 377 int ec_GF2m_simple_dbl(const EC_GROUP *, EC_POINT *r, const EC_POINT *a, BN_CTX *); 378 int ec_GF2m_simple_invert(const EC_GROUP *, EC_POINT *, BN_CTX *); 379 int ec_GF2m_simple_is_at_infinity(const EC_GROUP *, const EC_POINT *); 380 int ec_GF2m_simple_is_on_curve(const EC_GROUP *, const EC_POINT *, BN_CTX *); 381 int ec_GF2m_simple_cmp(const EC_GROUP *, const EC_POINT *a, const EC_POINT *b, BN_CTX *); 382 int ec_GF2m_simple_make_affine(const EC_GROUP *, EC_POINT *, BN_CTX *); 383 int ec_GF2m_simple_points_make_affine(const EC_GROUP *, size_t num, EC_POINT *[], BN_CTX *); 384 int ec_GF2m_simple_field_mul(const EC_GROUP *, BIGNUM *r, const BIGNUM *a, const BIGNUM *b, BN_CTX *); 385 int ec_GF2m_simple_field_sqr(const EC_GROUP *, BIGNUM *r, const BIGNUM *a, BN_CTX *); 386 int ec_GF2m_simple_field_div(const EC_GROUP *, BIGNUM *r, const BIGNUM *a, const BIGNUM *b, BN_CTX *); 387 388 389 /* method functions in ec2_mult.c */ 390 int ec_GF2m_simple_mul(const EC_GROUP *group, EC_POINT *r, const BIGNUM *scalar, 391 size_t num, const EC_POINT *points[], const BIGNUM *scalars[], BN_CTX *); 392 int ec_GF2m_precompute_mult(EC_GROUP *group, BN_CTX *ctx); 393 int ec_GF2m_have_precompute_mult(const EC_GROUP *group); 394