ec_lcl.h revision 296341
1/* crypto/ec/ec_lcl.h */ 2/* 3 * Originally written by Bodo Moeller for the OpenSSL project. 4 */ 5/* ==================================================================== 6 * Copyright (c) 1998-2010 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/* Use default functions for poin2oct, oct2point and compressed coordinates */ 85#define EC_FLAGS_DEFAULT_OCT 0x1 86 87/* 88 * Structure details are not part of the exported interface, so all this may 89 * change in future versions. 90 */ 91 92struct ec_method_st { 93 /* Various method flags */ 94 int flags; 95 /* used by EC_METHOD_get_field_type: */ 96 int field_type; /* a NID */ 97 /* 98 * used by EC_GROUP_new, EC_GROUP_free, EC_GROUP_clear_free, 99 * EC_GROUP_copy: 100 */ 101 int (*group_init) (EC_GROUP *); 102 void (*group_finish) (EC_GROUP *); 103 void (*group_clear_finish) (EC_GROUP *); 104 int (*group_copy) (EC_GROUP *, const EC_GROUP *); 105 /* used by EC_GROUP_set_curve_GFp, EC_GROUP_get_curve_GFp, */ 106 /* EC_GROUP_set_curve_GF2m, and EC_GROUP_get_curve_GF2m: */ 107 int (*group_set_curve) (EC_GROUP *, const BIGNUM *p, const BIGNUM *a, 108 const BIGNUM *b, BN_CTX *); 109 int (*group_get_curve) (const EC_GROUP *, BIGNUM *p, BIGNUM *a, BIGNUM *b, 110 BN_CTX *); 111 /* used by EC_GROUP_get_degree: */ 112 int (*group_get_degree) (const EC_GROUP *); 113 /* used by EC_GROUP_check: */ 114 int (*group_check_discriminant) (const EC_GROUP *, BN_CTX *); 115 /* 116 * used by EC_POINT_new, EC_POINT_free, EC_POINT_clear_free, 117 * EC_POINT_copy: 118 */ 119 int (*point_init) (EC_POINT *); 120 void (*point_finish) (EC_POINT *); 121 void (*point_clear_finish) (EC_POINT *); 122 int (*point_copy) (EC_POINT *, const EC_POINT *); 123 /*- 124 * used by EC_POINT_set_to_infinity, 125 * EC_POINT_set_Jprojective_coordinates_GFp, 126 * EC_POINT_get_Jprojective_coordinates_GFp, 127 * EC_POINT_set_affine_coordinates_GFp, ..._GF2m, 128 * EC_POINT_get_affine_coordinates_GFp, ..._GF2m, 129 * EC_POINT_set_compressed_coordinates_GFp, ..._GF2m: 130 */ 131 int (*point_set_to_infinity) (const EC_GROUP *, EC_POINT *); 132 int (*point_set_Jprojective_coordinates_GFp) (const EC_GROUP *, 133 EC_POINT *, const BIGNUM *x, 134 const BIGNUM *y, 135 const BIGNUM *z, BN_CTX *); 136 int (*point_get_Jprojective_coordinates_GFp) (const EC_GROUP *, 137 const EC_POINT *, BIGNUM *x, 138 BIGNUM *y, BIGNUM *z, 139 BN_CTX *); 140 int (*point_set_affine_coordinates) (const EC_GROUP *, EC_POINT *, 141 const BIGNUM *x, const BIGNUM *y, 142 BN_CTX *); 143 int (*point_get_affine_coordinates) (const EC_GROUP *, const EC_POINT *, 144 BIGNUM *x, BIGNUM *y, BN_CTX *); 145 int (*point_set_compressed_coordinates) (const EC_GROUP *, EC_POINT *, 146 const BIGNUM *x, int y_bit, 147 BN_CTX *); 148 /* used by EC_POINT_point2oct, EC_POINT_oct2point: */ 149 size_t (*point2oct) (const EC_GROUP *, const EC_POINT *, 150 point_conversion_form_t form, unsigned char *buf, 151 size_t len, BN_CTX *); 152 int (*oct2point) (const EC_GROUP *, EC_POINT *, const unsigned char *buf, 153 size_t len, BN_CTX *); 154 /* used by EC_POINT_add, EC_POINT_dbl, ECP_POINT_invert: */ 155 int (*add) (const EC_GROUP *, EC_POINT *r, const EC_POINT *a, 156 const EC_POINT *b, BN_CTX *); 157 int (*dbl) (const EC_GROUP *, EC_POINT *r, const EC_POINT *a, BN_CTX *); 158 int (*invert) (const EC_GROUP *, EC_POINT *, BN_CTX *); 159 /* 160 * used by EC_POINT_is_at_infinity, EC_POINT_is_on_curve, EC_POINT_cmp: 161 */ 162 int (*is_at_infinity) (const EC_GROUP *, const EC_POINT *); 163 int (*is_on_curve) (const EC_GROUP *, const EC_POINT *, BN_CTX *); 164 int (*point_cmp) (const EC_GROUP *, const EC_POINT *a, const EC_POINT *b, 165 BN_CTX *); 166 /* used by EC_POINT_make_affine, EC_POINTs_make_affine: */ 167 int (*make_affine) (const EC_GROUP *, EC_POINT *, BN_CTX *); 168 int (*points_make_affine) (const EC_GROUP *, size_t num, EC_POINT *[], 169 BN_CTX *); 170 /* 171 * used by EC_POINTs_mul, EC_POINT_mul, EC_POINT_precompute_mult, 172 * EC_POINT_have_precompute_mult (default implementations are used if the 173 * 'mul' pointer is 0): 174 */ 175 int (*mul) (const EC_GROUP *group, EC_POINT *r, const BIGNUM *scalar, 176 size_t num, const EC_POINT *points[], const BIGNUM *scalars[], 177 BN_CTX *); 178 int (*precompute_mult) (EC_GROUP *group, BN_CTX *); 179 int (*have_precompute_mult) (const EC_GROUP *group); 180 /* internal functions */ 181 /* 182 * 'field_mul', 'field_sqr', and 'field_div' can be used by 'add' and 183 * 'dbl' so that the same implementations of point operations can be used 184 * with different optimized implementations of expensive field 185 * operations: 186 */ 187 int (*field_mul) (const EC_GROUP *, BIGNUM *r, const BIGNUM *a, 188 const BIGNUM *b, BN_CTX *); 189 int (*field_sqr) (const EC_GROUP *, BIGNUM *r, const BIGNUM *a, BN_CTX *); 190 int (*field_div) (const EC_GROUP *, BIGNUM *r, const BIGNUM *a, 191 const BIGNUM *b, BN_CTX *); 192 /* e.g. to Montgomery */ 193 int (*field_encode) (const EC_GROUP *, BIGNUM *r, const BIGNUM *a, 194 BN_CTX *); 195 /* e.g. from Montgomery */ 196 int (*field_decode) (const EC_GROUP *, BIGNUM *r, const BIGNUM *a, 197 BN_CTX *); 198 int (*field_set_to_one) (const EC_GROUP *, BIGNUM *r, BN_CTX *); 199} /* EC_METHOD */ ; 200 201typedef struct ec_extra_data_st { 202 struct ec_extra_data_st *next; 203 void *data; 204 void *(*dup_func) (void *); 205 void (*free_func) (void *); 206 void (*clear_free_func) (void *); 207} EC_EXTRA_DATA; /* used in EC_GROUP */ 208 209struct ec_group_st { 210 const EC_METHOD *meth; 211 EC_POINT *generator; /* optional */ 212 BIGNUM order, cofactor; 213 int curve_name; /* optional NID for named curve */ 214 int asn1_flag; /* flag to control the asn1 encoding */ 215 point_conversion_form_t asn1_form; 216 unsigned char *seed; /* optional seed for parameters (appears in 217 * ASN1) */ 218 size_t seed_len; 219 EC_EXTRA_DATA *extra_data; /* linked list */ 220 /* 221 * The following members are handled by the method functions, even if 222 * they appear generic 223 */ 224 /* 225 * Field specification. For curves over GF(p), this is the modulus; for 226 * curves over GF(2^m), this is the irreducible polynomial defining the 227 * field. 228 */ 229 BIGNUM field; 230 /* 231 * Field specification for curves over GF(2^m). The irreducible f(t) is 232 * then of the form: t^poly[0] + t^poly[1] + ... + t^poly[k] where m = 233 * poly[0] > poly[1] > ... > poly[k] = 0. The array is terminated with 234 * poly[k+1]=-1. All elliptic curve irreducibles have at most 5 non-zero 235 * terms. 236 */ 237 int poly[6]; 238 /* 239 * Curve coefficients. (Here the assumption is that BIGNUMs can be used 240 * or abused for all kinds of fields, not just GF(p).) For characteristic 241 * > 3, the curve is defined by a Weierstrass equation of the form y^2 = 242 * x^3 + a*x + b. For characteristic 2, the curve is defined by an 243 * equation of the form y^2 + x*y = x^3 + a*x^2 + b. 244 */ 245 BIGNUM a, b; 246 /* enable optimized point arithmetics for special case */ 247 int a_is_minus3; 248 /* method-specific (e.g., Montgomery structure) */ 249 void *field_data1; 250 /* method-specific */ 251 void *field_data2; 252 /* method-specific */ 253 int (*field_mod_func) (BIGNUM *, const BIGNUM *, const BIGNUM *, 254 BN_CTX *); 255} /* EC_GROUP */ ; 256 257struct ec_key_st { 258 int version; 259 EC_GROUP *group; 260 EC_POINT *pub_key; 261 BIGNUM *priv_key; 262 unsigned int enc_flag; 263 point_conversion_form_t conv_form; 264 int references; 265 int flags; 266 EC_EXTRA_DATA *method_data; 267} /* EC_KEY */ ; 268 269/* 270 * Basically a 'mixin' for extra data, but available for EC_GROUPs/EC_KEYs 271 * only (with visibility limited to 'package' level for now). We use the 272 * function pointers as index for retrieval; this obviates global 273 * ex_data-style index tables. 274 */ 275int EC_EX_DATA_set_data(EC_EXTRA_DATA **, void *data, 276 void *(*dup_func) (void *), 277 void (*free_func) (void *), 278 void (*clear_free_func) (void *)); 279void *EC_EX_DATA_get_data(const EC_EXTRA_DATA *, void *(*dup_func) (void *), 280 void (*free_func) (void *), 281 void (*clear_free_func) (void *)); 282void EC_EX_DATA_free_data(EC_EXTRA_DATA **, void *(*dup_func) (void *), 283 void (*free_func) (void *), 284 void (*clear_free_func) (void *)); 285void EC_EX_DATA_clear_free_data(EC_EXTRA_DATA **, void *(*dup_func) (void *), 286 void (*free_func) (void *), 287 void (*clear_free_func) (void *)); 288void EC_EX_DATA_free_all_data(EC_EXTRA_DATA **); 289void EC_EX_DATA_clear_free_all_data(EC_EXTRA_DATA **); 290 291struct ec_point_st { 292 const EC_METHOD *meth; 293 /* 294 * All members except 'meth' are handled by the method functions, even if 295 * they appear generic 296 */ 297 BIGNUM X; 298 BIGNUM Y; 299 BIGNUM Z; /* Jacobian projective coordinates: (X, Y, Z) 300 * represents (X/Z^2, Y/Z^3) if Z != 0 */ 301 int Z_is_one; /* enable optimized point arithmetics for 302 * special case */ 303} /* EC_POINT */ ; 304 305/* 306 * method functions in ec_mult.c (ec_lib.c uses these as defaults if 307 * group->method->mul is 0) 308 */ 309int ec_wNAF_mul(const EC_GROUP *group, EC_POINT *r, const BIGNUM *scalar, 310 size_t num, const EC_POINT *points[], const BIGNUM *scalars[], 311 BN_CTX *); 312int ec_wNAF_precompute_mult(EC_GROUP *group, BN_CTX *); 313int ec_wNAF_have_precompute_mult(const EC_GROUP *group); 314 315/* method functions in ecp_smpl.c */ 316int ec_GFp_simple_group_init(EC_GROUP *); 317void ec_GFp_simple_group_finish(EC_GROUP *); 318void ec_GFp_simple_group_clear_finish(EC_GROUP *); 319int ec_GFp_simple_group_copy(EC_GROUP *, const EC_GROUP *); 320int ec_GFp_simple_group_set_curve(EC_GROUP *, const BIGNUM *p, 321 const BIGNUM *a, const BIGNUM *b, BN_CTX *); 322int ec_GFp_simple_group_get_curve(const EC_GROUP *, BIGNUM *p, BIGNUM *a, 323 BIGNUM *b, BN_CTX *); 324int ec_GFp_simple_group_get_degree(const EC_GROUP *); 325int ec_GFp_simple_group_check_discriminant(const EC_GROUP *, BN_CTX *); 326int ec_GFp_simple_point_init(EC_POINT *); 327void ec_GFp_simple_point_finish(EC_POINT *); 328void ec_GFp_simple_point_clear_finish(EC_POINT *); 329int ec_GFp_simple_point_copy(EC_POINT *, const EC_POINT *); 330int ec_GFp_simple_point_set_to_infinity(const EC_GROUP *, EC_POINT *); 331int ec_GFp_simple_set_Jprojective_coordinates_GFp(const EC_GROUP *, 332 EC_POINT *, const BIGNUM *x, 333 const BIGNUM *y, 334 const BIGNUM *z, BN_CTX *); 335int ec_GFp_simple_get_Jprojective_coordinates_GFp(const EC_GROUP *, 336 const EC_POINT *, BIGNUM *x, 337 BIGNUM *y, BIGNUM *z, 338 BN_CTX *); 339int ec_GFp_simple_point_set_affine_coordinates(const EC_GROUP *, EC_POINT *, 340 const BIGNUM *x, 341 const BIGNUM *y, BN_CTX *); 342int ec_GFp_simple_point_get_affine_coordinates(const EC_GROUP *, 343 const EC_POINT *, BIGNUM *x, 344 BIGNUM *y, BN_CTX *); 345int ec_GFp_simple_set_compressed_coordinates(const EC_GROUP *, EC_POINT *, 346 const BIGNUM *x, int y_bit, 347 BN_CTX *); 348size_t ec_GFp_simple_point2oct(const EC_GROUP *, const EC_POINT *, 349 point_conversion_form_t form, 350 unsigned char *buf, size_t len, BN_CTX *); 351int ec_GFp_simple_oct2point(const EC_GROUP *, EC_POINT *, 352 const unsigned char *buf, size_t len, BN_CTX *); 353int ec_GFp_simple_add(const EC_GROUP *, EC_POINT *r, const EC_POINT *a, 354 const EC_POINT *b, BN_CTX *); 355int ec_GFp_simple_dbl(const EC_GROUP *, EC_POINT *r, const EC_POINT *a, 356 BN_CTX *); 357int ec_GFp_simple_invert(const EC_GROUP *, EC_POINT *, BN_CTX *); 358int ec_GFp_simple_is_at_infinity(const EC_GROUP *, const EC_POINT *); 359int ec_GFp_simple_is_on_curve(const EC_GROUP *, const EC_POINT *, BN_CTX *); 360int ec_GFp_simple_cmp(const EC_GROUP *, const EC_POINT *a, const EC_POINT *b, 361 BN_CTX *); 362int ec_GFp_simple_make_affine(const EC_GROUP *, EC_POINT *, BN_CTX *); 363int ec_GFp_simple_points_make_affine(const EC_GROUP *, size_t num, 364 EC_POINT *[], BN_CTX *); 365int ec_GFp_simple_field_mul(const EC_GROUP *, BIGNUM *r, const BIGNUM *a, 366 const BIGNUM *b, BN_CTX *); 367int ec_GFp_simple_field_sqr(const EC_GROUP *, BIGNUM *r, const BIGNUM *a, 368 BN_CTX *); 369 370/* method functions in ecp_mont.c */ 371int ec_GFp_mont_group_init(EC_GROUP *); 372int ec_GFp_mont_group_set_curve(EC_GROUP *, const BIGNUM *p, const BIGNUM *a, 373 const BIGNUM *b, BN_CTX *); 374void ec_GFp_mont_group_finish(EC_GROUP *); 375void ec_GFp_mont_group_clear_finish(EC_GROUP *); 376int ec_GFp_mont_group_copy(EC_GROUP *, const EC_GROUP *); 377int ec_GFp_mont_field_mul(const EC_GROUP *, BIGNUM *r, const BIGNUM *a, 378 const BIGNUM *b, BN_CTX *); 379int ec_GFp_mont_field_sqr(const EC_GROUP *, BIGNUM *r, const BIGNUM *a, 380 BN_CTX *); 381int ec_GFp_mont_field_encode(const EC_GROUP *, BIGNUM *r, const BIGNUM *a, 382 BN_CTX *); 383int ec_GFp_mont_field_decode(const EC_GROUP *, BIGNUM *r, const BIGNUM *a, 384 BN_CTX *); 385int ec_GFp_mont_field_set_to_one(const EC_GROUP *, BIGNUM *r, BN_CTX *); 386 387/* method functions in ecp_nist.c */ 388int ec_GFp_nist_group_copy(EC_GROUP *dest, const EC_GROUP *src); 389int ec_GFp_nist_group_set_curve(EC_GROUP *, const BIGNUM *p, const BIGNUM *a, 390 const BIGNUM *b, BN_CTX *); 391int ec_GFp_nist_field_mul(const EC_GROUP *, BIGNUM *r, const BIGNUM *a, 392 const BIGNUM *b, BN_CTX *); 393int ec_GFp_nist_field_sqr(const EC_GROUP *, BIGNUM *r, const BIGNUM *a, 394 BN_CTX *); 395 396/* method functions in ec2_smpl.c */ 397int ec_GF2m_simple_group_init(EC_GROUP *); 398void ec_GF2m_simple_group_finish(EC_GROUP *); 399void ec_GF2m_simple_group_clear_finish(EC_GROUP *); 400int ec_GF2m_simple_group_copy(EC_GROUP *, const EC_GROUP *); 401int ec_GF2m_simple_group_set_curve(EC_GROUP *, const BIGNUM *p, 402 const BIGNUM *a, const BIGNUM *b, 403 BN_CTX *); 404int ec_GF2m_simple_group_get_curve(const EC_GROUP *, BIGNUM *p, BIGNUM *a, 405 BIGNUM *b, BN_CTX *); 406int ec_GF2m_simple_group_get_degree(const EC_GROUP *); 407int ec_GF2m_simple_group_check_discriminant(const EC_GROUP *, BN_CTX *); 408int ec_GF2m_simple_point_init(EC_POINT *); 409void ec_GF2m_simple_point_finish(EC_POINT *); 410void ec_GF2m_simple_point_clear_finish(EC_POINT *); 411int ec_GF2m_simple_point_copy(EC_POINT *, const EC_POINT *); 412int ec_GF2m_simple_point_set_to_infinity(const EC_GROUP *, EC_POINT *); 413int ec_GF2m_simple_point_set_affine_coordinates(const EC_GROUP *, EC_POINT *, 414 const BIGNUM *x, 415 const BIGNUM *y, BN_CTX *); 416int ec_GF2m_simple_point_get_affine_coordinates(const EC_GROUP *, 417 const EC_POINT *, BIGNUM *x, 418 BIGNUM *y, BN_CTX *); 419int ec_GF2m_simple_set_compressed_coordinates(const EC_GROUP *, EC_POINT *, 420 const BIGNUM *x, int y_bit, 421 BN_CTX *); 422size_t ec_GF2m_simple_point2oct(const EC_GROUP *, const EC_POINT *, 423 point_conversion_form_t form, 424 unsigned char *buf, size_t len, BN_CTX *); 425int ec_GF2m_simple_oct2point(const EC_GROUP *, EC_POINT *, 426 const unsigned char *buf, size_t len, BN_CTX *); 427int ec_GF2m_simple_add(const EC_GROUP *, EC_POINT *r, const EC_POINT *a, 428 const EC_POINT *b, BN_CTX *); 429int ec_GF2m_simple_dbl(const EC_GROUP *, EC_POINT *r, const EC_POINT *a, 430 BN_CTX *); 431int ec_GF2m_simple_invert(const EC_GROUP *, EC_POINT *, BN_CTX *); 432int ec_GF2m_simple_is_at_infinity(const EC_GROUP *, const EC_POINT *); 433int ec_GF2m_simple_is_on_curve(const EC_GROUP *, const EC_POINT *, BN_CTX *); 434int ec_GF2m_simple_cmp(const EC_GROUP *, const EC_POINT *a, const EC_POINT *b, 435 BN_CTX *); 436int ec_GF2m_simple_make_affine(const EC_GROUP *, EC_POINT *, BN_CTX *); 437int ec_GF2m_simple_points_make_affine(const EC_GROUP *, size_t num, 438 EC_POINT *[], BN_CTX *); 439int ec_GF2m_simple_field_mul(const EC_GROUP *, BIGNUM *r, const BIGNUM *a, 440 const BIGNUM *b, BN_CTX *); 441int ec_GF2m_simple_field_sqr(const EC_GROUP *, BIGNUM *r, const BIGNUM *a, 442 BN_CTX *); 443int ec_GF2m_simple_field_div(const EC_GROUP *, BIGNUM *r, const BIGNUM *a, 444 const BIGNUM *b, BN_CTX *); 445 446/* method functions in ec2_mult.c */ 447int ec_GF2m_simple_mul(const EC_GROUP *group, EC_POINT *r, 448 const BIGNUM *scalar, size_t num, 449 const EC_POINT *points[], const BIGNUM *scalars[], 450 BN_CTX *); 451int ec_GF2m_precompute_mult(EC_GROUP *group, BN_CTX *ctx); 452int ec_GF2m_have_precompute_mult(const EC_GROUP *group); 453 454#ifndef OPENSSL_NO_EC_NISTP_64_GCC_128 455/* method functions in ecp_nistp224.c */ 456int ec_GFp_nistp224_group_init(EC_GROUP *group); 457int ec_GFp_nistp224_group_set_curve(EC_GROUP *group, const BIGNUM *p, 458 const BIGNUM *a, const BIGNUM *n, 459 BN_CTX *); 460int ec_GFp_nistp224_point_get_affine_coordinates(const EC_GROUP *group, 461 const EC_POINT *point, 462 BIGNUM *x, BIGNUM *y, 463 BN_CTX *ctx); 464int ec_GFp_nistp224_mul(const EC_GROUP *group, EC_POINT *r, 465 const BIGNUM *scalar, size_t num, 466 const EC_POINT *points[], const BIGNUM *scalars[], 467 BN_CTX *); 468int ec_GFp_nistp224_points_mul(const EC_GROUP *group, EC_POINT *r, 469 const BIGNUM *scalar, size_t num, 470 const EC_POINT *points[], 471 const BIGNUM *scalars[], BN_CTX *ctx); 472int ec_GFp_nistp224_precompute_mult(EC_GROUP *group, BN_CTX *ctx); 473int ec_GFp_nistp224_have_precompute_mult(const EC_GROUP *group); 474 475/* method functions in ecp_nistp256.c */ 476int ec_GFp_nistp256_group_init(EC_GROUP *group); 477int ec_GFp_nistp256_group_set_curve(EC_GROUP *group, const BIGNUM *p, 478 const BIGNUM *a, const BIGNUM *n, 479 BN_CTX *); 480int ec_GFp_nistp256_point_get_affine_coordinates(const EC_GROUP *group, 481 const EC_POINT *point, 482 BIGNUM *x, BIGNUM *y, 483 BN_CTX *ctx); 484int ec_GFp_nistp256_mul(const EC_GROUP *group, EC_POINT *r, 485 const BIGNUM *scalar, size_t num, 486 const EC_POINT *points[], const BIGNUM *scalars[], 487 BN_CTX *); 488int ec_GFp_nistp256_points_mul(const EC_GROUP *group, EC_POINT *r, 489 const BIGNUM *scalar, size_t num, 490 const EC_POINT *points[], 491 const BIGNUM *scalars[], BN_CTX *ctx); 492int ec_GFp_nistp256_precompute_mult(EC_GROUP *group, BN_CTX *ctx); 493int ec_GFp_nistp256_have_precompute_mult(const EC_GROUP *group); 494 495/* method functions in ecp_nistp521.c */ 496int ec_GFp_nistp521_group_init(EC_GROUP *group); 497int ec_GFp_nistp521_group_set_curve(EC_GROUP *group, const BIGNUM *p, 498 const BIGNUM *a, const BIGNUM *n, 499 BN_CTX *); 500int ec_GFp_nistp521_point_get_affine_coordinates(const EC_GROUP *group, 501 const EC_POINT *point, 502 BIGNUM *x, BIGNUM *y, 503 BN_CTX *ctx); 504int ec_GFp_nistp521_mul(const EC_GROUP *group, EC_POINT *r, 505 const BIGNUM *scalar, size_t num, 506 const EC_POINT *points[], const BIGNUM *scalars[], 507 BN_CTX *); 508int ec_GFp_nistp521_points_mul(const EC_GROUP *group, EC_POINT *r, 509 const BIGNUM *scalar, size_t num, 510 const EC_POINT *points[], 511 const BIGNUM *scalars[], BN_CTX *ctx); 512int ec_GFp_nistp521_precompute_mult(EC_GROUP *group, BN_CTX *ctx); 513int ec_GFp_nistp521_have_precompute_mult(const EC_GROUP *group); 514 515/* utility functions in ecp_nistputil.c */ 516void ec_GFp_nistp_points_make_affine_internal(size_t num, void *point_array, 517 size_t felem_size, 518 void *tmp_felems, 519 void (*felem_one) (void *out), 520 int (*felem_is_zero) (const void 521 *in), 522 void (*felem_assign) (void *out, 523 const void 524 *in), 525 void (*felem_square) (void *out, 526 const void 527 *in), 528 void (*felem_mul) (void *out, 529 const void 530 *in1, 531 const void 532 *in2), 533 void (*felem_inv) (void *out, 534 const void 535 *in), 536 void (*felem_contract) (void 537 *out, 538 const 539 void 540 *in)); 541void ec_GFp_nistp_recode_scalar_bits(unsigned char *sign, 542 unsigned char *digit, unsigned char in); 543#endif 544