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 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 /* Use default functions for poin2oct, oct2point and compressed coordinates */ 86 #define EC_FLAGS_DEFAULT_OCT 0x1 87 88 /* Structure details are not part of the exported interface, 89 * so all this may change in future versions. */ 90 91 struct ec_method_st { 92 /* Various method flags */ 93 int flags; 94 /* used by EC_METHOD_get_field_type: */ 95 int field_type; /* a NID */ 96 97 /* used by EC_GROUP_new, EC_GROUP_free, EC_GROUP_clear_free, EC_GROUP_copy: */ 98 int (*group_init)(EC_GROUP *); 99 void (*group_finish)(EC_GROUP *); 100 void (*group_clear_finish)(EC_GROUP *); 101 int (*group_copy)(EC_GROUP *, const EC_GROUP *); 102 103 /* used by EC_GROUP_set_curve_GFp, EC_GROUP_get_curve_GFp, */ 104 /* EC_GROUP_set_curve_GF2m, and EC_GROUP_get_curve_GF2m: */ 105 int (*group_set_curve)(EC_GROUP *, const BIGNUM *p, const BIGNUM *a, const BIGNUM *b, BN_CTX *); 106 int (*group_get_curve)(const EC_GROUP *, BIGNUM *p, BIGNUM *a, BIGNUM *b, BN_CTX *); 107 108 /* used by EC_GROUP_get_degree: */ 109 int (*group_get_degree)(const EC_GROUP *); 110 111 /* used by EC_GROUP_check: */ 112 int (*group_check_discriminant)(const EC_GROUP *, BN_CTX *); 113 114 /* used by EC_POINT_new, EC_POINT_free, EC_POINT_clear_free, EC_POINT_copy: */ 115 int (*point_init)(EC_POINT *); 116 void (*point_finish)(EC_POINT *); 117 void (*point_clear_finish)(EC_POINT *); 118 int (*point_copy)(EC_POINT *, const EC_POINT *); 119 120 /* used by EC_POINT_set_to_infinity, 121 * EC_POINT_set_Jprojective_coordinates_GFp, 122 * EC_POINT_get_Jprojective_coordinates_GFp, 123 * EC_POINT_set_affine_coordinates_GFp, ..._GF2m, 124 * EC_POINT_get_affine_coordinates_GFp, ..._GF2m, 125 * EC_POINT_set_compressed_coordinates_GFp, ..._GF2m: 126 */ 127 int (*point_set_to_infinity)(const EC_GROUP *, EC_POINT *); 128 int (*point_set_Jprojective_coordinates_GFp)(const EC_GROUP *, EC_POINT *, 129 const BIGNUM *x, const BIGNUM *y, const BIGNUM *z, BN_CTX *); 130 int (*point_get_Jprojective_coordinates_GFp)(const EC_GROUP *, const EC_POINT *, 131 BIGNUM *x, BIGNUM *y, BIGNUM *z, BN_CTX *); 132 int (*point_set_affine_coordinates)(const EC_GROUP *, EC_POINT *, 133 const BIGNUM *x, const BIGNUM *y, BN_CTX *); 134 int (*point_get_affine_coordinates)(const EC_GROUP *, const EC_POINT *, 135 BIGNUM *x, BIGNUM *y, BN_CTX *); 136 int (*point_set_compressed_coordinates)(const EC_GROUP *, EC_POINT *, 137 const BIGNUM *x, int y_bit, BN_CTX *); 138 139 /* used by EC_POINT_point2oct, EC_POINT_oct2point: */ 140 size_t (*point2oct)(const EC_GROUP *, const EC_POINT *, point_conversion_form_t form, 141 unsigned char *buf, size_t len, BN_CTX *); 142 int (*oct2point)(const EC_GROUP *, EC_POINT *, 143 const unsigned char *buf, size_t len, BN_CTX *); 144 145 /* used by EC_POINT_add, EC_POINT_dbl, ECP_POINT_invert: */ 146 int (*add)(const EC_GROUP *, EC_POINT *r, const EC_POINT *a, const EC_POINT *b, BN_CTX *); 147 int (*dbl)(const EC_GROUP *, EC_POINT *r, const EC_POINT *a, BN_CTX *); 148 int (*invert)(const EC_GROUP *, EC_POINT *, BN_CTX *); 149 150 /* used by EC_POINT_is_at_infinity, EC_POINT_is_on_curve, EC_POINT_cmp: */ 151 int (*is_at_infinity)(const EC_GROUP *, const EC_POINT *); 152 int (*is_on_curve)(const EC_GROUP *, const EC_POINT *, BN_CTX *); 153 int (*point_cmp)(const EC_GROUP *, const EC_POINT *a, const EC_POINT *b, BN_CTX *); 154 155 /* used by EC_POINT_make_affine, EC_POINTs_make_affine: */ 156 int (*make_affine)(const EC_GROUP *, EC_POINT *, BN_CTX *); 157 int (*points_make_affine)(const EC_GROUP *, size_t num, EC_POINT *[], BN_CTX *); 158 159 /* used by EC_POINTs_mul, EC_POINT_mul, EC_POINT_precompute_mult, EC_POINT_have_precompute_mult 160 * (default implementations are used if the 'mul' pointer is 0): */ 161 int (*mul)(const EC_GROUP *group, EC_POINT *r, const BIGNUM *scalar, 162 size_t num, const EC_POINT *points[], const BIGNUM *scalars[], BN_CTX *); 163 int (*precompute_mult)(EC_GROUP *group, BN_CTX *); 164 int (*have_precompute_mult)(const EC_GROUP *group); 165 166 167 /* internal functions */ 168 169 /* 'field_mul', 'field_sqr', and 'field_div' can be used by 'add' and 'dbl' so that 170 * the same implementations of point operations can be used with different 171 * optimized implementations of expensive field operations: */ 172 int (*field_mul)(const EC_GROUP *, BIGNUM *r, const BIGNUM *a, const BIGNUM *b, BN_CTX *); 173 int (*field_sqr)(const EC_GROUP *, BIGNUM *r, const BIGNUM *a, BN_CTX *); 174 int (*field_div)(const EC_GROUP *, BIGNUM *r, const BIGNUM *a, const BIGNUM *b, BN_CTX *); 175 176 int (*field_encode)(const EC_GROUP *, BIGNUM *r, const BIGNUM *a, BN_CTX *); /* e.g. to Montgomery */ 177 int (*field_decode)(const EC_GROUP *, BIGNUM *r, const BIGNUM *a, BN_CTX *); /* e.g. from Montgomery */ 178 int (*field_set_to_one)(const EC_GROUP *, BIGNUM *r, BN_CTX *); 179 } /* EC_METHOD */; 180 181 typedef struct ec_extra_data_st { 182 struct ec_extra_data_st *next; 183 void *data; 184 void *(*dup_func)(void *); 185 void (*free_func)(void *); 186 void (*clear_free_func)(void *); 187 } EC_EXTRA_DATA; /* used in EC_GROUP */ 188 189 struct ec_group_st { 190 const EC_METHOD *meth; 191 192 EC_POINT *generator; /* optional */ 193 BIGNUM order, cofactor; 194 195 int curve_name;/* optional NID for named curve */ 196 int asn1_flag; /* flag to control the asn1 encoding */ 197 point_conversion_form_t asn1_form; 198 199 unsigned char *seed; /* optional seed for parameters (appears in ASN1) */ 200 size_t seed_len; 201 202 EC_EXTRA_DATA *extra_data; /* linked list */ 203 204 /* The following members are handled by the method functions, 205 * even if they appear generic */ 206 207 BIGNUM field; /* Field specification. 208 * For curves over GF(p), this is the modulus; 209 * for curves over GF(2^m), this is the 210 * irreducible polynomial defining the field. 211 */ 212 213 int poly[6]; /* Field specification for curves over GF(2^m). 214 * The irreducible f(t) is then of the form: 215 * t^poly[0] + t^poly[1] + ... + t^poly[k] 216 * where m = poly[0] > poly[1] > ... > poly[k] = 0. 217 * The array is terminated with poly[k+1]=-1. 218 * All elliptic curve irreducibles have at most 5 219 * non-zero terms. 220 */ 221 222 BIGNUM a, b; /* Curve coefficients. 223 * (Here the assumption is that BIGNUMs can be used 224 * or abused for all kinds of fields, not just GF(p).) 225 * For characteristic > 3, the curve is defined 226 * by a Weierstrass equation of the form 227 * y^2 = x^3 + a*x + b. 228 * For characteristic 2, the curve is defined by 229 * an equation of the form 230 * y^2 + x*y = x^3 + a*x^2 + b. 231 */ 232 233 int a_is_minus3; /* enable optimized point arithmetics for special case */ 234 235 void *field_data1; /* method-specific (e.g., Montgomery structure) */ 236 void *field_data2; /* method-specific */ 237 int (*field_mod_func)(BIGNUM *, const BIGNUM *, const BIGNUM *, BN_CTX *); /* method-specific */ 238 } /* EC_GROUP */; 239 240 struct ec_key_st { 241 int version; 242 243 EC_GROUP *group; 244 245 EC_POINT *pub_key; 246 BIGNUM *priv_key; 247 248 unsigned int enc_flag; 249 point_conversion_form_t conv_form; 250 251 int references; 252 int flags; 253 254 EC_EXTRA_DATA *method_data; 255 } /* EC_KEY */; 256 257 /* Basically a 'mixin' for extra data, but available for EC_GROUPs/EC_KEYs only 258 * (with visibility limited to 'package' level for now). 259 * We use the function pointers as index for retrieval; this obviates 260 * global ex_data-style index tables. 261 */ 262 int EC_EX_DATA_set_data(EC_EXTRA_DATA **, void *data, 263 void *(*dup_func)(void *), void (*free_func)(void *), void (*clear_free_func)(void *)); 264 void *EC_EX_DATA_get_data(const EC_EXTRA_DATA *, 265 void *(*dup_func)(void *), void (*free_func)(void *), void (*clear_free_func)(void *)); 266 void EC_EX_DATA_free_data(EC_EXTRA_DATA **, 267 void *(*dup_func)(void *), void (*free_func)(void *), void (*clear_free_func)(void *)); 268 void EC_EX_DATA_clear_free_data(EC_EXTRA_DATA **, 269 void *(*dup_func)(void *), void (*free_func)(void *), void (*clear_free_func)(void *)); 270 void EC_EX_DATA_free_all_data(EC_EXTRA_DATA **); 271 void EC_EX_DATA_clear_free_all_data(EC_EXTRA_DATA **); 272 273 274 275 struct ec_point_st { 276 const EC_METHOD *meth; 277 278 /* All members except 'meth' are handled by the method functions, 279 * even if they appear generic */ 280 281 BIGNUM X; 282 BIGNUM Y; 283 BIGNUM Z; /* Jacobian projective coordinates: 284 * (X, Y, Z) represents (X/Z^2, Y/Z^3) if Z != 0 */ 285 int Z_is_one; /* enable optimized point arithmetics for special case */ 286 } /* EC_POINT */; 287 288 289 290 /* method functions in ec_mult.c 291 * (ec_lib.c uses these as defaults if group->method->mul is 0) */ 292 int ec_wNAF_mul(const EC_GROUP *group, EC_POINT *r, const BIGNUM *scalar, 293 size_t num, const EC_POINT *points[], const BIGNUM *scalars[], BN_CTX *); 294 int ec_wNAF_precompute_mult(EC_GROUP *group, BN_CTX *); 295 int ec_wNAF_have_precompute_mult(const EC_GROUP *group); 296 297 298 /* method functions in ecp_smpl.c */ 299 int ec_GFp_simple_group_init(EC_GROUP *); 300 void ec_GFp_simple_group_finish(EC_GROUP *); 301 void ec_GFp_simple_group_clear_finish(EC_GROUP *); 302 int ec_GFp_simple_group_copy(EC_GROUP *, const EC_GROUP *); 303 int ec_GFp_simple_group_set_curve(EC_GROUP *, const BIGNUM *p, const BIGNUM *a, const BIGNUM *b, BN_CTX *); 304 int ec_GFp_simple_group_get_curve(const EC_GROUP *, BIGNUM *p, BIGNUM *a, BIGNUM *b, BN_CTX *); 305 int ec_GFp_simple_group_get_degree(const EC_GROUP *); 306 int ec_GFp_simple_group_check_discriminant(const EC_GROUP *, BN_CTX *); 307 int ec_GFp_simple_point_init(EC_POINT *); 308 void ec_GFp_simple_point_finish(EC_POINT *); 309 void ec_GFp_simple_point_clear_finish(EC_POINT *); 310 int ec_GFp_simple_point_copy(EC_POINT *, const EC_POINT *); 311 int ec_GFp_simple_point_set_to_infinity(const EC_GROUP *, EC_POINT *); 312 int ec_GFp_simple_set_Jprojective_coordinates_GFp(const EC_GROUP *, EC_POINT *, 313 const BIGNUM *x, const BIGNUM *y, const BIGNUM *z, BN_CTX *); 314 int ec_GFp_simple_get_Jprojective_coordinates_GFp(const EC_GROUP *, const EC_POINT *, 315 BIGNUM *x, BIGNUM *y, BIGNUM *z, BN_CTX *); 316 int ec_GFp_simple_point_set_affine_coordinates(const EC_GROUP *, EC_POINT *, 317 const BIGNUM *x, const BIGNUM *y, BN_CTX *); 318 int ec_GFp_simple_point_get_affine_coordinates(const EC_GROUP *, const EC_POINT *, 319 BIGNUM *x, BIGNUM *y, BN_CTX *); 320 int ec_GFp_simple_set_compressed_coordinates(const EC_GROUP *, EC_POINT *, 321 const BIGNUM *x, int y_bit, BN_CTX *); 322 size_t ec_GFp_simple_point2oct(const EC_GROUP *, const EC_POINT *, point_conversion_form_t form, 323 unsigned char *buf, size_t len, BN_CTX *); 324 int ec_GFp_simple_oct2point(const EC_GROUP *, EC_POINT *, 325 const unsigned char *buf, size_t len, BN_CTX *); 326 int ec_GFp_simple_add(const EC_GROUP *, EC_POINT *r, const EC_POINT *a, const EC_POINT *b, BN_CTX *); 327 int ec_GFp_simple_dbl(const EC_GROUP *, EC_POINT *r, const EC_POINT *a, BN_CTX *); 328 int ec_GFp_simple_invert(const EC_GROUP *, EC_POINT *, BN_CTX *); 329 int ec_GFp_simple_is_at_infinity(const EC_GROUP *, const EC_POINT *); 330 int ec_GFp_simple_is_on_curve(const EC_GROUP *, const EC_POINT *, BN_CTX *); 331 int ec_GFp_simple_cmp(const EC_GROUP *, const EC_POINT *a, const EC_POINT *b, BN_CTX *); 332 int ec_GFp_simple_make_affine(const EC_GROUP *, EC_POINT *, BN_CTX *); 333 int ec_GFp_simple_points_make_affine(const EC_GROUP *, size_t num, EC_POINT *[], BN_CTX *); 334 int ec_GFp_simple_field_mul(const EC_GROUP *, BIGNUM *r, const BIGNUM *a, const BIGNUM *b, BN_CTX *); 335 int ec_GFp_simple_field_sqr(const EC_GROUP *, BIGNUM *r, const BIGNUM *a, BN_CTX *); 336 337 338 /* method functions in ecp_mont.c */ 339 int ec_GFp_mont_group_init(EC_GROUP *); 340 int ec_GFp_mont_group_set_curve(EC_GROUP *, const BIGNUM *p, const BIGNUM *a, const BIGNUM *b, BN_CTX *); 341 void ec_GFp_mont_group_finish(EC_GROUP *); 342 void ec_GFp_mont_group_clear_finish(EC_GROUP *); 343 int ec_GFp_mont_group_copy(EC_GROUP *, const EC_GROUP *); 344 int ec_GFp_mont_field_mul(const EC_GROUP *, BIGNUM *r, const BIGNUM *a, const BIGNUM *b, BN_CTX *); 345 int ec_GFp_mont_field_sqr(const EC_GROUP *, BIGNUM *r, const BIGNUM *a, BN_CTX *); 346 int ec_GFp_mont_field_encode(const EC_GROUP *, BIGNUM *r, const BIGNUM *a, BN_CTX *); 347 int ec_GFp_mont_field_decode(const EC_GROUP *, BIGNUM *r, const BIGNUM *a, BN_CTX *); 348 int ec_GFp_mont_field_set_to_one(const EC_GROUP *, BIGNUM *r, BN_CTX *); 349 350 351 /* method functions in ecp_nist.c */ 352 int ec_GFp_nist_group_copy(EC_GROUP *dest, const EC_GROUP *src); 353 int ec_GFp_nist_group_set_curve(EC_GROUP *, const BIGNUM *p, const BIGNUM *a, const BIGNUM *b, BN_CTX *); 354 int ec_GFp_nist_field_mul(const EC_GROUP *, BIGNUM *r, const BIGNUM *a, const BIGNUM *b, BN_CTX *); 355 int ec_GFp_nist_field_sqr(const EC_GROUP *, BIGNUM *r, const BIGNUM *a, BN_CTX *); 356 357 358 /* method functions in ec2_smpl.c */ 359 int ec_GF2m_simple_group_init(EC_GROUP *); 360 void ec_GF2m_simple_group_finish(EC_GROUP *); 361 void ec_GF2m_simple_group_clear_finish(EC_GROUP *); 362 int ec_GF2m_simple_group_copy(EC_GROUP *, const EC_GROUP *); 363 int ec_GF2m_simple_group_set_curve(EC_GROUP *, const BIGNUM *p, const BIGNUM *a, const BIGNUM *b, BN_CTX *); 364 int ec_GF2m_simple_group_get_curve(const EC_GROUP *, BIGNUM *p, BIGNUM *a, BIGNUM *b, BN_CTX *); 365 int ec_GF2m_simple_group_get_degree(const EC_GROUP *); 366 int ec_GF2m_simple_group_check_discriminant(const EC_GROUP *, BN_CTX *); 367 int ec_GF2m_simple_point_init(EC_POINT *); 368 void ec_GF2m_simple_point_finish(EC_POINT *); 369 void ec_GF2m_simple_point_clear_finish(EC_POINT *); 370 int ec_GF2m_simple_point_copy(EC_POINT *, const EC_POINT *); 371 int ec_GF2m_simple_point_set_to_infinity(const EC_GROUP *, EC_POINT *); 372 int ec_GF2m_simple_point_set_affine_coordinates(const EC_GROUP *, EC_POINT *, 373 const BIGNUM *x, const BIGNUM *y, BN_CTX *); 374 int ec_GF2m_simple_point_get_affine_coordinates(const EC_GROUP *, const EC_POINT *, 375 BIGNUM *x, BIGNUM *y, BN_CTX *); 376 int ec_GF2m_simple_set_compressed_coordinates(const EC_GROUP *, EC_POINT *, 377 const BIGNUM *x, int y_bit, BN_CTX *); 378 size_t ec_GF2m_simple_point2oct(const EC_GROUP *, const EC_POINT *, point_conversion_form_t form, 379 unsigned char *buf, size_t len, BN_CTX *); 380 int ec_GF2m_simple_oct2point(const EC_GROUP *, EC_POINT *, 381 const unsigned char *buf, size_t len, BN_CTX *); 382 int ec_GF2m_simple_add(const EC_GROUP *, EC_POINT *r, const EC_POINT *a, const EC_POINT *b, BN_CTX *); 383 int ec_GF2m_simple_dbl(const EC_GROUP *, EC_POINT *r, const EC_POINT *a, BN_CTX *); 384 int ec_GF2m_simple_invert(const EC_GROUP *, EC_POINT *, BN_CTX *); 385 int ec_GF2m_simple_is_at_infinity(const EC_GROUP *, const EC_POINT *); 386 int ec_GF2m_simple_is_on_curve(const EC_GROUP *, const EC_POINT *, BN_CTX *); 387 int ec_GF2m_simple_cmp(const EC_GROUP *, const EC_POINT *a, const EC_POINT *b, BN_CTX *); 388 int ec_GF2m_simple_make_affine(const EC_GROUP *, EC_POINT *, BN_CTX *); 389 int ec_GF2m_simple_points_make_affine(const EC_GROUP *, size_t num, EC_POINT *[], BN_CTX *); 390 int ec_GF2m_simple_field_mul(const EC_GROUP *, BIGNUM *r, const BIGNUM *a, const BIGNUM *b, BN_CTX *); 391 int ec_GF2m_simple_field_sqr(const EC_GROUP *, BIGNUM *r, const BIGNUM *a, BN_CTX *); 392 int ec_GF2m_simple_field_div(const EC_GROUP *, BIGNUM *r, const BIGNUM *a, const BIGNUM *b, BN_CTX *); 393 394 395 /* method functions in ec2_mult.c */ 396 int ec_GF2m_simple_mul(const EC_GROUP *group, EC_POINT *r, const BIGNUM *scalar, 397 size_t num, const EC_POINT *points[], const BIGNUM *scalars[], BN_CTX *); 398 int ec_GF2m_precompute_mult(EC_GROUP *group, BN_CTX *ctx); 399 int ec_GF2m_have_precompute_mult(const EC_GROUP *group); 400 401 /* method functions in ec2_mult.c */ 402 int ec_GF2m_simple_mul(const EC_GROUP *group, EC_POINT *r, const BIGNUM *scalar, 403 size_t num, const EC_POINT *points[], const BIGNUM *scalars[], BN_CTX *); 404 int ec_GF2m_precompute_mult(EC_GROUP *group, BN_CTX *ctx); 405 int ec_GF2m_have_precompute_mult(const EC_GROUP *group); 406 407 #ifndef OPENSSL_EC_NISTP_64_GCC_128 408 /* method functions in ecp_nistp224.c */ 409 int ec_GFp_nistp224_group_init(EC_GROUP *group); 410 int ec_GFp_nistp224_group_set_curve(EC_GROUP *group, const BIGNUM *p, const BIGNUM *a, const BIGNUM *n, BN_CTX *); 411 int ec_GFp_nistp224_point_get_affine_coordinates(const EC_GROUP *group, const EC_POINT *point, BIGNUM *x, BIGNUM *y, BN_CTX *ctx); 412 int ec_GFp_nistp224_mul(const EC_GROUP *group, EC_POINT *r, const BIGNUM *scalar, size_t num, const EC_POINT *points[], const BIGNUM *scalars[], BN_CTX *); 413 int ec_GFp_nistp224_points_mul(const EC_GROUP *group, EC_POINT *r, const BIGNUM *scalar, size_t num, const EC_POINT *points[], const BIGNUM *scalars[], BN_CTX *ctx); 414 int ec_GFp_nistp224_precompute_mult(EC_GROUP *group, BN_CTX *ctx); 415 int ec_GFp_nistp224_have_precompute_mult(const EC_GROUP *group); 416 417 /* method functions in ecp_nistp256.c */ 418 int ec_GFp_nistp256_group_init(EC_GROUP *group); 419 int ec_GFp_nistp256_group_set_curve(EC_GROUP *group, const BIGNUM *p, const BIGNUM *a, const BIGNUM *n, BN_CTX *); 420 int ec_GFp_nistp256_point_get_affine_coordinates(const EC_GROUP *group, const EC_POINT *point, BIGNUM *x, BIGNUM *y, BN_CTX *ctx); 421 int ec_GFp_nistp256_mul(const EC_GROUP *group, EC_POINT *r, const BIGNUM *scalar, size_t num, const EC_POINT *points[], const BIGNUM *scalars[], BN_CTX *); 422 int ec_GFp_nistp256_points_mul(const EC_GROUP *group, EC_POINT *r, const BIGNUM *scalar, size_t num, const EC_POINT *points[], const BIGNUM *scalars[], BN_CTX *ctx); 423 int ec_GFp_nistp256_precompute_mult(EC_GROUP *group, BN_CTX *ctx); 424 int ec_GFp_nistp256_have_precompute_mult(const EC_GROUP *group); 425 426 /* method functions in ecp_nistp521.c */ 427 int ec_GFp_nistp521_group_init(EC_GROUP *group); 428 int ec_GFp_nistp521_group_set_curve(EC_GROUP *group, const BIGNUM *p, const BIGNUM *a, const BIGNUM *n, BN_CTX *); 429 int ec_GFp_nistp521_point_get_affine_coordinates(const EC_GROUP *group, const EC_POINT *point, BIGNUM *x, BIGNUM *y, BN_CTX *ctx); 430 int ec_GFp_nistp521_mul(const EC_GROUP *group, EC_POINT *r, const BIGNUM *scalar, size_t num, const EC_POINT *points[], const BIGNUM *scalars[], BN_CTX *); 431 int ec_GFp_nistp521_points_mul(const EC_GROUP *group, EC_POINT *r, const BIGNUM *scalar, size_t num, const EC_POINT *points[], const BIGNUM *scalars[], BN_CTX *ctx); 432 int ec_GFp_nistp521_precompute_mult(EC_GROUP *group, BN_CTX *ctx); 433 int ec_GFp_nistp521_have_precompute_mult(const EC_GROUP *group); 434 435 /* utility functions in ecp_nistputil.c */ 436 void ec_GFp_nistp_points_make_affine_internal(size_t num, void *point_array, 437 size_t felem_size, void *tmp_felems, 438 void (*felem_one)(void *out), 439 int (*felem_is_zero)(const void *in), 440 void (*felem_assign)(void *out, const void *in), 441 void (*felem_square)(void *out, const void *in), 442 void (*felem_mul)(void *out, const void *in1, const void *in2), 443 void (*felem_inv)(void *out, const void *in), 444 void (*felem_contract)(void *out, const void *in)); 445 void ec_GFp_nistp_recode_scalar_bits(unsigned char *sign, unsigned char *digit, unsigned char in); 446 #endif 447