1 /* Originally written by Bodo Moeller for the OpenSSL project. 2 * ==================================================================== 3 * Copyright (c) 1998-2005 The OpenSSL Project. All rights reserved. 4 * 5 * Redistribution and use in source and binary forms, with or without 6 * modification, are permitted provided that the following conditions 7 * are met: 8 * 9 * 1. Redistributions of source code must retain the above copyright 10 * notice, this list of conditions and the following disclaimer. 11 * 12 * 2. Redistributions in binary form must reproduce the above copyright 13 * notice, this list of conditions and the following disclaimer in 14 * the documentation and/or other materials provided with the 15 * distribution. 16 * 17 * 3. All advertising materials mentioning features or use of this 18 * software must display the following acknowledgment: 19 * "This product includes software developed by the OpenSSL Project 20 * for use in the OpenSSL Toolkit. (http://www.openssl.org/)" 21 * 22 * 4. The names "OpenSSL Toolkit" and "OpenSSL Project" must not be used to 23 * endorse or promote products derived from this software without 24 * prior written permission. For written permission, please contact 25 * openssl-core (at) openssl.org. 26 * 27 * 5. Products derived from this software may not be called "OpenSSL" 28 * nor may "OpenSSL" appear in their names without prior written 29 * permission of the OpenSSL Project. 30 * 31 * 6. Redistributions of any form whatsoever must retain the following 32 * acknowledgment: 33 * "This product includes software developed by the OpenSSL Project 34 * for use in the OpenSSL Toolkit (http://www.openssl.org/)" 35 * 36 * THIS SOFTWARE IS PROVIDED BY THE OpenSSL PROJECT ``AS IS'' AND ANY 37 * EXPRESSED OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE 38 * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR 39 * PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE OpenSSL PROJECT OR 40 * ITS CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, 41 * SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT 42 * NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; 43 * LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) 44 * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, 45 * STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) 46 * ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED 47 * OF THE POSSIBILITY OF SUCH DAMAGE. 48 * ==================================================================== 49 * 50 * This product includes cryptographic software written by Eric Young 51 * (eay (at) cryptsoft.com). This product includes software written by Tim 52 * Hudson (tjh (at) cryptsoft.com). 53 * 54 */ 55 /* ==================================================================== 56 * Copyright 2002 Sun Microsystems, Inc. ALL RIGHTS RESERVED. 57 * 58 * Portions of the attached software ("Contribution") are developed by 59 * SUN MICROSYSTEMS, INC., and are contributed to the OpenSSL project. 60 * 61 * The Contribution is licensed pursuant to the OpenSSL open source 62 * license provided above. 63 * 64 * The elliptic curve binary polynomial software is originally written by 65 * Sheueling Chang Shantz and Douglas Stebila of Sun Microsystems 66 * Laboratories. */ 67 68 #ifndef OPENSSL_HEADER_EC_INTERNAL_H 69 #define OPENSSL_HEADER_EC_INTERNAL_H 70 71 #include <openssl/base.h> 72 73 #include <openssl/bn.h> 74 #include <openssl/ex_data.h> 75 #include <openssl/thread.h> 76 #include <openssl/type_check.h> 77 78 #include "../bn/internal.h" 79 80 #if defined(__cplusplus) 81 extern "C" { 82 #endif 83 84 85 // Cap the size of all field elements and scalars, including custom curves, to 86 // 66 bytes, large enough to fit secp521r1 and brainpoolP512r1, which appear to 87 // be the largest fields anyone plausibly uses. 88 #define EC_MAX_BYTES 66 89 #define EC_MAX_WORDS ((EC_MAX_BYTES + BN_BYTES - 1) / BN_BYTES) 90 91 OPENSSL_STATIC_ASSERT(EC_MAX_WORDS <= BN_SMALL_MAX_WORDS, 92 "bn_*_small functions not usable"); 93 94 // An EC_SCALAR is an integer fully reduced modulo the order. Only the first 95 // |order->width| words are used. An |EC_SCALAR| is specific to an |EC_GROUP| 96 // and must not be mixed between groups. 97 typedef union { 98 // bytes is the representation of the scalar in little-endian order. 99 uint8_t bytes[EC_MAX_BYTES]; 100 BN_ULONG words[EC_MAX_WORDS]; 101 } EC_SCALAR; 102 103 // An EC_FELEM represents a field element. Only the first |field->width| words 104 // are used. An |EC_FELEM| is specific to an |EC_GROUP| and must not be mixed 105 // between groups. Additionally, the representation (whether or not elements are 106 // represented in Montgomery-form) may vary between |EC_METHOD|s. 107 typedef union { 108 // bytes is the representation of the field element in little-endian order. 109 uint8_t bytes[EC_MAX_BYTES]; 110 BN_ULONG words[EC_MAX_WORDS]; 111 } EC_FELEM; 112 113 // An EC_RAW_POINT represents an elliptic curve point. Unlike |EC_POINT|, it is 114 // a plain struct which can be stack-allocated and needs no cleanup. It is 115 // specific to an |EC_GROUP| and must not be mixed between groups. 116 typedef struct { 117 EC_FELEM X, Y, Z; 118 // X, Y, and Z are Jacobian projective coordinates. They represent 119 // (X/Z^2, Y/Z^3) if Z != 0 and the point at infinity otherwise. 120 } EC_RAW_POINT; 121 122 struct ec_method_st { 123 int (*group_init)(EC_GROUP *); 124 void (*group_finish)(EC_GROUP *); 125 int (*group_set_curve)(EC_GROUP *, const BIGNUM *p, const BIGNUM *a, 126 const BIGNUM *b, BN_CTX *); 127 128 // point_get_affine_coordinates sets |*x| and |*y| to the affine coordinates 129 // of |p|. Either |x| or |y| may be NULL to omit it. It returns one on success 130 // and zero if |p| is the point at infinity. 131 // 132 // Note: unlike |EC_FELEM|s used as intermediate values internal to the 133 // |EC_METHOD|, |*x| and |*y| are not encoded in Montgomery form. 134 int (*point_get_affine_coordinates)(const EC_GROUP *, const EC_RAW_POINT *p, 135 EC_FELEM *x, EC_FELEM *y); 136 137 // add sets |r| to |a| + |b|. 138 void (*add)(const EC_GROUP *group, EC_RAW_POINT *r, const EC_RAW_POINT *a, 139 const EC_RAW_POINT *b); 140 // dbl sets |r| to |a| + |a|. 141 void (*dbl)(const EC_GROUP *group, EC_RAW_POINT *r, const EC_RAW_POINT *a); 142 143 // Computes |r = g_scalar*generator + p_scalar*p| if |g_scalar| and |p_scalar| 144 // are both non-null. Computes |r = g_scalar*generator| if |p_scalar| is null. 145 // Computes |r = p_scalar*p| if g_scalar is null. At least one of |g_scalar| 146 // and |p_scalar| must be non-null, and |p| must be non-null if |p_scalar| is 147 // non-null. 148 void (*mul)(const EC_GROUP *group, EC_RAW_POINT *r, const EC_SCALAR *g_scalar, 149 const EC_RAW_POINT *p, const EC_SCALAR *p_scalar); 150 // mul_public performs the same computation as mul. It further assumes that 151 // the inputs are public so there is no concern about leaking their values 152 // through timing. 153 void (*mul_public)(const EC_GROUP *group, EC_RAW_POINT *r, 154 const EC_SCALAR *g_scalar, const EC_RAW_POINT *p, 155 const EC_SCALAR *p_scalar); 156 157 // felem_mul and felem_sqr implement multiplication and squaring, 158 // respectively, so that the generic |EC_POINT_add| and |EC_POINT_dbl| 159 // implementations can work both with |EC_GFp_mont_method| and the tuned 160 // operations. 161 // 162 // TODO(davidben): This constrains |EC_FELEM|'s internal representation, adds 163 // many indirect calls in the middle of the generic code, and a bunch of 164 // conversions. If p224-64.c were easily convertable to Montgomery form, we 165 // could say |EC_FELEM| is always in Montgomery form. If we routed the rest of 166 // simple.c to |EC_METHOD|, we could give |EC_POINT| an |EC_METHOD|-specific 167 // representation and say |EC_FELEM| is purely a |EC_GFp_mont_method| type. 168 void (*felem_mul)(const EC_GROUP *, EC_FELEM *r, const EC_FELEM *a, 169 const EC_FELEM *b); 170 void (*felem_sqr)(const EC_GROUP *, EC_FELEM *r, const EC_FELEM *a); 171 172 int (*bignum_to_felem)(const EC_GROUP *group, EC_FELEM *out, 173 const BIGNUM *in); 174 int (*felem_to_bignum)(const EC_GROUP *group, BIGNUM *out, 175 const EC_FELEM *in); 176 177 // scalar_inv_montgomery sets |out| to |in|^-1, where both input and output 178 // are in Montgomery form. 179 void (*scalar_inv_montgomery)(const EC_GROUP *group, EC_SCALAR *out, 180 const EC_SCALAR *in); 181 182 // scalar_inv_montgomery_vartime performs the same computation as 183 // |scalar_inv_montgomery|. It further assumes that the inputs are public so 184 // there is no concern about leaking their values through timing. 185 int (*scalar_inv_montgomery_vartime)(const EC_GROUP *group, EC_SCALAR *out, 186 const EC_SCALAR *in); 187 188 // cmp_x_coordinate compares the x (affine) coordinate of |p|, mod the group 189 // order, with |r|. It returns one if the values match and zero if |p| is the 190 // point at infinity of the values do not match. 191 int (*cmp_x_coordinate)(const EC_GROUP *group, const EC_RAW_POINT *p, 192 const EC_SCALAR *r); 193 } /* EC_METHOD */; 194 195 const EC_METHOD *EC_GFp_mont_method(void); 196 197 struct ec_group_st { 198 const EC_METHOD *meth; 199 200 // Unlike all other |EC_POINT|s, |generator| does not own |generator->group| 201 // to avoid a reference cycle. 202 EC_POINT *generator; 203 BIGNUM order; 204 205 int curve_name; // optional NID for named curve 206 207 BN_MONT_CTX *order_mont; // data for ECDSA inverse 208 209 // The following members are handled by the method functions, 210 // even if they appear generic 211 212 BIGNUM field; // For curves over GF(p), this is the modulus. 213 214 EC_FELEM a, b; // Curve coefficients. 215 216 // a_is_minus3 is one if |a| is -3 mod |field| and zero otherwise. Point 217 // arithmetic is optimized for -3. 218 int a_is_minus3; 219 220 // field_greater_than_order is one if |field| is greate than |order| and zero 221 // otherwise. 222 int field_greater_than_order; 223 224 // field_minus_order, if |field_greater_than_order| is true, is |field| minus 225 // |order| represented as an |EC_FELEM|. Otherwise, it is zero. 226 // 227 // Note: unlike |EC_FELEM|s used as intermediate values internal to the 228 // |EC_METHOD|, this value is not encoded in Montgomery form. 229 EC_FELEM field_minus_order; 230 231 CRYPTO_refcount_t references; 232 233 BN_MONT_CTX *mont; // Montgomery structure. 234 235 EC_FELEM one; // The value one. 236 } /* EC_GROUP */; 237 238 struct ec_point_st { 239 // group is an owning reference to |group|, unless this is 240 // |group->generator|. 241 EC_GROUP *group; 242 // raw is the group-specific point data. Functions that take |EC_POINT| 243 // typically check consistency with |EC_GROUP| while functions that take 244 // |EC_RAW_POINT| do not. Thus accesses to this field should be externally 245 // checked for consistency. 246 EC_RAW_POINT raw; 247 } /* EC_POINT */; 248 249 EC_GROUP *ec_group_new(const EC_METHOD *meth); 250 251 // ec_bignum_to_felem converts |in| to an |EC_FELEM|. It returns one on success 252 // and zero if |in| is out of range. 253 int ec_bignum_to_felem(const EC_GROUP *group, EC_FELEM *out, const BIGNUM *in); 254 255 // ec_felem_to_bignum converts |in| to a |BIGNUM|. It returns one on success and 256 // zero on allocation failure. 257 int ec_felem_to_bignum(const EC_GROUP *group, BIGNUM *out, const EC_FELEM *in); 258 259 // ec_felem_neg sets |out| to -|a|. 260 void ec_felem_neg(const EC_GROUP *group, EC_FELEM *out, const EC_FELEM *a); 261 262 // ec_felem_add sets |out| to |a| + |b|. 263 void ec_felem_add(const EC_GROUP *group, EC_FELEM *out, const EC_FELEM *a, 264 const EC_FELEM *b); 265 266 // ec_felem_add sets |out| to |a| - |b|. 267 void ec_felem_sub(const EC_GROUP *group, EC_FELEM *out, const EC_FELEM *a, 268 const EC_FELEM *b); 269 270 // ec_felem_non_zero_mask returns all ones if |a| is non-zero and all zeros 271 // otherwise. 272 BN_ULONG ec_felem_non_zero_mask(const EC_GROUP *group, const EC_FELEM *a); 273 274 // ec_felem_select, in constant time, sets |out| to |a| if |mask| is all ones 275 // and |b| if |mask| is all zeros. 276 void ec_felem_select(const EC_GROUP *group, EC_FELEM *out, BN_ULONG mask, 277 const EC_FELEM *a, const EC_FELEM *b); 278 279 // ec_felem_equal returns one if |a| and |b| are equal and zero otherwise. It 280 // treats |a| and |b| as public and does *not* run in constant time. 281 int ec_felem_equal(const EC_GROUP *group, const EC_FELEM *a, const EC_FELEM *b); 282 283 // ec_bignum_to_scalar converts |in| to an |EC_SCALAR| and writes it to 284 // |*out|. It returns one on success and zero if |in| is out of range. 285 OPENSSL_EXPORT int ec_bignum_to_scalar(const EC_GROUP *group, EC_SCALAR *out, 286 const BIGNUM *in); 287 288 // ec_random_nonzero_scalar sets |out| to a uniformly selected random value from 289 // 1 to |group->order| - 1. It returns one on success and zero on error. 290 int ec_random_nonzero_scalar(const EC_GROUP *group, EC_SCALAR *out, 291 const uint8_t additional_data[32]); 292 293 // ec_scalar_equal_vartime returns one if |a| and |b| are equal and zero 294 // otherwise. Both values are treated as public. 295 int ec_scalar_equal_vartime(const EC_GROUP *group, const EC_SCALAR *a, 296 const EC_SCALAR *b); 297 298 // ec_scalar_is_zero returns one if |a| is zero and zero otherwise. 299 int ec_scalar_is_zero(const EC_GROUP *group, const EC_SCALAR *a); 300 301 // ec_scalar_add sets |r| to |a| + |b|. 302 void ec_scalar_add(const EC_GROUP *group, EC_SCALAR *r, const EC_SCALAR *a, 303 const EC_SCALAR *b); 304 305 // ec_scalar_to_montgomery sets |r| to |a| in Montgomery form. 306 void ec_scalar_to_montgomery(const EC_GROUP *group, EC_SCALAR *r, 307 const EC_SCALAR *a); 308 309 // ec_scalar_to_montgomery sets |r| to |a| converted from Montgomery form. 310 void ec_scalar_from_montgomery(const EC_GROUP *group, EC_SCALAR *r, 311 const EC_SCALAR *a); 312 313 // ec_scalar_mul_montgomery sets |r| to |a| * |b| where inputs and outputs are 314 // in Montgomery form. 315 void ec_scalar_mul_montgomery(const EC_GROUP *group, EC_SCALAR *r, 316 const EC_SCALAR *a, const EC_SCALAR *b); 317 318 // ec_scalar_mul_montgomery sets |r| to |a|^-1 where inputs and outputs are in 319 // Montgomery form. 320 void ec_scalar_inv_montgomery(const EC_GROUP *group, EC_SCALAR *r, 321 const EC_SCALAR *a); 322 323 // ec_scalar_inv_montgomery_vartime performs the same actions as 324 // |ec_scalar_inv_montgomery|, but in variable time. 325 int ec_scalar_inv_montgomery_vartime(const EC_GROUP *group, EC_SCALAR *r, 326 const EC_SCALAR *a); 327 328 // ec_point_mul_scalar sets |r| to generator * |g_scalar| + |p| * 329 // |p_scalar|. Unlike other functions which take |EC_SCALAR|, |g_scalar| and 330 // |p_scalar| need not be fully reduced. They need only contain as many bits as 331 // the order. 332 int ec_point_mul_scalar(const EC_GROUP *group, EC_RAW_POINT *r, 333 const EC_SCALAR *g_scalar, const EC_RAW_POINT *p, 334 const EC_SCALAR *p_scalar); 335 336 // ec_point_mul_scalar_public performs the same computation as 337 // ec_point_mul_scalar. It further assumes that the inputs are public so 338 // there is no concern about leaking their values through timing. 339 OPENSSL_EXPORT int ec_point_mul_scalar_public(const EC_GROUP *group, 340 EC_RAW_POINT *r, 341 const EC_SCALAR *g_scalar, 342 const EC_RAW_POINT *p, 343 const EC_SCALAR *p_scalar); 344 345 // ec_cmp_x_coordinate compares the x (affine) coordinate of |p|, mod the group 346 // order, with |r|. It returns one if the values match and zero if |p| is the 347 // point at infinity of the values do not match. 348 int ec_cmp_x_coordinate(const EC_GROUP *group, const EC_RAW_POINT *p, 349 const EC_SCALAR *r); 350 351 // ec_get_x_coordinate_as_scalar sets |*out| to |p|'s x-coordinate, modulo 352 // |group->order|. It returns one on success and zero if |p| is the point at 353 // infinity. 354 int ec_get_x_coordinate_as_scalar(const EC_GROUP *group, EC_SCALAR *out, 355 const EC_RAW_POINT *p); 356 357 // ec_point_get_affine_coordinate_bytes writes |p|'s affine coordinates to 358 // |out_x| and |out_y|, each of which must have at must |max_out| bytes. It sets 359 // |*out_len| to the number of bytes written in each buffer. Coordinates are 360 // written big-endian and zero-padded to the size of the field. 361 // 362 // Either of |out_x| or |out_y| may be NULL to omit that coordinate. This 363 // function returns one on success and zero on failure. 364 int ec_point_get_affine_coordinate_bytes(const EC_GROUP *group, uint8_t *out_x, 365 uint8_t *out_y, size_t *out_len, 366 size_t max_out, const EC_RAW_POINT *p); 367 368 // ec_field_element_to_scalar reduces |r| modulo |group->order|. |r| must 369 // previously have been reduced modulo |group->field|. 370 int ec_field_element_to_scalar(const EC_GROUP *group, BIGNUM *r); 371 372 void ec_GFp_mont_mul(const EC_GROUP *group, EC_RAW_POINT *r, 373 const EC_SCALAR *g_scalar, const EC_RAW_POINT *p, 374 const EC_SCALAR *p_scalar); 375 376 // ec_compute_wNAF writes the modified width-(w+1) Non-Adjacent Form (wNAF) of 377 // |scalar| to |out|. |out| must have room for |bits| + 1 elements, each of 378 // which will be either zero or odd with an absolute value less than 2^w 379 // satisfying 380 // scalar = \sum_j out[j]*2^j 381 // where at most one of any w+1 consecutive digits is non-zero 382 // with the exception that the most significant digit may be only 383 // w-1 zeros away from that next non-zero digit. 384 void ec_compute_wNAF(const EC_GROUP *group, int8_t *out, 385 const EC_SCALAR *scalar, size_t bits, int w); 386 387 void ec_GFp_mont_mul_public(const EC_GROUP *group, EC_RAW_POINT *r, 388 const EC_SCALAR *g_scalar, const EC_RAW_POINT *p, 389 const EC_SCALAR *p_scalar); 390 391 // method functions in simple.c 392 int ec_GFp_simple_group_init(EC_GROUP *); 393 void ec_GFp_simple_group_finish(EC_GROUP *); 394 int ec_GFp_simple_group_set_curve(EC_GROUP *, const BIGNUM *p, const BIGNUM *a, 395 const BIGNUM *b, BN_CTX *); 396 int ec_GFp_simple_group_get_curve(const EC_GROUP *, BIGNUM *p, BIGNUM *a, 397 BIGNUM *b); 398 void ec_GFp_simple_point_init(EC_RAW_POINT *); 399 void ec_GFp_simple_point_copy(EC_RAW_POINT *, const EC_RAW_POINT *); 400 void ec_GFp_simple_point_set_to_infinity(const EC_GROUP *, EC_RAW_POINT *); 401 int ec_GFp_simple_point_set_affine_coordinates(const EC_GROUP *, EC_RAW_POINT *, 402 const BIGNUM *x, 403 const BIGNUM *y); 404 void ec_GFp_mont_add(const EC_GROUP *, EC_RAW_POINT *r, const EC_RAW_POINT *a, 405 const EC_RAW_POINT *b); 406 void ec_GFp_mont_dbl(const EC_GROUP *, EC_RAW_POINT *r, const EC_RAW_POINT *a); 407 void ec_GFp_simple_invert(const EC_GROUP *, EC_RAW_POINT *); 408 int ec_GFp_simple_is_at_infinity(const EC_GROUP *, const EC_RAW_POINT *); 409 int ec_GFp_simple_is_on_curve(const EC_GROUP *, const EC_RAW_POINT *); 410 int ec_GFp_simple_cmp(const EC_GROUP *, const EC_RAW_POINT *a, 411 const EC_RAW_POINT *b); 412 void ec_simple_scalar_inv_montgomery(const EC_GROUP *group, EC_SCALAR *r, 413 const EC_SCALAR *a); 414 415 int ec_GFp_simple_mont_inv_mod_ord_vartime(const EC_GROUP *group, EC_SCALAR *r, 416 const EC_SCALAR *a); 417 418 int ec_GFp_simple_cmp_x_coordinate(const EC_GROUP *group, const EC_RAW_POINT *p, 419 const EC_SCALAR *r); 420 421 // method functions in montgomery.c 422 int ec_GFp_mont_group_init(EC_GROUP *); 423 int ec_GFp_mont_group_set_curve(EC_GROUP *, const BIGNUM *p, const BIGNUM *a, 424 const BIGNUM *b, BN_CTX *); 425 void ec_GFp_mont_group_finish(EC_GROUP *); 426 void ec_GFp_mont_felem_mul(const EC_GROUP *, EC_FELEM *r, const EC_FELEM *a, 427 const EC_FELEM *b); 428 void ec_GFp_mont_felem_sqr(const EC_GROUP *, EC_FELEM *r, const EC_FELEM *a); 429 430 int ec_GFp_mont_bignum_to_felem(const EC_GROUP *group, EC_FELEM *out, 431 const BIGNUM *in); 432 int ec_GFp_mont_felem_to_bignum(const EC_GROUP *group, BIGNUM *out, 433 const EC_FELEM *in); 434 435 void ec_GFp_nistp_recode_scalar_bits(uint8_t *sign, uint8_t *digit, uint8_t in); 436 437 const EC_METHOD *EC_GFp_nistp224_method(void); 438 const EC_METHOD *EC_GFp_nistp256_method(void); 439 440 // EC_GFp_nistz256_method is a GFp method using montgomery multiplication, with 441 // x86-64 optimized P256. See http://eprint.iacr.org/2013/816. 442 const EC_METHOD *EC_GFp_nistz256_method(void); 443 444 // An EC_WRAPPED_SCALAR is an |EC_SCALAR| with a parallel |BIGNUM| 445 // representation. It exists to support the |EC_KEY_get0_private_key| API. 446 typedef struct { 447 BIGNUM bignum; 448 EC_SCALAR scalar; 449 } EC_WRAPPED_SCALAR; 450 451 struct ec_key_st { 452 EC_GROUP *group; 453 454 EC_POINT *pub_key; 455 EC_WRAPPED_SCALAR *priv_key; 456 457 // fixed_k may contain a specific value of 'k', to be used in ECDSA signing. 458 // This is only for the FIPS power-on tests. 459 BIGNUM *fixed_k; 460 461 unsigned int enc_flag; 462 point_conversion_form_t conv_form; 463 464 CRYPTO_refcount_t references; 465 466 ECDSA_METHOD *ecdsa_meth; 467 468 CRYPTO_EX_DATA ex_data; 469 } /* EC_KEY */; 470 471 struct built_in_curve { 472 int nid; 473 const uint8_t *oid; 474 uint8_t oid_len; 475 // comment is a human-readable string describing the curve. 476 const char *comment; 477 // param_len is the number of bytes needed to store a field element. 478 uint8_t param_len; 479 // params points to an array of 6*|param_len| bytes which hold the field 480 // elements of the following (in big-endian order): prime, a, b, generator x, 481 // generator y, order. 482 const uint8_t *params; 483 const EC_METHOD *method; 484 }; 485 486 #define OPENSSL_NUM_BUILT_IN_CURVES 4 487 488 struct built_in_curves { 489 struct built_in_curve curves[OPENSSL_NUM_BUILT_IN_CURVES]; 490 }; 491 492 // OPENSSL_built_in_curves returns a pointer to static information about 493 // standard curves. The array is terminated with an entry where |nid| is 494 // |NID_undef|. 495 const struct built_in_curves *OPENSSL_built_in_curves(void); 496 497 #if defined(__cplusplus) 498 } // extern C 499 #endif 500 501 #endif // OPENSSL_HEADER_EC_INTERNAL_H 502
