1/* 2 * Copyright 2001-2020 The OpenSSL Project Authors. All Rights Reserved. 3 * Copyright (c) 2002, Oracle and/or its affiliates. All rights reserved 4 * 5 * Licensed under the OpenSSL license (the "License"). You may not use 6 * this file except in compliance with the License. You can obtain a copy 7 * in the file LICENSE in the source distribution or at 8 * https://www.openssl.org/source/license.html 9 */ 10 11#include <stdlib.h> 12 13#include <openssl/obj_mac.h> 14#include <openssl/ec.h> 15#include <openssl/bn.h> 16#include "internal/refcount.h" 17#include "crypto/ec.h" 18 19#if defined(__SUNPRO_C) 20# if __SUNPRO_C >= 0x520 21# pragma error_messages (off,E_ARRAY_OF_INCOMPLETE_NONAME,E_ARRAY_OF_INCOMPLETE) 22# endif 23#endif 24 25/* Use default functions for poin2oct, oct2point and compressed coordinates */ 26#define EC_FLAGS_DEFAULT_OCT 0x1 27 28/* Use custom formats for EC_GROUP, EC_POINT and EC_KEY */ 29#define EC_FLAGS_CUSTOM_CURVE 0x2 30 31/* Curve does not support signing operations */ 32#define EC_FLAGS_NO_SIGN 0x4 33 34/* 35 * Structure details are not part of the exported interface, so all this may 36 * change in future versions. 37 */ 38 39struct ec_method_st { 40 /* Various method flags */ 41 int flags; 42 /* used by EC_METHOD_get_field_type: */ 43 int field_type; /* a NID */ 44 /* 45 * used by EC_GROUP_new, EC_GROUP_free, EC_GROUP_clear_free, 46 * EC_GROUP_copy: 47 */ 48 int (*group_init) (EC_GROUP *); 49 void (*group_finish) (EC_GROUP *); 50 void (*group_clear_finish) (EC_GROUP *); 51 int (*group_copy) (EC_GROUP *, const EC_GROUP *); 52 /* used by EC_GROUP_set_curve, EC_GROUP_get_curve: */ 53 int (*group_set_curve) (EC_GROUP *, const BIGNUM *p, const BIGNUM *a, 54 const BIGNUM *b, BN_CTX *); 55 int (*group_get_curve) (const EC_GROUP *, BIGNUM *p, BIGNUM *a, BIGNUM *b, 56 BN_CTX *); 57 /* used by EC_GROUP_get_degree: */ 58 int (*group_get_degree) (const EC_GROUP *); 59 int (*group_order_bits) (const EC_GROUP *); 60 /* used by EC_GROUP_check: */ 61 int (*group_check_discriminant) (const EC_GROUP *, BN_CTX *); 62 /* 63 * used by EC_POINT_new, EC_POINT_free, EC_POINT_clear_free, 64 * EC_POINT_copy: 65 */ 66 int (*point_init) (EC_POINT *); 67 void (*point_finish) (EC_POINT *); 68 void (*point_clear_finish) (EC_POINT *); 69 int (*point_copy) (EC_POINT *, const EC_POINT *); 70 /*- 71 * used by EC_POINT_set_to_infinity, 72 * EC_POINT_set_Jprojective_coordinates_GFp, 73 * EC_POINT_get_Jprojective_coordinates_GFp, 74 * EC_POINT_set_affine_coordinates, 75 * EC_POINT_get_affine_coordinates, 76 * EC_POINT_set_compressed_coordinates: 77 */ 78 int (*point_set_to_infinity) (const EC_GROUP *, EC_POINT *); 79 int (*point_set_Jprojective_coordinates_GFp) (const EC_GROUP *, 80 EC_POINT *, const BIGNUM *x, 81 const BIGNUM *y, 82 const BIGNUM *z, BN_CTX *); 83 int (*point_get_Jprojective_coordinates_GFp) (const EC_GROUP *, 84 const EC_POINT *, BIGNUM *x, 85 BIGNUM *y, BIGNUM *z, 86 BN_CTX *); 87 int (*point_set_affine_coordinates) (const EC_GROUP *, EC_POINT *, 88 const BIGNUM *x, const BIGNUM *y, 89 BN_CTX *); 90 int (*point_get_affine_coordinates) (const EC_GROUP *, const EC_POINT *, 91 BIGNUM *x, BIGNUM *y, BN_CTX *); 92 int (*point_set_compressed_coordinates) (const EC_GROUP *, EC_POINT *, 93 const BIGNUM *x, int y_bit, 94 BN_CTX *); 95 /* used by EC_POINT_point2oct, EC_POINT_oct2point: */ 96 size_t (*point2oct) (const EC_GROUP *, const EC_POINT *, 97 point_conversion_form_t form, unsigned char *buf, 98 size_t len, BN_CTX *); 99 int (*oct2point) (const EC_GROUP *, EC_POINT *, const unsigned char *buf, 100 size_t len, BN_CTX *); 101 /* used by EC_POINT_add, EC_POINT_dbl, ECP_POINT_invert: */ 102 int (*add) (const EC_GROUP *, EC_POINT *r, const EC_POINT *a, 103 const EC_POINT *b, BN_CTX *); 104 int (*dbl) (const EC_GROUP *, EC_POINT *r, const EC_POINT *a, BN_CTX *); 105 int (*invert) (const EC_GROUP *, EC_POINT *, BN_CTX *); 106 /* 107 * used by EC_POINT_is_at_infinity, EC_POINT_is_on_curve, EC_POINT_cmp: 108 */ 109 int (*is_at_infinity) (const EC_GROUP *, const EC_POINT *); 110 int (*is_on_curve) (const EC_GROUP *, const EC_POINT *, BN_CTX *); 111 int (*point_cmp) (const EC_GROUP *, const EC_POINT *a, const EC_POINT *b, 112 BN_CTX *); 113 /* used by EC_POINT_make_affine, EC_POINTs_make_affine: */ 114 int (*make_affine) (const EC_GROUP *, EC_POINT *, BN_CTX *); 115 int (*points_make_affine) (const EC_GROUP *, size_t num, EC_POINT *[], 116 BN_CTX *); 117 /* 118 * used by EC_POINTs_mul, EC_POINT_mul, EC_POINT_precompute_mult, 119 * EC_POINT_have_precompute_mult (default implementations are used if the 120 * 'mul' pointer is 0): 121 */ 122 /*- 123 * mul() calculates the value 124 * 125 * r := generator * scalar 126 * + points[0] * scalars[0] 127 * + ... 128 * + points[num-1] * scalars[num-1]. 129 * 130 * For a fixed point multiplication (scalar != NULL, num == 0) 131 * or a variable point multiplication (scalar == NULL, num == 1), 132 * mul() must use a constant time algorithm: in both cases callers 133 * should provide an input scalar (either scalar or scalars[0]) 134 * in the range [0, ec_group_order); for robustness, implementers 135 * should handle the case when the scalar has not been reduced, but 136 * may treat it as an unusual input, without any constant-timeness 137 * guarantee. 138 */ 139 int (*mul) (const EC_GROUP *group, EC_POINT *r, const BIGNUM *scalar, 140 size_t num, const EC_POINT *points[], const BIGNUM *scalars[], 141 BN_CTX *); 142 int (*precompute_mult) (EC_GROUP *group, BN_CTX *); 143 int (*have_precompute_mult) (const EC_GROUP *group); 144 /* internal functions */ 145 /* 146 * 'field_mul', 'field_sqr', and 'field_div' can be used by 'add' and 147 * 'dbl' so that the same implementations of point operations can be used 148 * with different optimized implementations of expensive field 149 * operations: 150 */ 151 int (*field_mul) (const EC_GROUP *, BIGNUM *r, const BIGNUM *a, 152 const BIGNUM *b, BN_CTX *); 153 int (*field_sqr) (const EC_GROUP *, BIGNUM *r, const BIGNUM *a, BN_CTX *); 154 int (*field_div) (const EC_GROUP *, BIGNUM *r, const BIGNUM *a, 155 const BIGNUM *b, BN_CTX *); 156 /*- 157 * 'field_inv' computes the multiplicative inverse of a in the field, 158 * storing the result in r. 159 * 160 * If 'a' is zero (or equivalent), you'll get an EC_R_CANNOT_INVERT error. 161 */ 162 int (*field_inv) (const EC_GROUP *, BIGNUM *r, const BIGNUM *a, BN_CTX *); 163 /* e.g. to Montgomery */ 164 int (*field_encode) (const EC_GROUP *, BIGNUM *r, const BIGNUM *a, 165 BN_CTX *); 166 /* e.g. from Montgomery */ 167 int (*field_decode) (const EC_GROUP *, BIGNUM *r, const BIGNUM *a, 168 BN_CTX *); 169 int (*field_set_to_one) (const EC_GROUP *, BIGNUM *r, BN_CTX *); 170 /* private key operations */ 171 size_t (*priv2oct)(const EC_KEY *eckey, unsigned char *buf, size_t len); 172 int (*oct2priv)(EC_KEY *eckey, const unsigned char *buf, size_t len); 173 int (*set_private)(EC_KEY *eckey, const BIGNUM *priv_key); 174 int (*keygen)(EC_KEY *eckey); 175 int (*keycheck)(const EC_KEY *eckey); 176 int (*keygenpub)(EC_KEY *eckey); 177 int (*keycopy)(EC_KEY *dst, const EC_KEY *src); 178 void (*keyfinish)(EC_KEY *eckey); 179 /* custom ECDH operation */ 180 int (*ecdh_compute_key)(unsigned char **pout, size_t *poutlen, 181 const EC_POINT *pub_key, const EC_KEY *ecdh); 182 /* Inverse modulo order */ 183 int (*field_inverse_mod_ord)(const EC_GROUP *, BIGNUM *r, 184 const BIGNUM *x, BN_CTX *); 185 int (*blind_coordinates)(const EC_GROUP *group, EC_POINT *p, BN_CTX *ctx); 186 int (*ladder_pre)(const EC_GROUP *group, 187 EC_POINT *r, EC_POINT *s, 188 EC_POINT *p, BN_CTX *ctx); 189 int (*ladder_step)(const EC_GROUP *group, 190 EC_POINT *r, EC_POINT *s, 191 EC_POINT *p, BN_CTX *ctx); 192 int (*ladder_post)(const EC_GROUP *group, 193 EC_POINT *r, EC_POINT *s, 194 EC_POINT *p, BN_CTX *ctx); 195}; 196 197/* 198 * Types and functions to manipulate pre-computed values. 199 */ 200typedef struct nistp224_pre_comp_st NISTP224_PRE_COMP; 201typedef struct nistp256_pre_comp_st NISTP256_PRE_COMP; 202typedef struct nistp521_pre_comp_st NISTP521_PRE_COMP; 203typedef struct nistz256_pre_comp_st NISTZ256_PRE_COMP; 204typedef struct ec_pre_comp_st EC_PRE_COMP; 205 206struct ec_group_st { 207 const EC_METHOD *meth; 208 EC_POINT *generator; /* optional */ 209 BIGNUM *order, *cofactor; 210 int curve_name; /* optional NID for named curve */ 211 int asn1_flag; /* flag to control the asn1 encoding */ 212 int decoded_from_explicit_params; /* set if decoded from explicit 213 * curve parameters encoding */ 214 point_conversion_form_t asn1_form; 215 unsigned char *seed; /* optional seed for parameters (appears in 216 * ASN1) */ 217 size_t seed_len; 218 /* 219 * The following members are handled by the method functions, even if 220 * they appear generic 221 */ 222 /* 223 * Field specification. For curves over GF(p), this is the modulus; for 224 * curves over GF(2^m), this is the irreducible polynomial defining the 225 * field. 226 */ 227 BIGNUM *field; 228 /* 229 * Field specification for curves over GF(2^m). The irreducible f(t) is 230 * then of the form: t^poly[0] + t^poly[1] + ... + t^poly[k] where m = 231 * poly[0] > poly[1] > ... > poly[k] = 0. The array is terminated with 232 * poly[k+1]=-1. All elliptic curve irreducibles have at most 5 non-zero 233 * terms. 234 */ 235 int poly[6]; 236 /* 237 * Curve coefficients. (Here the assumption is that BIGNUMs can be used 238 * or abused for all kinds of fields, not just GF(p).) For characteristic 239 * > 3, the curve is defined by a Weierstrass equation of the form y^2 = 240 * x^3 + a*x + b. For characteristic 2, the curve is defined by an 241 * equation of the form y^2 + x*y = x^3 + a*x^2 + b. 242 */ 243 BIGNUM *a, *b; 244 /* enable optimized point arithmetics for special case */ 245 int a_is_minus3; 246 /* method-specific (e.g., Montgomery structure) */ 247 void *field_data1; 248 /* method-specific */ 249 void *field_data2; 250 /* method-specific */ 251 int (*field_mod_func) (BIGNUM *, const BIGNUM *, const BIGNUM *, 252 BN_CTX *); 253 /* data for ECDSA inverse */ 254 BN_MONT_CTX *mont_data; 255 256 /* 257 * Precomputed values for speed. The PCT_xxx names match the 258 * pre_comp.xxx union names; see the SETPRECOMP and HAVEPRECOMP 259 * macros, below. 260 */ 261 enum { 262 PCT_none, 263 PCT_nistp224, PCT_nistp256, PCT_nistp521, PCT_nistz256, 264 PCT_ec 265 } pre_comp_type; 266 union { 267 NISTP224_PRE_COMP *nistp224; 268 NISTP256_PRE_COMP *nistp256; 269 NISTP521_PRE_COMP *nistp521; 270 NISTZ256_PRE_COMP *nistz256; 271 EC_PRE_COMP *ec; 272 } pre_comp; 273}; 274 275#define SETPRECOMP(g, type, pre) \ 276 g->pre_comp_type = PCT_##type, g->pre_comp.type = pre 277#define HAVEPRECOMP(g, type) \ 278 g->pre_comp_type == PCT_##type && g->pre_comp.type != NULL 279 280struct ec_key_st { 281 const EC_KEY_METHOD *meth; 282 ENGINE *engine; 283 int version; 284 EC_GROUP *group; 285 EC_POINT *pub_key; 286 BIGNUM *priv_key; 287 unsigned int enc_flag; 288 point_conversion_form_t conv_form; 289 CRYPTO_REF_COUNT references; 290 int flags; 291 CRYPTO_EX_DATA ex_data; 292 CRYPTO_RWLOCK *lock; 293}; 294 295struct ec_point_st { 296 const EC_METHOD *meth; 297 /* NID for the curve if known */ 298 int curve_name; 299 /* 300 * All members except 'meth' are handled by the method functions, even if 301 * they appear generic 302 */ 303 BIGNUM *X; 304 BIGNUM *Y; 305 BIGNUM *Z; /* Jacobian projective coordinates: * (X, Y, 306 * Z) represents (X/Z^2, Y/Z^3) if Z != 0 */ 307 int Z_is_one; /* enable optimized point arithmetics for 308 * special case */ 309}; 310 311static ossl_inline int ec_point_is_compat(const EC_POINT *point, 312 const EC_GROUP *group) 313{ 314 if (group->meth != point->meth 315 || (group->curve_name != 0 316 && point->curve_name != 0 317 && group->curve_name != point->curve_name)) 318 return 0; 319 320 return 1; 321} 322 323NISTP224_PRE_COMP *EC_nistp224_pre_comp_dup(NISTP224_PRE_COMP *); 324NISTP256_PRE_COMP *EC_nistp256_pre_comp_dup(NISTP256_PRE_COMP *); 325NISTP521_PRE_COMP *EC_nistp521_pre_comp_dup(NISTP521_PRE_COMP *); 326NISTZ256_PRE_COMP *EC_nistz256_pre_comp_dup(NISTZ256_PRE_COMP *); 327NISTP256_PRE_COMP *EC_nistp256_pre_comp_dup(NISTP256_PRE_COMP *); 328EC_PRE_COMP *EC_ec_pre_comp_dup(EC_PRE_COMP *); 329 330void EC_pre_comp_free(EC_GROUP *group); 331void EC_nistp224_pre_comp_free(NISTP224_PRE_COMP *); 332void EC_nistp256_pre_comp_free(NISTP256_PRE_COMP *); 333void EC_nistp521_pre_comp_free(NISTP521_PRE_COMP *); 334void EC_nistz256_pre_comp_free(NISTZ256_PRE_COMP *); 335void EC_ec_pre_comp_free(EC_PRE_COMP *); 336 337/* 338 * method functions in ec_mult.c (ec_lib.c uses these as defaults if 339 * group->method->mul is 0) 340 */ 341int ec_wNAF_mul(const EC_GROUP *group, EC_POINT *r, const BIGNUM *scalar, 342 size_t num, const EC_POINT *points[], const BIGNUM *scalars[], 343 BN_CTX *); 344int ec_wNAF_precompute_mult(EC_GROUP *group, BN_CTX *); 345int ec_wNAF_have_precompute_mult(const EC_GROUP *group); 346 347/* method functions in ecp_smpl.c */ 348int ec_GFp_simple_group_init(EC_GROUP *); 349void ec_GFp_simple_group_finish(EC_GROUP *); 350void ec_GFp_simple_group_clear_finish(EC_GROUP *); 351int ec_GFp_simple_group_copy(EC_GROUP *, const EC_GROUP *); 352int ec_GFp_simple_group_set_curve(EC_GROUP *, const BIGNUM *p, 353 const BIGNUM *a, const BIGNUM *b, BN_CTX *); 354int ec_GFp_simple_group_get_curve(const EC_GROUP *, BIGNUM *p, BIGNUM *a, 355 BIGNUM *b, BN_CTX *); 356int ec_GFp_simple_group_get_degree(const EC_GROUP *); 357int ec_GFp_simple_group_check_discriminant(const EC_GROUP *, BN_CTX *); 358int ec_GFp_simple_point_init(EC_POINT *); 359void ec_GFp_simple_point_finish(EC_POINT *); 360void ec_GFp_simple_point_clear_finish(EC_POINT *); 361int ec_GFp_simple_point_copy(EC_POINT *, const EC_POINT *); 362int ec_GFp_simple_point_set_to_infinity(const EC_GROUP *, EC_POINT *); 363int ec_GFp_simple_set_Jprojective_coordinates_GFp(const EC_GROUP *, 364 EC_POINT *, const BIGNUM *x, 365 const BIGNUM *y, 366 const BIGNUM *z, BN_CTX *); 367int ec_GFp_simple_get_Jprojective_coordinates_GFp(const EC_GROUP *, 368 const EC_POINT *, BIGNUM *x, 369 BIGNUM *y, BIGNUM *z, 370 BN_CTX *); 371int ec_GFp_simple_point_set_affine_coordinates(const EC_GROUP *, EC_POINT *, 372 const BIGNUM *x, 373 const BIGNUM *y, BN_CTX *); 374int ec_GFp_simple_point_get_affine_coordinates(const EC_GROUP *, 375 const EC_POINT *, BIGNUM *x, 376 BIGNUM *y, BN_CTX *); 377int ec_GFp_simple_set_compressed_coordinates(const EC_GROUP *, EC_POINT *, 378 const BIGNUM *x, int y_bit, 379 BN_CTX *); 380size_t ec_GFp_simple_point2oct(const EC_GROUP *, const EC_POINT *, 381 point_conversion_form_t form, 382 unsigned char *buf, size_t len, BN_CTX *); 383int ec_GFp_simple_oct2point(const EC_GROUP *, EC_POINT *, 384 const unsigned char *buf, size_t len, BN_CTX *); 385int ec_GFp_simple_add(const EC_GROUP *, EC_POINT *r, const EC_POINT *a, 386 const EC_POINT *b, BN_CTX *); 387int ec_GFp_simple_dbl(const EC_GROUP *, EC_POINT *r, const EC_POINT *a, 388 BN_CTX *); 389int ec_GFp_simple_invert(const EC_GROUP *, EC_POINT *, BN_CTX *); 390int ec_GFp_simple_is_at_infinity(const EC_GROUP *, const EC_POINT *); 391int ec_GFp_simple_is_on_curve(const EC_GROUP *, const EC_POINT *, BN_CTX *); 392int ec_GFp_simple_cmp(const EC_GROUP *, const EC_POINT *a, const EC_POINT *b, 393 BN_CTX *); 394int ec_GFp_simple_make_affine(const EC_GROUP *, EC_POINT *, BN_CTX *); 395int ec_GFp_simple_points_make_affine(const EC_GROUP *, size_t num, 396 EC_POINT *[], BN_CTX *); 397int ec_GFp_simple_field_mul(const EC_GROUP *, BIGNUM *r, const BIGNUM *a, 398 const BIGNUM *b, BN_CTX *); 399int ec_GFp_simple_field_sqr(const EC_GROUP *, BIGNUM *r, const BIGNUM *a, 400 BN_CTX *); 401int ec_GFp_simple_field_inv(const EC_GROUP *, BIGNUM *r, const BIGNUM *a, 402 BN_CTX *); 403int ec_GFp_simple_blind_coordinates(const EC_GROUP *group, EC_POINT *p, 404 BN_CTX *ctx); 405int ec_GFp_simple_ladder_pre(const EC_GROUP *group, 406 EC_POINT *r, EC_POINT *s, 407 EC_POINT *p, BN_CTX *ctx); 408int ec_GFp_simple_ladder_step(const EC_GROUP *group, 409 EC_POINT *r, EC_POINT *s, 410 EC_POINT *p, BN_CTX *ctx); 411int ec_GFp_simple_ladder_post(const EC_GROUP *group, 412 EC_POINT *r, EC_POINT *s, 413 EC_POINT *p, BN_CTX *ctx); 414 415/* method functions in ecp_mont.c */ 416int ec_GFp_mont_group_init(EC_GROUP *); 417int ec_GFp_mont_group_set_curve(EC_GROUP *, const BIGNUM *p, const BIGNUM *a, 418 const BIGNUM *b, BN_CTX *); 419void ec_GFp_mont_group_finish(EC_GROUP *); 420void ec_GFp_mont_group_clear_finish(EC_GROUP *); 421int ec_GFp_mont_group_copy(EC_GROUP *, const EC_GROUP *); 422int ec_GFp_mont_field_mul(const EC_GROUP *, BIGNUM *r, const BIGNUM *a, 423 const BIGNUM *b, BN_CTX *); 424int ec_GFp_mont_field_sqr(const EC_GROUP *, BIGNUM *r, const BIGNUM *a, 425 BN_CTX *); 426int ec_GFp_mont_field_inv(const EC_GROUP *, BIGNUM *r, const BIGNUM *a, 427 BN_CTX *); 428int ec_GFp_mont_field_encode(const EC_GROUP *, BIGNUM *r, const BIGNUM *a, 429 BN_CTX *); 430int ec_GFp_mont_field_decode(const EC_GROUP *, BIGNUM *r, const BIGNUM *a, 431 BN_CTX *); 432int ec_GFp_mont_field_set_to_one(const EC_GROUP *, BIGNUM *r, BN_CTX *); 433 434/* method functions in ecp_nist.c */ 435int ec_GFp_nist_group_copy(EC_GROUP *dest, const EC_GROUP *src); 436int ec_GFp_nist_group_set_curve(EC_GROUP *, const BIGNUM *p, const BIGNUM *a, 437 const BIGNUM *b, BN_CTX *); 438int ec_GFp_nist_field_mul(const EC_GROUP *, BIGNUM *r, const BIGNUM *a, 439 const BIGNUM *b, BN_CTX *); 440int ec_GFp_nist_field_sqr(const EC_GROUP *, BIGNUM *r, const BIGNUM *a, 441 BN_CTX *); 442 443/* method functions in ec2_smpl.c */ 444int ec_GF2m_simple_group_init(EC_GROUP *); 445void ec_GF2m_simple_group_finish(EC_GROUP *); 446void ec_GF2m_simple_group_clear_finish(EC_GROUP *); 447int ec_GF2m_simple_group_copy(EC_GROUP *, const EC_GROUP *); 448int ec_GF2m_simple_group_set_curve(EC_GROUP *, const BIGNUM *p, 449 const BIGNUM *a, const BIGNUM *b, 450 BN_CTX *); 451int ec_GF2m_simple_group_get_curve(const EC_GROUP *, BIGNUM *p, BIGNUM *a, 452 BIGNUM *b, BN_CTX *); 453int ec_GF2m_simple_group_get_degree(const EC_GROUP *); 454int ec_GF2m_simple_group_check_discriminant(const EC_GROUP *, BN_CTX *); 455int ec_GF2m_simple_point_init(EC_POINT *); 456void ec_GF2m_simple_point_finish(EC_POINT *); 457void ec_GF2m_simple_point_clear_finish(EC_POINT *); 458int ec_GF2m_simple_point_copy(EC_POINT *, const EC_POINT *); 459int ec_GF2m_simple_point_set_to_infinity(const EC_GROUP *, EC_POINT *); 460int ec_GF2m_simple_point_set_affine_coordinates(const EC_GROUP *, EC_POINT *, 461 const BIGNUM *x, 462 const BIGNUM *y, BN_CTX *); 463int ec_GF2m_simple_point_get_affine_coordinates(const EC_GROUP *, 464 const EC_POINT *, BIGNUM *x, 465 BIGNUM *y, BN_CTX *); 466int ec_GF2m_simple_set_compressed_coordinates(const EC_GROUP *, EC_POINT *, 467 const BIGNUM *x, int y_bit, 468 BN_CTX *); 469size_t ec_GF2m_simple_point2oct(const EC_GROUP *, const EC_POINT *, 470 point_conversion_form_t form, 471 unsigned char *buf, size_t len, BN_CTX *); 472int ec_GF2m_simple_oct2point(const EC_GROUP *, EC_POINT *, 473 const unsigned char *buf, size_t len, BN_CTX *); 474int ec_GF2m_simple_add(const EC_GROUP *, EC_POINT *r, const EC_POINT *a, 475 const EC_POINT *b, BN_CTX *); 476int ec_GF2m_simple_dbl(const EC_GROUP *, EC_POINT *r, const EC_POINT *a, 477 BN_CTX *); 478int ec_GF2m_simple_invert(const EC_GROUP *, EC_POINT *, BN_CTX *); 479int ec_GF2m_simple_is_at_infinity(const EC_GROUP *, const EC_POINT *); 480int ec_GF2m_simple_is_on_curve(const EC_GROUP *, const EC_POINT *, BN_CTX *); 481int ec_GF2m_simple_cmp(const EC_GROUP *, const EC_POINT *a, const EC_POINT *b, 482 BN_CTX *); 483int ec_GF2m_simple_make_affine(const EC_GROUP *, EC_POINT *, BN_CTX *); 484int ec_GF2m_simple_points_make_affine(const EC_GROUP *, size_t num, 485 EC_POINT *[], BN_CTX *); 486int ec_GF2m_simple_field_mul(const EC_GROUP *, BIGNUM *r, const BIGNUM *a, 487 const BIGNUM *b, BN_CTX *); 488int ec_GF2m_simple_field_sqr(const EC_GROUP *, BIGNUM *r, const BIGNUM *a, 489 BN_CTX *); 490int ec_GF2m_simple_field_div(const EC_GROUP *, BIGNUM *r, const BIGNUM *a, 491 const BIGNUM *b, BN_CTX *); 492 493#ifndef OPENSSL_NO_EC_NISTP_64_GCC_128 494/* method functions in ecp_nistp224.c */ 495int ec_GFp_nistp224_group_init(EC_GROUP *group); 496int ec_GFp_nistp224_group_set_curve(EC_GROUP *group, const BIGNUM *p, 497 const BIGNUM *a, const BIGNUM *n, 498 BN_CTX *); 499int ec_GFp_nistp224_point_get_affine_coordinates(const EC_GROUP *group, 500 const EC_POINT *point, 501 BIGNUM *x, BIGNUM *y, 502 BN_CTX *ctx); 503int ec_GFp_nistp224_mul(const EC_GROUP *group, EC_POINT *r, 504 const BIGNUM *scalar, size_t num, 505 const EC_POINT *points[], const BIGNUM *scalars[], 506 BN_CTX *); 507int ec_GFp_nistp224_points_mul(const EC_GROUP *group, EC_POINT *r, 508 const BIGNUM *scalar, size_t num, 509 const EC_POINT *points[], 510 const BIGNUM *scalars[], BN_CTX *ctx); 511int ec_GFp_nistp224_precompute_mult(EC_GROUP *group, BN_CTX *ctx); 512int ec_GFp_nistp224_have_precompute_mult(const EC_GROUP *group); 513 514/* method functions in ecp_nistp256.c */ 515int ec_GFp_nistp256_group_init(EC_GROUP *group); 516int ec_GFp_nistp256_group_set_curve(EC_GROUP *group, const BIGNUM *p, 517 const BIGNUM *a, const BIGNUM *n, 518 BN_CTX *); 519int ec_GFp_nistp256_point_get_affine_coordinates(const EC_GROUP *group, 520 const EC_POINT *point, 521 BIGNUM *x, BIGNUM *y, 522 BN_CTX *ctx); 523int ec_GFp_nistp256_mul(const EC_GROUP *group, EC_POINT *r, 524 const BIGNUM *scalar, size_t num, 525 const EC_POINT *points[], const BIGNUM *scalars[], 526 BN_CTX *); 527int ec_GFp_nistp256_points_mul(const EC_GROUP *group, EC_POINT *r, 528 const BIGNUM *scalar, size_t num, 529 const EC_POINT *points[], 530 const BIGNUM *scalars[], BN_CTX *ctx); 531int ec_GFp_nistp256_precompute_mult(EC_GROUP *group, BN_CTX *ctx); 532int ec_GFp_nistp256_have_precompute_mult(const EC_GROUP *group); 533 534/* method functions in ecp_nistp521.c */ 535int ec_GFp_nistp521_group_init(EC_GROUP *group); 536int ec_GFp_nistp521_group_set_curve(EC_GROUP *group, const BIGNUM *p, 537 const BIGNUM *a, const BIGNUM *n, 538 BN_CTX *); 539int ec_GFp_nistp521_point_get_affine_coordinates(const EC_GROUP *group, 540 const EC_POINT *point, 541 BIGNUM *x, BIGNUM *y, 542 BN_CTX *ctx); 543int ec_GFp_nistp521_mul(const EC_GROUP *group, EC_POINT *r, 544 const BIGNUM *scalar, size_t num, 545 const EC_POINT *points[], const BIGNUM *scalars[], 546 BN_CTX *); 547int ec_GFp_nistp521_points_mul(const EC_GROUP *group, EC_POINT *r, 548 const BIGNUM *scalar, size_t num, 549 const EC_POINT *points[], 550 const BIGNUM *scalars[], BN_CTX *ctx); 551int ec_GFp_nistp521_precompute_mult(EC_GROUP *group, BN_CTX *ctx); 552int ec_GFp_nistp521_have_precompute_mult(const EC_GROUP *group); 553 554/* utility functions in ecp_nistputil.c */ 555void ec_GFp_nistp_points_make_affine_internal(size_t num, void *point_array, 556 size_t felem_size, 557 void *tmp_felems, 558 void (*felem_one) (void *out), 559 int (*felem_is_zero) (const void 560 *in), 561 void (*felem_assign) (void *out, 562 const void 563 *in), 564 void (*felem_square) (void *out, 565 const void 566 *in), 567 void (*felem_mul) (void *out, 568 const void 569 *in1, 570 const void 571 *in2), 572 void (*felem_inv) (void *out, 573 const void 574 *in), 575 void (*felem_contract) (void 576 *out, 577 const 578 void 579 *in)); 580void ec_GFp_nistp_recode_scalar_bits(unsigned char *sign, 581 unsigned char *digit, unsigned char in); 582#endif 583int ec_group_simple_order_bits(const EC_GROUP *group); 584 585#ifdef ECP_NISTZ256_ASM 586/** Returns GFp methods using montgomery multiplication, with x86-64 optimized 587 * P256. See http://eprint.iacr.org/2013/816. 588 * \return EC_METHOD object 589 */ 590const EC_METHOD *EC_GFp_nistz256_method(void); 591#endif 592 593size_t ec_key_simple_priv2oct(const EC_KEY *eckey, 594 unsigned char *buf, size_t len); 595int ec_key_simple_oct2priv(EC_KEY *eckey, const unsigned char *buf, size_t len); 596int ec_key_simple_generate_key(EC_KEY *eckey); 597int ec_key_simple_generate_public_key(EC_KEY *eckey); 598int ec_key_simple_check_key(const EC_KEY *eckey); 599 600int ec_curve_nid_from_params(const EC_GROUP *group, BN_CTX *ctx); 601 602/* EC_METHOD definitions */ 603 604struct ec_key_method_st { 605 const char *name; 606 int32_t flags; 607 int (*init)(EC_KEY *key); 608 void (*finish)(EC_KEY *key); 609 int (*copy)(EC_KEY *dest, const EC_KEY *src); 610 int (*set_group)(EC_KEY *key, const EC_GROUP *grp); 611 int (*set_private)(EC_KEY *key, const BIGNUM *priv_key); 612 int (*set_public)(EC_KEY *key, const EC_POINT *pub_key); 613 int (*keygen)(EC_KEY *key); 614 int (*compute_key)(unsigned char **pout, size_t *poutlen, 615 const EC_POINT *pub_key, const EC_KEY *ecdh); 616 int (*sign)(int type, const unsigned char *dgst, int dlen, unsigned char 617 *sig, unsigned int *siglen, const BIGNUM *kinv, 618 const BIGNUM *r, EC_KEY *eckey); 619 int (*sign_setup)(EC_KEY *eckey, BN_CTX *ctx_in, BIGNUM **kinvp, 620 BIGNUM **rp); 621 ECDSA_SIG *(*sign_sig)(const unsigned char *dgst, int dgst_len, 622 const BIGNUM *in_kinv, const BIGNUM *in_r, 623 EC_KEY *eckey); 624 625 int (*verify)(int type, const unsigned char *dgst, int dgst_len, 626 const unsigned char *sigbuf, int sig_len, EC_KEY *eckey); 627 int (*verify_sig)(const unsigned char *dgst, int dgst_len, 628 const ECDSA_SIG *sig, EC_KEY *eckey); 629}; 630 631#define EC_KEY_METHOD_DYNAMIC 1 632 633int ossl_ec_key_gen(EC_KEY *eckey); 634int ossl_ecdh_compute_key(unsigned char **pout, size_t *poutlen, 635 const EC_POINT *pub_key, const EC_KEY *ecdh); 636int ecdh_simple_compute_key(unsigned char **pout, size_t *poutlen, 637 const EC_POINT *pub_key, const EC_KEY *ecdh); 638 639struct ECDSA_SIG_st { 640 BIGNUM *r; 641 BIGNUM *s; 642}; 643 644int ossl_ecdsa_sign_setup(EC_KEY *eckey, BN_CTX *ctx_in, BIGNUM **kinvp, 645 BIGNUM **rp); 646int ossl_ecdsa_sign(int type, const unsigned char *dgst, int dlen, 647 unsigned char *sig, unsigned int *siglen, 648 const BIGNUM *kinv, const BIGNUM *r, EC_KEY *eckey); 649ECDSA_SIG *ossl_ecdsa_sign_sig(const unsigned char *dgst, int dgst_len, 650 const BIGNUM *in_kinv, const BIGNUM *in_r, 651 EC_KEY *eckey); 652int ossl_ecdsa_verify(int type, const unsigned char *dgst, int dgst_len, 653 const unsigned char *sigbuf, int sig_len, EC_KEY *eckey); 654int ossl_ecdsa_verify_sig(const unsigned char *dgst, int dgst_len, 655 const ECDSA_SIG *sig, EC_KEY *eckey); 656 657int ED25519_sign(uint8_t *out_sig, const uint8_t *message, size_t message_len, 658 const uint8_t public_key[32], const uint8_t private_key[32]); 659int ED25519_verify(const uint8_t *message, size_t message_len, 660 const uint8_t signature[64], const uint8_t public_key[32]); 661void ED25519_public_from_private(uint8_t out_public_key[32], 662 const uint8_t private_key[32]); 663 664int X25519(uint8_t out_shared_key[32], const uint8_t private_key[32], 665 const uint8_t peer_public_value[32]); 666void X25519_public_from_private(uint8_t out_public_value[32], 667 const uint8_t private_key[32]); 668 669/*- 670 * This functions computes a single point multiplication over the EC group, 671 * using, at a high level, a Montgomery ladder with conditional swaps, with 672 * various timing attack defenses. 673 * 674 * It performs either a fixed point multiplication 675 * (scalar * generator) 676 * when point is NULL, or a variable point multiplication 677 * (scalar * point) 678 * when point is not NULL. 679 * 680 * `scalar` cannot be NULL and should be in the range [0,n) otherwise all 681 * constant time bets are off (where n is the cardinality of the EC group). 682 * 683 * This function expects `group->order` and `group->cardinality` to be well 684 * defined and non-zero: it fails with an error code otherwise. 685 * 686 * NB: This says nothing about the constant-timeness of the ladder step 687 * implementation (i.e., the default implementation is based on EC_POINT_add and 688 * EC_POINT_dbl, which of course are not constant time themselves) or the 689 * underlying multiprecision arithmetic. 690 * 691 * The product is stored in `r`. 692 * 693 * This is an internal function: callers are in charge of ensuring that the 694 * input parameters `group`, `r`, `scalar` and `ctx` are not NULL. 695 * 696 * Returns 1 on success, 0 otherwise. 697 */ 698int ec_scalar_mul_ladder(const EC_GROUP *group, EC_POINT *r, 699 const BIGNUM *scalar, const EC_POINT *point, 700 BN_CTX *ctx); 701 702int ec_point_blind_coordinates(const EC_GROUP *group, EC_POINT *p, BN_CTX *ctx); 703 704static ossl_inline int ec_point_ladder_pre(const EC_GROUP *group, 705 EC_POINT *r, EC_POINT *s, 706 EC_POINT *p, BN_CTX *ctx) 707{ 708 if (group->meth->ladder_pre != NULL) 709 return group->meth->ladder_pre(group, r, s, p, ctx); 710 711 if (!EC_POINT_copy(s, p) 712 || !EC_POINT_dbl(group, r, s, ctx)) 713 return 0; 714 715 return 1; 716} 717 718static ossl_inline int ec_point_ladder_step(const EC_GROUP *group, 719 EC_POINT *r, EC_POINT *s, 720 EC_POINT *p, BN_CTX *ctx) 721{ 722 if (group->meth->ladder_step != NULL) 723 return group->meth->ladder_step(group, r, s, p, ctx); 724 725 if (!EC_POINT_add(group, s, r, s, ctx) 726 || !EC_POINT_dbl(group, r, r, ctx)) 727 return 0; 728 729 return 1; 730 731} 732 733static ossl_inline int ec_point_ladder_post(const EC_GROUP *group, 734 EC_POINT *r, EC_POINT *s, 735 EC_POINT *p, BN_CTX *ctx) 736{ 737 if (group->meth->ladder_post != NULL) 738 return group->meth->ladder_post(group, r, s, p, ctx); 739 740 return 1; 741} 742