1 /* 2 * Copyright 2001-2019 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 39 struct 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 */ 200 typedef struct nistp224_pre_comp_st NISTP224_PRE_COMP; 201 typedef struct nistp256_pre_comp_st NISTP256_PRE_COMP; 202 typedef struct nistp521_pre_comp_st NISTP521_PRE_COMP; 203 typedef struct nistz256_pre_comp_st NISTZ256_PRE_COMP; 204 typedef struct ec_pre_comp_st EC_PRE_COMP; 205 206 struct 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 point_conversion_form_t asn1_form; 213 unsigned char *seed; /* optional seed for parameters (appears in 214 * ASN1) */ 215 size_t seed_len; 216 /* 217 * The following members are handled by the method functions, even if 218 * they appear generic 219 */ 220 /* 221 * Field specification. For curves over GF(p), this is the modulus; for 222 * curves over GF(2^m), this is the irreducible polynomial defining the 223 * field. 224 */ 225 BIGNUM *field; 226 /* 227 * Field specification for curves over GF(2^m). The irreducible f(t) is 228 * then of the form: t^poly[0] + t^poly[1] + ... + t^poly[k] where m = 229 * poly[0] > poly[1] > ... > poly[k] = 0. The array is terminated with 230 * poly[k+1]=-1. All elliptic curve irreducibles have at most 5 non-zero 231 * terms. 232 */ 233 int poly[6]; 234 /* 235 * Curve coefficients. (Here the assumption is that BIGNUMs can be used 236 * or abused for all kinds of fields, not just GF(p).) For characteristic 237 * > 3, the curve is defined by a Weierstrass equation of the form y^2 = 238 * x^3 + a*x + b. For characteristic 2, the curve is defined by an 239 * equation of the form y^2 + x*y = x^3 + a*x^2 + b. 240 */ 241 BIGNUM *a, *b; 242 /* enable optimized point arithmetics for special case */ 243 int a_is_minus3; 244 /* method-specific (e.g., Montgomery structure) */ 245 void *field_data1; 246 /* method-specific */ 247 void *field_data2; 248 /* method-specific */ 249 int (*field_mod_func) (BIGNUM *, const BIGNUM *, const BIGNUM *, 250 BN_CTX *); 251 /* data for ECDSA inverse */ 252 BN_MONT_CTX *mont_data; 253 254 /* 255 * Precomputed values for speed. The PCT_xxx names match the 256 * pre_comp.xxx union names; see the SETPRECOMP and HAVEPRECOMP 257 * macros, below. 258 */ 259 enum { 260 PCT_none, 261 PCT_nistp224, PCT_nistp256, PCT_nistp521, PCT_nistz256, 262 PCT_ec 263 } pre_comp_type; 264 union { 265 NISTP224_PRE_COMP *nistp224; 266 NISTP256_PRE_COMP *nistp256; 267 NISTP521_PRE_COMP *nistp521; 268 NISTZ256_PRE_COMP *nistz256; 269 EC_PRE_COMP *ec; 270 } pre_comp; 271 }; 272 273 #define SETPRECOMP(g, type, pre) \ 274 g->pre_comp_type = PCT_##type, g->pre_comp.type = pre 275 #define HAVEPRECOMP(g, type) \ 276 g->pre_comp_type == PCT_##type && g->pre_comp.type != NULL 277 278 struct ec_key_st { 279 const EC_KEY_METHOD *meth; 280 ENGINE *engine; 281 int version; 282 EC_GROUP *group; 283 EC_POINT *pub_key; 284 BIGNUM *priv_key; 285 unsigned int enc_flag; 286 point_conversion_form_t conv_form; 287 CRYPTO_REF_COUNT references; 288 int flags; 289 CRYPTO_EX_DATA ex_data; 290 CRYPTO_RWLOCK *lock; 291 }; 292 293 struct ec_point_st { 294 const EC_METHOD *meth; 295 /* NID for the curve if known */ 296 int curve_name; 297 /* 298 * All members except 'meth' are handled by the method functions, even if 299 * they appear generic 300 */ 301 BIGNUM *X; 302 BIGNUM *Y; 303 BIGNUM *Z; /* Jacobian projective coordinates: * (X, Y, 304 * Z) represents (X/Z^2, Y/Z^3) if Z != 0 */ 305 int Z_is_one; /* enable optimized point arithmetics for 306 * special case */ 307 }; 308 309 static ossl_inline int ec_point_is_compat(const EC_POINT *point, 310 const EC_GROUP *group) 311 { 312 if (group->meth != point->meth 313 || (group->curve_name != 0 314 && point->curve_name != 0 315 && group->curve_name != point->curve_name)) 316 return 0; 317 318 return 1; 319 } 320 321 NISTP224_PRE_COMP *EC_nistp224_pre_comp_dup(NISTP224_PRE_COMP *); 322 NISTP256_PRE_COMP *EC_nistp256_pre_comp_dup(NISTP256_PRE_COMP *); 323 NISTP521_PRE_COMP *EC_nistp521_pre_comp_dup(NISTP521_PRE_COMP *); 324 NISTZ256_PRE_COMP *EC_nistz256_pre_comp_dup(NISTZ256_PRE_COMP *); 325 NISTP256_PRE_COMP *EC_nistp256_pre_comp_dup(NISTP256_PRE_COMP *); 326 EC_PRE_COMP *EC_ec_pre_comp_dup(EC_PRE_COMP *); 327 328 void EC_pre_comp_free(EC_GROUP *group); 329 void EC_nistp224_pre_comp_free(NISTP224_PRE_COMP *); 330 void EC_nistp256_pre_comp_free(NISTP256_PRE_COMP *); 331 void EC_nistp521_pre_comp_free(NISTP521_PRE_COMP *); 332 void EC_nistz256_pre_comp_free(NISTZ256_PRE_COMP *); 333 void EC_ec_pre_comp_free(EC_PRE_COMP *); 334 335 /* 336 * method functions in ec_mult.c (ec_lib.c uses these as defaults if 337 * group->method->mul is 0) 338 */ 339 int ec_wNAF_mul(const EC_GROUP *group, EC_POINT *r, const BIGNUM *scalar, 340 size_t num, const EC_POINT *points[], const BIGNUM *scalars[], 341 BN_CTX *); 342 int ec_wNAF_precompute_mult(EC_GROUP *group, BN_CTX *); 343 int ec_wNAF_have_precompute_mult(const EC_GROUP *group); 344 345 /* method functions in ecp_smpl.c */ 346 int ec_GFp_simple_group_init(EC_GROUP *); 347 void ec_GFp_simple_group_finish(EC_GROUP *); 348 void ec_GFp_simple_group_clear_finish(EC_GROUP *); 349 int ec_GFp_simple_group_copy(EC_GROUP *, const EC_GROUP *); 350 int ec_GFp_simple_group_set_curve(EC_GROUP *, const BIGNUM *p, 351 const BIGNUM *a, const BIGNUM *b, BN_CTX *); 352 int ec_GFp_simple_group_get_curve(const EC_GROUP *, BIGNUM *p, BIGNUM *a, 353 BIGNUM *b, BN_CTX *); 354 int ec_GFp_simple_group_get_degree(const EC_GROUP *); 355 int ec_GFp_simple_group_check_discriminant(const EC_GROUP *, BN_CTX *); 356 int ec_GFp_simple_point_init(EC_POINT *); 357 void ec_GFp_simple_point_finish(EC_POINT *); 358 void ec_GFp_simple_point_clear_finish(EC_POINT *); 359 int ec_GFp_simple_point_copy(EC_POINT *, const EC_POINT *); 360 int ec_GFp_simple_point_set_to_infinity(const EC_GROUP *, EC_POINT *); 361 int ec_GFp_simple_set_Jprojective_coordinates_GFp(const EC_GROUP *, 362 EC_POINT *, const BIGNUM *x, 363 const BIGNUM *y, 364 const BIGNUM *z, BN_CTX *); 365 int ec_GFp_simple_get_Jprojective_coordinates_GFp(const EC_GROUP *, 366 const EC_POINT *, BIGNUM *x, 367 BIGNUM *y, BIGNUM *z, 368 BN_CTX *); 369 int ec_GFp_simple_point_set_affine_coordinates(const EC_GROUP *, EC_POINT *, 370 const BIGNUM *x, 371 const BIGNUM *y, BN_CTX *); 372 int ec_GFp_simple_point_get_affine_coordinates(const EC_GROUP *, 373 const EC_POINT *, BIGNUM *x, 374 BIGNUM *y, BN_CTX *); 375 int ec_GFp_simple_set_compressed_coordinates(const EC_GROUP *, EC_POINT *, 376 const BIGNUM *x, int y_bit, 377 BN_CTX *); 378 size_t ec_GFp_simple_point2oct(const EC_GROUP *, const EC_POINT *, 379 point_conversion_form_t form, 380 unsigned char *buf, size_t len, BN_CTX *); 381 int ec_GFp_simple_oct2point(const EC_GROUP *, EC_POINT *, 382 const unsigned char *buf, size_t len, BN_CTX *); 383 int ec_GFp_simple_add(const EC_GROUP *, EC_POINT *r, const EC_POINT *a, 384 const EC_POINT *b, BN_CTX *); 385 int ec_GFp_simple_dbl(const EC_GROUP *, EC_POINT *r, const EC_POINT *a, 386 BN_CTX *); 387 int ec_GFp_simple_invert(const EC_GROUP *, EC_POINT *, BN_CTX *); 388 int ec_GFp_simple_is_at_infinity(const EC_GROUP *, const EC_POINT *); 389 int ec_GFp_simple_is_on_curve(const EC_GROUP *, const EC_POINT *, BN_CTX *); 390 int ec_GFp_simple_cmp(const EC_GROUP *, const EC_POINT *a, const EC_POINT *b, 391 BN_CTX *); 392 int ec_GFp_simple_make_affine(const EC_GROUP *, EC_POINT *, BN_CTX *); 393 int ec_GFp_simple_points_make_affine(const EC_GROUP *, size_t num, 394 EC_POINT *[], BN_CTX *); 395 int ec_GFp_simple_field_mul(const EC_GROUP *, BIGNUM *r, const BIGNUM *a, 396 const BIGNUM *b, BN_CTX *); 397 int ec_GFp_simple_field_sqr(const EC_GROUP *, BIGNUM *r, const BIGNUM *a, 398 BN_CTX *); 399 int ec_GFp_simple_field_inv(const EC_GROUP *, BIGNUM *r, const BIGNUM *a, 400 BN_CTX *); 401 int ec_GFp_simple_blind_coordinates(const EC_GROUP *group, EC_POINT *p, 402 BN_CTX *ctx); 403 int ec_GFp_simple_ladder_pre(const EC_GROUP *group, 404 EC_POINT *r, EC_POINT *s, 405 EC_POINT *p, BN_CTX *ctx); 406 int ec_GFp_simple_ladder_step(const EC_GROUP *group, 407 EC_POINT *r, EC_POINT *s, 408 EC_POINT *p, BN_CTX *ctx); 409 int ec_GFp_simple_ladder_post(const EC_GROUP *group, 410 EC_POINT *r, EC_POINT *s, 411 EC_POINT *p, BN_CTX *ctx); 412 413 /* method functions in ecp_mont.c */ 414 int ec_GFp_mont_group_init(EC_GROUP *); 415 int ec_GFp_mont_group_set_curve(EC_GROUP *, const BIGNUM *p, const BIGNUM *a, 416 const BIGNUM *b, BN_CTX *); 417 void ec_GFp_mont_group_finish(EC_GROUP *); 418 void ec_GFp_mont_group_clear_finish(EC_GROUP *); 419 int ec_GFp_mont_group_copy(EC_GROUP *, const EC_GROUP *); 420 int ec_GFp_mont_field_mul(const EC_GROUP *, BIGNUM *r, const BIGNUM *a, 421 const BIGNUM *b, BN_CTX *); 422 int ec_GFp_mont_field_sqr(const EC_GROUP *, BIGNUM *r, const BIGNUM *a, 423 BN_CTX *); 424 int ec_GFp_mont_field_inv(const EC_GROUP *, BIGNUM *r, const BIGNUM *a, 425 BN_CTX *); 426 int ec_GFp_mont_field_encode(const EC_GROUP *, BIGNUM *r, const BIGNUM *a, 427 BN_CTX *); 428 int ec_GFp_mont_field_decode(const EC_GROUP *, BIGNUM *r, const BIGNUM *a, 429 BN_CTX *); 430 int ec_GFp_mont_field_set_to_one(const EC_GROUP *, BIGNUM *r, BN_CTX *); 431 432 /* method functions in ecp_nist.c */ 433 int ec_GFp_nist_group_copy(EC_GROUP *dest, const EC_GROUP *src); 434 int ec_GFp_nist_group_set_curve(EC_GROUP *, const BIGNUM *p, const BIGNUM *a, 435 const BIGNUM *b, BN_CTX *); 436 int ec_GFp_nist_field_mul(const EC_GROUP *, BIGNUM *r, const BIGNUM *a, 437 const BIGNUM *b, BN_CTX *); 438 int ec_GFp_nist_field_sqr(const EC_GROUP *, BIGNUM *r, const BIGNUM *a, 439 BN_CTX *); 440 441 /* method functions in ec2_smpl.c */ 442 int ec_GF2m_simple_group_init(EC_GROUP *); 443 void ec_GF2m_simple_group_finish(EC_GROUP *); 444 void ec_GF2m_simple_group_clear_finish(EC_GROUP *); 445 int ec_GF2m_simple_group_copy(EC_GROUP *, const EC_GROUP *); 446 int ec_GF2m_simple_group_set_curve(EC_GROUP *, const BIGNUM *p, 447 const BIGNUM *a, const BIGNUM *b, 448 BN_CTX *); 449 int ec_GF2m_simple_group_get_curve(const EC_GROUP *, BIGNUM *p, BIGNUM *a, 450 BIGNUM *b, BN_CTX *); 451 int ec_GF2m_simple_group_get_degree(const EC_GROUP *); 452 int ec_GF2m_simple_group_check_discriminant(const EC_GROUP *, BN_CTX *); 453 int ec_GF2m_simple_point_init(EC_POINT *); 454 void ec_GF2m_simple_point_finish(EC_POINT *); 455 void ec_GF2m_simple_point_clear_finish(EC_POINT *); 456 int ec_GF2m_simple_point_copy(EC_POINT *, const EC_POINT *); 457 int ec_GF2m_simple_point_set_to_infinity(const EC_GROUP *, EC_POINT *); 458 int ec_GF2m_simple_point_set_affine_coordinates(const EC_GROUP *, EC_POINT *, 459 const BIGNUM *x, 460 const BIGNUM *y, BN_CTX *); 461 int ec_GF2m_simple_point_get_affine_coordinates(const EC_GROUP *, 462 const EC_POINT *, BIGNUM *x, 463 BIGNUM *y, BN_CTX *); 464 int ec_GF2m_simple_set_compressed_coordinates(const EC_GROUP *, EC_POINT *, 465 const BIGNUM *x, int y_bit, 466 BN_CTX *); 467 size_t ec_GF2m_simple_point2oct(const EC_GROUP *, const EC_POINT *, 468 point_conversion_form_t form, 469 unsigned char *buf, size_t len, BN_CTX *); 470 int ec_GF2m_simple_oct2point(const EC_GROUP *, EC_POINT *, 471 const unsigned char *buf, size_t len, BN_CTX *); 472 int ec_GF2m_simple_add(const EC_GROUP *, EC_POINT *r, const EC_POINT *a, 473 const EC_POINT *b, BN_CTX *); 474 int ec_GF2m_simple_dbl(const EC_GROUP *, EC_POINT *r, const EC_POINT *a, 475 BN_CTX *); 476 int ec_GF2m_simple_invert(const EC_GROUP *, EC_POINT *, BN_CTX *); 477 int ec_GF2m_simple_is_at_infinity(const EC_GROUP *, const EC_POINT *); 478 int ec_GF2m_simple_is_on_curve(const EC_GROUP *, const EC_POINT *, BN_CTX *); 479 int ec_GF2m_simple_cmp(const EC_GROUP *, const EC_POINT *a, const EC_POINT *b, 480 BN_CTX *); 481 int ec_GF2m_simple_make_affine(const EC_GROUP *, EC_POINT *, BN_CTX *); 482 int ec_GF2m_simple_points_make_affine(const EC_GROUP *, size_t num, 483 EC_POINT *[], BN_CTX *); 484 int ec_GF2m_simple_field_mul(const EC_GROUP *, BIGNUM *r, const BIGNUM *a, 485 const BIGNUM *b, BN_CTX *); 486 int ec_GF2m_simple_field_sqr(const EC_GROUP *, BIGNUM *r, const BIGNUM *a, 487 BN_CTX *); 488 int ec_GF2m_simple_field_div(const EC_GROUP *, BIGNUM *r, const BIGNUM *a, 489 const BIGNUM *b, BN_CTX *); 490 491 #ifndef OPENSSL_NO_EC_NISTP_64_GCC_128 492 /* method functions in ecp_nistp224.c */ 493 int ec_GFp_nistp224_group_init(EC_GROUP *group); 494 int ec_GFp_nistp224_group_set_curve(EC_GROUP *group, const BIGNUM *p, 495 const BIGNUM *a, const BIGNUM *n, 496 BN_CTX *); 497 int ec_GFp_nistp224_point_get_affine_coordinates(const EC_GROUP *group, 498 const EC_POINT *point, 499 BIGNUM *x, BIGNUM *y, 500 BN_CTX *ctx); 501 int ec_GFp_nistp224_mul(const EC_GROUP *group, EC_POINT *r, 502 const BIGNUM *scalar, size_t num, 503 const EC_POINT *points[], const BIGNUM *scalars[], 504 BN_CTX *); 505 int ec_GFp_nistp224_points_mul(const EC_GROUP *group, EC_POINT *r, 506 const BIGNUM *scalar, size_t num, 507 const EC_POINT *points[], 508 const BIGNUM *scalars[], BN_CTX *ctx); 509 int ec_GFp_nistp224_precompute_mult(EC_GROUP *group, BN_CTX *ctx); 510 int ec_GFp_nistp224_have_precompute_mult(const EC_GROUP *group); 511 512 /* method functions in ecp_nistp256.c */ 513 int ec_GFp_nistp256_group_init(EC_GROUP *group); 514 int ec_GFp_nistp256_group_set_curve(EC_GROUP *group, const BIGNUM *p, 515 const BIGNUM *a, const BIGNUM *n, 516 BN_CTX *); 517 int ec_GFp_nistp256_point_get_affine_coordinates(const EC_GROUP *group, 518 const EC_POINT *point, 519 BIGNUM *x, BIGNUM *y, 520 BN_CTX *ctx); 521 int ec_GFp_nistp256_mul(const EC_GROUP *group, EC_POINT *r, 522 const BIGNUM *scalar, size_t num, 523 const EC_POINT *points[], const BIGNUM *scalars[], 524 BN_CTX *); 525 int ec_GFp_nistp256_points_mul(const EC_GROUP *group, EC_POINT *r, 526 const BIGNUM *scalar, size_t num, 527 const EC_POINT *points[], 528 const BIGNUM *scalars[], BN_CTX *ctx); 529 int ec_GFp_nistp256_precompute_mult(EC_GROUP *group, BN_CTX *ctx); 530 int ec_GFp_nistp256_have_precompute_mult(const EC_GROUP *group); 531 532 /* method functions in ecp_nistp521.c */ 533 int ec_GFp_nistp521_group_init(EC_GROUP *group); 534 int ec_GFp_nistp521_group_set_curve(EC_GROUP *group, const BIGNUM *p, 535 const BIGNUM *a, const BIGNUM *n, 536 BN_CTX *); 537 int ec_GFp_nistp521_point_get_affine_coordinates(const EC_GROUP *group, 538 const EC_POINT *point, 539 BIGNUM *x, BIGNUM *y, 540 BN_CTX *ctx); 541 int ec_GFp_nistp521_mul(const EC_GROUP *group, EC_POINT *r, 542 const BIGNUM *scalar, size_t num, 543 const EC_POINT *points[], const BIGNUM *scalars[], 544 BN_CTX *); 545 int ec_GFp_nistp521_points_mul(const EC_GROUP *group, EC_POINT *r, 546 const BIGNUM *scalar, size_t num, 547 const EC_POINT *points[], 548 const BIGNUM *scalars[], BN_CTX *ctx); 549 int ec_GFp_nistp521_precompute_mult(EC_GROUP *group, BN_CTX *ctx); 550 int ec_GFp_nistp521_have_precompute_mult(const EC_GROUP *group); 551 552 /* utility functions in ecp_nistputil.c */ 553 void ec_GFp_nistp_points_make_affine_internal(size_t num, void *point_array, 554 size_t felem_size, 555 void *tmp_felems, 556 void (*felem_one) (void *out), 557 int (*felem_is_zero) (const void 558 *in), 559 void (*felem_assign) (void *out, 560 const void 561 *in), 562 void (*felem_square) (void *out, 563 const void 564 *in), 565 void (*felem_mul) (void *out, 566 const void 567 *in1, 568 const void 569 *in2), 570 void (*felem_inv) (void *out, 571 const void 572 *in), 573 void (*felem_contract) (void 574 *out, 575 const 576 void 577 *in)); 578 void ec_GFp_nistp_recode_scalar_bits(unsigned char *sign, 579 unsigned char *digit, unsigned char in); 580 #endif 581 int ec_group_simple_order_bits(const EC_GROUP *group); 582 583 #ifdef ECP_NISTZ256_ASM 584 /** Returns GFp methods using montgomery multiplication, with x86-64 optimized 585 * P256. See http://eprint.iacr.org/2013/816. 586 * \return EC_METHOD object 587 */ 588 const EC_METHOD *EC_GFp_nistz256_method(void); 589 #endif 590 591 size_t ec_key_simple_priv2oct(const EC_KEY *eckey, 592 unsigned char *buf, size_t len); 593 int ec_key_simple_oct2priv(EC_KEY *eckey, const unsigned char *buf, size_t len); 594 int ec_key_simple_generate_key(EC_KEY *eckey); 595 int ec_key_simple_generate_public_key(EC_KEY *eckey); 596 int ec_key_simple_check_key(const EC_KEY *eckey); 597 598 int ec_curve_nid_from_params(const EC_GROUP *group, BN_CTX *ctx); 599 600 /* EC_METHOD definitions */ 601 602 struct ec_key_method_st { 603 const char *name; 604 int32_t flags; 605 int (*init)(EC_KEY *key); 606 void (*finish)(EC_KEY *key); 607 int (*copy)(EC_KEY *dest, const EC_KEY *src); 608 int (*set_group)(EC_KEY *key, const EC_GROUP *grp); 609 int (*set_private)(EC_KEY *key, const BIGNUM *priv_key); 610 int (*set_public)(EC_KEY *key, const EC_POINT *pub_key); 611 int (*keygen)(EC_KEY *key); 612 int (*compute_key)(unsigned char **pout, size_t *poutlen, 613 const EC_POINT *pub_key, const EC_KEY *ecdh); 614 int (*sign)(int type, const unsigned char *dgst, int dlen, unsigned char 615 *sig, unsigned int *siglen, const BIGNUM *kinv, 616 const BIGNUM *r, EC_KEY *eckey); 617 int (*sign_setup)(EC_KEY *eckey, BN_CTX *ctx_in, BIGNUM **kinvp, 618 BIGNUM **rp); 619 ECDSA_SIG *(*sign_sig)(const unsigned char *dgst, int dgst_len, 620 const BIGNUM *in_kinv, const BIGNUM *in_r, 621 EC_KEY *eckey); 622 623 int (*verify)(int type, const unsigned char *dgst, int dgst_len, 624 const unsigned char *sigbuf, int sig_len, EC_KEY *eckey); 625 int (*verify_sig)(const unsigned char *dgst, int dgst_len, 626 const ECDSA_SIG *sig, EC_KEY *eckey); 627 }; 628 629 #define EC_KEY_METHOD_DYNAMIC 1 630 631 int ossl_ec_key_gen(EC_KEY *eckey); 632 int ossl_ecdh_compute_key(unsigned char **pout, size_t *poutlen, 633 const EC_POINT *pub_key, const EC_KEY *ecdh); 634 int ecdh_simple_compute_key(unsigned char **pout, size_t *poutlen, 635 const EC_POINT *pub_key, const EC_KEY *ecdh); 636 637 struct ECDSA_SIG_st { 638 BIGNUM *r; 639 BIGNUM *s; 640 }; 641 642 int ossl_ecdsa_sign_setup(EC_KEY *eckey, BN_CTX *ctx_in, BIGNUM **kinvp, 643 BIGNUM **rp); 644 int ossl_ecdsa_sign(int type, const unsigned char *dgst, int dlen, 645 unsigned char *sig, unsigned int *siglen, 646 const BIGNUM *kinv, const BIGNUM *r, EC_KEY *eckey); 647 ECDSA_SIG *ossl_ecdsa_sign_sig(const unsigned char *dgst, int dgst_len, 648 const BIGNUM *in_kinv, const BIGNUM *in_r, 649 EC_KEY *eckey); 650 int ossl_ecdsa_verify(int type, const unsigned char *dgst, int dgst_len, 651 const unsigned char *sigbuf, int sig_len, EC_KEY *eckey); 652 int ossl_ecdsa_verify_sig(const unsigned char *dgst, int dgst_len, 653 const ECDSA_SIG *sig, EC_KEY *eckey); 654 655 int ED25519_sign(uint8_t *out_sig, const uint8_t *message, size_t message_len, 656 const uint8_t public_key[32], const uint8_t private_key[32]); 657 int ED25519_verify(const uint8_t *message, size_t message_len, 658 const uint8_t signature[64], const uint8_t public_key[32]); 659 void ED25519_public_from_private(uint8_t out_public_key[32], 660 const uint8_t private_key[32]); 661 662 int X25519(uint8_t out_shared_key[32], const uint8_t private_key[32], 663 const uint8_t peer_public_value[32]); 664 void X25519_public_from_private(uint8_t out_public_value[32], 665 const uint8_t private_key[32]); 666 667 /*- 668 * This functions computes a single point multiplication over the EC group, 669 * using, at a high level, a Montgomery ladder with conditional swaps, with 670 * various timing attack defenses. 671 * 672 * It performs either a fixed point multiplication 673 * (scalar * generator) 674 * when point is NULL, or a variable point multiplication 675 * (scalar * point) 676 * when point is not NULL. 677 * 678 * `scalar` cannot be NULL and should be in the range [0,n) otherwise all 679 * constant time bets are off (where n is the cardinality of the EC group). 680 * 681 * This function expects `group->order` and `group->cardinality` to be well 682 * defined and non-zero: it fails with an error code otherwise. 683 * 684 * NB: This says nothing about the constant-timeness of the ladder step 685 * implementation (i.e., the default implementation is based on EC_POINT_add and 686 * EC_POINT_dbl, which of course are not constant time themselves) or the 687 * underlying multiprecision arithmetic. 688 * 689 * The product is stored in `r`. 690 * 691 * This is an internal function: callers are in charge of ensuring that the 692 * input parameters `group`, `r`, `scalar` and `ctx` are not NULL. 693 * 694 * Returns 1 on success, 0 otherwise. 695 */ 696 int ec_scalar_mul_ladder(const EC_GROUP *group, EC_POINT *r, 697 const BIGNUM *scalar, const EC_POINT *point, 698 BN_CTX *ctx); 699 700 int ec_point_blind_coordinates(const EC_GROUP *group, EC_POINT *p, BN_CTX *ctx); 701 702 static ossl_inline int ec_point_ladder_pre(const EC_GROUP *group, 703 EC_POINT *r, EC_POINT *s, 704 EC_POINT *p, BN_CTX *ctx) 705 { 706 if (group->meth->ladder_pre != NULL) 707 return group->meth->ladder_pre(group, r, s, p, ctx); 708 709 if (!EC_POINT_copy(s, p) 710 || !EC_POINT_dbl(group, r, s, ctx)) 711 return 0; 712 713 return 1; 714 } 715 716 static ossl_inline int ec_point_ladder_step(const EC_GROUP *group, 717 EC_POINT *r, EC_POINT *s, 718 EC_POINT *p, BN_CTX *ctx) 719 { 720 if (group->meth->ladder_step != NULL) 721 return group->meth->ladder_step(group, r, s, p, ctx); 722 723 if (!EC_POINT_add(group, s, r, s, ctx) 724 || !EC_POINT_dbl(group, r, r, ctx)) 725 return 0; 726 727 return 1; 728 729 } 730 731 static ossl_inline int ec_point_ladder_post(const EC_GROUP *group, 732 EC_POINT *r, EC_POINT *s, 733 EC_POINT *p, BN_CTX *ctx) 734 { 735 if (group->meth->ladder_post != NULL) 736 return group->meth->ladder_post(group, r, s, p, ctx); 737 738 return 1; 739 } 740