1 /** 2 * \file ecp.h 3 * 4 * \brief This file provides an API for Elliptic Curves over GF(P) (ECP). 5 * 6 * The use of ECP in cryptography and TLS is defined in 7 * <em>Standards for Efficient Cryptography Group (SECG): SEC1 8 * Elliptic Curve Cryptography</em> and 9 * <em>RFC-4492: Elliptic Curve Cryptography (ECC) Cipher Suites 10 * for Transport Layer Security (TLS)</em>. 11 * 12 * <em>RFC-2409: The Internet Key Exchange (IKE)</em> defines ECP 13 * group types. 14 * 15 */ 16 17 /* 18 * Copyright The Mbed TLS Contributors 19 * SPDX-License-Identifier: Apache-2.0 20 * 21 * Licensed under the Apache License, Version 2.0 (the "License"); you may 22 * not use this file except in compliance with the License. 23 * You may obtain a copy of the License at 24 * 25 * http://www.apache.org/licenses/LICENSE-2.0 26 * 27 * Unless required by applicable law or agreed to in writing, software 28 * distributed under the License is distributed on an "AS IS" BASIS, WITHOUT 29 * WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. 30 * See the License for the specific language governing permissions and 31 * limitations under the License. 32 */ 33 34 #ifndef MBEDTLS_ECP_H 35 #define MBEDTLS_ECP_H 36 #include "mbedtls/private_access.h" 37 38 #include "mbedtls/build_info.h" 39 40 #include "mbedtls/bignum.h" 41 42 /* 43 * ECP error codes 44 */ 45 #define MBEDTLS_ERR_ECP_BAD_INPUT_DATA -0x4F80 /**< Bad input parameters to function. */ 46 #define MBEDTLS_ERR_ECP_BUFFER_TOO_SMALL -0x4F00 /**< The buffer is too small to write to. */ 47 #define MBEDTLS_ERR_ECP_FEATURE_UNAVAILABLE -0x4E80 /**< The requested feature is not available, for example, the requested curve is not supported. */ 48 #define MBEDTLS_ERR_ECP_VERIFY_FAILED -0x4E00 /**< The signature is not valid. */ 49 #define MBEDTLS_ERR_ECP_ALLOC_FAILED -0x4D80 /**< Memory allocation failed. */ 50 #define MBEDTLS_ERR_ECP_RANDOM_FAILED -0x4D00 /**< Generation of random value, such as ephemeral key, failed. */ 51 #define MBEDTLS_ERR_ECP_INVALID_KEY -0x4C80 /**< Invalid private or public key. */ 52 #define MBEDTLS_ERR_ECP_SIG_LEN_MISMATCH -0x4C00 /**< The buffer contains a valid signature followed by more data. */ 53 #define MBEDTLS_ERR_ECP_IN_PROGRESS -0x4B00 /**< Operation in progress, call again with the same parameters to continue. */ 54 55 /* Flags indicating whether to include code that is specific to certain 56 * types of curves. These flags are for internal library use only. */ 57 #if defined(MBEDTLS_ECP_DP_SECP192R1_ENABLED) || \ 58 defined(MBEDTLS_ECP_DP_SECP224R1_ENABLED) || \ 59 defined(MBEDTLS_ECP_DP_SECP256R1_ENABLED) || \ 60 defined(MBEDTLS_ECP_DP_SECP384R1_ENABLED) || \ 61 defined(MBEDTLS_ECP_DP_SECP521R1_ENABLED) || \ 62 defined(MBEDTLS_ECP_DP_BP256R1_ENABLED) || \ 63 defined(MBEDTLS_ECP_DP_BP384R1_ENABLED) || \ 64 defined(MBEDTLS_ECP_DP_BP512R1_ENABLED) || \ 65 defined(MBEDTLS_ECP_DP_SECP192K1_ENABLED) || \ 66 defined(MBEDTLS_ECP_DP_SECP224K1_ENABLED) || \ 67 defined(MBEDTLS_ECP_DP_SECP256K1_ENABLED) 68 #define MBEDTLS_ECP_SHORT_WEIERSTRASS_ENABLED 69 #endif 70 #if defined(MBEDTLS_ECP_DP_CURVE25519_ENABLED) || \ 71 defined(MBEDTLS_ECP_DP_CURVE448_ENABLED) 72 #define MBEDTLS_ECP_MONTGOMERY_ENABLED 73 #endif 74 75 #ifdef __cplusplus 76 extern "C" { 77 #endif 78 79 /** 80 * Domain-parameter identifiers: curve, subgroup, and generator. 81 * 82 * \note Only curves over prime fields are supported. 83 * 84 * \warning This library does not support validation of arbitrary domain 85 * parameters. Therefore, only standardized domain parameters from trusted 86 * sources should be used. See mbedtls_ecp_group_load(). 87 */ 88 /* Note: when adding a new curve: 89 * - Add it at the end of this enum, otherwise you'll break the ABI by 90 * changing the numerical value for existing curves. 91 * - Increment MBEDTLS_ECP_DP_MAX below if needed. 92 * - Update the calculation of MBEDTLS_ECP_MAX_BITS below. 93 * - Add the corresponding MBEDTLS_ECP_DP_xxx_ENABLED macro definition to 94 * mbedtls_config.h. 95 * - List the curve as a dependency of MBEDTLS_ECP_C and 96 * MBEDTLS_ECDSA_C if supported in check_config.h. 97 * - Add the curve to the appropriate curve type macro 98 * MBEDTLS_ECP_yyy_ENABLED above. 99 * - Add the necessary definitions to ecp_curves.c. 100 * - Add the curve to the ecp_supported_curves array in ecp.c. 101 * - Add the curve to applicable profiles in x509_crt.c. 102 * - Add the curve to applicable presets in ssl_tls.c. 103 */ 104 typedef enum 105 { 106 MBEDTLS_ECP_DP_NONE = 0, /*!< Curve not defined. */ 107 MBEDTLS_ECP_DP_SECP192R1, /*!< Domain parameters for the 192-bit curve defined by FIPS 186-4 and SEC1. */ 108 MBEDTLS_ECP_DP_SECP224R1, /*!< Domain parameters for the 224-bit curve defined by FIPS 186-4 and SEC1. */ 109 MBEDTLS_ECP_DP_SECP256R1, /*!< Domain parameters for the 256-bit curve defined by FIPS 186-4 and SEC1. */ 110 MBEDTLS_ECP_DP_SECP384R1, /*!< Domain parameters for the 384-bit curve defined by FIPS 186-4 and SEC1. */ 111 MBEDTLS_ECP_DP_SECP521R1, /*!< Domain parameters for the 521-bit curve defined by FIPS 186-4 and SEC1. */ 112 MBEDTLS_ECP_DP_BP256R1, /*!< Domain parameters for 256-bit Brainpool curve. */ 113 MBEDTLS_ECP_DP_BP384R1, /*!< Domain parameters for 384-bit Brainpool curve. */ 114 MBEDTLS_ECP_DP_BP512R1, /*!< Domain parameters for 512-bit Brainpool curve. */ 115 MBEDTLS_ECP_DP_CURVE25519, /*!< Domain parameters for Curve25519. */ 116 MBEDTLS_ECP_DP_SECP192K1, /*!< Domain parameters for 192-bit "Koblitz" curve. */ 117 MBEDTLS_ECP_DP_SECP224K1, /*!< Domain parameters for 224-bit "Koblitz" curve. */ 118 MBEDTLS_ECP_DP_SECP256K1, /*!< Domain parameters for 256-bit "Koblitz" curve. */ 119 MBEDTLS_ECP_DP_CURVE448, /*!< Domain parameters for Curve448. */ 120 } mbedtls_ecp_group_id; 121 122 /** 123 * The number of supported curves, plus one for #MBEDTLS_ECP_DP_NONE. 124 * 125 * \note Montgomery curves are currently excluded. 126 */ 127 #define MBEDTLS_ECP_DP_MAX 12 128 129 /* 130 * Curve types 131 */ 132 typedef enum 133 { 134 MBEDTLS_ECP_TYPE_NONE = 0, 135 MBEDTLS_ECP_TYPE_SHORT_WEIERSTRASS, /* y^2 = x^3 + a x + b */ 136 MBEDTLS_ECP_TYPE_MONTGOMERY, /* y^2 = x^3 + a x^2 + x */ 137 } mbedtls_ecp_curve_type; 138 139 /** 140 * Curve information, for use by other modules. 141 */ 142 typedef struct mbedtls_ecp_curve_info 143 { 144 mbedtls_ecp_group_id MBEDTLS_PRIVATE(grp_id); /*!< An internal identifier. */ 145 uint16_t MBEDTLS_PRIVATE(tls_id); /*!< The TLS NamedCurve identifier. */ 146 uint16_t MBEDTLS_PRIVATE(bit_size); /*!< The curve size in bits. */ 147 const char *MBEDTLS_PRIVATE(name); /*!< A human-friendly name. */ 148 } mbedtls_ecp_curve_info; 149 150 /** 151 * \brief The ECP point structure, in Jacobian coordinates. 152 * 153 * \note All functions expect and return points satisfying 154 * the following condition: <code>Z == 0</code> or 155 * <code>Z == 1</code>. Other values of \p Z are 156 * used only by internal functions. 157 * The point is zero, or "at infinity", if <code>Z == 0</code>. 158 * Otherwise, \p X and \p Y are its standard (affine) 159 * coordinates. 160 */ 161 typedef struct mbedtls_ecp_point 162 { 163 mbedtls_mpi MBEDTLS_PRIVATE(X); /*!< The X coordinate of the ECP point. */ 164 mbedtls_mpi MBEDTLS_PRIVATE(Y); /*!< The Y coordinate of the ECP point. */ 165 mbedtls_mpi MBEDTLS_PRIVATE(Z); /*!< The Z coordinate of the ECP point. */ 166 } 167 mbedtls_ecp_point; 168 169 #if !defined(MBEDTLS_ECP_ALT) 170 /* 171 * default mbed TLS elliptic curve arithmetic implementation 172 * 173 * (in case MBEDTLS_ECP_ALT is defined then the developer has to provide an 174 * alternative implementation for the whole module and it will replace this 175 * one.) 176 */ 177 178 /** 179 * \brief The ECP group structure. 180 * 181 * We consider two types of curve equations: 182 * <ul><li>Short Weierstrass: <code>y^2 = x^3 + A x + B mod P</code> 183 * (SEC1 + RFC-4492)</li> 184 * <li>Montgomery: <code>y^2 = x^3 + A x^2 + x mod P</code> (Curve25519, 185 * Curve448)</li></ul> 186 * In both cases, the generator (\p G) for a prime-order subgroup is fixed. 187 * 188 * For Short Weierstrass, this subgroup is the whole curve, and its 189 * cardinality is denoted by \p N. Our code requires that \p N is an 190 * odd prime as mbedtls_ecp_mul() requires an odd number, and 191 * mbedtls_ecdsa_sign() requires that it is prime for blinding purposes. 192 * 193 * For Montgomery curves, we do not store \p A, but <code>(A + 2) / 4</code>, 194 * which is the quantity used in the formulas. Additionally, \p nbits is 195 * not the size of \p N but the required size for private keys. 196 * 197 * If \p modp is NULL, reduction modulo \p P is done using a generic algorithm. 198 * Otherwise, \p modp must point to a function that takes an \p mbedtls_mpi in the 199 * range of <code>0..2^(2*pbits)-1</code>, and transforms it in-place to an integer 200 * which is congruent mod \p P to the given MPI, and is close enough to \p pbits 201 * in size, so that it may be efficiently brought in the 0..P-1 range by a few 202 * additions or subtractions. Therefore, it is only an approximative modular 203 * reduction. It must return 0 on success and non-zero on failure. 204 * 205 * \note Alternative implementations of the ECP module must obey the 206 * following constraints. 207 * * Group IDs must be distinct: if two group structures have 208 * the same ID, then they must be identical. 209 * * The fields \c id, \c P, \c A, \c B, \c G, \c N, 210 * \c pbits and \c nbits must have the same type and semantics 211 * as in the built-in implementation. 212 * They must be available for reading, but direct modification 213 * of these fields does not need to be supported. 214 * They do not need to be at the same offset in the structure. 215 */ 216 typedef struct mbedtls_ecp_group 217 { 218 mbedtls_ecp_group_id id; /*!< An internal group identifier. */ 219 mbedtls_mpi P; /*!< The prime modulus of the base field. */ 220 mbedtls_mpi A; /*!< For Short Weierstrass: \p A in the equation. For 221 Montgomery curves: <code>(A + 2) / 4</code>. */ 222 mbedtls_mpi B; /*!< For Short Weierstrass: \p B in the equation. 223 For Montgomery curves: unused. */ 224 mbedtls_ecp_point G; /*!< The generator of the subgroup used. */ 225 mbedtls_mpi N; /*!< The order of \p G. */ 226 size_t pbits; /*!< The number of bits in \p P.*/ 227 size_t nbits; /*!< For Short Weierstrass: The number of bits in \p P. 228 For Montgomery curves: the number of bits in the 229 private keys. */ 230 /* End of public fields */ 231 232 unsigned int MBEDTLS_PRIVATE(h); /*!< \internal 1 if the constants are static. */ 233 int (*MBEDTLS_PRIVATE(modp))(mbedtls_mpi *); /*!< The function for fast pseudo-reduction 234 mod \p P (see above).*/ 235 int (*MBEDTLS_PRIVATE(t_pre))(mbedtls_ecp_point *, void *); /*!< Unused. */ 236 int (*MBEDTLS_PRIVATE(t_post))(mbedtls_ecp_point *, void *); /*!< Unused. */ 237 void *MBEDTLS_PRIVATE(t_data); /*!< Unused. */ 238 mbedtls_ecp_point *MBEDTLS_PRIVATE(T); /*!< Pre-computed points for ecp_mul_comb(). */ 239 size_t MBEDTLS_PRIVATE(T_size); /*!< The number of dynamic allocated pre-computed points. */ 240 } 241 mbedtls_ecp_group; 242 243 /** 244 * \name SECTION: Module settings 245 * 246 * The configuration options you can set for this module are in this section. 247 * Either change them in mbedtls_config.h, or define them using the compiler command line. 248 * \{ 249 */ 250 251 #if !defined(MBEDTLS_ECP_WINDOW_SIZE) 252 /* 253 * Maximum "window" size used for point multiplication. 254 * Default: a point where higher memory usage yields disminishing performance 255 * returns. 256 * Minimum value: 2. Maximum value: 7. 257 * 258 * Result is an array of at most ( 1 << ( MBEDTLS_ECP_WINDOW_SIZE - 1 ) ) 259 * points used for point multiplication. This value is directly tied to EC 260 * peak memory usage, so decreasing it by one should roughly cut memory usage 261 * by two (if large curves are in use). 262 * 263 * Reduction in size may reduce speed, but larger curves are impacted first. 264 * Sample performances (in ECDHE handshakes/s, with FIXED_POINT_OPTIM = 1): 265 * w-size: 6 5 4 3 2 266 * 521 145 141 135 120 97 267 * 384 214 209 198 177 146 268 * 256 320 320 303 262 226 269 * 224 475 475 453 398 342 270 * 192 640 640 633 587 476 271 */ 272 #define MBEDTLS_ECP_WINDOW_SIZE 4 /**< The maximum window size used. */ 273 #endif /* MBEDTLS_ECP_WINDOW_SIZE */ 274 275 #if !defined(MBEDTLS_ECP_FIXED_POINT_OPTIM) 276 /* 277 * Trade code size for speed on fixed-point multiplication. 278 * 279 * This speeds up repeated multiplication of the generator (that is, the 280 * multiplication in ECDSA signatures, and half of the multiplications in 281 * ECDSA verification and ECDHE) by a factor roughly 3 to 4. 282 * 283 * For each n-bit Short Weierstrass curve that is enabled, this adds 4n bytes 284 * of code size if n < 384 and 8n otherwise. 285 * 286 * Change this value to 0 to reduce code size. 287 */ 288 #define MBEDTLS_ECP_FIXED_POINT_OPTIM 1 /**< Enable fixed-point speed-up. */ 289 #endif /* MBEDTLS_ECP_FIXED_POINT_OPTIM */ 290 291 /* \} name SECTION: Module settings */ 292 293 #else /* MBEDTLS_ECP_ALT */ 294 #include "ecp_alt.h" 295 #endif /* MBEDTLS_ECP_ALT */ 296 297 /** 298 * The maximum size of the groups, that is, of \c N and \c P. 299 */ 300 #if !defined(MBEDTLS_ECP_C) 301 /* Dummy definition to help code that has optional ECP support and 302 * defines an MBEDTLS_ECP_MAX_BYTES-sized array unconditionally. */ 303 #define MBEDTLS_ECP_MAX_BITS 1 304 /* Note: the curves must be listed in DECREASING size! */ 305 #elif defined(MBEDTLS_ECP_DP_SECP521R1_ENABLED) 306 #define MBEDTLS_ECP_MAX_BITS 521 307 #elif defined(MBEDTLS_ECP_DP_BP512R1_ENABLED) 308 #define MBEDTLS_ECP_MAX_BITS 512 309 #elif defined(MBEDTLS_ECP_DP_CURVE448_ENABLED) 310 #define MBEDTLS_ECP_MAX_BITS 448 311 #elif defined(MBEDTLS_ECP_DP_BP384R1_ENABLED) 312 #define MBEDTLS_ECP_MAX_BITS 384 313 #elif defined(MBEDTLS_ECP_DP_SECP384R1_ENABLED) 314 #define MBEDTLS_ECP_MAX_BITS 384 315 #elif defined(MBEDTLS_ECP_DP_BP256R1_ENABLED) 316 #define MBEDTLS_ECP_MAX_BITS 256 317 #elif defined(MBEDTLS_ECP_DP_SECP256K1_ENABLED) 318 #define MBEDTLS_ECP_MAX_BITS 256 319 #elif defined(MBEDTLS_ECP_DP_SECP256R1_ENABLED) 320 #define MBEDTLS_ECP_MAX_BITS 256 321 #elif defined(MBEDTLS_ECP_DP_CURVE25519_ENABLED) 322 #define MBEDTLS_ECP_MAX_BITS 255 323 #elif defined(MBEDTLS_ECP_DP_SECP224K1_ENABLED) 324 #define MBEDTLS_ECP_MAX_BITS 225 // n is slightly above 2^224 325 #elif defined(MBEDTLS_ECP_DP_SECP224R1_ENABLED) 326 #define MBEDTLS_ECP_MAX_BITS 224 327 #elif defined(MBEDTLS_ECP_DP_SECP192K1_ENABLED) 328 #define MBEDTLS_ECP_MAX_BITS 192 329 #elif defined(MBEDTLS_ECP_DP_SECP192R1_ENABLED) 330 #define MBEDTLS_ECP_MAX_BITS 192 331 #else 332 #error "Missing definition of MBEDTLS_ECP_MAX_BITS" 333 #endif 334 335 #define MBEDTLS_ECP_MAX_BYTES ( ( MBEDTLS_ECP_MAX_BITS + 7 ) / 8 ) 336 #define MBEDTLS_ECP_MAX_PT_LEN ( 2 * MBEDTLS_ECP_MAX_BYTES + 1 ) 337 338 #if defined(MBEDTLS_ECP_RESTARTABLE) 339 340 /** 341 * \brief Internal restart context for multiplication 342 * 343 * \note Opaque struct 344 */ 345 typedef struct mbedtls_ecp_restart_mul mbedtls_ecp_restart_mul_ctx; 346 347 /** 348 * \brief Internal restart context for ecp_muladd() 349 * 350 * \note Opaque struct 351 */ 352 typedef struct mbedtls_ecp_restart_muladd mbedtls_ecp_restart_muladd_ctx; 353 354 /** 355 * \brief General context for resuming ECC operations 356 */ 357 typedef struct 358 { 359 unsigned MBEDTLS_PRIVATE(ops_done); /*!< current ops count */ 360 unsigned MBEDTLS_PRIVATE(depth); /*!< call depth (0 = top-level) */ 361 mbedtls_ecp_restart_mul_ctx *MBEDTLS_PRIVATE(rsm); /*!< ecp_mul_comb() sub-context */ 362 mbedtls_ecp_restart_muladd_ctx *MBEDTLS_PRIVATE(ma); /*!< ecp_muladd() sub-context */ 363 } mbedtls_ecp_restart_ctx; 364 365 /* 366 * Operation counts for restartable functions 367 */ 368 #define MBEDTLS_ECP_OPS_CHK 3 /*!< basic ops count for ecp_check_pubkey() */ 369 #define MBEDTLS_ECP_OPS_DBL 8 /*!< basic ops count for ecp_double_jac() */ 370 #define MBEDTLS_ECP_OPS_ADD 11 /*!< basic ops count for see ecp_add_mixed() */ 371 #define MBEDTLS_ECP_OPS_INV 120 /*!< empirical equivalent for mpi_mod_inv() */ 372 373 /** 374 * \brief Internal; for restartable functions in other modules. 375 * Check and update basic ops budget. 376 * 377 * \param grp Group structure 378 * \param rs_ctx Restart context 379 * \param ops Number of basic ops to do 380 * 381 * \return \c 0 if doing \p ops basic ops is still allowed, 382 * \return #MBEDTLS_ERR_ECP_IN_PROGRESS otherwise. 383 */ 384 int mbedtls_ecp_check_budget( const mbedtls_ecp_group *grp, 385 mbedtls_ecp_restart_ctx *rs_ctx, 386 unsigned ops ); 387 388 /* Utility macro for checking and updating ops budget */ 389 #define MBEDTLS_ECP_BUDGET( ops ) \ 390 MBEDTLS_MPI_CHK( mbedtls_ecp_check_budget( grp, rs_ctx, \ 391 (unsigned) (ops) ) ); 392 393 #else /* MBEDTLS_ECP_RESTARTABLE */ 394 395 #define MBEDTLS_ECP_BUDGET( ops ) /* no-op; for compatibility */ 396 397 /* We want to declare restartable versions of existing functions anyway */ 398 typedef void mbedtls_ecp_restart_ctx; 399 400 #endif /* MBEDTLS_ECP_RESTARTABLE */ 401 402 /** 403 * \brief The ECP key-pair structure. 404 * 405 * A generic key-pair that may be used for ECDSA and fixed ECDH, for example. 406 * 407 * \note Members are deliberately in the same order as in the 408 * ::mbedtls_ecdsa_context structure. 409 */ 410 typedef struct mbedtls_ecp_keypair 411 { 412 mbedtls_ecp_group MBEDTLS_PRIVATE(grp); /*!< Elliptic curve and base point */ 413 mbedtls_mpi MBEDTLS_PRIVATE(d); /*!< our secret value */ 414 mbedtls_ecp_point MBEDTLS_PRIVATE(Q); /*!< our public value */ 415 } 416 mbedtls_ecp_keypair; 417 418 /* 419 * Point formats, from RFC 4492's enum ECPointFormat 420 */ 421 #define MBEDTLS_ECP_PF_UNCOMPRESSED 0 /**< Uncompressed point format. */ 422 #define MBEDTLS_ECP_PF_COMPRESSED 1 /**< Compressed point format. */ 423 424 /* 425 * Some other constants from RFC 4492 426 */ 427 #define MBEDTLS_ECP_TLS_NAMED_CURVE 3 /**< The named_curve of ECCurveType. */ 428 429 #if defined(MBEDTLS_ECP_RESTARTABLE) 430 /** 431 * \brief Set the maximum number of basic operations done in a row. 432 * 433 * If more operations are needed to complete a computation, 434 * #MBEDTLS_ERR_ECP_IN_PROGRESS will be returned by the 435 * function performing the computation. It is then the 436 * caller's responsibility to either call again with the same 437 * parameters until it returns 0 or an error code; or to free 438 * the restart context if the operation is to be aborted. 439 * 440 * It is strictly required that all input parameters and the 441 * restart context be the same on successive calls for the 442 * same operation, but output parameters need not be the 443 * same; they must not be used until the function finally 444 * returns 0. 445 * 446 * This only applies to functions whose documentation 447 * mentions they may return #MBEDTLS_ERR_ECP_IN_PROGRESS (or 448 * #MBEDTLS_ERR_SSL_CRYPTO_IN_PROGRESS for functions in the 449 * SSL module). For functions that accept a "restart context" 450 * argument, passing NULL disables restart and makes the 451 * function equivalent to the function with the same name 452 * with \c _restartable removed. For functions in the ECDH 453 * module, restart is disabled unless the function accepts 454 * an "ECDH context" argument and 455 * mbedtls_ecdh_enable_restart() was previously called on 456 * that context. For function in the SSL module, restart is 457 * only enabled for specific sides and key exchanges 458 * (currently only for clients and ECDHE-ECDSA). 459 * 460 * \param max_ops Maximum number of basic operations done in a row. 461 * Default: 0 (unlimited). 462 * Lower (non-zero) values mean ECC functions will block for 463 * a lesser maximum amount of time. 464 * 465 * \note A "basic operation" is defined as a rough equivalent of a 466 * multiplication in GF(p) for the NIST P-256 curve. 467 * As an indication, with default settings, a scalar 468 * multiplication (full run of \c mbedtls_ecp_mul()) is: 469 * - about 3300 basic operations for P-256 470 * - about 9400 basic operations for P-384 471 * 472 * \note Very low values are not always respected: sometimes 473 * functions need to block for a minimum number of 474 * operations, and will do so even if max_ops is set to a 475 * lower value. That minimum depends on the curve size, and 476 * can be made lower by decreasing the value of 477 * \c MBEDTLS_ECP_WINDOW_SIZE. As an indication, here is the 478 * lowest effective value for various curves and values of 479 * that parameter (w for short): 480 * w=6 w=5 w=4 w=3 w=2 481 * P-256 208 208 160 136 124 482 * P-384 682 416 320 272 248 483 * P-521 1364 832 640 544 496 484 * 485 * \note This setting is currently ignored by Curve25519. 486 */ 487 void mbedtls_ecp_set_max_ops( unsigned max_ops ); 488 489 /** 490 * \brief Check if restart is enabled (max_ops != 0) 491 * 492 * \return \c 0 if \c max_ops == 0 (restart disabled) 493 * \return \c 1 otherwise (restart enabled) 494 */ 495 int mbedtls_ecp_restart_is_enabled( void ); 496 #endif /* MBEDTLS_ECP_RESTARTABLE */ 497 498 /* 499 * Get the type of a curve 500 */ 501 mbedtls_ecp_curve_type mbedtls_ecp_get_type( const mbedtls_ecp_group *grp ); 502 503 /** 504 * \brief This function retrieves the information defined in 505 * mbedtls_ecp_curve_info() for all supported curves. 506 * 507 * \note This function returns information about all curves 508 * supported by the library. Some curves may not be 509 * supported for all algorithms. Call mbedtls_ecdh_can_do() 510 * or mbedtls_ecdsa_can_do() to check if a curve is 511 * supported for ECDH or ECDSA. 512 * 513 * \return A statically allocated array. The last entry is 0. 514 */ 515 const mbedtls_ecp_curve_info *mbedtls_ecp_curve_list( void ); 516 517 /** 518 * \brief This function retrieves the list of internal group 519 * identifiers of all supported curves in the order of 520 * preference. 521 * 522 * \note This function returns information about all curves 523 * supported by the library. Some curves may not be 524 * supported for all algorithms. Call mbedtls_ecdh_can_do() 525 * or mbedtls_ecdsa_can_do() to check if a curve is 526 * supported for ECDH or ECDSA. 527 * 528 * \return A statically allocated array, 529 * terminated with MBEDTLS_ECP_DP_NONE. 530 */ 531 const mbedtls_ecp_group_id *mbedtls_ecp_grp_id_list( void ); 532 533 /** 534 * \brief This function retrieves curve information from an internal 535 * group identifier. 536 * 537 * \param grp_id An \c MBEDTLS_ECP_DP_XXX value. 538 * 539 * \return The associated curve information on success. 540 * \return NULL on failure. 541 */ 542 const mbedtls_ecp_curve_info *mbedtls_ecp_curve_info_from_grp_id( mbedtls_ecp_group_id grp_id ); 543 544 /** 545 * \brief This function retrieves curve information from a TLS 546 * NamedCurve value. 547 * 548 * \param tls_id An \c MBEDTLS_ECP_DP_XXX value. 549 * 550 * \return The associated curve information on success. 551 * \return NULL on failure. 552 */ 553 const mbedtls_ecp_curve_info *mbedtls_ecp_curve_info_from_tls_id( uint16_t tls_id ); 554 555 /** 556 * \brief This function retrieves curve information from a 557 * human-readable name. 558 * 559 * \param name The human-readable name. 560 * 561 * \return The associated curve information on success. 562 * \return NULL on failure. 563 */ 564 const mbedtls_ecp_curve_info *mbedtls_ecp_curve_info_from_name( const char *name ); 565 566 /** 567 * \brief This function initializes a point as zero. 568 * 569 * \param pt The point to initialize. 570 */ 571 void mbedtls_ecp_point_init( mbedtls_ecp_point *pt ); 572 573 /** 574 * \brief This function initializes an ECP group context 575 * without loading any domain parameters. 576 * 577 * \note After this function is called, domain parameters 578 * for various ECP groups can be loaded through the 579 * mbedtls_ecp_group_load() or mbedtls_ecp_tls_read_group() 580 * functions. 581 */ 582 void mbedtls_ecp_group_init( mbedtls_ecp_group *grp ); 583 584 /** 585 * \brief This function initializes a key pair as an invalid one. 586 * 587 * \param key The key pair to initialize. 588 */ 589 void mbedtls_ecp_keypair_init( mbedtls_ecp_keypair *key ); 590 591 /** 592 * \brief This function frees the components of a point. 593 * 594 * \param pt The point to free. 595 */ 596 void mbedtls_ecp_point_free( mbedtls_ecp_point *pt ); 597 598 /** 599 * \brief This function frees the components of an ECP group. 600 * 601 * \param grp The group to free. This may be \c NULL, in which 602 * case this function returns immediately. If it is not 603 * \c NULL, it must point to an initialized ECP group. 604 */ 605 void mbedtls_ecp_group_free( mbedtls_ecp_group *grp ); 606 607 /** 608 * \brief This function frees the components of a key pair. 609 * 610 * \param key The key pair to free. This may be \c NULL, in which 611 * case this function returns immediately. If it is not 612 * \c NULL, it must point to an initialized ECP key pair. 613 */ 614 void mbedtls_ecp_keypair_free( mbedtls_ecp_keypair *key ); 615 616 #if defined(MBEDTLS_ECP_RESTARTABLE) 617 /** 618 * \brief Initialize a restart context. 619 * 620 * \param ctx The restart context to initialize. This must 621 * not be \c NULL. 622 */ 623 void mbedtls_ecp_restart_init( mbedtls_ecp_restart_ctx *ctx ); 624 625 /** 626 * \brief Free the components of a restart context. 627 * 628 * \param ctx The restart context to free. This may be \c NULL, in which 629 * case this function returns immediately. If it is not 630 * \c NULL, it must point to an initialized restart context. 631 */ 632 void mbedtls_ecp_restart_free( mbedtls_ecp_restart_ctx *ctx ); 633 #endif /* MBEDTLS_ECP_RESTARTABLE */ 634 635 /** 636 * \brief This function copies the contents of point \p Q into 637 * point \p P. 638 * 639 * \param P The destination point. This must be initialized. 640 * \param Q The source point. This must be initialized. 641 * 642 * \return \c 0 on success. 643 * \return #MBEDTLS_ERR_MPI_ALLOC_FAILED on memory-allocation failure. 644 * \return Another negative error code for other kinds of failure. 645 */ 646 int mbedtls_ecp_copy( mbedtls_ecp_point *P, const mbedtls_ecp_point *Q ); 647 648 /** 649 * \brief This function copies the contents of group \p src into 650 * group \p dst. 651 * 652 * \param dst The destination group. This must be initialized. 653 * \param src The source group. This must be initialized. 654 * 655 * \return \c 0 on success. 656 * \return #MBEDTLS_ERR_MPI_ALLOC_FAILED on memory-allocation failure. 657 * \return Another negative error code on other kinds of failure. 658 */ 659 int mbedtls_ecp_group_copy( mbedtls_ecp_group *dst, 660 const mbedtls_ecp_group *src ); 661 662 /** 663 * \brief This function sets a point to the point at infinity. 664 * 665 * \param pt The point to set. This must be initialized. 666 * 667 * \return \c 0 on success. 668 * \return #MBEDTLS_ERR_MPI_ALLOC_FAILED on memory-allocation failure. 669 * \return Another negative error code on other kinds of failure. 670 */ 671 int mbedtls_ecp_set_zero( mbedtls_ecp_point *pt ); 672 673 /** 674 * \brief This function checks if a point is the point at infinity. 675 * 676 * \param pt The point to test. This must be initialized. 677 * 678 * \return \c 1 if the point is zero. 679 * \return \c 0 if the point is non-zero. 680 * \return A negative error code on failure. 681 */ 682 int mbedtls_ecp_is_zero( mbedtls_ecp_point *pt ); 683 684 /** 685 * \brief This function compares two points. 686 * 687 * \note This assumes that the points are normalized. Otherwise, 688 * they may compare as "not equal" even if they are. 689 * 690 * \param P The first point to compare. This must be initialized. 691 * \param Q The second point to compare. This must be initialized. 692 * 693 * \return \c 0 if the points are equal. 694 * \return #MBEDTLS_ERR_ECP_BAD_INPUT_DATA if the points are not equal. 695 */ 696 int mbedtls_ecp_point_cmp( const mbedtls_ecp_point *P, 697 const mbedtls_ecp_point *Q ); 698 699 /** 700 * \brief This function imports a non-zero point from two ASCII 701 * strings. 702 * 703 * \param P The destination point. This must be initialized. 704 * \param radix The numeric base of the input. 705 * \param x The first affine coordinate, as a null-terminated string. 706 * \param y The second affine coordinate, as a null-terminated string. 707 * 708 * \return \c 0 on success. 709 * \return An \c MBEDTLS_ERR_MPI_XXX error code on failure. 710 */ 711 int mbedtls_ecp_point_read_string( mbedtls_ecp_point *P, int radix, 712 const char *x, const char *y ); 713 714 /** 715 * \brief This function exports a point into unsigned binary data. 716 * 717 * \param grp The group to which the point should belong. 718 * This must be initialized and have group parameters 719 * set, for example through mbedtls_ecp_group_load(). 720 * \param P The point to export. This must be initialized. 721 * \param format The point format. This must be either 722 * #MBEDTLS_ECP_PF_COMPRESSED or #MBEDTLS_ECP_PF_UNCOMPRESSED. 723 * (For groups without these formats, this parameter is 724 * ignored. But it still has to be either of the above 725 * values.) 726 * \param olen The address at which to store the length of 727 * the output in Bytes. This must not be \c NULL. 728 * \param buf The output buffer. This must be a writable buffer 729 * of length \p buflen Bytes. 730 * \param buflen The length of the output buffer \p buf in Bytes. 731 * 732 * \return \c 0 on success. 733 * \return #MBEDTLS_ERR_ECP_BUFFER_TOO_SMALL if the output buffer 734 * is too small to hold the point. 735 * \return #MBEDTLS_ERR_ECP_FEATURE_UNAVAILABLE if the point format 736 * or the export for the given group is not implemented. 737 * \return Another negative error code on other kinds of failure. 738 */ 739 int mbedtls_ecp_point_write_binary( const mbedtls_ecp_group *grp, 740 const mbedtls_ecp_point *P, 741 int format, size_t *olen, 742 unsigned char *buf, size_t buflen ); 743 744 /** 745 * \brief This function imports a point from unsigned binary data. 746 * 747 * \note This function does not check that the point actually 748 * belongs to the given group, see mbedtls_ecp_check_pubkey() 749 * for that. 750 * 751 * \param grp The group to which the point should belong. 752 * This must be initialized and have group parameters 753 * set, for example through mbedtls_ecp_group_load(). 754 * \param P The destination context to import the point to. 755 * This must be initialized. 756 * \param buf The input buffer. This must be a readable buffer 757 * of length \p ilen Bytes. 758 * \param ilen The length of the input buffer \p buf in Bytes. 759 * 760 * \return \c 0 on success. 761 * \return #MBEDTLS_ERR_ECP_BAD_INPUT_DATA if the input is invalid. 762 * \return #MBEDTLS_ERR_MPI_ALLOC_FAILED on memory-allocation failure. 763 * \return #MBEDTLS_ERR_ECP_FEATURE_UNAVAILABLE if the import for the 764 * given group is not implemented. 765 */ 766 int mbedtls_ecp_point_read_binary( const mbedtls_ecp_group *grp, 767 mbedtls_ecp_point *P, 768 const unsigned char *buf, size_t ilen ); 769 770 /** 771 * \brief This function imports a point from a TLS ECPoint record. 772 * 773 * \note On function return, \p *buf is updated to point immediately 774 * after the ECPoint record. 775 * 776 * \param grp The ECP group to use. 777 * This must be initialized and have group parameters 778 * set, for example through mbedtls_ecp_group_load(). 779 * \param pt The destination point. 780 * \param buf The address of the pointer to the start of the input buffer. 781 * \param len The length of the buffer. 782 * 783 * \return \c 0 on success. 784 * \return An \c MBEDTLS_ERR_MPI_XXX error code on initialization 785 * failure. 786 * \return #MBEDTLS_ERR_ECP_BAD_INPUT_DATA if input is invalid. 787 */ 788 int mbedtls_ecp_tls_read_point( const mbedtls_ecp_group *grp, 789 mbedtls_ecp_point *pt, 790 const unsigned char **buf, size_t len ); 791 792 /** 793 * \brief This function exports a point as a TLS ECPoint record 794 * defined in RFC 4492, Section 5.4. 795 * 796 * \param grp The ECP group to use. 797 * This must be initialized and have group parameters 798 * set, for example through mbedtls_ecp_group_load(). 799 * \param pt The point to be exported. This must be initialized. 800 * \param format The point format to use. This must be either 801 * #MBEDTLS_ECP_PF_COMPRESSED or #MBEDTLS_ECP_PF_UNCOMPRESSED. 802 * \param olen The address at which to store the length in Bytes 803 * of the data written. 804 * \param buf The target buffer. This must be a writable buffer of 805 * length \p blen Bytes. 806 * \param blen The length of the target buffer \p buf in Bytes. 807 * 808 * \return \c 0 on success. 809 * \return #MBEDTLS_ERR_ECP_BAD_INPUT_DATA if the input is invalid. 810 * \return #MBEDTLS_ERR_ECP_BUFFER_TOO_SMALL if the target buffer 811 * is too small to hold the exported point. 812 * \return Another negative error code on other kinds of failure. 813 */ 814 int mbedtls_ecp_tls_write_point( const mbedtls_ecp_group *grp, 815 const mbedtls_ecp_point *pt, 816 int format, size_t *olen, 817 unsigned char *buf, size_t blen ); 818 819 /** 820 * \brief This function sets up an ECP group context 821 * from a standardized set of domain parameters. 822 * 823 * \note The index should be a value of the NamedCurve enum, 824 * as defined in <em>RFC-4492: Elliptic Curve Cryptography 825 * (ECC) Cipher Suites for Transport Layer Security (TLS)</em>, 826 * usually in the form of an \c MBEDTLS_ECP_DP_XXX macro. 827 * 828 * \param grp The group context to setup. This must be initialized. 829 * \param id The identifier of the domain parameter set to load. 830 * 831 * \return \c 0 on success. 832 * \return #MBEDTLS_ERR_ECP_FEATURE_UNAVAILABLE if \p id doesn't 833 * correspond to a known group. 834 * \return Another negative error code on other kinds of failure. 835 */ 836 int mbedtls_ecp_group_load( mbedtls_ecp_group *grp, mbedtls_ecp_group_id id ); 837 838 /** 839 * \brief This function sets up an ECP group context from a TLS 840 * ECParameters record as defined in RFC 4492, Section 5.4. 841 * 842 * \note The read pointer \p buf is updated to point right after 843 * the ECParameters record on exit. 844 * 845 * \param grp The group context to setup. This must be initialized. 846 * \param buf The address of the pointer to the start of the input buffer. 847 * \param len The length of the input buffer \c *buf in Bytes. 848 * 849 * \return \c 0 on success. 850 * \return #MBEDTLS_ERR_ECP_BAD_INPUT_DATA if input is invalid. 851 * \return #MBEDTLS_ERR_ECP_FEATURE_UNAVAILABLE if the group is not 852 * recognized. 853 * \return Another negative error code on other kinds of failure. 854 */ 855 int mbedtls_ecp_tls_read_group( mbedtls_ecp_group *grp, 856 const unsigned char **buf, size_t len ); 857 858 /** 859 * \brief This function extracts an elliptic curve group ID from a 860 * TLS ECParameters record as defined in RFC 4492, Section 5.4. 861 * 862 * \note The read pointer \p buf is updated to point right after 863 * the ECParameters record on exit. 864 * 865 * \param grp The address at which to store the group id. 866 * This must not be \c NULL. 867 * \param buf The address of the pointer to the start of the input buffer. 868 * \param len The length of the input buffer \c *buf in Bytes. 869 * 870 * \return \c 0 on success. 871 * \return #MBEDTLS_ERR_ECP_BAD_INPUT_DATA if input is invalid. 872 * \return #MBEDTLS_ERR_ECP_FEATURE_UNAVAILABLE if the group is not 873 * recognized. 874 * \return Another negative error code on other kinds of failure. 875 */ 876 int mbedtls_ecp_tls_read_group_id( mbedtls_ecp_group_id *grp, 877 const unsigned char **buf, 878 size_t len ); 879 /** 880 * \brief This function exports an elliptic curve as a TLS 881 * ECParameters record as defined in RFC 4492, Section 5.4. 882 * 883 * \param grp The ECP group to be exported. 884 * This must be initialized and have group parameters 885 * set, for example through mbedtls_ecp_group_load(). 886 * \param olen The address at which to store the number of Bytes written. 887 * This must not be \c NULL. 888 * \param buf The buffer to write to. This must be a writable buffer 889 * of length \p blen Bytes. 890 * \param blen The length of the output buffer \p buf in Bytes. 891 * 892 * \return \c 0 on success. 893 * \return #MBEDTLS_ERR_ECP_BUFFER_TOO_SMALL if the output 894 * buffer is too small to hold the exported group. 895 * \return Another negative error code on other kinds of failure. 896 */ 897 int mbedtls_ecp_tls_write_group( const mbedtls_ecp_group *grp, 898 size_t *olen, 899 unsigned char *buf, size_t blen ); 900 901 /** 902 * \brief This function performs a scalar multiplication of a point 903 * by an integer: \p R = \p m * \p P. 904 * 905 * It is not thread-safe to use same group in multiple threads. 906 * 907 * \note To prevent timing attacks, this function 908 * executes the exact same sequence of base-field 909 * operations for any valid \p m. It avoids any if-branch or 910 * array index depending on the value of \p m. If also uses 911 * \p f_rng to randomize some intermediate results. 912 * 913 * \param grp The ECP group to use. 914 * This must be initialized and have group parameters 915 * set, for example through mbedtls_ecp_group_load(). 916 * \param R The point in which to store the result of the calculation. 917 * This must be initialized. 918 * \param m The integer by which to multiply. This must be initialized. 919 * \param P The point to multiply. This must be initialized. 920 * \param f_rng The RNG function. This must not be \c NULL. 921 * \param p_rng The RNG context to be passed to \p f_rng. This may be \c 922 * NULL if \p f_rng doesn't need a context. 923 * 924 * \return \c 0 on success. 925 * \return #MBEDTLS_ERR_ECP_INVALID_KEY if \p m is not a valid private 926 * key, or \p P is not a valid public key. 927 * \return #MBEDTLS_ERR_MPI_ALLOC_FAILED on memory-allocation failure. 928 * \return Another negative error code on other kinds of failure. 929 */ 930 int mbedtls_ecp_mul( mbedtls_ecp_group *grp, mbedtls_ecp_point *R, 931 const mbedtls_mpi *m, const mbedtls_ecp_point *P, 932 int (*f_rng)(void *, unsigned char *, size_t), void *p_rng ); 933 934 /** 935 * \brief This function performs multiplication of a point by 936 * an integer: \p R = \p m * \p P in a restartable way. 937 * 938 * \see mbedtls_ecp_mul() 939 * 940 * \note This function does the same as \c mbedtls_ecp_mul(), but 941 * it can return early and restart according to the limit set 942 * with \c mbedtls_ecp_set_max_ops() to reduce blocking. 943 * 944 * \param grp The ECP group to use. 945 * This must be initialized and have group parameters 946 * set, for example through mbedtls_ecp_group_load(). 947 * \param R The point in which to store the result of the calculation. 948 * This must be initialized. 949 * \param m The integer by which to multiply. This must be initialized. 950 * \param P The point to multiply. This must be initialized. 951 * \param f_rng The RNG function. This must not be \c NULL. 952 * \param p_rng The RNG context to be passed to \p f_rng. This may be \c 953 * NULL if \p f_rng doesn't need a context. 954 * \param rs_ctx The restart context (NULL disables restart). 955 * 956 * \return \c 0 on success. 957 * \return #MBEDTLS_ERR_ECP_INVALID_KEY if \p m is not a valid private 958 * key, or \p P is not a valid public key. 959 * \return #MBEDTLS_ERR_MPI_ALLOC_FAILED on memory-allocation failure. 960 * \return #MBEDTLS_ERR_ECP_IN_PROGRESS if maximum number of 961 * operations was reached: see \c mbedtls_ecp_set_max_ops(). 962 * \return Another negative error code on other kinds of failure. 963 */ 964 int mbedtls_ecp_mul_restartable( mbedtls_ecp_group *grp, mbedtls_ecp_point *R, 965 const mbedtls_mpi *m, const mbedtls_ecp_point *P, 966 int (*f_rng)(void *, unsigned char *, size_t), void *p_rng, 967 mbedtls_ecp_restart_ctx *rs_ctx ); 968 969 #if defined(MBEDTLS_ECP_SHORT_WEIERSTRASS_ENABLED) 970 /** 971 * \brief This function performs multiplication and addition of two 972 * points by integers: \p R = \p m * \p P + \p n * \p Q 973 * 974 * It is not thread-safe to use same group in multiple threads. 975 * 976 * \note In contrast to mbedtls_ecp_mul(), this function does not 977 * guarantee a constant execution flow and timing. 978 * 979 * \note This function is only defined for short Weierstrass curves. 980 * It may not be included in builds without any short 981 * Weierstrass curve. 982 * 983 * \param grp The ECP group to use. 984 * This must be initialized and have group parameters 985 * set, for example through mbedtls_ecp_group_load(). 986 * \param R The point in which to store the result of the calculation. 987 * This must be initialized. 988 * \param m The integer by which to multiply \p P. 989 * This must be initialized. 990 * \param P The point to multiply by \p m. This must be initialized. 991 * \param n The integer by which to multiply \p Q. 992 * This must be initialized. 993 * \param Q The point to be multiplied by \p n. 994 * This must be initialized. 995 * 996 * \return \c 0 on success. 997 * \return #MBEDTLS_ERR_ECP_INVALID_KEY if \p m or \p n are not 998 * valid private keys, or \p P or \p Q are not valid public 999 * keys. 1000 * \return #MBEDTLS_ERR_MPI_ALLOC_FAILED on memory-allocation failure. 1001 * \return #MBEDTLS_ERR_ECP_FEATURE_UNAVAILABLE if \p grp does not 1002 * designate a short Weierstrass curve. 1003 * \return Another negative error code on other kinds of failure. 1004 */ 1005 int mbedtls_ecp_muladd( mbedtls_ecp_group *grp, mbedtls_ecp_point *R, 1006 const mbedtls_mpi *m, const mbedtls_ecp_point *P, 1007 const mbedtls_mpi *n, const mbedtls_ecp_point *Q ); 1008 1009 /** 1010 * \brief This function performs multiplication and addition of two 1011 * points by integers: \p R = \p m * \p P + \p n * \p Q in a 1012 * restartable way. 1013 * 1014 * \see \c mbedtls_ecp_muladd() 1015 * 1016 * \note This function works the same as \c mbedtls_ecp_muladd(), 1017 * but it can return early and restart according to the limit 1018 * set with \c mbedtls_ecp_set_max_ops() to reduce blocking. 1019 * 1020 * \note This function is only defined for short Weierstrass curves. 1021 * It may not be included in builds without any short 1022 * Weierstrass curve. 1023 * 1024 * \param grp The ECP group to use. 1025 * This must be initialized and have group parameters 1026 * set, for example through mbedtls_ecp_group_load(). 1027 * \param R The point in which to store the result of the calculation. 1028 * This must be initialized. 1029 * \param m The integer by which to multiply \p P. 1030 * This must be initialized. 1031 * \param P The point to multiply by \p m. This must be initialized. 1032 * \param n The integer by which to multiply \p Q. 1033 * This must be initialized. 1034 * \param Q The point to be multiplied by \p n. 1035 * This must be initialized. 1036 * \param rs_ctx The restart context (NULL disables restart). 1037 * 1038 * \return \c 0 on success. 1039 * \return #MBEDTLS_ERR_ECP_INVALID_KEY if \p m or \p n are not 1040 * valid private keys, or \p P or \p Q are not valid public 1041 * keys. 1042 * \return #MBEDTLS_ERR_MPI_ALLOC_FAILED on memory-allocation failure. 1043 * \return #MBEDTLS_ERR_ECP_FEATURE_UNAVAILABLE if \p grp does not 1044 * designate a short Weierstrass curve. 1045 * \return #MBEDTLS_ERR_ECP_IN_PROGRESS if maximum number of 1046 * operations was reached: see \c mbedtls_ecp_set_max_ops(). 1047 * \return Another negative error code on other kinds of failure. 1048 */ 1049 int mbedtls_ecp_muladd_restartable( 1050 mbedtls_ecp_group *grp, mbedtls_ecp_point *R, 1051 const mbedtls_mpi *m, const mbedtls_ecp_point *P, 1052 const mbedtls_mpi *n, const mbedtls_ecp_point *Q, 1053 mbedtls_ecp_restart_ctx *rs_ctx ); 1054 #endif /* MBEDTLS_ECP_SHORT_WEIERSTRASS_ENABLED */ 1055 1056 /** 1057 * \brief This function checks that a point is a valid public key 1058 * on this curve. 1059 * 1060 * It only checks that the point is non-zero, has 1061 * valid coordinates and lies on the curve. It does not verify 1062 * that it is indeed a multiple of \p G. This additional 1063 * check is computationally more expensive, is not required 1064 * by standards, and should not be necessary if the group 1065 * used has a small cofactor. In particular, it is useless for 1066 * the NIST groups which all have a cofactor of 1. 1067 * 1068 * \note This function uses bare components rather than an 1069 * ::mbedtls_ecp_keypair structure, to ease use with other 1070 * structures, such as ::mbedtls_ecdh_context or 1071 * ::mbedtls_ecdsa_context. 1072 * 1073 * \param grp The ECP group the point should belong to. 1074 * This must be initialized and have group parameters 1075 * set, for example through mbedtls_ecp_group_load(). 1076 * \param pt The point to check. This must be initialized. 1077 * 1078 * \return \c 0 if the point is a valid public key. 1079 * \return #MBEDTLS_ERR_ECP_INVALID_KEY if the point is not 1080 * a valid public key for the given curve. 1081 * \return Another negative error code on other kinds of failure. 1082 */ 1083 int mbedtls_ecp_check_pubkey( const mbedtls_ecp_group *grp, 1084 const mbedtls_ecp_point *pt ); 1085 1086 /** 1087 * \brief This function checks that an \p mbedtls_mpi is a 1088 * valid private key for this curve. 1089 * 1090 * \note This function uses bare components rather than an 1091 * ::mbedtls_ecp_keypair structure to ease use with other 1092 * structures, such as ::mbedtls_ecdh_context or 1093 * ::mbedtls_ecdsa_context. 1094 * 1095 * \param grp The ECP group the private key should belong to. 1096 * This must be initialized and have group parameters 1097 * set, for example through mbedtls_ecp_group_load(). 1098 * \param d The integer to check. This must be initialized. 1099 * 1100 * \return \c 0 if the point is a valid private key. 1101 * \return #MBEDTLS_ERR_ECP_INVALID_KEY if the point is not a valid 1102 * private key for the given curve. 1103 * \return Another negative error code on other kinds of failure. 1104 */ 1105 int mbedtls_ecp_check_privkey( const mbedtls_ecp_group *grp, 1106 const mbedtls_mpi *d ); 1107 1108 /** 1109 * \brief This function generates a private key. 1110 * 1111 * \param grp The ECP group to generate a private key for. 1112 * This must be initialized and have group parameters 1113 * set, for example through mbedtls_ecp_group_load(). 1114 * \param d The destination MPI (secret part). This must be initialized. 1115 * \param f_rng The RNG function. This must not be \c NULL. 1116 * \param p_rng The RNG parameter to be passed to \p f_rng. This may be 1117 * \c NULL if \p f_rng doesn't need a context argument. 1118 * 1119 * \return \c 0 on success. 1120 * \return An \c MBEDTLS_ERR_ECP_XXX or \c MBEDTLS_MPI_XXX error code 1121 * on failure. 1122 */ 1123 int mbedtls_ecp_gen_privkey( const mbedtls_ecp_group *grp, 1124 mbedtls_mpi *d, 1125 int (*f_rng)(void *, unsigned char *, size_t), 1126 void *p_rng ); 1127 1128 /** 1129 * \brief This function generates a keypair with a configurable base 1130 * point. 1131 * 1132 * \note This function uses bare components rather than an 1133 * ::mbedtls_ecp_keypair structure to ease use with other 1134 * structures, such as ::mbedtls_ecdh_context or 1135 * ::mbedtls_ecdsa_context. 1136 * 1137 * \param grp The ECP group to generate a key pair for. 1138 * This must be initialized and have group parameters 1139 * set, for example through mbedtls_ecp_group_load(). 1140 * \param G The base point to use. This must be initialized 1141 * and belong to \p grp. It replaces the default base 1142 * point \c grp->G used by mbedtls_ecp_gen_keypair(). 1143 * \param d The destination MPI (secret part). 1144 * This must be initialized. 1145 * \param Q The destination point (public part). 1146 * This must be initialized. 1147 * \param f_rng The RNG function. This must not be \c NULL. 1148 * \param p_rng The RNG context to be passed to \p f_rng. This may 1149 * be \c NULL if \p f_rng doesn't need a context argument. 1150 * 1151 * \return \c 0 on success. 1152 * \return An \c MBEDTLS_ERR_ECP_XXX or \c MBEDTLS_MPI_XXX error code 1153 * on failure. 1154 */ 1155 int mbedtls_ecp_gen_keypair_base( mbedtls_ecp_group *grp, 1156 const mbedtls_ecp_point *G, 1157 mbedtls_mpi *d, mbedtls_ecp_point *Q, 1158 int (*f_rng)(void *, unsigned char *, size_t), 1159 void *p_rng ); 1160 1161 /** 1162 * \brief This function generates an ECP keypair. 1163 * 1164 * \note This function uses bare components rather than an 1165 * ::mbedtls_ecp_keypair structure to ease use with other 1166 * structures, such as ::mbedtls_ecdh_context or 1167 * ::mbedtls_ecdsa_context. 1168 * 1169 * \param grp The ECP group to generate a key pair for. 1170 * This must be initialized and have group parameters 1171 * set, for example through mbedtls_ecp_group_load(). 1172 * \param d The destination MPI (secret part). 1173 * This must be initialized. 1174 * \param Q The destination point (public part). 1175 * This must be initialized. 1176 * \param f_rng The RNG function. This must not be \c NULL. 1177 * \param p_rng The RNG context to be passed to \p f_rng. This may 1178 * be \c NULL if \p f_rng doesn't need a context argument. 1179 * 1180 * \return \c 0 on success. 1181 * \return An \c MBEDTLS_ERR_ECP_XXX or \c MBEDTLS_MPI_XXX error code 1182 * on failure. 1183 */ 1184 int mbedtls_ecp_gen_keypair( mbedtls_ecp_group *grp, mbedtls_mpi *d, 1185 mbedtls_ecp_point *Q, 1186 int (*f_rng)(void *, unsigned char *, size_t), 1187 void *p_rng ); 1188 1189 /** 1190 * \brief This function generates an ECP key. 1191 * 1192 * \param grp_id The ECP group identifier. 1193 * \param key The destination key. This must be initialized. 1194 * \param f_rng The RNG function to use. This must not be \c NULL. 1195 * \param p_rng The RNG context to be passed to \p f_rng. This may 1196 * be \c NULL if \p f_rng doesn't need a context argument. 1197 * 1198 * \return \c 0 on success. 1199 * \return An \c MBEDTLS_ERR_ECP_XXX or \c MBEDTLS_MPI_XXX error code 1200 * on failure. 1201 */ 1202 int mbedtls_ecp_gen_key( mbedtls_ecp_group_id grp_id, mbedtls_ecp_keypair *key, 1203 int (*f_rng)(void *, unsigned char *, size_t), 1204 void *p_rng ); 1205 1206 /** 1207 * \brief This function reads an elliptic curve private key. 1208 * 1209 * \param grp_id The ECP group identifier. 1210 * \param key The destination key. 1211 * \param buf The buffer containing the binary representation of the 1212 * key. (Big endian integer for Weierstrass curves, byte 1213 * string for Montgomery curves.) 1214 * \param buflen The length of the buffer in bytes. 1215 * 1216 * \return \c 0 on success. 1217 * \return #MBEDTLS_ERR_ECP_INVALID_KEY error if the key is 1218 * invalid. 1219 * \return #MBEDTLS_ERR_MPI_ALLOC_FAILED if memory allocation failed. 1220 * \return #MBEDTLS_ERR_ECP_FEATURE_UNAVAILABLE if the operation for 1221 * the group is not implemented. 1222 * \return Another negative error code on different kinds of failure. 1223 */ 1224 int mbedtls_ecp_read_key( mbedtls_ecp_group_id grp_id, mbedtls_ecp_keypair *key, 1225 const unsigned char *buf, size_t buflen ); 1226 1227 /** 1228 * \brief This function exports an elliptic curve private key. 1229 * 1230 * \param key The private key. 1231 * \param buf The output buffer for containing the binary representation 1232 * of the key. (Big endian integer for Weierstrass curves, byte 1233 * string for Montgomery curves.) 1234 * \param buflen The total length of the buffer in bytes. 1235 * 1236 * \return \c 0 on success. 1237 * \return #MBEDTLS_ERR_ECP_BUFFER_TOO_SMALL if the \p key 1238 representation is larger than the available space in \p buf. 1239 * \return #MBEDTLS_ERR_ECP_FEATURE_UNAVAILABLE if the operation for 1240 * the group is not implemented. 1241 * \return Another negative error code on different kinds of failure. 1242 */ 1243 int mbedtls_ecp_write_key( mbedtls_ecp_keypair *key, 1244 unsigned char *buf, size_t buflen ); 1245 1246 /** 1247 * \brief This function checks that the keypair objects 1248 * \p pub and \p prv have the same group and the 1249 * same public point, and that the private key in 1250 * \p prv is consistent with the public key. 1251 * 1252 * \param pub The keypair structure holding the public key. This 1253 * must be initialized. If it contains a private key, that 1254 * part is ignored. 1255 * \param prv The keypair structure holding the full keypair. 1256 * This must be initialized. 1257 * \param f_rng The RNG function. This must not be \c NULL. 1258 * \param p_rng The RNG context to be passed to \p f_rng. This may be \c 1259 * NULL if \p f_rng doesn't need a context. 1260 * 1261 * \return \c 0 on success, meaning that the keys are valid and match. 1262 * \return #MBEDTLS_ERR_ECP_BAD_INPUT_DATA if the keys are invalid or do not match. 1263 * \return An \c MBEDTLS_ERR_ECP_XXX or an \c MBEDTLS_ERR_MPI_XXX 1264 * error code on calculation failure. 1265 */ 1266 int mbedtls_ecp_check_pub_priv( 1267 const mbedtls_ecp_keypair *pub, const mbedtls_ecp_keypair *prv, 1268 int (*f_rng)(void *, unsigned char *, size_t), void *p_rng ); 1269 1270 #if defined(MBEDTLS_SELF_TEST) 1271 1272 /** 1273 * \brief The ECP checkup routine. 1274 * 1275 * \return \c 0 on success. 1276 * \return \c 1 on failure. 1277 */ 1278 int mbedtls_ecp_self_test( int verbose ); 1279 1280 #endif /* MBEDTLS_SELF_TEST */ 1281 1282 #ifdef __cplusplus 1283 } 1284 #endif 1285 1286 #endif /* ecp.h */ 1287
