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 /** Bad input parameters to function. */ 46 #define MBEDTLS_ERR_ECP_BAD_INPUT_DATA -0x4F80 47 /** The buffer is too small to write to. */ 48 #define MBEDTLS_ERR_ECP_BUFFER_TOO_SMALL -0x4F00 49 /** The requested feature is not available, for example, the requested curve is not supported. */ 50 #define MBEDTLS_ERR_ECP_FEATURE_UNAVAILABLE -0x4E80 51 /** The signature is not valid. */ 52 #define MBEDTLS_ERR_ECP_VERIFY_FAILED -0x4E00 53 /** Memory allocation failed. */ 54 #define MBEDTLS_ERR_ECP_ALLOC_FAILED -0x4D80 55 /** Generation of random value, such as ephemeral key, failed. */ 56 #define MBEDTLS_ERR_ECP_RANDOM_FAILED -0x4D00 57 /** Invalid private or public key. */ 58 #define MBEDTLS_ERR_ECP_INVALID_KEY -0x4C80 59 /** The buffer contains a valid signature followed by more data. */ 60 #define MBEDTLS_ERR_ECP_SIG_LEN_MISMATCH -0x4C00 61 /** Operation in progress, call again with the same parameters to continue. */ 62 #define MBEDTLS_ERR_ECP_IN_PROGRESS -0x4B00 63 64 /* Flags indicating whether to include code that is specific to certain 65 * types of curves. These flags are for internal library use only. */ 66 #if defined(MBEDTLS_ECP_DP_SECP192R1_ENABLED) || \ 67 defined(MBEDTLS_ECP_DP_SECP224R1_ENABLED) || \ 68 defined(MBEDTLS_ECP_DP_SECP256R1_ENABLED) || \ 69 defined(MBEDTLS_ECP_DP_SECP384R1_ENABLED) || \ 70 defined(MBEDTLS_ECP_DP_SECP521R1_ENABLED) || \ 71 defined(MBEDTLS_ECP_DP_BP256R1_ENABLED) || \ 72 defined(MBEDTLS_ECP_DP_BP384R1_ENABLED) || \ 73 defined(MBEDTLS_ECP_DP_BP512R1_ENABLED) || \ 74 defined(MBEDTLS_ECP_DP_SECP192K1_ENABLED) || \ 75 defined(MBEDTLS_ECP_DP_SECP224K1_ENABLED) || \ 76 defined(MBEDTLS_ECP_DP_SECP256K1_ENABLED) 77 #define MBEDTLS_ECP_SHORT_WEIERSTRASS_ENABLED 78 #endif 79 #if defined(MBEDTLS_ECP_DP_CURVE25519_ENABLED) || \ 80 defined(MBEDTLS_ECP_DP_CURVE448_ENABLED) 81 #define MBEDTLS_ECP_MONTGOMERY_ENABLED 82 #endif 83 84 #ifdef __cplusplus 85 extern "C" { 86 #endif 87 88 /** 89 * Domain-parameter identifiers: curve, subgroup, and generator. 90 * 91 * \note Only curves over prime fields are supported. 92 * 93 * \warning This library does not support validation of arbitrary domain 94 * parameters. Therefore, only standardized domain parameters from trusted 95 * sources should be used. See mbedtls_ecp_group_load(). 96 */ 97 /* Note: when adding a new curve: 98 * - Add it at the end of this enum, otherwise you'll break the ABI by 99 * changing the numerical value for existing curves. 100 * - Increment MBEDTLS_ECP_DP_MAX below if needed. 101 * - Update the calculation of MBEDTLS_ECP_MAX_BITS below. 102 * - Add the corresponding MBEDTLS_ECP_DP_xxx_ENABLED macro definition to 103 * mbedtls_config.h. 104 * - List the curve as a dependency of MBEDTLS_ECP_C and 105 * MBEDTLS_ECDSA_C if supported in check_config.h. 106 * - Add the curve to the appropriate curve type macro 107 * MBEDTLS_ECP_yyy_ENABLED above. 108 * - Add the necessary definitions to ecp_curves.c. 109 * - Add the curve to the ecp_supported_curves array in ecp.c. 110 * - Add the curve to applicable profiles in x509_crt.c. 111 * - Add the curve to applicable presets in ssl_tls.c. 112 */ 113 typedef enum 114 { 115 MBEDTLS_ECP_DP_NONE = 0, /*!< Curve not defined. */ 116 MBEDTLS_ECP_DP_SECP192R1, /*!< Domain parameters for the 192-bit curve defined by FIPS 186-4 and SEC1. */ 117 MBEDTLS_ECP_DP_SECP224R1, /*!< Domain parameters for the 224-bit curve defined by FIPS 186-4 and SEC1. */ 118 MBEDTLS_ECP_DP_SECP256R1, /*!< Domain parameters for the 256-bit curve defined by FIPS 186-4 and SEC1. */ 119 MBEDTLS_ECP_DP_SECP384R1, /*!< Domain parameters for the 384-bit curve defined by FIPS 186-4 and SEC1. */ 120 MBEDTLS_ECP_DP_SECP521R1, /*!< Domain parameters for the 521-bit curve defined by FIPS 186-4 and SEC1. */ 121 MBEDTLS_ECP_DP_BP256R1, /*!< Domain parameters for 256-bit Brainpool curve. */ 122 MBEDTLS_ECP_DP_BP384R1, /*!< Domain parameters for 384-bit Brainpool curve. */ 123 MBEDTLS_ECP_DP_BP512R1, /*!< Domain parameters for 512-bit Brainpool curve. */ 124 MBEDTLS_ECP_DP_CURVE25519, /*!< Domain parameters for Curve25519. */ 125 MBEDTLS_ECP_DP_SECP192K1, /*!< Domain parameters for 192-bit "Koblitz" curve. */ 126 MBEDTLS_ECP_DP_SECP224K1, /*!< Domain parameters for 224-bit "Koblitz" curve. */ 127 MBEDTLS_ECP_DP_SECP256K1, /*!< Domain parameters for 256-bit "Koblitz" curve. */ 128 MBEDTLS_ECP_DP_CURVE448, /*!< Domain parameters for Curve448. */ 129 } mbedtls_ecp_group_id; 130 131 /** 132 * The number of supported curves, plus one for #MBEDTLS_ECP_DP_NONE. 133 */ 134 #define MBEDTLS_ECP_DP_MAX 14 135 136 /* 137 * Curve types 138 */ 139 typedef enum 140 { 141 MBEDTLS_ECP_TYPE_NONE = 0, 142 MBEDTLS_ECP_TYPE_SHORT_WEIERSTRASS, /* y^2 = x^3 + a x + b */ 143 MBEDTLS_ECP_TYPE_MONTGOMERY, /* y^2 = x^3 + a x^2 + x */ 144 } mbedtls_ecp_curve_type; 145 146 /** 147 * Curve information, for use by other modules. 148 * 149 * The fields of this structure are part of the public API and can be 150 * accessed directly by applications. Future versions of the library may 151 * add extra fields or reorder existing fields. 152 */ 153 typedef struct mbedtls_ecp_curve_info 154 { 155 mbedtls_ecp_group_id grp_id; /*!< An internal identifier. */ 156 uint16_t tls_id; /*!< The TLS NamedCurve identifier. */ 157 uint16_t bit_size; /*!< The curve size in bits. */ 158 const char *name; /*!< A human-friendly name. */ 159 } mbedtls_ecp_curve_info; 160 161 /** 162 * \brief The ECP point structure, in Jacobian coordinates. 163 * 164 * \note All functions expect and return points satisfying 165 * the following condition: <code>Z == 0</code> or 166 * <code>Z == 1</code>. Other values of \p Z are 167 * used only by internal functions. 168 * The point is zero, or "at infinity", if <code>Z == 0</code>. 169 * Otherwise, \p X and \p Y are its standard (affine) 170 * coordinates. 171 */ 172 typedef struct mbedtls_ecp_point 173 { 174 mbedtls_mpi MBEDTLS_PRIVATE(X); /*!< The X coordinate of the ECP point. */ 175 mbedtls_mpi MBEDTLS_PRIVATE(Y); /*!< The Y coordinate of the ECP point. */ 176 mbedtls_mpi MBEDTLS_PRIVATE(Z); /*!< The Z coordinate of the ECP point. */ 177 } 178 mbedtls_ecp_point; 179 180 #if !defined(MBEDTLS_ECP_ALT) 181 /* 182 * default mbed TLS elliptic curve arithmetic implementation 183 * 184 * (in case MBEDTLS_ECP_ALT is defined then the developer has to provide an 185 * alternative implementation for the whole module and it will replace this 186 * one.) 187 */ 188 189 /** 190 * \brief The ECP group structure. 191 * 192 * We consider two types of curve equations: 193 * <ul><li>Short Weierstrass: <code>y^2 = x^3 + A x + B mod P</code> 194 * (SEC1 + RFC-4492)</li> 195 * <li>Montgomery: <code>y^2 = x^3 + A x^2 + x mod P</code> (Curve25519, 196 * Curve448)</li></ul> 197 * In both cases, the generator (\p G) for a prime-order subgroup is fixed. 198 * 199 * For Short Weierstrass, this subgroup is the whole curve, and its 200 * cardinality is denoted by \p N. Our code requires that \p N is an 201 * odd prime as mbedtls_ecp_mul() requires an odd number, and 202 * mbedtls_ecdsa_sign() requires that it is prime for blinding purposes. 203 * 204 * For Montgomery curves, we do not store \p A, but <code>(A + 2) / 4</code>, 205 * which is the quantity used in the formulas. Additionally, \p nbits is 206 * not the size of \p N but the required size for private keys. 207 * 208 * If \p modp is NULL, reduction modulo \p P is done using a generic algorithm. 209 * Otherwise, \p modp must point to a function that takes an \p mbedtls_mpi in the 210 * range of <code>0..2^(2*pbits)-1</code>, and transforms it in-place to an integer 211 * which is congruent mod \p P to the given MPI, and is close enough to \p pbits 212 * in size, so that it may be efficiently brought in the 0..P-1 range by a few 213 * additions or subtractions. Therefore, it is only an approximative modular 214 * reduction. It must return 0 on success and non-zero on failure. 215 * 216 * \note Alternative implementations of the ECP module must obey the 217 * following constraints. 218 * * Group IDs must be distinct: if two group structures have 219 * the same ID, then they must be identical. 220 * * The fields \c id, \c P, \c A, \c B, \c G, \c N, 221 * \c pbits and \c nbits must have the same type and semantics 222 * as in the built-in implementation. 223 * They must be available for reading, but direct modification 224 * of these fields does not need to be supported. 225 * They do not need to be at the same offset in the structure. 226 */ 227 typedef struct mbedtls_ecp_group 228 { 229 mbedtls_ecp_group_id id; /*!< An internal group identifier. */ 230 mbedtls_mpi P; /*!< The prime modulus of the base field. */ 231 mbedtls_mpi A; /*!< For Short Weierstrass: \p A in the equation. For 232 Montgomery curves: <code>(A + 2) / 4</code>. */ 233 mbedtls_mpi B; /*!< For Short Weierstrass: \p B in the equation. 234 For Montgomery curves: unused. */ 235 mbedtls_ecp_point G; /*!< The generator of the subgroup used. */ 236 mbedtls_mpi N; /*!< The order of \p G. */ 237 size_t pbits; /*!< The number of bits in \p P.*/ 238 size_t nbits; /*!< For Short Weierstrass: The number of bits in \p P. 239 For Montgomery curves: the number of bits in the 240 private keys. */ 241 /* End of public fields */ 242 243 unsigned int MBEDTLS_PRIVATE(h); /*!< \internal 1 if the constants are static. */ 244 int (*MBEDTLS_PRIVATE(modp))(mbedtls_mpi *); /*!< The function for fast pseudo-reduction 245 mod \p P (see above).*/ 246 int (*MBEDTLS_PRIVATE(t_pre))(mbedtls_ecp_point *, void *); /*!< Unused. */ 247 int (*MBEDTLS_PRIVATE(t_post))(mbedtls_ecp_point *, void *); /*!< Unused. */ 248 void *MBEDTLS_PRIVATE(t_data); /*!< Unused. */ 249 mbedtls_ecp_point *MBEDTLS_PRIVATE(T); /*!< Pre-computed points for ecp_mul_comb(). */ 250 size_t MBEDTLS_PRIVATE(T_size); /*!< The number of dynamic allocated pre-computed points. */ 251 } 252 mbedtls_ecp_group; 253 254 /** 255 * \name SECTION: Module settings 256 * 257 * The configuration options you can set for this module are in this section. 258 * Either change them in mbedtls_config.h, or define them using the compiler command line. 259 * \{ 260 */ 261 262 #if !defined(MBEDTLS_ECP_WINDOW_SIZE) 263 /* 264 * Maximum "window" size used for point multiplication. 265 * Default: a point where higher memory usage yields diminishing performance 266 * returns. 267 * Minimum value: 2. Maximum value: 7. 268 * 269 * Result is an array of at most ( 1 << ( MBEDTLS_ECP_WINDOW_SIZE - 1 ) ) 270 * points used for point multiplication. This value is directly tied to EC 271 * peak memory usage, so decreasing it by one should roughly cut memory usage 272 * by two (if large curves are in use). 273 * 274 * Reduction in size may reduce speed, but larger curves are impacted first. 275 * Sample performances (in ECDHE handshakes/s, with FIXED_POINT_OPTIM = 1): 276 * w-size: 6 5 4 3 2 277 * 521 145 141 135 120 97 278 * 384 214 209 198 177 146 279 * 256 320 320 303 262 226 280 * 224 475 475 453 398 342 281 * 192 640 640 633 587 476 282 */ 283 #define MBEDTLS_ECP_WINDOW_SIZE 4 /**< The maximum window size used. */ 284 #endif /* MBEDTLS_ECP_WINDOW_SIZE */ 285 286 #if !defined(MBEDTLS_ECP_FIXED_POINT_OPTIM) 287 /* 288 * Trade code size for speed on fixed-point multiplication. 289 * 290 * This speeds up repeated multiplication of the generator (that is, the 291 * multiplication in ECDSA signatures, and half of the multiplications in 292 * ECDSA verification and ECDHE) by a factor roughly 3 to 4. 293 * 294 * For each n-bit Short Weierstrass curve that is enabled, this adds 4n bytes 295 * of code size if n < 384 and 8n otherwise. 296 * 297 * Change this value to 0 to reduce code size. 298 */ 299 #define MBEDTLS_ECP_FIXED_POINT_OPTIM 1 /**< Enable fixed-point speed-up. */ 300 #endif /* MBEDTLS_ECP_FIXED_POINT_OPTIM */ 301 302 /** \} name SECTION: Module settings */ 303 304 #else /* MBEDTLS_ECP_ALT */ 305 #include "ecp_alt.h" 306 #endif /* MBEDTLS_ECP_ALT */ 307 308 /** 309 * The maximum size of the groups, that is, of \c N and \c P. 310 */ 311 #if !defined(MBEDTLS_ECP_C) 312 /* Dummy definition to help code that has optional ECP support and 313 * defines an MBEDTLS_ECP_MAX_BYTES-sized array unconditionally. */ 314 #define MBEDTLS_ECP_MAX_BITS 1 315 /* Note: the curves must be listed in DECREASING size! */ 316 #elif defined(MBEDTLS_ECP_DP_SECP521R1_ENABLED) 317 #define MBEDTLS_ECP_MAX_BITS 521 318 #elif defined(MBEDTLS_ECP_DP_BP512R1_ENABLED) 319 #define MBEDTLS_ECP_MAX_BITS 512 320 #elif defined(MBEDTLS_ECP_DP_CURVE448_ENABLED) 321 #define MBEDTLS_ECP_MAX_BITS 448 322 #elif defined(MBEDTLS_ECP_DP_BP384R1_ENABLED) 323 #define MBEDTLS_ECP_MAX_BITS 384 324 #elif defined(MBEDTLS_ECP_DP_SECP384R1_ENABLED) 325 #define MBEDTLS_ECP_MAX_BITS 384 326 #elif defined(MBEDTLS_ECP_DP_BP256R1_ENABLED) 327 #define MBEDTLS_ECP_MAX_BITS 256 328 #elif defined(MBEDTLS_ECP_DP_SECP256K1_ENABLED) 329 #define MBEDTLS_ECP_MAX_BITS 256 330 #elif defined(MBEDTLS_ECP_DP_SECP256R1_ENABLED) 331 #define MBEDTLS_ECP_MAX_BITS 256 332 #elif defined(MBEDTLS_ECP_DP_CURVE25519_ENABLED) 333 #define MBEDTLS_ECP_MAX_BITS 255 334 #elif defined(MBEDTLS_ECP_DP_SECP224K1_ENABLED) 335 #define MBEDTLS_ECP_MAX_BITS 225 // n is slightly above 2^224 336 #elif defined(MBEDTLS_ECP_DP_SECP224R1_ENABLED) 337 #define MBEDTLS_ECP_MAX_BITS 224 338 #elif defined(MBEDTLS_ECP_DP_SECP192K1_ENABLED) 339 #define MBEDTLS_ECP_MAX_BITS 192 340 #elif defined(MBEDTLS_ECP_DP_SECP192R1_ENABLED) 341 #define MBEDTLS_ECP_MAX_BITS 192 342 #else 343 #error "Missing definition of MBEDTLS_ECP_MAX_BITS" 344 #endif 345 346 #define MBEDTLS_ECP_MAX_BYTES ( ( MBEDTLS_ECP_MAX_BITS + 7 ) / 8 ) 347 #define MBEDTLS_ECP_MAX_PT_LEN ( 2 * MBEDTLS_ECP_MAX_BYTES + 1 ) 348 349 #if defined(MBEDTLS_ECP_RESTARTABLE) 350 351 /** 352 * \brief Internal restart context for multiplication 353 * 354 * \note Opaque struct 355 */ 356 typedef struct mbedtls_ecp_restart_mul mbedtls_ecp_restart_mul_ctx; 357 358 /** 359 * \brief Internal restart context for ecp_muladd() 360 * 361 * \note Opaque struct 362 */ 363 typedef struct mbedtls_ecp_restart_muladd mbedtls_ecp_restart_muladd_ctx; 364 365 /** 366 * \brief General context for resuming ECC operations 367 */ 368 typedef struct 369 { 370 unsigned MBEDTLS_PRIVATE(ops_done); /*!< current ops count */ 371 unsigned MBEDTLS_PRIVATE(depth); /*!< call depth (0 = top-level) */ 372 mbedtls_ecp_restart_mul_ctx *MBEDTLS_PRIVATE(rsm); /*!< ecp_mul_comb() sub-context */ 373 mbedtls_ecp_restart_muladd_ctx *MBEDTLS_PRIVATE(ma); /*!< ecp_muladd() sub-context */ 374 } mbedtls_ecp_restart_ctx; 375 376 /* 377 * Operation counts for restartable functions 378 */ 379 #define MBEDTLS_ECP_OPS_CHK 3 /*!< basic ops count for ecp_check_pubkey() */ 380 #define MBEDTLS_ECP_OPS_DBL 8 /*!< basic ops count for ecp_double_jac() */ 381 #define MBEDTLS_ECP_OPS_ADD 11 /*!< basic ops count for see ecp_add_mixed() */ 382 #define MBEDTLS_ECP_OPS_INV 120 /*!< empirical equivalent for mpi_mod_inv() */ 383 384 /** 385 * \brief Internal; for restartable functions in other modules. 386 * Check and update basic ops budget. 387 * 388 * \param grp Group structure 389 * \param rs_ctx Restart context 390 * \param ops Number of basic ops to do 391 * 392 * \return \c 0 if doing \p ops basic ops is still allowed, 393 * \return #MBEDTLS_ERR_ECP_IN_PROGRESS otherwise. 394 */ 395 int mbedtls_ecp_check_budget( const mbedtls_ecp_group *grp, 396 mbedtls_ecp_restart_ctx *rs_ctx, 397 unsigned ops ); 398 399 /* Utility macro for checking and updating ops budget */ 400 #define MBEDTLS_ECP_BUDGET( ops ) \ 401 MBEDTLS_MPI_CHK( mbedtls_ecp_check_budget( grp, rs_ctx, \ 402 (unsigned) (ops) ) ); 403 404 #else /* MBEDTLS_ECP_RESTARTABLE */ 405 406 #define MBEDTLS_ECP_BUDGET( ops ) /* no-op; for compatibility */ 407 408 /* We want to declare restartable versions of existing functions anyway */ 409 typedef void mbedtls_ecp_restart_ctx; 410 411 #endif /* MBEDTLS_ECP_RESTARTABLE */ 412 413 /** 414 * \brief The ECP key-pair structure. 415 * 416 * A generic key-pair that may be used for ECDSA and fixed ECDH, for example. 417 * 418 * \note Members are deliberately in the same order as in the 419 * ::mbedtls_ecdsa_context structure. 420 */ 421 typedef struct mbedtls_ecp_keypair 422 { 423 mbedtls_ecp_group MBEDTLS_PRIVATE(grp); /*!< Elliptic curve and base point */ 424 mbedtls_mpi MBEDTLS_PRIVATE(d); /*!< our secret value */ 425 mbedtls_ecp_point MBEDTLS_PRIVATE(Q); /*!< our public value */ 426 } 427 mbedtls_ecp_keypair; 428 429 /* 430 * Point formats, from RFC 4492's enum ECPointFormat 431 */ 432 #define MBEDTLS_ECP_PF_UNCOMPRESSED 0 /**< Uncompressed point format. */ 433 #define MBEDTLS_ECP_PF_COMPRESSED 1 /**< Compressed point format. */ 434 435 /* 436 * Some other constants from RFC 4492 437 */ 438 #define MBEDTLS_ECP_TLS_NAMED_CURVE 3 /**< The named_curve of ECCurveType. */ 439 440 #if defined(MBEDTLS_ECP_RESTARTABLE) 441 /** 442 * \brief Set the maximum number of basic operations done in a row. 443 * 444 * If more operations are needed to complete a computation, 445 * #MBEDTLS_ERR_ECP_IN_PROGRESS will be returned by the 446 * function performing the computation. It is then the 447 * caller's responsibility to either call again with the same 448 * parameters until it returns 0 or an error code; or to free 449 * the restart context if the operation is to be aborted. 450 * 451 * It is strictly required that all input parameters and the 452 * restart context be the same on successive calls for the 453 * same operation, but output parameters need not be the 454 * same; they must not be used until the function finally 455 * returns 0. 456 * 457 * This only applies to functions whose documentation 458 * mentions they may return #MBEDTLS_ERR_ECP_IN_PROGRESS (or 459 * #MBEDTLS_ERR_SSL_CRYPTO_IN_PROGRESS for functions in the 460 * SSL module). For functions that accept a "restart context" 461 * argument, passing NULL disables restart and makes the 462 * function equivalent to the function with the same name 463 * with \c _restartable removed. For functions in the ECDH 464 * module, restart is disabled unless the function accepts 465 * an "ECDH context" argument and 466 * mbedtls_ecdh_enable_restart() was previously called on 467 * that context. For function in the SSL module, restart is 468 * only enabled for specific sides and key exchanges 469 * (currently only for clients and ECDHE-ECDSA). 470 * 471 * \param max_ops Maximum number of basic operations done in a row. 472 * Default: 0 (unlimited). 473 * Lower (non-zero) values mean ECC functions will block for 474 * a lesser maximum amount of time. 475 * 476 * \note A "basic operation" is defined as a rough equivalent of a 477 * multiplication in GF(p) for the NIST P-256 curve. 478 * As an indication, with default settings, a scalar 479 * multiplication (full run of \c mbedtls_ecp_mul()) is: 480 * - about 3300 basic operations for P-256 481 * - about 9400 basic operations for P-384 482 * 483 * \note Very low values are not always respected: sometimes 484 * functions need to block for a minimum number of 485 * operations, and will do so even if max_ops is set to a 486 * lower value. That minimum depends on the curve size, and 487 * can be made lower by decreasing the value of 488 * \c MBEDTLS_ECP_WINDOW_SIZE. As an indication, here is the 489 * lowest effective value for various curves and values of 490 * that parameter (w for short): 491 * w=6 w=5 w=4 w=3 w=2 492 * P-256 208 208 160 136 124 493 * P-384 682 416 320 272 248 494 * P-521 1364 832 640 544 496 495 * 496 * \note This setting is currently ignored by Curve25519. 497 */ 498 void mbedtls_ecp_set_max_ops( unsigned max_ops ); 499 500 /** 501 * \brief Check if restart is enabled (max_ops != 0) 502 * 503 * \return \c 0 if \c max_ops == 0 (restart disabled) 504 * \return \c 1 otherwise (restart enabled) 505 */ 506 int mbedtls_ecp_restart_is_enabled( void ); 507 #endif /* MBEDTLS_ECP_RESTARTABLE */ 508 509 /* 510 * Get the type of a curve 511 */ 512 mbedtls_ecp_curve_type mbedtls_ecp_get_type( const mbedtls_ecp_group *grp ); 513 514 /** 515 * \brief This function retrieves the information defined in 516 * mbedtls_ecp_curve_info() for all supported curves. 517 * 518 * \note This function returns information about all curves 519 * supported by the library. Some curves may not be 520 * supported for all algorithms. Call mbedtls_ecdh_can_do() 521 * or mbedtls_ecdsa_can_do() to check if a curve is 522 * supported for ECDH or ECDSA. 523 * 524 * \return A statically allocated array. The last entry is 0. 525 */ 526 const mbedtls_ecp_curve_info *mbedtls_ecp_curve_list( void ); 527 528 /** 529 * \brief This function retrieves the list of internal group 530 * identifiers of all supported curves in the order of 531 * preference. 532 * 533 * \note This function returns information about all curves 534 * supported by the library. Some curves may not be 535 * supported for all algorithms. Call mbedtls_ecdh_can_do() 536 * or mbedtls_ecdsa_can_do() to check if a curve is 537 * supported for ECDH or ECDSA. 538 * 539 * \return A statically allocated array, 540 * terminated with MBEDTLS_ECP_DP_NONE. 541 */ 542 const mbedtls_ecp_group_id *mbedtls_ecp_grp_id_list( void ); 543 544 /** 545 * \brief This function retrieves curve information from an internal 546 * group identifier. 547 * 548 * \param grp_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_grp_id( mbedtls_ecp_group_id grp_id ); 554 555 /** 556 * \brief This function retrieves curve information from a TLS 557 * NamedCurve value. 558 * 559 * \param tls_id An \c MBEDTLS_ECP_DP_XXX value. 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_tls_id( uint16_t tls_id ); 565 566 /** 567 * \brief This function retrieves curve information from a 568 * human-readable name. 569 * 570 * \param name The human-readable name. 571 * 572 * \return The associated curve information on success. 573 * \return NULL on failure. 574 */ 575 const mbedtls_ecp_curve_info *mbedtls_ecp_curve_info_from_name( const char *name ); 576 577 /** 578 * \brief This function initializes a point as zero. 579 * 580 * \param pt The point to initialize. 581 */ 582 void mbedtls_ecp_point_init( mbedtls_ecp_point *pt ); 583 584 /** 585 * \brief This function initializes an ECP group context 586 * without loading any domain parameters. 587 * 588 * \note After this function is called, domain parameters 589 * for various ECP groups can be loaded through the 590 * mbedtls_ecp_group_load() or mbedtls_ecp_tls_read_group() 591 * functions. 592 */ 593 void mbedtls_ecp_group_init( mbedtls_ecp_group *grp ); 594 595 /** 596 * \brief This function initializes a key pair as an invalid one. 597 * 598 * \param key The key pair to initialize. 599 */ 600 void mbedtls_ecp_keypair_init( mbedtls_ecp_keypair *key ); 601 602 /** 603 * \brief This function frees the components of a point. 604 * 605 * \param pt The point to free. 606 */ 607 void mbedtls_ecp_point_free( mbedtls_ecp_point *pt ); 608 609 /** 610 * \brief This function frees the components of an ECP group. 611 * 612 * \param grp The group to free. This may be \c NULL, in which 613 * case this function returns immediately. If it is not 614 * \c NULL, it must point to an initialized ECP group. 615 */ 616 void mbedtls_ecp_group_free( mbedtls_ecp_group *grp ); 617 618 /** 619 * \brief This function frees the components of a key pair. 620 * 621 * \param key The key pair to free. This may be \c NULL, in which 622 * case this function returns immediately. If it is not 623 * \c NULL, it must point to an initialized ECP key pair. 624 */ 625 void mbedtls_ecp_keypair_free( mbedtls_ecp_keypair *key ); 626 627 #if defined(MBEDTLS_ECP_RESTARTABLE) 628 /** 629 * \brief Initialize a restart context. 630 * 631 * \param ctx The restart context to initialize. This must 632 * not be \c NULL. 633 */ 634 void mbedtls_ecp_restart_init( mbedtls_ecp_restart_ctx *ctx ); 635 636 /** 637 * \brief Free the components of a restart context. 638 * 639 * \param ctx The restart context to free. This may be \c NULL, in which 640 * case this function returns immediately. If it is not 641 * \c NULL, it must point to an initialized restart context. 642 */ 643 void mbedtls_ecp_restart_free( mbedtls_ecp_restart_ctx *ctx ); 644 #endif /* MBEDTLS_ECP_RESTARTABLE */ 645 646 /** 647 * \brief This function copies the contents of point \p Q into 648 * point \p P. 649 * 650 * \param P The destination point. This must be initialized. 651 * \param Q The source point. This must be initialized. 652 * 653 * \return \c 0 on success. 654 * \return #MBEDTLS_ERR_MPI_ALLOC_FAILED on memory-allocation failure. 655 * \return Another negative error code for other kinds of failure. 656 */ 657 int mbedtls_ecp_copy( mbedtls_ecp_point *P, const mbedtls_ecp_point *Q ); 658 659 /** 660 * \brief This function copies the contents of group \p src into 661 * group \p dst. 662 * 663 * \param dst The destination group. This must be initialized. 664 * \param src The source group. This must be initialized. 665 * 666 * \return \c 0 on success. 667 * \return #MBEDTLS_ERR_MPI_ALLOC_FAILED on memory-allocation failure. 668 * \return Another negative error code on other kinds of failure. 669 */ 670 int mbedtls_ecp_group_copy( mbedtls_ecp_group *dst, 671 const mbedtls_ecp_group *src ); 672 673 /** 674 * \brief This function sets a point to the point at infinity. 675 * 676 * \param pt The point to set. This must be initialized. 677 * 678 * \return \c 0 on success. 679 * \return #MBEDTLS_ERR_MPI_ALLOC_FAILED on memory-allocation failure. 680 * \return Another negative error code on other kinds of failure. 681 */ 682 int mbedtls_ecp_set_zero( mbedtls_ecp_point *pt ); 683 684 /** 685 * \brief This function checks if a point is the point at infinity. 686 * 687 * \param pt The point to test. This must be initialized. 688 * 689 * \return \c 1 if the point is zero. 690 * \return \c 0 if the point is non-zero. 691 * \return A negative error code on failure. 692 */ 693 int mbedtls_ecp_is_zero( mbedtls_ecp_point *pt ); 694 695 /** 696 * \brief This function compares two points. 697 * 698 * \note This assumes that the points are normalized. Otherwise, 699 * they may compare as "not equal" even if they are. 700 * 701 * \param P The first point to compare. This must be initialized. 702 * \param Q The second point to compare. This must be initialized. 703 * 704 * \return \c 0 if the points are equal. 705 * \return #MBEDTLS_ERR_ECP_BAD_INPUT_DATA if the points are not equal. 706 */ 707 int mbedtls_ecp_point_cmp( const mbedtls_ecp_point *P, 708 const mbedtls_ecp_point *Q ); 709 710 /** 711 * \brief This function imports a non-zero point from two ASCII 712 * strings. 713 * 714 * \param P The destination point. This must be initialized. 715 * \param radix The numeric base of the input. 716 * \param x The first affine coordinate, as a null-terminated string. 717 * \param y The second affine coordinate, as a null-terminated string. 718 * 719 * \return \c 0 on success. 720 * \return An \c MBEDTLS_ERR_MPI_XXX error code on failure. 721 */ 722 int mbedtls_ecp_point_read_string( mbedtls_ecp_point *P, int radix, 723 const char *x, const char *y ); 724 725 /** 726 * \brief This function exports a point into unsigned binary data. 727 * 728 * \param grp The group to which the point should belong. 729 * This must be initialized and have group parameters 730 * set, for example through mbedtls_ecp_group_load(). 731 * \param P The point to export. This must be initialized. 732 * \param format The point format. This must be either 733 * #MBEDTLS_ECP_PF_COMPRESSED or #MBEDTLS_ECP_PF_UNCOMPRESSED. 734 * (For groups without these formats, this parameter is 735 * ignored. But it still has to be either of the above 736 * values.) 737 * \param olen The address at which to store the length of 738 * the output in Bytes. This must not be \c NULL. 739 * \param buf The output buffer. This must be a writable buffer 740 * of length \p buflen Bytes. 741 * \param buflen The length of the output buffer \p buf in Bytes. 742 * 743 * \return \c 0 on success. 744 * \return #MBEDTLS_ERR_ECP_BUFFER_TOO_SMALL if the output buffer 745 * is too small to hold the point. 746 * \return #MBEDTLS_ERR_ECP_FEATURE_UNAVAILABLE if the point format 747 * or the export for the given group is not implemented. 748 * \return Another negative error code on other kinds of failure. 749 */ 750 int mbedtls_ecp_point_write_binary( const mbedtls_ecp_group *grp, 751 const mbedtls_ecp_point *P, 752 int format, size_t *olen, 753 unsigned char *buf, size_t buflen ); 754 755 /** 756 * \brief This function imports a point from unsigned binary data. 757 * 758 * \note This function does not check that the point actually 759 * belongs to the given group, see mbedtls_ecp_check_pubkey() 760 * for that. 761 * 762 * \param grp The group to which the point should belong. 763 * This must be initialized and have group parameters 764 * set, for example through mbedtls_ecp_group_load(). 765 * \param P The destination context to import the point to. 766 * This must be initialized. 767 * \param buf The input buffer. This must be a readable buffer 768 * of length \p ilen Bytes. 769 * \param ilen The length of the input buffer \p buf in Bytes. 770 * 771 * \return \c 0 on success. 772 * \return #MBEDTLS_ERR_ECP_BAD_INPUT_DATA if the input is invalid. 773 * \return #MBEDTLS_ERR_MPI_ALLOC_FAILED on memory-allocation failure. 774 * \return #MBEDTLS_ERR_ECP_FEATURE_UNAVAILABLE if the import for the 775 * given group is not implemented. 776 */ 777 int mbedtls_ecp_point_read_binary( const mbedtls_ecp_group *grp, 778 mbedtls_ecp_point *P, 779 const unsigned char *buf, size_t ilen ); 780 781 /** 782 * \brief This function imports a point from a TLS ECPoint record. 783 * 784 * \note On function return, \p *buf is updated to point immediately 785 * after the ECPoint record. 786 * 787 * \param grp The ECP group to use. 788 * This must be initialized and have group parameters 789 * set, for example through mbedtls_ecp_group_load(). 790 * \param pt The destination point. 791 * \param buf The address of the pointer to the start of the input buffer. 792 * \param len The length of the buffer. 793 * 794 * \return \c 0 on success. 795 * \return An \c MBEDTLS_ERR_MPI_XXX error code on initialization 796 * failure. 797 * \return #MBEDTLS_ERR_ECP_BAD_INPUT_DATA if input is invalid. 798 */ 799 int mbedtls_ecp_tls_read_point( const mbedtls_ecp_group *grp, 800 mbedtls_ecp_point *pt, 801 const unsigned char **buf, size_t len ); 802 803 /** 804 * \brief This function exports a point as a TLS ECPoint record 805 * defined in RFC 4492, Section 5.4. 806 * 807 * \param grp The ECP group to use. 808 * This must be initialized and have group parameters 809 * set, for example through mbedtls_ecp_group_load(). 810 * \param pt The point to be exported. This must be initialized. 811 * \param format The point format to use. This must be either 812 * #MBEDTLS_ECP_PF_COMPRESSED or #MBEDTLS_ECP_PF_UNCOMPRESSED. 813 * \param olen The address at which to store the length in Bytes 814 * of the data written. 815 * \param buf The target buffer. This must be a writable buffer of 816 * length \p blen Bytes. 817 * \param blen The length of the target buffer \p buf in Bytes. 818 * 819 * \return \c 0 on success. 820 * \return #MBEDTLS_ERR_ECP_BAD_INPUT_DATA if the input is invalid. 821 * \return #MBEDTLS_ERR_ECP_BUFFER_TOO_SMALL if the target buffer 822 * is too small to hold the exported point. 823 * \return Another negative error code on other kinds of failure. 824 */ 825 int mbedtls_ecp_tls_write_point( const mbedtls_ecp_group *grp, 826 const mbedtls_ecp_point *pt, 827 int format, size_t *olen, 828 unsigned char *buf, size_t blen ); 829 830 /** 831 * \brief This function sets up an ECP group context 832 * from a standardized set of domain parameters. 833 * 834 * \note The index should be a value of the NamedCurve enum, 835 * as defined in <em>RFC-4492: Elliptic Curve Cryptography 836 * (ECC) Cipher Suites for Transport Layer Security (TLS)</em>, 837 * usually in the form of an \c MBEDTLS_ECP_DP_XXX macro. 838 * 839 * \param grp The group context to setup. This must be initialized. 840 * \param id The identifier of the domain parameter set to load. 841 * 842 * \return \c 0 on success. 843 * \return #MBEDTLS_ERR_ECP_FEATURE_UNAVAILABLE if \p id doesn't 844 * correspond to a known group. 845 * \return Another negative error code on other kinds of failure. 846 */ 847 int mbedtls_ecp_group_load( mbedtls_ecp_group *grp, mbedtls_ecp_group_id id ); 848 849 /** 850 * \brief This function sets up an ECP group context from a TLS 851 * ECParameters record as defined in RFC 4492, Section 5.4. 852 * 853 * \note The read pointer \p buf is updated to point right after 854 * the ECParameters record on exit. 855 * 856 * \param grp The group context to setup. This must be initialized. 857 * \param buf The address of the pointer to the start of the input buffer. 858 * \param len The length of the input buffer \c *buf in Bytes. 859 * 860 * \return \c 0 on success. 861 * \return #MBEDTLS_ERR_ECP_BAD_INPUT_DATA if input is invalid. 862 * \return #MBEDTLS_ERR_ECP_FEATURE_UNAVAILABLE if the group is not 863 * recognized. 864 * \return Another negative error code on other kinds of failure. 865 */ 866 int mbedtls_ecp_tls_read_group( mbedtls_ecp_group *grp, 867 const unsigned char **buf, size_t len ); 868 869 /** 870 * \brief This function extracts an elliptic curve group ID from a 871 * TLS ECParameters record as defined in RFC 4492, Section 5.4. 872 * 873 * \note The read pointer \p buf is updated to point right after 874 * the ECParameters record on exit. 875 * 876 * \param grp The address at which to store the group id. 877 * This must not be \c NULL. 878 * \param buf The address of the pointer to the start of the input buffer. 879 * \param len The length of the input buffer \c *buf in Bytes. 880 * 881 * \return \c 0 on success. 882 * \return #MBEDTLS_ERR_ECP_BAD_INPUT_DATA if input is invalid. 883 * \return #MBEDTLS_ERR_ECP_FEATURE_UNAVAILABLE if the group is not 884 * recognized. 885 * \return Another negative error code on other kinds of failure. 886 */ 887 int mbedtls_ecp_tls_read_group_id( mbedtls_ecp_group_id *grp, 888 const unsigned char **buf, 889 size_t len ); 890 /** 891 * \brief This function exports an elliptic curve as a TLS 892 * ECParameters record as defined in RFC 4492, Section 5.4. 893 * 894 * \param grp The ECP group to be exported. 895 * This must be initialized and have group parameters 896 * set, for example through mbedtls_ecp_group_load(). 897 * \param olen The address at which to store the number of Bytes written. 898 * This must not be \c NULL. 899 * \param buf The buffer to write to. This must be a writable buffer 900 * of length \p blen Bytes. 901 * \param blen The length of the output buffer \p buf in Bytes. 902 * 903 * \return \c 0 on success. 904 * \return #MBEDTLS_ERR_ECP_BUFFER_TOO_SMALL if the output 905 * buffer is too small to hold the exported group. 906 * \return Another negative error code on other kinds of failure. 907 */ 908 int mbedtls_ecp_tls_write_group( const mbedtls_ecp_group *grp, 909 size_t *olen, 910 unsigned char *buf, size_t blen ); 911 912 /** 913 * \brief This function performs a scalar multiplication of a point 914 * by an integer: \p R = \p m * \p P. 915 * 916 * It is not thread-safe to use same group in multiple threads. 917 * 918 * \note To prevent timing attacks, this function 919 * executes the exact same sequence of base-field 920 * operations for any valid \p m. It avoids any if-branch or 921 * array index depending on the value of \p m. It also uses 922 * \p f_rng to randomize some intermediate results. 923 * 924 * \param grp The ECP group to use. 925 * This must be initialized and have group parameters 926 * set, for example through mbedtls_ecp_group_load(). 927 * \param R The point in which to store the result of the calculation. 928 * This must be initialized. 929 * \param m The integer by which to multiply. This must be initialized. 930 * \param P The point to multiply. This must be initialized. 931 * \param f_rng The RNG function. This must not be \c NULL. 932 * \param p_rng The RNG context to be passed to \p f_rng. This may be \c 933 * NULL if \p f_rng doesn't need a context. 934 * 935 * \return \c 0 on success. 936 * \return #MBEDTLS_ERR_ECP_INVALID_KEY if \p m is not a valid private 937 * key, or \p P is not a valid public key. 938 * \return #MBEDTLS_ERR_MPI_ALLOC_FAILED on memory-allocation failure. 939 * \return Another negative error code on other kinds of failure. 940 */ 941 int mbedtls_ecp_mul( mbedtls_ecp_group *grp, mbedtls_ecp_point *R, 942 const mbedtls_mpi *m, const mbedtls_ecp_point *P, 943 int (*f_rng)(void *, unsigned char *, size_t), void *p_rng ); 944 945 /** 946 * \brief This function performs multiplication of a point by 947 * an integer: \p R = \p m * \p P in a restartable way. 948 * 949 * \see mbedtls_ecp_mul() 950 * 951 * \note This function does the same as \c mbedtls_ecp_mul(), but 952 * it can return early and restart according to the limit set 953 * with \c mbedtls_ecp_set_max_ops() to reduce blocking. 954 * 955 * \param grp The ECP group to use. 956 * This must be initialized and have group parameters 957 * set, for example through mbedtls_ecp_group_load(). 958 * \param R The point in which to store the result of the calculation. 959 * This must be initialized. 960 * \param m The integer by which to multiply. This must be initialized. 961 * \param P The point to multiply. This must be initialized. 962 * \param f_rng The RNG function. This must not be \c NULL. 963 * \param p_rng The RNG context to be passed to \p f_rng. This may be \c 964 * NULL if \p f_rng doesn't need a context. 965 * \param rs_ctx The restart context (NULL disables restart). 966 * 967 * \return \c 0 on success. 968 * \return #MBEDTLS_ERR_ECP_INVALID_KEY if \p m is not a valid private 969 * key, or \p P is not a valid public key. 970 * \return #MBEDTLS_ERR_MPI_ALLOC_FAILED on memory-allocation failure. 971 * \return #MBEDTLS_ERR_ECP_IN_PROGRESS if maximum number of 972 * operations was reached: see \c mbedtls_ecp_set_max_ops(). 973 * \return Another negative error code on other kinds of failure. 974 */ 975 int mbedtls_ecp_mul_restartable( mbedtls_ecp_group *grp, mbedtls_ecp_point *R, 976 const mbedtls_mpi *m, const mbedtls_ecp_point *P, 977 int (*f_rng)(void *, unsigned char *, size_t), void *p_rng, 978 mbedtls_ecp_restart_ctx *rs_ctx ); 979 980 #if defined(MBEDTLS_ECP_SHORT_WEIERSTRASS_ENABLED) 981 /** 982 * \brief This function performs multiplication and addition of two 983 * points by integers: \p R = \p m * \p P + \p n * \p Q 984 * 985 * It is not thread-safe to use same group in multiple threads. 986 * 987 * \note In contrast to mbedtls_ecp_mul(), this function does not 988 * guarantee a constant execution flow and timing. 989 * 990 * \note This function is only defined for short Weierstrass curves. 991 * It may not be included in builds without any short 992 * Weierstrass curve. 993 * 994 * \param grp The ECP group to use. 995 * This must be initialized and have group parameters 996 * set, for example through mbedtls_ecp_group_load(). 997 * \param R The point in which to store the result of the calculation. 998 * This must be initialized. 999 * \param m The integer by which to multiply \p P. 1000 * This must be initialized. 1001 * \param P The point to multiply by \p m. This must be initialized. 1002 * \param n The integer by which to multiply \p Q. 1003 * This must be initialized. 1004 * \param Q The point to be multiplied by \p n. 1005 * This must be initialized. 1006 * 1007 * \return \c 0 on success. 1008 * \return #MBEDTLS_ERR_ECP_INVALID_KEY if \p m or \p n are not 1009 * valid private keys, or \p P or \p Q are not valid public 1010 * keys. 1011 * \return #MBEDTLS_ERR_MPI_ALLOC_FAILED on memory-allocation failure. 1012 * \return #MBEDTLS_ERR_ECP_FEATURE_UNAVAILABLE if \p grp does not 1013 * designate a short Weierstrass curve. 1014 * \return Another negative error code on other kinds of failure. 1015 */ 1016 int mbedtls_ecp_muladd( mbedtls_ecp_group *grp, mbedtls_ecp_point *R, 1017 const mbedtls_mpi *m, const mbedtls_ecp_point *P, 1018 const mbedtls_mpi *n, const mbedtls_ecp_point *Q ); 1019 1020 /** 1021 * \brief This function performs multiplication and addition of two 1022 * points by integers: \p R = \p m * \p P + \p n * \p Q in a 1023 * restartable way. 1024 * 1025 * \see \c mbedtls_ecp_muladd() 1026 * 1027 * \note This function works the same as \c mbedtls_ecp_muladd(), 1028 * but it can return early and restart according to the limit 1029 * set with \c mbedtls_ecp_set_max_ops() to reduce blocking. 1030 * 1031 * \note This function is only defined for short Weierstrass curves. 1032 * It may not be included in builds without any short 1033 * Weierstrass curve. 1034 * 1035 * \param grp The ECP group to use. 1036 * This must be initialized and have group parameters 1037 * set, for example through mbedtls_ecp_group_load(). 1038 * \param R The point in which to store the result of the calculation. 1039 * This must be initialized. 1040 * \param m The integer by which to multiply \p P. 1041 * This must be initialized. 1042 * \param P The point to multiply by \p m. This must be initialized. 1043 * \param n The integer by which to multiply \p Q. 1044 * This must be initialized. 1045 * \param Q The point to be multiplied by \p n. 1046 * This must be initialized. 1047 * \param rs_ctx The restart context (NULL disables restart). 1048 * 1049 * \return \c 0 on success. 1050 * \return #MBEDTLS_ERR_ECP_INVALID_KEY if \p m or \p n are not 1051 * valid private keys, or \p P or \p Q are not valid public 1052 * keys. 1053 * \return #MBEDTLS_ERR_MPI_ALLOC_FAILED on memory-allocation failure. 1054 * \return #MBEDTLS_ERR_ECP_FEATURE_UNAVAILABLE if \p grp does not 1055 * designate a short Weierstrass curve. 1056 * \return #MBEDTLS_ERR_ECP_IN_PROGRESS if maximum number of 1057 * operations was reached: see \c mbedtls_ecp_set_max_ops(). 1058 * \return Another negative error code on other kinds of failure. 1059 */ 1060 int mbedtls_ecp_muladd_restartable( 1061 mbedtls_ecp_group *grp, mbedtls_ecp_point *R, 1062 const mbedtls_mpi *m, const mbedtls_ecp_point *P, 1063 const mbedtls_mpi *n, const mbedtls_ecp_point *Q, 1064 mbedtls_ecp_restart_ctx *rs_ctx ); 1065 #endif /* MBEDTLS_ECP_SHORT_WEIERSTRASS_ENABLED */ 1066 1067 /** 1068 * \brief This function checks that a point is a valid public key 1069 * on this curve. 1070 * 1071 * It only checks that the point is non-zero, has 1072 * valid coordinates and lies on the curve. It does not verify 1073 * that it is indeed a multiple of \p G. This additional 1074 * check is computationally more expensive, is not required 1075 * by standards, and should not be necessary if the group 1076 * used has a small cofactor. In particular, it is useless for 1077 * the NIST groups which all have a cofactor of 1. 1078 * 1079 * \note This function uses bare components rather than an 1080 * ::mbedtls_ecp_keypair structure, to ease use with other 1081 * structures, such as ::mbedtls_ecdh_context or 1082 * ::mbedtls_ecdsa_context. 1083 * 1084 * \param grp The ECP group the point should belong to. 1085 * This must be initialized and have group parameters 1086 * set, for example through mbedtls_ecp_group_load(). 1087 * \param pt The point to check. This must be initialized. 1088 * 1089 * \return \c 0 if the point is a valid public key. 1090 * \return #MBEDTLS_ERR_ECP_INVALID_KEY if the point is not 1091 * a valid public key for the given curve. 1092 * \return Another negative error code on other kinds of failure. 1093 */ 1094 int mbedtls_ecp_check_pubkey( const mbedtls_ecp_group *grp, 1095 const mbedtls_ecp_point *pt ); 1096 1097 /** 1098 * \brief This function checks that an \p mbedtls_mpi is a 1099 * valid private key for this curve. 1100 * 1101 * \note This function uses bare components rather than an 1102 * ::mbedtls_ecp_keypair structure to ease use with other 1103 * structures, such as ::mbedtls_ecdh_context or 1104 * ::mbedtls_ecdsa_context. 1105 * 1106 * \param grp The ECP group the private key should belong to. 1107 * This must be initialized and have group parameters 1108 * set, for example through mbedtls_ecp_group_load(). 1109 * \param d The integer to check. This must be initialized. 1110 * 1111 * \return \c 0 if the point is a valid private key. 1112 * \return #MBEDTLS_ERR_ECP_INVALID_KEY if the point is not a valid 1113 * private key for the given curve. 1114 * \return Another negative error code on other kinds of failure. 1115 */ 1116 int mbedtls_ecp_check_privkey( const mbedtls_ecp_group *grp, 1117 const mbedtls_mpi *d ); 1118 1119 /** 1120 * \brief This function generates a private key. 1121 * 1122 * \param grp The ECP group to generate a private key for. 1123 * This must be initialized and have group parameters 1124 * set, for example through mbedtls_ecp_group_load(). 1125 * \param d The destination MPI (secret part). This must be initialized. 1126 * \param f_rng The RNG function. This must not be \c NULL. 1127 * \param p_rng The RNG parameter to be passed to \p f_rng. This may be 1128 * \c NULL if \p f_rng doesn't need a context argument. 1129 * 1130 * \return \c 0 on success. 1131 * \return An \c MBEDTLS_ERR_ECP_XXX or \c MBEDTLS_MPI_XXX error code 1132 * on failure. 1133 */ 1134 int mbedtls_ecp_gen_privkey( const mbedtls_ecp_group *grp, 1135 mbedtls_mpi *d, 1136 int (*f_rng)(void *, unsigned char *, size_t), 1137 void *p_rng ); 1138 1139 /** 1140 * \brief This function generates a keypair with a configurable base 1141 * point. 1142 * 1143 * \note This function uses bare components rather than an 1144 * ::mbedtls_ecp_keypair structure to ease use with other 1145 * structures, such as ::mbedtls_ecdh_context or 1146 * ::mbedtls_ecdsa_context. 1147 * 1148 * \param grp The ECP group to generate a key pair for. 1149 * This must be initialized and have group parameters 1150 * set, for example through mbedtls_ecp_group_load(). 1151 * \param G The base point to use. This must be initialized 1152 * and belong to \p grp. It replaces the default base 1153 * point \c grp->G used by mbedtls_ecp_gen_keypair(). 1154 * \param d The destination MPI (secret part). 1155 * This must be initialized. 1156 * \param Q The destination point (public part). 1157 * This must be initialized. 1158 * \param f_rng The RNG function. This must not be \c NULL. 1159 * \param p_rng The RNG context to be passed to \p f_rng. This may 1160 * be \c NULL if \p f_rng doesn't need a context argument. 1161 * 1162 * \return \c 0 on success. 1163 * \return An \c MBEDTLS_ERR_ECP_XXX or \c MBEDTLS_MPI_XXX error code 1164 * on failure. 1165 */ 1166 int mbedtls_ecp_gen_keypair_base( mbedtls_ecp_group *grp, 1167 const mbedtls_ecp_point *G, 1168 mbedtls_mpi *d, mbedtls_ecp_point *Q, 1169 int (*f_rng)(void *, unsigned char *, size_t), 1170 void *p_rng ); 1171 1172 /** 1173 * \brief This function generates an ECP keypair. 1174 * 1175 * \note This function uses bare components rather than an 1176 * ::mbedtls_ecp_keypair structure to ease use with other 1177 * structures, such as ::mbedtls_ecdh_context or 1178 * ::mbedtls_ecdsa_context. 1179 * 1180 * \param grp The ECP group to generate a key pair for. 1181 * This must be initialized and have group parameters 1182 * set, for example through mbedtls_ecp_group_load(). 1183 * \param d The destination MPI (secret part). 1184 * This must be initialized. 1185 * \param Q The destination point (public part). 1186 * This must be initialized. 1187 * \param f_rng The RNG function. This must not be \c NULL. 1188 * \param p_rng The RNG context to be passed to \p f_rng. This may 1189 * be \c NULL if \p f_rng doesn't need a context argument. 1190 * 1191 * \return \c 0 on success. 1192 * \return An \c MBEDTLS_ERR_ECP_XXX or \c MBEDTLS_MPI_XXX error code 1193 * on failure. 1194 */ 1195 int mbedtls_ecp_gen_keypair( mbedtls_ecp_group *grp, mbedtls_mpi *d, 1196 mbedtls_ecp_point *Q, 1197 int (*f_rng)(void *, unsigned char *, size_t), 1198 void *p_rng ); 1199 1200 /** 1201 * \brief This function generates an ECP key. 1202 * 1203 * \param grp_id The ECP group identifier. 1204 * \param key The destination key. This must be initialized. 1205 * \param f_rng The RNG function to use. This must not be \c NULL. 1206 * \param p_rng The RNG context to be passed to \p f_rng. This may 1207 * be \c NULL if \p f_rng doesn't need a context argument. 1208 * 1209 * \return \c 0 on success. 1210 * \return An \c MBEDTLS_ERR_ECP_XXX or \c MBEDTLS_MPI_XXX error code 1211 * on failure. 1212 */ 1213 int mbedtls_ecp_gen_key( mbedtls_ecp_group_id grp_id, mbedtls_ecp_keypair *key, 1214 int (*f_rng)(void *, unsigned char *, size_t), 1215 void *p_rng ); 1216 1217 /** 1218 * \brief This function reads an elliptic curve private key. 1219 * 1220 * \param grp_id The ECP group identifier. 1221 * \param key The destination key. 1222 * \param buf The buffer containing the binary representation of the 1223 * key. (Big endian integer for Weierstrass curves, byte 1224 * string for Montgomery curves.) 1225 * \param buflen The length of the buffer in bytes. 1226 * 1227 * \return \c 0 on success. 1228 * \return #MBEDTLS_ERR_ECP_INVALID_KEY error if the key is 1229 * invalid. 1230 * \return #MBEDTLS_ERR_MPI_ALLOC_FAILED if memory allocation failed. 1231 * \return #MBEDTLS_ERR_ECP_FEATURE_UNAVAILABLE if the operation for 1232 * the group is not implemented. 1233 * \return Another negative error code on different kinds of failure. 1234 */ 1235 int mbedtls_ecp_read_key( mbedtls_ecp_group_id grp_id, mbedtls_ecp_keypair *key, 1236 const unsigned char *buf, size_t buflen ); 1237 1238 /** 1239 * \brief This function exports an elliptic curve private key. 1240 * 1241 * \param key The private key. 1242 * \param buf The output buffer for containing the binary representation 1243 * of the key. (Big endian integer for Weierstrass curves, byte 1244 * string for Montgomery curves.) 1245 * \param buflen The total length of the buffer in bytes. 1246 * 1247 * \return \c 0 on success. 1248 * \return #MBEDTLS_ERR_ECP_BUFFER_TOO_SMALL if the \p key 1249 representation is larger than the available space in \p buf. 1250 * \return #MBEDTLS_ERR_ECP_FEATURE_UNAVAILABLE if the operation for 1251 * the group is not implemented. 1252 * \return Another negative error code on different kinds of failure. 1253 */ 1254 int mbedtls_ecp_write_key( mbedtls_ecp_keypair *key, 1255 unsigned char *buf, size_t buflen ); 1256 1257 /** 1258 * \brief This function checks that the keypair objects 1259 * \p pub and \p prv have the same group and the 1260 * same public point, and that the private key in 1261 * \p prv is consistent with the public key. 1262 * 1263 * \param pub The keypair structure holding the public key. This 1264 * must be initialized. If it contains a private key, that 1265 * part is ignored. 1266 * \param prv The keypair structure holding the full keypair. 1267 * This must be initialized. 1268 * \param f_rng The RNG function. This must not be \c NULL. 1269 * \param p_rng The RNG context to be passed to \p f_rng. This may be \c 1270 * NULL if \p f_rng doesn't need a context. 1271 * 1272 * \return \c 0 on success, meaning that the keys are valid and match. 1273 * \return #MBEDTLS_ERR_ECP_BAD_INPUT_DATA if the keys are invalid or do not match. 1274 * \return An \c MBEDTLS_ERR_ECP_XXX or an \c MBEDTLS_ERR_MPI_XXX 1275 * error code on calculation failure. 1276 */ 1277 int mbedtls_ecp_check_pub_priv( 1278 const mbedtls_ecp_keypair *pub, const mbedtls_ecp_keypair *prv, 1279 int (*f_rng)(void *, unsigned char *, size_t), void *p_rng ); 1280 1281 /** 1282 * \brief This function exports generic key-pair parameters. 1283 * 1284 * \param key The key pair to export from. 1285 * \param grp Slot for exported ECP group. 1286 * It must point to an initialized ECP group. 1287 * \param d Slot for the exported secret value. 1288 * It must point to an initialized mpi. 1289 * \param Q Slot for the exported public value. 1290 * It must point to an initialized ECP point. 1291 * 1292 * \return \c 0 on success, 1293 * \return #MBEDTLS_ERR_MPI_ALLOC_FAILED on memory-allocation failure. 1294 * \return #MBEDTLS_ERR_ECP_FEATURE_UNAVAILABLE if key id doesn't 1295 * correspond to a known group. 1296 * \return Another negative error code on other kinds of failure. 1297 */ 1298 int mbedtls_ecp_export(const mbedtls_ecp_keypair *key, mbedtls_ecp_group *grp, 1299 mbedtls_mpi *d, mbedtls_ecp_point *Q); 1300 1301 #if defined(MBEDTLS_SELF_TEST) 1302 1303 /** 1304 * \brief The ECP checkup routine. 1305 * 1306 * \return \c 0 on success. 1307 * \return \c 1 on failure. 1308 */ 1309 int mbedtls_ecp_self_test( int verbose ); 1310 1311 #endif /* MBEDTLS_SELF_TEST */ 1312 1313 #ifdef __cplusplus 1314 } 1315 #endif 1316 1317 #endif /* ecp.h */ 1318
