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 37 #if !defined(MBEDTLS_CONFIG_FILE) 38 #include "mbedtls/config.h" 39 #else 40 #include MBEDTLS_CONFIG_FILE 41 #endif 42 43 #include "mbedtls/bignum.h" 44 45 /* 46 * ECP error codes 47 */ 48 /** Bad input parameters to function. */ 49 #define MBEDTLS_ERR_ECP_BAD_INPUT_DATA -0x4F80 50 /** The buffer is too small to write to. */ 51 #define MBEDTLS_ERR_ECP_BUFFER_TOO_SMALL -0x4F00 52 /** The requested feature is not available, for example, the requested curve is not supported. */ 53 #define MBEDTLS_ERR_ECP_FEATURE_UNAVAILABLE -0x4E80 54 /** The signature is not valid. */ 55 #define MBEDTLS_ERR_ECP_VERIFY_FAILED -0x4E00 56 /** Memory allocation failed. */ 57 #define MBEDTLS_ERR_ECP_ALLOC_FAILED -0x4D80 58 /** Generation of random value, such as ephemeral key, failed. */ 59 #define MBEDTLS_ERR_ECP_RANDOM_FAILED -0x4D00 60 /** Invalid private or public key. */ 61 #define MBEDTLS_ERR_ECP_INVALID_KEY -0x4C80 62 /** The buffer contains a valid signature followed by more data. */ 63 #define MBEDTLS_ERR_ECP_SIG_LEN_MISMATCH -0x4C00 64 65 /* MBEDTLS_ERR_ECP_HW_ACCEL_FAILED is deprecated and should not be used. */ 66 /** The ECP hardware accelerator failed. */ 67 #define MBEDTLS_ERR_ECP_HW_ACCEL_FAILED -0x4B80 68 69 /** Operation in progress, call again with the same parameters to continue. */ 70 #define MBEDTLS_ERR_ECP_IN_PROGRESS -0x4B00 71 72 /* Flags indicating whether to include code that is specific to certain 73 * types of curves. These flags are for internal library use only. */ 74 #if defined(MBEDTLS_ECP_DP_SECP192R1_ENABLED) || \ 75 defined(MBEDTLS_ECP_DP_SECP224R1_ENABLED) || \ 76 defined(MBEDTLS_ECP_DP_SECP256R1_ENABLED) || \ 77 defined(MBEDTLS_ECP_DP_SECP384R1_ENABLED) || \ 78 defined(MBEDTLS_ECP_DP_SECP521R1_ENABLED) || \ 79 defined(MBEDTLS_ECP_DP_BP256R1_ENABLED) || \ 80 defined(MBEDTLS_ECP_DP_BP384R1_ENABLED) || \ 81 defined(MBEDTLS_ECP_DP_BP512R1_ENABLED) || \ 82 defined(MBEDTLS_ECP_DP_SECP192K1_ENABLED) || \ 83 defined(MBEDTLS_ECP_DP_SECP224K1_ENABLED) || \ 84 defined(MBEDTLS_ECP_DP_SECP256K1_ENABLED) || \ 85 defined(MBEDTLS_ECP_DP_SM2_ENABLED) 86 #define MBEDTLS_ECP_SHORT_WEIERSTRASS_ENABLED 87 #endif 88 #if defined(MBEDTLS_ECP_DP_CURVE25519_ENABLED) || \ 89 defined(MBEDTLS_ECP_DP_CURVE448_ENABLED) 90 #define MBEDTLS_ECP_MONTGOMERY_ENABLED 91 #endif 92 93 #ifdef __cplusplus 94 extern "C" { 95 #endif 96 97 /** 98 * Domain-parameter identifiers: curve, subgroup, and generator. 99 * 100 * \note Only curves over prime fields are supported. 101 * 102 * \warning This library does not support validation of arbitrary domain 103 * parameters. Therefore, only standardized domain parameters from trusted 104 * sources should be used. See mbedtls_ecp_group_load(). 105 */ 106 /* Note: when adding a new curve: 107 * - Add it at the end of this enum, otherwise you'll break the ABI by 108 * changing the numerical value for existing curves. 109 * - Increment MBEDTLS_ECP_DP_MAX below if needed. 110 * - Update the calculation of MBEDTLS_ECP_MAX_BITS_MIN below. 111 * - Add the corresponding MBEDTLS_ECP_DP_xxx_ENABLED macro definition to 112 * config.h. 113 * - List the curve as a dependency of MBEDTLS_ECP_C and 114 * MBEDTLS_ECDSA_C if supported in check_config.h. 115 * - Add the curve to the appropriate curve type macro 116 * MBEDTLS_ECP_yyy_ENABLED above. 117 * - Add the necessary definitions to ecp_curves.c. 118 * - Add the curve to the ecp_supported_curves array in ecp.c. 119 * - Add the curve to applicable profiles in x509_crt.c if applicable. 120 */ 121 typedef enum 122 { 123 MBEDTLS_ECP_DP_NONE = 0, /*!< Curve not defined. */ 124 MBEDTLS_ECP_DP_SECP192R1, /*!< Domain parameters for the 192-bit curve defined by FIPS 186-4 and SEC1. */ 125 MBEDTLS_ECP_DP_SECP224R1, /*!< Domain parameters for the 224-bit curve defined by FIPS 186-4 and SEC1. */ 126 MBEDTLS_ECP_DP_SECP256R1, /*!< Domain parameters for the 256-bit curve defined by FIPS 186-4 and SEC1. */ 127 MBEDTLS_ECP_DP_SECP384R1, /*!< Domain parameters for the 384-bit curve defined by FIPS 186-4 and SEC1. */ 128 MBEDTLS_ECP_DP_SECP521R1, /*!< Domain parameters for the 521-bit curve defined by FIPS 186-4 and SEC1. */ 129 MBEDTLS_ECP_DP_BP256R1, /*!< Domain parameters for 256-bit Brainpool curve. */ 130 MBEDTLS_ECP_DP_BP384R1, /*!< Domain parameters for 384-bit Brainpool curve. */ 131 MBEDTLS_ECP_DP_BP512R1, /*!< Domain parameters for 512-bit Brainpool curve. */ 132 MBEDTLS_ECP_DP_CURVE25519, /*!< Domain parameters for Curve25519. */ 133 MBEDTLS_ECP_DP_SECP192K1, /*!< Domain parameters for 192-bit "Koblitz" curve. */ 134 MBEDTLS_ECP_DP_SECP224K1, /*!< Domain parameters for 224-bit "Koblitz" curve. */ 135 MBEDTLS_ECP_DP_SECP256K1, /*!< Domain parameters for 256-bit "Koblitz" curve. */ 136 MBEDTLS_ECP_DP_CURVE448, /*!< Domain parameters for Curve448. */ 137 MBEDTLS_ECP_DP_SM2, /*!< Domain parameters for SM2. */ 138 } mbedtls_ecp_group_id; 139 140 /** 141 * The number of supported curves, plus one for #MBEDTLS_ECP_DP_NONE. 142 * 143 * \note Montgomery curves are currently excluded. 144 */ 145 #define MBEDTLS_ECP_DP_MAX 12 146 147 /* 148 * Curve types 149 */ 150 typedef enum 151 { 152 MBEDTLS_ECP_TYPE_NONE = 0, 153 MBEDTLS_ECP_TYPE_SHORT_WEIERSTRASS, /* y^2 = x^3 + a x + b */ 154 MBEDTLS_ECP_TYPE_MONTGOMERY, /* y^2 = x^3 + a x^2 + x */ 155 } mbedtls_ecp_curve_type; 156 157 /** 158 * Curve information, for use by other modules. 159 */ 160 typedef struct mbedtls_ecp_curve_info 161 { 162 mbedtls_ecp_group_id grp_id; /*!< An internal identifier. */ 163 uint16_t tls_id; /*!< The TLS NamedCurve identifier. */ 164 uint16_t bit_size; /*!< The curve size in bits. */ 165 const char *name; /*!< A human-friendly name. */ 166 } mbedtls_ecp_curve_info; 167 168 /** 169 * \brief The ECP point structure, in Jacobian coordinates. 170 * 171 * \note All functions expect and return points satisfying 172 * the following condition: <code>Z == 0</code> or 173 * <code>Z == 1</code>. Other values of \p Z are 174 * used only by internal functions. 175 * The point is zero, or "at infinity", if <code>Z == 0</code>. 176 * Otherwise, \p X and \p Y are its standard (affine) 177 * coordinates. 178 */ 179 typedef struct mbedtls_ecp_point 180 { 181 mbedtls_mpi X; /*!< The X coordinate of the ECP point. */ 182 mbedtls_mpi Y; /*!< The Y coordinate of the ECP point. */ 183 mbedtls_mpi Z; /*!< The Z coordinate of the ECP point. */ 184 } 185 mbedtls_ecp_point; 186 187 /* Determine the minimum safe value of MBEDTLS_ECP_MAX_BITS. */ 188 #if !defined(MBEDTLS_ECP_C) 189 #define MBEDTLS_ECP_MAX_BITS_MIN 0 190 /* Note: the curves must be listed in DECREASING size! */ 191 #elif defined(MBEDTLS_ECP_DP_SECP521R1_ENABLED) 192 #define MBEDTLS_ECP_MAX_BITS_MIN 521 193 #elif defined(MBEDTLS_ECP_DP_BP512R1_ENABLED) 194 #define MBEDTLS_ECP_MAX_BITS_MIN 512 195 #elif defined(MBEDTLS_ECP_DP_CURVE448_ENABLED) 196 #define MBEDTLS_ECP_MAX_BITS_MIN 448 197 #elif defined(MBEDTLS_ECP_DP_BP384R1_ENABLED) 198 #define MBEDTLS_ECP_MAX_BITS_MIN 384 199 #elif defined(MBEDTLS_ECP_DP_SECP384R1_ENABLED) 200 #define MBEDTLS_ECP_MAX_BITS_MIN 384 201 #elif defined(MBEDTLS_ECP_DP_BP256R1_ENABLED) 202 #define MBEDTLS_ECP_MAX_BITS_MIN 256 203 #elif defined(MBEDTLS_ECP_DP_SECP256K1_ENABLED) 204 #define MBEDTLS_ECP_MAX_BITS_MIN 256 205 #elif defined(MBEDTLS_ECP_DP_SECP256R1_ENABLED) 206 #define MBEDTLS_ECP_MAX_BITS_MIN 256 207 #elif defined(MBEDTLS_ECP_DP_SM2_ENABLED) 208 #define MBEDTLS_ECP_MAX_BITS_MIN 256 209 #elif defined(MBEDTLS_ECP_DP_CURVE25519_ENABLED) 210 #define MBEDTLS_ECP_MAX_BITS_MIN 255 211 #elif defined(MBEDTLS_ECP_DP_SECP224K1_ENABLED) 212 #define MBEDTLS_ECP_MAX_BITS_MIN 225 // n is slightly above 2^224 213 #elif defined(MBEDTLS_ECP_DP_SECP224R1_ENABLED) 214 #define MBEDTLS_ECP_MAX_BITS_MIN 224 215 #elif defined(MBEDTLS_ECP_DP_SECP192K1_ENABLED) 216 #define MBEDTLS_ECP_MAX_BITS_MIN 192 217 #elif defined(MBEDTLS_ECP_DP_SECP192R1_ENABLED) 218 #define MBEDTLS_ECP_MAX_BITS_MIN 192 219 #else 220 #error "MBEDTLS_ECP_C enabled, but no curve?" 221 #endif 222 223 #if !defined(MBEDTLS_ECP_ALT) 224 /* 225 * default mbed TLS elliptic curve arithmetic implementation 226 * 227 * (in case MBEDTLS_ECP_ALT is defined then the developer has to provide an 228 * alternative implementation for the whole module and it will replace this 229 * one.) 230 */ 231 232 /** 233 * \brief The ECP group structure. 234 * 235 * We consider two types of curve equations: 236 * <ul><li>Short Weierstrass: <code>y^2 = x^3 + A x + B mod P</code> 237 * (SEC1 + RFC-4492)</li> 238 * <li>Montgomery: <code>y^2 = x^3 + A x^2 + x mod P</code> (Curve25519, 239 * Curve448)</li></ul> 240 * In both cases, the generator (\p G) for a prime-order subgroup is fixed. 241 * 242 * For Short Weierstrass, this subgroup is the whole curve, and its 243 * cardinality is denoted by \p N. Our code requires that \p N is an 244 * odd prime as mbedtls_ecp_mul() requires an odd number, and 245 * mbedtls_ecdsa_sign() requires that it is prime for blinding purposes. 246 * 247 * For Montgomery curves, we do not store \p A, but <code>(A + 2) / 4</code>, 248 * which is the quantity used in the formulas. Additionally, \p nbits is 249 * not the size of \p N but the required size for private keys. 250 * 251 * If \p modp is NULL, reduction modulo \p P is done using a generic algorithm. 252 * Otherwise, \p modp must point to a function that takes an \p mbedtls_mpi in the 253 * range of <code>0..2^(2*pbits)-1</code>, and transforms it in-place to an integer 254 * which is congruent mod \p P to the given MPI, and is close enough to \p pbits 255 * in size, so that it may be efficiently brought in the 0..P-1 range by a few 256 * additions or subtractions. Therefore, it is only an approximative modular 257 * reduction. It must return 0 on success and non-zero on failure. 258 * 259 * \note Alternative implementations must keep the group IDs distinct. If 260 * two group structures have the same ID, then they must be 261 * identical. 262 * 263 */ 264 typedef struct mbedtls_ecp_group 265 { 266 mbedtls_ecp_group_id id; /*!< An internal group identifier. */ 267 mbedtls_mpi P; /*!< The prime modulus of the base field. */ 268 mbedtls_mpi A; /*!< For Short Weierstrass: \p A in the equation. For 269 Montgomery curves: <code>(A + 2) / 4</code>. */ 270 mbedtls_mpi B; /*!< For Short Weierstrass: \p B in the equation. 271 For Montgomery curves: unused. */ 272 mbedtls_ecp_point G; /*!< The generator of the subgroup used. */ 273 mbedtls_mpi N; /*!< The order of \p G. */ 274 size_t pbits; /*!< The number of bits in \p P.*/ 275 size_t nbits; /*!< For Short Weierstrass: The number of bits in \p P. 276 For Montgomery curves: the number of bits in the 277 private keys. */ 278 unsigned int h; /*!< \internal 1 if the constants are static. */ 279 int (*modp)(mbedtls_mpi *); /*!< The function for fast pseudo-reduction 280 mod \p P (see above).*/ 281 int (*t_pre)(mbedtls_ecp_point *, void *); /*!< Unused. */ 282 int (*t_post)(mbedtls_ecp_point *, void *); /*!< Unused. */ 283 void *t_data; /*!< Unused. */ 284 mbedtls_ecp_point *T; /*!< Pre-computed points for ecp_mul_comb(). */ 285 size_t T_size; /*!< The number of pre-computed points. */ 286 } 287 mbedtls_ecp_group; 288 289 /** 290 * \name SECTION: Module settings 291 * 292 * The configuration options you can set for this module are in this section. 293 * Either change them in config.h, or define them using the compiler command line. 294 * \{ 295 */ 296 297 #if defined(MBEDTLS_ECP_MAX_BITS) 298 299 #if MBEDTLS_ECP_MAX_BITS < MBEDTLS_ECP_MAX_BITS_MIN 300 #error "MBEDTLS_ECP_MAX_BITS is smaller than the largest supported curve" 301 #endif 302 303 #elif defined(MBEDTLS_ECP_C) 304 /** 305 * The maximum size of the groups, that is, of \c N and \c P. 306 */ 307 #define MBEDTLS_ECP_MAX_BITS MBEDTLS_ECP_MAX_BITS_MIN 308 309 #else 310 /* MBEDTLS_ECP_MAX_BITS is not relevant without MBEDTLS_ECP_C, but set it 311 * to a nonzero value so that code that unconditionally allocates an array 312 * of a size based on it keeps working if built without ECC support. */ 313 #define MBEDTLS_ECP_MAX_BITS 1 314 #endif 315 316 #define MBEDTLS_ECP_MAX_BYTES ( ( MBEDTLS_ECP_MAX_BITS + 7 ) / 8 ) 317 #define MBEDTLS_ECP_MAX_PT_LEN ( 2 * MBEDTLS_ECP_MAX_BYTES + 1 ) 318 319 #if !defined(MBEDTLS_ECP_WINDOW_SIZE) 320 /* 321 * Maximum "window" size used for point multiplication. 322 * Default: a point where higher memory usage yields diminishing performance 323 * returns. 324 * Minimum value: 2. Maximum value: 7. 325 * 326 * Result is an array of at most ( 1 << ( MBEDTLS_ECP_WINDOW_SIZE - 1 ) ) 327 * points used for point multiplication. This value is directly tied to EC 328 * peak memory usage, so decreasing it by one should roughly cut memory usage 329 * by two (if large curves are in use). 330 * 331 * Reduction in size may reduce speed, but larger curves are impacted first. 332 * Sample performances (in ECDHE handshakes/s, with FIXED_POINT_OPTIM = 1): 333 * w-size: 6 5 4 3 2 334 * 521 145 141 135 120 97 335 * 384 214 209 198 177 146 336 * 256 320 320 303 262 226 337 * 224 475 475 453 398 342 338 * 192 640 640 633 587 476 339 */ 340 #define MBEDTLS_ECP_WINDOW_SIZE 4 /**< The maximum window size used. */ 341 #endif /* MBEDTLS_ECP_WINDOW_SIZE */ 342 343 #if !defined(MBEDTLS_ECP_FIXED_POINT_OPTIM) 344 /* 345 * Trade memory for speed on fixed-point multiplication. 346 * 347 * This speeds up repeated multiplication of the generator (that is, the 348 * multiplication in ECDSA signatures, and half of the multiplications in 349 * ECDSA verification and ECDHE) by a factor roughly 3 to 4. 350 * 351 * The cost is increasing EC peak memory usage by a factor roughly 2. 352 * 353 * Change this value to 0 to reduce peak memory usage. 354 */ 355 #define MBEDTLS_ECP_FIXED_POINT_OPTIM 1 /**< Enable fixed-point speed-up. */ 356 #endif /* MBEDTLS_ECP_FIXED_POINT_OPTIM */ 357 358 /** \} name SECTION: Module settings */ 359 360 #else /* MBEDTLS_ECP_ALT */ 361 #include "ecp_alt.h" 362 #endif /* MBEDTLS_ECP_ALT */ 363 364 #if defined(MBEDTLS_ECP_RESTARTABLE) 365 366 /** 367 * \brief Internal restart context for multiplication 368 * 369 * \note Opaque struct 370 */ 371 typedef struct mbedtls_ecp_restart_mul mbedtls_ecp_restart_mul_ctx; 372 373 /** 374 * \brief Internal restart context for ecp_muladd() 375 * 376 * \note Opaque struct 377 */ 378 typedef struct mbedtls_ecp_restart_muladd mbedtls_ecp_restart_muladd_ctx; 379 380 /** 381 * \brief General context for resuming ECC operations 382 */ 383 typedef struct 384 { 385 unsigned ops_done; /*!< current ops count */ 386 unsigned depth; /*!< call depth (0 = top-level) */ 387 mbedtls_ecp_restart_mul_ctx *rsm; /*!< ecp_mul_comb() sub-context */ 388 mbedtls_ecp_restart_muladd_ctx *ma; /*!< ecp_muladd() sub-context */ 389 } mbedtls_ecp_restart_ctx; 390 391 /* 392 * Operation counts for restartable functions 393 */ 394 #define MBEDTLS_ECP_OPS_CHK 3 /*!< basic ops count for ecp_check_pubkey() */ 395 #define MBEDTLS_ECP_OPS_DBL 8 /*!< basic ops count for ecp_double_jac() */ 396 #define MBEDTLS_ECP_OPS_ADD 11 /*!< basic ops count for see ecp_add_mixed() */ 397 #define MBEDTLS_ECP_OPS_INV 120 /*!< empirical equivalent for mpi_mod_inv() */ 398 399 /** 400 * \brief Internal; for restartable functions in other modules. 401 * Check and update basic ops budget. 402 * 403 * \param grp Group structure 404 * \param rs_ctx Restart context 405 * \param ops Number of basic ops to do 406 * 407 * \return \c 0 if doing \p ops basic ops is still allowed, 408 * \return #MBEDTLS_ERR_ECP_IN_PROGRESS otherwise. 409 */ 410 int mbedtls_ecp_check_budget( const mbedtls_ecp_group *grp, 411 mbedtls_ecp_restart_ctx *rs_ctx, 412 unsigned ops ); 413 414 /* Utility macro for checking and updating ops budget */ 415 #define MBEDTLS_ECP_BUDGET( ops ) \ 416 MBEDTLS_MPI_CHK( mbedtls_ecp_check_budget( grp, rs_ctx, \ 417 (unsigned) (ops) ) ); 418 419 #else /* MBEDTLS_ECP_RESTARTABLE */ 420 421 #define MBEDTLS_ECP_BUDGET( ops ) /* no-op; for compatibility */ 422 423 /* We want to declare restartable versions of existing functions anyway */ 424 typedef void mbedtls_ecp_restart_ctx; 425 426 #endif /* MBEDTLS_ECP_RESTARTABLE */ 427 428 /** 429 * \brief The ECP key-pair structure. 430 * 431 * A generic key-pair that may be used for ECDSA and fixed ECDH, for example. 432 * 433 * \note Members are deliberately in the same order as in the 434 * ::mbedtls_ecdsa_context structure. 435 */ 436 typedef struct mbedtls_ecp_keypair 437 { 438 mbedtls_ecp_group grp; /*!< Elliptic curve and base point */ 439 mbedtls_mpi d; /*!< our secret value */ 440 mbedtls_ecp_point Q; /*!< our public value */ 441 } 442 mbedtls_ecp_keypair; 443 444 /* 445 * Point formats, from RFC 4492's enum ECPointFormat 446 */ 447 #define MBEDTLS_ECP_PF_UNCOMPRESSED 0 /**< Uncompressed point format. */ 448 #define MBEDTLS_ECP_PF_COMPRESSED 1 /**< Compressed point format. */ 449 450 /* 451 * Some other constants from RFC 4492 452 */ 453 #define MBEDTLS_ECP_TLS_NAMED_CURVE 3 /**< The named_curve of ECCurveType. */ 454 455 #if defined(MBEDTLS_ECP_RESTARTABLE) 456 /** 457 * \brief Set the maximum number of basic operations done in a row. 458 * 459 * If more operations are needed to complete a computation, 460 * #MBEDTLS_ERR_ECP_IN_PROGRESS will be returned by the 461 * function performing the computation. It is then the 462 * caller's responsibility to either call again with the same 463 * parameters until it returns 0 or an error code; or to free 464 * the restart context if the operation is to be aborted. 465 * 466 * It is strictly required that all input parameters and the 467 * restart context be the same on successive calls for the 468 * same operation, but output parameters need not be the 469 * same; they must not be used until the function finally 470 * returns 0. 471 * 472 * This only applies to functions whose documentation 473 * mentions they may return #MBEDTLS_ERR_ECP_IN_PROGRESS (or 474 * #MBEDTLS_ERR_SSL_CRYPTO_IN_PROGRESS for functions in the 475 * SSL module). For functions that accept a "restart context" 476 * argument, passing NULL disables restart and makes the 477 * function equivalent to the function with the same name 478 * with \c _restartable removed. For functions in the ECDH 479 * module, restart is disabled unless the function accepts 480 * an "ECDH context" argument and 481 * mbedtls_ecdh_enable_restart() was previously called on 482 * that context. For function in the SSL module, restart is 483 * only enabled for specific sides and key exchanges 484 * (currently only for clients and ECDHE-ECDSA). 485 * 486 * \param max_ops Maximum number of basic operations done in a row. 487 * Default: 0 (unlimited). 488 * Lower (non-zero) values mean ECC functions will block for 489 * a lesser maximum amount of time. 490 * 491 * \note A "basic operation" is defined as a rough equivalent of a 492 * multiplication in GF(p) for the NIST P-256 curve. 493 * As an indication, with default settings, a scalar 494 * multiplication (full run of \c mbedtls_ecp_mul()) is: 495 * - about 3300 basic operations for P-256 496 * - about 9400 basic operations for P-384 497 * 498 * \note Very low values are not always respected: sometimes 499 * functions need to block for a minimum number of 500 * operations, and will do so even if max_ops is set to a 501 * lower value. That minimum depends on the curve size, and 502 * can be made lower by decreasing the value of 503 * \c MBEDTLS_ECP_WINDOW_SIZE. As an indication, here is the 504 * lowest effective value for various curves and values of 505 * that parameter (w for short): 506 * w=6 w=5 w=4 w=3 w=2 507 * P-256 208 208 160 136 124 508 * P-384 682 416 320 272 248 509 * P-521 1364 832 640 544 496 510 * 511 * \note This setting is currently ignored by Curve25519. 512 */ 513 void mbedtls_ecp_set_max_ops( unsigned max_ops ); 514 515 /** 516 * \brief Check if restart is enabled (max_ops != 0) 517 * 518 * \return \c 0 if \c max_ops == 0 (restart disabled) 519 * \return \c 1 otherwise (restart enabled) 520 */ 521 int mbedtls_ecp_restart_is_enabled( void ); 522 #endif /* MBEDTLS_ECP_RESTARTABLE */ 523 524 /* 525 * Get the type of a curve 526 */ 527 mbedtls_ecp_curve_type mbedtls_ecp_get_type( const mbedtls_ecp_group *grp ); 528 529 /** 530 * \brief This function retrieves the information defined in 531 * mbedtls_ecp_curve_info() for all supported curves. 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. The last entry is 0. 540 */ 541 const mbedtls_ecp_curve_info *mbedtls_ecp_curve_list( void ); 542 543 /** 544 * \brief This function retrieves the list of internal group 545 * identifiers of all supported curves in the order of 546 * preference. 547 * 548 * \note This function returns information about all curves 549 * supported by the library. Some curves may not be 550 * supported for all algorithms. Call mbedtls_ecdh_can_do() 551 * or mbedtls_ecdsa_can_do() to check if a curve is 552 * supported for ECDH or ECDSA. 553 * 554 * \return A statically allocated array, 555 * terminated with MBEDTLS_ECP_DP_NONE. 556 */ 557 const mbedtls_ecp_group_id *mbedtls_ecp_grp_id_list( void ); 558 559 /** 560 * \brief This function retrieves curve information from an internal 561 * group identifier. 562 * 563 * \param grp_id An \c MBEDTLS_ECP_DP_XXX value. 564 * 565 * \return The associated curve information on success. 566 * \return NULL on failure. 567 */ 568 const mbedtls_ecp_curve_info *mbedtls_ecp_curve_info_from_grp_id( mbedtls_ecp_group_id grp_id ); 569 570 /** 571 * \brief This function retrieves curve information from a TLS 572 * NamedCurve value. 573 * 574 * \param tls_id An \c MBEDTLS_ECP_DP_XXX value. 575 * 576 * \return The associated curve information on success. 577 * \return NULL on failure. 578 */ 579 const mbedtls_ecp_curve_info *mbedtls_ecp_curve_info_from_tls_id( uint16_t tls_id ); 580 581 /** 582 * \brief This function retrieves curve information from a 583 * human-readable name. 584 * 585 * \param name The human-readable name. 586 * 587 * \return The associated curve information on success. 588 * \return NULL on failure. 589 */ 590 const mbedtls_ecp_curve_info *mbedtls_ecp_curve_info_from_name( const char *name ); 591 592 /** 593 * \brief This function initializes a point as zero. 594 * 595 * \param pt The point to initialize. 596 */ 597 void mbedtls_ecp_point_init( mbedtls_ecp_point *pt ); 598 599 /** 600 * \brief This function initializes an ECP group context 601 * without loading any domain parameters. 602 * 603 * \note After this function is called, domain parameters 604 * for various ECP groups can be loaded through the 605 * mbedtls_ecp_group_load() or mbedtls_ecp_tls_read_group() 606 * functions. 607 */ 608 void mbedtls_ecp_group_init( mbedtls_ecp_group *grp ); 609 610 /** 611 * \brief This function initializes a key pair as an invalid one. 612 * 613 * \param key The key pair to initialize. 614 */ 615 void mbedtls_ecp_keypair_init( mbedtls_ecp_keypair *key ); 616 617 /** 618 * \brief This function frees the components of a point. 619 * 620 * \param pt The point to free. 621 */ 622 void mbedtls_ecp_point_free( mbedtls_ecp_point *pt ); 623 624 /** 625 * \brief This function frees the components of an ECP group. 626 * 627 * \param grp The group to free. This may be \c NULL, in which 628 * case this function returns immediately. If it is not 629 * \c NULL, it must point to an initialized ECP group. 630 */ 631 void mbedtls_ecp_group_free( mbedtls_ecp_group *grp ); 632 633 /** 634 * \brief This function frees the components of a key pair. 635 * 636 * \param key The key pair to free. This may be \c NULL, in which 637 * case this function returns immediately. If it is not 638 * \c NULL, it must point to an initialized ECP key pair. 639 */ 640 void mbedtls_ecp_keypair_free( mbedtls_ecp_keypair *key ); 641 642 #if defined(MBEDTLS_ECP_RESTARTABLE) 643 /** 644 * \brief Initialize a restart context. 645 * 646 * \param ctx The restart context to initialize. This must 647 * not be \c NULL. 648 */ 649 void mbedtls_ecp_restart_init( mbedtls_ecp_restart_ctx *ctx ); 650 651 /** 652 * \brief Free the components of a restart context. 653 * 654 * \param ctx The restart context to free. This may be \c NULL, in which 655 * case this function returns immediately. If it is not 656 * \c NULL, it must point to an initialized restart context. 657 */ 658 void mbedtls_ecp_restart_free( mbedtls_ecp_restart_ctx *ctx ); 659 #endif /* MBEDTLS_ECP_RESTARTABLE */ 660 661 /** 662 * \brief This function copies the contents of point \p Q into 663 * point \p P. 664 * 665 * \param P The destination point. This must be initialized. 666 * \param Q The source point. This must be initialized. 667 * 668 * \return \c 0 on success. 669 * \return #MBEDTLS_ERR_MPI_ALLOC_FAILED on memory-allocation failure. 670 * \return Another negative error code for other kinds of failure. 671 */ 672 int mbedtls_ecp_copy( mbedtls_ecp_point *P, const mbedtls_ecp_point *Q ); 673 674 /** 675 * \brief This function copies the contents of group \p src into 676 * group \p dst. 677 * 678 * \param dst The destination group. This must be initialized. 679 * \param src The source group. This must be initialized. 680 * 681 * \return \c 0 on success. 682 * \return #MBEDTLS_ERR_MPI_ALLOC_FAILED on memory-allocation failure. 683 * \return Another negative error code on other kinds of failure. 684 */ 685 int mbedtls_ecp_group_copy( mbedtls_ecp_group *dst, 686 const mbedtls_ecp_group *src ); 687 688 /** 689 * \brief This function sets a point to the point at infinity. 690 * 691 * \param pt The point to set. This must be initialized. 692 * 693 * \return \c 0 on success. 694 * \return #MBEDTLS_ERR_MPI_ALLOC_FAILED on memory-allocation failure. 695 * \return Another negative error code on other kinds of failure. 696 */ 697 int mbedtls_ecp_set_zero( mbedtls_ecp_point *pt ); 698 699 /** 700 * \brief This function checks if a point is the point at infinity. 701 * 702 * \param pt The point to test. This must be initialized. 703 * 704 * \return \c 1 if the point is zero. 705 * \return \c 0 if the point is non-zero. 706 * \return A negative error code on failure. 707 */ 708 int mbedtls_ecp_is_zero( mbedtls_ecp_point *pt ); 709 710 /** 711 * \brief This function compares two points. 712 * 713 * \note This assumes that the points are normalized. Otherwise, 714 * they may compare as "not equal" even if they are. 715 * 716 * \param P The first point to compare. This must be initialized. 717 * \param Q The second point to compare. This must be initialized. 718 * 719 * \return \c 0 if the points are equal. 720 * \return #MBEDTLS_ERR_ECP_BAD_INPUT_DATA if the points are not equal. 721 */ 722 int mbedtls_ecp_point_cmp( const mbedtls_ecp_point *P, 723 const mbedtls_ecp_point *Q ); 724 725 /** 726 * \brief This function imports a non-zero point from two ASCII 727 * strings. 728 * 729 * \param P The destination point. This must be initialized. 730 * \param radix The numeric base of the input. 731 * \param x The first affine coordinate, as a null-terminated string. 732 * \param y The second affine coordinate, as a null-terminated string. 733 * 734 * \return \c 0 on success. 735 * \return An \c MBEDTLS_ERR_MPI_XXX error code on failure. 736 */ 737 int mbedtls_ecp_point_read_string( mbedtls_ecp_point *P, int radix, 738 const char *x, const char *y ); 739 740 /** 741 * \brief This function exports a point into unsigned binary data. 742 * 743 * \param grp The group to which the point should belong. 744 * This must be initialized and have group parameters 745 * set, for example through mbedtls_ecp_group_load(). 746 * \param P The point to export. This must be initialized. 747 * \param format The point format. This must be either 748 * #MBEDTLS_ECP_PF_COMPRESSED or #MBEDTLS_ECP_PF_UNCOMPRESSED. 749 * (For groups without these formats, this parameter is 750 * ignored. But it still has to be either of the above 751 * values.) 752 * \param olen The address at which to store the length of 753 * the output in Bytes. This must not be \c NULL. 754 * \param buf The output buffer. This must be a writable buffer 755 * of length \p buflen Bytes. 756 * \param buflen The length of the output buffer \p buf in Bytes. 757 * 758 * \return \c 0 on success. 759 * \return #MBEDTLS_ERR_ECP_BUFFER_TOO_SMALL if the output buffer 760 * is too small to hold the point. 761 * \return #MBEDTLS_ERR_ECP_FEATURE_UNAVAILABLE if the point format 762 * or the export for the given group is not implemented. 763 * \return Another negative error code on other kinds of failure. 764 */ 765 int mbedtls_ecp_point_write_binary( const mbedtls_ecp_group *grp, 766 const mbedtls_ecp_point *P, 767 int format, size_t *olen, 768 unsigned char *buf, size_t buflen ); 769 770 /** 771 * \brief This function imports a point from unsigned binary data. 772 * 773 * \note This function does not check that the point actually 774 * belongs to the given group, see mbedtls_ecp_check_pubkey() 775 * for that. 776 * 777 * \param grp The group to which the point should belong. 778 * This must be initialized and have group parameters 779 * set, for example through mbedtls_ecp_group_load(). 780 * \param P The destination context to import the point to. 781 * This must be initialized. 782 * \param buf The input buffer. This must be a readable buffer 783 * of length \p ilen Bytes. 784 * \param ilen The length of the input buffer \p buf in Bytes. 785 * 786 * \return \c 0 on success. 787 * \return #MBEDTLS_ERR_ECP_BAD_INPUT_DATA if the input is invalid. 788 * \return #MBEDTLS_ERR_MPI_ALLOC_FAILED on memory-allocation failure. 789 * \return #MBEDTLS_ERR_ECP_FEATURE_UNAVAILABLE if the import for the 790 * given group is not implemented. 791 */ 792 int mbedtls_ecp_point_read_binary( const mbedtls_ecp_group *grp, 793 mbedtls_ecp_point *P, 794 const unsigned char *buf, size_t ilen ); 795 796 /** 797 * \brief This function imports a point from a TLS ECPoint record. 798 * 799 * \note On function return, \p *buf is updated to point immediately 800 * after the ECPoint record. 801 * 802 * \param grp The ECP group to use. 803 * This must be initialized and have group parameters 804 * set, for example through mbedtls_ecp_group_load(). 805 * \param pt The destination point. 806 * \param buf The address of the pointer to the start of the input buffer. 807 * \param len The length of the buffer. 808 * 809 * \return \c 0 on success. 810 * \return An \c MBEDTLS_ERR_MPI_XXX error code on initialization 811 * failure. 812 * \return #MBEDTLS_ERR_ECP_BAD_INPUT_DATA if input is invalid. 813 */ 814 int mbedtls_ecp_tls_read_point( const mbedtls_ecp_group *grp, 815 mbedtls_ecp_point *pt, 816 const unsigned char **buf, size_t len ); 817 818 /** 819 * \brief This function exports a point as a TLS ECPoint record 820 * defined in RFC 4492, Section 5.4. 821 * 822 * \param grp The ECP group to use. 823 * This must be initialized and have group parameters 824 * set, for example through mbedtls_ecp_group_load(). 825 * \param pt The point to be exported. This must be initialized. 826 * \param format The point format to use. This must be either 827 * #MBEDTLS_ECP_PF_COMPRESSED or #MBEDTLS_ECP_PF_UNCOMPRESSED. 828 * \param olen The address at which to store the length in Bytes 829 * of the data written. 830 * \param buf The target buffer. This must be a writable buffer of 831 * length \p blen Bytes. 832 * \param blen The length of the target buffer \p buf in Bytes. 833 * 834 * \return \c 0 on success. 835 * \return #MBEDTLS_ERR_ECP_BAD_INPUT_DATA if the input is invalid. 836 * \return #MBEDTLS_ERR_ECP_BUFFER_TOO_SMALL if the target buffer 837 * is too small to hold the exported point. 838 * \return Another negative error code on other kinds of failure. 839 */ 840 int mbedtls_ecp_tls_write_point( const mbedtls_ecp_group *grp, 841 const mbedtls_ecp_point *pt, 842 int format, size_t *olen, 843 unsigned char *buf, size_t blen ); 844 845 /** 846 * \brief This function sets up an ECP group context 847 * from a standardized set of domain parameters. 848 * 849 * \note The index should be a value of the NamedCurve enum, 850 * as defined in <em>RFC-4492: Elliptic Curve Cryptography 851 * (ECC) Cipher Suites for Transport Layer Security (TLS)</em>, 852 * usually in the form of an \c MBEDTLS_ECP_DP_XXX macro. 853 * 854 * \param grp The group context to setup. This must be initialized. 855 * \param id The identifier of the domain parameter set to load. 856 * 857 * \return \c 0 on success. 858 * \return #MBEDTLS_ERR_ECP_FEATURE_UNAVAILABLE if \p id doesn't 859 * correspond to a known group. 860 * \return Another negative error code on other kinds of failure. 861 */ 862 int mbedtls_ecp_group_load( mbedtls_ecp_group *grp, mbedtls_ecp_group_id id ); 863 864 /** 865 * \brief This function sets up an ECP group context from a TLS 866 * ECParameters record as defined in RFC 4492, Section 5.4. 867 * 868 * \note The read pointer \p buf is updated to point right after 869 * the ECParameters record on exit. 870 * 871 * \param grp The group context to setup. This must be initialized. 872 * \param buf The address of the pointer to the start of the input buffer. 873 * \param len The length of the input buffer \c *buf in Bytes. 874 * 875 * \return \c 0 on success. 876 * \return #MBEDTLS_ERR_ECP_BAD_INPUT_DATA if input is invalid. 877 * \return #MBEDTLS_ERR_ECP_FEATURE_UNAVAILABLE if the group is not 878 * recognized. 879 * \return Another negative error code on other kinds of failure. 880 */ 881 int mbedtls_ecp_tls_read_group( mbedtls_ecp_group *grp, 882 const unsigned char **buf, size_t len ); 883 884 /** 885 * \brief This function extracts an elliptic curve group ID from a 886 * TLS ECParameters record as defined in RFC 4492, Section 5.4. 887 * 888 * \note The read pointer \p buf is updated to point right after 889 * the ECParameters record on exit. 890 * 891 * \param grp The address at which to store the group id. 892 * This must not be \c NULL. 893 * \param buf The address of the pointer to the start of the input buffer. 894 * \param len The length of the input buffer \c *buf in Bytes. 895 * 896 * \return \c 0 on success. 897 * \return #MBEDTLS_ERR_ECP_BAD_INPUT_DATA if input is invalid. 898 * \return #MBEDTLS_ERR_ECP_FEATURE_UNAVAILABLE if the group is not 899 * recognized. 900 * \return Another negative error code on other kinds of failure. 901 */ 902 int mbedtls_ecp_tls_read_group_id( mbedtls_ecp_group_id *grp, 903 const unsigned char **buf, 904 size_t len ); 905 /** 906 * \brief This function exports an elliptic curve as a TLS 907 * ECParameters record as defined in RFC 4492, Section 5.4. 908 * 909 * \param grp The ECP group to be exported. 910 * This must be initialized and have group parameters 911 * set, for example through mbedtls_ecp_group_load(). 912 * \param olen The address at which to store the number of Bytes written. 913 * This must not be \c NULL. 914 * \param buf The buffer to write to. This must be a writable buffer 915 * of length \p blen Bytes. 916 * \param blen The length of the output buffer \p buf in Bytes. 917 * 918 * \return \c 0 on success. 919 * \return #MBEDTLS_ERR_ECP_BUFFER_TOO_SMALL if the output 920 * buffer is too small to hold the exported group. 921 * \return Another negative error code on other kinds of failure. 922 */ 923 int mbedtls_ecp_tls_write_group( const mbedtls_ecp_group *grp, 924 size_t *olen, 925 unsigned char *buf, size_t blen ); 926 927 /** 928 * \brief This function performs a scalar multiplication of a point 929 * by an integer: \p R = \p m * \p P. 930 * 931 * It is not thread-safe to use same group in multiple threads. 932 * 933 * \note To prevent timing attacks, this function 934 * executes the exact same sequence of base-field 935 * operations for any valid \p m. It avoids any if-branch or 936 * array index depending on the value of \p m. 937 * 938 * \note If \p f_rng is not NULL, it is used to randomize 939 * intermediate results to prevent potential timing attacks 940 * targeting these results. We recommend always providing 941 * a non-NULL \p f_rng. The overhead is negligible. 942 * Note: unless #MBEDTLS_ECP_NO_INTERNAL_RNG is defined, when 943 * \p f_rng is NULL, an internal RNG (seeded from the value 944 * of \p m) will be used instead. 945 * 946 * \param grp The ECP group to use. 947 * This must be initialized and have group parameters 948 * set, for example through mbedtls_ecp_group_load(). 949 * \param R The point in which to store the result of the calculation. 950 * This must be initialized. 951 * \param m The integer by which to multiply. This must be initialized. 952 * \param P The point to multiply. This must be initialized. 953 * \param f_rng The RNG function. This may be \c NULL if randomization 954 * of intermediate results isn't desired (discouraged). 955 * \param p_rng The RNG context to be passed to \p p_rng. 956 * 957 * \return \c 0 on success. 958 * \return #MBEDTLS_ERR_ECP_INVALID_KEY if \p m is not a valid private 959 * key, or \p P is not a valid public key. 960 * \return #MBEDTLS_ERR_MPI_ALLOC_FAILED on memory-allocation failure. 961 * \return Another negative error code on other kinds of failure. 962 */ 963 int mbedtls_ecp_mul( mbedtls_ecp_group *grp, mbedtls_ecp_point *R, 964 const mbedtls_mpi *m, const mbedtls_ecp_point *P, 965 int (*f_rng)(void *, unsigned char *, size_t), void *p_rng ); 966 967 /** 968 * \brief This function performs multiplication of a point by 969 * an integer: \p R = \p m * \p P in a restartable way. 970 * 971 * \see mbedtls_ecp_mul() 972 * 973 * \note This function does the same as \c mbedtls_ecp_mul(), but 974 * it can return early and restart according to the limit set 975 * with \c mbedtls_ecp_set_max_ops() to reduce blocking. 976 * 977 * \param grp The ECP group to use. 978 * This must be initialized and have group parameters 979 * set, for example through mbedtls_ecp_group_load(). 980 * \param R The point in which to store the result of the calculation. 981 * This must be initialized. 982 * \param m The integer by which to multiply. This must be initialized. 983 * \param P The point to multiply. This must be initialized. 984 * \param f_rng The RNG function. This may be \c NULL if randomization 985 * of intermediate results isn't desired (discouraged). 986 * \param p_rng The RNG context to be passed to \p p_rng. 987 * \param rs_ctx The restart context (NULL disables restart). 988 * 989 * \return \c 0 on success. 990 * \return #MBEDTLS_ERR_ECP_INVALID_KEY if \p m is not a valid private 991 * key, or \p P is not a valid public key. 992 * \return #MBEDTLS_ERR_MPI_ALLOC_FAILED on memory-allocation failure. 993 * \return #MBEDTLS_ERR_ECP_IN_PROGRESS if maximum number of 994 * operations was reached: see \c mbedtls_ecp_set_max_ops(). 995 * \return Another negative error code on other kinds of failure. 996 */ 997 int mbedtls_ecp_mul_restartable( mbedtls_ecp_group *grp, mbedtls_ecp_point *R, 998 const mbedtls_mpi *m, const mbedtls_ecp_point *P, 999 int (*f_rng)(void *, unsigned char *, size_t), void *p_rng, 1000 mbedtls_ecp_restart_ctx *rs_ctx ); 1001 1002 #if defined(MBEDTLS_ECP_SHORT_WEIERSTRASS_ENABLED) 1003 /** 1004 * \brief This function performs multiplication and addition of two 1005 * points by integers: \p R = \p m * \p P + \p n * \p Q 1006 * 1007 * It is not thread-safe to use same group in multiple threads. 1008 * 1009 * \note In contrast to mbedtls_ecp_mul(), this function does not 1010 * guarantee a constant execution flow and timing. 1011 * 1012 * \note This function is only defined for short Weierstrass curves. 1013 * It may not be included in builds without any short 1014 * Weierstrass curve. 1015 * 1016 * \param grp The ECP group to use. 1017 * This must be initialized and have group parameters 1018 * set, for example through mbedtls_ecp_group_load(). 1019 * \param R The point in which to store the result of the calculation. 1020 * This must be initialized. 1021 * \param m The integer by which to multiply \p P. 1022 * This must be initialized. 1023 * \param P The point to multiply by \p m. This must be initialized. 1024 * \param n The integer by which to multiply \p Q. 1025 * This must be initialized. 1026 * \param Q The point to be multiplied by \p n. 1027 * This must be initialized. 1028 * 1029 * \return \c 0 on success. 1030 * \return #MBEDTLS_ERR_ECP_INVALID_KEY if \p m or \p n are not 1031 * valid private keys, or \p P or \p Q are not valid public 1032 * keys. 1033 * \return #MBEDTLS_ERR_MPI_ALLOC_FAILED on memory-allocation failure. 1034 * \return #MBEDTLS_ERR_ECP_FEATURE_UNAVAILABLE if \p grp does not 1035 * designate a short Weierstrass curve. 1036 * \return Another negative error code on other kinds of failure. 1037 */ 1038 int mbedtls_ecp_muladd( mbedtls_ecp_group *grp, mbedtls_ecp_point *R, 1039 const mbedtls_mpi *m, const mbedtls_ecp_point *P, 1040 const mbedtls_mpi *n, const mbedtls_ecp_point *Q ); 1041 1042 /** 1043 * \brief This function performs multiplication and addition of two 1044 * points by integers: \p R = \p m * \p P + \p n * \p Q in a 1045 * restartable way. 1046 * 1047 * \see \c mbedtls_ecp_muladd() 1048 * 1049 * \note This function works the same as \c mbedtls_ecp_muladd(), 1050 * but it can return early and restart according to the limit 1051 * set with \c mbedtls_ecp_set_max_ops() to reduce blocking. 1052 * 1053 * \note This function is only defined for short Weierstrass curves. 1054 * It may not be included in builds without any short 1055 * Weierstrass curve. 1056 * 1057 * \param grp The ECP group to use. 1058 * This must be initialized and have group parameters 1059 * set, for example through mbedtls_ecp_group_load(). 1060 * \param R The point in which to store the result of the calculation. 1061 * This must be initialized. 1062 * \param m The integer by which to multiply \p P. 1063 * This must be initialized. 1064 * \param P The point to multiply by \p m. This must be initialized. 1065 * \param n The integer by which to multiply \p Q. 1066 * This must be initialized. 1067 * \param Q The point to be multiplied by \p n. 1068 * This must be initialized. 1069 * \param rs_ctx The restart context (NULL disables restart). 1070 * 1071 * \return \c 0 on success. 1072 * \return #MBEDTLS_ERR_ECP_INVALID_KEY if \p m or \p n are not 1073 * valid private keys, or \p P or \p Q are not valid public 1074 * keys. 1075 * \return #MBEDTLS_ERR_MPI_ALLOC_FAILED on memory-allocation failure. 1076 * \return #MBEDTLS_ERR_ECP_FEATURE_UNAVAILABLE if \p grp does not 1077 * designate a short Weierstrass curve. 1078 * \return #MBEDTLS_ERR_ECP_IN_PROGRESS if maximum number of 1079 * operations was reached: see \c mbedtls_ecp_set_max_ops(). 1080 * \return Another negative error code on other kinds of failure. 1081 */ 1082 int mbedtls_ecp_muladd_restartable( 1083 mbedtls_ecp_group *grp, mbedtls_ecp_point *R, 1084 const mbedtls_mpi *m, const mbedtls_ecp_point *P, 1085 const mbedtls_mpi *n, const mbedtls_ecp_point *Q, 1086 mbedtls_ecp_restart_ctx *rs_ctx ); 1087 #endif /* MBEDTLS_ECP_SHORT_WEIERSTRASS_ENABLED */ 1088 1089 /** 1090 * \brief This function checks that a point is a valid public key 1091 * on this curve. 1092 * 1093 * It only checks that the point is non-zero, has 1094 * valid coordinates and lies on the curve. It does not verify 1095 * that it is indeed a multiple of \p G. This additional 1096 * check is computationally more expensive, is not required 1097 * by standards, and should not be necessary if the group 1098 * used has a small cofactor. In particular, it is useless for 1099 * the NIST groups which all have a cofactor of 1. 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 point should belong to. 1107 * This must be initialized and have group parameters 1108 * set, for example through mbedtls_ecp_group_load(). 1109 * \param pt The point to check. This must be initialized. 1110 * 1111 * \return \c 0 if the point is a valid public key. 1112 * \return #MBEDTLS_ERR_ECP_INVALID_KEY if the point is not 1113 * a valid public key for the given curve. 1114 * \return Another negative error code on other kinds of failure. 1115 */ 1116 int mbedtls_ecp_check_pubkey( const mbedtls_ecp_group *grp, 1117 const mbedtls_ecp_point *pt ); 1118 1119 /** 1120 * \brief This function checks that an \p mbedtls_mpi is a 1121 * valid private key for this curve. 1122 * 1123 * \note This function uses bare components rather than an 1124 * ::mbedtls_ecp_keypair structure to ease use with other 1125 * structures, such as ::mbedtls_ecdh_context or 1126 * ::mbedtls_ecdsa_context. 1127 * 1128 * \param grp The ECP group the private key should belong to. 1129 * This must be initialized and have group parameters 1130 * set, for example through mbedtls_ecp_group_load(). 1131 * \param d The integer to check. This must be initialized. 1132 * 1133 * \return \c 0 if the point is a valid private key. 1134 * \return #MBEDTLS_ERR_ECP_INVALID_KEY if the point is not a valid 1135 * private key for the given curve. 1136 * \return Another negative error code on other kinds of failure. 1137 */ 1138 int mbedtls_ecp_check_privkey( const mbedtls_ecp_group *grp, 1139 const mbedtls_mpi *d ); 1140 1141 /** 1142 * \brief This function generates a private key. 1143 * 1144 * \param grp The ECP group to generate a private key for. 1145 * This must be initialized and have group parameters 1146 * set, for example through mbedtls_ecp_group_load(). 1147 * \param d The destination MPI (secret part). This must be initialized. 1148 * \param f_rng The RNG function. This must not be \c NULL. 1149 * \param p_rng The RNG parameter to be passed to \p f_rng. This may be 1150 * \c NULL if \p f_rng doesn't need a context argument. 1151 * 1152 * \return \c 0 on success. 1153 * \return An \c MBEDTLS_ERR_ECP_XXX or \c MBEDTLS_MPI_XXX error code 1154 * on failure. 1155 */ 1156 int mbedtls_ecp_gen_privkey( const mbedtls_ecp_group *grp, 1157 mbedtls_mpi *d, 1158 int (*f_rng)(void *, unsigned char *, size_t), 1159 void *p_rng ); 1160 1161 /** 1162 * \brief This function generates a keypair with a configurable base 1163 * point. 1164 * 1165 * \note This function uses bare components rather than an 1166 * ::mbedtls_ecp_keypair structure to ease use with other 1167 * structures, such as ::mbedtls_ecdh_context or 1168 * ::mbedtls_ecdsa_context. 1169 * 1170 * \param grp The ECP group to generate a key pair for. 1171 * This must be initialized and have group parameters 1172 * set, for example through mbedtls_ecp_group_load(). 1173 * \param G The base point to use. This must be initialized 1174 * and belong to \p grp. It replaces the default base 1175 * point \c grp->G used by mbedtls_ecp_gen_keypair(). 1176 * \param d The destination MPI (secret part). 1177 * This must be initialized. 1178 * \param Q The destination point (public part). 1179 * This must be initialized. 1180 * \param f_rng The RNG function. This must not be \c NULL. 1181 * \param p_rng The RNG context to be passed to \p f_rng. This may 1182 * be \c NULL if \p f_rng doesn't need a context argument. 1183 * 1184 * \return \c 0 on success. 1185 * \return An \c MBEDTLS_ERR_ECP_XXX or \c MBEDTLS_MPI_XXX error code 1186 * on failure. 1187 */ 1188 int mbedtls_ecp_gen_keypair_base( mbedtls_ecp_group *grp, 1189 const mbedtls_ecp_point *G, 1190 mbedtls_mpi *d, mbedtls_ecp_point *Q, 1191 int (*f_rng)(void *, unsigned char *, size_t), 1192 void *p_rng ); 1193 1194 /** 1195 * \brief This function generates an ECP keypair. 1196 * 1197 * \note This function uses bare components rather than an 1198 * ::mbedtls_ecp_keypair structure to ease use with other 1199 * structures, such as ::mbedtls_ecdh_context or 1200 * ::mbedtls_ecdsa_context. 1201 * 1202 * \param grp The ECP group to generate a key pair for. 1203 * This must be initialized and have group parameters 1204 * set, for example through mbedtls_ecp_group_load(). 1205 * \param d The destination MPI (secret part). 1206 * This must be initialized. 1207 * \param Q The destination point (public part). 1208 * This must be initialized. 1209 * \param f_rng The RNG function. This must not be \c NULL. 1210 * \param p_rng The RNG context to be passed to \p f_rng. This may 1211 * be \c NULL if \p f_rng doesn't need a context argument. 1212 * 1213 * \return \c 0 on success. 1214 * \return An \c MBEDTLS_ERR_ECP_XXX or \c MBEDTLS_MPI_XXX error code 1215 * on failure. 1216 */ 1217 int mbedtls_ecp_gen_keypair( mbedtls_ecp_group *grp, mbedtls_mpi *d, 1218 mbedtls_ecp_point *Q, 1219 int (*f_rng)(void *, unsigned char *, size_t), 1220 void *p_rng ); 1221 1222 /** 1223 * \brief This function generates an ECP key. 1224 * 1225 * \param grp_id The ECP group identifier. 1226 * \param key The destination key. This must be initialized. 1227 * \param f_rng The RNG function to use. This must not be \c NULL. 1228 * \param p_rng The RNG context to be passed to \p f_rng. This may 1229 * be \c NULL if \p f_rng doesn't need a context argument. 1230 * 1231 * \return \c 0 on success. 1232 * \return An \c MBEDTLS_ERR_ECP_XXX or \c MBEDTLS_MPI_XXX error code 1233 * on failure. 1234 */ 1235 int mbedtls_ecp_gen_key( mbedtls_ecp_group_id grp_id, mbedtls_ecp_keypair *key, 1236 int (*f_rng)(void *, unsigned char *, size_t), 1237 void *p_rng ); 1238 1239 /** 1240 * \brief This function reads an elliptic curve private key. 1241 * 1242 * \param grp_id The ECP group identifier. 1243 * \param key The destination key. 1244 * \param buf The buffer containing the binary representation of the 1245 * key. (Big endian integer for Weierstrass curves, byte 1246 * string for Montgomery curves.) 1247 * \param buflen The length of the buffer in bytes. 1248 * 1249 * \return \c 0 on success. 1250 * \return #MBEDTLS_ERR_ECP_INVALID_KEY error if the key is 1251 * invalid. 1252 * \return #MBEDTLS_ERR_MPI_ALLOC_FAILED if memory allocation failed. 1253 * \return #MBEDTLS_ERR_ECP_FEATURE_UNAVAILABLE if the operation for 1254 * the group is not implemented. 1255 * \return Another negative error code on different kinds of failure. 1256 */ 1257 int mbedtls_ecp_read_key( mbedtls_ecp_group_id grp_id, mbedtls_ecp_keypair *key, 1258 const unsigned char *buf, size_t buflen ); 1259 1260 /** 1261 * \brief This function exports an elliptic curve private key. 1262 * 1263 * \param key The private key. 1264 * \param buf The output buffer for containing the binary representation 1265 * of the key. (Big endian integer for Weierstrass curves, byte 1266 * string for Montgomery curves.) 1267 * \param buflen The total length of the buffer in bytes. 1268 * 1269 * \return \c 0 on success. 1270 * \return #MBEDTLS_ERR_ECP_BUFFER_TOO_SMALL if the \p key 1271 representation is larger than the available space in \p buf. 1272 * \return #MBEDTLS_ERR_ECP_FEATURE_UNAVAILABLE if the operation for 1273 * the group is not implemented. 1274 * \return Another negative error code on different kinds of failure. 1275 */ 1276 int mbedtls_ecp_write_key( mbedtls_ecp_keypair *key, 1277 unsigned char *buf, size_t buflen ); 1278 1279 /** 1280 * \brief This function checks that the keypair objects 1281 * \p pub and \p prv have the same group and the 1282 * same public point, and that the private key in 1283 * \p prv is consistent with the public key. 1284 * 1285 * \param pub The keypair structure holding the public key. This 1286 * must be initialized. If it contains a private key, that 1287 * part is ignored. 1288 * \param prv The keypair structure holding the full keypair. 1289 * This must be initialized. 1290 * 1291 * \return \c 0 on success, meaning that the keys are valid and match. 1292 * \return #MBEDTLS_ERR_ECP_BAD_INPUT_DATA if the keys are invalid or do not match. 1293 * \return An \c MBEDTLS_ERR_ECP_XXX or an \c MBEDTLS_ERR_MPI_XXX 1294 * error code on calculation failure. 1295 */ 1296 int mbedtls_ecp_check_pub_priv( const mbedtls_ecp_keypair *pub, 1297 const mbedtls_ecp_keypair *prv ); 1298 1299 #if defined(MBEDTLS_SELF_TEST) 1300 1301 /** 1302 * \brief The ECP checkup routine. 1303 * 1304 * \return \c 0 on success. 1305 * \return \c 1 on failure. 1306 */ 1307 int mbedtls_ecp_self_test( int verbose ); 1308 1309 #endif /* MBEDTLS_SELF_TEST */ 1310 1311 #ifdef __cplusplus 1312 } 1313 #endif 1314 1315 #endif /* ecp.h */ 1316