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 #define MBEDTLS_ERR_ECP_BAD_INPUT_DATA -0x4F80 /**< Bad input parameters to function. */ 49 #define MBEDTLS_ERR_ECP_BUFFER_TOO_SMALL -0x4F00 /**< The buffer is too small to write to. */ 50 #define MBEDTLS_ERR_ECP_FEATURE_UNAVAILABLE -0x4E80 /**< The requested feature is not available, for example, the requested curve is not supported. */ 51 #define MBEDTLS_ERR_ECP_VERIFY_FAILED -0x4E00 /**< The signature is not valid. */ 52 #define MBEDTLS_ERR_ECP_ALLOC_FAILED -0x4D80 /**< Memory allocation failed. */ 53 #define MBEDTLS_ERR_ECP_RANDOM_FAILED -0x4D00 /**< Generation of random value, such as ephemeral key, failed. */ 54 #define MBEDTLS_ERR_ECP_INVALID_KEY -0x4C80 /**< Invalid private or public key. */ 55 #define MBEDTLS_ERR_ECP_SIG_LEN_MISMATCH -0x4C00 /**< The buffer contains a valid signature followed by more data. */ 56 57 /* MBEDTLS_ERR_ECP_HW_ACCEL_FAILED is deprecated and should not be used. */ 58 #define MBEDTLS_ERR_ECP_HW_ACCEL_FAILED -0x4B80 /**< The ECP hardware accelerator failed. */ 59 60 #define MBEDTLS_ERR_ECP_IN_PROGRESS -0x4B00 /**< Operation in progress, call again with the same parameters to continue. */ 61 62 /* Flags indicating whether to include code that is specific to certain 63 * types of curves. These flags are for internal library use only. */ 64 #if defined(MBEDTLS_ECP_DP_SECP192R1_ENABLED) || \ 65 defined(MBEDTLS_ECP_DP_SECP224R1_ENABLED) || \ 66 defined(MBEDTLS_ECP_DP_SECP256R1_ENABLED) || \ 67 defined(MBEDTLS_ECP_DP_SECP384R1_ENABLED) || \ 68 defined(MBEDTLS_ECP_DP_SECP521R1_ENABLED) || \ 69 defined(MBEDTLS_ECP_DP_BP256R1_ENABLED) || \ 70 defined(MBEDTLS_ECP_DP_BP384R1_ENABLED) || \ 71 defined(MBEDTLS_ECP_DP_BP512R1_ENABLED) || \ 72 defined(MBEDTLS_ECP_DP_SECP192K1_ENABLED) || \ 73 defined(MBEDTLS_ECP_DP_SECP224K1_ENABLED) || \ 74 defined(MBEDTLS_ECP_DP_SECP256K1_ENABLED) || \ 75 defined(MBEDTLS_ECP_DP_SM2_ENABLED) 76 #define MBEDTLS_ECP_SHORT_WEIERSTRASS_ENABLED 77 #endif 78 #if defined(MBEDTLS_ECP_DP_CURVE25519_ENABLED) || \ 79 defined(MBEDTLS_ECP_DP_CURVE448_ENABLED) 80 #define MBEDTLS_ECP_MONTGOMERY_ENABLED 81 #endif 82 83 #ifdef __cplusplus 84 extern "C" { 85 #endif 86 87 /** 88 * Domain-parameter identifiers: curve, subgroup, and generator. 89 * 90 * \note Only curves over prime fields are supported. 91 * 92 * \warning This library does not support validation of arbitrary domain 93 * parameters. Therefore, only standardized domain parameters from trusted 94 * sources should be used. See mbedtls_ecp_group_load(). 95 */ 96 /* Note: when adding a new curve: 97 * - Add it at the end of this enum, otherwise you'll break the ABI by 98 * changing the numerical value for existing curves. 99 * - Increment MBEDTLS_ECP_DP_MAX below if needed. 100 * - Update the calculation of MBEDTLS_ECP_MAX_BITS_MIN below. 101 * - Add the corresponding MBEDTLS_ECP_DP_xxx_ENABLED macro definition to 102 * config.h. 103 * - List the curve as a dependency of MBEDTLS_ECP_C and 104 * MBEDTLS_ECDSA_C if supported in check_config.h. 105 * - Add the curve to the appropriate curve type macro 106 * MBEDTLS_ECP_yyy_ENABLED above. 107 * - Add the necessary definitions to ecp_curves.c. 108 * - Add the curve to the ecp_supported_curves array in ecp.c. 109 * - Add the curve to applicable profiles in x509_crt.c if applicable. 110 */ 111 typedef enum 112 { 113 MBEDTLS_ECP_DP_NONE = 0, /*!< Curve not defined. */ 114 MBEDTLS_ECP_DP_SECP192R1, /*!< Domain parameters for the 192-bit curve defined by FIPS 186-4 and SEC1. */ 115 MBEDTLS_ECP_DP_SECP224R1, /*!< Domain parameters for the 224-bit curve defined by FIPS 186-4 and SEC1. */ 116 MBEDTLS_ECP_DP_SECP256R1, /*!< Domain parameters for the 256-bit curve defined by FIPS 186-4 and SEC1. */ 117 MBEDTLS_ECP_DP_SECP384R1, /*!< Domain parameters for the 384-bit curve defined by FIPS 186-4 and SEC1. */ 118 MBEDTLS_ECP_DP_SECP521R1, /*!< Domain parameters for the 521-bit curve defined by FIPS 186-4 and SEC1. */ 119 MBEDTLS_ECP_DP_BP256R1, /*!< Domain parameters for 256-bit Brainpool curve. */ 120 MBEDTLS_ECP_DP_BP384R1, /*!< Domain parameters for 384-bit Brainpool curve. */ 121 MBEDTLS_ECP_DP_BP512R1, /*!< Domain parameters for 512-bit Brainpool curve. */ 122 MBEDTLS_ECP_DP_CURVE25519, /*!< Domain parameters for Curve25519. */ 123 MBEDTLS_ECP_DP_SECP192K1, /*!< Domain parameters for 192-bit "Koblitz" curve. */ 124 MBEDTLS_ECP_DP_SECP224K1, /*!< Domain parameters for 224-bit "Koblitz" curve. */ 125 MBEDTLS_ECP_DP_SECP256K1, /*!< Domain parameters for 256-bit "Koblitz" curve. */ 126 MBEDTLS_ECP_DP_CURVE448, /*!< Domain parameters for Curve448. */ 127 MBEDTLS_ECP_DP_SM2, /*!< Domain parameters for SM2. */ 128 } mbedtls_ecp_group_id; 129 130 /** 131 * The number of supported curves, plus one for #MBEDTLS_ECP_DP_NONE. 132 * 133 * \note Montgomery curves are currently excluded. 134 */ 135 #define MBEDTLS_ECP_DP_MAX 12 136 137 /* 138 * Curve types 139 */ 140 typedef enum 141 { 142 MBEDTLS_ECP_TYPE_NONE = 0, 143 MBEDTLS_ECP_TYPE_SHORT_WEIERSTRASS, /* y^2 = x^3 + a x + b */ 144 MBEDTLS_ECP_TYPE_MONTGOMERY, /* y^2 = x^3 + a x^2 + x */ 145 } mbedtls_ecp_curve_type; 146 147 /** 148 * Curve information, for use by other modules. 149 */ 150 typedef struct mbedtls_ecp_curve_info 151 { 152 mbedtls_ecp_group_id grp_id; /*!< An internal identifier. */ 153 uint16_t tls_id; /*!< The TLS NamedCurve identifier. */ 154 uint16_t bit_size; /*!< The curve size in bits. */ 155 const char *name; /*!< A human-friendly name. */ 156 } mbedtls_ecp_curve_info; 157 158 /** 159 * \brief The ECP point structure, in Jacobian coordinates. 160 * 161 * \note All functions expect and return points satisfying 162 * the following condition: <code>Z == 0</code> or 163 * <code>Z == 1</code>. Other values of \p Z are 164 * used only by internal functions. 165 * The point is zero, or "at infinity", if <code>Z == 0</code>. 166 * Otherwise, \p X and \p Y are its standard (affine) 167 * coordinates. 168 */ 169 typedef struct mbedtls_ecp_point 170 { 171 mbedtls_mpi X; /*!< The X coordinate of the ECP point. */ 172 mbedtls_mpi Y; /*!< The Y coordinate of the ECP point. */ 173 mbedtls_mpi Z; /*!< The Z coordinate of the ECP point. */ 174 } 175 mbedtls_ecp_point; 176 177 /* Determine the minimum safe value of MBEDTLS_ECP_MAX_BITS. */ 178 #if !defined(MBEDTLS_ECP_C) 179 #define MBEDTLS_ECP_MAX_BITS_MIN 0 180 /* Note: the curves must be listed in DECREASING size! */ 181 #elif defined(MBEDTLS_ECP_DP_SECP521R1_ENABLED) 182 #define MBEDTLS_ECP_MAX_BITS_MIN 521 183 #elif defined(MBEDTLS_ECP_DP_BP512R1_ENABLED) 184 #define MBEDTLS_ECP_MAX_BITS_MIN 512 185 #elif defined(MBEDTLS_ECP_DP_CURVE448_ENABLED) 186 #define MBEDTLS_ECP_MAX_BITS_MIN 448 187 #elif defined(MBEDTLS_ECP_DP_BP384R1_ENABLED) 188 #define MBEDTLS_ECP_MAX_BITS_MIN 384 189 #elif defined(MBEDTLS_ECP_DP_SECP384R1_ENABLED) 190 #define MBEDTLS_ECP_MAX_BITS_MIN 384 191 #elif defined(MBEDTLS_ECP_DP_BP256R1_ENABLED) 192 #define MBEDTLS_ECP_MAX_BITS_MIN 256 193 #elif defined(MBEDTLS_ECP_DP_SECP256K1_ENABLED) 194 #define MBEDTLS_ECP_MAX_BITS_MIN 256 195 #elif defined(MBEDTLS_ECP_DP_SECP256R1_ENABLED) 196 #define MBEDTLS_ECP_MAX_BITS_MIN 256 197 #elif defined(MBEDTLS_ECP_DP_SM2_ENABLED) 198 #define MBEDTLS_ECP_MAX_BITS_MIN 256 199 #elif defined(MBEDTLS_ECP_DP_CURVE25519_ENABLED) 200 #define MBEDTLS_ECP_MAX_BITS_MIN 255 201 #elif defined(MBEDTLS_ECP_DP_SECP224K1_ENABLED) 202 #define MBEDTLS_ECP_MAX_BITS_MIN 225 // n is slightly above 2^224 203 #elif defined(MBEDTLS_ECP_DP_SECP224R1_ENABLED) 204 #define MBEDTLS_ECP_MAX_BITS_MIN 224 205 #elif defined(MBEDTLS_ECP_DP_SECP192K1_ENABLED) 206 #define MBEDTLS_ECP_MAX_BITS_MIN 192 207 #elif defined(MBEDTLS_ECP_DP_SECP192R1_ENABLED) 208 #define MBEDTLS_ECP_MAX_BITS_MIN 192 209 #else 210 #error "MBEDTLS_ECP_C enabled, but no curve?" 211 #endif 212 213 #if !defined(MBEDTLS_ECP_ALT) 214 /* 215 * default mbed TLS elliptic curve arithmetic implementation 216 * 217 * (in case MBEDTLS_ECP_ALT is defined then the developer has to provide an 218 * alternative implementation for the whole module and it will replace this 219 * one.) 220 */ 221 222 /** 223 * \brief The ECP group structure. 224 * 225 * We consider two types of curve equations: 226 * <ul><li>Short Weierstrass: <code>y^2 = x^3 + A x + B mod P</code> 227 * (SEC1 + RFC-4492)</li> 228 * <li>Montgomery: <code>y^2 = x^3 + A x^2 + x mod P</code> (Curve25519, 229 * Curve448)</li></ul> 230 * In both cases, the generator (\p G) for a prime-order subgroup is fixed. 231 * 232 * For Short Weierstrass, this subgroup is the whole curve, and its 233 * cardinality is denoted by \p N. Our code requires that \p N is an 234 * odd prime as mbedtls_ecp_mul() requires an odd number, and 235 * mbedtls_ecdsa_sign() requires that it is prime for blinding purposes. 236 * 237 * For Montgomery curves, we do not store \p A, but <code>(A + 2) / 4</code>, 238 * which is the quantity used in the formulas. Additionally, \p nbits is 239 * not the size of \p N but the required size for private keys. 240 * 241 * If \p modp is NULL, reduction modulo \p P is done using a generic algorithm. 242 * Otherwise, \p modp must point to a function that takes an \p mbedtls_mpi in the 243 * range of <code>0..2^(2*pbits)-1</code>, and transforms it in-place to an integer 244 * which is congruent mod \p P to the given MPI, and is close enough to \p pbits 245 * in size, so that it may be efficiently brought in the 0..P-1 range by a few 246 * additions or subtractions. Therefore, it is only an approximative modular 247 * reduction. It must return 0 on success and non-zero on failure. 248 * 249 * \note Alternative implementations must keep the group IDs distinct. If 250 * two group structures have the same ID, then they must be 251 * identical. 252 * 253 */ 254 typedef struct mbedtls_ecp_group 255 { 256 mbedtls_ecp_group_id id; /*!< An internal group identifier. */ 257 mbedtls_mpi P; /*!< The prime modulus of the base field. */ 258 mbedtls_mpi A; /*!< For Short Weierstrass: \p A in the equation. For 259 Montgomery curves: <code>(A + 2) / 4</code>. */ 260 mbedtls_mpi B; /*!< For Short Weierstrass: \p B in the equation. 261 For Montgomery curves: unused. */ 262 mbedtls_ecp_point G; /*!< The generator of the subgroup used. */ 263 mbedtls_mpi N; /*!< The order of \p G. */ 264 size_t pbits; /*!< The number of bits in \p P.*/ 265 size_t nbits; /*!< For Short Weierstrass: The number of bits in \p P. 266 For Montgomery curves: the number of bits in the 267 private keys. */ 268 unsigned int h; /*!< \internal 1 if the constants are static. */ 269 int (*modp)(mbedtls_mpi *); /*!< The function for fast pseudo-reduction 270 mod \p P (see above).*/ 271 int (*t_pre)(mbedtls_ecp_point *, void *); /*!< Unused. */ 272 int (*t_post)(mbedtls_ecp_point *, void *); /*!< Unused. */ 273 void *t_data; /*!< Unused. */ 274 mbedtls_ecp_point *T; /*!< Pre-computed points for ecp_mul_comb(). */ 275 size_t T_size; /*!< The number of pre-computed points. */ 276 } 277 mbedtls_ecp_group; 278 279 /** 280 * \name SECTION: Module settings 281 * 282 * The configuration options you can set for this module are in this section. 283 * Either change them in config.h, or define them using the compiler command line. 284 * \{ 285 */ 286 287 #if defined(MBEDTLS_ECP_MAX_BITS) 288 289 #if MBEDTLS_ECP_MAX_BITS < MBEDTLS_ECP_MAX_BITS_MIN 290 #error "MBEDTLS_ECP_MAX_BITS is smaller than the largest supported curve" 291 #endif 292 293 #elif defined(MBEDTLS_ECP_C) 294 /** 295 * The maximum size of the groups, that is, of \c N and \c P. 296 */ 297 #define MBEDTLS_ECP_MAX_BITS MBEDTLS_ECP_MAX_BITS_MIN 298 299 #else 300 /* MBEDTLS_ECP_MAX_BITS is not relevant without MBEDTLS_ECP_C, but set it 301 * to a nonzero value so that code that unconditionally allocates an array 302 * of a size based on it keeps working if built without ECC support. */ 303 #define MBEDTLS_ECP_MAX_BITS 1 304 #endif 305 306 #define MBEDTLS_ECP_MAX_BYTES ( ( MBEDTLS_ECP_MAX_BITS + 7 ) / 8 ) 307 #define MBEDTLS_ECP_MAX_PT_LEN ( 2 * MBEDTLS_ECP_MAX_BYTES + 1 ) 308 309 #if !defined(MBEDTLS_ECP_WINDOW_SIZE) 310 /* 311 * Maximum "window" size used for point multiplication. 312 * Default: a point where higher memory usage yields disminishing performance 313 * returns. 314 * Minimum value: 2. Maximum value: 7. 315 * 316 * Result is an array of at most ( 1 << ( MBEDTLS_ECP_WINDOW_SIZE - 1 ) ) 317 * points used for point multiplication. This value is directly tied to EC 318 * peak memory usage, so decreasing it by one should roughly cut memory usage 319 * by two (if large curves are in use). 320 * 321 * Reduction in size may reduce speed, but larger curves are impacted first. 322 * Sample performances (in ECDHE handshakes/s, with FIXED_POINT_OPTIM = 1): 323 * w-size: 6 5 4 3 2 324 * 521 145 141 135 120 97 325 * 384 214 209 198 177 146 326 * 256 320 320 303 262 226 327 * 224 475 475 453 398 342 328 * 192 640 640 633 587 476 329 */ 330 #define MBEDTLS_ECP_WINDOW_SIZE 4 /**< The maximum window size used. */ 331 #endif /* MBEDTLS_ECP_WINDOW_SIZE */ 332 333 #if !defined(MBEDTLS_ECP_FIXED_POINT_OPTIM) 334 /* 335 * Trade memory for speed on fixed-point multiplication. 336 * 337 * This speeds up repeated multiplication of the generator (that is, the 338 * multiplication in ECDSA signatures, and half of the multiplications in 339 * ECDSA verification and ECDHE) by a factor roughly 3 to 4. 340 * 341 * The cost is increasing EC peak memory usage by a factor roughly 2. 342 * 343 * Change this value to 0 to reduce peak memory usage. 344 */ 345 #define MBEDTLS_ECP_FIXED_POINT_OPTIM 1 /**< Enable fixed-point speed-up. */ 346 #endif /* MBEDTLS_ECP_FIXED_POINT_OPTIM */ 347 348 /* \} name SECTION: Module settings */ 349 350 #else /* MBEDTLS_ECP_ALT */ 351 #include "ecp_alt.h" 352 #endif /* MBEDTLS_ECP_ALT */ 353 354 #if defined(MBEDTLS_ECP_RESTARTABLE) 355 356 /** 357 * \brief Internal restart context for multiplication 358 * 359 * \note Opaque struct 360 */ 361 typedef struct mbedtls_ecp_restart_mul mbedtls_ecp_restart_mul_ctx; 362 363 /** 364 * \brief Internal restart context for ecp_muladd() 365 * 366 * \note Opaque struct 367 */ 368 typedef struct mbedtls_ecp_restart_muladd mbedtls_ecp_restart_muladd_ctx; 369 370 /** 371 * \brief General context for resuming ECC operations 372 */ 373 typedef struct 374 { 375 unsigned ops_done; /*!< current ops count */ 376 unsigned depth; /*!< call depth (0 = top-level) */ 377 mbedtls_ecp_restart_mul_ctx *rsm; /*!< ecp_mul_comb() sub-context */ 378 mbedtls_ecp_restart_muladd_ctx *ma; /*!< ecp_muladd() sub-context */ 379 } mbedtls_ecp_restart_ctx; 380 381 /* 382 * Operation counts for restartable functions 383 */ 384 #define MBEDTLS_ECP_OPS_CHK 3 /*!< basic ops count for ecp_check_pubkey() */ 385 #define MBEDTLS_ECP_OPS_DBL 8 /*!< basic ops count for ecp_double_jac() */ 386 #define MBEDTLS_ECP_OPS_ADD 11 /*!< basic ops count for see ecp_add_mixed() */ 387 #define MBEDTLS_ECP_OPS_INV 120 /*!< empirical equivalent for mpi_mod_inv() */ 388 389 /** 390 * \brief Internal; for restartable functions in other modules. 391 * Check and update basic ops budget. 392 * 393 * \param grp Group structure 394 * \param rs_ctx Restart context 395 * \param ops Number of basic ops to do 396 * 397 * \return \c 0 if doing \p ops basic ops is still allowed, 398 * \return #MBEDTLS_ERR_ECP_IN_PROGRESS otherwise. 399 */ 400 int mbedtls_ecp_check_budget( const mbedtls_ecp_group *grp, 401 mbedtls_ecp_restart_ctx *rs_ctx, 402 unsigned ops ); 403 404 /* Utility macro for checking and updating ops budget */ 405 #define MBEDTLS_ECP_BUDGET( ops ) \ 406 MBEDTLS_MPI_CHK( mbedtls_ecp_check_budget( grp, rs_ctx, \ 407 (unsigned) (ops) ) ); 408 409 #else /* MBEDTLS_ECP_RESTARTABLE */ 410 411 #define MBEDTLS_ECP_BUDGET( ops ) /* no-op; for compatibility */ 412 413 /* We want to declare restartable versions of existing functions anyway */ 414 typedef void mbedtls_ecp_restart_ctx; 415 416 #endif /* MBEDTLS_ECP_RESTARTABLE */ 417 418 /** 419 * \brief The ECP key-pair structure. 420 * 421 * A generic key-pair that may be used for ECDSA and fixed ECDH, for example. 422 * 423 * \note Members are deliberately in the same order as in the 424 * ::mbedtls_ecdsa_context structure. 425 */ 426 typedef struct mbedtls_ecp_keypair 427 { 428 mbedtls_ecp_group grp; /*!< Elliptic curve and base point */ 429 mbedtls_mpi d; /*!< our secret value */ 430 mbedtls_ecp_point Q; /*!< our public value */ 431 } 432 mbedtls_ecp_keypair; 433 434 /* 435 * Point formats, from RFC 4492's enum ECPointFormat 436 */ 437 #define MBEDTLS_ECP_PF_UNCOMPRESSED 0 /**< Uncompressed point format. */ 438 #define MBEDTLS_ECP_PF_COMPRESSED 1 /**< Compressed point format. */ 439 440 /* 441 * Some other constants from RFC 4492 442 */ 443 #define MBEDTLS_ECP_TLS_NAMED_CURVE 3 /**< The named_curve of ECCurveType. */ 444 445 #if defined(MBEDTLS_ECP_RESTARTABLE) 446 /** 447 * \brief Set the maximum number of basic operations done in a row. 448 * 449 * If more operations are needed to complete a computation, 450 * #MBEDTLS_ERR_ECP_IN_PROGRESS will be returned by the 451 * function performing the computation. It is then the 452 * caller's responsibility to either call again with the same 453 * parameters until it returns 0 or an error code; or to free 454 * the restart context if the operation is to be aborted. 455 * 456 * It is strictly required that all input parameters and the 457 * restart context be the same on successive calls for the 458 * same operation, but output parameters need not be the 459 * same; they must not be used until the function finally 460 * returns 0. 461 * 462 * This only applies to functions whose documentation 463 * mentions they may return #MBEDTLS_ERR_ECP_IN_PROGRESS (or 464 * #MBEDTLS_ERR_SSL_CRYPTO_IN_PROGRESS for functions in the 465 * SSL module). For functions that accept a "restart context" 466 * argument, passing NULL disables restart and makes the 467 * function equivalent to the function with the same name 468 * with \c _restartable removed. For functions in the ECDH 469 * module, restart is disabled unless the function accepts 470 * an "ECDH context" argument and 471 * mbedtls_ecdh_enable_restart() was previously called on 472 * that context. For function in the SSL module, restart is 473 * only enabled for specific sides and key exchanges 474 * (currently only for clients and ECDHE-ECDSA). 475 * 476 * \param max_ops Maximum number of basic operations done in a row. 477 * Default: 0 (unlimited). 478 * Lower (non-zero) values mean ECC functions will block for 479 * a lesser maximum amount of time. 480 * 481 * \note A "basic operation" is defined as a rough equivalent of a 482 * multiplication in GF(p) for the NIST P-256 curve. 483 * As an indication, with default settings, a scalar 484 * multiplication (full run of \c mbedtls_ecp_mul()) is: 485 * - about 3300 basic operations for P-256 486 * - about 9400 basic operations for P-384 487 * 488 * \note Very low values are not always respected: sometimes 489 * functions need to block for a minimum number of 490 * operations, and will do so even if max_ops is set to a 491 * lower value. That minimum depends on the curve size, and 492 * can be made lower by decreasing the value of 493 * \c MBEDTLS_ECP_WINDOW_SIZE. As an indication, here is the 494 * lowest effective value for various curves and values of 495 * that parameter (w for short): 496 * w=6 w=5 w=4 w=3 w=2 497 * P-256 208 208 160 136 124 498 * P-384 682 416 320 272 248 499 * P-521 1364 832 640 544 496 500 * 501 * \note This setting is currently ignored by Curve25519. 502 */ 503 void mbedtls_ecp_set_max_ops( unsigned max_ops ); 504 505 /** 506 * \brief Check if restart is enabled (max_ops != 0) 507 * 508 * \return \c 0 if \c max_ops == 0 (restart disabled) 509 * \return \c 1 otherwise (restart enabled) 510 */ 511 int mbedtls_ecp_restart_is_enabled( void ); 512 #endif /* MBEDTLS_ECP_RESTARTABLE */ 513 514 /* 515 * Get the type of a curve 516 */ 517 mbedtls_ecp_curve_type mbedtls_ecp_get_type( const mbedtls_ecp_group *grp ); 518 519 /** 520 * \brief This function retrieves the information defined in 521 * mbedtls_ecp_curve_info() for all supported curves. 522 * 523 * \note This function returns information about all curves 524 * supported by the library. Some curves may not be 525 * supported for all algorithms. Call mbedtls_ecdh_can_do() 526 * or mbedtls_ecdsa_can_do() to check if a curve is 527 * supported for ECDH or ECDSA. 528 * 529 * \return A statically allocated array. The last entry is 0. 530 */ 531 const mbedtls_ecp_curve_info *mbedtls_ecp_curve_list( void ); 532 533 /** 534 * \brief This function retrieves the list of internal group 535 * identifiers of all supported curves in the order of 536 * preference. 537 * 538 * \note This function returns information about all curves 539 * supported by the library. Some curves may not be 540 * supported for all algorithms. Call mbedtls_ecdh_can_do() 541 * or mbedtls_ecdsa_can_do() to check if a curve is 542 * supported for ECDH or ECDSA. 543 * 544 * \return A statically allocated array, 545 * terminated with MBEDTLS_ECP_DP_NONE. 546 */ 547 const mbedtls_ecp_group_id *mbedtls_ecp_grp_id_list( void ); 548 549 /** 550 * \brief This function retrieves curve information from an internal 551 * group identifier. 552 * 553 * \param grp_id An \c MBEDTLS_ECP_DP_XXX value. 554 * 555 * \return The associated curve information on success. 556 * \return NULL on failure. 557 */ 558 const mbedtls_ecp_curve_info *mbedtls_ecp_curve_info_from_grp_id( mbedtls_ecp_group_id grp_id ); 559 560 /** 561 * \brief This function retrieves curve information from a TLS 562 * NamedCurve value. 563 * 564 * \param tls_id An \c MBEDTLS_ECP_DP_XXX value. 565 * 566 * \return The associated curve information on success. 567 * \return NULL on failure. 568 */ 569 const mbedtls_ecp_curve_info *mbedtls_ecp_curve_info_from_tls_id( uint16_t tls_id ); 570 571 /** 572 * \brief This function retrieves curve information from a 573 * human-readable name. 574 * 575 * \param name The human-readable name. 576 * 577 * \return The associated curve information on success. 578 * \return NULL on failure. 579 */ 580 const mbedtls_ecp_curve_info *mbedtls_ecp_curve_info_from_name( const char *name ); 581 582 /** 583 * \brief This function initializes a point as zero. 584 * 585 * \param pt The point to initialize. 586 */ 587 void mbedtls_ecp_point_init( mbedtls_ecp_point *pt ); 588 589 /** 590 * \brief This function initializes an ECP group context 591 * without loading any domain parameters. 592 * 593 * \note After this function is called, domain parameters 594 * for various ECP groups can be loaded through the 595 * mbedtls_ecp_group_load() or mbedtls_ecp_tls_read_group() 596 * functions. 597 */ 598 void mbedtls_ecp_group_init( mbedtls_ecp_group *grp ); 599 600 /** 601 * \brief This function initializes a key pair as an invalid one. 602 * 603 * \param key The key pair to initialize. 604 */ 605 void mbedtls_ecp_keypair_init( mbedtls_ecp_keypair *key ); 606 607 /** 608 * \brief This function frees the components of a point. 609 * 610 * \param pt The point to free. 611 */ 612 void mbedtls_ecp_point_free( mbedtls_ecp_point *pt ); 613 614 /** 615 * \brief This function frees the components of an ECP group. 616 * 617 * \param grp The group to free. This may be \c NULL, in which 618 * case this function returns immediately. If it is not 619 * \c NULL, it must point to an initialized ECP group. 620 */ 621 void mbedtls_ecp_group_free( mbedtls_ecp_group *grp ); 622 623 /** 624 * \brief This function frees the components of a key pair. 625 * 626 * \param key The key pair to free. This may be \c NULL, in which 627 * case this function returns immediately. If it is not 628 * \c NULL, it must point to an initialized ECP key pair. 629 */ 630 void mbedtls_ecp_keypair_free( mbedtls_ecp_keypair *key ); 631 632 #if defined(MBEDTLS_ECP_RESTARTABLE) 633 /** 634 * \brief Initialize a restart context. 635 * 636 * \param ctx The restart context to initialize. This must 637 * not be \c NULL. 638 */ 639 void mbedtls_ecp_restart_init( mbedtls_ecp_restart_ctx *ctx ); 640 641 /** 642 * \brief Free the components of a restart context. 643 * 644 * \param ctx The restart context to free. This may be \c NULL, in which 645 * case this function returns immediately. If it is not 646 * \c NULL, it must point to an initialized restart context. 647 */ 648 void mbedtls_ecp_restart_free( mbedtls_ecp_restart_ctx *ctx ); 649 #endif /* MBEDTLS_ECP_RESTARTABLE */ 650 651 /** 652 * \brief This function copies the contents of point \p Q into 653 * point \p P. 654 * 655 * \param P The destination point. This must be initialized. 656 * \param Q The source point. This must be initialized. 657 * 658 * \return \c 0 on success. 659 * \return #MBEDTLS_ERR_MPI_ALLOC_FAILED on memory-allocation failure. 660 * \return Another negative error code for other kinds of failure. 661 */ 662 int mbedtls_ecp_copy( mbedtls_ecp_point *P, const mbedtls_ecp_point *Q ); 663 664 /** 665 * \brief This function copies the contents of group \p src into 666 * group \p dst. 667 * 668 * \param dst The destination group. This must be initialized. 669 * \param src The source group. This must be initialized. 670 * 671 * \return \c 0 on success. 672 * \return #MBEDTLS_ERR_MPI_ALLOC_FAILED on memory-allocation failure. 673 * \return Another negative error code on other kinds of failure. 674 */ 675 int mbedtls_ecp_group_copy( mbedtls_ecp_group *dst, 676 const mbedtls_ecp_group *src ); 677 678 /** 679 * \brief This function sets a point to the point at infinity. 680 * 681 * \param pt The point to set. This must be initialized. 682 * 683 * \return \c 0 on success. 684 * \return #MBEDTLS_ERR_MPI_ALLOC_FAILED on memory-allocation failure. 685 * \return Another negative error code on other kinds of failure. 686 */ 687 int mbedtls_ecp_set_zero( mbedtls_ecp_point *pt ); 688 689 /** 690 * \brief This function checks if a point is the point at infinity. 691 * 692 * \param pt The point to test. This must be initialized. 693 * 694 * \return \c 1 if the point is zero. 695 * \return \c 0 if the point is non-zero. 696 * \return A negative error code on failure. 697 */ 698 int mbedtls_ecp_is_zero( mbedtls_ecp_point *pt ); 699 700 /** 701 * \brief This function compares two points. 702 * 703 * \note This assumes that the points are normalized. Otherwise, 704 * they may compare as "not equal" even if they are. 705 * 706 * \param P The first point to compare. This must be initialized. 707 * \param Q The second point to compare. This must be initialized. 708 * 709 * \return \c 0 if the points are equal. 710 * \return #MBEDTLS_ERR_ECP_BAD_INPUT_DATA if the points are not equal. 711 */ 712 int mbedtls_ecp_point_cmp( const mbedtls_ecp_point *P, 713 const mbedtls_ecp_point *Q ); 714 715 /** 716 * \brief This function imports a non-zero point from two ASCII 717 * strings. 718 * 719 * \param P The destination point. This must be initialized. 720 * \param radix The numeric base of the input. 721 * \param x The first affine coordinate, as a null-terminated string. 722 * \param y The second affine coordinate, as a null-terminated string. 723 * 724 * \return \c 0 on success. 725 * \return An \c MBEDTLS_ERR_MPI_XXX error code on failure. 726 */ 727 int mbedtls_ecp_point_read_string( mbedtls_ecp_point *P, int radix, 728 const char *x, const char *y ); 729 730 /** 731 * \brief This function exports a point into unsigned binary data. 732 * 733 * \param grp The group to which the point should belong. 734 * This must be initialized and have group parameters 735 * set, for example through mbedtls_ecp_group_load(). 736 * \param P The point to export. This must be initialized. 737 * \param format The point format. This must be either 738 * #MBEDTLS_ECP_PF_COMPRESSED or #MBEDTLS_ECP_PF_UNCOMPRESSED. 739 * (For groups without these formats, this parameter is 740 * ignored. But it still has to be either of the above 741 * values.) 742 * \param olen The address at which to store the length of 743 * the output in Bytes. This must not be \c NULL. 744 * \param buf The output buffer. This must be a writable buffer 745 * of length \p buflen Bytes. 746 * \param buflen The length of the output buffer \p buf in Bytes. 747 * 748 * \return \c 0 on success. 749 * \return #MBEDTLS_ERR_ECP_BUFFER_TOO_SMALL if the output buffer 750 * is too small to hold the point. 751 * \return #MBEDTLS_ERR_ECP_FEATURE_UNAVAILABLE if the point format 752 * or the export for the given group is not implemented. 753 * \return Another negative error code on other kinds of failure. 754 */ 755 int mbedtls_ecp_point_write_binary( const mbedtls_ecp_group *grp, 756 const mbedtls_ecp_point *P, 757 int format, size_t *olen, 758 unsigned char *buf, size_t buflen ); 759 760 /** 761 * \brief This function imports a point from unsigned binary data. 762 * 763 * \note This function does not check that the point actually 764 * belongs to the given group, see mbedtls_ecp_check_pubkey() 765 * for that. 766 * 767 * \param grp The group to which the point should belong. 768 * This must be initialized and have group parameters 769 * set, for example through mbedtls_ecp_group_load(). 770 * \param P The destination context to import the point to. 771 * This must be initialized. 772 * \param buf The input buffer. This must be a readable buffer 773 * of length \p ilen Bytes. 774 * \param ilen The length of the input buffer \p buf in Bytes. 775 * 776 * \return \c 0 on success. 777 * \return #MBEDTLS_ERR_ECP_BAD_INPUT_DATA if the input is invalid. 778 * \return #MBEDTLS_ERR_MPI_ALLOC_FAILED on memory-allocation failure. 779 * \return #MBEDTLS_ERR_ECP_FEATURE_UNAVAILABLE if the import for the 780 * given group is not implemented. 781 */ 782 int mbedtls_ecp_point_read_binary( const mbedtls_ecp_group *grp, 783 mbedtls_ecp_point *P, 784 const unsigned char *buf, size_t ilen ); 785 786 /** 787 * \brief This function imports a point from a TLS ECPoint record. 788 * 789 * \note On function return, \p *buf is updated to point immediately 790 * after the ECPoint record. 791 * 792 * \param grp The ECP group to use. 793 * This must be initialized and have group parameters 794 * set, for example through mbedtls_ecp_group_load(). 795 * \param pt The destination point. 796 * \param buf The address of the pointer to the start of the input buffer. 797 * \param len The length of the buffer. 798 * 799 * \return \c 0 on success. 800 * \return An \c MBEDTLS_ERR_MPI_XXX error code on initialization 801 * failure. 802 * \return #MBEDTLS_ERR_ECP_BAD_INPUT_DATA if input is invalid. 803 */ 804 int mbedtls_ecp_tls_read_point( const mbedtls_ecp_group *grp, 805 mbedtls_ecp_point *pt, 806 const unsigned char **buf, size_t len ); 807 808 /** 809 * \brief This function exports a point as a TLS ECPoint record 810 * defined in RFC 4492, Section 5.4. 811 * 812 * \param grp The ECP group to use. 813 * This must be initialized and have group parameters 814 * set, for example through mbedtls_ecp_group_load(). 815 * \param pt The point to be exported. This must be initialized. 816 * \param format The point format to use. This must be either 817 * #MBEDTLS_ECP_PF_COMPRESSED or #MBEDTLS_ECP_PF_UNCOMPRESSED. 818 * \param olen The address at which to store the length in Bytes 819 * of the data written. 820 * \param buf The target buffer. This must be a writable buffer of 821 * length \p blen Bytes. 822 * \param blen The length of the target buffer \p buf in Bytes. 823 * 824 * \return \c 0 on success. 825 * \return #MBEDTLS_ERR_ECP_BAD_INPUT_DATA if the input is invalid. 826 * \return #MBEDTLS_ERR_ECP_BUFFER_TOO_SMALL if the target buffer 827 * is too small to hold the exported point. 828 * \return Another negative error code on other kinds of failure. 829 */ 830 int mbedtls_ecp_tls_write_point( const mbedtls_ecp_group *grp, 831 const mbedtls_ecp_point *pt, 832 int format, size_t *olen, 833 unsigned char *buf, size_t blen ); 834 835 /** 836 * \brief This function sets up an ECP group context 837 * from a standardized set of domain parameters. 838 * 839 * \note The index should be a value of the NamedCurve enum, 840 * as defined in <em>RFC-4492: Elliptic Curve Cryptography 841 * (ECC) Cipher Suites for Transport Layer Security (TLS)</em>, 842 * usually in the form of an \c MBEDTLS_ECP_DP_XXX macro. 843 * 844 * \param grp The group context to setup. This must be initialized. 845 * \param id The identifier of the domain parameter set to load. 846 * 847 * \return \c 0 on success. 848 * \return #MBEDTLS_ERR_ECP_FEATURE_UNAVAILABLE if \p id doesn't 849 * correspond to a known group. 850 * \return Another negative error code on other kinds of failure. 851 */ 852 int mbedtls_ecp_group_load( mbedtls_ecp_group *grp, mbedtls_ecp_group_id id ); 853 854 /** 855 * \brief This function sets up an ECP group context from a TLS 856 * ECParameters record as defined in RFC 4492, Section 5.4. 857 * 858 * \note The read pointer \p buf is updated to point right after 859 * the ECParameters record on exit. 860 * 861 * \param grp The group context to setup. This must be initialized. 862 * \param buf The address of the pointer to the start of the input buffer. 863 * \param len The length of the input buffer \c *buf in Bytes. 864 * 865 * \return \c 0 on success. 866 * \return #MBEDTLS_ERR_ECP_BAD_INPUT_DATA if input is invalid. 867 * \return #MBEDTLS_ERR_ECP_FEATURE_UNAVAILABLE if the group is not 868 * recognized. 869 * \return Another negative error code on other kinds of failure. 870 */ 871 int mbedtls_ecp_tls_read_group( mbedtls_ecp_group *grp, 872 const unsigned char **buf, size_t len ); 873 874 /** 875 * \brief This function extracts an elliptic curve group ID from a 876 * TLS ECParameters record as defined in RFC 4492, Section 5.4. 877 * 878 * \note The read pointer \p buf is updated to point right after 879 * the ECParameters record on exit. 880 * 881 * \param grp The address at which to store the group id. 882 * This must not be \c NULL. 883 * \param buf The address of the pointer to the start of the input buffer. 884 * \param len The length of the input buffer \c *buf in Bytes. 885 * 886 * \return \c 0 on success. 887 * \return #MBEDTLS_ERR_ECP_BAD_INPUT_DATA if input is invalid. 888 * \return #MBEDTLS_ERR_ECP_FEATURE_UNAVAILABLE if the group is not 889 * recognized. 890 * \return Another negative error code on other kinds of failure. 891 */ 892 int mbedtls_ecp_tls_read_group_id( mbedtls_ecp_group_id *grp, 893 const unsigned char **buf, 894 size_t len ); 895 /** 896 * \brief This function exports an elliptic curve as a TLS 897 * ECParameters record as defined in RFC 4492, Section 5.4. 898 * 899 * \param grp The ECP group to be exported. 900 * This must be initialized and have group parameters 901 * set, for example through mbedtls_ecp_group_load(). 902 * \param olen The address at which to store the number of Bytes written. 903 * This must not be \c NULL. 904 * \param buf The buffer to write to. This must be a writable buffer 905 * of length \p blen Bytes. 906 * \param blen The length of the output buffer \p buf in Bytes. 907 * 908 * \return \c 0 on success. 909 * \return #MBEDTLS_ERR_ECP_BUFFER_TOO_SMALL if the output 910 * buffer is too small to hold the exported group. 911 * \return Another negative error code on other kinds of failure. 912 */ 913 int mbedtls_ecp_tls_write_group( const mbedtls_ecp_group *grp, 914 size_t *olen, 915 unsigned char *buf, size_t blen ); 916 917 /** 918 * \brief This function performs a scalar multiplication of a point 919 * by an integer: \p R = \p m * \p P. 920 * 921 * It is not thread-safe to use same group in multiple threads. 922 * 923 * \note To prevent timing attacks, this function 924 * executes the exact same sequence of base-field 925 * operations for any valid \p m. It avoids any if-branch or 926 * array index depending on the value of \p m. 927 * 928 * \note If \p f_rng is not NULL, it is used to randomize 929 * intermediate results to prevent potential timing attacks 930 * targeting these results. We recommend always providing 931 * a non-NULL \p f_rng. The overhead is negligible. 932 * Note: unless #MBEDTLS_ECP_NO_INTERNAL_RNG is defined, when 933 * \p f_rng is NULL, an internal RNG (seeded from the value 934 * of \p m) will be used instead. 935 * 936 * \param grp The ECP group to use. 937 * This must be initialized and have group parameters 938 * set, for example through mbedtls_ecp_group_load(). 939 * \param R The point in which to store the result of the calculation. 940 * This must be initialized. 941 * \param m The integer by which to multiply. This must be initialized. 942 * \param P The point to multiply. This must be initialized. 943 * \param f_rng The RNG function. This may be \c NULL if randomization 944 * of intermediate results isn't desired (discouraged). 945 * \param p_rng The RNG context to be passed to \p p_rng. 946 * 947 * \return \c 0 on success. 948 * \return #MBEDTLS_ERR_ECP_INVALID_KEY if \p m is not a valid private 949 * key, or \p P is not a valid public key. 950 * \return #MBEDTLS_ERR_MPI_ALLOC_FAILED on memory-allocation failure. 951 * \return Another negative error code on other kinds of failure. 952 */ 953 int mbedtls_ecp_mul( mbedtls_ecp_group *grp, mbedtls_ecp_point *R, 954 const mbedtls_mpi *m, const mbedtls_ecp_point *P, 955 int (*f_rng)(void *, unsigned char *, size_t), void *p_rng ); 956 957 /** 958 * \brief This function performs multiplication of a point by 959 * an integer: \p R = \p m * \p P in a restartable way. 960 * 961 * \see mbedtls_ecp_mul() 962 * 963 * \note This function does the same as \c mbedtls_ecp_mul(), but 964 * it can return early and restart according to the limit set 965 * with \c mbedtls_ecp_set_max_ops() to reduce blocking. 966 * 967 * \param grp The ECP group to use. 968 * This must be initialized and have group parameters 969 * set, for example through mbedtls_ecp_group_load(). 970 * \param R The point in which to store the result of the calculation. 971 * This must be initialized. 972 * \param m The integer by which to multiply. This must be initialized. 973 * \param P The point to multiply. This must be initialized. 974 * \param f_rng The RNG function. This may be \c NULL if randomization 975 * of intermediate results isn't desired (discouraged). 976 * \param p_rng The RNG context to be passed to \p p_rng. 977 * \param rs_ctx The restart context (NULL disables restart). 978 * 979 * \return \c 0 on success. 980 * \return #MBEDTLS_ERR_ECP_INVALID_KEY if \p m is not a valid private 981 * key, or \p P is not a valid public key. 982 * \return #MBEDTLS_ERR_MPI_ALLOC_FAILED on memory-allocation failure. 983 * \return #MBEDTLS_ERR_ECP_IN_PROGRESS if maximum number of 984 * operations was reached: see \c mbedtls_ecp_set_max_ops(). 985 * \return Another negative error code on other kinds of failure. 986 */ 987 int mbedtls_ecp_mul_restartable( mbedtls_ecp_group *grp, mbedtls_ecp_point *R, 988 const mbedtls_mpi *m, const mbedtls_ecp_point *P, 989 int (*f_rng)(void *, unsigned char *, size_t), void *p_rng, 990 mbedtls_ecp_restart_ctx *rs_ctx ); 991 992 #if defined(MBEDTLS_ECP_SHORT_WEIERSTRASS_ENABLED) 993 /** 994 * \brief This function performs multiplication and addition of two 995 * points by integers: \p R = \p m * \p P + \p n * \p Q 996 * 997 * It is not thread-safe to use same group in multiple threads. 998 * 999 * \note In contrast to mbedtls_ecp_mul(), this function does not 1000 * guarantee a constant execution flow and timing. 1001 * 1002 * \note This function is only defined for short Weierstrass curves. 1003 * It may not be included in builds without any short 1004 * Weierstrass curve. 1005 * 1006 * \param grp The ECP group to use. 1007 * This must be initialized and have group parameters 1008 * set, for example through mbedtls_ecp_group_load(). 1009 * \param R The point in which to store the result of the calculation. 1010 * This must be initialized. 1011 * \param m The integer by which to multiply \p P. 1012 * This must be initialized. 1013 * \param P The point to multiply by \p m. This must be initialized. 1014 * \param n The integer by which to multiply \p Q. 1015 * This must be initialized. 1016 * \param Q The point to be multiplied by \p n. 1017 * This must be initialized. 1018 * 1019 * \return \c 0 on success. 1020 * \return #MBEDTLS_ERR_ECP_INVALID_KEY if \p m or \p n are not 1021 * valid private keys, or \p P or \p Q are not valid public 1022 * keys. 1023 * \return #MBEDTLS_ERR_MPI_ALLOC_FAILED on memory-allocation failure. 1024 * \return #MBEDTLS_ERR_ECP_FEATURE_UNAVAILABLE if \p grp does not 1025 * designate a short Weierstrass curve. 1026 * \return Another negative error code on other kinds of failure. 1027 */ 1028 int mbedtls_ecp_muladd( mbedtls_ecp_group *grp, mbedtls_ecp_point *R, 1029 const mbedtls_mpi *m, const mbedtls_ecp_point *P, 1030 const mbedtls_mpi *n, const mbedtls_ecp_point *Q ); 1031 1032 /** 1033 * \brief This function performs multiplication and addition of two 1034 * points by integers: \p R = \p m * \p P + \p n * \p Q in a 1035 * restartable way. 1036 * 1037 * \see \c mbedtls_ecp_muladd() 1038 * 1039 * \note This function works the same as \c mbedtls_ecp_muladd(), 1040 * but it can return early and restart according to the limit 1041 * set with \c mbedtls_ecp_set_max_ops() to reduce blocking. 1042 * 1043 * \note This function is only defined for short Weierstrass curves. 1044 * It may not be included in builds without any short 1045 * Weierstrass curve. 1046 * 1047 * \param grp The ECP group to use. 1048 * This must be initialized and have group parameters 1049 * set, for example through mbedtls_ecp_group_load(). 1050 * \param R The point in which to store the result of the calculation. 1051 * This must be initialized. 1052 * \param m The integer by which to multiply \p P. 1053 * This must be initialized. 1054 * \param P The point to multiply by \p m. This must be initialized. 1055 * \param n The integer by which to multiply \p Q. 1056 * This must be initialized. 1057 * \param Q The point to be multiplied by \p n. 1058 * This must be initialized. 1059 * \param rs_ctx The restart context (NULL disables restart). 1060 * 1061 * \return \c 0 on success. 1062 * \return #MBEDTLS_ERR_ECP_INVALID_KEY if \p m or \p n are not 1063 * valid private keys, or \p P or \p Q are not valid public 1064 * keys. 1065 * \return #MBEDTLS_ERR_MPI_ALLOC_FAILED on memory-allocation failure. 1066 * \return #MBEDTLS_ERR_ECP_FEATURE_UNAVAILABLE if \p grp does not 1067 * designate a short Weierstrass curve. 1068 * \return #MBEDTLS_ERR_ECP_IN_PROGRESS if maximum number of 1069 * operations was reached: see \c mbedtls_ecp_set_max_ops(). 1070 * \return Another negative error code on other kinds of failure. 1071 */ 1072 int mbedtls_ecp_muladd_restartable( 1073 mbedtls_ecp_group *grp, mbedtls_ecp_point *R, 1074 const mbedtls_mpi *m, const mbedtls_ecp_point *P, 1075 const mbedtls_mpi *n, const mbedtls_ecp_point *Q, 1076 mbedtls_ecp_restart_ctx *rs_ctx ); 1077 #endif /* MBEDTLS_ECP_SHORT_WEIERSTRASS_ENABLED */ 1078 1079 /** 1080 * \brief This function checks that a point is a valid public key 1081 * on this curve. 1082 * 1083 * It only checks that the point is non-zero, has 1084 * valid coordinates and lies on the curve. It does not verify 1085 * that it is indeed a multiple of \p G. This additional 1086 * check is computationally more expensive, is not required 1087 * by standards, and should not be necessary if the group 1088 * used has a small cofactor. In particular, it is useless for 1089 * the NIST groups which all have a cofactor of 1. 1090 * 1091 * \note This function uses bare components rather than an 1092 * ::mbedtls_ecp_keypair structure, to ease use with other 1093 * structures, such as ::mbedtls_ecdh_context or 1094 * ::mbedtls_ecdsa_context. 1095 * 1096 * \param grp The ECP group the point should belong to. 1097 * This must be initialized and have group parameters 1098 * set, for example through mbedtls_ecp_group_load(). 1099 * \param pt The point to check. This must be initialized. 1100 * 1101 * \return \c 0 if the point is a valid public key. 1102 * \return #MBEDTLS_ERR_ECP_INVALID_KEY if the point is not 1103 * a valid public key for the given curve. 1104 * \return Another negative error code on other kinds of failure. 1105 */ 1106 int mbedtls_ecp_check_pubkey( const mbedtls_ecp_group *grp, 1107 const mbedtls_ecp_point *pt ); 1108 1109 /** 1110 * \brief This function checks that an \p mbedtls_mpi is a 1111 * valid private key for this curve. 1112 * 1113 * \note This function uses bare components rather than an 1114 * ::mbedtls_ecp_keypair structure to ease use with other 1115 * structures, such as ::mbedtls_ecdh_context or 1116 * ::mbedtls_ecdsa_context. 1117 * 1118 * \param grp The ECP group the private key should belong to. 1119 * This must be initialized and have group parameters 1120 * set, for example through mbedtls_ecp_group_load(). 1121 * \param d The integer to check. This must be initialized. 1122 * 1123 * \return \c 0 if the point is a valid private key. 1124 * \return #MBEDTLS_ERR_ECP_INVALID_KEY if the point is not a valid 1125 * private key for the given curve. 1126 * \return Another negative error code on other kinds of failure. 1127 */ 1128 int mbedtls_ecp_check_privkey( const mbedtls_ecp_group *grp, 1129 const mbedtls_mpi *d ); 1130 1131 /** 1132 * \brief This function generates a private key. 1133 * 1134 * \param grp The ECP group to generate a private key for. 1135 * This must be initialized and have group parameters 1136 * set, for example through mbedtls_ecp_group_load(). 1137 * \param d The destination MPI (secret part). This must be initialized. 1138 * \param f_rng The RNG function. This must not be \c NULL. 1139 * \param p_rng The RNG parameter to be passed to \p f_rng. This may be 1140 * \c NULL if \p f_rng doesn't need a context argument. 1141 * 1142 * \return \c 0 on success. 1143 * \return An \c MBEDTLS_ERR_ECP_XXX or \c MBEDTLS_MPI_XXX error code 1144 * on failure. 1145 */ 1146 int mbedtls_ecp_gen_privkey( const mbedtls_ecp_group *grp, 1147 mbedtls_mpi *d, 1148 int (*f_rng)(void *, unsigned char *, size_t), 1149 void *p_rng ); 1150 1151 /** 1152 * \brief This function generates a keypair with a configurable base 1153 * point. 1154 * 1155 * \note This function uses bare components rather than an 1156 * ::mbedtls_ecp_keypair structure to ease use with other 1157 * structures, such as ::mbedtls_ecdh_context or 1158 * ::mbedtls_ecdsa_context. 1159 * 1160 * \param grp The ECP group to generate a key pair for. 1161 * This must be initialized and have group parameters 1162 * set, for example through mbedtls_ecp_group_load(). 1163 * \param G The base point to use. This must be initialized 1164 * and belong to \p grp. It replaces the default base 1165 * point \c grp->G used by mbedtls_ecp_gen_keypair(). 1166 * \param d The destination MPI (secret part). 1167 * This must be initialized. 1168 * \param Q The destination point (public part). 1169 * This must be initialized. 1170 * \param f_rng The RNG function. This must not be \c NULL. 1171 * \param p_rng The RNG context to be passed to \p f_rng. This may 1172 * be \c NULL if \p f_rng doesn't need a context argument. 1173 * 1174 * \return \c 0 on success. 1175 * \return An \c MBEDTLS_ERR_ECP_XXX or \c MBEDTLS_MPI_XXX error code 1176 * on failure. 1177 */ 1178 int mbedtls_ecp_gen_keypair_base( mbedtls_ecp_group *grp, 1179 const mbedtls_ecp_point *G, 1180 mbedtls_mpi *d, mbedtls_ecp_point *Q, 1181 int (*f_rng)(void *, unsigned char *, size_t), 1182 void *p_rng ); 1183 1184 /** 1185 * \brief This function generates an ECP keypair. 1186 * 1187 * \note This function uses bare components rather than an 1188 * ::mbedtls_ecp_keypair structure to ease use with other 1189 * structures, such as ::mbedtls_ecdh_context or 1190 * ::mbedtls_ecdsa_context. 1191 * 1192 * \param grp The ECP group to generate a key pair for. 1193 * This must be initialized and have group parameters 1194 * set, for example through mbedtls_ecp_group_load(). 1195 * \param d The destination MPI (secret part). 1196 * This must be initialized. 1197 * \param Q The destination point (public part). 1198 * This must be initialized. 1199 * \param f_rng The RNG function. This must not be \c NULL. 1200 * \param p_rng The RNG context to be passed to \p f_rng. This may 1201 * be \c NULL if \p f_rng doesn't need a context argument. 1202 * 1203 * \return \c 0 on success. 1204 * \return An \c MBEDTLS_ERR_ECP_XXX or \c MBEDTLS_MPI_XXX error code 1205 * on failure. 1206 */ 1207 int mbedtls_ecp_gen_keypair( mbedtls_ecp_group *grp, mbedtls_mpi *d, 1208 mbedtls_ecp_point *Q, 1209 int (*f_rng)(void *, unsigned char *, size_t), 1210 void *p_rng ); 1211 1212 /** 1213 * \brief This function generates an ECP key. 1214 * 1215 * \param grp_id The ECP group identifier. 1216 * \param key The destination key. This must be initialized. 1217 * \param f_rng The RNG function to use. This must not be \c NULL. 1218 * \param p_rng The RNG context to be passed to \p f_rng. This may 1219 * be \c NULL if \p f_rng doesn't need a context argument. 1220 * 1221 * \return \c 0 on success. 1222 * \return An \c MBEDTLS_ERR_ECP_XXX or \c MBEDTLS_MPI_XXX error code 1223 * on failure. 1224 */ 1225 int mbedtls_ecp_gen_key( mbedtls_ecp_group_id grp_id, mbedtls_ecp_keypair *key, 1226 int (*f_rng)(void *, unsigned char *, size_t), 1227 void *p_rng ); 1228 1229 /** 1230 * \brief This function reads an elliptic curve private key. 1231 * 1232 * \param grp_id The ECP group identifier. 1233 * \param key The destination key. 1234 * \param buf The buffer containing the binary representation of the 1235 * key. (Big endian integer for Weierstrass curves, byte 1236 * string for Montgomery curves.) 1237 * \param buflen The length of the buffer in bytes. 1238 * 1239 * \return \c 0 on success. 1240 * \return #MBEDTLS_ERR_ECP_INVALID_KEY error if the key is 1241 * invalid. 1242 * \return #MBEDTLS_ERR_MPI_ALLOC_FAILED if memory allocation failed. 1243 * \return #MBEDTLS_ERR_ECP_FEATURE_UNAVAILABLE if the operation for 1244 * the group is not implemented. 1245 * \return Another negative error code on different kinds of failure. 1246 */ 1247 int mbedtls_ecp_read_key( mbedtls_ecp_group_id grp_id, mbedtls_ecp_keypair *key, 1248 const unsigned char *buf, size_t buflen ); 1249 1250 /** 1251 * \brief This function exports an elliptic curve private key. 1252 * 1253 * \param key The private key. 1254 * \param buf The output buffer for containing the binary representation 1255 * of the key. (Big endian integer for Weierstrass curves, byte 1256 * string for Montgomery curves.) 1257 * \param buflen The total length of the buffer in bytes. 1258 * 1259 * \return \c 0 on success. 1260 * \return #MBEDTLS_ERR_ECP_BUFFER_TOO_SMALL if the \p key 1261 representation is larger than the available space in \p buf. 1262 * \return #MBEDTLS_ERR_ECP_FEATURE_UNAVAILABLE if the operation for 1263 * the group is not implemented. 1264 * \return Another negative error code on different kinds of failure. 1265 */ 1266 int mbedtls_ecp_write_key( mbedtls_ecp_keypair *key, 1267 unsigned char *buf, size_t buflen ); 1268 1269 /** 1270 * \brief This function checks that the keypair objects 1271 * \p pub and \p prv have the same group and the 1272 * same public point, and that the private key in 1273 * \p prv is consistent with the public key. 1274 * 1275 * \param pub The keypair structure holding the public key. This 1276 * must be initialized. If it contains a private key, that 1277 * part is ignored. 1278 * \param prv The keypair structure holding the full keypair. 1279 * This must be initialized. 1280 * 1281 * \return \c 0 on success, meaning that the keys are valid and match. 1282 * \return #MBEDTLS_ERR_ECP_BAD_INPUT_DATA if the keys are invalid or do not match. 1283 * \return An \c MBEDTLS_ERR_ECP_XXX or an \c MBEDTLS_ERR_MPI_XXX 1284 * error code on calculation failure. 1285 */ 1286 int mbedtls_ecp_check_pub_priv( const mbedtls_ecp_keypair *pub, 1287 const mbedtls_ecp_keypair *prv ); 1288 1289 #if defined(MBEDTLS_SELF_TEST) 1290 1291 /** 1292 * \brief The ECP checkup routine. 1293 * 1294 * \return \c 0 on success. 1295 * \return \c 1 on failure. 1296 */ 1297 int mbedtls_ecp_self_test( int verbose ); 1298 1299 #endif /* MBEDTLS_SELF_TEST */ 1300 1301 #ifdef __cplusplus 1302 } 1303 #endif 1304 1305 #endif /* ecp.h */ 1306