1 /** 2 * \file bignum.h 3 * 4 * \brief Multi-precision integer library 5 */ 6 /* 7 * Copyright The Mbed TLS Contributors 8 * SPDX-License-Identifier: Apache-2.0 OR GPL-2.0-or-later 9 */ 10 #ifndef MBEDTLS_BIGNUM_H 11 #define MBEDTLS_BIGNUM_H 12 #include "mbedtls/private_access.h" 13 14 #include "mbedtls/build_info.h" 15 16 #include <stddef.h> 17 #include <stdint.h> 18 19 #if defined(MBEDTLS_FS_IO) 20 #include <stdio.h> 21 #endif 22 23 /** An error occurred while reading from or writing to a file. */ 24 #define MBEDTLS_ERR_MPI_FILE_IO_ERROR -0x0002 25 /** Bad input parameters to function. */ 26 #define MBEDTLS_ERR_MPI_BAD_INPUT_DATA -0x0004 27 /** There is an invalid character in the digit string. */ 28 #define MBEDTLS_ERR_MPI_INVALID_CHARACTER -0x0006 29 /** The buffer is too small to write to. */ 30 #define MBEDTLS_ERR_MPI_BUFFER_TOO_SMALL -0x0008 31 /** The input arguments are negative or result in illegal output. */ 32 #define MBEDTLS_ERR_MPI_NEGATIVE_VALUE -0x000A 33 /** The input argument for division is zero, which is not allowed. */ 34 #define MBEDTLS_ERR_MPI_DIVISION_BY_ZERO -0x000C 35 /** The input arguments are not acceptable. */ 36 #define MBEDTLS_ERR_MPI_NOT_ACCEPTABLE -0x000E 37 /** Memory allocation failed. */ 38 #define MBEDTLS_ERR_MPI_ALLOC_FAILED -0x0010 39 40 #define MBEDTLS_MPI_CHK(f) \ 41 do \ 42 { \ 43 if ((ret = (f)) != 0) \ 44 goto cleanup; \ 45 } while (0) 46 47 /* 48 * Maximum size MPIs are allowed to grow to in number of limbs. 49 */ 50 #define MBEDTLS_MPI_MAX_LIMBS 10000 51 52 #if !defined(MBEDTLS_MPI_WINDOW_SIZE) 53 /* 54 * Maximum window size used for modular exponentiation. Default: 3 55 * Minimum value: 1. Maximum value: 6. 56 * 57 * Result is an array of ( 2 ** MBEDTLS_MPI_WINDOW_SIZE ) MPIs used 58 * for the sliding window calculation. (So 8 by default) 59 * 60 * Reduction in size, reduces speed. 61 */ 62 #define MBEDTLS_MPI_WINDOW_SIZE 3 /**< Maximum window size used. */ 63 #endif /* !MBEDTLS_MPI_WINDOW_SIZE */ 64 65 #if !defined(MBEDTLS_MPI_MAX_SIZE) 66 /* 67 * Maximum size of MPIs allowed in bits and bytes for user-MPIs. 68 * ( Default: 512 bytes => 4096 bits, Maximum tested: 2048 bytes => 16384 bits ) 69 * 70 * Note: Calculations can temporarily result in larger MPIs. So the number 71 * of limbs required (MBEDTLS_MPI_MAX_LIMBS) is higher. 72 */ 73 #define MBEDTLS_MPI_MAX_SIZE 1024 /**< Maximum number of bytes for usable MPIs. */ 74 #endif /* !MBEDTLS_MPI_MAX_SIZE */ 75 76 #define MBEDTLS_MPI_MAX_BITS (8 * MBEDTLS_MPI_MAX_SIZE) /**< Maximum number of bits for usable MPIs. */ 77 78 /* 79 * When reading from files with mbedtls_mpi_read_file() and writing to files with 80 * mbedtls_mpi_write_file() the buffer should have space 81 * for a (short) label, the MPI (in the provided radix), the newline 82 * characters and the '\0'. 83 * 84 * By default we assume at least a 10 char label, a minimum radix of 10 85 * (decimal) and a maximum of 4096 bit numbers (1234 decimal chars). 86 * Autosized at compile time for at least a 10 char label, a minimum radix 87 * of 10 (decimal) for a number of MBEDTLS_MPI_MAX_BITS size. 88 * 89 * This used to be statically sized to 1250 for a maximum of 4096 bit 90 * numbers (1234 decimal chars). 91 * 92 * Calculate using the formula: 93 * MBEDTLS_MPI_RW_BUFFER_SIZE = ceil(MBEDTLS_MPI_MAX_BITS / ln(10) * ln(2)) + 94 * LabelSize + 6 95 */ 96 #define MBEDTLS_MPI_MAX_BITS_SCALE100 (100 * MBEDTLS_MPI_MAX_BITS) 97 #define MBEDTLS_LN_2_DIV_LN_10_SCALE100 332 98 #define MBEDTLS_MPI_RW_BUFFER_SIZE (((MBEDTLS_MPI_MAX_BITS_SCALE100 + \ 99 MBEDTLS_LN_2_DIV_LN_10_SCALE100 - 1) / \ 100 MBEDTLS_LN_2_DIV_LN_10_SCALE100) + 10 + 6) 101 102 /* 103 * Define the base integer type, architecture-wise. 104 * 105 * 32 or 64-bit integer types can be forced regardless of the underlying 106 * architecture by defining MBEDTLS_HAVE_INT32 or MBEDTLS_HAVE_INT64 107 * respectively and undefining MBEDTLS_HAVE_ASM. 108 * 109 * Double-width integers (e.g. 128-bit in 64-bit architectures) can be 110 * disabled by defining MBEDTLS_NO_UDBL_DIVISION. 111 */ 112 #if !defined(MBEDTLS_HAVE_INT32) 113 #if defined(_MSC_VER) && defined(_M_AMD64) 114 /* Always choose 64-bit when using MSC */ 115 #if !defined(MBEDTLS_HAVE_INT64) 116 #define MBEDTLS_HAVE_INT64 117 #endif /* !MBEDTLS_HAVE_INT64 */ 118 typedef int64_t mbedtls_mpi_sint; 119 typedef uint64_t mbedtls_mpi_uint; 120 #define MBEDTLS_MPI_UINT_MAX UINT64_MAX 121 #elif defined(__GNUC__) && ( \ 122 defined(__amd64__) || defined(__x86_64__) || \ 123 defined(__ppc64__) || defined(__powerpc64__) || \ 124 defined(__ia64__) || defined(__alpha__) || \ 125 (defined(__sparc__) && defined(__arch64__)) || \ 126 defined(__s390x__) || defined(__mips64) || \ 127 defined(__aarch64__)) 128 #if !defined(MBEDTLS_HAVE_INT64) 129 #define MBEDTLS_HAVE_INT64 130 #endif /* MBEDTLS_HAVE_INT64 */ 131 typedef int64_t mbedtls_mpi_sint; 132 typedef uint64_t mbedtls_mpi_uint; 133 #define MBEDTLS_MPI_UINT_MAX UINT64_MAX 134 #if !defined(MBEDTLS_NO_UDBL_DIVISION) 135 /* mbedtls_t_udbl defined as 128-bit unsigned int */ 136 typedef unsigned int mbedtls_t_udbl __attribute__((mode(TI))); 137 #define MBEDTLS_HAVE_UDBL 138 #endif /* !MBEDTLS_NO_UDBL_DIVISION */ 139 #elif defined(__ARMCC_VERSION) && defined(__aarch64__) 140 /* 141 * __ARMCC_VERSION is defined for both armcc and armclang and 142 * __aarch64__ is only defined by armclang when compiling 64-bit code 143 */ 144 #if !defined(MBEDTLS_HAVE_INT64) 145 #define MBEDTLS_HAVE_INT64 146 #endif /* !MBEDTLS_HAVE_INT64 */ 147 typedef int64_t mbedtls_mpi_sint; 148 typedef uint64_t mbedtls_mpi_uint; 149 #define MBEDTLS_MPI_UINT_MAX UINT64_MAX 150 #if !defined(MBEDTLS_NO_UDBL_DIVISION) 151 /* mbedtls_t_udbl defined as 128-bit unsigned int */ 152 typedef __uint128_t mbedtls_t_udbl; 153 #define MBEDTLS_HAVE_UDBL 154 #endif /* !MBEDTLS_NO_UDBL_DIVISION */ 155 #elif defined(MBEDTLS_HAVE_INT64) 156 /* Force 64-bit integers with unknown compiler */ 157 typedef int64_t mbedtls_mpi_sint; 158 typedef uint64_t mbedtls_mpi_uint; 159 #define MBEDTLS_MPI_UINT_MAX UINT64_MAX 160 #endif 161 #endif /* !MBEDTLS_HAVE_INT32 */ 162 163 #if !defined(MBEDTLS_HAVE_INT64) 164 /* Default to 32-bit compilation */ 165 #if !defined(MBEDTLS_HAVE_INT32) 166 #define MBEDTLS_HAVE_INT32 167 #endif /* !MBEDTLS_HAVE_INT32 */ 168 typedef int32_t mbedtls_mpi_sint; 169 typedef uint32_t mbedtls_mpi_uint; 170 #define MBEDTLS_MPI_UINT_MAX UINT32_MAX 171 #if !defined(MBEDTLS_NO_UDBL_DIVISION) 172 typedef uint64_t mbedtls_t_udbl; 173 #define MBEDTLS_HAVE_UDBL 174 #endif /* !MBEDTLS_NO_UDBL_DIVISION */ 175 #endif /* !MBEDTLS_HAVE_INT64 */ 176 177 /* 178 * Sanity check that exactly one of MBEDTLS_HAVE_INT32 or MBEDTLS_HAVE_INT64 is defined, 179 * so that code elsewhere doesn't have to check. 180 */ 181 #if (!(defined(MBEDTLS_HAVE_INT32) || defined(MBEDTLS_HAVE_INT64))) || \ 182 (defined(MBEDTLS_HAVE_INT32) && defined(MBEDTLS_HAVE_INT64)) 183 #error "Only 32-bit or 64-bit limbs are supported in bignum" 184 #endif 185 186 /** \typedef mbedtls_mpi_uint 187 * \brief The type of machine digits in a bignum, called _limbs_. 188 * 189 * This is always an unsigned integer type with no padding bits. The size 190 * is platform-dependent. 191 */ 192 193 /** \typedef mbedtls_mpi_sint 194 * \brief The signed type corresponding to #mbedtls_mpi_uint. 195 * 196 * This is always an signed integer type with no padding bits. The size 197 * is platform-dependent. 198 */ 199 200 #ifdef __cplusplus 201 extern "C" { 202 #endif 203 204 /** 205 * \brief MPI structure 206 */ 207 typedef struct mbedtls_mpi { 208 /** Pointer to limbs. 209 * 210 * This may be \c NULL if \c n is 0. 211 */ 212 mbedtls_mpi_uint *MBEDTLS_PRIVATE(p); 213 214 /** Sign: -1 if the mpi is negative, 1 otherwise. 215 * 216 * The number 0 must be represented with `s = +1`. Although many library 217 * functions treat all-limbs-zero as equivalent to a valid representation 218 * of 0 regardless of the sign bit, there are exceptions, so bignum 219 * functions and external callers must always set \c s to +1 for the 220 * number zero. 221 * 222 * Note that this implies that calloc() or `... = {0}` does not create 223 * a valid MPI representation. You must call mbedtls_mpi_init(). 224 */ 225 signed short MBEDTLS_PRIVATE(s); 226 227 /** Total number of limbs in \c p. */ 228 unsigned short MBEDTLS_PRIVATE(n); 229 /* Make sure that MBEDTLS_MPI_MAX_LIMBS fits in n. 230 * Use the same limit value on all platforms so that we don't have to 231 * think about different behavior on the rare platforms where 232 * unsigned short can store values larger than the minimum required by 233 * the C language, which is 65535. 234 */ 235 #if MBEDTLS_MPI_MAX_LIMBS > 65535 236 #error "MBEDTLS_MPI_MAX_LIMBS > 65535 is not supported" 237 #endif 238 239 short use_mempool; 240 241 } 242 mbedtls_mpi; 243 244 extern void *mbedtls_mpi_mempool; 245 246 /** 247 * \brief Initialize an MPI context. 248 * 249 * This makes the MPI ready to be set or freed, 250 * but does not define a value for the MPI. 251 * 252 * \param X The MPI context to initialize. This must not be \c NULL. 253 */ 254 void mbedtls_mpi_init(mbedtls_mpi *X); 255 void mbedtls_mpi_init_mempool(mbedtls_mpi *X); 256 257 /** 258 * \brief This function frees the components of an MPI context. 259 * 260 * \param X The MPI context to be cleared. This may be \c NULL, 261 * in which case this function is a no-op. If it is 262 * not \c NULL, it must point to an initialized MPI. 263 */ 264 void mbedtls_mpi_free(mbedtls_mpi *X); 265 266 /** 267 * \brief Enlarge an MPI to the specified number of limbs. 268 * 269 * \note This function does nothing if the MPI is 270 * already large enough. 271 * 272 * \param X The MPI to grow. It must be initialized. 273 * \param nblimbs The target number of limbs. 274 * 275 * \return \c 0 if successful. 276 * \return #MBEDTLS_ERR_MPI_ALLOC_FAILED if memory allocation failed. 277 * \return Another negative error code on other kinds of failure. 278 */ 279 int mbedtls_mpi_grow(mbedtls_mpi *X, size_t nblimbs); 280 281 /** 282 * \brief This function resizes an MPI downwards, keeping at least the 283 * specified number of limbs. 284 * 285 * If \c X is smaller than \c nblimbs, it is resized up 286 * instead. 287 * 288 * \param X The MPI to shrink. This must point to an initialized MPI. 289 * \param nblimbs The minimum number of limbs to keep. 290 * 291 * \return \c 0 if successful. 292 * \return #MBEDTLS_ERR_MPI_ALLOC_FAILED if memory allocation failed 293 * (this can only happen when resizing up). 294 * \return Another negative error code on other kinds of failure. 295 */ 296 int mbedtls_mpi_shrink(mbedtls_mpi *X, size_t nblimbs); 297 298 /** 299 * \brief Make a copy of an MPI. 300 * 301 * \param X The destination MPI. This must point to an initialized MPI. 302 * \param Y The source MPI. This must point to an initialized MPI. 303 * 304 * \note The limb-buffer in the destination MPI is enlarged 305 * if necessary to hold the value in the source MPI. 306 * 307 * \return \c 0 if successful. 308 * \return #MBEDTLS_ERR_MPI_ALLOC_FAILED if memory allocation failed. 309 * \return Another negative error code on other kinds of failure. 310 */ 311 int mbedtls_mpi_copy(mbedtls_mpi *X, const mbedtls_mpi *Y); 312 313 /** 314 * \brief Swap the contents of two MPIs. 315 * 316 * \param X The first MPI. It must be initialized. 317 * \param Y The second MPI. It must be initialized. 318 */ 319 void mbedtls_mpi_swap(mbedtls_mpi *X, mbedtls_mpi *Y); 320 321 /** 322 * \brief Perform a safe conditional copy of MPI which doesn't 323 * reveal whether the condition was true or not. 324 * 325 * \param X The MPI to conditionally assign to. This must point 326 * to an initialized MPI. 327 * \param Y The MPI to be assigned from. This must point to an 328 * initialized MPI. 329 * \param assign The condition deciding whether to perform the 330 * assignment or not. Must be either 0 or 1: 331 * * \c 1: Perform the assignment `X = Y`. 332 * * \c 0: Keep the original value of \p X. 333 * 334 * \note This function is equivalent to 335 * `if( assign ) mbedtls_mpi_copy( X, Y );` 336 * except that it avoids leaking any information about whether 337 * the assignment was done or not (the above code may leak 338 * information through branch prediction and/or memory access 339 * patterns analysis). 340 * 341 * \warning If \p assign is neither 0 nor 1, the result of this function 342 * is indeterminate, and the resulting value in \p X might be 343 * neither its original value nor the value in \p Y. 344 * 345 * \return \c 0 if successful. 346 * \return #MBEDTLS_ERR_MPI_ALLOC_FAILED if memory allocation failed. 347 * \return Another negative error code on other kinds of failure. 348 */ 349 int mbedtls_mpi_safe_cond_assign(mbedtls_mpi *X, const mbedtls_mpi *Y, unsigned char assign); 350 351 /** 352 * \brief Perform a safe conditional swap which doesn't 353 * reveal whether the condition was true or not. 354 * 355 * \param X The first MPI. This must be initialized. 356 * \param Y The second MPI. This must be initialized. 357 * \param swap The condition deciding whether to perform 358 * the swap or not. Must be either 0 or 1: 359 * * \c 1: Swap the values of \p X and \p Y. 360 * * \c 0: Keep the original values of \p X and \p Y. 361 * 362 * \note This function is equivalent to 363 * if( swap ) mbedtls_mpi_swap( X, Y ); 364 * except that it avoids leaking any information about whether 365 * the swap was done or not (the above code may leak 366 * information through branch prediction and/or memory access 367 * patterns analysis). 368 * 369 * \warning If \p swap is neither 0 nor 1, the result of this function 370 * is indeterminate, and both \p X and \p Y might end up with 371 * values different to either of the original ones. 372 * 373 * \return \c 0 if successful. 374 * \return #MBEDTLS_ERR_MPI_ALLOC_FAILED if memory allocation failed. 375 * \return Another negative error code on other kinds of failure. 376 * 377 */ 378 int mbedtls_mpi_safe_cond_swap(mbedtls_mpi *X, mbedtls_mpi *Y, unsigned char swap); 379 380 /** 381 * \brief Store integer value in MPI. 382 * 383 * \param X The MPI to set. This must be initialized. 384 * \param z The value to use. 385 * 386 * \return \c 0 if successful. 387 * \return #MBEDTLS_ERR_MPI_ALLOC_FAILED if memory allocation failed. 388 * \return Another negative error code on other kinds of failure. 389 */ 390 int mbedtls_mpi_lset(mbedtls_mpi *X, mbedtls_mpi_sint z); 391 392 /** 393 * \brief Get a specific bit from an MPI. 394 * 395 * \param X The MPI to query. This must be initialized. 396 * \param pos Zero-based index of the bit to query. 397 * 398 * \return \c 0 or \c 1 on success, depending on whether bit \c pos 399 * of \c X is unset or set. 400 * \return A negative error code on failure. 401 */ 402 int mbedtls_mpi_get_bit(const mbedtls_mpi *X, size_t pos); 403 404 /** 405 * \brief Modify a specific bit in an MPI. 406 * 407 * \note This function will grow the target MPI if necessary to set a 408 * bit to \c 1 in a not yet existing limb. It will not grow if 409 * the bit should be set to \c 0. 410 * 411 * \param X The MPI to modify. This must be initialized. 412 * \param pos Zero-based index of the bit to modify. 413 * \param val The desired value of bit \c pos: \c 0 or \c 1. 414 * 415 * \return \c 0 if successful. 416 * \return #MBEDTLS_ERR_MPI_ALLOC_FAILED if memory allocation failed. 417 * \return Another negative error code on other kinds of failure. 418 */ 419 int mbedtls_mpi_set_bit(mbedtls_mpi *X, size_t pos, unsigned char val); 420 421 /** 422 * \brief Return the number of bits of value \c 0 before the 423 * least significant bit of value \c 1. 424 * 425 * \note This is the same as the zero-based index of 426 * the least significant bit of value \c 1. 427 * 428 * \param X The MPI to query. 429 * 430 * \return The number of bits of value \c 0 before the least significant 431 * bit of value \c 1 in \p X. 432 */ 433 size_t mbedtls_mpi_lsb(const mbedtls_mpi *X); 434 435 /** 436 * \brief Return the number of bits up to and including the most 437 * significant bit of value \c 1. 438 * 439 * * \note This is same as the one-based index of the most 440 * significant bit of value \c 1. 441 * 442 * \param X The MPI to query. This must point to an initialized MPI. 443 * 444 * \return The number of bits up to and including the most 445 * significant bit of value \c 1. 446 */ 447 size_t mbedtls_mpi_bitlen(const mbedtls_mpi *X); 448 449 /** 450 * \brief Return the total size of an MPI value in bytes. 451 * 452 * \param X The MPI to use. This must point to an initialized MPI. 453 * 454 * \note The value returned by this function may be less than 455 * the number of bytes used to store \p X internally. 456 * This happens if and only if there are trailing bytes 457 * of value zero. 458 * 459 * \return The least number of bytes capable of storing 460 * the absolute value of \p X. 461 */ 462 size_t mbedtls_mpi_size(const mbedtls_mpi *X); 463 464 /** 465 * \brief Import an MPI from an ASCII string. 466 * 467 * \param X The destination MPI. This must point to an initialized MPI. 468 * \param radix The numeric base of the input string. 469 * \param s Null-terminated string buffer. 470 * 471 * \return \c 0 if successful. 472 * \return A negative error code on failure. 473 */ 474 int mbedtls_mpi_read_string(mbedtls_mpi *X, int radix, const char *s); 475 476 /** 477 * \brief Export an MPI to an ASCII string. 478 * 479 * \param X The source MPI. This must point to an initialized MPI. 480 * \param radix The numeric base of the output string. 481 * \param buf The buffer to write the string to. This must be writable 482 * buffer of length \p buflen Bytes. 483 * \param buflen The available size in Bytes of \p buf. 484 * \param olen The address at which to store the length of the string 485 * written, including the final \c NULL byte. This must 486 * not be \c NULL. 487 * 488 * \note You can call this function with `buflen == 0` to obtain the 489 * minimum required buffer size in `*olen`. 490 * 491 * \return \c 0 if successful. 492 * \return #MBEDTLS_ERR_MPI_BUFFER_TOO_SMALL if the target buffer \p buf 493 * is too small to hold the value of \p X in the desired base. 494 * In this case, `*olen` is nonetheless updated to contain the 495 * size of \p buf required for a successful call. 496 * \return Another negative error code on different kinds of failure. 497 */ 498 int mbedtls_mpi_write_string(const mbedtls_mpi *X, int radix, 499 char *buf, size_t buflen, size_t *olen); 500 501 #if defined(MBEDTLS_FS_IO) 502 /** 503 * \brief Read an MPI from a line in an opened file. 504 * 505 * \param X The destination MPI. This must point to an initialized MPI. 506 * \param radix The numeric base of the string representation used 507 * in the source line. 508 * \param fin The input file handle to use. This must not be \c NULL. 509 * 510 * \note On success, this function advances the file stream 511 * to the end of the current line or to EOF. 512 * 513 * The function returns \c 0 on an empty line. 514 * 515 * Leading whitespaces are ignored, as is a 516 * '0x' prefix for radix \c 16. 517 * 518 * \return \c 0 if successful. 519 * \return #MBEDTLS_ERR_MPI_BUFFER_TOO_SMALL if the file read buffer 520 * is too small. 521 * \return Another negative error code on failure. 522 */ 523 int mbedtls_mpi_read_file(mbedtls_mpi *X, int radix, FILE *fin); 524 525 /** 526 * \brief Export an MPI into an opened file. 527 * 528 * \param p A string prefix to emit prior to the MPI data. 529 * For example, this might be a label, or "0x" when 530 * printing in base \c 16. This may be \c NULL if no prefix 531 * is needed. 532 * \param X The source MPI. This must point to an initialized MPI. 533 * \param radix The numeric base to be used in the emitted string. 534 * \param fout The output file handle. This may be \c NULL, in which case 535 * the output is written to \c stdout. 536 * 537 * \return \c 0 if successful. 538 * \return A negative error code on failure. 539 */ 540 int mbedtls_mpi_write_file(const char *p, const mbedtls_mpi *X, 541 int radix, FILE *fout); 542 #endif /* MBEDTLS_FS_IO */ 543 544 /** 545 * \brief Import an MPI from unsigned big endian binary data. 546 * 547 * \param X The destination MPI. This must point to an initialized MPI. 548 * \param buf The input buffer. This must be a readable buffer of length 549 * \p buflen Bytes. 550 * \param buflen The length of the input buffer \p buf in Bytes. 551 * 552 * \return \c 0 if successful. 553 * \return #MBEDTLS_ERR_MPI_ALLOC_FAILED if memory allocation failed. 554 * \return Another negative error code on different kinds of failure. 555 */ 556 int mbedtls_mpi_read_binary(mbedtls_mpi *X, const unsigned char *buf, 557 size_t buflen); 558 559 /** 560 * \brief Import X from unsigned binary data, little endian 561 * 562 * \param X The destination MPI. This must point to an initialized MPI. 563 * \param buf The input buffer. This must be a readable buffer of length 564 * \p buflen Bytes. 565 * \param buflen The length of the input buffer \p buf in Bytes. 566 * 567 * \return \c 0 if successful. 568 * \return #MBEDTLS_ERR_MPI_ALLOC_FAILED if memory allocation failed. 569 * \return Another negative error code on different kinds of failure. 570 */ 571 int mbedtls_mpi_read_binary_le(mbedtls_mpi *X, 572 const unsigned char *buf, size_t buflen); 573 574 /** 575 * \brief Export X into unsigned binary data, big endian. 576 * Always fills the whole buffer, which will start with zeros 577 * if the number is smaller. 578 * 579 * \param X The source MPI. This must point to an initialized MPI. 580 * \param buf The output buffer. This must be a writable buffer of length 581 * \p buflen Bytes. 582 * \param buflen The size of the output buffer \p buf in Bytes. 583 * 584 * \return \c 0 if successful. 585 * \return #MBEDTLS_ERR_MPI_BUFFER_TOO_SMALL if \p buf isn't 586 * large enough to hold the value of \p X. 587 * \return Another negative error code on different kinds of failure. 588 */ 589 int mbedtls_mpi_write_binary(const mbedtls_mpi *X, unsigned char *buf, 590 size_t buflen); 591 592 /** 593 * \brief Export X into unsigned binary data, little endian. 594 * Always fills the whole buffer, which will end with zeros 595 * if the number is smaller. 596 * 597 * \param X The source MPI. This must point to an initialized MPI. 598 * \param buf The output buffer. This must be a writable buffer of length 599 * \p buflen Bytes. 600 * \param buflen The size of the output buffer \p buf in Bytes. 601 * 602 * \return \c 0 if successful. 603 * \return #MBEDTLS_ERR_MPI_BUFFER_TOO_SMALL if \p buf isn't 604 * large enough to hold the value of \p X. 605 * \return Another negative error code on different kinds of failure. 606 */ 607 int mbedtls_mpi_write_binary_le(const mbedtls_mpi *X, 608 unsigned char *buf, size_t buflen); 609 610 /** 611 * \brief Perform a left-shift on an MPI: X <<= count 612 * 613 * \param X The MPI to shift. This must point to an initialized MPI. 614 * The MPI pointed by \p X may be resized to fit 615 * the resulting number. 616 * \param count The number of bits to shift by. 617 * 618 * \return \c 0 if successful. 619 * \return #MBEDTLS_ERR_MPI_ALLOC_FAILED if a memory allocation failed. 620 * \return Another negative error code on different kinds of failure. 621 */ 622 int mbedtls_mpi_shift_l(mbedtls_mpi *X, size_t count); 623 624 /** 625 * \brief Perform a right-shift on an MPI: X >>= count 626 * 627 * \param X The MPI to shift. This must point to an initialized MPI. 628 * \param count The number of bits to shift by. 629 * 630 * \return \c 0 if successful. 631 * \return #MBEDTLS_ERR_MPI_ALLOC_FAILED if a memory allocation failed. 632 * \return Another negative error code on different kinds of failure. 633 */ 634 int mbedtls_mpi_shift_r(mbedtls_mpi *X, size_t count); 635 636 /** 637 * \brief Compare the absolute values of two MPIs. 638 * 639 * \param X The left-hand MPI. This must point to an initialized MPI. 640 * \param Y The right-hand MPI. This must point to an initialized MPI. 641 * 642 * \return \c 1 if `|X|` is greater than `|Y|`. 643 * \return \c -1 if `|X|` is lesser than `|Y|`. 644 * \return \c 0 if `|X|` is equal to `|Y|`. 645 */ 646 int mbedtls_mpi_cmp_abs(const mbedtls_mpi *X, const mbedtls_mpi *Y); 647 648 /** 649 * \brief Compare two MPIs. 650 * 651 * \param X The left-hand MPI. This must point to an initialized MPI. 652 * \param Y The right-hand MPI. This must point to an initialized MPI. 653 * 654 * \return \c 1 if \p X is greater than \p Y. 655 * \return \c -1 if \p X is lesser than \p Y. 656 * \return \c 0 if \p X is equal to \p Y. 657 */ 658 int mbedtls_mpi_cmp_mpi(const mbedtls_mpi *X, const mbedtls_mpi *Y); 659 660 /** 661 * \brief Check if an MPI is less than the other in constant time. 662 * 663 * \param X The left-hand MPI. This must point to an initialized MPI 664 * with the same allocated length as Y. 665 * \param Y The right-hand MPI. This must point to an initialized MPI 666 * with the same allocated length as X. 667 * \param ret The result of the comparison: 668 * \c 1 if \p X is less than \p Y. 669 * \c 0 if \p X is greater than or equal to \p Y. 670 * 671 * \return 0 on success. 672 * \return MBEDTLS_ERR_MPI_BAD_INPUT_DATA if the allocated length of 673 * the two input MPIs is not the same. 674 */ 675 int mbedtls_mpi_lt_mpi_ct(const mbedtls_mpi *X, const mbedtls_mpi *Y, 676 unsigned *ret); 677 678 /** 679 * \brief Compare an MPI with an integer. 680 * 681 * \param X The left-hand MPI. This must point to an initialized MPI. 682 * \param z The integer value to compare \p X to. 683 * 684 * \return \c 1 if \p X is greater than \p z. 685 * \return \c -1 if \p X is lesser than \p z. 686 * \return \c 0 if \p X is equal to \p z. 687 */ 688 int mbedtls_mpi_cmp_int(const mbedtls_mpi *X, mbedtls_mpi_sint z); 689 690 /** 691 * \brief Perform an unsigned addition of MPIs: X = |A| + |B| 692 * 693 * \param X The destination MPI. This must point to an initialized MPI. 694 * \param A The first summand. This must point to an initialized MPI. 695 * \param B The second summand. This must point to an initialized MPI. 696 * 697 * \return \c 0 if successful. 698 * \return #MBEDTLS_ERR_MPI_ALLOC_FAILED if a memory allocation failed. 699 * \return Another negative error code on different kinds of failure. 700 */ 701 int mbedtls_mpi_add_abs(mbedtls_mpi *X, const mbedtls_mpi *A, 702 const mbedtls_mpi *B); 703 704 /** 705 * \brief Perform an unsigned subtraction of MPIs: X = |A| - |B| 706 * 707 * \param X The destination MPI. This must point to an initialized MPI. 708 * \param A The minuend. This must point to an initialized MPI. 709 * \param B The subtrahend. This must point to an initialized MPI. 710 * 711 * \return \c 0 if successful. 712 * \return #MBEDTLS_ERR_MPI_NEGATIVE_VALUE if \p B is greater than \p A. 713 * \return Another negative error code on different kinds of failure. 714 * 715 */ 716 int mbedtls_mpi_sub_abs(mbedtls_mpi *X, const mbedtls_mpi *A, 717 const mbedtls_mpi *B); 718 719 /** 720 * \brief Perform a signed addition of MPIs: X = A + B 721 * 722 * \param X The destination MPI. This must point to an initialized MPI. 723 * \param A The first summand. This must point to an initialized MPI. 724 * \param B The second summand. This must point to an initialized MPI. 725 * 726 * \return \c 0 if successful. 727 * \return #MBEDTLS_ERR_MPI_ALLOC_FAILED if a memory allocation failed. 728 * \return Another negative error code on different kinds of failure. 729 */ 730 int mbedtls_mpi_add_mpi(mbedtls_mpi *X, const mbedtls_mpi *A, 731 const mbedtls_mpi *B); 732 733 /** 734 * \brief Perform a signed subtraction of MPIs: X = A - B 735 * 736 * \param X The destination MPI. This must point to an initialized MPI. 737 * \param A The minuend. This must point to an initialized MPI. 738 * \param B The subtrahend. This must point to an initialized MPI. 739 * 740 * \return \c 0 if successful. 741 * \return #MBEDTLS_ERR_MPI_ALLOC_FAILED if a memory allocation failed. 742 * \return Another negative error code on different kinds of failure. 743 */ 744 int mbedtls_mpi_sub_mpi(mbedtls_mpi *X, const mbedtls_mpi *A, 745 const mbedtls_mpi *B); 746 747 /** 748 * \brief Perform a signed addition of an MPI and an integer: X = A + b 749 * 750 * \param X The destination MPI. This must point to an initialized MPI. 751 * \param A The first summand. This must point to an initialized MPI. 752 * \param b The second summand. 753 * 754 * \return \c 0 if successful. 755 * \return #MBEDTLS_ERR_MPI_ALLOC_FAILED if a memory allocation failed. 756 * \return Another negative error code on different kinds of failure. 757 */ 758 int mbedtls_mpi_add_int(mbedtls_mpi *X, const mbedtls_mpi *A, 759 mbedtls_mpi_sint b); 760 761 /** 762 * \brief Perform a signed subtraction of an MPI and an integer: 763 * X = A - b 764 * 765 * \param X The destination MPI. This must point to an initialized MPI. 766 * \param A The minuend. This must point to an initialized MPI. 767 * \param b The subtrahend. 768 * 769 * \return \c 0 if successful. 770 * \return #MBEDTLS_ERR_MPI_ALLOC_FAILED if a memory allocation failed. 771 * \return Another negative error code on different kinds of failure. 772 */ 773 int mbedtls_mpi_sub_int(mbedtls_mpi *X, const mbedtls_mpi *A, 774 mbedtls_mpi_sint b); 775 776 /** 777 * \brief Perform a multiplication of two MPIs: X = A * B 778 * 779 * \param X The destination MPI. This must point to an initialized MPI. 780 * \param A The first factor. This must point to an initialized MPI. 781 * \param B The second factor. This must point to an initialized MPI. 782 * 783 * \return \c 0 if successful. 784 * \return #MBEDTLS_ERR_MPI_ALLOC_FAILED if a memory allocation failed. 785 * \return Another negative error code on different kinds of failure. 786 * 787 */ 788 int mbedtls_mpi_mul_mpi(mbedtls_mpi *X, const mbedtls_mpi *A, 789 const mbedtls_mpi *B); 790 791 /** 792 * \brief Perform a multiplication of an MPI with an unsigned integer: 793 * X = A * b 794 * 795 * \param X The destination MPI. This must point to an initialized MPI. 796 * \param A The first factor. This must point to an initialized MPI. 797 * \param b The second factor. 798 * 799 * \return \c 0 if successful. 800 * \return #MBEDTLS_ERR_MPI_ALLOC_FAILED if a memory allocation failed. 801 * \return Another negative error code on different kinds of failure. 802 * 803 */ 804 int mbedtls_mpi_mul_int(mbedtls_mpi *X, const mbedtls_mpi *A, 805 mbedtls_mpi_uint b); 806 807 /** 808 * \brief Perform a division with remainder of two MPIs: 809 * A = Q * B + R 810 * 811 * \param Q The destination MPI for the quotient. 812 * This may be \c NULL if the value of the 813 * quotient is not needed. This must not alias A or B. 814 * \param R The destination MPI for the remainder value. 815 * This may be \c NULL if the value of the 816 * remainder is not needed. This must not alias A or B. 817 * \param A The dividend. This must point to an initialized MPI. 818 * \param B The divisor. This must point to an initialized MPI. 819 * 820 * \return \c 0 if successful. 821 * \return #MBEDTLS_ERR_MPI_ALLOC_FAILED if memory allocation failed. 822 * \return #MBEDTLS_ERR_MPI_DIVISION_BY_ZERO if \p B equals zero. 823 * \return Another negative error code on different kinds of failure. 824 */ 825 int mbedtls_mpi_div_mpi(mbedtls_mpi *Q, mbedtls_mpi *R, const mbedtls_mpi *A, 826 const mbedtls_mpi *B); 827 828 /** 829 * \brief Perform a division with remainder of an MPI by an integer: 830 * A = Q * b + R 831 * 832 * \param Q The destination MPI for the quotient. 833 * This may be \c NULL if the value of the 834 * quotient is not needed. This must not alias A. 835 * \param R The destination MPI for the remainder value. 836 * This may be \c NULL if the value of the 837 * remainder is not needed. This must not alias A. 838 * \param A The dividend. This must point to an initialized MPi. 839 * \param b The divisor. 840 * 841 * \return \c 0 if successful. 842 * \return #MBEDTLS_ERR_MPI_ALLOC_FAILED if memory allocation failed. 843 * \return #MBEDTLS_ERR_MPI_DIVISION_BY_ZERO if \p b equals zero. 844 * \return Another negative error code on different kinds of failure. 845 */ 846 int mbedtls_mpi_div_int(mbedtls_mpi *Q, mbedtls_mpi *R, const mbedtls_mpi *A, 847 mbedtls_mpi_sint b); 848 849 /** 850 * \brief Perform a modular reduction. R = A mod B 851 * 852 * \param R The destination MPI for the residue value. 853 * This must point to an initialized MPI. 854 * \param A The MPI to compute the residue of. 855 * This must point to an initialized MPI. 856 * \param B The base of the modular reduction. 857 * This must point to an initialized MPI. 858 * 859 * \return \c 0 if successful. 860 * \return #MBEDTLS_ERR_MPI_ALLOC_FAILED if a memory allocation failed. 861 * \return #MBEDTLS_ERR_MPI_DIVISION_BY_ZERO if \p B equals zero. 862 * \return #MBEDTLS_ERR_MPI_NEGATIVE_VALUE if \p B is negative. 863 * \return Another negative error code on different kinds of failure. 864 * 865 */ 866 int mbedtls_mpi_mod_mpi(mbedtls_mpi *R, const mbedtls_mpi *A, 867 const mbedtls_mpi *B); 868 869 /** 870 * \brief Perform a modular reduction with respect to an integer. 871 * r = A mod b 872 * 873 * \param r The address at which to store the residue. 874 * This must not be \c NULL. 875 * \param A The MPI to compute the residue of. 876 * This must point to an initialized MPi. 877 * \param b The integer base of the modular reduction. 878 * 879 * \return \c 0 if successful. 880 * \return #MBEDTLS_ERR_MPI_ALLOC_FAILED if a memory allocation failed. 881 * \return #MBEDTLS_ERR_MPI_DIVISION_BY_ZERO if \p b equals zero. 882 * \return #MBEDTLS_ERR_MPI_NEGATIVE_VALUE if \p b is negative. 883 * \return Another negative error code on different kinds of failure. 884 */ 885 int mbedtls_mpi_mod_int(mbedtls_mpi_uint *r, const mbedtls_mpi *A, 886 mbedtls_mpi_sint b); 887 888 /** 889 * \brief Perform a modular exponentiation: X = A^E mod N 890 * 891 * \param X The destination MPI. This must point to an initialized MPI. 892 * This must not alias E or N. 893 * \param A The base of the exponentiation. 894 * This must point to an initialized MPI. 895 * \param E The exponent MPI. This must point to an initialized MPI. 896 * \param N The base for the modular reduction. This must point to an 897 * initialized MPI. 898 * \param prec_RR A helper MPI depending solely on \p N which can be used to 899 * speed-up multiple modular exponentiations for the same value 900 * of \p N. This may be \c NULL. If it is not \c NULL, it must 901 * point to an initialized MPI. If it hasn't been used after 902 * the call to mbedtls_mpi_init(), this function will compute 903 * the helper value and store it in \p prec_RR for reuse on 904 * subsequent calls to this function. Otherwise, the function 905 * will assume that \p prec_RR holds the helper value set by a 906 * previous call to mbedtls_mpi_exp_mod(), and reuse it. 907 * 908 * \return \c 0 if successful. 909 * \return #MBEDTLS_ERR_MPI_ALLOC_FAILED if a memory allocation failed. 910 * \return #MBEDTLS_ERR_MPI_BAD_INPUT_DATA if \c N is negative or 911 * even, or if \c E is negative. 912 * \return Another negative error code on different kinds of failures. 913 * 914 */ 915 int mbedtls_mpi_exp_mod(mbedtls_mpi *X, const mbedtls_mpi *A, 916 const mbedtls_mpi *E, const mbedtls_mpi *N, 917 mbedtls_mpi *prec_RR); 918 919 /** 920 * \brief Fill an MPI with a number of random bytes. 921 * 922 * \param X The destination MPI. This must point to an initialized MPI. 923 * \param size The number of random bytes to generate. 924 * \param f_rng The RNG function to use. This must not be \c NULL. 925 * \param p_rng The RNG parameter to be passed to \p f_rng. This may be 926 * \c NULL if \p f_rng doesn't need a context argument. 927 * 928 * \return \c 0 if successful. 929 * \return #MBEDTLS_ERR_MPI_ALLOC_FAILED if a memory allocation failed. 930 * \return Another negative error code on failure. 931 * 932 * \note The bytes obtained from the RNG are interpreted 933 * as a big-endian representation of an MPI; this can 934 * be relevant in applications like deterministic ECDSA. 935 */ 936 int mbedtls_mpi_fill_random(mbedtls_mpi *X, size_t size, 937 int (*f_rng)(void *, unsigned char *, size_t), 938 void *p_rng); 939 940 /** Generate a random number uniformly in a range. 941 * 942 * This function generates a random number between \p min inclusive and 943 * \p N exclusive. 944 * 945 * The procedure complies with RFC 6979 §3.3 (deterministic ECDSA) 946 * when the RNG is a suitably parametrized instance of HMAC_DRBG 947 * and \p min is \c 1. 948 * 949 * \note There are `N - min` possible outputs. The lower bound 950 * \p min can be reached, but the upper bound \p N cannot. 951 * 952 * \param X The destination MPI. This must point to an initialized MPI. 953 * \param min The minimum value to return. 954 * It must be nonnegative. 955 * \param N The upper bound of the range, exclusive. 956 * In other words, this is one plus the maximum value to return. 957 * \p N must be strictly larger than \p min. 958 * \param f_rng The RNG function to use. This must not be \c NULL. 959 * \param p_rng The RNG parameter to be passed to \p f_rng. 960 * 961 * \return \c 0 if successful. 962 * \return #MBEDTLS_ERR_MPI_ALLOC_FAILED if a memory allocation failed. 963 * \return #MBEDTLS_ERR_MPI_BAD_INPUT_DATA if \p min or \p N is invalid 964 * or if they are incompatible. 965 * \return #MBEDTLS_ERR_MPI_NOT_ACCEPTABLE if the implementation was 966 * unable to find a suitable value within a limited number 967 * of attempts. This has a negligible probability if \p N 968 * is significantly larger than \p min, which is the case 969 * for all usual cryptographic applications. 970 * \return Another negative error code on failure. 971 */ 972 int mbedtls_mpi_random(mbedtls_mpi *X, 973 mbedtls_mpi_sint min, 974 const mbedtls_mpi *N, 975 int (*f_rng)(void *, unsigned char *, size_t), 976 void *p_rng); 977 978 /** 979 * \brief Compute the greatest common divisor: G = gcd(A, B) 980 * 981 * \param G The destination MPI. This must point to an initialized MPI. 982 * \param A The first operand. This must point to an initialized MPI. 983 * \param B The second operand. This must point to an initialized MPI. 984 * 985 * \return \c 0 if successful. 986 * \return #MBEDTLS_ERR_MPI_ALLOC_FAILED if a memory allocation failed. 987 * \return Another negative error code on different kinds of failure. 988 */ 989 int mbedtls_mpi_gcd(mbedtls_mpi *G, const mbedtls_mpi *A, 990 const mbedtls_mpi *B); 991 992 /** 993 * \brief Compute the modular inverse: X = A^-1 mod N 994 * 995 * \param X The destination MPI. This must point to an initialized MPI. 996 * \param A The MPI to calculate the modular inverse of. This must point 997 * to an initialized MPI. 998 * \param N The base of the modular inversion. This must point to an 999 * initialized MPI. 1000 * 1001 * \return \c 0 if successful. 1002 * \return #MBEDTLS_ERR_MPI_ALLOC_FAILED if a memory allocation failed. 1003 * \return #MBEDTLS_ERR_MPI_BAD_INPUT_DATA if \p N is less than 1004 * or equal to one. 1005 * \return #MBEDTLS_ERR_MPI_NOT_ACCEPTABLE if \p A has no modular 1006 * inverse with respect to \p N. 1007 */ 1008 int mbedtls_mpi_inv_mod(mbedtls_mpi *X, const mbedtls_mpi *A, 1009 const mbedtls_mpi *N); 1010 1011 /** 1012 * \brief Miller-Rabin primality test. 1013 * 1014 * \warning If \p X is potentially generated by an adversary, for example 1015 * when validating cryptographic parameters that you didn't 1016 * generate yourself and that are supposed to be prime, then 1017 * \p rounds should be at least the half of the security 1018 * strength of the cryptographic algorithm. On the other hand, 1019 * if \p X is chosen uniformly or non-adversarially (as is the 1020 * case when mbedtls_mpi_gen_prime calls this function), then 1021 * \p rounds can be much lower. 1022 * 1023 * \param X The MPI to check for primality. 1024 * This must point to an initialized MPI. 1025 * \param rounds The number of bases to perform the Miller-Rabin primality 1026 * test for. The probability of returning 0 on a composite is 1027 * at most 2<sup>-2*\p rounds </sup>. 1028 * \param f_rng The RNG function to use. This must not be \c NULL. 1029 * \param p_rng The RNG parameter to be passed to \p f_rng. 1030 * This may be \c NULL if \p f_rng doesn't use 1031 * a context parameter. 1032 * 1033 * \return \c 0 if successful, i.e. \p X is probably prime. 1034 * \return #MBEDTLS_ERR_MPI_ALLOC_FAILED if a memory allocation failed. 1035 * \return #MBEDTLS_ERR_MPI_NOT_ACCEPTABLE if \p X is not prime. 1036 * \return Another negative error code on other kinds of failure. 1037 */ 1038 int mbedtls_mpi_is_prime_ext(const mbedtls_mpi *X, int rounds, 1039 int (*f_rng)(void *, unsigned char *, size_t), 1040 void *p_rng); 1041 /** 1042 * \brief Flags for mbedtls_mpi_gen_prime() 1043 * 1044 * Each of these flags is a constraint on the result X returned by 1045 * mbedtls_mpi_gen_prime(). 1046 */ 1047 typedef enum { 1048 MBEDTLS_MPI_GEN_PRIME_FLAG_DH = 0x0001, /**< (X-1)/2 is prime too */ 1049 MBEDTLS_MPI_GEN_PRIME_FLAG_LOW_ERR = 0x0002, /**< lower error rate from 2<sup>-80</sup> to 2<sup>-128</sup> */ 1050 } mbedtls_mpi_gen_prime_flag_t; 1051 1052 /** 1053 * \brief Generate a prime number. 1054 * 1055 * \param X The destination MPI to store the generated prime in. 1056 * This must point to an initialized MPi. 1057 * \param nbits The required size of the destination MPI in bits. 1058 * This must be between \c 3 and #MBEDTLS_MPI_MAX_BITS. 1059 * \param flags A mask of flags of type #mbedtls_mpi_gen_prime_flag_t. 1060 * \param f_rng The RNG function to use. This must not be \c NULL. 1061 * \param p_rng The RNG parameter to be passed to \p f_rng. 1062 * This may be \c NULL if \p f_rng doesn't use 1063 * a context parameter. 1064 * 1065 * \return \c 0 if successful, in which case \p X holds a 1066 * probably prime number. 1067 * \return #MBEDTLS_ERR_MPI_ALLOC_FAILED if a memory allocation failed. 1068 * \return #MBEDTLS_ERR_MPI_BAD_INPUT_DATA if `nbits` is not between 1069 * \c 3 and #MBEDTLS_MPI_MAX_BITS. 1070 */ 1071 int mbedtls_mpi_gen_prime(mbedtls_mpi *X, size_t nbits, int flags, 1072 int (*f_rng)(void *, unsigned char *, size_t), 1073 void *p_rng); 1074 1075 /** 1076 * \brief Montgomery initialization 1077 * 1078 * \param mm The -1/m mod N result 1079 * \param N The modulus 1080 */ 1081 void mbedtls_mpi_montg_init( mbedtls_mpi_uint *mm, const mbedtls_mpi *N ); 1082 1083 /** 1084 * \brief Montgomery multiplication: A = A * B * R^-1 mod N 1085 * \A Parameter and result 1086 * \B Parameter 1087 * \N Modulus 1088 * \mm Parameter from mbedtls_mpi_montg_init() 1089 * \T Temporary variable, should be as twice as big as N + 2 1090 */ 1091 void mbedtls_mpi_montmul(mbedtls_mpi *A, const mbedtls_mpi *B, 1092 const mbedtls_mpi *N, mbedtls_mpi_uint mm, 1093 mbedtls_mpi *T ); 1094 1095 /** 1096 * \brief Montgomery reduction: A = A * R^-1 mod N 1097 * \A Parameter and result 1098 * \N Modulus 1099 * \mm Parameter from mbedtls_mpi_montg_init() 1100 * \T Temporary variable, should be as twice as big as N + 2 1101 */ 1102 void mbedtls_mpi_montred(mbedtls_mpi *A, const mbedtls_mpi *N, 1103 mbedtls_mpi_uint mm, mbedtls_mpi *T); 1104 1105 #if defined(MBEDTLS_SELF_TEST) 1106 1107 /** 1108 * \brief Checkup routine 1109 * 1110 * \return 0 if successful, or 1 if the test failed 1111 */ 1112 int mbedtls_mpi_self_test(int verbose); 1113 1114 #endif /* MBEDTLS_SELF_TEST */ 1115 1116 #ifdef __cplusplus 1117 } 1118 #endif 1119 1120 #endif /* bignum.h */ 1121