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