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