1 /** 2 * \file bignum.h 3 * 4 * \brief Multi-precision integer library 5 */ 6 /* 7 * Copyright (C) 2006-2015, ARM Limited, All Rights Reserved 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 * This file is part of mbed TLS (https://tls.mbed.org) 23 */ 24 #ifndef MBEDTLS_BIGNUM_H 25 #define MBEDTLS_BIGNUM_H 26 27 #if !defined(MBEDTLS_CONFIG_FILE) 28 #include "config.h" 29 #else 30 #include MBEDTLS_CONFIG_FILE 31 #endif 32 33 #include <stddef.h> 34 #include <stdint.h> 35 36 #if defined(MBEDTLS_FS_IO) 37 #include <stdio.h> 38 #endif 39 40 #define MBEDTLS_ERR_MPI_FILE_IO_ERROR -0x0002 /**< An error occurred while reading from or writing to a file. */ 41 #define MBEDTLS_ERR_MPI_BAD_INPUT_DATA -0x0004 /**< Bad input parameters to function. */ 42 #define MBEDTLS_ERR_MPI_INVALID_CHARACTER -0x0006 /**< There is an invalid character in the digit string. */ 43 #define MBEDTLS_ERR_MPI_BUFFER_TOO_SMALL -0x0008 /**< The buffer is too small to write to. */ 44 #define MBEDTLS_ERR_MPI_NEGATIVE_VALUE -0x000A /**< The input arguments are negative or result in illegal output. */ 45 #define MBEDTLS_ERR_MPI_DIVISION_BY_ZERO -0x000C /**< The input argument for division is zero, which is not allowed. */ 46 #define MBEDTLS_ERR_MPI_NOT_ACCEPTABLE -0x000E /**< The input arguments are not acceptable. */ 47 #define MBEDTLS_ERR_MPI_ALLOC_FAILED -0x0010 /**< Memory allocation failed. */ 48 49 #define MBEDTLS_MPI_CHK(f) do { if( ( ret = f ) != 0 ) goto cleanup; } while( 0 ) 50 51 /* 52 * Maximum size MPIs are allowed to grow to in number of limbs. 53 */ 54 #define MBEDTLS_MPI_MAX_LIMBS 10000 55 56 #if !defined(MBEDTLS_MPI_WINDOW_SIZE) 57 /* 58 * Maximum window size used for modular exponentiation. Default: 6 59 * Minimum value: 1. Maximum value: 6. 60 * 61 * Result is an array of ( 2 << MBEDTLS_MPI_WINDOW_SIZE ) MPIs used 62 * for the sliding window calculation. (So 64 by default) 63 * 64 * Reduction in size, reduces speed. 65 */ 66 #define MBEDTLS_MPI_WINDOW_SIZE 6 /**< Maximum windows size used. */ 67 #endif /* !MBEDTLS_MPI_WINDOW_SIZE */ 68 69 #if !defined(MBEDTLS_MPI_MAX_SIZE) 70 /* 71 * Maximum size of MPIs allowed in bits and bytes for user-MPIs. 72 * ( Default: 512 bytes => 4096 bits, Maximum tested: 2048 bytes => 16384 bits ) 73 * 74 * Note: Calculations can temporarily result in larger MPIs. So the number 75 * of limbs required (MBEDTLS_MPI_MAX_LIMBS) is higher. 76 */ 77 #define MBEDTLS_MPI_MAX_SIZE 1024 /**< Maximum number of bytes for usable MPIs. */ 78 #endif /* !MBEDTLS_MPI_MAX_SIZE */ 79 80 #define MBEDTLS_MPI_MAX_BITS ( 8 * MBEDTLS_MPI_MAX_SIZE ) /**< Maximum number of bits for usable MPIs. */ 81 82 /* 83 * When reading from files with mbedtls_mpi_read_file() and writing to files with 84 * mbedtls_mpi_write_file() the buffer should have space 85 * for a (short) label, the MPI (in the provided radix), the newline 86 * characters and the '\0'. 87 * 88 * By default we assume at least a 10 char label, a minimum radix of 10 89 * (decimal) and a maximum of 4096 bit numbers (1234 decimal chars). 90 * Autosized at compile time for at least a 10 char label, a minimum radix 91 * of 10 (decimal) for a number of MBEDTLS_MPI_MAX_BITS size. 92 * 93 * This used to be statically sized to 1250 for a maximum of 4096 bit 94 * numbers (1234 decimal chars). 95 * 96 * Calculate using the formula: 97 * MBEDTLS_MPI_RW_BUFFER_SIZE = ceil(MBEDTLS_MPI_MAX_BITS / ln(10) * ln(2)) + 98 * LabelSize + 6 99 */ 100 #define MBEDTLS_MPI_MAX_BITS_SCALE100 ( 100 * MBEDTLS_MPI_MAX_BITS ) 101 #define MBEDTLS_LN_2_DIV_LN_10_SCALE100 332 102 #define MBEDTLS_MPI_RW_BUFFER_SIZE ( ((MBEDTLS_MPI_MAX_BITS_SCALE100 + MBEDTLS_LN_2_DIV_LN_10_SCALE100 - 1) / MBEDTLS_LN_2_DIV_LN_10_SCALE100) + 10 + 6 ) 103 104 /* 105 * Define the base integer type, architecture-wise. 106 * 107 * 32 or 64-bit integer types can be forced regardless of the underlying 108 * architecture by defining MBEDTLS_HAVE_INT32 or MBEDTLS_HAVE_INT64 109 * respectively and undefining MBEDTLS_HAVE_ASM. 110 * 111 * Double-width integers (e.g. 128-bit in 64-bit architectures) can be 112 * disabled by defining MBEDTLS_NO_UDBL_DIVISION. 113 */ 114 #if !defined(MBEDTLS_HAVE_INT32) 115 #if defined(_MSC_VER) && defined(_M_AMD64) 116 /* Always choose 64-bit when using MSC */ 117 #if !defined(MBEDTLS_HAVE_INT64) 118 #define MBEDTLS_HAVE_INT64 119 #endif /* !MBEDTLS_HAVE_INT64 */ 120 typedef int64_t mbedtls_mpi_sint; 121 typedef uint64_t mbedtls_mpi_uint; 122 #elif defined(__GNUC__) && ( \ 123 defined(__amd64__) || defined(__x86_64__) || \ 124 defined(__ppc64__) || defined(__powerpc64__) || \ 125 defined(__ia64__) || defined(__alpha__) || \ 126 ( defined(__sparc__) && defined(__arch64__) ) || \ 127 defined(__s390x__) || defined(__mips64) ) 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 #if !defined(MBEDTLS_NO_UDBL_DIVISION) 134 /* mbedtls_t_udbl defined as 128-bit unsigned int */ 135 typedef unsigned int mbedtls_t_udbl __attribute__((mode(TI))); 136 #define MBEDTLS_HAVE_UDBL 137 #endif /* !MBEDTLS_NO_UDBL_DIVISION */ 138 #elif defined(__ARMCC_VERSION) && defined(__aarch64__) 139 /* 140 * __ARMCC_VERSION is defined for both armcc and armclang and 141 * __aarch64__ is only defined by armclang when compiling 64-bit code 142 */ 143 #if !defined(MBEDTLS_HAVE_INT64) 144 #define MBEDTLS_HAVE_INT64 145 #endif /* !MBEDTLS_HAVE_INT64 */ 146 typedef int64_t mbedtls_mpi_sint; 147 typedef uint64_t mbedtls_mpi_uint; 148 #if !defined(MBEDTLS_NO_UDBL_DIVISION) 149 /* mbedtls_t_udbl defined as 128-bit unsigned int */ 150 typedef __uint128_t mbedtls_t_udbl; 151 #define MBEDTLS_HAVE_UDBL 152 #endif /* !MBEDTLS_NO_UDBL_DIVISION */ 153 #elif defined(MBEDTLS_HAVE_INT64) 154 /* Force 64-bit integers with unknown compiler */ 155 typedef int64_t mbedtls_mpi_sint; 156 typedef uint64_t mbedtls_mpi_uint; 157 #endif 158 #endif /* !MBEDTLS_HAVE_INT32 */ 159 160 #if !defined(MBEDTLS_HAVE_INT64) 161 /* Default to 32-bit compilation */ 162 #if !defined(MBEDTLS_HAVE_INT32) 163 #define MBEDTLS_HAVE_INT32 164 #endif /* !MBEDTLS_HAVE_INT32 */ 165 typedef int32_t mbedtls_mpi_sint; 166 typedef uint32_t mbedtls_mpi_uint; 167 #if !defined(MBEDTLS_NO_UDBL_DIVISION) 168 typedef uint64_t mbedtls_t_udbl; 169 #define MBEDTLS_HAVE_UDBL 170 #endif /* !MBEDTLS_NO_UDBL_DIVISION */ 171 #endif /* !MBEDTLS_HAVE_INT64 */ 172 173 #ifdef __cplusplus 174 extern "C" { 175 #endif 176 177 /** 178 * \brief MPI structure 179 */ 180 typedef struct mbedtls_mpi 181 { 182 int s; /*!< integer sign */ 183 size_t n; /*!< total # of limbs */ 184 mbedtls_mpi_uint *p; /*!< pointer to limbs */ 185 } 186 mbedtls_mpi; 187 188 /** 189 * \brief Initialize an MPI context. 190 * 191 * This makes the MPI ready to be set or freed, 192 * but does not define a value for the MPI. 193 * 194 * \param X The MPI context to initialize. This must not be \c NULL. 195 */ 196 void mbedtls_mpi_init( mbedtls_mpi *X ); 197 198 /** 199 * \brief This function frees the components of an MPI context. 200 * 201 * \param X The MPI context to be cleared. This may be \c NULL, 202 * in which case this function is a no-op. If it is 203 * not \c NULL, it must point to an initialized MPI. 204 */ 205 void mbedtls_mpi_free( mbedtls_mpi *X ); 206 207 /** 208 * \brief Enlarge an MPI to the specified number of limbs. 209 * 210 * \note This function does nothing if the MPI is 211 * already large enough. 212 * 213 * \param X The MPI to grow. It must be initialized. 214 * \param nblimbs The target number of limbs. 215 * 216 * \return \c 0 if successful. 217 * \return #MBEDTLS_ERR_MPI_ALLOC_FAILED if memory allocation failed. 218 * \return Another negative error code on other kinds of failure. 219 */ 220 int mbedtls_mpi_grow( mbedtls_mpi *X, size_t nblimbs ); 221 222 /** 223 * \brief This function resizes an MPI downwards, keeping at least the 224 * specified number of limbs. 225 * 226 * If \c X is smaller than \c nblimbs, it is resized up 227 * instead. 228 * 229 * \param X The MPI to shrink. This must point to an initialized MPI. 230 * \param nblimbs The minimum number of limbs to keep. 231 * 232 * \return \c 0 if successful. 233 * \return #MBEDTLS_ERR_MPI_ALLOC_FAILED if memory allocation failed 234 * (this can only happen when resizing up). 235 * \return Another negative error code on other kinds of failure. 236 */ 237 int mbedtls_mpi_shrink( mbedtls_mpi *X, size_t nblimbs ); 238 239 /** 240 * \brief Make a copy of an MPI. 241 * 242 * \param X The destination MPI. This must point to an initialized MPI. 243 * \param Y The source MPI. This must point to an initialized MPI. 244 * 245 * \note The limb-buffer in the destination MPI is enlarged 246 * if necessary to hold the value in the source MPI. 247 * 248 * \return \c 0 if successful. 249 * \return #MBEDTLS_ERR_MPI_ALLOC_FAILED if memory allocation failed. 250 * \return Another negative error code on other kinds of failure. 251 */ 252 int mbedtls_mpi_copy( mbedtls_mpi *X, const mbedtls_mpi *Y ); 253 254 /** 255 * \brief Swap the contents of two MPIs. 256 * 257 * \param X The first MPI. It must be initialized. 258 * \param Y The second MPI. It must be initialized. 259 */ 260 void mbedtls_mpi_swap( mbedtls_mpi *X, mbedtls_mpi *Y ); 261 262 /** 263 * \brief Perform a safe conditional copy of MPI which doesn't 264 * reveal whether the condition was true or not. 265 * 266 * \param X The MPI to conditionally assign to. This must point 267 * to an initialized MPI. 268 * \param Y The MPI to be assigned from. This must point to an 269 * initialized MPI. 270 * \param assign The condition deciding whether to perform the 271 * assignment or not. Possible values: 272 * * \c 1: Perform the assignment `X = Y`. 273 * * \c 0: Keep the original value of \p X. 274 * 275 * \note This function is equivalent to 276 * `if( assign ) mbedtls_mpi_copy( X, Y );` 277 * except that it avoids leaking any information about whether 278 * the assignment was done or not (the above code may leak 279 * information through branch prediction and/or memory access 280 * patterns analysis). 281 * 282 * \return \c 0 if successful. 283 * \return #MBEDTLS_ERR_MPI_ALLOC_FAILED if memory allocation failed. 284 * \return Another negative error code on other kinds of failure. 285 */ 286 int mbedtls_mpi_safe_cond_assign( mbedtls_mpi *X, const mbedtls_mpi *Y, unsigned char assign ); 287 288 /** 289 * \brief Perform a safe conditional swap which doesn't 290 * reveal whether the condition was true or not. 291 * 292 * \param X The first MPI. This must be initialized. 293 * \param Y The second MPI. This must be initialized. 294 * \param assign The condition deciding whether to perform 295 * the swap or not. Possible values: 296 * * \c 1: Swap the values of \p X and \p Y. 297 * * \c 0: Keep the original values of \p X and \p Y. 298 * 299 * \note This function is equivalent to 300 * if( assign ) mbedtls_mpi_swap( X, Y ); 301 * except that it avoids leaking any information about whether 302 * the assignment was done or not (the above code may leak 303 * information through branch prediction and/or memory access 304 * patterns analysis). 305 * 306 * \return \c 0 if successful. 307 * \return #MBEDTLS_ERR_MPI_ALLOC_FAILED if memory allocation failed. 308 * \return Another negative error code on other kinds of failure. 309 * 310 */ 311 int mbedtls_mpi_safe_cond_swap( mbedtls_mpi *X, mbedtls_mpi *Y, unsigned char assign ); 312 313 /** 314 * \brief Store integer value in MPI. 315 * 316 * \param X The MPI to set. This must be initialized. 317 * \param z The value to use. 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_lset( mbedtls_mpi *X, mbedtls_mpi_sint z ); 324 325 /** 326 * \brief Get a specific bit from an MPI. 327 * 328 * \param X The MPI to query. This must be initialized. 329 * \param pos Zero-based index of the bit to query. 330 * 331 * \return \c 0 or \c 1 on success, depending on whether bit \c pos 332 * of \c X is unset or set. 333 * \return A negative error code on failure. 334 */ 335 int mbedtls_mpi_get_bit( const mbedtls_mpi *X, size_t pos ); 336 337 /** 338 * \brief Modify a specific bit in an MPI. 339 * 340 * \note This function will grow the target MPI if necessary to set a 341 * bit to \c 1 in a not yet existing limb. It will not grow if 342 * the bit should be set to \c 0. 343 * 344 * \param X The MPI to modify. This must be initialized. 345 * \param pos Zero-based index of the bit to modify. 346 * \param val The desired value of bit \c pos: \c 0 or \c 1. 347 * 348 * \return \c 0 if successful. 349 * \return #MBEDTLS_ERR_MPI_ALLOC_FAILED if memory allocation failed. 350 * \return Another negative error code on other kinds of failure. 351 */ 352 int mbedtls_mpi_set_bit( mbedtls_mpi *X, size_t pos, unsigned char val ); 353 354 /** 355 * \brief Return the number of bits of value \c 0 before the 356 * least significant bit of value \c 1. 357 * 358 * \note This is the same as the zero-based index of 359 * the least significant bit of value \c 1. 360 * 361 * \param X The MPI to query. 362 * 363 * \return The number of bits of value \c 0 before the least significant 364 * bit of value \c 1 in \p X. 365 */ 366 size_t mbedtls_mpi_lsb( const mbedtls_mpi *X ); 367 368 /** 369 * \brief Return the number of bits up to and including the most 370 * significant bit of value \c 1. 371 * 372 * * \note This is same as the one-based index of the most 373 * significant bit of value \c 1. 374 * 375 * \param X The MPI to query. This must point to an initialized MPI. 376 * 377 * \return The number of bits up to and including the most 378 * significant bit of value \c 1. 379 */ 380 size_t mbedtls_mpi_bitlen( const mbedtls_mpi *X ); 381 382 /** 383 * \brief Return the total size of an MPI value in bytes. 384 * 385 * \param X The MPI to use. This must point to an initialized MPI. 386 * 387 * \note The value returned by this function may be less than 388 * the number of bytes used to store \p X internally. 389 * This happens if and only if there are trailing bytes 390 * of value zero. 391 * 392 * \return The least number of bytes capable of storing 393 * the absolute value of \p X. 394 */ 395 size_t mbedtls_mpi_size( const mbedtls_mpi *X ); 396 397 /** 398 * \brief Import an MPI from an ASCII string. 399 * 400 * \param X The destination MPI. This must point to an initialized MPI. 401 * \param radix The numeric base of the input string. 402 * \param s Null-terminated string buffer. 403 * 404 * \return \c 0 if successful. 405 * \return A negative error code on failure. 406 */ 407 int mbedtls_mpi_read_string( mbedtls_mpi *X, int radix, const char *s ); 408 409 /** 410 * \brief Export an MPI to an ASCII string. 411 * 412 * \param X The source MPI. This must point to an initialized MPI. 413 * \param radix The numeric base of the output string. 414 * \param buf The buffer to write the string to. This must be writable 415 * buffer of length \p buflen Bytes. 416 * \param buflen The available size in Bytes of \p buf. 417 * \param olen The address at which to store the length of the string 418 * written, including the final \c NULL byte. This must 419 * not be \c NULL. 420 * 421 * \note You can call this function with `buflen == 0` to obtain the 422 * minimum required buffer size in `*olen`. 423 * 424 * \return \c 0 if successful. 425 * \return #MBEDTLS_ERR_MPI_BUFFER_TOO_SMALL if the target buffer \p buf 426 * is too small to hold the value of \p X in the desired base. 427 * In this case, `*olen` is nonetheless updated to contain the 428 * size of \p buf required for a successful call. 429 * \return Another negative error code on different kinds of failure. 430 */ 431 int mbedtls_mpi_write_string( const mbedtls_mpi *X, int radix, 432 char *buf, size_t buflen, size_t *olen ); 433 434 #if defined(MBEDTLS_FS_IO) 435 /** 436 * \brief Read an MPI from a line in an opened file. 437 * 438 * \param X The destination MPI. This must point to an initialized MPI. 439 * \param radix The numeric base of the string representation used 440 * in the source line. 441 * \param fin The input file handle to use. This must not be \c NULL. 442 * 443 * \note On success, this function advances the file stream 444 * to the end of the current line or to EOF. 445 * 446 * The function returns \c 0 on an empty line. 447 * 448 * Leading whitespaces are ignored, as is a 449 * '0x' prefix for radix \c 16. 450 * 451 * \return \c 0 if successful. 452 * \return #MBEDTLS_ERR_MPI_BUFFER_TOO_SMALL if the file read buffer 453 * is too small. 454 * \return Another negative error code on failure. 455 */ 456 int mbedtls_mpi_read_file( mbedtls_mpi *X, int radix, FILE *fin ); 457 458 /** 459 * \brief Export an MPI into an opened file. 460 * 461 * \param p A string prefix to emit prior to the MPI data. 462 * For example, this might be a label, or "0x" when 463 * printing in base \c 16. This may be \c NULL if no prefix 464 * is needed. 465 * \param X The source MPI. This must point to an initialized MPI. 466 * \param radix The numeric base to be used in the emitted string. 467 * \param fout The output file handle. This may be \c NULL, in which case 468 * the output is written to \c stdout. 469 * 470 * \return \c 0 if successful. 471 * \return A negative error code on failure. 472 */ 473 int mbedtls_mpi_write_file( const char *p, const mbedtls_mpi *X, 474 int radix, FILE *fout ); 475 #endif /* MBEDTLS_FS_IO */ 476 477 /** 478 * \brief Import an MPI from unsigned big endian binary data. 479 * 480 * \param X The destination MPI. This must point to an initialized MPI. 481 * \param buf The input buffer. This must be a readable buffer of length 482 * \p buflen Bytes. 483 * \param buflen The length of the input buffer \p p in Bytes. 484 * 485 * \return \c 0 if successful. 486 * \return #MBEDTLS_ERR_MPI_ALLOC_FAILED if memory allocation failed. 487 * \return Another negative error code on different kinds of failure. 488 */ 489 int mbedtls_mpi_read_binary( mbedtls_mpi *X, const unsigned char *buf, 490 size_t buflen ); 491 492 /** 493 * \brief Export an MPI into unsigned big endian binary data 494 * of fixed size. 495 * 496 * \param X The source MPI. This must point to an initialized MPI. 497 * \param buf The output buffer. This must be a writable buffer of length 498 * \p buflen Bytes. 499 * \param buflen The size of the output buffer \p buf in Bytes. 500 * 501 * \return \c 0 if successful. 502 * \return #MBEDTLS_ERR_MPI_BUFFER_TOO_SMALL if \p buf isn't 503 * large enough to hold the value of \p X. 504 * \return Another negative error code on different kinds of failure. 505 */ 506 int mbedtls_mpi_write_binary( const mbedtls_mpi *X, unsigned char *buf, 507 size_t buflen ); 508 509 /** 510 * \brief Perform a left-shift on an MPI: X <<= count 511 * 512 * \param X The MPI to shift. This must point to an initialized MPI. 513 * \param count The number of bits to shift by. 514 * 515 * \return \c 0 if successful. 516 * \return #MBEDTLS_ERR_MPI_ALLOC_FAILED if a memory allocation failed. 517 * \return Another negative error code on different kinds of failure. 518 */ 519 int mbedtls_mpi_shift_l( mbedtls_mpi *X, size_t count ); 520 521 /** 522 * \brief Perform a right-shift on an MPI: X >>= count 523 * 524 * \param X The MPI to shift. This must point to an initialized MPI. 525 * \param count The number of bits to shift by. 526 * 527 * \return \c 0 if successful. 528 * \return #MBEDTLS_ERR_MPI_ALLOC_FAILED if a memory allocation failed. 529 * \return Another negative error code on different kinds of failure. 530 */ 531 int mbedtls_mpi_shift_r( mbedtls_mpi *X, size_t count ); 532 533 /** 534 * \brief Compare the absolute values of two MPIs. 535 * 536 * \param X The left-hand MPI. This must point to an initialized MPI. 537 * \param Y The right-hand MPI. This must point to an initialized MPI. 538 * 539 * \return \c 1 if `|X|` is greater than `|Y|`. 540 * \return \c -1 if `|X|` is lesser than `|Y|`. 541 * \return \c 0 if `|X|` is equal to `|Y|`. 542 */ 543 int mbedtls_mpi_cmp_abs( const mbedtls_mpi *X, const mbedtls_mpi *Y ); 544 545 /** 546 * \brief Compare two MPIs. 547 * 548 * \param X The left-hand MPI. This must point to an initialized MPI. 549 * \param Y The right-hand MPI. This must point to an initialized MPI. 550 * 551 * \return \c 1 if \p X is greater than \p Y. 552 * \return \c -1 if \p X is lesser than \p Y. 553 * \return \c 0 if \p X is equal to \p Y. 554 */ 555 int mbedtls_mpi_cmp_mpi( const mbedtls_mpi *X, const mbedtls_mpi *Y ); 556 557 /** 558 * \brief Compare an MPI with an integer. 559 * 560 * \param X The left-hand MPI. This must point to an initialized MPI. 561 * \param z The integer value to compare \p X to. 562 * 563 * \return \c 1 if \p X is greater than \p z. 564 * \return \c -1 if \p X is lesser than \p z. 565 * \return \c 0 if \p X is equal to \p z. 566 */ 567 int mbedtls_mpi_cmp_int( const mbedtls_mpi *X, mbedtls_mpi_sint z ); 568 569 /** 570 * \brief Perform an unsigned addition of MPIs: X = |A| + |B| 571 * 572 * \param X The destination MPI. This must point to an initialized MPI. 573 * \param A The first summand. This must point to an initialized MPI. 574 * \param B The second summand. This must point to an initialized MPI. 575 * 576 * \return \c 0 if successful. 577 * \return #MBEDTLS_ERR_MPI_ALLOC_FAILED if a memory allocation failed. 578 * \return Another negative error code on different kinds of failure. 579 */ 580 int mbedtls_mpi_add_abs( mbedtls_mpi *X, const mbedtls_mpi *A, 581 const mbedtls_mpi *B ); 582 583 /** 584 * \brief Perform an unsigned subtraction of MPIs: X = |A| - |B| 585 * 586 * \param X The destination MPI. This must point to an initialized MPI. 587 * \param A The minuend. This must point to an initialized MPI. 588 * \param B The subtrahend. This must point to an initialized MPI. 589 * 590 * \return \c 0 if successful. 591 * \return #MBEDTLS_ERR_MPI_NEGATIVE_VALUE if \p B is greater than \p A. 592 * \return Another negative error code on different kinds of failure. 593 * 594 */ 595 int mbedtls_mpi_sub_abs( mbedtls_mpi *X, const mbedtls_mpi *A, 596 const mbedtls_mpi *B ); 597 598 /** 599 * \brief Perform a signed addition of MPIs: X = A + B 600 * 601 * \param X The destination MPI. This must point to an initialized MPI. 602 * \param A The first summand. This must point to an initialized MPI. 603 * \param B The second summand. This must point to an initialized MPI. 604 * 605 * \return \c 0 if successful. 606 * \return #MBEDTLS_ERR_MPI_ALLOC_FAILED if a memory allocation failed. 607 * \return Another negative error code on different kinds of failure. 608 */ 609 int mbedtls_mpi_add_mpi( mbedtls_mpi *X, const mbedtls_mpi *A, 610 const mbedtls_mpi *B ); 611 612 /** 613 * \brief Perform a signed subtraction of MPIs: X = A - B 614 * 615 * \param X The destination MPI. This must point to an initialized MPI. 616 * \param A The minuend. This must point to an initialized MPI. 617 * \param B The subtrahend. This must point to an initialized MPI. 618 * 619 * \return \c 0 if successful. 620 * \return #MBEDTLS_ERR_MPI_ALLOC_FAILED if a memory allocation failed. 621 * \return Another negative error code on different kinds of failure. 622 */ 623 int mbedtls_mpi_sub_mpi( mbedtls_mpi *X, const mbedtls_mpi *A, 624 const mbedtls_mpi *B ); 625 626 /** 627 * \brief Perform a signed addition of an MPI and an integer: X = A + b 628 * 629 * \param X The destination MPI. This must point to an initialized MPI. 630 * \param A The first summand. This must point to an initialized MPI. 631 * \param b The second summand. 632 * 633 * \return \c 0 if successful. 634 * \return #MBEDTLS_ERR_MPI_ALLOC_FAILED if a memory allocation failed. 635 * \return Another negative error code on different kinds of failure. 636 */ 637 int mbedtls_mpi_add_int( mbedtls_mpi *X, const mbedtls_mpi *A, 638 mbedtls_mpi_sint b ); 639 640 /** 641 * \brief Perform a signed subtraction of an MPI and an integer: 642 * X = A - b 643 * 644 * \param X The destination MPI. This must point to an initialized MPI. 645 * \param A The minuend. This must point to an initialized MPI. 646 * \param b The subtrahend. 647 * 648 * \return \c 0 if successful. 649 * \return #MBEDTLS_ERR_MPI_ALLOC_FAILED if a memory allocation failed. 650 * \return Another negative error code on different kinds of failure. 651 */ 652 int mbedtls_mpi_sub_int( mbedtls_mpi *X, const mbedtls_mpi *A, 653 mbedtls_mpi_sint b ); 654 655 /** 656 * \brief Perform a multiplication of two MPIs: X = A * B 657 * 658 * \param X The destination MPI. This must point to an initialized MPI. 659 * \param A The first factor. This must point to an initialized MPI. 660 * \param B The second factor. This must point to an initialized MPI. 661 * 662 * \return \c 0 if successful. 663 * \return #MBEDTLS_ERR_MPI_ALLOC_FAILED if a memory allocation failed. 664 * \return Another negative error code on different kinds of failure. 665 * 666 */ 667 int mbedtls_mpi_mul_mpi( mbedtls_mpi *X, const mbedtls_mpi *A, 668 const mbedtls_mpi *B ); 669 670 /** 671 * \brief Perform a multiplication of an MPI with an unsigned integer: 672 * X = A * b 673 * 674 * \param X The destination MPI. This must point to an initialized MPI. 675 * \param A The first factor. This must point to an initialized MPI. 676 * \param b The second factor. 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 */ 683 int mbedtls_mpi_mul_int( mbedtls_mpi *X, const mbedtls_mpi *A, 684 mbedtls_mpi_uint b ); 685 686 /** 687 * \brief Perform a division with remainder of two MPIs: 688 * A = Q * B + R 689 * 690 * \param Q The destination MPI for the quotient. 691 * This may be \c NULL if the value of the 692 * quotient is not needed. 693 * \param R The destination MPI for the remainder value. 694 * This may be \c NULL if the value of the 695 * remainder is not needed. 696 * \param A The dividend. This must point to an initialized MPi. 697 * \param B The divisor. This must point to an initialized MPI. 698 * 699 * \return \c 0 if successful. 700 * \return #MBEDTLS_ERR_MPI_ALLOC_FAILED if memory allocation failed. 701 * \return #MBEDTLS_ERR_MPI_DIVISION_BY_ZERO if \p B equals zero. 702 * \return Another negative error code on different kinds of failure. 703 */ 704 int mbedtls_mpi_div_mpi( mbedtls_mpi *Q, mbedtls_mpi *R, const mbedtls_mpi *A, 705 const mbedtls_mpi *B ); 706 707 /** 708 * \brief Perform a division with remainder of an MPI by an integer: 709 * A = Q * b + R 710 * 711 * \param Q The destination MPI for the quotient. 712 * This may be \c NULL if the value of the 713 * quotient is not needed. 714 * \param R The destination MPI for the remainder value. 715 * This may be \c NULL if the value of the 716 * remainder is not needed. 717 * \param A The dividend. This must point to an initialized MPi. 718 * \param b The divisor. 719 * 720 * \return \c 0 if successful. 721 * \return #MBEDTLS_ERR_MPI_ALLOC_FAILED if memory allocation failed. 722 * \return #MBEDTLS_ERR_MPI_DIVISION_BY_ZERO if \p b equals zero. 723 * \return Another negative error code on different kinds of failure. 724 */ 725 int mbedtls_mpi_div_int( mbedtls_mpi *Q, mbedtls_mpi *R, const mbedtls_mpi *A, 726 mbedtls_mpi_sint b ); 727 728 /** 729 * \brief Perform a modular reduction. R = A mod B 730 * 731 * \param R The destination MPI for the residue value. 732 * This must point to an initialized MPI. 733 * \param A The MPI to compute the residue of. 734 * This must point to an initialized MPI. 735 * \param B The base of the modular reduction. 736 * This must point to an initialized MPI. 737 * 738 * \return \c 0 if successful. 739 * \return #MBEDTLS_ERR_MPI_ALLOC_FAILED if a memory allocation failed. 740 * \return #MBEDTLS_ERR_MPI_DIVISION_BY_ZERO if \p B equals zero. 741 * \return #MBEDTLS_ERR_MPI_NEGATIVE_VALUE if \p B is negative. 742 * \return Another negative error code on different kinds of failure. 743 * 744 */ 745 int mbedtls_mpi_mod_mpi( mbedtls_mpi *R, const mbedtls_mpi *A, 746 const mbedtls_mpi *B ); 747 748 /** 749 * \brief Perform a modular reduction with respect to an integer. 750 * r = A mod b 751 * 752 * \param r The address at which to store the residue. 753 * This must not be \c NULL. 754 * \param A The MPI to compute the residue of. 755 * This must point to an initialized MPi. 756 * \param b The integer base of the modular reduction. 757 * 758 * \return \c 0 if successful. 759 * \return #MBEDTLS_ERR_MPI_ALLOC_FAILED if a memory allocation failed. 760 * \return #MBEDTLS_ERR_MPI_DIVISION_BY_ZERO if \p b equals zero. 761 * \return #MBEDTLS_ERR_MPI_NEGATIVE_VALUE if \p b is negative. 762 * \return Another negative error code on different kinds of failure. 763 */ 764 int mbedtls_mpi_mod_int( mbedtls_mpi_uint *r, const mbedtls_mpi *A, 765 mbedtls_mpi_sint b ); 766 767 /** 768 * \brief Perform a sliding-window exponentiation: X = A^E mod N 769 * 770 * \param X The destination MPI. This must point to an initialized MPI. 771 * \param A The base of the exponentiation. 772 * This must point to an initialized MPI. 773 * \param E The exponent MPI. This must point to an initialized MPI. 774 * \param N The base for the modular reduction. This must point to an 775 * initialized MPI. 776 * \param _RR A helper MPI depending solely on \p N which can be used to 777 * speed-up multiple modular exponentiations for the same value 778 * of \p N. This may be \c NULL. If it is not \c NULL, it must 779 * point to an initialized MPI. If it hasn't been used after 780 * the call to mbedtls_mpi_init(), this function will compute 781 * the helper value and store it in \p _RR for reuse on 782 * subsequent calls to this function. Otherwise, the function 783 * will assume that \p _RR holds the helper value set by a 784 * previous call to mbedtls_mpi_exp_mod(), and reuse it. 785 * 786 * \return \c 0 if successful. 787 * \return #MBEDTLS_ERR_MPI_ALLOC_FAILED if a memory allocation failed. 788 * \return #MBEDTLS_ERR_MPI_BAD_INPUT_DATA if \c N is negative or 789 * even, or if \c E is negative. 790 * \return Another negative error code on different kinds of failures. 791 * 792 */ 793 int mbedtls_mpi_exp_mod( mbedtls_mpi *X, const mbedtls_mpi *A, 794 const mbedtls_mpi *E, const mbedtls_mpi *N, 795 mbedtls_mpi *_RR ); 796 797 /** 798 * \brief Fill an MPI with a number of random bytes. 799 * 800 * \param X The destination MPI. This must point to an initialized MPI. 801 * \param size The number of random bytes to generate. 802 * \param f_rng The RNG function to use. This must not be \c NULL. 803 * \param p_rng The RNG parameter to be passed to \p f_rng. This may be 804 * \c NULL if \p f_rng doesn't need a context argument. 805 * 806 * \return \c 0 if successful. 807 * \return #MBEDTLS_ERR_MPI_ALLOC_FAILED if a memory allocation failed. 808 * \return Another negative error code on failure. 809 * 810 * \note The bytes obtained from the RNG are interpreted 811 * as a big-endian representation of an MPI; this can 812 * be relevant in applications like deterministic ECDSA. 813 */ 814 int mbedtls_mpi_fill_random( mbedtls_mpi *X, size_t size, 815 int (*f_rng)(void *, unsigned char *, size_t), 816 void *p_rng ); 817 818 /** 819 * \brief Compute the greatest common divisor: G = gcd(A, B) 820 * 821 * \param G The destination MPI. This must point to an initialized MPI. 822 * \param A The first operand. This must point to an initialized MPI. 823 * \param B The second operand. This must point to an initialized MPI. 824 * 825 * \return \c 0 if successful. 826 * \return #MBEDTLS_ERR_MPI_ALLOC_FAILED if a memory allocation failed. 827 * \return Another negative error code on different kinds of failure. 828 */ 829 int mbedtls_mpi_gcd( mbedtls_mpi *G, const mbedtls_mpi *A, 830 const mbedtls_mpi *B ); 831 832 /** 833 * \brief Compute the modular inverse: X = A^-1 mod N 834 * 835 * \param X The destination MPI. This must point to an initialized MPI. 836 * \param A The MPI to calculate the modular inverse of. This must point 837 * to an initialized MPI. 838 * \param N The base of the modular inversion. This must point to an 839 * initialized MPI. 840 * 841 * \return \c 0 if successful. 842 * \return #MBEDTLS_ERR_MPI_ALLOC_FAILED if a memory allocation failed. 843 * \return #MBEDTLS_ERR_MPI_BAD_INPUT_DATA if \p N is less than 844 * or equal to one. 845 * \return #MBEDTLS_ERR_MPI_NOT_ACCEPTABLE if \p has no modular inverse 846 * with respect to \p N. 847 */ 848 int mbedtls_mpi_inv_mod( mbedtls_mpi *X, const mbedtls_mpi *A, 849 const mbedtls_mpi *N ); 850 851 #if !defined(MBEDTLS_DEPRECATED_REMOVED) 852 #if defined(MBEDTLS_DEPRECATED_WARNING) 853 #define MBEDTLS_DEPRECATED __attribute__((deprecated)) 854 #else 855 #define MBEDTLS_DEPRECATED 856 #endif 857 /** 858 * \brief Perform a Miller-Rabin primality test with error 859 * probability of 2<sup>-80</sup>. 860 * 861 * \deprecated Superseded by mbedtls_mpi_is_prime_ext() which allows 862 * specifying the number of Miller-Rabin rounds. 863 * 864 * \param X The MPI to check for primality. 865 * This must point to an initialized MPI. 866 * \param f_rng The RNG function to use. This must not be \c NULL. 867 * \param p_rng The RNG parameter to be passed to \p f_rng. 868 * This may be \c NULL if \p f_rng doesn't use a 869 * context parameter. 870 * 871 * \return \c 0 if successful, i.e. \p X is probably prime. 872 * \return #MBEDTLS_ERR_MPI_ALLOC_FAILED if a memory allocation failed. 873 * \return #MBEDTLS_ERR_MPI_NOT_ACCEPTABLE if \p X is not prime. 874 * \return Another negative error code on other kinds of failure. 875 */ 876 MBEDTLS_DEPRECATED int mbedtls_mpi_is_prime( const mbedtls_mpi *X, 877 int (*f_rng)(void *, unsigned char *, size_t), 878 void *p_rng ); 879 #undef MBEDTLS_DEPRECATED 880 #endif /* !MBEDTLS_DEPRECATED_REMOVED */ 881 882 /** 883 * \brief Miller-Rabin primality test. 884 * 885 * \warning If \p X is potentially generated by an adversary, for example 886 * when validating cryptographic parameters that you didn't 887 * generate yourself and that are supposed to be prime, then 888 * \p rounds should be at least the half of the security 889 * strength of the cryptographic algorithm. On the other hand, 890 * if \p X is chosen uniformly or non-adversially (as is the 891 * case when mbedtls_mpi_gen_prime calls this function), then 892 * \p rounds can be much lower. 893 * 894 * \param X The MPI to check for primality. 895 * This must point to an initialized MPI. 896 * \param rounds The number of bases to perform the Miller-Rabin primality 897 * test for. The probability of returning 0 on a composite is 898 * at most 2<sup>-2*\p rounds</sup>. 899 * \param f_rng The RNG function to use. This must not be \c NULL. 900 * \param p_rng The RNG parameter to be passed to \p f_rng. 901 * This may be \c NULL if \p f_rng doesn't use 902 * a context parameter. 903 * 904 * \return \c 0 if successful, i.e. \p X is probably prime. 905 * \return #MBEDTLS_ERR_MPI_ALLOC_FAILED if a memory allocation failed. 906 * \return #MBEDTLS_ERR_MPI_NOT_ACCEPTABLE if \p X is not prime. 907 * \return Another negative error code on other kinds of failure. 908 */ 909 int mbedtls_mpi_is_prime_ext( const mbedtls_mpi *X, int rounds, 910 int (*f_rng)(void *, unsigned char *, size_t), 911 void *p_rng ); 912 /** 913 * \brief Flags for mbedtls_mpi_gen_prime() 914 * 915 * Each of these flags is a constraint on the result X returned by 916 * mbedtls_mpi_gen_prime(). 917 */ 918 typedef enum { 919 MBEDTLS_MPI_GEN_PRIME_FLAG_DH = 0x0001, /**< (X-1)/2 is prime too */ 920 MBEDTLS_MPI_GEN_PRIME_FLAG_LOW_ERR = 0x0002, /**< lower error rate from 2<sup>-80</sup> to 2<sup>-128</sup> */ 921 } mbedtls_mpi_gen_prime_flag_t; 922 923 /** 924 * \brief Generate a prime number. 925 * 926 * \param X The destination MPI to store the generated prime in. 927 * This must point to an initialized MPi. 928 * \param nbits The required size of the destination MPI in bits. 929 * This must be between \c 3 and #MBEDTLS_MPI_MAX_BITS. 930 * \param flags A mask of flags of type #mbedtls_mpi_gen_prime_flag_t. 931 * \param f_rng The RNG function to use. This must not be \c NULL. 932 * \param p_rng The RNG parameter to be passed to \p f_rng. 933 * This may be \c NULL if \p f_rng doesn't use 934 * a context parameter. 935 * 936 * \return \c 0 if successful, in which case \p X holds a 937 * probably prime number. 938 * \return #MBEDTLS_ERR_MPI_ALLOC_FAILED if a memory allocation failed. 939 * \return #MBEDTLS_ERR_MPI_BAD_INPUT_DATA if `nbits` is not between 940 * \c 3 and #MBEDTLS_MPI_MAX_BITS. 941 */ 942 int mbedtls_mpi_gen_prime( mbedtls_mpi *X, size_t nbits, int flags, 943 int (*f_rng)(void *, unsigned char *, size_t), 944 void *p_rng ); 945 946 /** 947 * \brief Checkup routine 948 * 949 * \return 0 if successful, or 1 if the test failed 950 */ 951 int mbedtls_mpi_self_test( int verbose ); 952 953 #ifdef __cplusplus 954 } 955 #endif 956 957 #endif /* bignum.h */ 958