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