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