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