1 /** 2 * \file bignum.h 3 * 4 * \brief Multi-precision integer library 5 */ 6 /* 7 * Copyright The Mbed TLS Contributors 8 * SPDX-License-Identifier: Apache-2.0 9 * 10 * Licensed under the Apache License, Version 2.0 (the "License"); you may 11 * not use this file except in compliance with the License. 12 * You may obtain a copy of the License at 13 * 14 * http://www.apache.org/licenses/LICENSE-2.0 15 * 16 * Unless required by applicable law or agreed to in writing, software 17 * distributed under the License is distributed on an "AS IS" BASIS, WITHOUT 18 * WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. 19 * See the License for the specific language governing permissions and 20 * limitations under the License. 21 */ 22 #ifndef MBEDTLS_BIGNUM_H 23 #define MBEDTLS_BIGNUM_H 24 #include "mbedtls/private_access.h" 25 26 #include "mbedtls/build_info.h" 27 28 #include <stddef.h> 29 #include <stdint.h> 30 31 #if defined(MBEDTLS_FS_IO) 32 #include <stdio.h> 33 #endif 34 35 #define MBEDTLS_ERR_MPI_FILE_IO_ERROR -0x0002 /**< An error occurred while reading from or writing to a file. */ 36 #define MBEDTLS_ERR_MPI_BAD_INPUT_DATA -0x0004 /**< Bad input parameters to function. */ 37 #define MBEDTLS_ERR_MPI_INVALID_CHARACTER -0x0006 /**< There is an invalid character in the digit string. */ 38 #define MBEDTLS_ERR_MPI_BUFFER_TOO_SMALL -0x0008 /**< The buffer is too small to write to. */ 39 #define MBEDTLS_ERR_MPI_NEGATIVE_VALUE -0x000A /**< The input arguments are negative or result in illegal output. */ 40 #define MBEDTLS_ERR_MPI_DIVISION_BY_ZERO -0x000C /**< The input argument for division is zero, which is not allowed. */ 41 #define MBEDTLS_ERR_MPI_NOT_ACCEPTABLE -0x000E /**< The input arguments are not acceptable. */ 42 #define MBEDTLS_ERR_MPI_ALLOC_FAILED -0x0010 /**< Memory allocation failed. */ 43 44 #define MBEDTLS_MPI_CHK(f) \ 45 do \ 46 { \ 47 if( ( ret = (f) ) != 0 ) \ 48 goto cleanup; \ 49 } while( 0 ) 50 51 /* 52 * Maximum size MPIs are allowed to grow to in number of limbs. 53 */ 54 #define MBEDTLS_MPI_MAX_LIMBS 10000 55 56 #if !defined(MBEDTLS_MPI_WINDOW_SIZE) 57 /* 58 * Maximum window size used for modular exponentiation. Default: 6 59 * Minimum value: 1. Maximum value: 6. 60 * 61 * Result is an array of ( 2 ** MBEDTLS_MPI_WINDOW_SIZE ) MPIs used 62 * for the sliding window calculation. (So 64 by default) 63 * 64 * Reduction in size, reduces speed. 65 */ 66 #define MBEDTLS_MPI_WINDOW_SIZE 6 /**< Maximum window size used. */ 67 #endif /* !MBEDTLS_MPI_WINDOW_SIZE */ 68 69 #if !defined(MBEDTLS_MPI_MAX_SIZE) 70 /* 71 * Maximum size of MPIs allowed in bits and bytes for user-MPIs. 72 * ( Default: 512 bytes => 4096 bits, Maximum tested: 2048 bytes => 16384 bits ) 73 * 74 * Note: Calculations can temporarily result in larger MPIs. So the number 75 * of limbs required (MBEDTLS_MPI_MAX_LIMBS) is higher. 76 */ 77 #define MBEDTLS_MPI_MAX_SIZE 1024 /**< Maximum number of bytes for usable MPIs. */ 78 #endif /* !MBEDTLS_MPI_MAX_SIZE */ 79 80 #define MBEDTLS_MPI_MAX_BITS ( 8 * MBEDTLS_MPI_MAX_SIZE ) /**< Maximum number of bits for usable MPIs. */ 81 82 /* 83 * When reading from files with mbedtls_mpi_read_file() and writing to files with 84 * mbedtls_mpi_write_file() the buffer should have space 85 * for a (short) label, the MPI (in the provided radix), the newline 86 * characters and the '\0'. 87 * 88 * By default we assume at least a 10 char label, a minimum radix of 10 89 * (decimal) and a maximum of 4096 bit numbers (1234 decimal chars). 90 * Autosized at compile time for at least a 10 char label, a minimum radix 91 * of 10 (decimal) for a number of MBEDTLS_MPI_MAX_BITS size. 92 * 93 * This used to be statically sized to 1250 for a maximum of 4096 bit 94 * numbers (1234 decimal chars). 95 * 96 * Calculate using the formula: 97 * MBEDTLS_MPI_RW_BUFFER_SIZE = ceil(MBEDTLS_MPI_MAX_BITS / ln(10) * ln(2)) + 98 * LabelSize + 6 99 */ 100 #define MBEDTLS_MPI_MAX_BITS_SCALE100 ( 100 * MBEDTLS_MPI_MAX_BITS ) 101 #define MBEDTLS_LN_2_DIV_LN_10_SCALE100 332 102 #define MBEDTLS_MPI_RW_BUFFER_SIZE ( ((MBEDTLS_MPI_MAX_BITS_SCALE100 + MBEDTLS_LN_2_DIV_LN_10_SCALE100 - 1) / MBEDTLS_LN_2_DIV_LN_10_SCALE100) + 10 + 6 ) 103 104 /* 105 * Define the base integer type, architecture-wise. 106 * 107 * 32 or 64-bit integer types can be forced regardless of the underlying 108 * architecture by defining MBEDTLS_HAVE_INT32 or MBEDTLS_HAVE_INT64 109 * respectively and undefining MBEDTLS_HAVE_ASM. 110 * 111 * Double-width integers (e.g. 128-bit in 64-bit architectures) can be 112 * disabled by defining MBEDTLS_NO_UDBL_DIVISION. 113 */ 114 #if !defined(MBEDTLS_HAVE_INT32) 115 #if defined(_MSC_VER) && defined(_M_AMD64) 116 /* Always choose 64-bit when using MSC */ 117 #if !defined(MBEDTLS_HAVE_INT64) 118 #define MBEDTLS_HAVE_INT64 119 #endif /* !MBEDTLS_HAVE_INT64 */ 120 typedef int64_t mbedtls_mpi_sint; 121 typedef uint64_t mbedtls_mpi_uint; 122 #elif defined(__GNUC__) && ( \ 123 defined(__amd64__) || defined(__x86_64__) || \ 124 defined(__ppc64__) || defined(__powerpc64__) || \ 125 defined(__ia64__) || defined(__alpha__) || \ 126 ( defined(__sparc__) && defined(__arch64__) ) || \ 127 defined(__s390x__) || defined(__mips64) || \ 128 defined(__aarch64__) ) 129 #if !defined(MBEDTLS_HAVE_INT64) 130 #define MBEDTLS_HAVE_INT64 131 #endif /* MBEDTLS_HAVE_INT64 */ 132 typedef int64_t mbedtls_mpi_sint; 133 typedef uint64_t mbedtls_mpi_uint; 134 #if !defined(MBEDTLS_NO_UDBL_DIVISION) 135 /* mbedtls_t_udbl defined as 128-bit unsigned int */ 136 typedef unsigned int mbedtls_t_udbl __attribute__((mode(TI))); 137 #define MBEDTLS_HAVE_UDBL 138 #endif /* !MBEDTLS_NO_UDBL_DIVISION */ 139 #elif defined(__ARMCC_VERSION) && defined(__aarch64__) 140 /* 141 * __ARMCC_VERSION is defined for both armcc and armclang and 142 * __aarch64__ is only defined by armclang when compiling 64-bit code 143 */ 144 #if !defined(MBEDTLS_HAVE_INT64) 145 #define MBEDTLS_HAVE_INT64 146 #endif /* !MBEDTLS_HAVE_INT64 */ 147 typedef int64_t mbedtls_mpi_sint; 148 typedef uint64_t mbedtls_mpi_uint; 149 #if !defined(MBEDTLS_NO_UDBL_DIVISION) 150 /* mbedtls_t_udbl defined as 128-bit unsigned int */ 151 typedef __uint128_t mbedtls_t_udbl; 152 #define MBEDTLS_HAVE_UDBL 153 #endif /* !MBEDTLS_NO_UDBL_DIVISION */ 154 #elif defined(MBEDTLS_HAVE_INT64) 155 /* Force 64-bit integers with unknown compiler */ 156 typedef int64_t mbedtls_mpi_sint; 157 typedef uint64_t mbedtls_mpi_uint; 158 #endif 159 #endif /* !MBEDTLS_HAVE_INT32 */ 160 161 #if !defined(MBEDTLS_HAVE_INT64) 162 /* Default to 32-bit compilation */ 163 #if !defined(MBEDTLS_HAVE_INT32) 164 #define MBEDTLS_HAVE_INT32 165 #endif /* !MBEDTLS_HAVE_INT32 */ 166 typedef int32_t mbedtls_mpi_sint; 167 typedef uint32_t mbedtls_mpi_uint; 168 #if !defined(MBEDTLS_NO_UDBL_DIVISION) 169 typedef uint64_t mbedtls_t_udbl; 170 #define MBEDTLS_HAVE_UDBL 171 #endif /* !MBEDTLS_NO_UDBL_DIVISION */ 172 #endif /* !MBEDTLS_HAVE_INT64 */ 173 174 #ifdef __cplusplus 175 extern "C" { 176 #endif 177 178 /** 179 * \brief MPI structure 180 */ 181 typedef struct mbedtls_mpi 182 { 183 int MBEDTLS_PRIVATE(s); /*!< Sign: -1 if the mpi is negative, 1 otherwise */ 184 size_t MBEDTLS_PRIVATE(n); /*!< total # of limbs */ 185 mbedtls_mpi_uint *MBEDTLS_PRIVATE(p); /*!< pointer to limbs */ 186 } 187 mbedtls_mpi; 188 189 /** 190 * \brief Initialize an MPI context. 191 * 192 * This makes the MPI ready to be set or freed, 193 * but does not define a value for the MPI. 194 * 195 * \param X The MPI context to initialize. This must not be \c NULL. 196 */ 197 void mbedtls_mpi_init( mbedtls_mpi *X ); 198 199 /** 200 * \brief This function frees the components of an MPI context. 201 * 202 * \param X The MPI context to be cleared. This may be \c NULL, 203 * in which case this function is a no-op. If it is 204 * not \c NULL, it must point to an initialized MPI. 205 */ 206 void mbedtls_mpi_free( mbedtls_mpi *X ); 207 208 /** 209 * \brief Enlarge an MPI to the specified number of limbs. 210 * 211 * \note This function does nothing if the MPI is 212 * already large enough. 213 * 214 * \param X The MPI to grow. It must be initialized. 215 * \param nblimbs The target number of limbs. 216 * 217 * \return \c 0 if successful. 218 * \return #MBEDTLS_ERR_MPI_ALLOC_FAILED if memory allocation failed. 219 * \return Another negative error code on other kinds of failure. 220 */ 221 int mbedtls_mpi_grow( mbedtls_mpi *X, size_t nblimbs ); 222 223 /** 224 * \brief This function resizes an MPI downwards, keeping at least the 225 * specified number of limbs. 226 * 227 * If \c X is smaller than \c nblimbs, it is resized up 228 * instead. 229 * 230 * \param X The MPI to shrink. This must point to an initialized MPI. 231 * \param nblimbs The minimum number of limbs to keep. 232 * 233 * \return \c 0 if successful. 234 * \return #MBEDTLS_ERR_MPI_ALLOC_FAILED if memory allocation failed 235 * (this can only happen when resizing up). 236 * \return Another negative error code on other kinds of failure. 237 */ 238 int mbedtls_mpi_shrink( mbedtls_mpi *X, size_t nblimbs ); 239 240 /** 241 * \brief Make a copy of an MPI. 242 * 243 * \param X The destination MPI. This must point to an initialized MPI. 244 * \param Y The source MPI. This must point to an initialized MPI. 245 * 246 * \note The limb-buffer in the destination MPI is enlarged 247 * if necessary to hold the value in the source MPI. 248 * 249 * \return \c 0 if successful. 250 * \return #MBEDTLS_ERR_MPI_ALLOC_FAILED if memory allocation failed. 251 * \return Another negative error code on other kinds of failure. 252 */ 253 int mbedtls_mpi_copy( mbedtls_mpi *X, const mbedtls_mpi *Y ); 254 255 /** 256 * \brief Swap the contents of two MPIs. 257 * 258 * \param X The first MPI. It must be initialized. 259 * \param Y The second MPI. It must be initialized. 260 */ 261 void mbedtls_mpi_swap( mbedtls_mpi *X, mbedtls_mpi *Y ); 262 263 /** 264 * \brief Perform a safe conditional copy of MPI which doesn't 265 * reveal whether the condition was true or not. 266 * 267 * \param X The MPI to conditionally assign to. This must point 268 * to an initialized MPI. 269 * \param Y The MPI to be assigned from. This must point to an 270 * initialized MPI. 271 * \param assign The condition deciding whether to perform the 272 * assignment or not. Possible values: 273 * * \c 1: Perform the assignment `X = Y`. 274 * * \c 0: Keep the original value of \p X. 275 * 276 * \note This function is equivalent to 277 * `if( assign ) mbedtls_mpi_copy( X, Y );` 278 * except that it avoids leaking any information about whether 279 * the assignment was done or not (the above code may leak 280 * information through branch prediction and/or memory access 281 * patterns analysis). 282 * 283 * \return \c 0 if successful. 284 * \return #MBEDTLS_ERR_MPI_ALLOC_FAILED if memory allocation failed. 285 * \return Another negative error code on other kinds of failure. 286 */ 287 int mbedtls_mpi_safe_cond_assign( mbedtls_mpi *X, const mbedtls_mpi *Y, unsigned char assign ); 288 289 /** 290 * \brief Perform a safe conditional swap which doesn't 291 * reveal whether the condition was true or not. 292 * 293 * \param X The first MPI. This must be initialized. 294 * \param Y The second MPI. This must be initialized. 295 * \param assign The condition deciding whether to perform 296 * the swap or not. Possible values: 297 * * \c 1: Swap the values of \p X and \p Y. 298 * * \c 0: Keep the original values of \p X and \p Y. 299 * 300 * \note This function is equivalent to 301 * if( assign ) mbedtls_mpi_swap( X, Y ); 302 * except that it avoids leaking any information about whether 303 * the assignment was done or not (the above code may leak 304 * information through branch prediction and/or memory access 305 * patterns analysis). 306 * 307 * \return \c 0 if successful. 308 * \return #MBEDTLS_ERR_MPI_ALLOC_FAILED if memory allocation failed. 309 * \return Another negative error code on other kinds of failure. 310 * 311 */ 312 int mbedtls_mpi_safe_cond_swap( mbedtls_mpi *X, mbedtls_mpi *Y, unsigned char assign ); 313 314 /** 315 * \brief Store integer value in MPI. 316 * 317 * \param X The MPI to set. This must be initialized. 318 * \param z The value to use. 319 * 320 * \return \c 0 if successful. 321 * \return #MBEDTLS_ERR_MPI_ALLOC_FAILED if memory allocation failed. 322 * \return Another negative error code on other kinds of failure. 323 */ 324 int mbedtls_mpi_lset( mbedtls_mpi *X, mbedtls_mpi_sint z ); 325 326 /** 327 * \brief Get a specific bit from an MPI. 328 * 329 * \param X The MPI to query. This must be initialized. 330 * \param pos Zero-based index of the bit to query. 331 * 332 * \return \c 0 or \c 1 on success, depending on whether bit \c pos 333 * of \c X is unset or set. 334 * \return A negative error code on failure. 335 */ 336 int mbedtls_mpi_get_bit( const mbedtls_mpi *X, size_t pos ); 337 338 /** 339 * \brief Modify a specific bit in an MPI. 340 * 341 * \note This function will grow the target MPI if necessary to set a 342 * bit to \c 1 in a not yet existing limb. It will not grow if 343 * the bit should be set to \c 0. 344 * 345 * \param X The MPI to modify. This must be initialized. 346 * \param pos Zero-based index of the bit to modify. 347 * \param val The desired value of bit \c pos: \c 0 or \c 1. 348 * 349 * \return \c 0 if successful. 350 * \return #MBEDTLS_ERR_MPI_ALLOC_FAILED if memory allocation failed. 351 * \return Another negative error code on other kinds of failure. 352 */ 353 int mbedtls_mpi_set_bit( mbedtls_mpi *X, size_t pos, unsigned char val ); 354 355 /** 356 * \brief Return the number of bits of value \c 0 before the 357 * least significant bit of value \c 1. 358 * 359 * \note This is the same as the zero-based index of 360 * the least significant bit of value \c 1. 361 * 362 * \param X The MPI to query. 363 * 364 * \return The number of bits of value \c 0 before the least significant 365 * bit of value \c 1 in \p X. 366 */ 367 size_t mbedtls_mpi_lsb( const mbedtls_mpi *X ); 368 369 /** 370 * \brief Return the number of bits up to and including the most 371 * significant bit of value \c 1. 372 * 373 * * \note This is same as the one-based index of the most 374 * significant bit of value \c 1. 375 * 376 * \param X The MPI to query. This must point to an initialized MPI. 377 * 378 * \return The number of bits up to and including the most 379 * significant bit of value \c 1. 380 */ 381 size_t mbedtls_mpi_bitlen( const mbedtls_mpi *X ); 382 383 /** 384 * \brief Return the total size of an MPI value in bytes. 385 * 386 * \param X The MPI to use. This must point to an initialized MPI. 387 * 388 * \note The value returned by this function may be less than 389 * the number of bytes used to store \p X internally. 390 * This happens if and only if there are trailing bytes 391 * of value zero. 392 * 393 * \return The least number of bytes capable of storing 394 * the absolute value of \p X. 395 */ 396 size_t mbedtls_mpi_size( const mbedtls_mpi *X ); 397 398 /** 399 * \brief Import an MPI from an ASCII string. 400 * 401 * \param X The destination MPI. This must point to an initialized MPI. 402 * \param radix The numeric base of the input string. 403 * \param s Null-terminated string buffer. 404 * 405 * \return \c 0 if successful. 406 * \return A negative error code on failure. 407 */ 408 int mbedtls_mpi_read_string( mbedtls_mpi *X, int radix, const char *s ); 409 410 /** 411 * \brief Export an MPI to an ASCII string. 412 * 413 * \param X The source MPI. This must point to an initialized MPI. 414 * \param radix The numeric base of the output string. 415 * \param buf The buffer to write the string to. This must be writable 416 * buffer of length \p buflen Bytes. 417 * \param buflen The available size in Bytes of \p buf. 418 * \param olen The address at which to store the length of the string 419 * written, including the final \c NULL byte. This must 420 * not be \c NULL. 421 * 422 * \note You can call this function with `buflen == 0` to obtain the 423 * minimum required buffer size in `*olen`. 424 * 425 * \return \c 0 if successful. 426 * \return #MBEDTLS_ERR_MPI_BUFFER_TOO_SMALL if the target buffer \p buf 427 * is too small to hold the value of \p X in the desired base. 428 * In this case, `*olen` is nonetheless updated to contain the 429 * size of \p buf required for a successful call. 430 * \return Another negative error code on different kinds of failure. 431 */ 432 int mbedtls_mpi_write_string( const mbedtls_mpi *X, int radix, 433 char *buf, size_t buflen, size_t *olen ); 434 435 #if defined(MBEDTLS_FS_IO) 436 /** 437 * \brief Read an MPI from a line in an opened file. 438 * 439 * \param X The destination MPI. This must point to an initialized MPI. 440 * \param radix The numeric base of the string representation used 441 * in the source line. 442 * \param fin The input file handle to use. This must not be \c NULL. 443 * 444 * \note On success, this function advances the file stream 445 * to the end of the current line or to EOF. 446 * 447 * The function returns \c 0 on an empty line. 448 * 449 * Leading whitespaces are ignored, as is a 450 * '0x' prefix for radix \c 16. 451 * 452 * \return \c 0 if successful. 453 * \return #MBEDTLS_ERR_MPI_BUFFER_TOO_SMALL if the file read buffer 454 * is too small. 455 * \return Another negative error code on failure. 456 */ 457 int mbedtls_mpi_read_file( mbedtls_mpi *X, int radix, FILE *fin ); 458 459 /** 460 * \brief Export an MPI into an opened file. 461 * 462 * \param p A string prefix to emit prior to the MPI data. 463 * For example, this might be a label, or "0x" when 464 * printing in base \c 16. This may be \c NULL if no prefix 465 * is needed. 466 * \param X The source MPI. This must point to an initialized MPI. 467 * \param radix The numeric base to be used in the emitted string. 468 * \param fout The output file handle. This may be \c NULL, in which case 469 * the output is written to \c stdout. 470 * 471 * \return \c 0 if successful. 472 * \return A negative error code on failure. 473 */ 474 int mbedtls_mpi_write_file( const char *p, const mbedtls_mpi *X, 475 int radix, FILE *fout ); 476 #endif /* MBEDTLS_FS_IO */ 477 478 /** 479 * \brief Import an MPI from unsigned big endian binary data. 480 * 481 * \param X The destination MPI. This must point to an initialized MPI. 482 * \param buf The input buffer. This must be a readable buffer of length 483 * \p buflen Bytes. 484 * \param buflen The length of the input buffer \p p in Bytes. 485 * 486 * \return \c 0 if successful. 487 * \return #MBEDTLS_ERR_MPI_ALLOC_FAILED if memory allocation failed. 488 * \return Another negative error code on different kinds of failure. 489 */ 490 int mbedtls_mpi_read_binary( mbedtls_mpi *X, const unsigned char *buf, 491 size_t buflen ); 492 493 /** 494 * \brief Import X from unsigned binary data, little endian 495 * 496 * \param X The destination MPI. This must point to an initialized MPI. 497 * \param buf The input buffer. This must be a readable buffer of length 498 * \p buflen Bytes. 499 * \param buflen The length of the input buffer \p p in Bytes. 500 * 501 * \return \c 0 if successful. 502 * \return #MBEDTLS_ERR_MPI_ALLOC_FAILED if memory allocation failed. 503 * \return Another negative error code on different kinds of failure. 504 */ 505 int mbedtls_mpi_read_binary_le( mbedtls_mpi *X, 506 const unsigned char *buf, size_t buflen ); 507 508 /** 509 * \brief Export X into unsigned binary data, big endian. 510 * Always fills the whole buffer, which will start with zeros 511 * if the number is smaller. 512 * 513 * \param X The source MPI. This must point to an initialized MPI. 514 * \param buf The output buffer. This must be a writable buffer of length 515 * \p buflen Bytes. 516 * \param buflen The size of the output buffer \p buf in Bytes. 517 * 518 * \return \c 0 if successful. 519 * \return #MBEDTLS_ERR_MPI_BUFFER_TOO_SMALL if \p buf isn't 520 * large enough to hold the value of \p X. 521 * \return Another negative error code on different kinds of failure. 522 */ 523 int mbedtls_mpi_write_binary( const mbedtls_mpi *X, unsigned char *buf, 524 size_t buflen ); 525 526 /** 527 * \brief Export X into unsigned binary data, little endian. 528 * Always fills the whole buffer, which will end with zeros 529 * if the number is smaller. 530 * 531 * \param X The source MPI. This must point to an initialized MPI. 532 * \param buf The output buffer. This must be a writable buffer of length 533 * \p buflen Bytes. 534 * \param buflen The size of the output buffer \p buf in Bytes. 535 * 536 * \return \c 0 if successful. 537 * \return #MBEDTLS_ERR_MPI_BUFFER_TOO_SMALL if \p buf isn't 538 * large enough to hold the value of \p X. 539 * \return Another negative error code on different kinds of failure. 540 */ 541 int mbedtls_mpi_write_binary_le( const mbedtls_mpi *X, 542 unsigned char *buf, size_t buflen ); 543 544 /** 545 * \brief Perform a left-shift on an MPI: X <<= count 546 * 547 * \param X The MPI to shift. This must point to an initialized MPI. 548 * \param count The number of bits to shift by. 549 * 550 * \return \c 0 if successful. 551 * \return #MBEDTLS_ERR_MPI_ALLOC_FAILED if a memory allocation failed. 552 * \return Another negative error code on different kinds of failure. 553 */ 554 int mbedtls_mpi_shift_l( mbedtls_mpi *X, size_t count ); 555 556 /** 557 * \brief Perform a right-shift on an MPI: X >>= count 558 * 559 * \param X The MPI to shift. This must point to an initialized MPI. 560 * \param count The number of bits to shift by. 561 * 562 * \return \c 0 if successful. 563 * \return #MBEDTLS_ERR_MPI_ALLOC_FAILED if a memory allocation failed. 564 * \return Another negative error code on different kinds of failure. 565 */ 566 int mbedtls_mpi_shift_r( mbedtls_mpi *X, size_t count ); 567 568 /** 569 * \brief Compare the absolute values of two MPIs. 570 * 571 * \param X The left-hand MPI. This must point to an initialized MPI. 572 * \param Y The right-hand MPI. This must point to an initialized MPI. 573 * 574 * \return \c 1 if `|X|` is greater than `|Y|`. 575 * \return \c -1 if `|X|` is lesser than `|Y|`. 576 * \return \c 0 if `|X|` is equal to `|Y|`. 577 */ 578 int mbedtls_mpi_cmp_abs( const mbedtls_mpi *X, const mbedtls_mpi *Y ); 579 580 /** 581 * \brief Compare two MPIs. 582 * 583 * \param X The left-hand MPI. This must point to an initialized MPI. 584 * \param Y The right-hand MPI. This must point to an initialized MPI. 585 * 586 * \return \c 1 if \p X is greater than \p Y. 587 * \return \c -1 if \p X is lesser than \p Y. 588 * \return \c 0 if \p X is equal to \p Y. 589 */ 590 int mbedtls_mpi_cmp_mpi( const mbedtls_mpi *X, const mbedtls_mpi *Y ); 591 592 /** 593 * \brief Check if an MPI is less than the other in constant time. 594 * 595 * \param X The left-hand MPI. This must point to an initialized MPI 596 * with the same allocated length as Y. 597 * \param Y The right-hand MPI. This must point to an initialized MPI 598 * with the same allocated length as X. 599 * \param ret The result of the comparison: 600 * \c 1 if \p X is less than \p Y. 601 * \c 0 if \p X is greater than or equal to \p Y. 602 * 603 * \return 0 on success. 604 * \return MBEDTLS_ERR_MPI_BAD_INPUT_DATA if the allocated length of 605 * the two input MPIs is not the same. 606 */ 607 int mbedtls_mpi_lt_mpi_ct( const mbedtls_mpi *X, const mbedtls_mpi *Y, 608 unsigned *ret ); 609 610 /** 611 * \brief Compare an MPI with an integer. 612 * 613 * \param X The left-hand MPI. This must point to an initialized MPI. 614 * \param z The integer value to compare \p X to. 615 * 616 * \return \c 1 if \p X is greater than \p z. 617 * \return \c -1 if \p X is lesser than \p z. 618 * \return \c 0 if \p X is equal to \p z. 619 */ 620 int mbedtls_mpi_cmp_int( const mbedtls_mpi *X, mbedtls_mpi_sint z ); 621 622 /** 623 * \brief Perform an unsigned addition of MPIs: X = |A| + |B| 624 * 625 * \param X The destination MPI. This must point to an initialized MPI. 626 * \param A The first summand. This must point to an initialized MPI. 627 * \param B The second summand. This must point to an initialized MPI. 628 * 629 * \return \c 0 if successful. 630 * \return #MBEDTLS_ERR_MPI_ALLOC_FAILED if a memory allocation failed. 631 * \return Another negative error code on different kinds of failure. 632 */ 633 int mbedtls_mpi_add_abs( mbedtls_mpi *X, const mbedtls_mpi *A, 634 const mbedtls_mpi *B ); 635 636 /** 637 * \brief Perform an unsigned subtraction of MPIs: X = |A| - |B| 638 * 639 * \param X The destination MPI. This must point to an initialized MPI. 640 * \param A The minuend. This must point to an initialized MPI. 641 * \param B The subtrahend. This must point to an initialized MPI. 642 * 643 * \return \c 0 if successful. 644 * \return #MBEDTLS_ERR_MPI_NEGATIVE_VALUE if \p B is greater than \p A. 645 * \return Another negative error code on different kinds of failure. 646 * 647 */ 648 int mbedtls_mpi_sub_abs( mbedtls_mpi *X, const mbedtls_mpi *A, 649 const mbedtls_mpi *B ); 650 651 /** 652 * \brief Perform a signed addition of MPIs: X = A + B 653 * 654 * \param X The destination MPI. This must point to an initialized MPI. 655 * \param A The first summand. This must point to an initialized MPI. 656 * \param B The second summand. This must point to an initialized MPI. 657 * 658 * \return \c 0 if successful. 659 * \return #MBEDTLS_ERR_MPI_ALLOC_FAILED if a memory allocation failed. 660 * \return Another negative error code on different kinds of failure. 661 */ 662 int mbedtls_mpi_add_mpi( mbedtls_mpi *X, const mbedtls_mpi *A, 663 const mbedtls_mpi *B ); 664 665 /** 666 * \brief Perform a signed subtraction of MPIs: X = A - B 667 * 668 * \param X The destination MPI. This must point to an initialized MPI. 669 * \param A The minuend. This must point to an initialized MPI. 670 * \param B The subtrahend. This must point to an initialized MPI. 671 * 672 * \return \c 0 if successful. 673 * \return #MBEDTLS_ERR_MPI_ALLOC_FAILED if a memory allocation failed. 674 * \return Another negative error code on different kinds of failure. 675 */ 676 int mbedtls_mpi_sub_mpi( mbedtls_mpi *X, const mbedtls_mpi *A, 677 const mbedtls_mpi *B ); 678 679 /** 680 * \brief Perform a signed addition of an MPI and an integer: X = A + b 681 * 682 * \param X The destination MPI. This must point to an initialized MPI. 683 * \param A The first summand. This must point to an initialized MPI. 684 * \param b The second summand. 685 * 686 * \return \c 0 if successful. 687 * \return #MBEDTLS_ERR_MPI_ALLOC_FAILED if a memory allocation failed. 688 * \return Another negative error code on different kinds of failure. 689 */ 690 int mbedtls_mpi_add_int( mbedtls_mpi *X, const mbedtls_mpi *A, 691 mbedtls_mpi_sint b ); 692 693 /** 694 * \brief Perform a signed subtraction of an MPI and an integer: 695 * X = A - b 696 * 697 * \param X The destination MPI. This must point to an initialized MPI. 698 * \param A The minuend. This must point to an initialized MPI. 699 * \param b The subtrahend. 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 int mbedtls_mpi_sub_int( mbedtls_mpi *X, const mbedtls_mpi *A, 706 mbedtls_mpi_sint b ); 707 708 /** 709 * \brief Perform a multiplication of two MPIs: X = A * B 710 * 711 * \param X The destination MPI. This must point to an initialized MPI. 712 * \param A The first factor. This must point to an initialized MPI. 713 * \param B The second factor. This must point to an initialized MPI. 714 * 715 * \return \c 0 if successful. 716 * \return #MBEDTLS_ERR_MPI_ALLOC_FAILED if a memory allocation failed. 717 * \return Another negative error code on different kinds of failure. 718 * 719 */ 720 int mbedtls_mpi_mul_mpi( mbedtls_mpi *X, const mbedtls_mpi *A, 721 const mbedtls_mpi *B ); 722 723 /** 724 * \brief Perform a multiplication of an MPI with an unsigned integer: 725 * X = A * b 726 * 727 * \param X The destination MPI. This must point to an initialized MPI. 728 * \param A The first factor. This must point to an initialized MPI. 729 * \param b The second factor. 730 * 731 * \return \c 0 if successful. 732 * \return #MBEDTLS_ERR_MPI_ALLOC_FAILED if a memory allocation failed. 733 * \return Another negative error code on different kinds of failure. 734 * 735 */ 736 int mbedtls_mpi_mul_int( mbedtls_mpi *X, const mbedtls_mpi *A, 737 mbedtls_mpi_uint b ); 738 739 /** 740 * \brief Perform a division with remainder of two MPIs: 741 * A = Q * B + R 742 * 743 * \param Q The destination MPI for the quotient. 744 * This may be \c NULL if the value of the 745 * quotient is not needed. 746 * \param R The destination MPI for the remainder value. 747 * This may be \c NULL if the value of the 748 * remainder is not needed. 749 * \param A The dividend. This must point to an initialized MPi. 750 * \param B The divisor. This must point to an initialized MPI. 751 * 752 * \return \c 0 if successful. 753 * \return #MBEDTLS_ERR_MPI_ALLOC_FAILED if memory allocation failed. 754 * \return #MBEDTLS_ERR_MPI_DIVISION_BY_ZERO if \p B equals zero. 755 * \return Another negative error code on different kinds of failure. 756 */ 757 int mbedtls_mpi_div_mpi( mbedtls_mpi *Q, mbedtls_mpi *R, const mbedtls_mpi *A, 758 const mbedtls_mpi *B ); 759 760 /** 761 * \brief Perform a division with remainder of an MPI by an integer: 762 * A = Q * b + R 763 * 764 * \param Q The destination MPI for the quotient. 765 * This may be \c NULL if the value of the 766 * quotient is not needed. 767 * \param R The destination MPI for the remainder value. 768 * This may be \c NULL if the value of the 769 * remainder is not needed. 770 * \param A The dividend. This must point to an initialized MPi. 771 * \param b The divisor. 772 * 773 * \return \c 0 if successful. 774 * \return #MBEDTLS_ERR_MPI_ALLOC_FAILED if memory allocation failed. 775 * \return #MBEDTLS_ERR_MPI_DIVISION_BY_ZERO if \p b equals zero. 776 * \return Another negative error code on different kinds of failure. 777 */ 778 int mbedtls_mpi_div_int( mbedtls_mpi *Q, mbedtls_mpi *R, const mbedtls_mpi *A, 779 mbedtls_mpi_sint b ); 780 781 /** 782 * \brief Perform a modular reduction. R = A mod B 783 * 784 * \param R The destination MPI for the residue value. 785 * This must point to an initialized MPI. 786 * \param A The MPI to compute the residue of. 787 * This must point to an initialized MPI. 788 * \param B The base of the modular reduction. 789 * This must point to an initialized MPI. 790 * 791 * \return \c 0 if successful. 792 * \return #MBEDTLS_ERR_MPI_ALLOC_FAILED if a memory allocation failed. 793 * \return #MBEDTLS_ERR_MPI_DIVISION_BY_ZERO if \p B equals zero. 794 * \return #MBEDTLS_ERR_MPI_NEGATIVE_VALUE if \p B is negative. 795 * \return Another negative error code on different kinds of failure. 796 * 797 */ 798 int mbedtls_mpi_mod_mpi( mbedtls_mpi *R, const mbedtls_mpi *A, 799 const mbedtls_mpi *B ); 800 801 /** 802 * \brief Perform a modular reduction with respect to an integer. 803 * r = A mod b 804 * 805 * \param r The address at which to store the residue. 806 * This must not be \c NULL. 807 * \param A The MPI to compute the residue of. 808 * This must point to an initialized MPi. 809 * \param b The integer base of the modular reduction. 810 * 811 * \return \c 0 if successful. 812 * \return #MBEDTLS_ERR_MPI_ALLOC_FAILED if a memory allocation failed. 813 * \return #MBEDTLS_ERR_MPI_DIVISION_BY_ZERO if \p b equals zero. 814 * \return #MBEDTLS_ERR_MPI_NEGATIVE_VALUE if \p b is negative. 815 * \return Another negative error code on different kinds of failure. 816 */ 817 int mbedtls_mpi_mod_int( mbedtls_mpi_uint *r, const mbedtls_mpi *A, 818 mbedtls_mpi_sint b ); 819 820 /** 821 * \brief Perform a sliding-window exponentiation: X = A^E mod N 822 * 823 * \param X The destination MPI. This must point to an initialized MPI. 824 * \param A The base of the exponentiation. 825 * This must point to an initialized MPI. 826 * \param E The exponent MPI. This must point to an initialized MPI. 827 * \param N The base for the modular reduction. This must point to an 828 * initialized MPI. 829 * \param _RR A helper MPI depending solely on \p N which can be used to 830 * speed-up multiple modular exponentiations for the same value 831 * of \p N. This may be \c NULL. If it is not \c NULL, it must 832 * point to an initialized MPI. If it hasn't been used after 833 * the call to mbedtls_mpi_init(), this function will compute 834 * the helper value and store it in \p _RR for reuse on 835 * subsequent calls to this function. Otherwise, the function 836 * will assume that \p _RR holds the helper value set by a 837 * previous call to mbedtls_mpi_exp_mod(), and reuse it. 838 * 839 * \return \c 0 if successful. 840 * \return #MBEDTLS_ERR_MPI_ALLOC_FAILED if a memory allocation failed. 841 * \return #MBEDTLS_ERR_MPI_BAD_INPUT_DATA if \c N is negative or 842 * even, or if \c E is negative. 843 * \return Another negative error code on different kinds of failures. 844 * 845 */ 846 int mbedtls_mpi_exp_mod( mbedtls_mpi *X, const mbedtls_mpi *A, 847 const mbedtls_mpi *E, const mbedtls_mpi *N, 848 mbedtls_mpi *_RR ); 849 850 /** 851 * \brief Fill an MPI with a number of random bytes. 852 * 853 * \param X The destination MPI. This must point to an initialized MPI. 854 * \param size The number of random bytes to generate. 855 * \param f_rng The RNG function to use. This must not be \c NULL. 856 * \param p_rng The RNG parameter to be passed to \p f_rng. This may be 857 * \c NULL if \p f_rng doesn't need a context argument. 858 * 859 * \return \c 0 if successful. 860 * \return #MBEDTLS_ERR_MPI_ALLOC_FAILED if a memory allocation failed. 861 * \return Another negative error code on failure. 862 * 863 * \note The bytes obtained from the RNG are interpreted 864 * as a big-endian representation of an MPI; this can 865 * be relevant in applications like deterministic ECDSA. 866 */ 867 int mbedtls_mpi_fill_random( mbedtls_mpi *X, size_t size, 868 int (*f_rng)(void *, unsigned char *, size_t), 869 void *p_rng ); 870 871 /** Generate a random number uniformly in a range. 872 * 873 * This function generates a random number between \p min inclusive and 874 * \p N exclusive. 875 * 876 * The procedure complies with RFC 6979 §3.3 (deterministic ECDSA) 877 * when the RNG is a suitably parametrized instance of HMAC_DRBG 878 * and \p min is \c 1. 879 * 880 * \note There are `N - min` possible outputs. The lower bound 881 * \p min can be reached, but the upper bound \p N cannot. 882 * 883 * \param X The destination MPI. This must point to an initialized MPI. 884 * \param min The minimum value to return. 885 * It must be nonnegative. 886 * \param N The upper bound of the range, exclusive. 887 * In other words, this is one plus the maximum value to return. 888 * \p N must be strictly larger than \p min. 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 * 892 * \return \c 0 if successful. 893 * \return #MBEDTLS_ERR_MPI_ALLOC_FAILED if a memory allocation failed. 894 * \return #MBEDTLS_ERR_MPI_BAD_INPUT_DATA if \p min or \p N is invalid 895 * or if they are incompatible. 896 * \return #MBEDTLS_ERR_MPI_NOT_ACCEPTABLE if the implementation was 897 * unable to find a suitable value within a limited number 898 * of attempts. This has a negligible probability if \p N 899 * is significantly larger than \p min, which is the case 900 * for all usual cryptographic applications. 901 * \return Another negative error code on failure. 902 */ 903 int mbedtls_mpi_random( mbedtls_mpi *X, 904 mbedtls_mpi_sint min, 905 const mbedtls_mpi *N, 906 int (*f_rng)(void *, unsigned char *, size_t), 907 void *p_rng ); 908 909 /** 910 * \brief Compute the greatest common divisor: G = gcd(A, B) 911 * 912 * \param G The destination MPI. This must point to an initialized MPI. 913 * \param A The first operand. This must point to an initialized MPI. 914 * \param B The second operand. This must point to an initialized MPI. 915 * 916 * \return \c 0 if successful. 917 * \return #MBEDTLS_ERR_MPI_ALLOC_FAILED if a memory allocation failed. 918 * \return Another negative error code on different kinds of failure. 919 */ 920 int mbedtls_mpi_gcd( mbedtls_mpi *G, const mbedtls_mpi *A, 921 const mbedtls_mpi *B ); 922 923 /** 924 * \brief Compute the modular inverse: X = A^-1 mod N 925 * 926 * \param X The destination MPI. This must point to an initialized MPI. 927 * \param A The MPI to calculate the modular inverse of. This must point 928 * to an initialized MPI. 929 * \param N The base of the modular inversion. This must point to an 930 * initialized MPI. 931 * 932 * \return \c 0 if successful. 933 * \return #MBEDTLS_ERR_MPI_ALLOC_FAILED if a memory allocation failed. 934 * \return #MBEDTLS_ERR_MPI_BAD_INPUT_DATA if \p N is less than 935 * or equal to one. 936 * \return #MBEDTLS_ERR_MPI_NOT_ACCEPTABLE if \p has no modular inverse 937 * with respect to \p N. 938 */ 939 int mbedtls_mpi_inv_mod( mbedtls_mpi *X, const mbedtls_mpi *A, 940 const mbedtls_mpi *N ); 941 942 /** 943 * \brief Miller-Rabin primality test. 944 * 945 * \warning If \p X is potentially generated by an adversary, for example 946 * when validating cryptographic parameters that you didn't 947 * generate yourself and that are supposed to be prime, then 948 * \p rounds should be at least the half of the security 949 * strength of the cryptographic algorithm. On the other hand, 950 * if \p X is chosen uniformly or non-adversially (as is the 951 * case when mbedtls_mpi_gen_prime calls this function), then 952 * \p rounds can be much lower. 953 * 954 * \param X The MPI to check for primality. 955 * This must point to an initialized MPI. 956 * \param rounds The number of bases to perform the Miller-Rabin primality 957 * test for. The probability of returning 0 on a composite is 958 * at most 2<sup>-2*\p rounds</sup>. 959 * \param f_rng The RNG function to use. This must not be \c NULL. 960 * \param p_rng The RNG parameter to be passed to \p f_rng. 961 * This may be \c NULL if \p f_rng doesn't use 962 * a context parameter. 963 * 964 * \return \c 0 if successful, i.e. \p X is probably prime. 965 * \return #MBEDTLS_ERR_MPI_ALLOC_FAILED if a memory allocation failed. 966 * \return #MBEDTLS_ERR_MPI_NOT_ACCEPTABLE if \p X is not prime. 967 * \return Another negative error code on other kinds of failure. 968 */ 969 int mbedtls_mpi_is_prime_ext( const mbedtls_mpi *X, int rounds, 970 int (*f_rng)(void *, unsigned char *, size_t), 971 void *p_rng ); 972 /** 973 * \brief Flags for mbedtls_mpi_gen_prime() 974 * 975 * Each of these flags is a constraint on the result X returned by 976 * mbedtls_mpi_gen_prime(). 977 */ 978 typedef enum { 979 MBEDTLS_MPI_GEN_PRIME_FLAG_DH = 0x0001, /**< (X-1)/2 is prime too */ 980 MBEDTLS_MPI_GEN_PRIME_FLAG_LOW_ERR = 0x0002, /**< lower error rate from 2<sup>-80</sup> to 2<sup>-128</sup> */ 981 } mbedtls_mpi_gen_prime_flag_t; 982 983 /** 984 * \brief Generate a prime number. 985 * 986 * \param X The destination MPI to store the generated prime in. 987 * This must point to an initialized MPi. 988 * \param nbits The required size of the destination MPI in bits. 989 * This must be between \c 3 and #MBEDTLS_MPI_MAX_BITS. 990 * \param flags A mask of flags of type #mbedtls_mpi_gen_prime_flag_t. 991 * \param f_rng The RNG function to use. This must not be \c NULL. 992 * \param p_rng The RNG parameter to be passed to \p f_rng. 993 * This may be \c NULL if \p f_rng doesn't use 994 * a context parameter. 995 * 996 * \return \c 0 if successful, in which case \p X holds a 997 * probably prime number. 998 * \return #MBEDTLS_ERR_MPI_ALLOC_FAILED if a memory allocation failed. 999 * \return #MBEDTLS_ERR_MPI_BAD_INPUT_DATA if `nbits` is not between 1000 * \c 3 and #MBEDTLS_MPI_MAX_BITS. 1001 */ 1002 int mbedtls_mpi_gen_prime( mbedtls_mpi *X, size_t nbits, int flags, 1003 int (*f_rng)(void *, unsigned char *, size_t), 1004 void *p_rng ); 1005 1006 #if defined(MBEDTLS_SELF_TEST) 1007 1008 /** 1009 * \brief Checkup routine 1010 * 1011 * \return 0 if successful, or 1 if the test failed 1012 */ 1013 int mbedtls_mpi_self_test( int verbose ); 1014 1015 #endif /* MBEDTLS_SELF_TEST */ 1016 1017 #ifdef __cplusplus 1018 } 1019 #endif 1020 1021 #endif /* bignum.h */ 1022
