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 /** An error occurred while reading from or writing to a file. */ 36 #define MBEDTLS_ERR_MPI_FILE_IO_ERROR -0x0002 37 /** Bad input parameters to function. */ 38 #define MBEDTLS_ERR_MPI_BAD_INPUT_DATA -0x0004 39 /** There is an invalid character in the digit string. */ 40 #define MBEDTLS_ERR_MPI_INVALID_CHARACTER -0x0006 41 /** The buffer is too small to write to. */ 42 #define MBEDTLS_ERR_MPI_BUFFER_TOO_SMALL -0x0008 43 /** The input arguments are negative or result in illegal output. */ 44 #define MBEDTLS_ERR_MPI_NEGATIVE_VALUE -0x000A 45 /** The input argument for division is zero, which is not allowed. */ 46 #define MBEDTLS_ERR_MPI_DIVISION_BY_ZERO -0x000C 47 /** The input arguments are not acceptable. */ 48 #define MBEDTLS_ERR_MPI_NOT_ACCEPTABLE -0x000E 49 /** Memory allocation failed. */ 50 #define MBEDTLS_ERR_MPI_ALLOC_FAILED -0x0010 51 52 #define MBEDTLS_MPI_CHK(f) \ 53 do \ 54 { \ 55 if( ( ret = (f) ) != 0 ) \ 56 goto cleanup; \ 57 } while( 0 ) 58 59 /* 60 * Maximum size MPIs are allowed to grow to in number of limbs. 61 */ 62 #define MBEDTLS_MPI_MAX_LIMBS 10000 63 64 #if !defined(MBEDTLS_MPI_WINDOW_SIZE) 65 /* 66 * Maximum window size used for modular exponentiation. Default: 6 67 * Minimum value: 1. Maximum value: 6. 68 * 69 * Result is an array of ( 2 ** MBEDTLS_MPI_WINDOW_SIZE ) MPIs used 70 * for the sliding window calculation. (So 64 by default) 71 * 72 * Reduction in size, reduces speed. 73 */ 74 #define MBEDTLS_MPI_WINDOW_SIZE 6 /**< Maximum window size used. */ 75 #endif /* !MBEDTLS_MPI_WINDOW_SIZE */ 76 77 #if !defined(MBEDTLS_MPI_MAX_SIZE) 78 /* 79 * Maximum size of MPIs allowed in bits and bytes for user-MPIs. 80 * ( Default: 512 bytes => 4096 bits, Maximum tested: 2048 bytes => 16384 bits ) 81 * 82 * Note: Calculations can temporarily result in larger MPIs. So the number 83 * of limbs required (MBEDTLS_MPI_MAX_LIMBS) is higher. 84 */ 85 #define MBEDTLS_MPI_MAX_SIZE 1024 /**< Maximum number of bytes for usable MPIs. */ 86 #endif /* !MBEDTLS_MPI_MAX_SIZE */ 87 88 #define MBEDTLS_MPI_MAX_BITS ( 8 * MBEDTLS_MPI_MAX_SIZE ) /**< Maximum number of bits for usable MPIs. */ 89 90 /* 91 * When reading from files with mbedtls_mpi_read_file() and writing to files with 92 * mbedtls_mpi_write_file() the buffer should have space 93 * for a (short) label, the MPI (in the provided radix), the newline 94 * characters and the '\0'. 95 * 96 * By default we assume at least a 10 char label, a minimum radix of 10 97 * (decimal) and a maximum of 4096 bit numbers (1234 decimal chars). 98 * Autosized at compile time for at least a 10 char label, a minimum radix 99 * of 10 (decimal) for a number of MBEDTLS_MPI_MAX_BITS size. 100 * 101 * This used to be statically sized to 1250 for a maximum of 4096 bit 102 * numbers (1234 decimal chars). 103 * 104 * Calculate using the formula: 105 * MBEDTLS_MPI_RW_BUFFER_SIZE = ceil(MBEDTLS_MPI_MAX_BITS / ln(10) * ln(2)) + 106 * LabelSize + 6 107 */ 108 #define MBEDTLS_MPI_MAX_BITS_SCALE100 ( 100 * MBEDTLS_MPI_MAX_BITS ) 109 #define MBEDTLS_LN_2_DIV_LN_10_SCALE100 332 110 #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 ) 111 112 /* 113 * Define the base integer type, architecture-wise. 114 * 115 * 32 or 64-bit integer types can be forced regardless of the underlying 116 * architecture by defining MBEDTLS_HAVE_INT32 or MBEDTLS_HAVE_INT64 117 * respectively and undefining MBEDTLS_HAVE_ASM. 118 * 119 * Double-width integers (e.g. 128-bit in 64-bit architectures) can be 120 * disabled by defining MBEDTLS_NO_UDBL_DIVISION. 121 */ 122 #if !defined(MBEDTLS_HAVE_INT32) 123 #if defined(_MSC_VER) && defined(_M_AMD64) 124 /* Always choose 64-bit when using MSC */ 125 #if !defined(MBEDTLS_HAVE_INT64) 126 #define MBEDTLS_HAVE_INT64 127 #endif /* !MBEDTLS_HAVE_INT64 */ 128 typedef int64_t mbedtls_mpi_sint; 129 typedef uint64_t mbedtls_mpi_uint; 130 #elif defined(__GNUC__) && ( \ 131 defined(__amd64__) || defined(__x86_64__) || \ 132 defined(__ppc64__) || defined(__powerpc64__) || \ 133 defined(__ia64__) || defined(__alpha__) || \ 134 ( defined(__sparc__) && defined(__arch64__) ) || \ 135 defined(__s390x__) || defined(__mips64) || \ 136 defined(__aarch64__) ) 137 #if !defined(MBEDTLS_HAVE_INT64) 138 #define MBEDTLS_HAVE_INT64 139 #endif /* MBEDTLS_HAVE_INT64 */ 140 typedef int64_t mbedtls_mpi_sint; 141 typedef uint64_t mbedtls_mpi_uint; 142 #if !defined(MBEDTLS_NO_UDBL_DIVISION) 143 /* mbedtls_t_udbl defined as 128-bit unsigned int */ 144 typedef unsigned int mbedtls_t_udbl __attribute__((mode(TI))); 145 #define MBEDTLS_HAVE_UDBL 146 #endif /* !MBEDTLS_NO_UDBL_DIVISION */ 147 #elif defined(__ARMCC_VERSION) && defined(__aarch64__) 148 /* 149 * __ARMCC_VERSION is defined for both armcc and armclang and 150 * __aarch64__ is only defined by armclang when compiling 64-bit code 151 */ 152 #if !defined(MBEDTLS_HAVE_INT64) 153 #define MBEDTLS_HAVE_INT64 154 #endif /* !MBEDTLS_HAVE_INT64 */ 155 typedef int64_t mbedtls_mpi_sint; 156 typedef uint64_t mbedtls_mpi_uint; 157 #if !defined(MBEDTLS_NO_UDBL_DIVISION) 158 /* mbedtls_t_udbl defined as 128-bit unsigned int */ 159 typedef __uint128_t mbedtls_t_udbl; 160 #define MBEDTLS_HAVE_UDBL 161 #endif /* !MBEDTLS_NO_UDBL_DIVISION */ 162 #elif defined(MBEDTLS_HAVE_INT64) 163 /* Force 64-bit integers with unknown compiler */ 164 typedef int64_t mbedtls_mpi_sint; 165 typedef uint64_t mbedtls_mpi_uint; 166 #endif 167 #endif /* !MBEDTLS_HAVE_INT32 */ 168 169 #if !defined(MBEDTLS_HAVE_INT64) 170 /* Default to 32-bit compilation */ 171 #if !defined(MBEDTLS_HAVE_INT32) 172 #define MBEDTLS_HAVE_INT32 173 #endif /* !MBEDTLS_HAVE_INT32 */ 174 typedef int32_t mbedtls_mpi_sint; 175 typedef uint32_t mbedtls_mpi_uint; 176 #if !defined(MBEDTLS_NO_UDBL_DIVISION) 177 typedef uint64_t mbedtls_t_udbl; 178 #define MBEDTLS_HAVE_UDBL 179 #endif /* !MBEDTLS_NO_UDBL_DIVISION */ 180 #endif /* !MBEDTLS_HAVE_INT64 */ 181 182 /** \typedef mbedtls_mpi_uint 183 * \brief The type of machine digits in a bignum, called _limbs_. 184 * 185 * This is always an unsigned integer type with no padding bits. The size 186 * is platform-dependent. 187 */ 188 189 /** \typedef mbedtls_mpi_sint 190 * \brief The signed type corresponding to #mbedtls_mpi_uint. 191 * 192 * This is always an signed integer type with no padding bits. The size 193 * is platform-dependent. 194 */ 195 196 #ifdef __cplusplus 197 extern "C" { 198 #endif 199 200 /** 201 * \brief MPI structure 202 */ 203 typedef struct mbedtls_mpi 204 { 205 /** Sign: -1 if the mpi is negative, 1 otherwise. 206 * 207 * The number 0 must be represented with `s = +1`. Although many library 208 * functions treat all-limbs-zero as equivalent to a valid representation 209 * of 0 regardless of the sign bit, there are exceptions, so bignum 210 * functions and external callers must always set \c s to +1 for the 211 * number zero. 212 * 213 * Note that this implies that calloc() or `... = {0}` does not create 214 * a valid MPI representation. You must call mbedtls_mpi_init(). 215 */ 216 int MBEDTLS_PRIVATE(s); 217 218 /** Total number of limbs in \c p. */ 219 size_t MBEDTLS_PRIVATE(n); 220 221 /** Pointer to limbs. 222 * 223 * This may be \c NULL if \c n is 0. 224 */ 225 mbedtls_mpi_uint *MBEDTLS_PRIVATE(p); 226 } 227 mbedtls_mpi; 228 229 /** 230 * \brief Initialize an MPI context. 231 * 232 * This makes the MPI ready to be set or freed, 233 * but does not define a value for the MPI. 234 * 235 * \param X The MPI context to initialize. This must not be \c NULL. 236 */ 237 void mbedtls_mpi_init( mbedtls_mpi *X ); 238 239 /** 240 * \brief This function frees the components of an MPI context. 241 * 242 * \param X The MPI context to be cleared. This may be \c NULL, 243 * in which case this function is a no-op. If it is 244 * not \c NULL, it must point to an initialized MPI. 245 */ 246 void mbedtls_mpi_free( mbedtls_mpi *X ); 247 248 /** 249 * \brief Enlarge an MPI to the specified number of limbs. 250 * 251 * \note This function does nothing if the MPI is 252 * already large enough. 253 * 254 * \param X The MPI to grow. It must be initialized. 255 * \param nblimbs The target number of limbs. 256 * 257 * \return \c 0 if successful. 258 * \return #MBEDTLS_ERR_MPI_ALLOC_FAILED if memory allocation failed. 259 * \return Another negative error code on other kinds of failure. 260 */ 261 int mbedtls_mpi_grow( mbedtls_mpi *X, size_t nblimbs ); 262 263 /** 264 * \brief This function resizes an MPI downwards, keeping at least the 265 * specified number of limbs. 266 * 267 * If \c X is smaller than \c nblimbs, it is resized up 268 * instead. 269 * 270 * \param X The MPI to shrink. This must point to an initialized MPI. 271 * \param nblimbs The minimum number of limbs to keep. 272 * 273 * \return \c 0 if successful. 274 * \return #MBEDTLS_ERR_MPI_ALLOC_FAILED if memory allocation failed 275 * (this can only happen when resizing up). 276 * \return Another negative error code on other kinds of failure. 277 */ 278 int mbedtls_mpi_shrink( mbedtls_mpi *X, size_t nblimbs ); 279 280 /** 281 * \brief Make a copy of an MPI. 282 * 283 * \param X The destination MPI. This must point to an initialized MPI. 284 * \param Y The source MPI. This must point to an initialized MPI. 285 * 286 * \note The limb-buffer in the destination MPI is enlarged 287 * if necessary to hold the value in the source MPI. 288 * 289 * \return \c 0 if successful. 290 * \return #MBEDTLS_ERR_MPI_ALLOC_FAILED if memory allocation failed. 291 * \return Another negative error code on other kinds of failure. 292 */ 293 int mbedtls_mpi_copy( mbedtls_mpi *X, const mbedtls_mpi *Y ); 294 295 /** 296 * \brief Swap the contents of two MPIs. 297 * 298 * \param X The first MPI. It must be initialized. 299 * \param Y The second MPI. It must be initialized. 300 */ 301 void mbedtls_mpi_swap( mbedtls_mpi *X, mbedtls_mpi *Y ); 302 303 /** 304 * \brief Perform a safe conditional copy of MPI which doesn't 305 * reveal whether the condition was true or not. 306 * 307 * \param X The MPI to conditionally assign to. This must point 308 * to an initialized MPI. 309 * \param Y The MPI to be assigned from. This must point to an 310 * initialized MPI. 311 * \param assign The condition deciding whether to perform the 312 * assignment or not. Must be either 0 or 1: 313 * * \c 1: Perform the assignment `X = Y`. 314 * * \c 0: Keep the original value of \p X. 315 * 316 * \note This function is equivalent to 317 * `if( assign ) mbedtls_mpi_copy( X, Y );` 318 * except that it avoids leaking any information about whether 319 * the assignment was done or not (the above code may leak 320 * information through branch prediction and/or memory access 321 * patterns analysis). 322 * 323 * \warning If \p assign is neither 0 nor 1, the result of this function 324 * is indeterminate, and the resulting value in \p X might be 325 * neither its original value nor the value in \p Y. 326 * 327 * \return \c 0 if successful. 328 * \return #MBEDTLS_ERR_MPI_ALLOC_FAILED if memory allocation failed. 329 * \return Another negative error code on other kinds of failure. 330 */ 331 int mbedtls_mpi_safe_cond_assign( mbedtls_mpi *X, const mbedtls_mpi *Y, unsigned char assign ); 332 333 /** 334 * \brief Perform a safe conditional swap which doesn't 335 * reveal whether the condition was true or not. 336 * 337 * \param X The first MPI. This must be initialized. 338 * \param Y The second MPI. This must be initialized. 339 * \param swap The condition deciding whether to perform 340 * the swap or not. Must be either 0 or 1: 341 * * \c 1: Swap the values of \p X and \p Y. 342 * * \c 0: Keep the original values of \p X and \p Y. 343 * 344 * \note This function is equivalent to 345 * if( swap ) mbedtls_mpi_swap( X, Y ); 346 * except that it avoids leaking any information about whether 347 * the swap was done or not (the above code may leak 348 * information through branch prediction and/or memory access 349 * patterns analysis). 350 * 351 * \warning If \p swap is neither 0 nor 1, the result of this function 352 * is indeterminate, and both \p X and \p Y might end up with 353 * values different to either of the original ones. 354 * 355 * \return \c 0 if successful. 356 * \return #MBEDTLS_ERR_MPI_ALLOC_FAILED if memory allocation failed. 357 * \return Another negative error code on other kinds of failure. 358 * 359 */ 360 int mbedtls_mpi_safe_cond_swap( mbedtls_mpi *X, mbedtls_mpi *Y, unsigned char swap ); 361 362 /** 363 * \brief Store integer value in MPI. 364 * 365 * \param X The MPI to set. This must be initialized. 366 * \param z The value to use. 367 * 368 * \return \c 0 if successful. 369 * \return #MBEDTLS_ERR_MPI_ALLOC_FAILED if memory allocation failed. 370 * \return Another negative error code on other kinds of failure. 371 */ 372 int mbedtls_mpi_lset( mbedtls_mpi *X, mbedtls_mpi_sint z ); 373 374 /** 375 * \brief Get a specific bit from an MPI. 376 * 377 * \param X The MPI to query. This must be initialized. 378 * \param pos Zero-based index of the bit to query. 379 * 380 * \return \c 0 or \c 1 on success, depending on whether bit \c pos 381 * of \c X is unset or set. 382 * \return A negative error code on failure. 383 */ 384 int mbedtls_mpi_get_bit( const mbedtls_mpi *X, size_t pos ); 385 386 /** 387 * \brief Modify a specific bit in an MPI. 388 * 389 * \note This function will grow the target MPI if necessary to set a 390 * bit to \c 1 in a not yet existing limb. It will not grow if 391 * the bit should be set to \c 0. 392 * 393 * \param X The MPI to modify. This must be initialized. 394 * \param pos Zero-based index of the bit to modify. 395 * \param val The desired value of bit \c pos: \c 0 or \c 1. 396 * 397 * \return \c 0 if successful. 398 * \return #MBEDTLS_ERR_MPI_ALLOC_FAILED if memory allocation failed. 399 * \return Another negative error code on other kinds of failure. 400 */ 401 int mbedtls_mpi_set_bit( mbedtls_mpi *X, size_t pos, unsigned char val ); 402 403 /** 404 * \brief Return the number of bits of value \c 0 before the 405 * least significant bit of value \c 1. 406 * 407 * \note This is the same as the zero-based index of 408 * the least significant bit of value \c 1. 409 * 410 * \param X The MPI to query. 411 * 412 * \return The number of bits of value \c 0 before the least significant 413 * bit of value \c 1 in \p X. 414 */ 415 size_t mbedtls_mpi_lsb( const mbedtls_mpi *X ); 416 417 /** 418 * \brief Return the number of bits up to and including the most 419 * significant bit of value \c 1. 420 * 421 * * \note This is same as the one-based index of the most 422 * significant bit of value \c 1. 423 * 424 * \param X The MPI to query. This must point to an initialized MPI. 425 * 426 * \return The number of bits up to and including the most 427 * significant bit of value \c 1. 428 */ 429 size_t mbedtls_mpi_bitlen( const mbedtls_mpi *X ); 430 431 /** 432 * \brief Return the total size of an MPI value in bytes. 433 * 434 * \param X The MPI to use. This must point to an initialized MPI. 435 * 436 * \note The value returned by this function may be less than 437 * the number of bytes used to store \p X internally. 438 * This happens if and only if there are trailing bytes 439 * of value zero. 440 * 441 * \return The least number of bytes capable of storing 442 * the absolute value of \p X. 443 */ 444 size_t mbedtls_mpi_size( const mbedtls_mpi *X ); 445 446 /** 447 * \brief Import an MPI from an ASCII string. 448 * 449 * \param X The destination MPI. This must point to an initialized MPI. 450 * \param radix The numeric base of the input string. 451 * \param s Null-terminated string buffer. 452 * 453 * \return \c 0 if successful. 454 * \return A negative error code on failure. 455 */ 456 int mbedtls_mpi_read_string( mbedtls_mpi *X, int radix, const char *s ); 457 458 /** 459 * \brief Export an MPI to an ASCII string. 460 * 461 * \param X The source MPI. This must point to an initialized MPI. 462 * \param radix The numeric base of the output string. 463 * \param buf The buffer to write the string to. This must be writable 464 * buffer of length \p buflen Bytes. 465 * \param buflen The available size in Bytes of \p buf. 466 * \param olen The address at which to store the length of the string 467 * written, including the final \c NULL byte. This must 468 * not be \c NULL. 469 * 470 * \note You can call this function with `buflen == 0` to obtain the 471 * minimum required buffer size in `*olen`. 472 * 473 * \return \c 0 if successful. 474 * \return #MBEDTLS_ERR_MPI_BUFFER_TOO_SMALL if the target buffer \p buf 475 * is too small to hold the value of \p X in the desired base. 476 * In this case, `*olen` is nonetheless updated to contain the 477 * size of \p buf required for a successful call. 478 * \return Another negative error code on different kinds of failure. 479 */ 480 int mbedtls_mpi_write_string( const mbedtls_mpi *X, int radix, 481 char *buf, size_t buflen, size_t *olen ); 482 483 #if defined(MBEDTLS_FS_IO) 484 /** 485 * \brief Read an MPI from a line in an opened file. 486 * 487 * \param X The destination MPI. This must point to an initialized MPI. 488 * \param radix The numeric base of the string representation used 489 * in the source line. 490 * \param fin The input file handle to use. This must not be \c NULL. 491 * 492 * \note On success, this function advances the file stream 493 * to the end of the current line or to EOF. 494 * 495 * The function returns \c 0 on an empty line. 496 * 497 * Leading whitespaces are ignored, as is a 498 * '0x' prefix for radix \c 16. 499 * 500 * \return \c 0 if successful. 501 * \return #MBEDTLS_ERR_MPI_BUFFER_TOO_SMALL if the file read buffer 502 * is too small. 503 * \return Another negative error code on failure. 504 */ 505 int mbedtls_mpi_read_file( mbedtls_mpi *X, int radix, FILE *fin ); 506 507 /** 508 * \brief Export an MPI into an opened file. 509 * 510 * \param p A string prefix to emit prior to the MPI data. 511 * For example, this might be a label, or "0x" when 512 * printing in base \c 16. This may be \c NULL if no prefix 513 * is needed. 514 * \param X The source MPI. This must point to an initialized MPI. 515 * \param radix The numeric base to be used in the emitted string. 516 * \param fout The output file handle. This may be \c NULL, in which case 517 * the output is written to \c stdout. 518 * 519 * \return \c 0 if successful. 520 * \return A negative error code on failure. 521 */ 522 int mbedtls_mpi_write_file( const char *p, const mbedtls_mpi *X, 523 int radix, FILE *fout ); 524 #endif /* MBEDTLS_FS_IO */ 525 526 /** 527 * \brief Import an MPI from unsigned big endian binary data. 528 * 529 * \param X The destination MPI. This must point to an initialized MPI. 530 * \param buf The input buffer. This must be a readable buffer of length 531 * \p buflen Bytes. 532 * \param buflen The length of the input buffer \p p in Bytes. 533 * 534 * \return \c 0 if successful. 535 * \return #MBEDTLS_ERR_MPI_ALLOC_FAILED if memory allocation failed. 536 * \return Another negative error code on different kinds of failure. 537 */ 538 int mbedtls_mpi_read_binary( mbedtls_mpi *X, const unsigned char *buf, 539 size_t buflen ); 540 541 /** 542 * \brief Import X from unsigned binary data, little endian 543 * 544 * \param X The destination MPI. This must point to an initialized MPI. 545 * \param buf The input buffer. This must be a readable buffer of length 546 * \p buflen Bytes. 547 * \param buflen The length of the input buffer \p p in Bytes. 548 * 549 * \return \c 0 if successful. 550 * \return #MBEDTLS_ERR_MPI_ALLOC_FAILED if memory allocation failed. 551 * \return Another negative error code on different kinds of failure. 552 */ 553 int mbedtls_mpi_read_binary_le( mbedtls_mpi *X, 554 const unsigned char *buf, size_t buflen ); 555 556 /** 557 * \brief Export X into unsigned binary data, big endian. 558 * Always fills the whole buffer, which will start with zeros 559 * if the number is smaller. 560 * 561 * \param X The source MPI. This must point to an initialized MPI. 562 * \param buf The output buffer. This must be a writable buffer of length 563 * \p buflen Bytes. 564 * \param buflen The size of the output buffer \p buf in Bytes. 565 * 566 * \return \c 0 if successful. 567 * \return #MBEDTLS_ERR_MPI_BUFFER_TOO_SMALL if \p buf isn't 568 * large enough to hold the value of \p X. 569 * \return Another negative error code on different kinds of failure. 570 */ 571 int mbedtls_mpi_write_binary( const mbedtls_mpi *X, unsigned char *buf, 572 size_t buflen ); 573 574 /** 575 * \brief Export X into unsigned binary data, little endian. 576 * Always fills the whole buffer, which will end with zeros 577 * if the number is smaller. 578 * 579 * \param X The source MPI. This must point to an initialized MPI. 580 * \param buf The output buffer. This must be a writable buffer of length 581 * \p buflen Bytes. 582 * \param buflen The size of the output buffer \p buf in Bytes. 583 * 584 * \return \c 0 if successful. 585 * \return #MBEDTLS_ERR_MPI_BUFFER_TOO_SMALL if \p buf isn't 586 * large enough to hold the value of \p X. 587 * \return Another negative error code on different kinds of failure. 588 */ 589 int mbedtls_mpi_write_binary_le( const mbedtls_mpi *X, 590 unsigned char *buf, size_t buflen ); 591 592 /** 593 * \brief Perform a left-shift on an MPI: X <<= count 594 * 595 * \param X The MPI to shift. This must point to an initialized MPI. 596 * \param count The number of bits to shift by. 597 * 598 * \return \c 0 if successful. 599 * \return #MBEDTLS_ERR_MPI_ALLOC_FAILED if a memory allocation failed. 600 * \return Another negative error code on different kinds of failure. 601 */ 602 int mbedtls_mpi_shift_l( mbedtls_mpi *X, size_t count ); 603 604 /** 605 * \brief Perform a right-shift on an MPI: X >>= count 606 * 607 * \param X The MPI to shift. This must point to an initialized MPI. 608 * \param count The number of bits to shift by. 609 * 610 * \return \c 0 if successful. 611 * \return #MBEDTLS_ERR_MPI_ALLOC_FAILED if a memory allocation failed. 612 * \return Another negative error code on different kinds of failure. 613 */ 614 int mbedtls_mpi_shift_r( mbedtls_mpi *X, size_t count ); 615 616 /** 617 * \brief Compare the absolute values of two MPIs. 618 * 619 * \param X The left-hand MPI. This must point to an initialized MPI. 620 * \param Y The right-hand MPI. This must point to an initialized MPI. 621 * 622 * \return \c 1 if `|X|` is greater than `|Y|`. 623 * \return \c -1 if `|X|` is lesser than `|Y|`. 624 * \return \c 0 if `|X|` is equal to `|Y|`. 625 */ 626 int mbedtls_mpi_cmp_abs( const mbedtls_mpi *X, const mbedtls_mpi *Y ); 627 628 /** 629 * \brief Compare two MPIs. 630 * 631 * \param X The left-hand MPI. This must point to an initialized MPI. 632 * \param Y The right-hand MPI. This must point to an initialized MPI. 633 * 634 * \return \c 1 if \p X is greater than \p Y. 635 * \return \c -1 if \p X is lesser than \p Y. 636 * \return \c 0 if \p X is equal to \p Y. 637 */ 638 int mbedtls_mpi_cmp_mpi( const mbedtls_mpi *X, const mbedtls_mpi *Y ); 639 640 /** 641 * \brief Check if an MPI is less than the other in constant time. 642 * 643 * \param X The left-hand MPI. This must point to an initialized MPI 644 * with the same allocated length as Y. 645 * \param Y The right-hand MPI. This must point to an initialized MPI 646 * with the same allocated length as X. 647 * \param ret The result of the comparison: 648 * \c 1 if \p X is less than \p Y. 649 * \c 0 if \p X is greater than or equal to \p Y. 650 * 651 * \return 0 on success. 652 * \return MBEDTLS_ERR_MPI_BAD_INPUT_DATA if the allocated length of 653 * the two input MPIs is not the same. 654 */ 655 int mbedtls_mpi_lt_mpi_ct( const mbedtls_mpi *X, const mbedtls_mpi *Y, 656 unsigned *ret ); 657 658 /** 659 * \brief Compare an MPI with an integer. 660 * 661 * \param X The left-hand MPI. This must point to an initialized MPI. 662 * \param z The integer value to compare \p X to. 663 * 664 * \return \c 1 if \p X is greater than \p z. 665 * \return \c -1 if \p X is lesser than \p z. 666 * \return \c 0 if \p X is equal to \p z. 667 */ 668 int mbedtls_mpi_cmp_int( const mbedtls_mpi *X, mbedtls_mpi_sint z ); 669 670 /** 671 * \brief Perform an unsigned addition of MPIs: X = |A| + |B| 672 * 673 * \param X The destination MPI. This must point to an initialized MPI. 674 * \param A The first summand. This must point to an initialized MPI. 675 * \param B The second summand. This must point to an initialized MPI. 676 * 677 * \return \c 0 if successful. 678 * \return #MBEDTLS_ERR_MPI_ALLOC_FAILED if a memory allocation failed. 679 * \return Another negative error code on different kinds of failure. 680 */ 681 int mbedtls_mpi_add_abs( mbedtls_mpi *X, const mbedtls_mpi *A, 682 const mbedtls_mpi *B ); 683 684 /** 685 * \brief Perform an unsigned subtraction of MPIs: X = |A| - |B| 686 * 687 * \param X The destination MPI. This must point to an initialized MPI. 688 * \param A The minuend. This must point to an initialized MPI. 689 * \param B The subtrahend. This must point to an initialized MPI. 690 * 691 * \return \c 0 if successful. 692 * \return #MBEDTLS_ERR_MPI_NEGATIVE_VALUE if \p B is greater than \p A. 693 * \return Another negative error code on different kinds of failure. 694 * 695 */ 696 int mbedtls_mpi_sub_abs( mbedtls_mpi *X, const mbedtls_mpi *A, 697 const mbedtls_mpi *B ); 698 699 /** 700 * \brief Perform a signed addition of MPIs: X = A + B 701 * 702 * \param X The destination MPI. This must point to an initialized MPI. 703 * \param A The first summand. This must point to an initialized MPI. 704 * \param B The second summand. This must point to an initialized MPI. 705 * 706 * \return \c 0 if successful. 707 * \return #MBEDTLS_ERR_MPI_ALLOC_FAILED if a memory allocation failed. 708 * \return Another negative error code on different kinds of failure. 709 */ 710 int mbedtls_mpi_add_mpi( mbedtls_mpi *X, const mbedtls_mpi *A, 711 const mbedtls_mpi *B ); 712 713 /** 714 * \brief Perform a signed subtraction of MPIs: X = A - B 715 * 716 * \param X The destination MPI. This must point to an initialized MPI. 717 * \param A The minuend. This must point to an initialized MPI. 718 * \param B The subtrahend. This must point to an initialized MPI. 719 * 720 * \return \c 0 if successful. 721 * \return #MBEDTLS_ERR_MPI_ALLOC_FAILED if a memory allocation failed. 722 * \return Another negative error code on different kinds of failure. 723 */ 724 int mbedtls_mpi_sub_mpi( mbedtls_mpi *X, const mbedtls_mpi *A, 725 const mbedtls_mpi *B ); 726 727 /** 728 * \brief Perform a signed addition of an MPI and an integer: X = A + b 729 * 730 * \param X The destination MPI. This must point to an initialized MPI. 731 * \param A The first summand. This must point to an initialized MPI. 732 * \param b The second summand. 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 int mbedtls_mpi_add_int( mbedtls_mpi *X, const mbedtls_mpi *A, 739 mbedtls_mpi_sint b ); 740 741 /** 742 * \brief Perform a signed subtraction of an MPI and an integer: 743 * X = A - b 744 * 745 * \param X The destination MPI. This must point to an initialized MPI. 746 * \param A The minuend. This must point to an initialized MPI. 747 * \param b The subtrahend. 748 * 749 * \return \c 0 if successful. 750 * \return #MBEDTLS_ERR_MPI_ALLOC_FAILED if a memory allocation failed. 751 * \return Another negative error code on different kinds of failure. 752 */ 753 int mbedtls_mpi_sub_int( mbedtls_mpi *X, const mbedtls_mpi *A, 754 mbedtls_mpi_sint b ); 755 756 /** 757 * \brief Perform a multiplication of two MPIs: X = A * B 758 * 759 * \param X The destination MPI. This must point to an initialized MPI. 760 * \param A The first factor. This must point to an initialized MPI. 761 * \param B The second factor. This must point to an initialized MPI. 762 * 763 * \return \c 0 if successful. 764 * \return #MBEDTLS_ERR_MPI_ALLOC_FAILED if a memory allocation failed. 765 * \return Another negative error code on different kinds of failure. 766 * 767 */ 768 int mbedtls_mpi_mul_mpi( mbedtls_mpi *X, const mbedtls_mpi *A, 769 const mbedtls_mpi *B ); 770 771 /** 772 * \brief Perform a multiplication of an MPI with an unsigned integer: 773 * X = A * b 774 * 775 * \param X The destination MPI. This must point to an initialized MPI. 776 * \param A The first factor. This must point to an initialized MPI. 777 * \param b The second factor. 778 * 779 * \return \c 0 if successful. 780 * \return #MBEDTLS_ERR_MPI_ALLOC_FAILED if a memory allocation failed. 781 * \return Another negative error code on different kinds of failure. 782 * 783 */ 784 int mbedtls_mpi_mul_int( mbedtls_mpi *X, const mbedtls_mpi *A, 785 mbedtls_mpi_uint b ); 786 787 /** 788 * \brief Perform a division with remainder of two MPIs: 789 * A = Q * B + R 790 * 791 * \param Q The destination MPI for the quotient. 792 * This may be \c NULL if the value of the 793 * quotient is not needed. This must not alias A or B. 794 * \param R The destination MPI for the remainder value. 795 * This may be \c NULL if the value of the 796 * remainder is not needed. This must not alias A or B. 797 * \param A The dividend. This must point to an initialized MPI. 798 * \param B The divisor. This must point to an initialized MPI. 799 * 800 * \return \c 0 if successful. 801 * \return #MBEDTLS_ERR_MPI_ALLOC_FAILED if memory allocation failed. 802 * \return #MBEDTLS_ERR_MPI_DIVISION_BY_ZERO if \p B equals zero. 803 * \return Another negative error code on different kinds of failure. 804 */ 805 int mbedtls_mpi_div_mpi( mbedtls_mpi *Q, mbedtls_mpi *R, const mbedtls_mpi *A, 806 const mbedtls_mpi *B ); 807 808 /** 809 * \brief Perform a division with remainder of an MPI by an integer: 810 * A = Q * b + R 811 * 812 * \param Q The destination MPI for the quotient. 813 * This may be \c NULL if the value of the 814 * quotient is not needed. This must not alias A. 815 * \param R The destination MPI for the remainder value. 816 * This may be \c NULL if the value of the 817 * remainder is not needed. This must not alias A. 818 * \param A The dividend. This must point to an initialized MPi. 819 * \param b The divisor. 820 * 821 * \return \c 0 if successful. 822 * \return #MBEDTLS_ERR_MPI_ALLOC_FAILED if memory allocation failed. 823 * \return #MBEDTLS_ERR_MPI_DIVISION_BY_ZERO if \p b equals zero. 824 * \return Another negative error code on different kinds of failure. 825 */ 826 int mbedtls_mpi_div_int( mbedtls_mpi *Q, mbedtls_mpi *R, const mbedtls_mpi *A, 827 mbedtls_mpi_sint b ); 828 829 /** 830 * \brief Perform a modular reduction. R = A mod B 831 * 832 * \param R The destination MPI for the residue value. 833 * This must point to an initialized MPI. 834 * \param A The MPI to compute the residue of. 835 * This must point to an initialized MPI. 836 * \param B The base of the modular reduction. 837 * This must point to an initialized MPI. 838 * 839 * \return \c 0 if successful. 840 * \return #MBEDTLS_ERR_MPI_ALLOC_FAILED if a memory allocation failed. 841 * \return #MBEDTLS_ERR_MPI_DIVISION_BY_ZERO if \p B equals zero. 842 * \return #MBEDTLS_ERR_MPI_NEGATIVE_VALUE if \p B is negative. 843 * \return Another negative error code on different kinds of failure. 844 * 845 */ 846 int mbedtls_mpi_mod_mpi( mbedtls_mpi *R, const mbedtls_mpi *A, 847 const mbedtls_mpi *B ); 848 849 /** 850 * \brief Perform a modular reduction with respect to an integer. 851 * r = A mod b 852 * 853 * \param r The address at which to store the residue. 854 * This must not be \c NULL. 855 * \param A The MPI to compute the residue of. 856 * This must point to an initialized MPi. 857 * \param b The integer base of the modular reduction. 858 * 859 * \return \c 0 if successful. 860 * \return #MBEDTLS_ERR_MPI_ALLOC_FAILED if a memory allocation failed. 861 * \return #MBEDTLS_ERR_MPI_DIVISION_BY_ZERO if \p b equals zero. 862 * \return #MBEDTLS_ERR_MPI_NEGATIVE_VALUE if \p b is negative. 863 * \return Another negative error code on different kinds of failure. 864 */ 865 int mbedtls_mpi_mod_int( mbedtls_mpi_uint *r, const mbedtls_mpi *A, 866 mbedtls_mpi_sint b ); 867 868 /** 869 * \brief Perform a sliding-window exponentiation: X = A^E mod N 870 * 871 * \param X The destination MPI. This must point to an initialized MPI. 872 * This must not alias E or N. 873 * \param A The base of the exponentiation. 874 * This must point to an initialized MPI. 875 * \param E The exponent MPI. This must point to an initialized MPI. 876 * \param N The base for the modular reduction. This must point to an 877 * initialized MPI. 878 * \param prec_RR A helper MPI depending solely on \p N which can be used to 879 * speed-up multiple modular exponentiations for the same value 880 * of \p N. This may be \c NULL. If it is not \c NULL, it must 881 * point to an initialized MPI. If it hasn't been used after 882 * the call to mbedtls_mpi_init(), this function will compute 883 * the helper value and store it in \p prec_RR for reuse on 884 * subsequent calls to this function. Otherwise, the function 885 * will assume that \p prec_RR holds the helper value set by a 886 * previous call to mbedtls_mpi_exp_mod(), and reuse it. 887 * 888 * \return \c 0 if successful. 889 * \return #MBEDTLS_ERR_MPI_ALLOC_FAILED if a memory allocation failed. 890 * \return #MBEDTLS_ERR_MPI_BAD_INPUT_DATA if \c N is negative or 891 * even, or if \c E is negative. 892 * \return Another negative error code on different kinds of failures. 893 * 894 */ 895 int mbedtls_mpi_exp_mod( mbedtls_mpi *X, const mbedtls_mpi *A, 896 const mbedtls_mpi *E, const mbedtls_mpi *N, 897 mbedtls_mpi *prec_RR ); 898 899 /** 900 * \brief Fill an MPI with a number of random bytes. 901 * 902 * \param X The destination MPI. This must point to an initialized MPI. 903 * \param size The number of random bytes to generate. 904 * \param f_rng The RNG function to use. This must not be \c NULL. 905 * \param p_rng The RNG parameter to be passed to \p f_rng. This may be 906 * \c NULL if \p f_rng doesn't need a context argument. 907 * 908 * \return \c 0 if successful. 909 * \return #MBEDTLS_ERR_MPI_ALLOC_FAILED if a memory allocation failed. 910 * \return Another negative error code on failure. 911 * 912 * \note The bytes obtained from the RNG are interpreted 913 * as a big-endian representation of an MPI; this can 914 * be relevant in applications like deterministic ECDSA. 915 */ 916 int mbedtls_mpi_fill_random( mbedtls_mpi *X, size_t size, 917 int (*f_rng)(void *, unsigned char *, size_t), 918 void *p_rng ); 919 920 /** Generate a random number uniformly in a range. 921 * 922 * This function generates a random number between \p min inclusive and 923 * \p N exclusive. 924 * 925 * The procedure complies with RFC 6979 §3.3 (deterministic ECDSA) 926 * when the RNG is a suitably parametrized instance of HMAC_DRBG 927 * and \p min is \c 1. 928 * 929 * \note There are `N - min` possible outputs. The lower bound 930 * \p min can be reached, but the upper bound \p N cannot. 931 * 932 * \param X The destination MPI. This must point to an initialized MPI. 933 * \param min The minimum value to return. 934 * It must be nonnegative. 935 * \param N The upper bound of the range, exclusive. 936 * In other words, this is one plus the maximum value to return. 937 * \p N must be strictly larger than \p min. 938 * \param f_rng The RNG function to use. This must not be \c NULL. 939 * \param p_rng The RNG parameter to be passed to \p f_rng. 940 * 941 * \return \c 0 if successful. 942 * \return #MBEDTLS_ERR_MPI_ALLOC_FAILED if a memory allocation failed. 943 * \return #MBEDTLS_ERR_MPI_BAD_INPUT_DATA if \p min or \p N is invalid 944 * or if they are incompatible. 945 * \return #MBEDTLS_ERR_MPI_NOT_ACCEPTABLE if the implementation was 946 * unable to find a suitable value within a limited number 947 * of attempts. This has a negligible probability if \p N 948 * is significantly larger than \p min, which is the case 949 * for all usual cryptographic applications. 950 * \return Another negative error code on failure. 951 */ 952 int mbedtls_mpi_random( mbedtls_mpi *X, 953 mbedtls_mpi_sint min, 954 const mbedtls_mpi *N, 955 int (*f_rng)(void *, unsigned char *, size_t), 956 void *p_rng ); 957 958 /** 959 * \brief Compute the greatest common divisor: G = gcd(A, B) 960 * 961 * \param G The destination MPI. This must point to an initialized MPI. 962 * \param A The first operand. This must point to an initialized MPI. 963 * \param B The second operand. This must point to an initialized MPI. 964 * 965 * \return \c 0 if successful. 966 * \return #MBEDTLS_ERR_MPI_ALLOC_FAILED if a memory allocation failed. 967 * \return Another negative error code on different kinds of failure. 968 */ 969 int mbedtls_mpi_gcd( mbedtls_mpi *G, const mbedtls_mpi *A, 970 const mbedtls_mpi *B ); 971 972 /** 973 * \brief Compute the modular inverse: X = A^-1 mod N 974 * 975 * \param X The destination MPI. This must point to an initialized MPI. 976 * \param A The MPI to calculate the modular inverse of. This must point 977 * to an initialized MPI. 978 * \param N The base of the modular inversion. This must point to an 979 * initialized MPI. 980 * 981 * \return \c 0 if successful. 982 * \return #MBEDTLS_ERR_MPI_ALLOC_FAILED if a memory allocation failed. 983 * \return #MBEDTLS_ERR_MPI_BAD_INPUT_DATA if \p N is less than 984 * or equal to one. 985 * \return #MBEDTLS_ERR_MPI_NOT_ACCEPTABLE if \p has no modular inverse 986 * with respect to \p N. 987 */ 988 int mbedtls_mpi_inv_mod( mbedtls_mpi *X, const mbedtls_mpi *A, 989 const mbedtls_mpi *N ); 990 991 /** 992 * \brief Miller-Rabin primality test. 993 * 994 * \warning If \p X is potentially generated by an adversary, for example 995 * when validating cryptographic parameters that you didn't 996 * generate yourself and that are supposed to be prime, then 997 * \p rounds should be at least the half of the security 998 * strength of the cryptographic algorithm. On the other hand, 999 * if \p X is chosen uniformly or non-adversarially (as is the 1000 * case when mbedtls_mpi_gen_prime calls this function), then 1001 * \p rounds can be much lower. 1002 * 1003 * \param X The MPI to check for primality. 1004 * This must point to an initialized MPI. 1005 * \param rounds The number of bases to perform the Miller-Rabin primality 1006 * test for. The probability of returning 0 on a composite is 1007 * at most 2<sup>-2*\p rounds</sup>. 1008 * \param f_rng The RNG function to use. This must not be \c NULL. 1009 * \param p_rng The RNG parameter to be passed to \p f_rng. 1010 * This may be \c NULL if \p f_rng doesn't use 1011 * a context parameter. 1012 * 1013 * \return \c 0 if successful, i.e. \p X is probably prime. 1014 * \return #MBEDTLS_ERR_MPI_ALLOC_FAILED if a memory allocation failed. 1015 * \return #MBEDTLS_ERR_MPI_NOT_ACCEPTABLE if \p X is not prime. 1016 * \return Another negative error code on other kinds of failure. 1017 */ 1018 int mbedtls_mpi_is_prime_ext( const mbedtls_mpi *X, int rounds, 1019 int (*f_rng)(void *, unsigned char *, size_t), 1020 void *p_rng ); 1021 /** 1022 * \brief Flags for mbedtls_mpi_gen_prime() 1023 * 1024 * Each of these flags is a constraint on the result X returned by 1025 * mbedtls_mpi_gen_prime(). 1026 */ 1027 typedef enum { 1028 MBEDTLS_MPI_GEN_PRIME_FLAG_DH = 0x0001, /**< (X-1)/2 is prime too */ 1029 MBEDTLS_MPI_GEN_PRIME_FLAG_LOW_ERR = 0x0002, /**< lower error rate from 2<sup>-80</sup> to 2<sup>-128</sup> */ 1030 } mbedtls_mpi_gen_prime_flag_t; 1031 1032 /** 1033 * \brief Generate a prime number. 1034 * 1035 * \param X The destination MPI to store the generated prime in. 1036 * This must point to an initialized MPi. 1037 * \param nbits The required size of the destination MPI in bits. 1038 * This must be between \c 3 and #MBEDTLS_MPI_MAX_BITS. 1039 * \param flags A mask of flags of type #mbedtls_mpi_gen_prime_flag_t. 1040 * \param f_rng The RNG function to use. This must not be \c NULL. 1041 * \param p_rng The RNG parameter to be passed to \p f_rng. 1042 * This may be \c NULL if \p f_rng doesn't use 1043 * a context parameter. 1044 * 1045 * \return \c 0 if successful, in which case \p X holds a 1046 * probably prime number. 1047 * \return #MBEDTLS_ERR_MPI_ALLOC_FAILED if a memory allocation failed. 1048 * \return #MBEDTLS_ERR_MPI_BAD_INPUT_DATA if `nbits` is not between 1049 * \c 3 and #MBEDTLS_MPI_MAX_BITS. 1050 */ 1051 int mbedtls_mpi_gen_prime( mbedtls_mpi *X, size_t nbits, int flags, 1052 int (*f_rng)(void *, unsigned char *, size_t), 1053 void *p_rng ); 1054 1055 #if defined(MBEDTLS_SELF_TEST) 1056 1057 /** 1058 * \brief Checkup routine 1059 * 1060 * \return 0 if successful, or 1 if the test failed 1061 */ 1062 int mbedtls_mpi_self_test( int verbose ); 1063 1064 #endif /* MBEDTLS_SELF_TEST */ 1065 1066 #ifdef __cplusplus 1067 } 1068 #endif 1069 1070 #endif /* bignum.h */ 1071
