| 1 | /** |
| 2 | * \file bignum.h |
| 3 | * |
| 4 | * \brief Multi-precision integer library |
| 5 | */ |
| 6 | /* |
| 7 | * Copyright (C) 2006-2015, ARM Limited, All Rights Reserved |
| 8 | * SPDX-License-Identifier: GPL-2.0 |
| 9 | * |
| 10 | * This program is free software; you can redistribute it and/or modify |
| 11 | * it under the terms of the GNU General Public License as published by |
| 12 | * the Free Software Foundation; either version 2 of the License, or |
| 13 | * (at your option) any later version. |
| 14 | * |
| 15 | * This program is distributed in the hope that it will be useful, |
| 16 | * but WITHOUT ANY WARRANTY; without even the implied warranty of |
| 17 | * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the |
| 18 | * GNU General Public License for more details. |
| 19 | * |
| 20 | * You should have received a copy of the GNU General Public License along |
| 21 | * with this program; if not, write to the Free Software Foundation, Inc., |
| 22 | * 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA. |
| 23 | * |
| 24 | * This file is part of mbed TLS (https://tls.mbed.org) |
| 25 | */ |
| 26 | #ifndef MBEDTLS_BIGNUM_H |
| 27 | #define MBEDTLS_BIGNUM_H |
| 28 | |
| 29 | #if !defined(MBEDTLS_CONFIG_FILE) |
| 30 | #include "config.h" |
| 31 | #else |
| 32 | #include MBEDTLS_CONFIG_FILE |
| 33 | #endif |
| 34 | |
| 35 | #include <stddef.h> |
| 36 | #include <stdint.h> |
| 37 | |
| 38 | #if defined(MBEDTLS_FS_IO) |
| 39 | #include <stdio.h> |
| 40 | #endif |
| 41 | |
| 42 | #define MBEDTLS_ERR_MPI_FILE_IO_ERROR -0x0002 /**< An error occurred while reading from or writing to a file. */ |
| 43 | #define MBEDTLS_ERR_MPI_BAD_INPUT_DATA -0x0004 /**< Bad input parameters to function. */ |
| 44 | #define MBEDTLS_ERR_MPI_INVALID_CHARACTER -0x0006 /**< There is an invalid character in the digit string. */ |
| 45 | #define MBEDTLS_ERR_MPI_BUFFER_TOO_SMALL -0x0008 /**< The buffer is too small to write to. */ |
| 46 | #define MBEDTLS_ERR_MPI_NEGATIVE_VALUE -0x000A /**< The input arguments are negative or result in illegal output. */ |
| 47 | #define MBEDTLS_ERR_MPI_DIVISION_BY_ZERO -0x000C /**< The input argument for division is zero, which is not allowed. */ |
| 48 | #define MBEDTLS_ERR_MPI_NOT_ACCEPTABLE -0x000E /**< The input arguments are not acceptable. */ |
| 49 | #define MBEDTLS_ERR_MPI_ALLOC_FAILED -0x0010 /**< Memory allocation failed. */ |
| 50 | |
| 51 | #define MBEDTLS_MPI_CHK(f) do { if( ( ret = f ) != 0 ) goto cleanup; } while( 0 ) |
| 52 | |
| 53 | /* |
| 54 | * Maximum size MPIs are allowed to grow to in number of limbs. |
| 55 | */ |
| 56 | #define MBEDTLS_MPI_MAX_LIMBS 10000 |
| 57 | |
| 58 | #if !defined(MBEDTLS_MPI_WINDOW_SIZE) |
| 59 | /* |
| 60 | * Maximum window size used for modular exponentiation. Default: 6 |
| 61 | * Minimum value: 1. Maximum value: 6. |
| 62 | * |
| 63 | * Result is an array of ( 2 << MBEDTLS_MPI_WINDOW_SIZE ) MPIs used |
| 64 | * for the sliding window calculation. (So 64 by default) |
| 65 | * |
| 66 | * Reduction in size, reduces speed. |
| 67 | */ |
| 68 | #define MBEDTLS_MPI_WINDOW_SIZE 6 /**< Maximum windows size used. */ |
| 69 | #endif /* !MBEDTLS_MPI_WINDOW_SIZE */ |
| 70 | |
| 71 | #if !defined(MBEDTLS_MPI_MAX_SIZE) |
| 72 | /* |
| 73 | * Maximum size of MPIs allowed in bits and bytes for user-MPIs. |
| 74 | * ( Default: 512 bytes => 4096 bits, Maximum tested: 2048 bytes => 16384 bits ) |
| 75 | * |
| 76 | * Note: Calculations can temporarily result in larger MPIs. So the number |
| 77 | * of limbs required (MBEDTLS_MPI_MAX_LIMBS) is higher. |
| 78 | */ |
| 79 | #define MBEDTLS_MPI_MAX_SIZE 1024 /**< Maximum number of bytes for usable MPIs. */ |
| 80 | #endif /* !MBEDTLS_MPI_MAX_SIZE */ |
| 81 | |
| 82 | #define MBEDTLS_MPI_MAX_BITS ( 8 * MBEDTLS_MPI_MAX_SIZE ) /**< Maximum number of bits for usable MPIs. */ |
| 83 | |
| 84 | /* |
| 85 | * When reading from files with mbedtls_mpi_read_file() and writing to files with |
| 86 | * mbedtls_mpi_write_file() the buffer should have space |
| 87 | * for a (short) label, the MPI (in the provided radix), the newline |
| 88 | * characters and the '\0'. |
| 89 | * |
| 90 | * By default we assume at least a 10 char label, a minimum radix of 10 |
| 91 | * (decimal) and a maximum of 4096 bit numbers (1234 decimal chars). |
| 92 | * Autosized at compile time for at least a 10 char label, a minimum radix |
| 93 | * of 10 (decimal) for a number of MBEDTLS_MPI_MAX_BITS size. |
| 94 | * |
| 95 | * This used to be statically sized to 1250 for a maximum of 4096 bit |
| 96 | * numbers (1234 decimal chars). |
| 97 | * |
| 98 | * Calculate using the formula: |
| 99 | * MBEDTLS_MPI_RW_BUFFER_SIZE = ceil(MBEDTLS_MPI_MAX_BITS / ln(10) * ln(2)) + |
| 100 | * LabelSize + 6 |
| 101 | */ |
| 102 | #define MBEDTLS_MPI_MAX_BITS_SCALE100 ( 100 * MBEDTLS_MPI_MAX_BITS ) |
| 103 | #define MBEDTLS_LN_2_DIV_LN_10_SCALE100 332 |
| 104 | #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 ) |
| 105 | |
| 106 | /* |
| 107 | * Define the base integer type, architecture-wise. |
| 108 | * |
| 109 | * 32 or 64-bit integer types can be forced regardless of the underlying |
| 110 | * architecture by defining MBEDTLS_HAVE_INT32 or MBEDTLS_HAVE_INT64 |
| 111 | * respectively and undefining MBEDTLS_HAVE_ASM. |
| 112 | * |
| 113 | * Double-width integers (e.g. 128-bit in 64-bit architectures) can be |
| 114 | * disabled by defining MBEDTLS_NO_UDBL_DIVISION. |
| 115 | */ |
| 116 | #if !defined(MBEDTLS_HAVE_INT32) |
| 117 | #if defined(_MSC_VER) && defined(_M_AMD64) |
| 118 | /* Always choose 64-bit when using MSC */ |
| 119 | #if !defined(MBEDTLS_HAVE_INT64) |
| 120 | #define MBEDTLS_HAVE_INT64 |
| 121 | #endif /* !MBEDTLS_HAVE_INT64 */ |
| 122 | typedef int64_t mbedtls_mpi_sint; |
| 123 | typedef uint64_t mbedtls_mpi_uint; |
| 124 | #elif defined(__GNUC__) && ( \ |
| 125 | defined(__amd64__) || defined(__x86_64__) || \ |
| 126 | defined(__ppc64__) || defined(__powerpc64__) || \ |
| 127 | defined(__ia64__) || defined(__alpha__) || \ |
| 128 | ( defined(__sparc__) && defined(__arch64__) ) || \ |
| 129 | defined(__s390x__) || defined(__mips64) ) |
| 130 | #if !defined(MBEDTLS_HAVE_INT64) |
| 131 | #define MBEDTLS_HAVE_INT64 |
| 132 | #endif /* MBEDTLS_HAVE_INT64 */ |
| 133 | typedef int64_t mbedtls_mpi_sint; |
| 134 | typedef uint64_t mbedtls_mpi_uint; |
| 135 | #if !defined(MBEDTLS_NO_UDBL_DIVISION) |
| 136 | /* mbedtls_t_udbl defined as 128-bit unsigned int */ |
| 137 | typedef unsigned int mbedtls_t_udbl __attribute__((mode(TI))); |
| 138 | #define MBEDTLS_HAVE_UDBL |
| 139 | #endif /* !MBEDTLS_NO_UDBL_DIVISION */ |
| 140 | #elif defined(__ARMCC_VERSION) && defined(__aarch64__) |
| 141 | /* |
| 142 | * __ARMCC_VERSION is defined for both armcc and armclang and |
| 143 | * __aarch64__ is only defined by armclang when compiling 64-bit code |
| 144 | */ |
| 145 | #if !defined(MBEDTLS_HAVE_INT64) |
| 146 | #define MBEDTLS_HAVE_INT64 |
| 147 | #endif /* !MBEDTLS_HAVE_INT64 */ |
| 148 | typedef int64_t mbedtls_mpi_sint; |
| 149 | typedef uint64_t mbedtls_mpi_uint; |
| 150 | #if !defined(MBEDTLS_NO_UDBL_DIVISION) |
| 151 | /* mbedtls_t_udbl defined as 128-bit unsigned int */ |
| 152 | typedef __uint128_t mbedtls_t_udbl; |
| 153 | #define MBEDTLS_HAVE_UDBL |
| 154 | #endif /* !MBEDTLS_NO_UDBL_DIVISION */ |
| 155 | #elif defined(MBEDTLS_HAVE_INT64) |
| 156 | /* Force 64-bit integers with unknown compiler */ |
| 157 | typedef int64_t mbedtls_mpi_sint; |
| 158 | typedef uint64_t mbedtls_mpi_uint; |
| 159 | #endif |
| 160 | #endif /* !MBEDTLS_HAVE_INT32 */ |
| 161 | |
| 162 | #if !defined(MBEDTLS_HAVE_INT64) |
| 163 | /* Default to 32-bit compilation */ |
| 164 | #if !defined(MBEDTLS_HAVE_INT32) |
| 165 | #define MBEDTLS_HAVE_INT32 |
| 166 | #endif /* !MBEDTLS_HAVE_INT32 */ |
| 167 | typedef int32_t mbedtls_mpi_sint; |
| 168 | typedef uint32_t mbedtls_mpi_uint; |
| 169 | #if !defined(MBEDTLS_NO_UDBL_DIVISION) |
| 170 | typedef uint64_t mbedtls_t_udbl; |
| 171 | #define MBEDTLS_HAVE_UDBL |
| 172 | #endif /* !MBEDTLS_NO_UDBL_DIVISION */ |
| 173 | #endif /* !MBEDTLS_HAVE_INT64 */ |
| 174 | |
| 175 | #ifdef __cplusplus |
| 176 | extern "C" { |
| 177 | #endif |
| 178 | |
| 179 | /** |
| 180 | * \brief MPI structure |
| 181 | */ |
| 182 | typedef struct mbedtls_mpi |
| 183 | { |
| 184 | int s; /*!< integer sign */ |
| 185 | size_t n; /*!< total # of limbs */ |
| 186 | mbedtls_mpi_uint *p; /*!< pointer to limbs */ |
| 187 | } |
| 188 | mbedtls_mpi; |
| 189 | |
| 190 | /** |
| 191 | * \brief Initialize one MPI (make internal references valid) |
| 192 | * This just makes it ready to be set or freed, |
| 193 | * but does not define a value for the MPI. |
| 194 | * |
| 195 | * \param X One MPI to initialize. |
| 196 | */ |
| 197 | void mbedtls_mpi_init( mbedtls_mpi *X ); |
| 198 | |
| 199 | /** |
| 200 | * \brief Unallocate one MPI |
| 201 | * |
| 202 | * \param X One MPI to unallocate. |
| 203 | */ |
| 204 | void mbedtls_mpi_free( mbedtls_mpi *X ); |
| 205 | |
| 206 | /** |
| 207 | * \brief Enlarge to the specified number of limbs |
| 208 | * |
| 209 | * This function does nothing if the MPI is already large enough. |
| 210 | * |
| 211 | * \param X MPI to grow |
| 212 | * \param nblimbs The target number of limbs |
| 213 | * |
| 214 | * \return 0 if successful, |
| 215 | * MBEDTLS_ERR_MPI_ALLOC_FAILED if memory allocation failed |
| 216 | */ |
| 217 | int mbedtls_mpi_grow( mbedtls_mpi *X, size_t nblimbs ); |
| 218 | |
| 219 | /** |
| 220 | * \brief Resize down, keeping at least the specified number of limbs |
| 221 | * |
| 222 | * If \c X is smaller than \c nblimbs, it is resized up |
| 223 | * instead. |
| 224 | * |
| 225 | * \param X MPI to shrink |
| 226 | * \param nblimbs The minimum number of limbs to keep |
| 227 | * |
| 228 | * \return 0 if successful, |
| 229 | * MBEDTLS_ERR_MPI_ALLOC_FAILED if memory allocation failed |
| 230 | * (this can only happen when resizing up). |
| 231 | */ |
| 232 | int mbedtls_mpi_shrink( mbedtls_mpi *X, size_t nblimbs ); |
| 233 | |
| 234 | /** |
| 235 | * \brief Copy the contents of Y into X |
| 236 | * |
| 237 | * \param X Destination MPI. It is enlarged if necessary. |
| 238 | * \param Y Source MPI. |
| 239 | * |
| 240 | * \return 0 if successful, |
| 241 | * MBEDTLS_ERR_MPI_ALLOC_FAILED if memory allocation failed |
| 242 | */ |
| 243 | int mbedtls_mpi_copy( mbedtls_mpi *X, const mbedtls_mpi *Y ); |
| 244 | |
| 245 | /** |
| 246 | * \brief Swap the contents of X and Y |
| 247 | * |
| 248 | * \param X First MPI value |
| 249 | * \param Y Second MPI value |
| 250 | */ |
| 251 | void mbedtls_mpi_swap( mbedtls_mpi *X, mbedtls_mpi *Y ); |
| 252 | |
| 253 | /** |
| 254 | * \brief Safe conditional assignement X = Y if assign is 1 |
| 255 | * |
| 256 | * \param X MPI to conditionally assign to |
| 257 | * \param Y Value to be assigned |
| 258 | * \param assign 1: perform the assignment, 0: keep X's original value |
| 259 | * |
| 260 | * \return 0 if successful, |
| 261 | * MBEDTLS_ERR_MPI_ALLOC_FAILED if memory allocation failed, |
| 262 | * |
| 263 | * \note This function is equivalent to |
| 264 | * if( assign ) mbedtls_mpi_copy( X, Y ); |
| 265 | * except that it avoids leaking any information about whether |
| 266 | * the assignment was done or not (the above code may leak |
| 267 | * information through branch prediction and/or memory access |
| 268 | * patterns analysis). |
| 269 | */ |
| 270 | int mbedtls_mpi_safe_cond_assign( mbedtls_mpi *X, const mbedtls_mpi *Y, unsigned char assign ); |
| 271 | |
| 272 | /** |
| 273 | * \brief Safe conditional swap X <-> Y if swap is 1 |
| 274 | * |
| 275 | * \param X First mbedtls_mpi value |
| 276 | * \param Y Second mbedtls_mpi value |
| 277 | * \param assign 1: perform the swap, 0: keep X and Y's original values |
| 278 | * |
| 279 | * \return 0 if successful, |
| 280 | * MBEDTLS_ERR_MPI_ALLOC_FAILED if memory allocation failed, |
| 281 | * |
| 282 | * \note This function is equivalent to |
| 283 | * if( assign ) mbedtls_mpi_swap( X, Y ); |
| 284 | * except that it avoids leaking any information about whether |
| 285 | * the assignment was done or not (the above code may leak |
| 286 | * information through branch prediction and/or memory access |
| 287 | * patterns analysis). |
| 288 | */ |
| 289 | int mbedtls_mpi_safe_cond_swap( mbedtls_mpi *X, mbedtls_mpi *Y, unsigned char assign ); |
| 290 | |
| 291 | /** |
| 292 | * \brief Set value from integer |
| 293 | * |
| 294 | * \param X MPI to set |
| 295 | * \param z Value to use |
| 296 | * |
| 297 | * \return 0 if successful, |
| 298 | * MBEDTLS_ERR_MPI_ALLOC_FAILED if memory allocation failed |
| 299 | */ |
| 300 | int mbedtls_mpi_lset( mbedtls_mpi *X, mbedtls_mpi_sint z ); |
| 301 | |
| 302 | /** |
| 303 | * \brief Get a specific bit from X |
| 304 | * |
| 305 | * \param X MPI to use |
| 306 | * \param pos Zero-based index of the bit in X |
| 307 | * |
| 308 | * \return Either a 0 or a 1 |
| 309 | */ |
| 310 | int mbedtls_mpi_get_bit( const mbedtls_mpi *X, size_t pos ); |
| 311 | |
| 312 | /** |
| 313 | * \brief Set a bit of X to a specific value of 0 or 1 |
| 314 | * |
| 315 | * \note Will grow X if necessary to set a bit to 1 in a not yet |
| 316 | * existing limb. Will not grow if bit should be set to 0 |
| 317 | * |
| 318 | * \param X MPI to use |
| 319 | * \param pos Zero-based index of the bit in X |
| 320 | * \param val The value to set the bit to (0 or 1) |
| 321 | * |
| 322 | * \return 0 if successful, |
| 323 | * MBEDTLS_ERR_MPI_ALLOC_FAILED if memory allocation failed, |
| 324 | * MBEDTLS_ERR_MPI_BAD_INPUT_DATA if val is not 0 or 1 |
| 325 | */ |
| 326 | int mbedtls_mpi_set_bit( mbedtls_mpi *X, size_t pos, unsigned char val ); |
| 327 | |
| 328 | /** |
| 329 | * \brief Return the number of zero-bits before the least significant |
| 330 | * '1' bit |
| 331 | * |
| 332 | * Note: Thus also the zero-based index of the least significant '1' bit |
| 333 | * |
| 334 | * \param X MPI to use |
| 335 | */ |
| 336 | size_t mbedtls_mpi_lsb( const mbedtls_mpi *X ); |
| 337 | |
| 338 | /** |
| 339 | * \brief Return the number of bits up to and including the most |
| 340 | * significant '1' bit' |
| 341 | * |
| 342 | * Note: Thus also the one-based index of the most significant '1' bit |
| 343 | * |
| 344 | * \param X MPI to use |
| 345 | */ |
| 346 | size_t mbedtls_mpi_bitlen( const mbedtls_mpi *X ); |
| 347 | |
| 348 | /** |
| 349 | * \brief Return the total size in bytes |
| 350 | * |
| 351 | * \param X MPI to use |
| 352 | */ |
| 353 | size_t mbedtls_mpi_size( const mbedtls_mpi *X ); |
| 354 | |
| 355 | /** |
| 356 | * \brief Import from an ASCII string |
| 357 | * |
| 358 | * \param X Destination MPI |
| 359 | * \param radix Input numeric base |
| 360 | * \param s Null-terminated string buffer |
| 361 | * |
| 362 | * \return 0 if successful, or a MBEDTLS_ERR_MPI_XXX error code |
| 363 | */ |
| 364 | int mbedtls_mpi_read_string( mbedtls_mpi *X, int radix, const char *s ); |
| 365 | |
| 366 | /** |
| 367 | * \brief Export into an ASCII string |
| 368 | * |
| 369 | * \param X Source MPI |
| 370 | * \param radix Output numeric base |
| 371 | * \param buf Buffer to write the string to |
| 372 | * \param buflen Length of buf |
| 373 | * \param olen Length of the string written, including final NUL byte |
| 374 | * |
| 375 | * \return 0 if successful, or a MBEDTLS_ERR_MPI_XXX error code. |
| 376 | * *olen is always updated to reflect the amount |
| 377 | * of data that has (or would have) been written. |
| 378 | * |
| 379 | * \note Call this function with buflen = 0 to obtain the |
| 380 | * minimum required buffer size in *olen. |
| 381 | */ |
| 382 | int mbedtls_mpi_write_string( const mbedtls_mpi *X, int radix, |
| 383 | char *buf, size_t buflen, size_t *olen ); |
| 384 | |
| 385 | #if defined(MBEDTLS_FS_IO) |
| 386 | /** |
| 387 | * \brief Read MPI from a line in an opened file |
| 388 | * |
| 389 | * \param X Destination MPI |
| 390 | * \param radix Input numeric base |
| 391 | * \param fin Input file handle |
| 392 | * |
| 393 | * \return 0 if successful, MBEDTLS_ERR_MPI_BUFFER_TOO_SMALL if |
| 394 | * the file read buffer is too small or a |
| 395 | * MBEDTLS_ERR_MPI_XXX error code |
| 396 | * |
| 397 | * \note On success, this function advances the file stream |
| 398 | * to the end of the current line or to EOF. |
| 399 | * |
| 400 | * The function returns 0 on an empty line. |
| 401 | * |
| 402 | * Leading whitespaces are ignored, as is a |
| 403 | * '0x' prefix for radix 16. |
| 404 | * |
| 405 | */ |
| 406 | int mbedtls_mpi_read_file( mbedtls_mpi *X, int radix, FILE *fin ); |
| 407 | |
| 408 | /** |
| 409 | * \brief Write X into an opened file, or stdout if fout is NULL |
| 410 | * |
| 411 | * \param p Prefix, can be NULL |
| 412 | * \param X Source MPI |
| 413 | * \param radix Output numeric base |
| 414 | * \param fout Output file handle (can be NULL) |
| 415 | * |
| 416 | * \return 0 if successful, or a MBEDTLS_ERR_MPI_XXX error code |
| 417 | * |
| 418 | * \note Set fout == NULL to print X on the console. |
| 419 | */ |
| 420 | int mbedtls_mpi_write_file( const char *p, const mbedtls_mpi *X, int radix, FILE *fout ); |
| 421 | #endif /* MBEDTLS_FS_IO */ |
| 422 | |
| 423 | /** |
| 424 | * \brief Import X from unsigned binary data, big endian |
| 425 | * |
| 426 | * \param X Destination MPI |
| 427 | * \param buf Input buffer |
| 428 | * \param buflen Input buffer size |
| 429 | * |
| 430 | * \return 0 if successful, |
| 431 | * MBEDTLS_ERR_MPI_ALLOC_FAILED if memory allocation failed |
| 432 | */ |
| 433 | int mbedtls_mpi_read_binary( mbedtls_mpi *X, const unsigned char *buf, size_t buflen ); |
| 434 | |
| 435 | /** |
| 436 | * \brief Export X into unsigned binary data, big endian. |
| 437 | * Always fills the whole buffer, which will start with zeros |
| 438 | * if the number is smaller. |
| 439 | * |
| 440 | * \param X Source MPI |
| 441 | * \param buf Output buffer |
| 442 | * \param buflen Output buffer size |
| 443 | * |
| 444 | * \return 0 if successful, |
| 445 | * MBEDTLS_ERR_MPI_BUFFER_TOO_SMALL if buf isn't large enough |
| 446 | */ |
| 447 | int mbedtls_mpi_write_binary( const mbedtls_mpi *X, unsigned char *buf, size_t buflen ); |
| 448 | |
| 449 | /** |
| 450 | * \brief Left-shift: X <<= count |
| 451 | * |
| 452 | * \param X MPI to shift |
| 453 | * \param count Amount to shift |
| 454 | * |
| 455 | * \return 0 if successful, |
| 456 | * MBEDTLS_ERR_MPI_ALLOC_FAILED if memory allocation failed |
| 457 | */ |
| 458 | int mbedtls_mpi_shift_l( mbedtls_mpi *X, size_t count ); |
| 459 | |
| 460 | /** |
| 461 | * \brief Right-shift: X >>= count |
| 462 | * |
| 463 | * \param X MPI to shift |
| 464 | * \param count Amount to shift |
| 465 | * |
| 466 | * \return 0 if successful, |
| 467 | * MBEDTLS_ERR_MPI_ALLOC_FAILED if memory allocation failed |
| 468 | */ |
| 469 | int mbedtls_mpi_shift_r( mbedtls_mpi *X, size_t count ); |
| 470 | |
| 471 | /** |
| 472 | * \brief Compare unsigned values |
| 473 | * |
| 474 | * \param X Left-hand MPI |
| 475 | * \param Y Right-hand MPI |
| 476 | * |
| 477 | * \return 1 if |X| is greater than |Y|, |
| 478 | * -1 if |X| is lesser than |Y| or |
| 479 | * 0 if |X| is equal to |Y| |
| 480 | */ |
| 481 | int mbedtls_mpi_cmp_abs( const mbedtls_mpi *X, const mbedtls_mpi *Y ); |
| 482 | |
| 483 | /** |
| 484 | * \brief Compare signed values |
| 485 | * |
| 486 | * \param X Left-hand MPI |
| 487 | * \param Y Right-hand MPI |
| 488 | * |
| 489 | * \return 1 if X is greater than Y, |
| 490 | * -1 if X is lesser than Y or |
| 491 | * 0 if X is equal to Y |
| 492 | */ |
| 493 | int mbedtls_mpi_cmp_mpi( const mbedtls_mpi *X, const mbedtls_mpi *Y ); |
| 494 | |
| 495 | /** |
| 496 | * \brief Compare signed values |
| 497 | * |
| 498 | * \param X Left-hand MPI |
| 499 | * \param z The integer value to compare to |
| 500 | * |
| 501 | * \return 1 if X is greater than z, |
| 502 | * -1 if X is lesser than z or |
| 503 | * 0 if X is equal to z |
| 504 | */ |
| 505 | int mbedtls_mpi_cmp_int( const mbedtls_mpi *X, mbedtls_mpi_sint z ); |
| 506 | |
| 507 | /** |
| 508 | * \brief Unsigned addition: X = |A| + |B| |
| 509 | * |
| 510 | * \param X Destination MPI |
| 511 | * \param A Left-hand MPI |
| 512 | * \param B Right-hand MPI |
| 513 | * |
| 514 | * \return 0 if successful, |
| 515 | * MBEDTLS_ERR_MPI_ALLOC_FAILED if memory allocation failed |
| 516 | */ |
| 517 | int mbedtls_mpi_add_abs( mbedtls_mpi *X, const mbedtls_mpi *A, const mbedtls_mpi *B ); |
| 518 | |
| 519 | /** |
| 520 | * \brief Unsigned subtraction: X = |A| - |B| |
| 521 | * |
| 522 | * \param X Destination MPI |
| 523 | * \param A Left-hand MPI |
| 524 | * \param B Right-hand MPI |
| 525 | * |
| 526 | * \return 0 if successful, |
| 527 | * MBEDTLS_ERR_MPI_NEGATIVE_VALUE if B is greater than A |
| 528 | */ |
| 529 | int mbedtls_mpi_sub_abs( mbedtls_mpi *X, const mbedtls_mpi *A, const mbedtls_mpi *B ); |
| 530 | |
| 531 | /** |
| 532 | * \brief Signed addition: X = A + B |
| 533 | * |
| 534 | * \param X Destination MPI |
| 535 | * \param A Left-hand MPI |
| 536 | * \param B Right-hand MPI |
| 537 | * |
| 538 | * \return 0 if successful, |
| 539 | * MBEDTLS_ERR_MPI_ALLOC_FAILED if memory allocation failed |
| 540 | */ |
| 541 | int mbedtls_mpi_add_mpi( mbedtls_mpi *X, const mbedtls_mpi *A, const mbedtls_mpi *B ); |
| 542 | |
| 543 | /** |
| 544 | * \brief Signed subtraction: X = A - B |
| 545 | * |
| 546 | * \param X Destination MPI |
| 547 | * \param A Left-hand MPI |
| 548 | * \param B Right-hand MPI |
| 549 | * |
| 550 | * \return 0 if successful, |
| 551 | * MBEDTLS_ERR_MPI_ALLOC_FAILED if memory allocation failed |
| 552 | */ |
| 553 | int mbedtls_mpi_sub_mpi( mbedtls_mpi *X, const mbedtls_mpi *A, const mbedtls_mpi *B ); |
| 554 | |
| 555 | /** |
| 556 | * \brief Signed addition: X = A + b |
| 557 | * |
| 558 | * \param X Destination MPI |
| 559 | * \param A Left-hand MPI |
| 560 | * \param b The integer value to add |
| 561 | * |
| 562 | * \return 0 if successful, |
| 563 | * MBEDTLS_ERR_MPI_ALLOC_FAILED if memory allocation failed |
| 564 | */ |
| 565 | int mbedtls_mpi_add_int( mbedtls_mpi *X, const mbedtls_mpi *A, mbedtls_mpi_sint b ); |
| 566 | |
| 567 | /** |
| 568 | * \brief Signed subtraction: X = A - b |
| 569 | * |
| 570 | * \param X Destination MPI |
| 571 | * \param A Left-hand MPI |
| 572 | * \param b The integer value to subtract |
| 573 | * |
| 574 | * \return 0 if successful, |
| 575 | * MBEDTLS_ERR_MPI_ALLOC_FAILED if memory allocation failed |
| 576 | */ |
| 577 | int mbedtls_mpi_sub_int( mbedtls_mpi *X, const mbedtls_mpi *A, mbedtls_mpi_sint b ); |
| 578 | |
| 579 | /** |
| 580 | * \brief Baseline multiplication: X = A * B |
| 581 | * |
| 582 | * \param X Destination MPI |
| 583 | * \param A Left-hand MPI |
| 584 | * \param B Right-hand MPI |
| 585 | * |
| 586 | * \return 0 if successful, |
| 587 | * MBEDTLS_ERR_MPI_ALLOC_FAILED if memory allocation failed |
| 588 | */ |
| 589 | int mbedtls_mpi_mul_mpi( mbedtls_mpi *X, const mbedtls_mpi *A, const mbedtls_mpi *B ); |
| 590 | |
| 591 | /** |
| 592 | * \brief Baseline multiplication: X = A * b |
| 593 | * |
| 594 | * \param X Destination MPI |
| 595 | * \param A Left-hand MPI |
| 596 | * \param b The unsigned integer value to multiply with |
| 597 | * |
| 598 | * \note b is unsigned |
| 599 | * |
| 600 | * \return 0 if successful, |
| 601 | * MBEDTLS_ERR_MPI_ALLOC_FAILED if memory allocation failed |
| 602 | */ |
| 603 | int mbedtls_mpi_mul_int( mbedtls_mpi *X, const mbedtls_mpi *A, mbedtls_mpi_uint b ); |
| 604 | |
| 605 | /** |
| 606 | * \brief Division by mbedtls_mpi: A = Q * B + R |
| 607 | * |
| 608 | * \param Q Destination MPI for the quotient |
| 609 | * \param R Destination MPI for the rest value |
| 610 | * \param A Left-hand MPI |
| 611 | * \param B Right-hand MPI |
| 612 | * |
| 613 | * \return 0 if successful, |
| 614 | * MBEDTLS_ERR_MPI_ALLOC_FAILED if memory allocation failed, |
| 615 | * MBEDTLS_ERR_MPI_DIVISION_BY_ZERO if B == 0 |
| 616 | * |
| 617 | * \note Either Q or R can be NULL. |
| 618 | */ |
| 619 | int mbedtls_mpi_div_mpi( mbedtls_mpi *Q, mbedtls_mpi *R, const mbedtls_mpi *A, const mbedtls_mpi *B ); |
| 620 | |
| 621 | /** |
| 622 | * \brief Division by int: A = Q * b + R |
| 623 | * |
| 624 | * \param Q Destination MPI for the quotient |
| 625 | * \param R Destination MPI for the rest value |
| 626 | * \param A Left-hand MPI |
| 627 | * \param b Integer to divide by |
| 628 | * |
| 629 | * \return 0 if successful, |
| 630 | * MBEDTLS_ERR_MPI_ALLOC_FAILED if memory allocation failed, |
| 631 | * MBEDTLS_ERR_MPI_DIVISION_BY_ZERO if b == 0 |
| 632 | * |
| 633 | * \note Either Q or R can be NULL. |
| 634 | */ |
| 635 | int mbedtls_mpi_div_int( mbedtls_mpi *Q, mbedtls_mpi *R, const mbedtls_mpi *A, mbedtls_mpi_sint b ); |
| 636 | |
| 637 | /** |
| 638 | * \brief Modulo: R = A mod B |
| 639 | * |
| 640 | * \param R Destination MPI for the rest value |
| 641 | * \param A Left-hand MPI |
| 642 | * \param B Right-hand MPI |
| 643 | * |
| 644 | * \return 0 if successful, |
| 645 | * MBEDTLS_ERR_MPI_ALLOC_FAILED if memory allocation failed, |
| 646 | * MBEDTLS_ERR_MPI_DIVISION_BY_ZERO if B == 0, |
| 647 | * MBEDTLS_ERR_MPI_NEGATIVE_VALUE if B < 0 |
| 648 | */ |
| 649 | int mbedtls_mpi_mod_mpi( mbedtls_mpi *R, const mbedtls_mpi *A, const mbedtls_mpi *B ); |
| 650 | |
| 651 | /** |
| 652 | * \brief Modulo: r = A mod b |
| 653 | * |
| 654 | * \param r Destination mbedtls_mpi_uint |
| 655 | * \param A Left-hand MPI |
| 656 | * \param b Integer to divide by |
| 657 | * |
| 658 | * \return 0 if successful, |
| 659 | * MBEDTLS_ERR_MPI_ALLOC_FAILED if memory allocation failed, |
| 660 | * MBEDTLS_ERR_MPI_DIVISION_BY_ZERO if b == 0, |
| 661 | * MBEDTLS_ERR_MPI_NEGATIVE_VALUE if b < 0 |
| 662 | */ |
| 663 | int mbedtls_mpi_mod_int( mbedtls_mpi_uint *r, const mbedtls_mpi *A, mbedtls_mpi_sint b ); |
| 664 | |
| 665 | /** |
| 666 | * \brief Sliding-window exponentiation: X = A^E mod N |
| 667 | * |
| 668 | * \param X Destination MPI |
| 669 | * \param A Left-hand MPI |
| 670 | * \param E Exponent MPI |
| 671 | * \param N Modular MPI |
| 672 | * \param _RR Speed-up MPI used for recalculations |
| 673 | * |
| 674 | * \return 0 if successful, |
| 675 | * MBEDTLS_ERR_MPI_ALLOC_FAILED if memory allocation failed, |
| 676 | * MBEDTLS_ERR_MPI_BAD_INPUT_DATA if N is negative or even or |
| 677 | * if E is negative |
| 678 | * |
| 679 | * \note _RR is used to avoid re-computing R*R mod N across |
| 680 | * multiple calls, which speeds up things a bit. It can |
| 681 | * be set to NULL if the extra performance is unneeded. |
| 682 | */ |
| 683 | int mbedtls_mpi_exp_mod( mbedtls_mpi *X, const mbedtls_mpi *A, const mbedtls_mpi *E, const mbedtls_mpi *N, mbedtls_mpi *_RR ); |
| 684 | |
| 685 | /** |
| 686 | * \brief Fill an MPI X with size bytes of random |
| 687 | * |
| 688 | * \param X Destination MPI |
| 689 | * \param size Size in bytes |
| 690 | * \param f_rng RNG function |
| 691 | * \param p_rng RNG parameter |
| 692 | * |
| 693 | * \return 0 if successful, |
| 694 | * MBEDTLS_ERR_MPI_ALLOC_FAILED if memory allocation failed |
| 695 | * |
| 696 | * \note The bytes obtained from the PRNG are interpreted |
| 697 | * as a big-endian representation of an MPI; this can |
| 698 | * be relevant in applications like deterministic ECDSA. |
| 699 | */ |
| 700 | int mbedtls_mpi_fill_random( mbedtls_mpi *X, size_t size, |
| 701 | int (*f_rng)(void *, unsigned char *, size_t), |
| 702 | void *p_rng ); |
| 703 | |
| 704 | /** |
| 705 | * \brief Greatest common divisor: G = gcd(A, B) |
| 706 | * |
| 707 | * \param G Destination MPI |
| 708 | * \param A Left-hand MPI |
| 709 | * \param B Right-hand MPI |
| 710 | * |
| 711 | * \return 0 if successful, |
| 712 | * MBEDTLS_ERR_MPI_ALLOC_FAILED if memory allocation failed |
| 713 | */ |
| 714 | int mbedtls_mpi_gcd( mbedtls_mpi *G, const mbedtls_mpi *A, const mbedtls_mpi *B ); |
| 715 | |
| 716 | /** |
| 717 | * \brief Modular inverse: X = A^-1 mod N |
| 718 | * |
| 719 | * \param X Destination MPI |
| 720 | * \param A Left-hand MPI |
| 721 | * \param N Right-hand MPI |
| 722 | * |
| 723 | * \return 0 if successful, |
| 724 | * MBEDTLS_ERR_MPI_ALLOC_FAILED if memory allocation failed, |
| 725 | * MBEDTLS_ERR_MPI_BAD_INPUT_DATA if N is <= 1, |
| 726 | MBEDTLS_ERR_MPI_NOT_ACCEPTABLE if A has no inverse mod N. |
| 727 | */ |
| 728 | int mbedtls_mpi_inv_mod( mbedtls_mpi *X, const mbedtls_mpi *A, const mbedtls_mpi *N ); |
| 729 | |
| 730 | /** |
| 731 | * \brief Miller-Rabin primality test |
| 732 | * |
| 733 | * \param X MPI to check |
| 734 | * \param f_rng RNG function |
| 735 | * \param p_rng RNG parameter |
| 736 | * |
| 737 | * \return 0 if successful (probably prime), |
| 738 | * MBEDTLS_ERR_MPI_ALLOC_FAILED if memory allocation failed, |
| 739 | * MBEDTLS_ERR_MPI_NOT_ACCEPTABLE if X is not prime |
| 740 | */ |
| 741 | int mbedtls_mpi_is_prime( const mbedtls_mpi *X, |
| 742 | int (*f_rng)(void *, unsigned char *, size_t), |
| 743 | void *p_rng ); |
| 744 | |
| 745 | /** |
| 746 | * \brief Prime number generation |
| 747 | * |
| 748 | * \param X Destination MPI |
| 749 | * \param nbits Required size of X in bits |
| 750 | * ( 3 <= nbits <= MBEDTLS_MPI_MAX_BITS ) |
| 751 | * \param dh_flag If 1, then (X-1)/2 will be prime too |
| 752 | * \param f_rng RNG function |
| 753 | * \param p_rng RNG parameter |
| 754 | * |
| 755 | * \return 0 if successful (probably prime), |
| 756 | * MBEDTLS_ERR_MPI_ALLOC_FAILED if memory allocation failed, |
| 757 | * MBEDTLS_ERR_MPI_BAD_INPUT_DATA if nbits is < 3 |
| 758 | */ |
| 759 | int mbedtls_mpi_gen_prime( mbedtls_mpi *X, size_t nbits, int dh_flag, |
| 760 | int (*f_rng)(void *, unsigned char *, size_t), |
| 761 | void *p_rng ); |
| 762 | |
| 763 | /** |
| 764 | * \brief Checkup routine |
| 765 | * |
| 766 | * \return 0 if successful, or 1 if the test failed |
| 767 | */ |
| 768 | int mbedtls_mpi_self_test( int verbose ); |
| 769 | |
| 770 | #ifdef __cplusplus |
| 771 | } |
| 772 | #endif |
| 773 | |
| 774 | #endif /* bignum.h */ |