bignum.h

00001 /**
00002  * \file bignum.h
00003  *
00004  * \brief  Multi-precision integer library
00005  *
00006  *  Copyright (C) 2006-2015, ARM Limited, All Rights Reserved
00007  *  SPDX-License-Identifier: Apache-2.0
00008  *
00009  *  Licensed under the Apache License, Version 2.0 (the "License"); you may
00010  *  not use this file except in compliance with the License.
00011  *  You may obtain a copy of the License at
00012  *
00013  *  http://www.apache.org/licenses/LICENSE-2.0
00014  *
00015  *  Unless required by applicable law or agreed to in writing, software
00016  *  distributed under the License is distributed on an "AS IS" BASIS, WITHOUT
00017  *  WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
00018  *  See the License for the specific language governing permissions and
00019  *  limitations under the License.
00020  *
00021  *  This file is part of mbed TLS (https://tls.mbed.org)
00022  */
00023 #ifndef MBEDTLS_BIGNUM_H
00024 #define MBEDTLS_BIGNUM_H
00025 
00026 #if !defined(MBEDTLS_CONFIG_FILE)
00027 #include "config.h"
00028 #else
00029 #include MBEDTLS_CONFIG_FILE
00030 #endif
00031 
00032 #include <stddef.h>
00033 #include <stdint.h>
00034 
00035 #if defined(MBEDTLS_FS_IO)
00036 #include <stdio.h>
00037 #endif
00038 
00039 #define MBEDTLS_ERR_MPI_FILE_IO_ERROR                     -0x0002  /**< An error occurred while reading from or writing to a file. */
00040 #define MBEDTLS_ERR_MPI_BAD_INPUT_DATA                    -0x0004  /**< Bad input parameters to function. */
00041 #define MBEDTLS_ERR_MPI_INVALID_CHARACTER                 -0x0006  /**< There is an invalid character in the digit string. */
00042 #define MBEDTLS_ERR_MPI_BUFFER_TOO_SMALL                  -0x0008  /**< The buffer is too small to write to. */
00043 #define MBEDTLS_ERR_MPI_NEGATIVE_VALUE                    -0x000A  /**< The input arguments are negative or result in illegal output. */
00044 #define MBEDTLS_ERR_MPI_DIVISION_BY_ZERO                  -0x000C  /**< The input argument for division is zero, which is not allowed. */
00045 #define MBEDTLS_ERR_MPI_NOT_ACCEPTABLE                    -0x000E  /**< The input arguments are not acceptable. */
00046 #define MBEDTLS_ERR_MPI_ALLOC_FAILED                      -0x0010  /**< Memory allocation failed. */
00047 
00048 #define MBEDTLS_MPI_CHK(f) do { if( ( ret = f ) != 0 ) goto cleanup; } while( 0 )
00049 
00050 /*
00051  * Maximum size MPIs are allowed to grow to in number of limbs.
00052  */
00053 #define MBEDTLS_MPI_MAX_LIMBS                             10000
00054 
00055 #if !defined(MBEDTLS_MPI_WINDOW_SIZE)
00056 /*
00057  * Maximum window size used for modular exponentiation. Default: 6
00058  * Minimum value: 1. Maximum value: 6.
00059  *
00060  * Result is an array of ( 2 << MBEDTLS_MPI_WINDOW_SIZE ) MPIs used
00061  * for the sliding window calculation. (So 64 by default)
00062  *
00063  * Reduction in size, reduces speed.
00064  */
00065 #define MBEDTLS_MPI_WINDOW_SIZE                           6        /**< Maximum windows size used. */
00066 #endif /* !MBEDTLS_MPI_WINDOW_SIZE */
00067 
00068 #if !defined(MBEDTLS_MPI_MAX_SIZE)
00069 /*
00070  * Maximum size of MPIs allowed in bits and bytes for user-MPIs.
00071  * ( Default: 512 bytes => 4096 bits, Maximum tested: 2048 bytes => 16384 bits )
00072  *
00073  * Note: Calculations can results temporarily in larger MPIs. So the number
00074  * of limbs required (MBEDTLS_MPI_MAX_LIMBS) is higher.
00075  */
00076 #define MBEDTLS_MPI_MAX_SIZE                              1024     /**< Maximum number of bytes for usable MPIs. */
00077 #endif /* !MBEDTLS_MPI_MAX_SIZE */
00078 
00079 #define MBEDTLS_MPI_MAX_BITS                              ( 8 * MBEDTLS_MPI_MAX_SIZE )    /**< Maximum number of bits for usable MPIs. */
00080 
00081 /*
00082  * When reading from files with mbedtls_mpi_read_file() and writing to files with
00083  * mbedtls_mpi_write_file() the buffer should have space
00084  * for a (short) label, the MPI (in the provided radix), the newline
00085  * characters and the '\0'.
00086  *
00087  * By default we assume at least a 10 char label, a minimum radix of 10
00088  * (decimal) and a maximum of 4096 bit numbers (1234 decimal chars).
00089  * Autosized at compile time for at least a 10 char label, a minimum radix
00090  * of 10 (decimal) for a number of MBEDTLS_MPI_MAX_BITS size.
00091  *
00092  * This used to be statically sized to 1250 for a maximum of 4096 bit
00093  * numbers (1234 decimal chars).
00094  *
00095  * Calculate using the formula:
00096  *  MBEDTLS_MPI_RW_BUFFER_SIZE = ceil(MBEDTLS_MPI_MAX_BITS / ln(10) * ln(2)) +
00097  *                                LabelSize + 6
00098  */
00099 #define MBEDTLS_MPI_MAX_BITS_SCALE100          ( 100 * MBEDTLS_MPI_MAX_BITS )
00100 #define MBEDTLS_LN_2_DIV_LN_10_SCALE100                 332
00101 #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 )
00102 
00103 /*
00104  * Define the base integer type, architecture-wise.
00105  *
00106  * 32 or 64-bit integer types can be forced regardless of the underlying
00107  * architecture by defining MBEDTLS_HAVE_INT32 or MBEDTLS_HAVE_INT64
00108  * respectively and undefining MBEDTLS_HAVE_ASM.
00109  *
00110  * Double-width integers (e.g. 128-bit in 64-bit architectures) can be
00111  * disabled by defining MBEDTLS_NO_UDBL_DIVISION.
00112  */
00113 #if !defined(MBEDTLS_HAVE_INT32)
00114     #if defined(_MSC_VER) && defined(_M_AMD64)
00115         /* Always choose 64-bit when using MSC */
00116         #if !defined(MBEDTLS_HAVE_INT64)
00117             #define MBEDTLS_HAVE_INT64
00118         #endif /* !MBEDTLS_HAVE_INT64 */
00119         typedef  int64_t mbedtls_mpi_sint;
00120         typedef uint64_t mbedtls_mpi_uint;
00121     #elif defined(__GNUC__) && (                         \
00122         defined(__amd64__) || defined(__x86_64__)     || \
00123         defined(__ppc64__) || defined(__powerpc64__)  || \
00124         defined(__ia64__)  || defined(__alpha__)      || \
00125         ( defined(__sparc__) && defined(__arch64__) ) || \
00126         defined(__s390x__) || defined(__mips64) )
00127         #if !defined(MBEDTLS_HAVE_INT64)
00128             #define MBEDTLS_HAVE_INT64
00129         #endif /* MBEDTLS_HAVE_INT64 */
00130         typedef  int64_t mbedtls_mpi_sint;
00131         typedef uint64_t mbedtls_mpi_uint;
00132         #if !defined(MBEDTLS_NO_UDBL_DIVISION)
00133             /* mbedtls_t_udbl defined as 128-bit unsigned int */
00134             typedef unsigned int mbedtls_t_udbl __attribute__((mode(TI)));
00135             #define MBEDTLS_HAVE_UDBL
00136         #endif /* !MBEDTLS_NO_UDBL_DIVISION */
00137     #elif defined(__ARMCC_VERSION) && defined(__aarch64__)
00138         /*
00139          * __ARMCC_VERSION is defined for both armcc and armclang and
00140          * __aarch64__ is only defined by armclang when compiling 64-bit code
00141          */
00142         #if !defined(MBEDTLS_HAVE_INT64)
00143             #define MBEDTLS_HAVE_INT64
00144         #endif /* !MBEDTLS_HAVE_INT64 */
00145         typedef  int64_t mbedtls_mpi_sint;
00146         typedef uint64_t mbedtls_mpi_uint;
00147         #if !defined(MBEDTLS_NO_UDBL_DIVISION)
00148             /* mbedtls_t_udbl defined as 128-bit unsigned int */
00149             typedef __uint128_t mbedtls_t_udbl;
00150             #define MBEDTLS_HAVE_UDBL
00151         #endif /* !MBEDTLS_NO_UDBL_DIVISION */
00152     #elif defined(MBEDTLS_HAVE_INT64)
00153         /* Force 64-bit integers with unknown compiler */
00154         typedef  int64_t mbedtls_mpi_sint;
00155         typedef uint64_t mbedtls_mpi_uint;
00156     #endif
00157 #endif /* !MBEDTLS_HAVE_INT32 */
00158 
00159 #if !defined(MBEDTLS_HAVE_INT64)
00160     /* Default to 32-bit compilation */
00161     #if !defined(MBEDTLS_HAVE_INT32)
00162         #define MBEDTLS_HAVE_INT32
00163     #endif /* !MBEDTLS_HAVE_INT32 */
00164     typedef  int32_t mbedtls_mpi_sint;
00165     typedef uint32_t mbedtls_mpi_uint;
00166     #if !defined(MBEDTLS_NO_UDBL_DIVISION)
00167         typedef uint64_t mbedtls_t_udbl;
00168         #define MBEDTLS_HAVE_UDBL
00169     #endif /* !MBEDTLS_NO_UDBL_DIVISION */
00170 #endif /* !MBEDTLS_HAVE_INT64 */
00171 
00172 #ifdef __cplusplus
00173 extern "C" {
00174 #endif
00175 
00176 /**
00177  * \brief          MPI structure
00178  */
00179 typedef struct
00180 {
00181     int s ;              /*!<  integer sign      */
00182     size_t n ;           /*!<  total # of limbs  */
00183     mbedtls_mpi_uint *p ;          /*!<  pointer to limbs  */
00184 }
00185 mbedtls_mpi;
00186 
00187 /**
00188  * \brief           Initialize one MPI (make internal references valid)
00189  *                  This just makes it ready to be set or freed,
00190  *                  but does not define a value for the MPI.
00191  *
00192  * \param X         One MPI to initialize.
00193  */
00194 void mbedtls_mpi_init( mbedtls_mpi *X );
00195 
00196 /**
00197  * \brief          Unallocate one MPI
00198  *
00199  * \param X        One MPI to unallocate.
00200  */
00201 void mbedtls_mpi_free( mbedtls_mpi *X );
00202 
00203 /**
00204  * \brief          Enlarge to the specified number of limbs
00205  *
00206  * \param X        MPI to grow
00207  * \param nblimbs  The target number of limbs
00208  *
00209  * \return         0 if successful,
00210  *                 MBEDTLS_ERR_MPI_ALLOC_FAILED if memory allocation failed
00211  */
00212 int mbedtls_mpi_grow( mbedtls_mpi *X, size_t nblimbs );
00213 
00214 /**
00215  * \brief          Resize down, keeping at least the specified number of limbs
00216  *
00217  * \param X        MPI to shrink
00218  * \param nblimbs  The minimum number of limbs to keep
00219  *
00220  * \return         0 if successful,
00221  *                 MBEDTLS_ERR_MPI_ALLOC_FAILED if memory allocation failed
00222  */
00223 int mbedtls_mpi_shrink( mbedtls_mpi *X, size_t nblimbs );
00224 
00225 /**
00226  * \brief          Copy the contents of Y into X
00227  *
00228  * \param X        Destination MPI
00229  * \param Y        Source MPI
00230  *
00231  * \return         0 if successful,
00232  *                 MBEDTLS_ERR_MPI_ALLOC_FAILED if memory allocation failed
00233  */
00234 int mbedtls_mpi_copy( mbedtls_mpi *X, const mbedtls_mpi *Y );
00235 
00236 /**
00237  * \brief          Swap the contents of X and Y
00238  *
00239  * \param X        First MPI value
00240  * \param Y        Second MPI value
00241  */
00242 void mbedtls_mpi_swap( mbedtls_mpi *X, mbedtls_mpi *Y );
00243 
00244 /**
00245  * \brief          Safe conditional assignement X = Y if assign is 1
00246  *
00247  * \param X        MPI to conditionally assign to
00248  * \param Y        Value to be assigned
00249  * \param assign   1: perform the assignment, 0: keep X's original value
00250  *
00251  * \return         0 if successful,
00252  *                 MBEDTLS_ERR_MPI_ALLOC_FAILED if memory allocation failed,
00253  *
00254  * \note           This function is equivalent to
00255  *                      if( assign ) mbedtls_mpi_copy( X, Y );
00256  *                 except that it avoids leaking any information about whether
00257  *                 the assignment was done or not (the above code may leak
00258  *                 information through branch prediction and/or memory access
00259  *                 patterns analysis).
00260  */
00261 int mbedtls_mpi_safe_cond_assign( mbedtls_mpi *X, const mbedtls_mpi *Y, unsigned char assign );
00262 
00263 /**
00264  * \brief          Safe conditional swap X <-> Y if swap is 1
00265  *
00266  * \param X        First mbedtls_mpi value
00267  * \param Y        Second mbedtls_mpi value
00268  * \param assign   1: perform the swap, 0: keep X and Y's original values
00269  *
00270  * \return         0 if successful,
00271  *                 MBEDTLS_ERR_MPI_ALLOC_FAILED if memory allocation failed,
00272  *
00273  * \note           This function is equivalent to
00274  *                      if( assign ) mbedtls_mpi_swap( X, Y );
00275  *                 except that it avoids leaking any information about whether
00276  *                 the assignment was done or not (the above code may leak
00277  *                 information through branch prediction and/or memory access
00278  *                 patterns analysis).
00279  */
00280 int mbedtls_mpi_safe_cond_swap( mbedtls_mpi *X, mbedtls_mpi *Y, unsigned char assign );
00281 
00282 /**
00283  * \brief          Set value from integer
00284  *
00285  * \param X        MPI to set
00286  * \param z        Value to use
00287  *
00288  * \return         0 if successful,
00289  *                 MBEDTLS_ERR_MPI_ALLOC_FAILED if memory allocation failed
00290  */
00291 int mbedtls_mpi_lset( mbedtls_mpi *X, mbedtls_mpi_sint z );
00292 
00293 /**
00294  * \brief          Get a specific bit from X
00295  *
00296  * \param X        MPI to use
00297  * \param pos      Zero-based index of the bit in X
00298  *
00299  * \return         Either a 0 or a 1
00300  */
00301 int mbedtls_mpi_get_bit( const mbedtls_mpi *X, size_t pos );
00302 
00303 /**
00304  * \brief          Set a bit of X to a specific value of 0 or 1
00305  *
00306  * \note           Will grow X if necessary to set a bit to 1 in a not yet
00307  *                 existing limb. Will not grow if bit should be set to 0
00308  *
00309  * \param X        MPI to use
00310  * \param pos      Zero-based index of the bit in X
00311  * \param val      The value to set the bit to (0 or 1)
00312  *
00313  * \return         0 if successful,
00314  *                 MBEDTLS_ERR_MPI_ALLOC_FAILED if memory allocation failed,
00315  *                 MBEDTLS_ERR_MPI_BAD_INPUT_DATA if val is not 0 or 1
00316  */
00317 int mbedtls_mpi_set_bit( mbedtls_mpi *X, size_t pos, unsigned char val );
00318 
00319 /**
00320  * \brief          Return the number of zero-bits before the least significant
00321  *                 '1' bit
00322  *
00323  * Note: Thus also the zero-based index of the least significant '1' bit
00324  *
00325  * \param X        MPI to use
00326  */
00327 size_t mbedtls_mpi_lsb( const mbedtls_mpi *X );
00328 
00329 /**
00330  * \brief          Return the number of bits up to and including the most
00331  *                 significant '1' bit'
00332  *
00333  * Note: Thus also the one-based index of the most significant '1' bit
00334  *
00335  * \param X        MPI to use
00336  */
00337 size_t mbedtls_mpi_bitlen( const mbedtls_mpi *X );
00338 
00339 /**
00340  * \brief          Return the total size in bytes
00341  *
00342  * \param X        MPI to use
00343  */
00344 size_t mbedtls_mpi_size( const mbedtls_mpi *X );
00345 
00346 /**
00347  * \brief          Import from an ASCII string
00348  *
00349  * \param X        Destination MPI
00350  * \param radix    Input numeric base
00351  * \param s        Null-terminated string buffer
00352  *
00353  * \return         0 if successful, or a MBEDTLS_ERR_MPI_XXX error code
00354  */
00355 int mbedtls_mpi_read_string( mbedtls_mpi *X, int radix, const char *s );
00356 
00357 /**
00358  * \brief          Export into an ASCII string
00359  *
00360  * \param X        Source MPI
00361  * \param radix    Output numeric base
00362  * \param buf      Buffer to write the string to
00363  * \param buflen   Length of buf
00364  * \param olen     Length of the string written, including final NUL byte
00365  *
00366  * \return         0 if successful, or a MBEDTLS_ERR_MPI_XXX error code.
00367  *                 *olen is always updated to reflect the amount
00368  *                 of data that has (or would have) been written.
00369  *
00370  * \note           Call this function with buflen = 0 to obtain the
00371  *                 minimum required buffer size in *olen.
00372  */
00373 int mbedtls_mpi_write_string( const mbedtls_mpi *X, int radix,
00374                               char *buf, size_t buflen, size_t *olen );
00375 
00376 #if defined(MBEDTLS_FS_IO)
00377 /**
00378  * \brief          Read MPI from a line in an opened file
00379  *
00380  * \param X        Destination MPI
00381  * \param radix    Input numeric base
00382  * \param fin      Input file handle
00383  *
00384  * \return         0 if successful, MBEDTLS_ERR_MPI_BUFFER_TOO_SMALL if
00385  *                 the file read buffer is too small or a
00386  *                 MBEDTLS_ERR_MPI_XXX error code
00387  *
00388  * \note           On success, this function advances the file stream
00389  *                 to the end of the current line or to EOF.
00390  *
00391  *                 The function returns 0 on an empty line.
00392  *
00393  *                 Leading whitespaces are ignored, as is a
00394  *                 '0x' prefix for radix 16.
00395  *
00396  */
00397 int mbedtls_mpi_read_file( mbedtls_mpi *X, int radix, FILE *fin );
00398 
00399 /**
00400  * \brief          Write X into an opened file, or stdout if fout is NULL
00401  *
00402  * \param p        Prefix, can be NULL
00403  * \param X        Source MPI
00404  * \param radix    Output numeric base
00405  * \param fout     Output file handle (can be NULL)
00406  *
00407  * \return         0 if successful, or a MBEDTLS_ERR_MPI_XXX error code
00408  *
00409  * \note           Set fout == NULL to print X on the console.
00410  */
00411 int mbedtls_mpi_write_file( const char *p, const mbedtls_mpi *X, int radix, FILE *fout );
00412 #endif /* MBEDTLS_FS_IO */
00413 
00414 /**
00415  * \brief          Import X from unsigned binary data, big endian
00416  *
00417  * \param X        Destination MPI
00418  * \param buf      Input buffer
00419  * \param buflen   Input buffer size
00420  *
00421  * \return         0 if successful,
00422  *                 MBEDTLS_ERR_MPI_ALLOC_FAILED if memory allocation failed
00423  */
00424 int mbedtls_mpi_read_binary( mbedtls_mpi *X, const unsigned char *buf, size_t buflen );
00425 
00426 /**
00427  * \brief          Export X into unsigned binary data, big endian.
00428  *                 Always fills the whole buffer, which will start with zeros
00429  *                 if the number is smaller.
00430  *
00431  * \param X        Source MPI
00432  * \param buf      Output buffer
00433  * \param buflen   Output buffer size
00434  *
00435  * \return         0 if successful,
00436  *                 MBEDTLS_ERR_MPI_BUFFER_TOO_SMALL if buf isn't large enough
00437  */
00438 int mbedtls_mpi_write_binary( const mbedtls_mpi *X, unsigned char *buf, size_t buflen );
00439 
00440 /**
00441  * \brief          Left-shift: X <<= count
00442  *
00443  * \param X        MPI to shift
00444  * \param count    Amount to shift
00445  *
00446  * \return         0 if successful,
00447  *                 MBEDTLS_ERR_MPI_ALLOC_FAILED if memory allocation failed
00448  */
00449 int mbedtls_mpi_shift_l( mbedtls_mpi *X, size_t count );
00450 
00451 /**
00452  * \brief          Right-shift: X >>= count
00453  *
00454  * \param X        MPI to shift
00455  * \param count    Amount to shift
00456  *
00457  * \return         0 if successful,
00458  *                 MBEDTLS_ERR_MPI_ALLOC_FAILED if memory allocation failed
00459  */
00460 int mbedtls_mpi_shift_r( mbedtls_mpi *X, size_t count );
00461 
00462 /**
00463  * \brief          Compare unsigned values
00464  *
00465  * \param X        Left-hand MPI
00466  * \param Y        Right-hand MPI
00467  *
00468  * \return         1 if |X| is greater than |Y|,
00469  *                -1 if |X| is lesser  than |Y| or
00470  *                 0 if |X| is equal to |Y|
00471  */
00472 int mbedtls_mpi_cmp_abs( const mbedtls_mpi *X, const mbedtls_mpi *Y );
00473 
00474 /**
00475  * \brief          Compare signed values
00476  *
00477  * \param X        Left-hand MPI
00478  * \param Y        Right-hand MPI
00479  *
00480  * \return         1 if X is greater than Y,
00481  *                -1 if X is lesser  than Y or
00482  *                 0 if X is equal to Y
00483  */
00484 int mbedtls_mpi_cmp_mpi( const mbedtls_mpi *X, const mbedtls_mpi *Y );
00485 
00486 /**
00487  * \brief          Compare signed values
00488  *
00489  * \param X        Left-hand MPI
00490  * \param z        The integer value to compare to
00491  *
00492  * \return         1 if X is greater than z,
00493  *                -1 if X is lesser  than z or
00494  *                 0 if X is equal to z
00495  */
00496 int mbedtls_mpi_cmp_int( const mbedtls_mpi *X, mbedtls_mpi_sint z );
00497 
00498 /**
00499  * \brief          Unsigned addition: X = |A| + |B|
00500  *
00501  * \param X        Destination MPI
00502  * \param A        Left-hand MPI
00503  * \param B        Right-hand MPI
00504  *
00505  * \return         0 if successful,
00506  *                 MBEDTLS_ERR_MPI_ALLOC_FAILED if memory allocation failed
00507  */
00508 int mbedtls_mpi_add_abs( mbedtls_mpi *X, const mbedtls_mpi *A, const mbedtls_mpi *B );
00509 
00510 /**
00511  * \brief          Unsigned subtraction: X = |A| - |B|
00512  *
00513  * \param X        Destination MPI
00514  * \param A        Left-hand MPI
00515  * \param B        Right-hand MPI
00516  *
00517  * \return         0 if successful,
00518  *                 MBEDTLS_ERR_MPI_NEGATIVE_VALUE if B is greater than A
00519  */
00520 int mbedtls_mpi_sub_abs( mbedtls_mpi *X, const mbedtls_mpi *A, const mbedtls_mpi *B );
00521 
00522 /**
00523  * \brief          Signed addition: X = A + B
00524  *
00525  * \param X        Destination MPI
00526  * \param A        Left-hand MPI
00527  * \param B        Right-hand MPI
00528  *
00529  * \return         0 if successful,
00530  *                 MBEDTLS_ERR_MPI_ALLOC_FAILED if memory allocation failed
00531  */
00532 int mbedtls_mpi_add_mpi( mbedtls_mpi *X, const mbedtls_mpi *A, const mbedtls_mpi *B );
00533 
00534 /**
00535  * \brief          Signed subtraction: X = A - B
00536  *
00537  * \param X        Destination MPI
00538  * \param A        Left-hand MPI
00539  * \param B        Right-hand MPI
00540  *
00541  * \return         0 if successful,
00542  *                 MBEDTLS_ERR_MPI_ALLOC_FAILED if memory allocation failed
00543  */
00544 int mbedtls_mpi_sub_mpi( mbedtls_mpi *X, const mbedtls_mpi *A, const mbedtls_mpi *B );
00545 
00546 /**
00547  * \brief          Signed addition: X = A + b
00548  *
00549  * \param X        Destination MPI
00550  * \param A        Left-hand MPI
00551  * \param b        The integer value to add
00552  *
00553  * \return         0 if successful,
00554  *                 MBEDTLS_ERR_MPI_ALLOC_FAILED if memory allocation failed
00555  */
00556 int mbedtls_mpi_add_int( mbedtls_mpi *X, const mbedtls_mpi *A, mbedtls_mpi_sint b );
00557 
00558 /**
00559  * \brief          Signed subtraction: X = A - b
00560  *
00561  * \param X        Destination MPI
00562  * \param A        Left-hand MPI
00563  * \param b        The integer value to subtract
00564  *
00565  * \return         0 if successful,
00566  *                 MBEDTLS_ERR_MPI_ALLOC_FAILED if memory allocation failed
00567  */
00568 int mbedtls_mpi_sub_int( mbedtls_mpi *X, const mbedtls_mpi *A, mbedtls_mpi_sint b );
00569 
00570 /**
00571  * \brief          Baseline multiplication: X = A * B
00572  *
00573  * \param X        Destination MPI
00574  * \param A        Left-hand MPI
00575  * \param B        Right-hand MPI
00576  *
00577  * \return         0 if successful,
00578  *                 MBEDTLS_ERR_MPI_ALLOC_FAILED if memory allocation failed
00579  */
00580 int mbedtls_mpi_mul_mpi( mbedtls_mpi *X, const mbedtls_mpi *A, const mbedtls_mpi *B );
00581 
00582 /**
00583  * \brief          Baseline multiplication: X = A * b
00584  *
00585  * \param X        Destination MPI
00586  * \param A        Left-hand MPI
00587  * \param b        The unsigned integer value to multiply with
00588  *
00589  * \note           b is unsigned
00590  *
00591  * \return         0 if successful,
00592  *                 MBEDTLS_ERR_MPI_ALLOC_FAILED if memory allocation failed
00593  */
00594 int mbedtls_mpi_mul_int( mbedtls_mpi *X, const mbedtls_mpi *A, mbedtls_mpi_uint b );
00595 
00596 /**
00597  * \brief          Division by mbedtls_mpi: A = Q * B + R
00598  *
00599  * \param Q        Destination MPI for the quotient
00600  * \param R        Destination MPI for the rest value
00601  * \param A        Left-hand MPI
00602  * \param B        Right-hand MPI
00603  *
00604  * \return         0 if successful,
00605  *                 MBEDTLS_ERR_MPI_ALLOC_FAILED if memory allocation failed,
00606  *                 MBEDTLS_ERR_MPI_DIVISION_BY_ZERO if B == 0
00607  *
00608  * \note           Either Q or R can be NULL.
00609  */
00610 int mbedtls_mpi_div_mpi( mbedtls_mpi *Q, mbedtls_mpi *R, const mbedtls_mpi *A, const mbedtls_mpi *B );
00611 
00612 /**
00613  * \brief          Division by int: A = Q * b + R
00614  *
00615  * \param Q        Destination MPI for the quotient
00616  * \param R        Destination MPI for the rest value
00617  * \param A        Left-hand MPI
00618  * \param b        Integer to divide by
00619  *
00620  * \return         0 if successful,
00621  *                 MBEDTLS_ERR_MPI_ALLOC_FAILED if memory allocation failed,
00622  *                 MBEDTLS_ERR_MPI_DIVISION_BY_ZERO if b == 0
00623  *
00624  * \note           Either Q or R can be NULL.
00625  */
00626 int mbedtls_mpi_div_int( mbedtls_mpi *Q, mbedtls_mpi *R, const mbedtls_mpi *A, mbedtls_mpi_sint b );
00627 
00628 /**
00629  * \brief          Modulo: R = A mod B
00630  *
00631  * \param R        Destination MPI for the rest value
00632  * \param A        Left-hand MPI
00633  * \param B        Right-hand MPI
00634  *
00635  * \return         0 if successful,
00636  *                 MBEDTLS_ERR_MPI_ALLOC_FAILED if memory allocation failed,
00637  *                 MBEDTLS_ERR_MPI_DIVISION_BY_ZERO if B == 0,
00638  *                 MBEDTLS_ERR_MPI_NEGATIVE_VALUE if B < 0
00639  */
00640 int mbedtls_mpi_mod_mpi( mbedtls_mpi *R, const mbedtls_mpi *A, const mbedtls_mpi *B );
00641 
00642 /**
00643  * \brief          Modulo: r = A mod b
00644  *
00645  * \param r        Destination mbedtls_mpi_uint
00646  * \param A        Left-hand MPI
00647  * \param b        Integer to divide by
00648  *
00649  * \return         0 if successful,
00650  *                 MBEDTLS_ERR_MPI_ALLOC_FAILED if memory allocation failed,
00651  *                 MBEDTLS_ERR_MPI_DIVISION_BY_ZERO if b == 0,
00652  *                 MBEDTLS_ERR_MPI_NEGATIVE_VALUE if b < 0
00653  */
00654 int mbedtls_mpi_mod_int( mbedtls_mpi_uint *r, const mbedtls_mpi *A, mbedtls_mpi_sint b );
00655 
00656 /**
00657  * \brief          Sliding-window exponentiation: X = A^E mod N
00658  *
00659  * \param X        Destination MPI
00660  * \param A        Left-hand MPI
00661  * \param E        Exponent MPI
00662  * \param N        Modular MPI
00663  * \param _RR      Speed-up MPI used for recalculations
00664  *
00665  * \return         0 if successful,
00666  *                 MBEDTLS_ERR_MPI_ALLOC_FAILED if memory allocation failed,
00667  *                 MBEDTLS_ERR_MPI_BAD_INPUT_DATA if N is negative or even or
00668  *                 if E is negative
00669  *
00670  * \note           _RR is used to avoid re-computing R*R mod N across
00671  *                 multiple calls, which speeds up things a bit. It can
00672  *                 be set to NULL if the extra performance is unneeded.
00673  */
00674 int mbedtls_mpi_exp_mod( mbedtls_mpi *X, const mbedtls_mpi *A, const mbedtls_mpi *E, const mbedtls_mpi *N, mbedtls_mpi *_RR );
00675 
00676 /**
00677  * \brief          Fill an MPI X with size bytes of random
00678  *
00679  * \param X        Destination MPI
00680  * \param size     Size in bytes
00681  * \param f_rng    RNG function
00682  * \param p_rng    RNG parameter
00683  *
00684  * \return         0 if successful,
00685  *                 MBEDTLS_ERR_MPI_ALLOC_FAILED if memory allocation failed
00686  */
00687 int mbedtls_mpi_fill_random( mbedtls_mpi *X, size_t size,
00688                      int (*f_rng)(void *, unsigned char *, size_t),
00689                      void *p_rng );
00690 
00691 /**
00692  * \brief          Greatest common divisor: G = gcd(A, B)
00693  *
00694  * \param G        Destination MPI
00695  * \param A        Left-hand MPI
00696  * \param B        Right-hand MPI
00697  *
00698  * \return         0 if successful,
00699  *                 MBEDTLS_ERR_MPI_ALLOC_FAILED if memory allocation failed
00700  */
00701 int mbedtls_mpi_gcd( mbedtls_mpi *G, const mbedtls_mpi *A, const mbedtls_mpi *B );
00702 
00703 /**
00704  * \brief          Modular inverse: X = A^-1 mod N
00705  *
00706  * \param X        Destination MPI
00707  * \param A        Left-hand MPI
00708  * \param N        Right-hand MPI
00709  *
00710  * \return         0 if successful,
00711  *                 MBEDTLS_ERR_MPI_ALLOC_FAILED if memory allocation failed,
00712  *                 MBEDTLS_ERR_MPI_BAD_INPUT_DATA if N is <= 1,
00713                    MBEDTLS_ERR_MPI_NOT_ACCEPTABLE if A has no inverse mod N.
00714  */
00715 int mbedtls_mpi_inv_mod( mbedtls_mpi *X, const mbedtls_mpi *A, const mbedtls_mpi *N );
00716 
00717 /**
00718  * \brief          Miller-Rabin primality test
00719  *
00720  * \param X        MPI to check
00721  * \param f_rng    RNG function
00722  * \param p_rng    RNG parameter
00723  *
00724  * \return         0 if successful (probably prime),
00725  *                 MBEDTLS_ERR_MPI_ALLOC_FAILED if memory allocation failed,
00726  *                 MBEDTLS_ERR_MPI_NOT_ACCEPTABLE if X is not prime
00727  */
00728 int mbedtls_mpi_is_prime( const mbedtls_mpi *X,
00729                   int (*f_rng)(void *, unsigned char *, size_t),
00730                   void *p_rng );
00731 
00732 /**
00733  * \brief          Prime number generation
00734  *
00735  * \param X        Destination MPI
00736  * \param nbits    Required size of X in bits
00737  *                 ( 3 <= nbits <= MBEDTLS_MPI_MAX_BITS )
00738  * \param dh_flag  If 1, then (X-1)/2 will be prime too
00739  * \param f_rng    RNG function
00740  * \param p_rng    RNG parameter
00741  *
00742  * \return         0 if successful (probably prime),
00743  *                 MBEDTLS_ERR_MPI_ALLOC_FAILED if memory allocation failed,
00744  *                 MBEDTLS_ERR_MPI_BAD_INPUT_DATA if nbits is < 3
00745  */
00746 int mbedtls_mpi_gen_prime( mbedtls_mpi *X, size_t nbits, int dh_flag,
00747                    int (*f_rng)(void *, unsigned char *, size_t),
00748                    void *p_rng );
00749 
00750 /**
00751  * \brief          Checkup routine
00752  *
00753  * \return         0 if successful, or 1 if the test failed
00754  */
00755 int mbedtls_mpi_self_test( int verbose );
00756 
00757 #ifdef __cplusplus
00758 }
00759 #endif
00760 
00761 #endif /* bignum.h */