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-bit integers can be forced on 64-bit arches (eg. for testing purposes)
00107  * by defining MBEDTLS_HAVE_INT32 and undefining MBEDTLS_HAVE_ASM
00108  */
00109 #if ( ! defined(MBEDTLS_HAVE_INT32) && \
00110         defined(_MSC_VER) && defined(_M_AMD64) )
00111   #define MBEDTLS_HAVE_INT64
00112   typedef  int64_t mbedtls_mpi_sint;
00113   typedef uint64_t mbedtls_mpi_uint;
00114 #else
00115   #if ( ! defined(MBEDTLS_HAVE_INT32) &&               \
00116         defined(__GNUC__) && (                          \
00117         defined(__amd64__) || defined(__x86_64__)    || \
00118         defined(__ppc64__) || defined(__powerpc64__) || \
00119         defined(__ia64__)  || defined(__alpha__)     || \
00120         (defined(__sparc__) && defined(__arch64__))  || \
00121         defined(__s390x__) || defined(__mips64) ) )
00122      #define MBEDTLS_HAVE_INT64
00123      typedef  int64_t mbedtls_mpi_sint;
00124      typedef uint64_t mbedtls_mpi_uint;
00125      /* mbedtls_t_udbl defined as 128-bit unsigned int */
00126      typedef unsigned int mbedtls_t_udbl __attribute__((mode(TI)));
00127      #define MBEDTLS_HAVE_UDBL
00128   #else
00129      #define MBEDTLS_HAVE_INT32
00130      typedef  int32_t mbedtls_mpi_sint;
00131      typedef uint32_t mbedtls_mpi_uint;
00132      typedef uint64_t mbedtls_t_udbl;
00133      #define MBEDTLS_HAVE_UDBL
00134   #endif /* !MBEDTLS_HAVE_INT32 && __GNUC__ && 64-bit platform */
00135 #endif /* !MBEDTLS_HAVE_INT32 && _MSC_VER && _M_AMD64 */
00136 
00137 #ifdef __cplusplus
00138 extern "C" {
00139 #endif
00140 
00141 /**
00142  * \brief          MPI structure
00143  */
00144 typedef struct
00145 {
00146     int s ;              /*!<  integer sign      */
00147     size_t n ;           /*!<  total # of limbs  */
00148     mbedtls_mpi_uint *p ;          /*!<  pointer to limbs  */
00149 }
00150 mbedtls_mpi;
00151 
00152 /**
00153  * \brief           Initialize one MPI (make internal references valid)
00154  *                  This just makes it ready to be set or freed,
00155  *                  but does not define a value for the MPI.
00156  *
00157  * \param X         One MPI to initialize.
00158  */
00159 void mbedtls_mpi_init( mbedtls_mpi *X );
00160 
00161 /**
00162  * \brief          Unallocate one MPI
00163  *
00164  * \param X        One MPI to unallocate.
00165  */
00166 void mbedtls_mpi_free( mbedtls_mpi *X );
00167 
00168 /**
00169  * \brief          Enlarge to the specified number of limbs
00170  *
00171  * \param X        MPI to grow
00172  * \param nblimbs  The target number of limbs
00173  *
00174  * \return         0 if successful,
00175  *                 MBEDTLS_ERR_MPI_ALLOC_FAILED if memory allocation failed
00176  */
00177 int mbedtls_mpi_grow( mbedtls_mpi *X, size_t nblimbs );
00178 
00179 /**
00180  * \brief          Resize down, keeping at least the specified number of limbs
00181  *
00182  * \param X        MPI to shrink
00183  * \param nblimbs  The minimum number of limbs to keep
00184  *
00185  * \return         0 if successful,
00186  *                 MBEDTLS_ERR_MPI_ALLOC_FAILED if memory allocation failed
00187  */
00188 int mbedtls_mpi_shrink( mbedtls_mpi *X, size_t nblimbs );
00189 
00190 /**
00191  * \brief          Copy the contents of Y into X
00192  *
00193  * \param X        Destination MPI
00194  * \param Y        Source MPI
00195  *
00196  * \return         0 if successful,
00197  *                 MBEDTLS_ERR_MPI_ALLOC_FAILED if memory allocation failed
00198  */
00199 int mbedtls_mpi_copy( mbedtls_mpi *X, const mbedtls_mpi *Y );
00200 
00201 /**
00202  * \brief          Swap the contents of X and Y
00203  *
00204  * \param X        First MPI value
00205  * \param Y        Second MPI value
00206  */
00207 void mbedtls_mpi_swap( mbedtls_mpi *X, mbedtls_mpi *Y );
00208 
00209 /**
00210  * \brief          Safe conditional assignement X = Y if assign is 1
00211  *
00212  * \param X        MPI to conditionally assign to
00213  * \param Y        Value to be assigned
00214  * \param assign   1: perform the assignment, 0: keep X's original value
00215  *
00216  * \return         0 if successful,
00217  *                 MBEDTLS_ERR_MPI_ALLOC_FAILED if memory allocation failed,
00218  *
00219  * \note           This function is equivalent to
00220  *                      if( assign ) mbedtls_mpi_copy( X, Y );
00221  *                 except that it avoids leaking any information about whether
00222  *                 the assignment was done or not (the above code may leak
00223  *                 information through branch prediction and/or memory access
00224  *                 patterns analysis).
00225  */
00226 int mbedtls_mpi_safe_cond_assign( mbedtls_mpi *X, const mbedtls_mpi *Y, unsigned char assign );
00227 
00228 /**
00229  * \brief          Safe conditional swap X <-> Y if swap is 1
00230  *
00231  * \param X        First mbedtls_mpi value
00232  * \param Y        Second mbedtls_mpi value
00233  * \param assign   1: perform the swap, 0: keep X and Y's original values
00234  *
00235  * \return         0 if successful,
00236  *                 MBEDTLS_ERR_MPI_ALLOC_FAILED if memory allocation failed,
00237  *
00238  * \note           This function is equivalent to
00239  *                      if( assign ) mbedtls_mpi_swap( X, Y );
00240  *                 except that it avoids leaking any information about whether
00241  *                 the assignment was done or not (the above code may leak
00242  *                 information through branch prediction and/or memory access
00243  *                 patterns analysis).
00244  */
00245 int mbedtls_mpi_safe_cond_swap( mbedtls_mpi *X, mbedtls_mpi *Y, unsigned char assign );
00246 
00247 /**
00248  * \brief          Set value from integer
00249  *
00250  * \param X        MPI to set
00251  * \param z        Value to use
00252  *
00253  * \return         0 if successful,
00254  *                 MBEDTLS_ERR_MPI_ALLOC_FAILED if memory allocation failed
00255  */
00256 int mbedtls_mpi_lset( mbedtls_mpi *X, mbedtls_mpi_sint z );
00257 
00258 /**
00259  * \brief          Get a specific bit from X
00260  *
00261  * \param X        MPI to use
00262  * \param pos      Zero-based index of the bit in X
00263  *
00264  * \return         Either a 0 or a 1
00265  */
00266 int mbedtls_mpi_get_bit( const mbedtls_mpi *X, size_t pos );
00267 
00268 /**
00269  * \brief          Set a bit of X to a specific value of 0 or 1
00270  *
00271  * \note           Will grow X if necessary to set a bit to 1 in a not yet
00272  *                 existing limb. Will not grow if bit should be set to 0
00273  *
00274  * \param X        MPI to use
00275  * \param pos      Zero-based index of the bit in X
00276  * \param val      The value to set the bit to (0 or 1)
00277  *
00278  * \return         0 if successful,
00279  *                 MBEDTLS_ERR_MPI_ALLOC_FAILED if memory allocation failed,
00280  *                 MBEDTLS_ERR_MPI_BAD_INPUT_DATA if val is not 0 or 1
00281  */
00282 int mbedtls_mpi_set_bit( mbedtls_mpi *X, size_t pos, unsigned char val );
00283 
00284 /**
00285  * \brief          Return the number of zero-bits before the least significant
00286  *                 '1' bit
00287  *
00288  * Note: Thus also the zero-based index of the least significant '1' bit
00289  *
00290  * \param X        MPI to use
00291  */
00292 size_t mbedtls_mpi_lsb( const mbedtls_mpi *X );
00293 
00294 /**
00295  * \brief          Return the number of bits up to and including the most
00296  *                 significant '1' bit'
00297  *
00298  * Note: Thus also the one-based index of the most significant '1' bit
00299  *
00300  * \param X        MPI to use
00301  */
00302 size_t mbedtls_mpi_bitlen( const mbedtls_mpi *X );
00303 
00304 /**
00305  * \brief          Return the total size in bytes
00306  *
00307  * \param X        MPI to use
00308  */
00309 size_t mbedtls_mpi_size( const mbedtls_mpi *X );
00310 
00311 /**
00312  * \brief          Import from an ASCII string
00313  *
00314  * \param X        Destination MPI
00315  * \param radix    Input numeric base
00316  * \param s        Null-terminated string buffer
00317  *
00318  * \return         0 if successful, or a MBEDTLS_ERR_MPI_XXX error code
00319  */
00320 int mbedtls_mpi_read_string( mbedtls_mpi *X, int radix, const char *s );
00321 
00322 /**
00323  * \brief          Export into an ASCII string
00324  *
00325  * \param X        Source MPI
00326  * \param radix    Output numeric base
00327  * \param buf      Buffer to write the string to
00328  * \param buflen   Length of buf
00329  * \param olen     Length of the string written, including final NUL byte
00330  *
00331  * \return         0 if successful, or a MBEDTLS_ERR_MPI_XXX error code.
00332  *                 *olen is always updated to reflect the amount
00333  *                 of data that has (or would have) been written.
00334  *
00335  * \note           Call this function with buflen = 0 to obtain the
00336  *                 minimum required buffer size in *olen.
00337  */
00338 int mbedtls_mpi_write_string( const mbedtls_mpi *X, int radix,
00339                               char *buf, size_t buflen, size_t *olen );
00340 
00341 #if defined(MBEDTLS_FS_IO)
00342 /**
00343  * \brief          Read X from an opened file
00344  *
00345  * \param X        Destination MPI
00346  * \param radix    Input numeric base
00347  * \param fin      Input file handle
00348  *
00349  * \return         0 if successful, MBEDTLS_ERR_MPI_BUFFER_TOO_SMALL if
00350  *                 the file read buffer is too small or a
00351  *                 MBEDTLS_ERR_MPI_XXX error code
00352  */
00353 int mbedtls_mpi_read_file( mbedtls_mpi *X, int radix, FILE *fin );
00354 
00355 /**
00356  * \brief          Write X into an opened file, or stdout if fout is NULL
00357  *
00358  * \param p        Prefix, can be NULL
00359  * \param X        Source MPI
00360  * \param radix    Output numeric base
00361  * \param fout     Output file handle (can be NULL)
00362  *
00363  * \return         0 if successful, or a MBEDTLS_ERR_MPI_XXX error code
00364  *
00365  * \note           Set fout == NULL to print X on the console.
00366  */
00367 int mbedtls_mpi_write_file( const char *p, const mbedtls_mpi *X, int radix, FILE *fout );
00368 #endif /* MBEDTLS_FS_IO */
00369 
00370 /**
00371  * \brief          Import X from unsigned binary data, big endian
00372  *
00373  * \param X        Destination MPI
00374  * \param buf      Input buffer
00375  * \param buflen   Input buffer size
00376  *
00377  * \return         0 if successful,
00378  *                 MBEDTLS_ERR_MPI_ALLOC_FAILED if memory allocation failed
00379  */
00380 int mbedtls_mpi_read_binary( mbedtls_mpi *X, const unsigned char *buf, size_t buflen );
00381 
00382 /**
00383  * \brief          Export X into unsigned binary data, big endian.
00384  *                 Always fills the whole buffer, which will start with zeros
00385  *                 if the number is smaller.
00386  *
00387  * \param X        Source MPI
00388  * \param buf      Output buffer
00389  * \param buflen   Output buffer size
00390  *
00391  * \return         0 if successful,
00392  *                 MBEDTLS_ERR_MPI_BUFFER_TOO_SMALL if buf isn't large enough
00393  */
00394 int mbedtls_mpi_write_binary( const mbedtls_mpi *X, unsigned char *buf, size_t buflen );
00395 
00396 /**
00397  * \brief          Left-shift: X <<= count
00398  *
00399  * \param X        MPI to shift
00400  * \param count    Amount to shift
00401  *
00402  * \return         0 if successful,
00403  *                 MBEDTLS_ERR_MPI_ALLOC_FAILED if memory allocation failed
00404  */
00405 int mbedtls_mpi_shift_l( mbedtls_mpi *X, size_t count );
00406 
00407 /**
00408  * \brief          Right-shift: X >>= count
00409  *
00410  * \param X        MPI to shift
00411  * \param count    Amount to shift
00412  *
00413  * \return         0 if successful,
00414  *                 MBEDTLS_ERR_MPI_ALLOC_FAILED if memory allocation failed
00415  */
00416 int mbedtls_mpi_shift_r( mbedtls_mpi *X, size_t count );
00417 
00418 /**
00419  * \brief          Compare unsigned values
00420  *
00421  * \param X        Left-hand MPI
00422  * \param Y        Right-hand MPI
00423  *
00424  * \return         1 if |X| is greater than |Y|,
00425  *                -1 if |X| is lesser  than |Y| or
00426  *                 0 if |X| is equal to |Y|
00427  */
00428 int mbedtls_mpi_cmp_abs( const mbedtls_mpi *X, const mbedtls_mpi *Y );
00429 
00430 /**
00431  * \brief          Compare signed values
00432  *
00433  * \param X        Left-hand MPI
00434  * \param Y        Right-hand MPI
00435  *
00436  * \return         1 if X is greater than Y,
00437  *                -1 if X is lesser  than Y or
00438  *                 0 if X is equal to Y
00439  */
00440 int mbedtls_mpi_cmp_mpi( const mbedtls_mpi *X, const mbedtls_mpi *Y );
00441 
00442 /**
00443  * \brief          Compare signed values
00444  *
00445  * \param X        Left-hand MPI
00446  * \param z        The integer value to compare to
00447  *
00448  * \return         1 if X is greater than z,
00449  *                -1 if X is lesser  than z or
00450  *                 0 if X is equal to z
00451  */
00452 int mbedtls_mpi_cmp_int( const mbedtls_mpi *X, mbedtls_mpi_sint z );
00453 
00454 /**
00455  * \brief          Unsigned addition: X = |A| + |B|
00456  *
00457  * \param X        Destination MPI
00458  * \param A        Left-hand MPI
00459  * \param B        Right-hand MPI
00460  *
00461  * \return         0 if successful,
00462  *                 MBEDTLS_ERR_MPI_ALLOC_FAILED if memory allocation failed
00463  */
00464 int mbedtls_mpi_add_abs( mbedtls_mpi *X, const mbedtls_mpi *A, const mbedtls_mpi *B );
00465 
00466 /**
00467  * \brief          Unsigned subtraction: X = |A| - |B|
00468  *
00469  * \param X        Destination MPI
00470  * \param A        Left-hand MPI
00471  * \param B        Right-hand MPI
00472  *
00473  * \return         0 if successful,
00474  *                 MBEDTLS_ERR_MPI_NEGATIVE_VALUE if B is greater than A
00475  */
00476 int mbedtls_mpi_sub_abs( mbedtls_mpi *X, const mbedtls_mpi *A, const mbedtls_mpi *B );
00477 
00478 /**
00479  * \brief          Signed addition: X = A + B
00480  *
00481  * \param X        Destination MPI
00482  * \param A        Left-hand MPI
00483  * \param B        Right-hand MPI
00484  *
00485  * \return         0 if successful,
00486  *                 MBEDTLS_ERR_MPI_ALLOC_FAILED if memory allocation failed
00487  */
00488 int mbedtls_mpi_add_mpi( mbedtls_mpi *X, const mbedtls_mpi *A, const mbedtls_mpi *B );
00489 
00490 /**
00491  * \brief          Signed subtraction: X = A - B
00492  *
00493  * \param X        Destination MPI
00494  * \param A        Left-hand MPI
00495  * \param B        Right-hand MPI
00496  *
00497  * \return         0 if successful,
00498  *                 MBEDTLS_ERR_MPI_ALLOC_FAILED if memory allocation failed
00499  */
00500 int mbedtls_mpi_sub_mpi( mbedtls_mpi *X, const mbedtls_mpi *A, const mbedtls_mpi *B );
00501 
00502 /**
00503  * \brief          Signed addition: X = A + b
00504  *
00505  * \param X        Destination MPI
00506  * \param A        Left-hand MPI
00507  * \param b        The integer value to add
00508  *
00509  * \return         0 if successful,
00510  *                 MBEDTLS_ERR_MPI_ALLOC_FAILED if memory allocation failed
00511  */
00512 int mbedtls_mpi_add_int( mbedtls_mpi *X, const mbedtls_mpi *A, mbedtls_mpi_sint b );
00513 
00514 /**
00515  * \brief          Signed subtraction: X = A - b
00516  *
00517  * \param X        Destination MPI
00518  * \param A        Left-hand MPI
00519  * \param b        The integer value to subtract
00520  *
00521  * \return         0 if successful,
00522  *                 MBEDTLS_ERR_MPI_ALLOC_FAILED if memory allocation failed
00523  */
00524 int mbedtls_mpi_sub_int( mbedtls_mpi *X, const mbedtls_mpi *A, mbedtls_mpi_sint b );
00525 
00526 /**
00527  * \brief          Baseline multiplication: X = A * B
00528  *
00529  * \param X        Destination MPI
00530  * \param A        Left-hand MPI
00531  * \param B        Right-hand MPI
00532  *
00533  * \return         0 if successful,
00534  *                 MBEDTLS_ERR_MPI_ALLOC_FAILED if memory allocation failed
00535  */
00536 int mbedtls_mpi_mul_mpi( mbedtls_mpi *X, const mbedtls_mpi *A, const mbedtls_mpi *B );
00537 
00538 /**
00539  * \brief          Baseline multiplication: X = A * b
00540  *
00541  * \param X        Destination MPI
00542  * \param A        Left-hand MPI
00543  * \param b        The unsigned integer value to multiply with
00544  *
00545  * \note           b is unsigned
00546  *
00547  * \return         0 if successful,
00548  *                 MBEDTLS_ERR_MPI_ALLOC_FAILED if memory allocation failed
00549  */
00550 int mbedtls_mpi_mul_int( mbedtls_mpi *X, const mbedtls_mpi *A, mbedtls_mpi_uint b );
00551 
00552 /**
00553  * \brief          Division by mbedtls_mpi: A = Q * B + R
00554  *
00555  * \param Q        Destination MPI for the quotient
00556  * \param R        Destination MPI for the rest value
00557  * \param A        Left-hand MPI
00558  * \param B        Right-hand MPI
00559  *
00560  * \return         0 if successful,
00561  *                 MBEDTLS_ERR_MPI_ALLOC_FAILED if memory allocation failed,
00562  *                 MBEDTLS_ERR_MPI_DIVISION_BY_ZERO if B == 0
00563  *
00564  * \note           Either Q or R can be NULL.
00565  */
00566 int mbedtls_mpi_div_mpi( mbedtls_mpi *Q, mbedtls_mpi *R, const mbedtls_mpi *A, const mbedtls_mpi *B );
00567 
00568 /**
00569  * \brief          Division by int: A = Q * b + R
00570  *
00571  * \param Q        Destination MPI for the quotient
00572  * \param R        Destination MPI for the rest value
00573  * \param A        Left-hand MPI
00574  * \param b        Integer to divide by
00575  *
00576  * \return         0 if successful,
00577  *                 MBEDTLS_ERR_MPI_ALLOC_FAILED if memory allocation failed,
00578  *                 MBEDTLS_ERR_MPI_DIVISION_BY_ZERO if b == 0
00579  *
00580  * \note           Either Q or R can be NULL.
00581  */
00582 int mbedtls_mpi_div_int( mbedtls_mpi *Q, mbedtls_mpi *R, const mbedtls_mpi *A, mbedtls_mpi_sint b );
00583 
00584 /**
00585  * \brief          Modulo: R = A mod B
00586  *
00587  * \param R        Destination MPI for the rest value
00588  * \param A        Left-hand MPI
00589  * \param B        Right-hand MPI
00590  *
00591  * \return         0 if successful,
00592  *                 MBEDTLS_ERR_MPI_ALLOC_FAILED if memory allocation failed,
00593  *                 MBEDTLS_ERR_MPI_DIVISION_BY_ZERO if B == 0,
00594  *                 MBEDTLS_ERR_MPI_NEGATIVE_VALUE if B < 0
00595  */
00596 int mbedtls_mpi_mod_mpi( mbedtls_mpi *R, const mbedtls_mpi *A, const mbedtls_mpi *B );
00597 
00598 /**
00599  * \brief          Modulo: r = A mod b
00600  *
00601  * \param r        Destination mbedtls_mpi_uint
00602  * \param A        Left-hand MPI
00603  * \param b        Integer to divide by
00604  *
00605  * \return         0 if successful,
00606  *                 MBEDTLS_ERR_MPI_ALLOC_FAILED if memory allocation failed,
00607  *                 MBEDTLS_ERR_MPI_DIVISION_BY_ZERO if b == 0,
00608  *                 MBEDTLS_ERR_MPI_NEGATIVE_VALUE if b < 0
00609  */
00610 int mbedtls_mpi_mod_int( mbedtls_mpi_uint *r, const mbedtls_mpi *A, mbedtls_mpi_sint b );
00611 
00612 /**
00613  * \brief          Sliding-window exponentiation: X = A^E mod N
00614  *
00615  * \param X        Destination MPI
00616  * \param A        Left-hand MPI
00617  * \param E        Exponent MPI
00618  * \param N        Modular MPI
00619  * \param _RR      Speed-up MPI used for recalculations
00620  *
00621  * \return         0 if successful,
00622  *                 MBEDTLS_ERR_MPI_ALLOC_FAILED if memory allocation failed,
00623  *                 MBEDTLS_ERR_MPI_BAD_INPUT_DATA if N is negative or even or
00624  *                 if E is negative
00625  *
00626  * \note           _RR is used to avoid re-computing R*R mod N across
00627  *                 multiple calls, which speeds up things a bit. It can
00628  *                 be set to NULL if the extra performance is unneeded.
00629  */
00630 int mbedtls_mpi_exp_mod( mbedtls_mpi *X, const mbedtls_mpi *A, const mbedtls_mpi *E, const mbedtls_mpi *N, mbedtls_mpi *_RR );
00631 
00632 /**
00633  * \brief          Fill an MPI X with size bytes of random
00634  *
00635  * \param X        Destination MPI
00636  * \param size     Size in bytes
00637  * \param f_rng    RNG function
00638  * \param p_rng    RNG parameter
00639  *
00640  * \return         0 if successful,
00641  *                 MBEDTLS_ERR_MPI_ALLOC_FAILED if memory allocation failed
00642  */
00643 int mbedtls_mpi_fill_random( mbedtls_mpi *X, size_t size,
00644                      int (*f_rng)(void *, unsigned char *, size_t),
00645                      void *p_rng );
00646 
00647 /**
00648  * \brief          Greatest common divisor: G = gcd(A, B)
00649  *
00650  * \param G        Destination MPI
00651  * \param A        Left-hand MPI
00652  * \param B        Right-hand MPI
00653  *
00654  * \return         0 if successful,
00655  *                 MBEDTLS_ERR_MPI_ALLOC_FAILED if memory allocation failed
00656  */
00657 int mbedtls_mpi_gcd( mbedtls_mpi *G, const mbedtls_mpi *A, const mbedtls_mpi *B );
00658 
00659 /**
00660  * \brief          Modular inverse: X = A^-1 mod N
00661  *
00662  * \param X        Destination MPI
00663  * \param A        Left-hand MPI
00664  * \param N        Right-hand MPI
00665  *
00666  * \return         0 if successful,
00667  *                 MBEDTLS_ERR_MPI_ALLOC_FAILED if memory allocation failed,
00668  *                 MBEDTLS_ERR_MPI_BAD_INPUT_DATA if N is negative or nil
00669                    MBEDTLS_ERR_MPI_NOT_ACCEPTABLE if A has no inverse mod N
00670  */
00671 int mbedtls_mpi_inv_mod( mbedtls_mpi *X, const mbedtls_mpi *A, const mbedtls_mpi *N );
00672 
00673 /**
00674  * \brief          Miller-Rabin primality test
00675  *
00676  * \param X        MPI to check
00677  * \param f_rng    RNG function
00678  * \param p_rng    RNG parameter
00679  *
00680  * \return         0 if successful (probably prime),
00681  *                 MBEDTLS_ERR_MPI_ALLOC_FAILED if memory allocation failed,
00682  *                 MBEDTLS_ERR_MPI_NOT_ACCEPTABLE if X is not prime
00683  */
00684 int mbedtls_mpi_is_prime( const mbedtls_mpi *X,
00685                   int (*f_rng)(void *, unsigned char *, size_t),
00686                   void *p_rng );
00687 
00688 /**
00689  * \brief          Prime number generation
00690  *
00691  * \param X        Destination MPI
00692  * \param nbits    Required size of X in bits
00693  *                 ( 3 <= nbits <= MBEDTLS_MPI_MAX_BITS )
00694  * \param dh_flag  If 1, then (X-1)/2 will be prime too
00695  * \param f_rng    RNG function
00696  * \param p_rng    RNG parameter
00697  *
00698  * \return         0 if successful (probably prime),
00699  *                 MBEDTLS_ERR_MPI_ALLOC_FAILED if memory allocation failed,
00700  *                 MBEDTLS_ERR_MPI_BAD_INPUT_DATA if nbits is < 3
00701  */
00702 int mbedtls_mpi_gen_prime( mbedtls_mpi *X, size_t nbits, int dh_flag,
00703                    int (*f_rng)(void *, unsigned char *, size_t),
00704                    void *p_rng );
00705 
00706 /**
00707  * \brief          Checkup routine
00708  *
00709  * \return         0 if successful, or 1 if the test failed
00710  */
00711 int mbedtls_mpi_self_test( int verbose );
00712 
00713 #ifdef __cplusplus
00714 }
00715 #endif
00716 
00717 #endif /* bignum.h */