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