bignum.h

00001 /**
00002  * \file bignum.h
00003  *
00004  * \brief Multi-precision integer library
00005  */
00006 /*
00007  *  Copyright (C) 2006-2015, ARM Limited, All Rights Reserved
00008  *  SPDX-License-Identifier: Apache-2.0
00009  *
00010  *  Licensed under the Apache License, Version 2.0 (the "License"); you may
00011  *  not use this file except in compliance with the License.
00012  *  You may obtain a copy of the License at
00013  *
00014  *  http://www.apache.org/licenses/LICENSE-2.0
00015  *
00016  *  Unless required by applicable law or agreed to in writing, software
00017  *  distributed under the License is distributed on an "AS IS" BASIS, WITHOUT
00018  *  WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
00019  *  See the License for the specific language governing permissions and
00020  *  limitations under the License.
00021  *
00022  *  This file is part of mbed TLS (https://tls.mbed.org)
00023  */
00024 #ifndef MBEDTLS_BIGNUM_H
00025 #define MBEDTLS_BIGNUM_H
00026 
00027 #if !defined(MBEDTLS_CONFIG_FILE)
00028 #include "config.h"
00029 #else
00030 #include MBEDTLS_CONFIG_FILE
00031 #endif
00032 
00033 #include <stddef.h>
00034 #include <stdint.h>
00035 
00036 #if defined(MBEDTLS_FS_IO)
00037 #include <stdio.h>
00038 #endif
00039 
00040 #define MBEDTLS_ERR_MPI_FILE_IO_ERROR                     -0x0002  /**< An error occurred while reading from or writing to a file. */
00041 #define MBEDTLS_ERR_MPI_BAD_INPUT_DATA                    -0x0004  /**< Bad input parameters to function. */
00042 #define MBEDTLS_ERR_MPI_INVALID_CHARACTER                 -0x0006  /**< There is an invalid character in the digit string. */
00043 #define MBEDTLS_ERR_MPI_BUFFER_TOO_SMALL                  -0x0008  /**< The buffer is too small to write to. */
00044 #define MBEDTLS_ERR_MPI_NEGATIVE_VALUE                    -0x000A  /**< The input arguments are negative or result in illegal output. */
00045 #define MBEDTLS_ERR_MPI_DIVISION_BY_ZERO                  -0x000C  /**< The input argument for division is zero, which is not allowed. */
00046 #define MBEDTLS_ERR_MPI_NOT_ACCEPTABLE                    -0x000E  /**< The input arguments are not acceptable. */
00047 #define MBEDTLS_ERR_MPI_ALLOC_FAILED                      -0x0010  /**< Memory allocation failed. */
00048 
00049 #define MBEDTLS_MPI_CHK(f) do { if( ( ret = f ) != 0 ) goto cleanup; } while( 0 )
00050 
00051 /*
00052  * Maximum size MPIs are allowed to grow to in number of limbs.
00053  */
00054 #define MBEDTLS_MPI_MAX_LIMBS                             10000
00055 
00056 #if !defined(MBEDTLS_MPI_WINDOW_SIZE)
00057 /*
00058  * Maximum window size used for modular exponentiation. Default: 6
00059  * Minimum value: 1. Maximum value: 6.
00060  *
00061  * Result is an array of ( 2 << MBEDTLS_MPI_WINDOW_SIZE ) MPIs used
00062  * for the sliding window calculation. (So 64 by default)
00063  *
00064  * Reduction in size, reduces speed.
00065  */
00066 #define MBEDTLS_MPI_WINDOW_SIZE                           6        /**< Maximum windows size used. */
00067 #endif /* !MBEDTLS_MPI_WINDOW_SIZE */
00068 
00069 #if !defined(MBEDTLS_MPI_MAX_SIZE)
00070 /*
00071  * Maximum size of MPIs allowed in bits and bytes for user-MPIs.
00072  * ( Default: 512 bytes => 4096 bits, Maximum tested: 2048 bytes => 16384 bits )
00073  *
00074  * Note: Calculations can temporarily result in larger MPIs. So the number
00075  * of limbs required (MBEDTLS_MPI_MAX_LIMBS) is higher.
00076  */
00077 #define MBEDTLS_MPI_MAX_SIZE                              1024     /**< Maximum number of bytes for usable MPIs. */
00078 #endif /* !MBEDTLS_MPI_MAX_SIZE */
00079 
00080 #define MBEDTLS_MPI_MAX_BITS                              ( 8 * MBEDTLS_MPI_MAX_SIZE )    /**< Maximum number of bits for usable MPIs. */
00081 
00082 /*
00083  * When reading from files with mbedtls_mpi_read_file() and writing to files with
00084  * mbedtls_mpi_write_file() the buffer should have space
00085  * for a (short) label, the MPI (in the provided radix), the newline
00086  * characters and the '\0'.
00087  *
00088  * By default we assume at least a 10 char label, a minimum radix of 10
00089  * (decimal) and a maximum of 4096 bit numbers (1234 decimal chars).
00090  * Autosized at compile time for at least a 10 char label, a minimum radix
00091  * of 10 (decimal) for a number of MBEDTLS_MPI_MAX_BITS size.
00092  *
00093  * This used to be statically sized to 1250 for a maximum of 4096 bit
00094  * numbers (1234 decimal chars).
00095  *
00096  * Calculate using the formula:
00097  *  MBEDTLS_MPI_RW_BUFFER_SIZE = ceil(MBEDTLS_MPI_MAX_BITS / ln(10) * ln(2)) +
00098  *                                LabelSize + 6
00099  */
00100 #define MBEDTLS_MPI_MAX_BITS_SCALE100          ( 100 * MBEDTLS_MPI_MAX_BITS )
00101 #define MBEDTLS_LN_2_DIV_LN_10_SCALE100                 332
00102 #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 )
00103 
00104 /*
00105  * Define the base integer type, architecture-wise.
00106  *
00107  * 32 or 64-bit integer types can be forced regardless of the underlying
00108  * architecture by defining MBEDTLS_HAVE_INT32 or MBEDTLS_HAVE_INT64
00109  * respectively and undefining MBEDTLS_HAVE_ASM.
00110  *
00111  * Double-width integers (e.g. 128-bit in 64-bit architectures) can be
00112  * disabled by defining MBEDTLS_NO_UDBL_DIVISION.
00113  */
00114 #if !defined(MBEDTLS_HAVE_INT32)
00115     #if defined(_MSC_VER) && defined(_M_AMD64)
00116         /* Always choose 64-bit when using MSC */
00117         #if !defined(MBEDTLS_HAVE_INT64)
00118             #define MBEDTLS_HAVE_INT64
00119         #endif /* !MBEDTLS_HAVE_INT64 */
00120         typedef  int64_t mbedtls_mpi_sint;
00121         typedef uint64_t mbedtls_mpi_uint;
00122     #elif defined(__GNUC__) && (                         \
00123         defined(__amd64__) || defined(__x86_64__)     || \
00124         defined(__ppc64__) || defined(__powerpc64__)  || \
00125         defined(__ia64__)  || defined(__alpha__)      || \
00126         ( defined(__sparc__) && defined(__arch64__) ) || \
00127         defined(__s390x__) || defined(__mips64) )
00128         #if !defined(MBEDTLS_HAVE_INT64)
00129             #define MBEDTLS_HAVE_INT64
00130         #endif /* MBEDTLS_HAVE_INT64 */
00131         typedef  int64_t mbedtls_mpi_sint;
00132         typedef uint64_t mbedtls_mpi_uint;
00133         #if !defined(MBEDTLS_NO_UDBL_DIVISION)
00134             /* mbedtls_t_udbl defined as 128-bit unsigned int */
00135             typedef unsigned int mbedtls_t_udbl __attribute__((mode(TI)));
00136             #define MBEDTLS_HAVE_UDBL
00137         #endif /* !MBEDTLS_NO_UDBL_DIVISION */
00138     #elif defined(__ARMCC_VERSION) && defined(__aarch64__)
00139         /*
00140          * __ARMCC_VERSION is defined for both armcc and armclang and
00141          * __aarch64__ is only defined by armclang when compiling 64-bit code
00142          */
00143         #if !defined(MBEDTLS_HAVE_INT64)
00144             #define MBEDTLS_HAVE_INT64
00145         #endif /* !MBEDTLS_HAVE_INT64 */
00146         typedef  int64_t mbedtls_mpi_sint;
00147         typedef uint64_t mbedtls_mpi_uint;
00148         #if !defined(MBEDTLS_NO_UDBL_DIVISION)
00149             /* mbedtls_t_udbl defined as 128-bit unsigned int */
00150             typedef __uint128_t mbedtls_t_udbl;
00151             #define MBEDTLS_HAVE_UDBL
00152         #endif /* !MBEDTLS_NO_UDBL_DIVISION */
00153     #elif defined(MBEDTLS_HAVE_INT64)
00154         /* Force 64-bit integers with unknown compiler */
00155         typedef  int64_t mbedtls_mpi_sint;
00156         typedef uint64_t mbedtls_mpi_uint;
00157     #endif
00158 #endif /* !MBEDTLS_HAVE_INT32 */
00159 
00160 #if !defined(MBEDTLS_HAVE_INT64)
00161     /* Default to 32-bit compilation */
00162     #if !defined(MBEDTLS_HAVE_INT32)
00163         #define MBEDTLS_HAVE_INT32
00164     #endif /* !MBEDTLS_HAVE_INT32 */
00165     typedef  int32_t mbedtls_mpi_sint;
00166     typedef uint32_t mbedtls_mpi_uint;
00167     #if !defined(MBEDTLS_NO_UDBL_DIVISION)
00168         typedef uint64_t mbedtls_t_udbl;
00169         #define MBEDTLS_HAVE_UDBL
00170     #endif /* !MBEDTLS_NO_UDBL_DIVISION */
00171 #endif /* !MBEDTLS_HAVE_INT64 */
00172 
00173 #ifdef __cplusplus
00174 extern "C" {
00175 #endif
00176 
00177 /**
00178  * \brief          MPI structure
00179  */
00180 typedef struct
00181 {
00182     int s ;              /*!<  integer sign      */
00183     size_t n ;           /*!<  total # of limbs  */
00184     mbedtls_mpi_uint *p ;          /*!<  pointer to limbs  */
00185 }
00186 mbedtls_mpi;
00187 
00188 /**
00189  * \brief           Initialize one MPI (make internal references valid)
00190  *                  This just makes it ready to be set or freed,
00191  *                  but does not define a value for the MPI.
00192  *
00193  * \param X         One MPI to initialize.
00194  */
00195 void mbedtls_mpi_init( mbedtls_mpi *X );
00196 
00197 /**
00198  * \brief          Unallocate one MPI
00199  *
00200  * \param X        One MPI to unallocate.
00201  */
00202 void mbedtls_mpi_free( mbedtls_mpi *X );
00203 
00204 /**
00205  * \brief          Enlarge to the specified number of limbs
00206  *
00207  *                 This function does nothing if the MPI is already large enough.
00208  *
00209  * \param X        MPI to grow
00210  * \param nblimbs  The target number of limbs
00211  *
00212  * \return         0 if successful,
00213  *                 MBEDTLS_ERR_MPI_ALLOC_FAILED if memory allocation failed
00214  */
00215 int mbedtls_mpi_grow( mbedtls_mpi *X, size_t nblimbs );
00216 
00217 /**
00218  * \brief          Resize down, keeping at least the specified number of limbs
00219  *
00220  *                 If \c X is smaller than \c nblimbs, it is resized up
00221  *                 instead.
00222  *
00223  * \param X        MPI to shrink
00224  * \param nblimbs  The minimum number of limbs to keep
00225  *
00226  * \return         0 if successful,
00227  *                 MBEDTLS_ERR_MPI_ALLOC_FAILED if memory allocation failed
00228  *                 (this can only happen when resizing up).
00229  */
00230 int mbedtls_mpi_shrink( mbedtls_mpi *X, size_t nblimbs );
00231 
00232 /**
00233  * \brief          Copy the contents of Y into X
00234  *
00235  * \param X        Destination MPI. It is enlarged if necessary.
00236  * \param Y        Source MPI.
00237  *
00238  * \return         0 if successful,
00239  *                 MBEDTLS_ERR_MPI_ALLOC_FAILED if memory allocation failed
00240  */
00241 int mbedtls_mpi_copy( mbedtls_mpi *X, const mbedtls_mpi *Y );
00242 
00243 /**
00244  * \brief          Swap the contents of X and Y
00245  *
00246  * \param X        First MPI value
00247  * \param Y        Second MPI value
00248  */
00249 void mbedtls_mpi_swap( mbedtls_mpi *X, mbedtls_mpi *Y );
00250 
00251 /**
00252  * \brief          Safe conditional assignement X = Y if assign is 1
00253  *
00254  * \param X        MPI to conditionally assign to
00255  * \param Y        Value to be assigned
00256  * \param assign   1: perform the assignment, 0: keep X's original value
00257  *
00258  * \return         0 if successful,
00259  *                 MBEDTLS_ERR_MPI_ALLOC_FAILED if memory allocation failed,
00260  *
00261  * \note           This function is equivalent to
00262  *                      if( assign ) mbedtls_mpi_copy( X, Y );
00263  *                 except that it avoids leaking any information about whether
00264  *                 the assignment was done or not (the above code may leak
00265  *                 information through branch prediction and/or memory access
00266  *                 patterns analysis).
00267  */
00268 int mbedtls_mpi_safe_cond_assign( mbedtls_mpi *X, const mbedtls_mpi *Y, unsigned char assign );
00269 
00270 /**
00271  * \brief          Safe conditional swap X <-> Y if swap is 1
00272  *
00273  * \param X        First mbedtls_mpi value
00274  * \param Y        Second mbedtls_mpi value
00275  * \param assign   1: perform the swap, 0: keep X and Y's original values
00276  *
00277  * \return         0 if successful,
00278  *                 MBEDTLS_ERR_MPI_ALLOC_FAILED if memory allocation failed,
00279  *
00280  * \note           This function is equivalent to
00281  *                      if( assign ) mbedtls_mpi_swap( X, Y );
00282  *                 except that it avoids leaking any information about whether
00283  *                 the assignment was done or not (the above code may leak
00284  *                 information through branch prediction and/or memory access
00285  *                 patterns analysis).
00286  */
00287 int mbedtls_mpi_safe_cond_swap( mbedtls_mpi *X, mbedtls_mpi *Y, unsigned char assign );
00288 
00289 /**
00290  * \brief          Set value from integer
00291  *
00292  * \param X        MPI to set
00293  * \param z        Value to use
00294  *
00295  * \return         0 if successful,
00296  *                 MBEDTLS_ERR_MPI_ALLOC_FAILED if memory allocation failed
00297  */
00298 int mbedtls_mpi_lset( mbedtls_mpi *X, mbedtls_mpi_sint z );
00299 
00300 /**
00301  * \brief          Get a specific bit from X
00302  *
00303  * \param X        MPI to use
00304  * \param pos      Zero-based index of the bit in X
00305  *
00306  * \return         Either a 0 or a 1
00307  */
00308 int mbedtls_mpi_get_bit( const mbedtls_mpi *X, size_t pos );
00309 
00310 /**
00311  * \brief          Set a bit of X to a specific value of 0 or 1
00312  *
00313  * \note           Will grow X if necessary to set a bit to 1 in a not yet
00314  *                 existing limb. Will not grow if bit should be set to 0
00315  *
00316  * \param X        MPI to use
00317  * \param pos      Zero-based index of the bit in X
00318  * \param val      The value to set the bit to (0 or 1)
00319  *
00320  * \return         0 if successful,
00321  *                 MBEDTLS_ERR_MPI_ALLOC_FAILED if memory allocation failed,
00322  *                 MBEDTLS_ERR_MPI_BAD_INPUT_DATA if val is not 0 or 1
00323  */
00324 int mbedtls_mpi_set_bit( mbedtls_mpi *X, size_t pos, unsigned char val );
00325 
00326 /**
00327  * \brief          Return the number of zero-bits before the least significant
00328  *                 '1' bit
00329  *
00330  * Note: Thus also the zero-based index of the least significant '1' bit
00331  *
00332  * \param X        MPI to use
00333  */
00334 size_t mbedtls_mpi_lsb( const mbedtls_mpi *X );
00335 
00336 /**
00337  * \brief          Return the number of bits up to and including the most
00338  *                 significant '1' bit'
00339  *
00340  * Note: Thus also the one-based index of the most significant '1' bit
00341  *
00342  * \param X        MPI to use
00343  */
00344 size_t mbedtls_mpi_bitlen( const mbedtls_mpi *X );
00345 
00346 /**
00347  * \brief          Return the total size in bytes
00348  *
00349  * \param X        MPI to use
00350  */
00351 size_t mbedtls_mpi_size( const mbedtls_mpi *X );
00352 
00353 /**
00354  * \brief          Import from an ASCII string
00355  *
00356  * \param X        Destination MPI
00357  * \param radix    Input numeric base
00358  * \param s        Null-terminated string buffer
00359  *
00360  * \return         0 if successful, or a MBEDTLS_ERR_MPI_XXX error code
00361  */
00362 int mbedtls_mpi_read_string( mbedtls_mpi *X, int radix, const char *s );
00363 
00364 /**
00365  * \brief          Export into an ASCII string
00366  *
00367  * \param X        Source MPI
00368  * \param radix    Output numeric base
00369  * \param buf      Buffer to write the string to
00370  * \param buflen   Length of buf
00371  * \param olen     Length of the string written, including final NUL byte
00372  *
00373  * \return         0 if successful, or a MBEDTLS_ERR_MPI_XXX error code.
00374  *                 *olen is always updated to reflect the amount
00375  *                 of data that has (or would have) been written.
00376  *
00377  * \note           Call this function with buflen = 0 to obtain the
00378  *                 minimum required buffer size in *olen.
00379  */
00380 int mbedtls_mpi_write_string( const mbedtls_mpi *X, int radix,
00381                               char *buf, size_t buflen, size_t *olen );
00382 
00383 #if defined(MBEDTLS_FS_IO)
00384 /**
00385  * \brief          Read MPI from a line in an opened file
00386  *
00387  * \param X        Destination MPI
00388  * \param radix    Input numeric base
00389  * \param fin      Input file handle
00390  *
00391  * \return         0 if successful, MBEDTLS_ERR_MPI_BUFFER_TOO_SMALL if
00392  *                 the file read buffer is too small or a
00393  *                 MBEDTLS_ERR_MPI_XXX error code
00394  *
00395  * \note           On success, this function advances the file stream
00396  *                 to the end of the current line or to EOF.
00397  *
00398  *                 The function returns 0 on an empty line.
00399  *
00400  *                 Leading whitespaces are ignored, as is a
00401  *                 '0x' prefix for radix 16.
00402  *
00403  */
00404 int mbedtls_mpi_read_file( mbedtls_mpi *X, int radix, FILE *fin );
00405 
00406 /**
00407  * \brief          Write X into an opened file, or stdout if fout is NULL
00408  *
00409  * \param p        Prefix, can be NULL
00410  * \param X        Source MPI
00411  * \param radix    Output numeric base
00412  * \param fout     Output file handle (can be NULL)
00413  *
00414  * \return         0 if successful, or a MBEDTLS_ERR_MPI_XXX error code
00415  *
00416  * \note           Set fout == NULL to print X on the console.
00417  */
00418 int mbedtls_mpi_write_file( const char *p, const mbedtls_mpi *X, int radix, FILE *fout );
00419 #endif /* MBEDTLS_FS_IO */
00420 
00421 /**
00422  * \brief          Import X from unsigned binary data, big endian
00423  *
00424  * \param X        Destination MPI
00425  * \param buf      Input buffer
00426  * \param buflen   Input buffer size
00427  *
00428  * \return         0 if successful,
00429  *                 MBEDTLS_ERR_MPI_ALLOC_FAILED if memory allocation failed
00430  */
00431 int mbedtls_mpi_read_binary( mbedtls_mpi *X, const unsigned char *buf, size_t buflen );
00432 
00433 /**
00434  * \brief          Export X into unsigned binary data, big endian.
00435  *                 Always fills the whole buffer, which will start with zeros
00436  *                 if the number is smaller.
00437  *
00438  * \param X        Source MPI
00439  * \param buf      Output buffer
00440  * \param buflen   Output buffer size
00441  *
00442  * \return         0 if successful,
00443  *                 MBEDTLS_ERR_MPI_BUFFER_TOO_SMALL if buf isn't large enough
00444  */
00445 int mbedtls_mpi_write_binary( const mbedtls_mpi *X, unsigned char *buf, size_t buflen );
00446 
00447 /**
00448  * \brief          Left-shift: X <<= count
00449  *
00450  * \param X        MPI to shift
00451  * \param count    Amount to shift
00452  *
00453  * \return         0 if successful,
00454  *                 MBEDTLS_ERR_MPI_ALLOC_FAILED if memory allocation failed
00455  */
00456 int mbedtls_mpi_shift_l( mbedtls_mpi *X, size_t count );
00457 
00458 /**
00459  * \brief          Right-shift: X >>= count
00460  *
00461  * \param X        MPI to shift
00462  * \param count    Amount to shift
00463  *
00464  * \return         0 if successful,
00465  *                 MBEDTLS_ERR_MPI_ALLOC_FAILED if memory allocation failed
00466  */
00467 int mbedtls_mpi_shift_r( mbedtls_mpi *X, size_t count );
00468 
00469 /**
00470  * \brief          Compare unsigned values
00471  *
00472  * \param X        Left-hand MPI
00473  * \param Y        Right-hand MPI
00474  *
00475  * \return         1 if |X| is greater than |Y|,
00476  *                -1 if |X| is lesser  than |Y| or
00477  *                 0 if |X| is equal to |Y|
00478  */
00479 int mbedtls_mpi_cmp_abs( const mbedtls_mpi *X, const mbedtls_mpi *Y );
00480 
00481 /**
00482  * \brief          Compare signed values
00483  *
00484  * \param X        Left-hand MPI
00485  * \param Y        Right-hand MPI
00486  *
00487  * \return         1 if X is greater than Y,
00488  *                -1 if X is lesser  than Y or
00489  *                 0 if X is equal to Y
00490  */
00491 int mbedtls_mpi_cmp_mpi( const mbedtls_mpi *X, const mbedtls_mpi *Y );
00492 
00493 /**
00494  * \brief          Compare signed values
00495  *
00496  * \param X        Left-hand MPI
00497  * \param z        The integer value to compare to
00498  *
00499  * \return         1 if X is greater than z,
00500  *                -1 if X is lesser  than z or
00501  *                 0 if X is equal to z
00502  */
00503 int mbedtls_mpi_cmp_int( const mbedtls_mpi *X, mbedtls_mpi_sint z );
00504 
00505 /**
00506  * \brief          Unsigned addition: X = |A| + |B|
00507  *
00508  * \param X        Destination MPI
00509  * \param A        Left-hand MPI
00510  * \param B        Right-hand MPI
00511  *
00512  * \return         0 if successful,
00513  *                 MBEDTLS_ERR_MPI_ALLOC_FAILED if memory allocation failed
00514  */
00515 int mbedtls_mpi_add_abs( mbedtls_mpi *X, const mbedtls_mpi *A, const mbedtls_mpi *B );
00516 
00517 /**
00518  * \brief          Unsigned subtraction: X = |A| - |B|
00519  *
00520  * \param X        Destination MPI
00521  * \param A        Left-hand MPI
00522  * \param B        Right-hand MPI
00523  *
00524  * \return         0 if successful,
00525  *                 MBEDTLS_ERR_MPI_NEGATIVE_VALUE if B is greater than A
00526  */
00527 int mbedtls_mpi_sub_abs( mbedtls_mpi *X, const mbedtls_mpi *A, const mbedtls_mpi *B );
00528 
00529 /**
00530  * \brief          Signed addition: X = A + B
00531  *
00532  * \param X        Destination MPI
00533  * \param A        Left-hand MPI
00534  * \param B        Right-hand MPI
00535  *
00536  * \return         0 if successful,
00537  *                 MBEDTLS_ERR_MPI_ALLOC_FAILED if memory allocation failed
00538  */
00539 int mbedtls_mpi_add_mpi( mbedtls_mpi *X, const mbedtls_mpi *A, const mbedtls_mpi *B );
00540 
00541 /**
00542  * \brief          Signed subtraction: X = A - B
00543  *
00544  * \param X        Destination MPI
00545  * \param A        Left-hand MPI
00546  * \param B        Right-hand MPI
00547  *
00548  * \return         0 if successful,
00549  *                 MBEDTLS_ERR_MPI_ALLOC_FAILED if memory allocation failed
00550  */
00551 int mbedtls_mpi_sub_mpi( mbedtls_mpi *X, const mbedtls_mpi *A, const mbedtls_mpi *B );
00552 
00553 /**
00554  * \brief          Signed addition: X = A + b
00555  *
00556  * \param X        Destination MPI
00557  * \param A        Left-hand MPI
00558  * \param b        The integer value to add
00559  *
00560  * \return         0 if successful,
00561  *                 MBEDTLS_ERR_MPI_ALLOC_FAILED if memory allocation failed
00562  */
00563 int mbedtls_mpi_add_int( mbedtls_mpi *X, const mbedtls_mpi *A, mbedtls_mpi_sint b );
00564 
00565 /**
00566  * \brief          Signed subtraction: X = A - b
00567  *
00568  * \param X        Destination MPI
00569  * \param A        Left-hand MPI
00570  * \param b        The integer value to subtract
00571  *
00572  * \return         0 if successful,
00573  *                 MBEDTLS_ERR_MPI_ALLOC_FAILED if memory allocation failed
00574  */
00575 int mbedtls_mpi_sub_int( mbedtls_mpi *X, const mbedtls_mpi *A, mbedtls_mpi_sint b );
00576 
00577 /**
00578  * \brief          Baseline multiplication: X = A * B
00579  *
00580  * \param X        Destination MPI
00581  * \param A        Left-hand MPI
00582  * \param B        Right-hand MPI
00583  *
00584  * \return         0 if successful,
00585  *                 MBEDTLS_ERR_MPI_ALLOC_FAILED if memory allocation failed
00586  */
00587 int mbedtls_mpi_mul_mpi( mbedtls_mpi *X, const mbedtls_mpi *A, const mbedtls_mpi *B );
00588 
00589 /**
00590  * \brief          Baseline multiplication: X = A * b
00591  *
00592  * \param X        Destination MPI
00593  * \param A        Left-hand MPI
00594  * \param b        The unsigned integer value to multiply with
00595  *
00596  * \note           b is unsigned
00597  *
00598  * \return         0 if successful,
00599  *                 MBEDTLS_ERR_MPI_ALLOC_FAILED if memory allocation failed
00600  */
00601 int mbedtls_mpi_mul_int( mbedtls_mpi *X, const mbedtls_mpi *A, mbedtls_mpi_uint b );
00602 
00603 /**
00604  * \brief          Division by mbedtls_mpi: A = Q * B + R
00605  *
00606  * \param Q        Destination MPI for the quotient
00607  * \param R        Destination MPI for the rest value
00608  * \param A        Left-hand MPI
00609  * \param B        Right-hand MPI
00610  *
00611  * \return         0 if successful,
00612  *                 MBEDTLS_ERR_MPI_ALLOC_FAILED if memory allocation failed,
00613  *                 MBEDTLS_ERR_MPI_DIVISION_BY_ZERO if B == 0
00614  *
00615  * \note           Either Q or R can be NULL.
00616  */
00617 int mbedtls_mpi_div_mpi( mbedtls_mpi *Q, mbedtls_mpi *R, const mbedtls_mpi *A, const mbedtls_mpi *B );
00618 
00619 /**
00620  * \brief          Division by int: A = Q * b + R
00621  *
00622  * \param Q        Destination MPI for the quotient
00623  * \param R        Destination MPI for the rest value
00624  * \param A        Left-hand MPI
00625  * \param b        Integer to divide by
00626  *
00627  * \return         0 if successful,
00628  *                 MBEDTLS_ERR_MPI_ALLOC_FAILED if memory allocation failed,
00629  *                 MBEDTLS_ERR_MPI_DIVISION_BY_ZERO if b == 0
00630  *
00631  * \note           Either Q or R can be NULL.
00632  */
00633 int mbedtls_mpi_div_int( mbedtls_mpi *Q, mbedtls_mpi *R, const mbedtls_mpi *A, mbedtls_mpi_sint b );
00634 
00635 /**
00636  * \brief          Modulo: R = A mod B
00637  *
00638  * \param R        Destination MPI for the rest value
00639  * \param A        Left-hand MPI
00640  * \param B        Right-hand MPI
00641  *
00642  * \return         0 if successful,
00643  *                 MBEDTLS_ERR_MPI_ALLOC_FAILED if memory allocation failed,
00644  *                 MBEDTLS_ERR_MPI_DIVISION_BY_ZERO if B == 0,
00645  *                 MBEDTLS_ERR_MPI_NEGATIVE_VALUE if B < 0
00646  */
00647 int mbedtls_mpi_mod_mpi( mbedtls_mpi *R, const mbedtls_mpi *A, const mbedtls_mpi *B );
00648 
00649 /**
00650  * \brief          Modulo: r = A mod b
00651  *
00652  * \param r        Destination mbedtls_mpi_uint
00653  * \param A        Left-hand MPI
00654  * \param b        Integer to divide by
00655  *
00656  * \return         0 if successful,
00657  *                 MBEDTLS_ERR_MPI_ALLOC_FAILED if memory allocation failed,
00658  *                 MBEDTLS_ERR_MPI_DIVISION_BY_ZERO if b == 0,
00659  *                 MBEDTLS_ERR_MPI_NEGATIVE_VALUE if b < 0
00660  */
00661 int mbedtls_mpi_mod_int( mbedtls_mpi_uint *r, const mbedtls_mpi *A, mbedtls_mpi_sint b );
00662 
00663 /**
00664  * \brief          Sliding-window exponentiation: X = A^E mod N
00665  *
00666  * \param X        Destination MPI
00667  * \param A        Left-hand MPI
00668  * \param E        Exponent MPI
00669  * \param N        Modular MPI
00670  * \param _RR      Speed-up MPI used for recalculations
00671  *
00672  * \return         0 if successful,
00673  *                 MBEDTLS_ERR_MPI_ALLOC_FAILED if memory allocation failed,
00674  *                 MBEDTLS_ERR_MPI_BAD_INPUT_DATA if N is negative or even or
00675  *                 if E is negative
00676  *
00677  * \note           _RR is used to avoid re-computing R*R mod N across
00678  *                 multiple calls, which speeds up things a bit. It can
00679  *                 be set to NULL if the extra performance is unneeded.
00680  */
00681 int mbedtls_mpi_exp_mod( mbedtls_mpi *X, const mbedtls_mpi *A, const mbedtls_mpi *E, const mbedtls_mpi *N, mbedtls_mpi *_RR );
00682 
00683 /**
00684  * \brief          Fill an MPI X with size bytes of random
00685  *
00686  * \param X        Destination MPI
00687  * \param size     Size in bytes
00688  * \param f_rng    RNG function
00689  * \param p_rng    RNG parameter
00690  *
00691  * \return         0 if successful,
00692  *                 MBEDTLS_ERR_MPI_ALLOC_FAILED if memory allocation failed
00693  *
00694  * \note           The bytes obtained from the PRNG are interpreted
00695  *                 as a big-endian representation of an MPI; this can
00696  *                 be relevant in applications like deterministic ECDSA.
00697  */
00698 int mbedtls_mpi_fill_random( mbedtls_mpi *X, size_t size,
00699                      int (*f_rng)(void *, unsigned char *, size_t),
00700                      void *p_rng );
00701 
00702 /**
00703  * \brief          Greatest common divisor: G = gcd(A, B)
00704  *
00705  * \param G        Destination MPI
00706  * \param A        Left-hand MPI
00707  * \param B        Right-hand MPI
00708  *
00709  * \return         0 if successful,
00710  *                 MBEDTLS_ERR_MPI_ALLOC_FAILED if memory allocation failed
00711  */
00712 int mbedtls_mpi_gcd( mbedtls_mpi *G, const mbedtls_mpi *A, const mbedtls_mpi *B );
00713 
00714 /**
00715  * \brief          Modular inverse: X = A^-1 mod N
00716  *
00717  * \param X        Destination MPI
00718  * \param A        Left-hand MPI
00719  * \param N        Right-hand MPI
00720  *
00721  * \return         0 if successful,
00722  *                 MBEDTLS_ERR_MPI_ALLOC_FAILED if memory allocation failed,
00723  *                 MBEDTLS_ERR_MPI_BAD_INPUT_DATA if N is <= 1,
00724                    MBEDTLS_ERR_MPI_NOT_ACCEPTABLE if A has no inverse mod N.
00725  */
00726 int mbedtls_mpi_inv_mod( mbedtls_mpi *X, const mbedtls_mpi *A, const mbedtls_mpi *N );
00727 
00728 /**
00729  * \brief          Miller-Rabin primality test
00730  *
00731  * \param X        MPI to check
00732  * \param f_rng    RNG function
00733  * \param p_rng    RNG parameter
00734  *
00735  * \return         0 if successful (probably prime),
00736  *                 MBEDTLS_ERR_MPI_ALLOC_FAILED if memory allocation failed,
00737  *                 MBEDTLS_ERR_MPI_NOT_ACCEPTABLE if X is not prime
00738  */
00739 int mbedtls_mpi_is_prime( const mbedtls_mpi *X,
00740                   int (*f_rng)(void *, unsigned char *, size_t),
00741                   void *p_rng );
00742 
00743 /**
00744  * \brief          Prime number generation
00745  *
00746  * \param X        Destination MPI
00747  * \param nbits    Required size of X in bits
00748  *                 ( 3 <= nbits <= MBEDTLS_MPI_MAX_BITS )
00749  * \param dh_flag  If 1, then (X-1)/2 will be prime too
00750  * \param f_rng    RNG function
00751  * \param p_rng    RNG parameter
00752  *
00753  * \return         0 if successful (probably prime),
00754  *                 MBEDTLS_ERR_MPI_ALLOC_FAILED if memory allocation failed,
00755  *                 MBEDTLS_ERR_MPI_BAD_INPUT_DATA if nbits is < 3
00756  */
00757 int mbedtls_mpi_gen_prime( mbedtls_mpi *X, size_t nbits, int dh_flag,
00758                    int (*f_rng)(void *, unsigned char *, size_t),
00759                    void *p_rng );
00760 
00761 /**
00762  * \brief          Checkup routine
00763  *
00764  * \return         0 if successful, or 1 if the test failed
00765  */
00766 int mbedtls_mpi_self_test( int verbose );
00767 
00768 #ifdef __cplusplus
00769 }
00770 #endif
00771 
00772 #endif /* bignum.h */