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/**

 * \file bignum.h

 *

 * \brief  Multi-precision integer library

 *

 *  Copyright (C) 2006-2010, Brainspark B.V.

 *

 *  This file is part of PolarSSL (http://www.polarssl.org)

 *  Lead Maintainer: Paul Bakker 

 *

 *  All rights reserved.

 *

 *  This program is free software; you can redistribute it and/or modify

 *  it under the terms of the GNU General Public License as published by

 *  the Free Software Foundation; either version 2 of the License, or

 *  (at your option) any later version.

 *

 *  This program is distributed in the hope that it will be useful,

 *  but WITHOUT ANY WARRANTY; without even the implied warranty of

 *  MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the

 *  GNU General Public License for more details.

 *

 *  You should have received a copy of the GNU General Public License along

 *  with this program; if not, write to the Free Software Foundation, Inc.,

 *  51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA.

 */

#ifndef POLARSSL_BIGNUM_H

#define POLARSSL_BIGNUM_H

#include 

#include 

#include "config.h"

#ifdef _MSC_VER

#include 

#if (_MSC_VER <= 1200)

typedef   signed short  int16_t;

typedef unsigned short uint16_t;

#else

typedef  INT16  int16_t;

typedef UINT16 uint16_t;

#endif

typedef  INT32  int32_t;

typedef  INT64  int64_t;

typedef UINT32 uint32_t;

typedef UINT64 uint64_t;

#else

#include 

#endif

#define POLARSSL_ERR_MPI_FILE_IO_ERROR                     -0x0002  /**< An error occurred while reading from or writing to a file. */

#define POLARSSL_ERR_MPI_BAD_INPUT_DATA                    -0x0004  /**< Bad input parameters to function. */

#define POLARSSL_ERR_MPI_INVALID_CHARACTER                 -0x0006  /**< There is an invalid character in the digit string. */

#define POLARSSL_ERR_MPI_BUFFER_TOO_SMALL                  -0x0008  /**< The buffer is too small to write to. */

#define POLARSSL_ERR_MPI_NEGATIVE_VALUE                    -0x000A  /**< The input arguments are negative or result in illegal output. */

#define POLARSSL_ERR_MPI_DIVISION_BY_ZERO                  -0x000C  /**< The input argument for division is zero, which is not allowed. */

#define POLARSSL_ERR_MPI_NOT_ACCEPTABLE                    -0x000E  /**< The input arguments are not acceptable. */

#define POLARSSL_ERR_MPI_MALLOC_FAILED                     -0x0010  /**< Memory allocation failed. */

#define MPI_CHK(f) if( ( ret = f ) != 0 ) goto cleanup

/*

 * Maximum size MPIs are allowed to grow to in number of limbs.

 */

#define POLARSSL_MPI_MAX_LIMBS                             10000

/*

 * Maximum window size used for modular exponentiation. Default: 6

 * Minimum value: 1. Maximum value: 6.

 *

 * Result is an array of ( 2 << POLARSSL_MPI_WINDOW_SIZE ) MPIs used

 * for the sliding window calculation. (So 64 by default)

 *

 * Reduction in size, reduces speed.

 */

#define POLARSSL_MPI_WINDOW_SIZE                           6        /**< Maximum windows size used. */

/*

 * Maximum size of MPIs allowed in bits and bytes for user-MPIs.

 * ( Default: 512 bytes => 4096 bits, Maximum tested: 2048 bytes => 16384 bits )

 *

 * Note: Calculations can results temporarily in larger MPIs. So the number

 * of limbs required (POLARSSL_MPI_MAX_LIMBS) is higher.

 */

#define POLARSSL_MPI_MAX_SIZE                              512      /**< Maximum number of bytes for usable MPIs. */

#define POLARSSL_MPI_MAX_BITS                              ( 8 * POLARSSL_MPI_MAX_SIZE )    /**< Maximum number of bits for usable MPIs. */

/*

 * When reading from files with mpi_read_file() and writing to files with

 * mpi_write_file() the buffer should have space

 * for a (short) label, the MPI (in the provided radix), the newline

 * characters and the '\0'.

 *

 * By default we assume at least a 10 char label, a minimum radix of 10

 * (decimal) and a maximum of 4096 bit numbers (1234 decimal chars).

 * Autosized at compile time for at least a 10 char label, a minimum radix

 * of 10 (decimal) for a number of POLARSSL_MPI_MAX_BITS size.

 *

 * This used to be statically sized to 1250 for a maximum of 4096 bit

 * numbers (1234 decimal chars).

 *

 * Calculate using the formula:

 *  POLARSSL_MPI_RW_BUFFER_SIZE = ceil(POLARSSL_MPI_MAX_BITS / ln(10) * ln(2)) +

 *                                LabelSize + 6

 */

#define POLARSSL_MPI_MAX_BITS_SCALE100          ( 100 * POLARSSL_MPI_MAX_BITS )

#define LN_2_DIV_LN_10_SCALE100                 332

#define POLARSSL_MPI_RW_BUFFER_SIZE             ( ((POLARSSL_MPI_MAX_BITS_SCALE100 + LN_2_DIV_LN_10_SCALE100 - 1) / LN_2_DIV_LN_10_SCALE100) + 10 + 6 )

/*

 * Define the base integer type, architecture-wise

 */

#if defined(POLARSSL_HAVE_INT8)

typedef   signed char  t_sint;

typedef unsigned char  t_uint;

typedef uint16_t       t_udbl;

#define POLARSSL_HAVE_UDBL

#else

#if defined(POLARSSL_HAVE_INT16)

typedef  int16_t t_sint;

typedef uint16_t t_uint;

typedef uint32_t t_udbl;

#define POLARSSL_HAVE_UDBL

#else

  #if ( defined(_MSC_VER) && defined(_M_AMD64) )

    typedef  int64_t t_sint;

    typedef uint64_t t_uint;

  #else

    #if ( defined(__GNUC__) && (                          \

          defined(__amd64__) || defined(__x86_64__)    || \

          defined(__ppc64__) || defined(__powerpc64__) || \

          defined(__ia64__)  || defined(__alpha__)     || \

          (defined(__sparc__) && defined(__arch64__))  || \

          defined(__s390x__) ) )

       typedef  int64_t t_sint;

       typedef uint64_t t_uint;

       typedef unsigned int t_udbl __attribute__((mode(TI)));

       #define POLARSSL_HAVE_UDBL

    #else

       typedef  int32_t t_sint;

       typedef uint32_t t_uint;

       #if ( defined(_MSC_VER) && defined(_M_IX86) )

         typedef uint64_t t_udbl;

         #define POLARSSL_HAVE_UDBL

       #else

         #if defined( POLARSSL_HAVE_LONGLONG )

           typedef unsigned long long t_udbl;

           #define POLARSSL_HAVE_UDBL

         #endif

       #endif

    #endif

  #endif

#endif /* POLARSSL_HAVE_INT16 */

#endif /* POLARSSL_HAVE_INT8  */

/**

 * \brief          MPI structure

 */

typedef struct

{

    int s;              /*!<  integer sign      */

    size_t n;           /*!<  total # of limbs  */

    t_uint *p;          /*!<  pointer to limbs  */

}

mpi;

#ifdef __cplusplus

extern "C" {

#endif

/**

 * \brief           Initialize one MPI

 *

 * \param X         One MPI to initialize.

 */

void mpi_init( mpi *X );

/**

 * \brief          Unallocate one MPI

 *

 * \param X        One MPI to unallocate.

 */

void mpi_free( mpi *X );

/**

 * \brief          Enlarge to the specified number of limbs

 *

 * \param X        MPI to grow

 * \param nblimbs  The target number of limbs

 *

 * \return         0 if successful,

 *                 POLARSSL_ERR_MPI_MALLOC_FAILED if memory allocation failed

 */

int mpi_grow( mpi *X, size_t nblimbs );

/**

 * \brief          Copy the contents of Y into X

 *

 * \param X        Destination MPI

 * \param Y        Source MPI

 *

 * \return         0 if successful,

 *                 POLARSSL_ERR_MPI_MALLOC_FAILED if memory allocation failed

 */

int mpi_copy( mpi *X, const mpi *Y );

/**

 * \brief          Swap the contents of X and Y

 *

 * \param X        First MPI value

 * \param Y        Second MPI value

 */

void mpi_swap( mpi *X, mpi *Y );

/**

 * \brief          Set value from integer

 *

 * \param X        MPI to set

 * \param z        Value to use

 *

 * \return         0 if successful,

 *                 POLARSSL_ERR_MPI_MALLOC_FAILED if memory allocation failed

 */

int mpi_lset( mpi *X, t_sint z );

/**

 * \brief          Get a specific bit from X

 *

 * \param X        MPI to use

 * \param pos      Zero-based index of the bit in X

 *

 * \return         Either a 0 or a 1

 */

int mpi_get_bit( const mpi *X, size_t pos );

/**

 * \brief          Set a bit of X to a specific value of 0 or 1

 *

 * \note           Will grow X if necessary to set a bit to 1 in a not yet

 *                 existing limb. Will not grow if bit should be set to 0

 *

 * \param X        MPI to use

 * \param pos      Zero-based index of the bit in X

 * \param val      The value to set the bit to (0 or 1)

 *

 * \return         0 if successful,

 *                 POLARSSL_ERR_MPI_MALLOC_FAILED if memory allocation failed,

 *                 POLARSSL_ERR_MPI_BAD_INPUT_DATA if val is not 0 or 1

 */

int mpi_set_bit( mpi *X, size_t pos, unsigned char val );

/**

 * \brief          Return the number of zero-bits before the least significant

 *                 '1' bit

 *

 * Note: Thus also the zero-based index of the least significant '1' bit

 *

 * \param X        MPI to use

 */

size_t mpi_lsb( const mpi *X );

/**

 * \brief          Return the number of bits up to and including the most

 *                 significant '1' bit'

 *

 * Note: Thus also the one-based index of the most significant '1' bit

 *

 * \param X        MPI to use

 */

size_t mpi_msb( const mpi *X );

/**

 * \brief          Return the total size in bytes

 *

 * \param X        MPI to use

 */

size_t mpi_size( const mpi *X );

/**

 * \brief          Import from an ASCII string

 *

 * \param X        Destination MPI

 * \param radix    Input numeric base

 * \param s        Null-terminated string buffer

 *

 * \return         0 if successful, or a POLARSSL_ERR_MPI_XXX error code

 */

int mpi_read_string( mpi *X, int radix, const char *s );

/**

 * \brief          Export into an ASCII string

 *

 * \param X        Source MPI

 * \param radix    Output numeric base

 * \param s        String buffer

 * \param slen     String buffer size

 *

 * \return         0 if successful, or a POLARSSL_ERR_MPI_XXX error code.

 *                 *slen is always updated to reflect the amount

 *                 of data that has (or would have) been written.

 *

 * \note           Call this function with *slen = 0 to obtain the

 *                 minimum required buffer size in *slen.

 */

int mpi_write_string( const mpi *X, int radix, char *s, size_t *slen );

#if defined(POLARSSL_FS_IO)

/**

 * \brief          Read X from an opened file

 *

 * \param X        Destination MPI

 * \param radix    Input numeric base

 * \param fin      Input file handle

 *

 * \return         0 if successful, POLARSSL_ERR_MPI_BUFFER_TOO_SMALL if

 *                 the file read buffer is too small or a

 *                 POLARSSL_ERR_MPI_XXX error code

 */

int mpi_read_file( mpi *X, int radix, FILE *fin );

/**

 * \brief          Write X into an opened file, or stdout if fout is NULL

 *

 * \param p        Prefix, can be NULL

 * \param X        Source MPI

 * \param radix    Output numeric base

 * \param fout     Output file handle (can be NULL)

 *

 * \return         0 if successful, or a POLARSSL_ERR_MPI_XXX error code

 *

 * \note           Set fout == NULL to print X on the console.

 */

int mpi_write_file( const char *p, const mpi *X, int radix, FILE *fout );

#endif /* POLARSSL_FS_IO */

/**

 * \brief          Import X from unsigned binary data, big endian

 *

 * \param X        Destination MPI

 * \param buf      Input buffer

 * \param buflen   Input buffer size

 *

 * \return         0 if successful,

 *                 POLARSSL_ERR_MPI_MALLOC_FAILED if memory allocation failed

 */

int mpi_read_binary( mpi *X, const unsigned char *buf, size_t buflen );

/**

 * \brief          Export X into unsigned binary data, big endian

 *

 * \param X        Source MPI

 * \param buf      Output buffer

 * \param buflen   Output buffer size

 *

 * \return         0 if successful,

 *                 POLARSSL_ERR_MPI_BUFFER_TOO_SMALL if buf isn't large enough

 */

int mpi_write_binary( const mpi *X, unsigned char *buf, size_t buflen );

/**

 * \brief          Left-shift: X <<= count

 *

 * \param X        MPI to shift

 * \param count    Amount to shift

 *

 * \return         0 if successful,

 *                 POLARSSL_ERR_MPI_MALLOC_FAILED if memory allocation failed

 */

int mpi_shift_l( mpi *X, size_t count );

/**

 * \brief          Right-shift: X >>= count

 *

 * \param X        MPI to shift

 * \param count    Amount to shift

 *

 * \return         0 if successful,

 *                 POLARSSL_ERR_MPI_MALLOC_FAILED if memory allocation failed

 */

int mpi_shift_r( mpi *X, size_t count );

/**

 * \brief          Compare unsigned values

 *

 * \param X        Left-hand MPI

 * \param Y        Right-hand MPI

 *

 * \return         1 if |X| is greater than |Y|,

 *                -1 if |X| is lesser  than |Y| or

 *                 0 if |X| is equal to |Y|

 */

int mpi_cmp_abs( const mpi *X, const mpi *Y );

/**

 * \brief          Compare signed values

 *

 * \param X        Left-hand MPI

 * \param Y        Right-hand MPI

 *

 * \return         1 if X is greater than Y,

 *                -1 if X is lesser  than Y or

 *                 0 if X is equal to Y

 */

int mpi_cmp_mpi( const mpi *X, const mpi *Y );

/**

 * \brief          Compare signed values

 *

 * \param X        Left-hand MPI

 * \param z        The integer value to compare to

 *

 * \return         1 if X is greater than z,

 *                -1 if X is lesser  than z or

 *                 0 if X is equal to z

 */

int mpi_cmp_int( const mpi *X, t_sint z );

/**

 * \brief          Unsigned addition: X = |A| + |B|

 *

 * \param X        Destination MPI

 * \param A        Left-hand MPI

 * \param B        Right-hand MPI

 *

 * \return         0 if successful,

 *                 POLARSSL_ERR_MPI_MALLOC_FAILED if memory allocation failed

 */

int mpi_add_abs( mpi *X, const mpi *A, const mpi *B );

/**

 * \brief          Unsigned substraction: X = |A| - |B|

 *

 * \param X        Destination MPI

 * \param A        Left-hand MPI

 * \param B        Right-hand MPI

 *

 * \return         0 if successful,

 *                 POLARSSL_ERR_MPI_NEGATIVE_VALUE if B is greater than A

 */

int mpi_sub_abs( mpi *X, const mpi *A, const mpi *B );

/**

 * \brief          Signed addition: X = A + B

 *

 * \param X        Destination MPI

 * \param A        Left-hand MPI

 * \param B        Right-hand MPI

 *

 * \return         0 if successful,

 *                 POLARSSL_ERR_MPI_MALLOC_FAILED if memory allocation failed

 */

int mpi_add_mpi( mpi *X, const mpi *A, const mpi *B );

/**

 * \brief          Signed substraction: X = A - B

 *

 * \param X        Destination MPI

 * \param A        Left-hand MPI

 * \param B        Right-hand MPI

 *

 * \return         0 if successful,

 *                 POLARSSL_ERR_MPI_MALLOC_FAILED if memory allocation failed

 */

int mpi_sub_mpi( mpi *X, const mpi *A, const mpi *B );

/**

 * \brief          Signed addition: X = A + b

 *

 * \param X        Destination MPI

 * \param A        Left-hand MPI

 * \param b        The integer value to add

 *

 * \return         0 if successful,

 *                 POLARSSL_ERR_MPI_MALLOC_FAILED if memory allocation failed

 */

int mpi_add_int( mpi *X, const mpi *A, t_sint b );

/**

 * \brief          Signed substraction: X = A - b

 *

 * \param X        Destination MPI

 * \param A        Left-hand MPI

 * \param b        The integer value to subtract

 *

 * \return         0 if successful,

 *                 POLARSSL_ERR_MPI_MALLOC_FAILED if memory allocation failed

 */

int mpi_sub_int( mpi *X, const mpi *A, t_sint b );

/**

 * \brief          Baseline multiplication: X = A * B

 *

 * \param X        Destination MPI

 * \param A        Left-hand MPI

 * \param B        Right-hand MPI

 *

 * \return         0 if successful,

 *                 POLARSSL_ERR_MPI_MALLOC_FAILED if memory allocation failed

 */

int mpi_mul_mpi( mpi *X, const mpi *A, const mpi *B );

/**

 * \brief          Baseline multiplication: X = A * b

 *                 Note: b is an unsigned integer type, thus

 *                 Negative values of b are ignored.

 *

 * \param X        Destination MPI

 * \param A        Left-hand MPI

 * \param b        The integer value to multiply with

 *

 * \return         0 if successful,

 *                 POLARSSL_ERR_MPI_MALLOC_FAILED if memory allocation failed

 */

int mpi_mul_int( mpi *X, const mpi *A, t_sint b );

/**

 * \brief          Division by mpi: A = Q * B + R

 *

 * \param Q        Destination MPI for the quotient

 * \param R        Destination MPI for the rest value

 * \param A        Left-hand MPI

 * \param B        Right-hand MPI

 *

 * \return         0 if successful,

 *                 POLARSSL_ERR_MPI_MALLOC_FAILED if memory allocation failed,

 *                 POLARSSL_ERR_MPI_DIVISION_BY_ZERO if B == 0

 *

 * \note           Either Q or R can be NULL.

 */

int mpi_div_mpi( mpi *Q, mpi *R, const mpi *A, const mpi *B );

/**

 * \brief          Division by int: A = Q * b + R

 *

 * \param Q        Destination MPI for the quotient

 * \param R        Destination MPI for the rest value

 * \param A        Left-hand MPI

 * \param b        Integer to divide by

 *

 * \return         0 if successful,

 *                 POLARSSL_ERR_MPI_MALLOC_FAILED if memory allocation failed,

 *                 POLARSSL_ERR_MPI_DIVISION_BY_ZERO if b == 0

 *

 * \note           Either Q or R can be NULL.

 */

int mpi_div_int( mpi *Q, mpi *R, const mpi *A, t_sint b );

/**

 * \brief          Modulo: R = A mod B

 *

 * \param R        Destination MPI for the rest value

 * \param A        Left-hand MPI

 * \param B        Right-hand MPI

 *

 * \return         0 if successful,

 *                 POLARSSL_ERR_MPI_MALLOC_FAILED if memory allocation failed,

 *                 POLARSSL_ERR_MPI_DIVISION_BY_ZERO if B == 0,

 *                 POLARSSL_ERR_MPI_NEGATIVE_VALUE if B < 0

 */

int mpi_mod_mpi( mpi *R, const mpi *A, const mpi *B );

/**

 * \brief          Modulo: r = A mod b

 *

 * \param r        Destination t_uint

 * \param A        Left-hand MPI

 * \param b        Integer to divide by

 *

 * \return         0 if successful,

 *                 POLARSSL_ERR_MPI_MALLOC_FAILED if memory allocation failed,

 *                 POLARSSL_ERR_MPI_DIVISION_BY_ZERO if b == 0,

 *                 POLARSSL_ERR_MPI_NEGATIVE_VALUE if b < 0

 */

int mpi_mod_int( t_uint *r, const mpi *A, t_sint b );

/**

 * \brief          Sliding-window exponentiation: X = A^E mod N

 *

 * \param X        Destination MPI

 * \param A        Left-hand MPI

 * \param E        Exponent MPI

 * \param N        Modular MPI

 * \param _RR      Speed-up MPI used for recalculations

 *

 * \return         0 if successful,

 *                 POLARSSL_ERR_MPI_MALLOC_FAILED if memory allocation failed,

 *                 POLARSSL_ERR_MPI_BAD_INPUT_DATA if N is negative or even or if

 *                 E is negative

 *

 * \note           _RR is used to avoid re-computing R*R mod N across

 *                 multiple calls, which speeds up things a bit. It can

 *                 be set to NULL if the extra performance is unneeded.

 */

int mpi_exp_mod( mpi *X, const mpi *A, const mpi *E, const mpi *N, mpi *_RR );

/**

 * \brief          Fill an MPI X with size bytes of random

 *

 * \param X        Destination MPI

 * \param size     Size in bytes

 * \param f_rng    RNG function

 * \param p_rng    RNG parameter

 *

 * \return         0 if successful,

 *                 POLARSSL_ERR_MPI_MALLOC_FAILED if memory allocation failed

 */

int mpi_fill_random( mpi *X, size_t size,

                     int (*f_rng)(void *, unsigned char *, size_t),

                     void *p_rng );

/**

 * \brief          Greatest common divisor: G = gcd(A, B)

 *

 * \param G        Destination MPI

 * \param A        Left-hand MPI

 * \param B        Right-hand MPI

 *

 * \return         0 if successful,

 *                 POLARSSL_ERR_MPI_MALLOC_FAILED if memory allocation failed

 */

int mpi_gcd( mpi *G, const mpi *A, const mpi *B );

/**

 * \brief          Modular inverse: X = A^-1 mod N

 *

 * \param X        Destination MPI

 * \param A        Left-hand MPI

 * \param N        Right-hand MPI

 *

 * \return         0 if successful,

 *                 POLARSSL_ERR_MPI_MALLOC_FAILED if memory allocation failed,

 *                 POLARSSL_ERR_MPI_BAD_INPUT_DATA if N is negative or nil

                   POLARSSL_ERR_MPI_NOT_ACCEPTABLE if A has no inverse mod N

 */

int mpi_inv_mod( mpi *X, const mpi *A, const mpi *N );

/**

 * \brief          Miller-Rabin primality test

 *

 * \param X        MPI to check

 * \param f_rng    RNG function

 * \param p_rng    RNG parameter

 *

 * \return         0 if successful (probably prime),

 *                 POLARSSL_ERR_MPI_MALLOC_FAILED if memory allocation failed,

 *                 POLARSSL_ERR_MPI_NOT_ACCEPTABLE if X is not prime

 */

int mpi_is_prime( mpi *X,

                  int (*f_rng)(void *, unsigned char *, size_t),

                  void *p_rng );

/**

 * \brief          Prime number generation

 *

 * \param X        Destination MPI

 * \param nbits    Required size of X in bits ( 3 <= nbits <= POLARSSL_MPI_MAX_BITS )

 * \param dh_flag  If 1, then (X-1)/2 will be prime too

 * \param f_rng    RNG function

 * \param p_rng    RNG parameter

 *

 * \return         0 if successful (probably prime),

 *                 POLARSSL_ERR_MPI_MALLOC_FAILED if memory allocation failed,

 *                 POLARSSL_ERR_MPI_BAD_INPUT_DATA if nbits is < 3

 */

int mpi_gen_prime( mpi *X, size_t nbits, int dh_flag,

                   int (*f_rng)(void *, unsigned char *, size_t),

                   void *p_rng );

/**

 * \brief          Checkup routine

 *

 * \return         0 if successful, or 1 if the test failed

 */

int mpi_self_test( int verbose );

#ifdef __cplusplus

}

#endif

#endif /* bignum.h */