text: /* SPDX-License-Identifier: Apache-2.0 */
  /**
   * \file bignum.h
   *
   * \brief  Multi-precision integer library
   *
   *  Copyright (C) 2006-2015, ARM Limited, All Rights Reserved
   *
   *  Licensed under the Apache License, Version 2.0 (the "License"); you may
   *  not use this file except in compliance with the License.
   *  You may obtain a copy of the License at
   *
   *  http://www.apache.org/licenses/LICENSE-2.0
   *
   *  Unless required by applicable law or agreed to in writing, software
   *  distributed under the License is distributed on an "AS IS" BASIS, WITHOUT
   *  WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
   *  See the License for the specific language governing permissions and
   *  limitations under the License.
   *
   *  This file is part of mbed TLS (https://tls.mbed.org)
   */
  #ifndef MBEDTLS_BIGNUM_H
  #define MBEDTLS_BIGNUM_H
  
  #if !defined(MBEDTLS_CONFIG_FILE)
  #include "config.h"
  #else
  #include MBEDTLS_CONFIG_FILE
  #endif
  
  #include <stddef.h>
  #include <stdint.h>
  
  #if defined(MBEDTLS_FS_IO)
  #include <stdio.h>
  #endif
  
  #define MBEDTLS_ERR_MPI_FILE_IO_ERROR                     -0x0002  /**< An error occurred while reading from or writing to a file. */
  #define MBEDTLS_ERR_MPI_BAD_INPUT_DATA                    -0x0004  /**< Bad input parameters to function. */
  #define MBEDTLS_ERR_MPI_INVALID_CHARACTER                 -0x0006  /**< There is an invalid character in the digit string. */
  #define MBEDTLS_ERR_MPI_BUFFER_TOO_SMALL                  -0x0008  /**< The buffer is too small to write to. */
  #define MBEDTLS_ERR_MPI_NEGATIVE_VALUE                    -0x000A  /**< The input arguments are negative or result in illegal output. */
  #define MBEDTLS_ERR_MPI_DIVISION_BY_ZERO                  -0x000C  /**< The input argument for division is zero, which is not allowed. */
  #define MBEDTLS_ERR_MPI_NOT_ACCEPTABLE                    -0x000E  /**< The input arguments are not acceptable. */
  #define MBEDTLS_ERR_MPI_ALLOC_FAILED                      -0x0010  /**< Memory allocation failed. */
  
  #define MBEDTLS_MPI_CHK(f) do { if( ( ret = f ) != 0 ) goto cleanup; } while( 0 )
  
  /*
   * Maximum size MPIs are allowed to grow to in number of limbs.
   */
  #define MBEDTLS_MPI_MAX_LIMBS                             10000
  
  #if !defined(MBEDTLS_MPI_WINDOW_SIZE)
  /*
   * Maximum window size used for modular exponentiation. Default: 6
   * Minimum value: 1. Maximum value: 6.
   *
   * Result is an array of ( 2 << MBEDTLS_MPI_WINDOW_SIZE ) MPIs used
   * for the sliding window calculation. (So 64 by default)
   *
   * Reduction in size, reduces speed.
   */
  #define MBEDTLS_MPI_WINDOW_SIZE                           6        /**< Maximum windows size used. */
  #endif /* !MBEDTLS_MPI_WINDOW_SIZE */
  
  #if !defined(MBEDTLS_MPI_MAX_SIZE)
  /*
   * 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 (MBEDTLS_MPI_MAX_LIMBS) is higher.
   */
  #define MBEDTLS_MPI_MAX_SIZE                              1024     /**< Maximum number of bytes for usable MPIs. */
  #endif /* !MBEDTLS_MPI_MAX_SIZE */
  
  #define MBEDTLS_MPI_MAX_BITS                              ( 8 * MBEDTLS_MPI_MAX_SIZE )    /**< Maximum number of bits for usable MPIs. */
  
  /*
   * When reading from files with mbedtls_mpi_read_file() and writing to files with
   * mbedtls_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 MBEDTLS_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:
   *  MBEDTLS_MPI_RW_BUFFER_SIZE = ceil(MBEDTLS_MPI_MAX_BITS / ln(10) * ln(2)) +
   *                                LabelSize + 6
   */
  #define MBEDTLS_MPI_MAX_BITS_SCALE100          ( 100 * MBEDTLS_MPI_MAX_BITS )
  #define MBEDTLS_LN_2_DIV_LN_10_SCALE100                 332
  #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 )
  
  /*
   * Define the base integer type, architecture-wise.
   *
   * 32 or 64-bit integer types can be forced regardless of the underlying
   * architecture by defining MBEDTLS_HAVE_INT32 or MBEDTLS_HAVE_INT64
   * respectively and undefining MBEDTLS_HAVE_ASM.
   *
   * Double-width integers (e.g. 128-bit in 64-bit architectures) can be
   * disabled by defining MBEDTLS_NO_UDBL_DIVISION.
   */
  #if !defined(MBEDTLS_HAVE_INT32)
      #if defined(_MSC_VER) && defined(_M_AMD64)
          /* Always choose 64-bit when using MSC */
          #if !defined(MBEDTLS_HAVE_INT64)
              #define MBEDTLS_HAVE_INT64
          #endif /* !MBEDTLS_HAVE_INT64 */
          typedef  int64_t mbedtls_mpi_sint;
          typedef uint64_t mbedtls_mpi_uint;
      #elif defined(__GNUC__) && (                         \
          defined(__amd64__) || defined(__x86_64__)     || \
          defined(__ppc64__) || defined(__powerpc64__)  || \
          defined(__ia64__)  || defined(__alpha__)      || \
          ( defined(__sparc__) && defined(__arch64__) ) || \
          defined(__s390x__) || defined(__mips64) )
          #if !defined(MBEDTLS_HAVE_INT64)
              #define MBEDTLS_HAVE_INT64
          #endif /* MBEDTLS_HAVE_INT64 */
          typedef  int64_t mbedtls_mpi_sint;
          typedef uint64_t mbedtls_mpi_uint;
          #if !defined(MBEDTLS_NO_UDBL_DIVISION)
              /* mbedtls_t_udbl defined as 128-bit unsigned int */
              typedef unsigned int mbedtls_t_udbl __attribute__((mode(TI)));
              #define MBEDTLS_HAVE_UDBL
          #endif /* !MBEDTLS_NO_UDBL_DIVISION */
      #elif defined(__ARMCC_VERSION) && defined(__aarch64__)
          /*
           * __ARMCC_VERSION is defined for both armcc and armclang and
           * __aarch64__ is only defined by armclang when compiling 64-bit code
           */
          #if !defined(MBEDTLS_HAVE_INT64)
              #define MBEDTLS_HAVE_INT64
          #endif /* !MBEDTLS_HAVE_INT64 */
          typedef  int64_t mbedtls_mpi_sint;
          typedef uint64_t mbedtls_mpi_uint;
          #if !defined(MBEDTLS_NO_UDBL_DIVISION)
              /* mbedtls_t_udbl defined as 128-bit unsigned int */
              typedef __uint128_t mbedtls_t_udbl;
              #define MBEDTLS_HAVE_UDBL
          #endif /* !MBEDTLS_NO_UDBL_DIVISION */
      #elif defined(MBEDTLS_HAVE_INT64)
          /* Force 64-bit integers with unknown compiler */
          typedef  int64_t mbedtls_mpi_sint;
          typedef uint64_t mbedtls_mpi_uint;
      #endif
  #endif /* !MBEDTLS_HAVE_INT32 */
  
  #if !defined(MBEDTLS_HAVE_INT64)
      /* Default to 32-bit compilation */
      #if !defined(MBEDTLS_HAVE_INT32)
          #define MBEDTLS_HAVE_INT32
      #endif /* !MBEDTLS_HAVE_INT32 */
      typedef  int32_t mbedtls_mpi_sint;
      typedef uint32_t mbedtls_mpi_uint;
      #if !defined(MBEDTLS_NO_UDBL_DIVISION)
          typedef uint64_t mbedtls_t_udbl;
          #define MBEDTLS_HAVE_UDBL
      #endif /* !MBEDTLS_NO_UDBL_DIVISION */
  #endif /* !MBEDTLS_HAVE_INT64 */
  
  #ifdef __cplusplus
  extern "C" {
  #endif
  
  /**
   * \brief          MPI structure
   */
  typedef struct
  {
      short s;              /*!<  integer sign      */
      short use_mempool;
      size_t n;           /*!<  total # of limbs  */
      mbedtls_mpi_uint *p;          /*!<  pointer to limbs  */
  }
  mbedtls_mpi;
  
  extern void *mbedtls_mpi_mempool;
  
  /**
   * \brief           Initialize one MPI (make internal references valid)
   *                  This just makes it ready to be set or freed,
   *                  but does not define a value for the MPI.
   *
   * \param X         One MPI to initialize.
   */
  void mbedtls_mpi_init( mbedtls_mpi *X );
  void mbedtls_mpi_init_mempool( mbedtls_mpi *X );
  
  /**
   * \brief          Unallocate one MPI
   *
   * \param X        One MPI to unallocate.
   */
  void mbedtls_mpi_free( mbedtls_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,
   *                 MBEDTLS_ERR_MPI_ALLOC_FAILED if memory allocation failed
   */
  int mbedtls_mpi_grow( mbedtls_mpi *X, size_t nblimbs );
  
  /**
   * \brief          Resize down, keeping at least the specified number of limbs
   *
   * \param X        MPI to shrink
   * \param nblimbs  The minimum number of limbs to keep
   *
   * \return         0 if successful,
   *                 MBEDTLS_ERR_MPI_ALLOC_FAILED if memory allocation failed
   */
  int mbedtls_mpi_shrink( mbedtls_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,
   *                 MBEDTLS_ERR_MPI_ALLOC_FAILED if memory allocation failed
   */
  int mbedtls_mpi_copy( mbedtls_mpi *X, const mbedtls_mpi *Y );
  
  /**
   * \brief          Swap the contents of X and Y
   *
   * \param X        First MPI value
   * \param Y        Second MPI value
   */
  void mbedtls_mpi_swap( mbedtls_mpi *X, mbedtls_mpi *Y );
  
  /**
   * \brief          Safe conditional assignement X = Y if assign is 1
   *
   * \param X        MPI to conditionally assign to
   * \param Y        Value to be assigned
   * \param assign   1: perform the assignment, 0: keep X's original value
   *
   * \return         0 if successful,
   *                 MBEDTLS_ERR_MPI_ALLOC_FAILED if memory allocation failed,
   *
   * \note           This function is equivalent to
   *                      if( assign ) mbedtls_mpi_copy( X, Y );
   *                 except that it avoids leaking any information about whether
   *                 the assignment was done or not (the above code may leak
   *                 information through branch prediction and/or memory access
   *                 patterns analysis).
   */
  int mbedtls_mpi_safe_cond_assign( mbedtls_mpi *X, const mbedtls_mpi *Y, unsigned char assign );
  
  /**
   * \brief          Safe conditional swap X <-> Y if swap is 1
   *
   * \param X        First mbedtls_mpi value
   * \param Y        Second mbedtls_mpi value
   * \param assign   1: perform the swap, 0: keep X and Y's original values
   *
   * \return         0 if successful,
   *                 MBEDTLS_ERR_MPI_ALLOC_FAILED if memory allocation failed,
   *
   * \note           This function is equivalent to
   *                      if( assign ) mbedtls_mpi_swap( X, Y );
   *                 except that it avoids leaking any information about whether
   *                 the assignment was done or not (the above code may leak
   *                 information through branch prediction and/or memory access
   *                 patterns analysis).
   */
  int mbedtls_mpi_safe_cond_swap( mbedtls_mpi *X, mbedtls_mpi *Y, unsigned char assign );
  
  /**
   * \brief          Set value from integer
   *
   * \param X        MPI to set
   * \param z        Value to use
   *
   * \return         0 if successful,
   *                 MBEDTLS_ERR_MPI_ALLOC_FAILED if memory allocation failed
   */
  int mbedtls_mpi_lset( mbedtls_mpi *X, mbedtls_mpi_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 mbedtls_mpi_get_bit( const mbedtls_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,
   *                 MBEDTLS_ERR_MPI_ALLOC_FAILED if memory allocation failed,
   *                 MBEDTLS_ERR_MPI_BAD_INPUT_DATA if val is not 0 or 1
   */
  int mbedtls_mpi_set_bit( mbedtls_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 mbedtls_mpi_lsb( const mbedtls_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 mbedtls_mpi_bitlen( const mbedtls_mpi *X );
  
  /**
   * \brief          Return the total size in bytes
   *
   * \param X        MPI to use
   */
  size_t mbedtls_mpi_size( const mbedtls_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 MBEDTLS_ERR_MPI_XXX error code
   */
  int mbedtls_mpi_read_string( mbedtls_mpi *X, int radix, const char *s );
  
  /**
   * \brief          Export into an ASCII string
   *
   * \param X        Source MPI
   * \param radix    Output numeric base
   * \param buf      Buffer to write the string to
   * \param buflen   Length of buf
   * \param olen     Length of the string written, including final NUL byte
   *
   * \return         0 if successful, or a MBEDTLS_ERR_MPI_XXX error code.
   *                 *olen is always updated to reflect the amount
   *                 of data that has (or would have) been written.
   *
   * \note           Call this function with buflen = 0 to obtain the
   *                 minimum required buffer size in *olen.
   */
  int mbedtls_mpi_write_string( const mbedtls_mpi *X, int radix,
                                char *buf, size_t buflen, size_t *olen );
  
  #if defined(MBEDTLS_FS_IO)
  /**
   * \brief          Read MPI from a line in an opened file
   *
   * \param X        Destination MPI
   * \param radix    Input numeric base
   * \param fin      Input file handle
   *
   * \return         0 if successful, MBEDTLS_ERR_MPI_BUFFER_TOO_SMALL if
   *                 the file read buffer is too small or a
   *                 MBEDTLS_ERR_MPI_XXX error code
   *
   * \note           On success, this function advances the file stream
   *                 to the end of the current line or to EOF.
   *
   *                 The function returns 0 on an empty line.
   *
   *                 Leading whitespaces are ignored, as is a
   *                 '0x' prefix for radix 16.
   *
   */
  int mbedtls_mpi_read_file( mbedtls_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 MBEDTLS_ERR_MPI_XXX error code
   *
   * \note           Set fout == NULL to print X on the console.
   */
  int mbedtls_mpi_write_file( const char *p, const mbedtls_mpi *X, int radix, FILE *fout );
  #endif /* MBEDTLS_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,
   *                 MBEDTLS_ERR_MPI_ALLOC_FAILED if memory allocation failed
   */
  int mbedtls_mpi_read_binary( mbedtls_mpi *X, const unsigned char *buf, size_t buflen );
  
  /**
   * \brief          Export X into unsigned binary data, big endian.
   *                 Always fills the whole buffer, which will start with zeros
   *                 if the number is smaller.
   *
   * \param X        Source MPI
   * \param buf      Output buffer
   * \param buflen   Output buffer size
   *
   * \return         0 if successful,
   *                 MBEDTLS_ERR_MPI_BUFFER_TOO_SMALL if buf isn't large enough
   */
  int mbedtls_mpi_write_binary( const mbedtls_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,
   *                 MBEDTLS_ERR_MPI_ALLOC_FAILED if memory allocation failed
   */
  int mbedtls_mpi_shift_l( mbedtls_mpi *X, size_t count );
  
  /**
   * \brief          Right-shift: X >>= count
   *
   * \param X        MPI to shift
   * \param count    Amount to shift
   *
   * \return         0 if successful,
   *                 MBEDTLS_ERR_MPI_ALLOC_FAILED if memory allocation failed
   */
  int mbedtls_mpi_shift_r( mbedtls_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 mbedtls_mpi_cmp_abs( const mbedtls_mpi *X, const mbedtls_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 mbedtls_mpi_cmp_mpi( const mbedtls_mpi *X, const mbedtls_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 mbedtls_mpi_cmp_int( const mbedtls_mpi *X, mbedtls_mpi_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,
   *                 MBEDTLS_ERR_MPI_ALLOC_FAILED if memory allocation failed
   */
  int mbedtls_mpi_add_abs( mbedtls_mpi *X, const mbedtls_mpi *A, const mbedtls_mpi *B );
  
  /**
   * \brief          Unsigned subtraction: X = |A| - |B|
   *
   * \param X        Destination MPI
   * \param A        Left-hand MPI
   * \param B        Right-hand MPI
   *
   * \return         0 if successful,
   *                 MBEDTLS_ERR_MPI_NEGATIVE_VALUE if B is greater than A
   */
  int mbedtls_mpi_sub_abs( mbedtls_mpi *X, const mbedtls_mpi *A, const mbedtls_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,
   *                 MBEDTLS_ERR_MPI_ALLOC_FAILED if memory allocation failed
   */
  int mbedtls_mpi_add_mpi( mbedtls_mpi *X, const mbedtls_mpi *A, const mbedtls_mpi *B );
  
  /**
   * \brief          Signed subtraction: X = A - B
   *
   * \param X        Destination MPI
   * \param A        Left-hand MPI
   * \param B        Right-hand MPI
   *
   * \return         0 if successful,
   *                 MBEDTLS_ERR_MPI_ALLOC_FAILED if memory allocation failed
   */
  int mbedtls_mpi_sub_mpi( mbedtls_mpi *X, const mbedtls_mpi *A, const mbedtls_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,
   *                 MBEDTLS_ERR_MPI_ALLOC_FAILED if memory allocation failed
   */
  int mbedtls_mpi_add_int( mbedtls_mpi *X, const mbedtls_mpi *A, mbedtls_mpi_sint b );
  
  /**
   * \brief          Signed subtraction: X = A - b
   *
   * \param X        Destination MPI
   * \param A        Left-hand MPI
   * \param b        The integer value to subtract
   *
   * \return         0 if successful,
   *                 MBEDTLS_ERR_MPI_ALLOC_FAILED if memory allocation failed
   */
  int mbedtls_mpi_sub_int( mbedtls_mpi *X, const mbedtls_mpi *A, mbedtls_mpi_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,
   *                 MBEDTLS_ERR_MPI_ALLOC_FAILED if memory allocation failed
   */
  int mbedtls_mpi_mul_mpi( mbedtls_mpi *X, const mbedtls_mpi *A, const mbedtls_mpi *B );
  
  /**
   * \brief          Baseline multiplication: X = A * b
   *
   * \param X        Destination MPI
   * \param A        Left-hand MPI
   * \param b        The unsigned integer value to multiply with
   *
   * \note           b is unsigned
   *
   * \return         0 if successful,
   *                 MBEDTLS_ERR_MPI_ALLOC_FAILED if memory allocation failed
   */
  int mbedtls_mpi_mul_int( mbedtls_mpi *X, const mbedtls_mpi *A, mbedtls_mpi_uint b );
  
  /**
   * \brief          Division by mbedtls_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,
   *                 MBEDTLS_ERR_MPI_ALLOC_FAILED if memory allocation failed,
   *                 MBEDTLS_ERR_MPI_DIVISION_BY_ZERO if B == 0
   *
   * \note           Either Q or R can be NULL.
   */
  int mbedtls_mpi_div_mpi( mbedtls_mpi *Q, mbedtls_mpi *R, const mbedtls_mpi *A, const mbedtls_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,
   *                 MBEDTLS_ERR_MPI_ALLOC_FAILED if memory allocation failed,
   *                 MBEDTLS_ERR_MPI_DIVISION_BY_ZERO if b == 0
   *
   * \note           Either Q or R can be NULL.
   */
  int mbedtls_mpi_div_int( mbedtls_mpi *Q, mbedtls_mpi *R, const mbedtls_mpi *A, mbedtls_mpi_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,
   *                 MBEDTLS_ERR_MPI_ALLOC_FAILED if memory allocation failed,
   *                 MBEDTLS_ERR_MPI_DIVISION_BY_ZERO if B == 0,
   *                 MBEDTLS_ERR_MPI_NEGATIVE_VALUE if B < 0
   */
  int mbedtls_mpi_mod_mpi( mbedtls_mpi *R, const mbedtls_mpi *A, const mbedtls_mpi *B );
  
  /**
   * \brief          Modulo: r = A mod b
   *
   * \param r        Destination mbedtls_mpi_uint
   * \param A        Left-hand MPI
   * \param b        Integer to divide by
   *
   * \return         0 if successful,
   *                 MBEDTLS_ERR_MPI_ALLOC_FAILED if memory allocation failed,
   *                 MBEDTLS_ERR_MPI_DIVISION_BY_ZERO if b == 0,
   *                 MBEDTLS_ERR_MPI_NEGATIVE_VALUE if b < 0
   */
  int mbedtls_mpi_mod_int( mbedtls_mpi_uint *r, const mbedtls_mpi *A, mbedtls_mpi_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,
   *                 MBEDTLS_ERR_MPI_ALLOC_FAILED if memory allocation failed,
   *                 MBEDTLS_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 mbedtls_mpi_exp_mod( mbedtls_mpi *X, const mbedtls_mpi *A, const mbedtls_mpi *E, const mbedtls_mpi *N, mbedtls_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,
   *                 MBEDTLS_ERR_MPI_ALLOC_FAILED if memory allocation failed
   */
  int mbedtls_mpi_fill_random( mbedtls_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,
   *                 MBEDTLS_ERR_MPI_ALLOC_FAILED if memory allocation failed
   */
  int mbedtls_mpi_gcd( mbedtls_mpi *G, const mbedtls_mpi *A, const mbedtls_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,
   *                 MBEDTLS_ERR_MPI_ALLOC_FAILED if memory allocation failed,
   *                 MBEDTLS_ERR_MPI_BAD_INPUT_DATA if N is <= 1,
                     MBEDTLS_ERR_MPI_NOT_ACCEPTABLE if A has no inverse mod N.
   */
  int mbedtls_mpi_inv_mod( mbedtls_mpi *X, const mbedtls_mpi *A, const mbedtls_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),
   *                 MBEDTLS_ERR_MPI_ALLOC_FAILED if memory allocation failed,
   *                 MBEDTLS_ERR_MPI_NOT_ACCEPTABLE if X is not prime
   */
  int mbedtls_mpi_is_prime( const mbedtls_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 <= MBEDTLS_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),
   *                 MBEDTLS_ERR_MPI_ALLOC_FAILED if memory allocation failed,
   *                 MBEDTLS_ERR_MPI_BAD_INPUT_DATA if nbits is < 3
   */
  int mbedtls_mpi_gen_prime( mbedtls_mpi *X, size_t nbits, int dh_flag,
                     int (*f_rng)(void *, unsigned char *, size_t),
                     void *p_rng );
  
  
  /**
   * \brief          Montgomery initialization
   *
   * \param mm       The -1/m mod N result
   * \param N        The modulus
   */
  void mbedtls_mpi_montg_init( mbedtls_mpi_uint *mm, const mbedtls_mpi *N );
  
  /**
   * \brief          Montgomery multiplication: A = A * B * R^-1 mod N
   * \A              Parameter and result
   * \B              Parameter
   * \N              Modulus
   * \mm             Parameter from mbedtls_mpi_montg_init()
   * \T              Temporary variable, should be as twice as big as N + 2
   * \return         0 if successful,
   *                 MBEDTLS_ERR_MPI_BAD_INPUT_DATA if nbits is < 3
   */
  int mbedtls_mpi_montmul( mbedtls_mpi *A, const mbedtls_mpi *B,
  			 const mbedtls_mpi *N, mbedtls_mpi_uint mm,
                           const mbedtls_mpi *T );
  
  /**
   * \brief          Montgomery reduction: A = A * R^-1 mod N
   * \A              Parameter and result
   * \N              Modulus
   * \mm             Parameter from mbedtls_mpi_montg_init()
   * \T              Temporary variable, should be as twice as big as N + 2
   * \return         0 if successful,
   *                 MBEDTLS_ERR_MPI_BAD_INPUT_DATA if nbits is < 3
   */
  int mbedtls_mpi_montred( mbedtls_mpi *A, const mbedtls_mpi *N,
  			 mbedtls_mpi_uint mm, const mbedtls_mpi *T );
  
  /**
   * \brief          Checkup routine
   *
   * \return         0 if successful, or 1 if the test failed
   */
  int mbedtls_mpi_self_test( int verbose );
  
  #ifdef __cplusplus
  }
  #endif
  
  #endif /* bignum.h */
  