text: /*
   *  Multi-precision integer library
   *
   *  Copyright (C) 2006-2015, ARM Limited, All Rights Reserved
   *  SPDX-License-Identifier: Apache-2.0
   *
   *  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)
   */
  /*
   *  This MPI implementation is based on:
   *
   *  http://www.cacr.math.uwaterloo.ca/hac/about/chap14.pdf
   *  http://www.stillhq.com/extracted/gnupg-api/mbedtls_mpi/
   *  http://math.libtomcrypt.com/files/tommath.pdf
   */
  
  /*
      GameSparks LLC:
          The Source files have been changed so that they can be compiled by a C++
          Compiler. This was required, because the Unreal Engine and Windows 10
          Phone / Universal Apps do not support direct compilation of C Source
          code. Also changes where made to enable the compilation from a single
          translation unit (amalgamated build).
  */
  
  #if !defined(MBEDTLS_CONFIG_FILE)
  #include "../../include/mbedtls/config.h"
  #else
  #include MBEDTLS_CONFIG_FILE
  #endif
  
  #if defined(MBEDTLS_BIGNUM_C)
  
  #include "../../include/mbedtls/bignum.h"
  #include "../../include/mbedtls/bn_mul.h"
  
  #include <string.h>
  
  #if defined(MBEDTLS_PLATFORM_C)
  #include "../../include/mbedtls/platform.h"
  #else
  #include <stdio.h>
  #include <stdlib.h>
  #define mbedtls_printf     printf
  #define mbedtls_calloc    calloc
  #define mbedtls_free       free
  #endif
  
  /* Implementation that should never be optimized out by the compiler */
  #if !defined(MBEDTLS_AMALGAMATE)
  static void mbedtls_zeroize( void *v, size_t n ) {
      volatile unsigned char *p = v; while( n-- ) *p++ = 0;
  }
  #endif /* MBEDTLS_AMALGAMATE */
  
  #define ciL    (sizeof(mbedtls_mpi_uint))         /* chars in limb  */
  #define biL    (ciL << 3)               /* bits  in limb  */
  #define biH    (ciL << 2)               /* half limb size */
  
  /*
   * Convert between bits/chars and number of limbs
   */
  #define BITS_TO_LIMBS(i)  (((i) + biL - 1) / biL)
  #define CHARS_TO_LIMBS(i) (((i) + ciL - 1) / ciL)
  
  /*
   * Initialize one MPI
   */
  void mbedtls_mpi_init( mbedtls_mpi *X )
  {
      if( X == NULL )
          return;
  
      X->s = 1;
      X->n = 0;
      X->p = NULL;
  }
  
  /*
   * Unallocate one MPI
   */
  void mbedtls_mpi_free( mbedtls_mpi *X )
  {
      if( X == NULL )
          return;
  
      if( X->p != NULL )
      {
          mbedtls_zeroize( X->p, X->n * ciL );
          mbedtls_free( X->p );
      }
  
      X->s = 1;
      X->n = 0;
      X->p = NULL;
  }
  
  /*
   * Enlarge to the specified number of limbs
   */
  int mbedtls_mpi_grow( mbedtls_mpi *X, size_t nblimbs )
  {
      mbedtls_mpi_uint *p;
  
      if( nblimbs > MBEDTLS_MPI_MAX_LIMBS )
          return( MBEDTLS_ERR_MPI_ALLOC_FAILED );
  
      if( X->n < nblimbs )
      {
  		if ((p = (mbedtls_mpi_uint *)mbedtls_calloc(nblimbs, ciL)) == NULL)
              return( MBEDTLS_ERR_MPI_ALLOC_FAILED );
  
          if( X->p != NULL )
          {
              memcpy( p, X->p, X->n * ciL );
              mbedtls_zeroize( X->p, X->n * ciL );
              mbedtls_free( X->p );
          }
  
          X->n = nblimbs;
          X->p = p;
      }
  
      return( 0 );
  }
  
  /*
   * Resize down as much as possible,
   * while keeping at least the specified number of limbs
   */
  int mbedtls_mpi_shrink( mbedtls_mpi *X, size_t nblimbs )
  {
      mbedtls_mpi_uint *p;
      size_t i;
  
      /* Actually resize up in this case */
      if( X->n <= nblimbs )
          return( mbedtls_mpi_grow( X, nblimbs ) );
  
      for( i = X->n - 1; i > 0; i-- )
          if( X->p[i] != 0 )
              break;
      i++;
  
      if( i < nblimbs )
          i = nblimbs;
  
  	if ((p = (mbedtls_mpi_uint *)mbedtls_calloc(i, ciL)) == NULL)
          return( MBEDTLS_ERR_MPI_ALLOC_FAILED );
  
      if( X->p != NULL )
      {
          memcpy( p, X->p, i * ciL );
          mbedtls_zeroize( X->p, X->n * ciL );
          mbedtls_free( X->p );
      }
  
      X->n = i;
      X->p = p;
  
      return( 0 );
  }
  
  /*
   * Copy the contents of Y into X
   */
  int mbedtls_mpi_copy( mbedtls_mpi *X, const mbedtls_mpi *Y )
  {
      int ret;
      size_t i;
  
      if( X == Y )
          return( 0 );
  
      if( Y->p == NULL )
      {
          mbedtls_mpi_free( X );
          return( 0 );
      }
  
      for( i = Y->n - 1; i > 0; i-- )
          if( Y->p[i] != 0 )
              break;
      i++;
  
      X->s = Y->s;
  
      MBEDTLS_MPI_CHK( mbedtls_mpi_grow( X, i ) );
  
      memset( X->p, 0, X->n * ciL );
      memcpy( X->p, Y->p, i * ciL );
  
  cleanup:
  
      return( ret );
  }
  
  /*
   * Swap the contents of X and Y
   */
  void mbedtls_mpi_swap( mbedtls_mpi *X, mbedtls_mpi *Y )
  {
      mbedtls_mpi T;
  
      memcpy( &T,  X, sizeof( mbedtls_mpi ) );
      memcpy(  X,  Y, sizeof( mbedtls_mpi ) );
      memcpy(  Y, &T, sizeof( mbedtls_mpi ) );
  }
  
  /*
   * Conditionally assign X = Y, without leaking information
   * about whether the assignment was made or not.
   * (Leaking information about the respective sizes of X and Y is ok however.)
   */
  int mbedtls_mpi_safe_cond_assign( mbedtls_mpi *X, const mbedtls_mpi *Y, unsigned char assign )
  {
      int ret = 0;
      size_t i;
  
      /* make sure assign is 0 or 1 in a time-constant manner */
      assign = (assign | (unsigned char)-assign) >> 7;
  
      MBEDTLS_MPI_CHK( mbedtls_mpi_grow( X, Y->n ) );
  
      X->s = X->s * ( 1 - assign ) + Y->s * assign;
  
      for( i = 0; i < Y->n; i++ )
          X->p[i] = X->p[i] * ( 1 - assign ) + Y->p[i] * assign;
  
      for( ; i < X->n; i++ )
          X->p[i] *= ( 1 - assign );
  
  cleanup:
      return( ret );
  }
  
  /*
   * Conditionally swap X and Y, without leaking information
   * about whether the swap was made or not.
   * Here it is not ok to simply swap the pointers, which whould lead to
   * different memory access patterns when X and Y are used afterwards.
   */
  int mbedtls_mpi_safe_cond_swap( mbedtls_mpi *X, mbedtls_mpi *Y, unsigned char swap )
  {
      int ret, s;
      size_t i;
      mbedtls_mpi_uint tmp;
  
      if( X == Y )
          return( 0 );
  
      /* make sure swap is 0 or 1 in a time-constant manner */
      swap = (swap | (unsigned char)-swap) >> 7;
  
      MBEDTLS_MPI_CHK( mbedtls_mpi_grow( X, Y->n ) );
      MBEDTLS_MPI_CHK( mbedtls_mpi_grow( Y, X->n ) );
  
      s = X->s;
      X->s = X->s * ( 1 - swap ) + Y->s * swap;
      Y->s = Y->s * ( 1 - swap ) +    s * swap;
  
  
      for( i = 0; i < X->n; i++ )
      {
          tmp = X->p[i];
          X->p[i] = X->p[i] * ( 1 - swap ) + Y->p[i] * swap;
          Y->p[i] = Y->p[i] * ( 1 - swap ) +     tmp * swap;
      }
  
  cleanup:
      return( ret );
  }
  
  /*
   * Set value from integer
   */
  int mbedtls_mpi_lset( mbedtls_mpi *X, mbedtls_mpi_sint z )
  {
      int ret;
  
      MBEDTLS_MPI_CHK( mbedtls_mpi_grow( X, 1 ) );
      memset( X->p, 0, X->n * ciL );
  
      X->p[0] = ( z < 0 ) ? -z : z;
      X->s    = ( z < 0 ) ? -1 : 1;
  
  cleanup:
  
      return( ret );
  }
  
  /*
   * Get a specific bit
   */
  int mbedtls_mpi_get_bit( const mbedtls_mpi *X, size_t pos )
  {
      if( X->n * biL <= pos )
          return( 0 );
  
      return( ( X->p[pos / biL] >> ( pos % biL ) ) & 0x01 );
  }
  
  /*
   * Set a bit to a specific value of 0 or 1
   */
  int mbedtls_mpi_set_bit( mbedtls_mpi *X, size_t pos, unsigned char val )
  {
      int ret = 0;
      size_t off = pos / biL;
      size_t idx = pos % biL;
  
      if( val != 0 && val != 1 )
          return( MBEDTLS_ERR_MPI_BAD_INPUT_DATA );
  
      if( X->n * biL <= pos )
      {
          if( val == 0 )
              return( 0 );
  
          MBEDTLS_MPI_CHK( mbedtls_mpi_grow( X, off + 1 ) );
      }
  
      X->p[off] &= ~( (mbedtls_mpi_uint) 0x01 << idx );
      X->p[off] |= (mbedtls_mpi_uint) val << idx;
  
  cleanup:
  
      return( ret );
  }
  
  /*
   * Return the number of less significant zero-bits
   */
  size_t mbedtls_mpi_lsb( const mbedtls_mpi *X )
  {
      size_t i, j, count = 0;
  
      for( i = 0; i < X->n; i++ )
          for( j = 0; j < biL; j++, count++ )
              if( ( ( X->p[i] >> j ) & 1 ) != 0 )
                  return( count );
  
      return( 0 );
  }
  
  /*
   * Return the number of bits
   */
  size_t mbedtls_mpi_bitlen( const mbedtls_mpi *X )
  {
      size_t i, j;
  
      if( X->n == 0 )
          return( 0 );
  
      for( i = X->n - 1; i > 0; i-- )
          if( X->p[i] != 0 )
              break;
  
      for( j = biL; j > 0; j-- )
          if( ( ( X->p[i] >> ( j - 1 ) ) & 1 ) != 0 )
              break;
  
      return( ( i * biL ) + j );
  }
  
  /*
   * Return the total size in bytes
   */
  size_t mbedtls_mpi_size( const mbedtls_mpi *X )
  {
      return( ( mbedtls_mpi_bitlen( X ) + 7 ) >> 3 );
  }
  
  /*
   * Convert an ASCII character to digit value
   */
  static int mpi_get_digit( mbedtls_mpi_uint *d, int radix, char c )
  {
      *d = 255;
  
      if( c >= 0x30 && c <= 0x39 ) *d = c - 0x30;
      if( c >= 0x41 && c <= 0x46 ) *d = c - 0x37;
      if( c >= 0x61 && c <= 0x66 ) *d = c - 0x57;
  
      if( *d >= (mbedtls_mpi_uint) radix )
          return( MBEDTLS_ERR_MPI_INVALID_CHARACTER );
  
      return( 0 );
  }
  
  /*
   * Import from an ASCII string
   */
  int mbedtls_mpi_read_string( mbedtls_mpi *X, int radix, const char *s )
  {
      int ret;
      size_t i, j, slen, n;
      mbedtls_mpi_uint d;
      mbedtls_mpi T;
  
      if( radix < 2 || radix > 16 )
          return( MBEDTLS_ERR_MPI_BAD_INPUT_DATA );
  
      mbedtls_mpi_init( &T );
  
      slen = strlen( s );
  
      if( radix == 16 )
      {
          n = BITS_TO_LIMBS( slen << 2 );
  
          MBEDTLS_MPI_CHK( mbedtls_mpi_grow( X, n ) );
          MBEDTLS_MPI_CHK( mbedtls_mpi_lset( X, 0 ) );
  
          for( i = slen, j = 0; i > 0; i--, j++ )
          {
              if( i == 1 && s[i - 1] == '-' )
              {
                  X->s = -1;
                  break;
              }
  
              MBEDTLS_MPI_CHK( mpi_get_digit( &d, radix, s[i - 1] ) );
              X->p[j / ( 2 * ciL )] |= d << ( ( j % ( 2 * ciL ) ) << 2 );
          }
      }
      else
      {
          MBEDTLS_MPI_CHK( mbedtls_mpi_lset( X, 0 ) );
  
          for( i = 0; i < slen; i++ )
          {
              if( i == 0 && s[i] == '-' )
              {
                  X->s = -1;
                  continue;
              }
  
              MBEDTLS_MPI_CHK( mpi_get_digit( &d, radix, s[i] ) );
              MBEDTLS_MPI_CHK( mbedtls_mpi_mul_int( &T, X, radix ) );
  
              if( X->s == 1 )
              {
                  MBEDTLS_MPI_CHK( mbedtls_mpi_add_int( X, &T, d ) );
              }
              else
              {
                  MBEDTLS_MPI_CHK( mbedtls_mpi_sub_int( X, &T, d ) );
              }
          }
      }
  
  cleanup:
  
      mbedtls_mpi_free( &T );
  
      return( ret );
  }
  
  /*
   * Helper to write the digits high-order first
   */
  static int mpi_write_hlp( mbedtls_mpi *X, int radix, char **p )
  {
      int ret;
      mbedtls_mpi_uint r;
  
      if( radix < 2 || radix > 16 )
          return( MBEDTLS_ERR_MPI_BAD_INPUT_DATA );
  
      MBEDTLS_MPI_CHK( mbedtls_mpi_mod_int( &r, X, radix ) );
      MBEDTLS_MPI_CHK( mbedtls_mpi_div_int( X, NULL, X, radix ) );
  
      if( mbedtls_mpi_cmp_int( X, 0 ) != 0 )
          MBEDTLS_MPI_CHK( mpi_write_hlp( X, radix, p ) );
  
      if( r < 10 )
          *(*p)++ = (char)( r + 0x30 );
      else
          *(*p)++ = (char)( r + 0x37 );
  
  cleanup:
  
      return( ret );
  }
  
  /*
   * Export into an ASCII string
   */
  int mbedtls_mpi_write_string( const mbedtls_mpi *X, int radix,
                                char *buf, size_t buflen, size_t *olen )
  {
      int ret = 0;
      size_t n;
      char *p;
      mbedtls_mpi T;
  
      if( radix < 2 || radix > 16 )
          return( MBEDTLS_ERR_MPI_BAD_INPUT_DATA );
  
      n = mbedtls_mpi_bitlen( X );
      if( radix >=  4 ) n >>= 1;
      if( radix >= 16 ) n >>= 1;
      n += 3;
  
      if( buflen < n )
      {
          *olen = n;
          return( MBEDTLS_ERR_MPI_BUFFER_TOO_SMALL );
      }
  
      p = buf;
      mbedtls_mpi_init( &T );
  
      if( X->s == -1 )
          *p++ = '-';
  
      if( radix == 16 )
      {
          int c;
          size_t i, j, k;
  
          for( i = X->n, k = 0; i > 0; i-- )
          {
              for( j = ciL; j > 0; j-- )
              {
                  c = ( X->p[i - 1] >> ( ( j - 1 ) << 3) ) & 0xFF;
  
                  if( c == 0 && k == 0 && ( i + j ) != 2 )
                      continue;
  
                  *(p++) = "0123456789ABCDEF" [c / 16];
                  *(p++) = "0123456789ABCDEF" [c % 16];
                  k = 1;
              }
          }
      }
      else
      {
          MBEDTLS_MPI_CHK( mbedtls_mpi_copy( &T, X ) );
  
          if( T.s == -1 )
              T.s = 1;
  
          MBEDTLS_MPI_CHK( mpi_write_hlp( &T, radix, &p ) );
      }
  
      *p++ = '\0';
      *olen = p - buf;
  
  cleanup:
  
      mbedtls_mpi_free( &T );
  
      return( ret );
  }
  
  #if defined(MBEDTLS_FS_IO)
  /*
   * Read X from an opened file
   */
  int mbedtls_mpi_read_file( mbedtls_mpi *X, int radix, FILE *fin )
  {
      mbedtls_mpi_uint d;
      size_t slen;
      char *p;
      /*
       * Buffer should have space for (short) label and decimal formatted MPI,
       * newline characters and '\0'
       */
      char s[ MBEDTLS_MPI_RW_BUFFER_SIZE ];
  
      memset( s, 0, sizeof( s ) );
      if( fgets( s, sizeof( s ) - 1, fin ) == NULL )
          return( MBEDTLS_ERR_MPI_FILE_IO_ERROR );
  
      slen = strlen( s );
      if( slen == sizeof( s ) - 2 )
          return( MBEDTLS_ERR_MPI_BUFFER_TOO_SMALL );
  
      if( s[slen - 1] == '\n' ) { slen--; s[slen] = '\0'; }
      if( s[slen - 1] == '\r' ) { slen--; s[slen] = '\0'; }
  
      p = s + slen;
      while( --p >= s )
          if( mpi_get_digit( &d, radix, *p ) != 0 )
              break;
  
      return( mbedtls_mpi_read_string( X, radix, p + 1 ) );
  }
  
  /*
   * Write X into an opened file (or stdout if fout == NULL)
   */
  int mbedtls_mpi_write_file( const char *p, const mbedtls_mpi *X, int radix, FILE *fout )
  {
      int ret;
      size_t n, slen, plen;
      /*
       * Buffer should have space for (short) label and decimal formatted MPI,
       * newline characters and '\0'
       */
      char s[ MBEDTLS_MPI_RW_BUFFER_SIZE ];
  
      memset( s, 0, sizeof( s ) );
  
      MBEDTLS_MPI_CHK( mbedtls_mpi_write_string( X, radix, s, sizeof( s ) - 2, &n ) );
  
      if( p == NULL ) p = "";
  
      plen = strlen( p );
      slen = strlen( s );
      s[slen++] = '\r';
      s[slen++] = '\n';
  
      if( fout != NULL )
      {
          if( fwrite( p, 1, plen, fout ) != plen ||
              fwrite( s, 1, slen, fout ) != slen )
              return( MBEDTLS_ERR_MPI_FILE_IO_ERROR );
      }
      else
          mbedtls_printf( "%s%s", p, s );
  
  cleanup:
  
      return( ret );
  }
  #endif /* MBEDTLS_FS_IO */
  
  /*
   * Import X from unsigned binary data, big endian
   */
  int mbedtls_mpi_read_binary( mbedtls_mpi *X, const unsigned char *buf, size_t buflen )
  {
      int ret;
      size_t i, j, n;
  
      for( n = 0; n < buflen; n++ )
          if( buf[n] != 0 )
              break;
  
      MBEDTLS_MPI_CHK( mbedtls_mpi_grow( X, CHARS_TO_LIMBS( buflen - n ) ) );
      MBEDTLS_MPI_CHK( mbedtls_mpi_lset( X, 0 ) );
  
      for( i = buflen, j = 0; i > n; i--, j++ )
          X->p[j / ciL] |= ((mbedtls_mpi_uint) buf[i - 1]) << ((j % ciL) << 3);
  
  cleanup:
  
      return( ret );
  }
  
  /*
   * Export X into unsigned binary data, big endian
   */
  int mbedtls_mpi_write_binary( const mbedtls_mpi *X, unsigned char *buf, size_t buflen )
  {
      size_t i, j, n;
  
      n = mbedtls_mpi_size( X );
  
      if( buflen < n )
          return( MBEDTLS_ERR_MPI_BUFFER_TOO_SMALL );
  
      memset( buf, 0, buflen );
  
      for( i = buflen - 1, j = 0; n > 0; i--, j++, n-- )
          buf[i] = (unsigned char)( X->p[j / ciL] >> ((j % ciL) << 3) );
  
      return( 0 );
  }
  
  /*
   * Left-shift: X <<= count
   */
  int mbedtls_mpi_shift_l( mbedtls_mpi *X, size_t count )
  {
      int ret;
      size_t i, v0, t1;
      mbedtls_mpi_uint r0 = 0, r1;
  
      v0 = count / (biL    );
      t1 = count & (biL - 1);
  
      i = mbedtls_mpi_bitlen( X ) + count;
  
      if( X->n * biL < i )
          MBEDTLS_MPI_CHK( mbedtls_mpi_grow( X, BITS_TO_LIMBS( i ) ) );
  
      ret = 0;
  
      /*
       * shift by count / limb_size
       */
      if( v0 > 0 )
      {
          for( i = X->n; i > v0; i-- )
              X->p[i - 1] = X->p[i - v0 - 1];
  
          for( ; i > 0; i-- )
              X->p[i - 1] = 0;
      }
  
      /*
       * shift by count % limb_size
       */
      if( t1 > 0 )
      {
          for( i = v0; i < X->n; i++ )
          {
              r1 = X->p[i] >> (biL - t1);
              X->p[i] <<= t1;
              X->p[i] |= r0;
              r0 = r1;
          }
      }
  
  cleanup:
  
      return( ret );
  }
  
  /*
   * Right-shift: X >>= count
   */
  int mbedtls_mpi_shift_r( mbedtls_mpi *X, size_t count )
  {
      size_t i, v0, v1;
      mbedtls_mpi_uint r0 = 0, r1;
  
      v0 = count /  biL;
      v1 = count & (biL - 1);
  
      if( v0 > X->n || ( v0 == X->n && v1 > 0 ) )
          return mbedtls_mpi_lset( X, 0 );
  
      /*
       * shift by count / limb_size
       */
      if( v0 > 0 )
      {
          for( i = 0; i < X->n - v0; i++ )
              X->p[i] = X->p[i + v0];
  
          for( ; i < X->n; i++ )
              X->p[i] = 0;
      }
  
      /*
       * shift by count % limb_size
       */
      if( v1 > 0 )
      {
          for( i = X->n; i > 0; i-- )
          {
              r1 = X->p[i - 1] << (biL - v1);
              X->p[i - 1] >>= v1;
              X->p[i - 1] |= r0;
              r0 = r1;
          }
      }
  
      return( 0 );
  }
  
  /*
   * Compare unsigned values
   */
  int mbedtls_mpi_cmp_abs( const mbedtls_mpi *X, const mbedtls_mpi *Y )
  {
      size_t i, j;
  
      for( i = X->n; i > 0; i-- )
          if( X->p[i - 1] != 0 )
              break;
  
      for( j = Y->n; j > 0; j-- )
          if( Y->p[j - 1] != 0 )
              break;
  
      if( i == 0 && j == 0 )
          return( 0 );
  
      if( i > j ) return(  1 );
      if( j > i ) return( -1 );
  
      for( ; i > 0; i-- )
      {
          if( X->p[i - 1] > Y->p[i - 1] ) return(  1 );
          if( X->p[i - 1] < Y->p[i - 1] ) return( -1 );
      }
  
      return( 0 );
  }
  
  /*
   * Compare signed values
   */
  int mbedtls_mpi_cmp_mpi( const mbedtls_mpi *X, const mbedtls_mpi *Y )
  {
      size_t i, j;
  
      for( i = X->n; i > 0; i-- )
          if( X->p[i - 1] != 0 )
              break;
  
      for( j = Y->n; j > 0; j-- )
          if( Y->p[j - 1] != 0 )
              break;
  
      if( i == 0 && j == 0 )
          return( 0 );
  
      if( i > j ) return(  X->s );
      if( j > i ) return( -Y->s );
  
      if( X->s > 0 && Y->s < 0 ) return(  1 );
      if( Y->s > 0 && X->s < 0 ) return( -1 );
  
      for( ; i > 0; i-- )
      {
          if( X->p[i - 1] > Y->p[i - 1] ) return(  X->s );
          if( X->p[i - 1] < Y->p[i - 1] ) return( -X->s );
      }
  
      return( 0 );
  }
  
  /*
   * Compare signed values
   */
  int mbedtls_mpi_cmp_int( const mbedtls_mpi *X, mbedtls_mpi_sint z )
  {
      mbedtls_mpi Y;
      mbedtls_mpi_uint p[1];
  
      *p  = ( z < 0 ) ? -z : z;
      Y.s = ( z < 0 ) ? -1 : 1;
      Y.n = 1;
      Y.p = p;
  
      return( mbedtls_mpi_cmp_mpi( X, &Y ) );
  }
  
  /*
   * Unsigned addition: X = |A| + |B|  (HAC 14.7)
   */
  int mbedtls_mpi_add_abs( mbedtls_mpi *X, const mbedtls_mpi *A, const mbedtls_mpi *B )
  {
      int ret;
      size_t i, j;
      mbedtls_mpi_uint *o, *p, c;
  
      if( X == B )
      {
          const mbedtls_mpi *T = A; A = X; B = T;
      }
  
      if( X != A )
          MBEDTLS_MPI_CHK( mbedtls_mpi_copy( X, A ) );
  
      /*
       * X should always be positive as a result of unsigned additions.
       */
      X->s = 1;
  
      for( j = B->n; j > 0; j-- )
          if( B->p[j - 1] != 0 )
              break;
  
      MBEDTLS_MPI_CHK( mbedtls_mpi_grow( X, j ) );
  
      o = B->p; p = X->p; c = 0;
  
      for( i = 0; i < j; i++, o++, p++ )
      {
          *p +=  c; c  = ( *p <  c );
          *p += *o; c += ( *p < *o );
      }
  
      while( c != 0 )
      {
          if( i >= X->n )
          {
              MBEDTLS_MPI_CHK( mbedtls_mpi_grow( X, i + 1 ) );
              p = X->p + i;
          }
  
          *p += c; c = ( *p < c ); i++; p++;
      }
  
  cleanup:
  
      return( ret );
  }
  
  /*
   * Helper for mbedtls_mpi subtraction
   */
  static void mpi_sub_hlp( size_t n, mbedtls_mpi_uint *s, mbedtls_mpi_uint *d )
  {
      size_t i;
      mbedtls_mpi_uint c, z;
  
      for( i = c = 0; i < n; i++, s++, d++ )
      {
          z = ( *d <  c );     *d -=  c;
          c = ( *d < *s ) + z; *d -= *s;
      }
  
      while( c != 0 )
      {
          z = ( *d < c ); *d -= c;
          c = z; i++; d++;
      }
  }
  
  /*
   * Unsigned subtraction: X = |A| - |B|  (HAC 14.9)
   */
  int mbedtls_mpi_sub_abs( mbedtls_mpi *X, const mbedtls_mpi *A, const mbedtls_mpi *B )
  {
      mbedtls_mpi TB;
      int ret;
      size_t n;
  
      if( mbedtls_mpi_cmp_abs( A, B ) < 0 )
          return( MBEDTLS_ERR_MPI_NEGATIVE_VALUE );
  
      mbedtls_mpi_init( &TB );
  
      if( X == B )
      {
          MBEDTLS_MPI_CHK( mbedtls_mpi_copy( &TB, B ) );
          B = &TB;
      }
  
      if( X != A )
          MBEDTLS_MPI_CHK( mbedtls_mpi_copy( X, A ) );
  
      /*
       * X should always be positive as a result of unsigned subtractions.
       */
      X->s = 1;
  
      ret = 0;
  
      for( n = B->n; n > 0; n-- )
          if( B->p[n - 1] != 0 )
              break;
  
      mpi_sub_hlp( n, B->p, X->p );
  
  cleanup:
  
      mbedtls_mpi_free( &TB );
  
      return( ret );
  }
  
  /*
   * Signed addition: X = A + B
   */
  int mbedtls_mpi_add_mpi( mbedtls_mpi *X, const mbedtls_mpi *A, const mbedtls_mpi *B )
  {
      int ret, s = A->s;
  
      if( A->s * B->s < 0 )
      {
          if( mbedtls_mpi_cmp_abs( A, B ) >= 0 )
          {
              MBEDTLS_MPI_CHK( mbedtls_mpi_sub_abs( X, A, B ) );
              X->s =  s;
          }
          else
          {
              MBEDTLS_MPI_CHK( mbedtls_mpi_sub_abs( X, B, A ) );
              X->s = -s;
          }
      }
      else
      {
          MBEDTLS_MPI_CHK( mbedtls_mpi_add_abs( X, A, B ) );
          X->s = s;
      }
  
  cleanup:
  
      return( ret );
  }
  
  /*
   * Signed subtraction: X = A - B
   */
  int mbedtls_mpi_sub_mpi( mbedtls_mpi *X, const mbedtls_mpi *A, const mbedtls_mpi *B )
  {
      int ret, s = A->s;
  
      if( A->s * B->s > 0 )
      {
          if( mbedtls_mpi_cmp_abs( A, B ) >= 0 )
          {
              MBEDTLS_MPI_CHK( mbedtls_mpi_sub_abs( X, A, B ) );
              X->s =  s;
          }
          else
          {
              MBEDTLS_MPI_CHK( mbedtls_mpi_sub_abs( X, B, A ) );
              X->s = -s;
          }
      }
      else
      {
          MBEDTLS_MPI_CHK( mbedtls_mpi_add_abs( X, A, B ) );
          X->s = s;
      }
  
  cleanup:
  
      return( ret );
  }
  
  /*
   * Signed addition: X = A + b
   */
  int mbedtls_mpi_add_int( mbedtls_mpi *X, const mbedtls_mpi *A, mbedtls_mpi_sint b )
  {
      mbedtls_mpi _B;
      mbedtls_mpi_uint p[1];
  
      p[0] = ( b < 0 ) ? -b : b;
      _B.s = ( b < 0 ) ? -1 : 1;
      _B.n = 1;
      _B.p = p;
  
      return( mbedtls_mpi_add_mpi( X, A, &_B ) );
  }
  
  /*
   * Signed subtraction: X = A - b
   */
  int mbedtls_mpi_sub_int( mbedtls_mpi *X, const mbedtls_mpi *A, mbedtls_mpi_sint b )
  {
      mbedtls_mpi _B;
      mbedtls_mpi_uint p[1];
  
      p[0] = ( b < 0 ) ? -b : b;
      _B.s = ( b < 0 ) ? -1 : 1;
      _B.n = 1;
      _B.p = p;
  
      return( mbedtls_mpi_sub_mpi( X, A, &_B ) );
  }
  
  /*
   * Helper for mbedtls_mpi multiplication
   */
  static
  #if defined(__APPLE__) && defined(__arm__)
  /*
   * Apple LLVM version 4.2 (clang-425.0.24) (based on LLVM 3.2svn)
   * appears to need this to prevent bad ARM code generation at -O3.
   */
  __attribute__ ((noinline))
  #endif
  void mpi_mul_hlp( size_t i, mbedtls_mpi_uint *s, mbedtls_mpi_uint *d, mbedtls_mpi_uint b )
  {
      mbedtls_mpi_uint c = 0, t = 0;
  
  #if defined(MULADDC_HUIT)
      for( ; i >= 8; i -= 8 )
      {
          MULADDC_INIT
          MULADDC_HUIT
          MULADDC_STOP
      }
  
      for( ; i > 0; i-- )
      {
          MULADDC_INIT
          MULADDC_CORE
          MULADDC_STOP
      }
  #else /* MULADDC_HUIT */
      for( ; i >= 16; i -= 16 )
      {
          MULADDC_INIT
          MULADDC_CORE   MULADDC_CORE
          MULADDC_CORE   MULADDC_CORE
          MULADDC_CORE   MULADDC_CORE
          MULADDC_CORE   MULADDC_CORE
  
          MULADDC_CORE   MULADDC_CORE
          MULADDC_CORE   MULADDC_CORE
          MULADDC_CORE   MULADDC_CORE
          MULADDC_CORE   MULADDC_CORE
          MULADDC_STOP
      }
  
      for( ; i >= 8; i -= 8 )
      {
          MULADDC_INIT
          MULADDC_CORE   MULADDC_CORE
          MULADDC_CORE   MULADDC_CORE
  
          MULADDC_CORE   MULADDC_CORE
          MULADDC_CORE   MULADDC_CORE
          MULADDC_STOP
      }
  
      for( ; i > 0; i-- )
      {
          MULADDC_INIT
          MULADDC_CORE
          MULADDC_STOP
      }
  #endif /* MULADDC_HUIT */
  
      t++;
  
      do {
          *d += c; c = ( *d < c ); d++;
      }
      while( c != 0 );
  }
  
  /*
   * Baseline multiplication: X = A * B  (HAC 14.12)
   */
  int mbedtls_mpi_mul_mpi( mbedtls_mpi *X, const mbedtls_mpi *A, const mbedtls_mpi *B )
  {
      int ret;
      size_t i, j;
      mbedtls_mpi TA, TB;
  
      mbedtls_mpi_init( &TA ); mbedtls_mpi_init( &TB );
  
      if( X == A ) { MBEDTLS_MPI_CHK( mbedtls_mpi_copy( &TA, A ) ); A = &TA; }
      if( X == B ) { MBEDTLS_MPI_CHK( mbedtls_mpi_copy( &TB, B ) ); B = &TB; }
  
      for( i = A->n; i > 0; i-- )
          if( A->p[i - 1] != 0 )
              break;
  
      for( j = B->n; j > 0; j-- )
          if( B->p[j - 1] != 0 )
              break;
  
      MBEDTLS_MPI_CHK( mbedtls_mpi_grow( X, i + j ) );
      MBEDTLS_MPI_CHK( mbedtls_mpi_lset( X, 0 ) );
  
      for( i++; j > 0; j-- )
          mpi_mul_hlp( i - 1, A->p, X->p + j - 1, B->p[j - 1] );
  
      X->s = A->s * B->s;
  
  cleanup:
  
      mbedtls_mpi_free( &TB ); mbedtls_mpi_free( &TA );
  
      return( ret );
  }
  
  /*
   * Baseline multiplication: X = A * b
   */
  int mbedtls_mpi_mul_int( mbedtls_mpi *X, const mbedtls_mpi *A, mbedtls_mpi_uint b )
  {
      mbedtls_mpi _B;
      mbedtls_mpi_uint p[1];
  
      _B.s = 1;
      _B.n = 1;
      _B.p = p;
      p[0] = b;
  
      return( mbedtls_mpi_mul_mpi( X, A, &_B ) );
  }
  
  /*
   * Division by mbedtls_mpi: A = Q * B + R  (HAC 14.20)
   */
  int mbedtls_mpi_div_mpi( mbedtls_mpi *Q, mbedtls_mpi *R, const mbedtls_mpi *A, const mbedtls_mpi *B )
  {
      int ret;
      size_t i, n, t, k;
      mbedtls_mpi X, Y, Z, T1, T2;
  
      if( mbedtls_mpi_cmp_int( B, 0 ) == 0 )
          return( MBEDTLS_ERR_MPI_DIVISION_BY_ZERO );
  
      mbedtls_mpi_init( &X ); mbedtls_mpi_init( &Y ); mbedtls_mpi_init( &Z );
      mbedtls_mpi_init( &T1 ); mbedtls_mpi_init( &T2 );
  
      if( mbedtls_mpi_cmp_abs( A, B ) < 0 )
      {
          if( Q != NULL ) MBEDTLS_MPI_CHK( mbedtls_mpi_lset( Q, 0 ) );
          if( R != NULL ) MBEDTLS_MPI_CHK( mbedtls_mpi_copy( R, A ) );
          return( 0 );
      }
  
      MBEDTLS_MPI_CHK( mbedtls_mpi_copy( &X, A ) );
      MBEDTLS_MPI_CHK( mbedtls_mpi_copy( &Y, B ) );
      X.s = Y.s = 1;
  
      MBEDTLS_MPI_CHK( mbedtls_mpi_grow( &Z, A->n + 2 ) );
      MBEDTLS_MPI_CHK( mbedtls_mpi_lset( &Z,  0 ) );
      MBEDTLS_MPI_CHK( mbedtls_mpi_grow( &T1, 2 ) );
      MBEDTLS_MPI_CHK( mbedtls_mpi_grow( &T2, 3 ) );
  
      k = mbedtls_mpi_bitlen( &Y ) % biL;
      if( k < biL - 1 )
      {
          k = biL - 1 - k;
          MBEDTLS_MPI_CHK( mbedtls_mpi_shift_l( &X, k ) );
          MBEDTLS_MPI_CHK( mbedtls_mpi_shift_l( &Y, k ) );
      }
      else k = 0;
  
      n = X.n - 1;
      t = Y.n - 1;
      MBEDTLS_MPI_CHK( mbedtls_mpi_shift_l( &Y, biL * ( n - t ) ) );
  
      while( mbedtls_mpi_cmp_mpi( &X, &Y ) >= 0 )
      {
          Z.p[n - t]++;
          MBEDTLS_MPI_CHK( mbedtls_mpi_sub_mpi( &X, &X, &Y ) );
      }
      MBEDTLS_MPI_CHK( mbedtls_mpi_shift_r( &Y, biL * ( n - t ) ) );
  
      for( i = n; i > t ; i-- )
      {
          if( X.p[i] >= Y.p[t] )
              Z.p[i - t - 1] = (mbedtls_mpi_uint)(~0);
          else
          {
  #if defined(MBEDTLS_HAVE_UDBL)
              mbedtls_t_udbl r;
  
              r  = (mbedtls_t_udbl) X.p[i] << biL;
              r |= (mbedtls_t_udbl) X.p[i - 1];
              r /= Y.p[t];
              if( r > ( (mbedtls_t_udbl) 1 << biL ) - 1 )
                  r = ( (mbedtls_t_udbl) 1 << biL ) - 1;
  
              Z.p[i - t - 1] = (mbedtls_mpi_uint) r;
  #else
              /*
               * __udiv_qrnnd_c, from gmp/longlong.h
               */
              mbedtls_mpi_uint q0, q1, r0, r1;
              mbedtls_mpi_uint d0, d1, d, m;
  
              d  = Y.p[t];
              d0 = ( d << biH ) >> biH;
              d1 = ( d >> biH );
  
              q1 = X.p[i] / d1;
              r1 = X.p[i] - d1 * q1;
              r1 <<= biH;
              r1 |= ( X.p[i - 1] >> biH );
  
              m = q1 * d0;
              if( r1 < m )
              {
                  q1--, r1 += d;
                  while( r1 >= d && r1 < m )
                      q1--, r1 += d;
              }
              r1 -= m;
  
              q0 = r1 / d1;
              r0 = r1 - d1 * q0;
              r0 <<= biH;
              r0 |= ( X.p[i - 1] << biH ) >> biH;
  
              m = q0 * d0;
              if( r0 < m )
              {
                  q0--, r0 += d;
                  while( r0 >= d && r0 < m )
                      q0--, r0 += d;
              }
              r0 -= m;
  
              Z.p[i - t - 1] = ( q1 << biH ) | q0;
  #endif /* MBEDTLS_HAVE_UDBL && !64-bit Apple with Clang 5.0 */
          }
  
          Z.p[i - t - 1]++;
          do
          {
              Z.p[i - t - 1]--;
  
              MBEDTLS_MPI_CHK( mbedtls_mpi_lset( &T1, 0 ) );
              T1.p[0] = ( t < 1 ) ? 0 : Y.p[t - 1];
              T1.p[1] = Y.p[t];
              MBEDTLS_MPI_CHK( mbedtls_mpi_mul_int( &T1, &T1, Z.p[i - t - 1] ) );
  
              MBEDTLS_MPI_CHK( mbedtls_mpi_lset( &T2, 0 ) );
              T2.p[0] = ( i < 2 ) ? 0 : X.p[i - 2];
              T2.p[1] = ( i < 1 ) ? 0 : X.p[i - 1];
              T2.p[2] = X.p[i];
          }
          while( mbedtls_mpi_cmp_mpi( &T1, &T2 ) > 0 );
  
          MBEDTLS_MPI_CHK( mbedtls_mpi_mul_int( &T1, &Y, Z.p[i - t - 1] ) );
          MBEDTLS_MPI_CHK( mbedtls_mpi_shift_l( &T1,  biL * ( i - t - 1 ) ) );
          MBEDTLS_MPI_CHK( mbedtls_mpi_sub_mpi( &X, &X, &T1 ) );
  
          if( mbedtls_mpi_cmp_int( &X, 0 ) < 0 )
          {
              MBEDTLS_MPI_CHK( mbedtls_mpi_copy( &T1, &Y ) );
              MBEDTLS_MPI_CHK( mbedtls_mpi_shift_l( &T1, biL * ( i - t - 1 ) ) );
              MBEDTLS_MPI_CHK( mbedtls_mpi_add_mpi( &X, &X, &T1 ) );
              Z.p[i - t - 1]--;
          }
      }
  
      if( Q != NULL )
      {
          MBEDTLS_MPI_CHK( mbedtls_mpi_copy( Q, &Z ) );
          Q->s = A->s * B->s;
      }
  
      if( R != NULL )
      {
          MBEDTLS_MPI_CHK( mbedtls_mpi_shift_r( &X, k ) );
          X.s = A->s;
          MBEDTLS_MPI_CHK( mbedtls_mpi_copy( R, &X ) );
  
          if( mbedtls_mpi_cmp_int( R, 0 ) == 0 )
              R->s = 1;
      }
  
  cleanup:
  
      mbedtls_mpi_free( &X ); mbedtls_mpi_free( &Y ); mbedtls_mpi_free( &Z );
      mbedtls_mpi_free( &T1 ); mbedtls_mpi_free( &T2 );
  
      return( ret );
  }
  
  /*
   * Division by int: A = Q * b + R
   */
  int mbedtls_mpi_div_int( mbedtls_mpi *Q, mbedtls_mpi *R, const mbedtls_mpi *A, mbedtls_mpi_sint b )
  {
      mbedtls_mpi _B;
      mbedtls_mpi_uint p[1];
  
      p[0] = ( b < 0 ) ? -b : b;
      _B.s = ( b < 0 ) ? -1 : 1;
      _B.n = 1;
      _B.p = p;
  
      return( mbedtls_mpi_div_mpi( Q, R, A, &_B ) );
  }
  
  /*
   * Modulo: R = A mod B
   */
  int mbedtls_mpi_mod_mpi( mbedtls_mpi *R, const mbedtls_mpi *A, const mbedtls_mpi *B )
  {
      int ret;
  
      if( mbedtls_mpi_cmp_int( B, 0 ) < 0 )
          return( MBEDTLS_ERR_MPI_NEGATIVE_VALUE );
  
      MBEDTLS_MPI_CHK( mbedtls_mpi_div_mpi( NULL, R, A, B ) );
  
      while( mbedtls_mpi_cmp_int( R, 0 ) < 0 )
        MBEDTLS_MPI_CHK( mbedtls_mpi_add_mpi( R, R, B ) );
  
      while( mbedtls_mpi_cmp_mpi( R, B ) >= 0 )
        MBEDTLS_MPI_CHK( mbedtls_mpi_sub_mpi( R, R, B ) );
  
  cleanup:
  
      return( ret );
  }
  
  /*
   * Modulo: r = A mod b
   */
  int mbedtls_mpi_mod_int( mbedtls_mpi_uint *r, const mbedtls_mpi *A, mbedtls_mpi_sint b )
  {
      size_t i;
      mbedtls_mpi_uint x, y, z;
  
      if( b == 0 )
          return( MBEDTLS_ERR_MPI_DIVISION_BY_ZERO );
  
      if( b < 0 )
          return( MBEDTLS_ERR_MPI_NEGATIVE_VALUE );
  
      /*
       * handle trivial cases
       */
      if( b == 1 )
      {
          *r = 0;
          return( 0 );
      }
  
      if( b == 2 )
      {
          *r = A->p[0] & 1;
          return( 0 );
      }
  
      /*
       * general case
       */
      for( i = A->n, y = 0; i > 0; i-- )
      {
          x  = A->p[i - 1];
          y  = ( y << biH ) | ( x >> biH );
          z  = y / b;
          y -= z * b;
  
          x <<= biH;
          y  = ( y << biH ) | ( x >> biH );
          z  = y / b;
          y -= z * b;
      }
  
      /*
       * If A is negative, then the current y represents a negative value.
       * Flipping it to the positive side.
       */
      if( A->s < 0 && y != 0 )
          y = b - y;
  
      *r = y;
  
      return( 0 );
  }
  
  /*
   * Fast Montgomery initialization (thanks to Tom St Denis)
   */
  static void mpi_montg_init( mbedtls_mpi_uint *mm, const mbedtls_mpi *N )
  {
      mbedtls_mpi_uint x, m0 = N->p[0];
      unsigned int i;
  
      x  = m0;
      x += ( ( m0 + 2 ) & 4 ) << 1;
  
      for( i = biL; i >= 8; i /= 2 )
          x *= ( 2 - ( m0 * x ) );
  
      *mm = ~x + 1;
  }
  
  /*
   * Montgomery multiplication: A = A * B * R^-1 mod N  (HAC 14.36)
   */
  static void mpi_montmul( mbedtls_mpi *A, const mbedtls_mpi *B, const mbedtls_mpi *N, mbedtls_mpi_uint mm,
                           const mbedtls_mpi *T )
  {
      size_t i, n, m;
      mbedtls_mpi_uint u0, u1, *d;
  
      memset( T->p, 0, T->n * ciL );
  
      d = T->p;
      n = N->n;
      m = ( B->n < n ) ? B->n : n;
  
      for( i = 0; i < n; i++ )
      {
          /*
           * T = (T + u0*B + u1*N) / 2^biL
           */
          u0 = A->p[i];
          u1 = ( d[0] + u0 * B->p[0] ) * mm;
  
          mpi_mul_hlp( m, B->p, d, u0 );
          mpi_mul_hlp( n, N->p, d, u1 );
  
          *d++ = u0; d[n + 1] = 0;
      }
  
      memcpy( A->p, d, ( n + 1 ) * ciL );
  
      if( mbedtls_mpi_cmp_abs( A, N ) >= 0 )
          mpi_sub_hlp( n, N->p, A->p );
      else
          /* prevent timing attacks */
          mpi_sub_hlp( n, A->p, T->p );
  }
  
  /*
   * Montgomery reduction: A = A * R^-1 mod N
   */
  static void mpi_montred( mbedtls_mpi *A, const mbedtls_mpi *N, mbedtls_mpi_uint mm, const mbedtls_mpi *T )
  {
      mbedtls_mpi_uint z = 1;
      mbedtls_mpi U;
  
      U.n = U.s = (int) z;
      U.p = &z;
  
      mpi_montmul( A, &U, N, mm, T );
  }
  
  /*
   * Sliding-window exponentiation: X = A^E mod N  (HAC 14.85)
   */
  int mbedtls_mpi_exp_mod( mbedtls_mpi *X, const mbedtls_mpi *A, const mbedtls_mpi *E, const mbedtls_mpi *N, mbedtls_mpi *_RR )
  {
      int ret;
      size_t wbits, wsize, one = 1;
      size_t i, j, nblimbs;
      size_t bufsize, nbits;
      mbedtls_mpi_uint ei, mm, state;
      mbedtls_mpi RR, T, W[ 2 << MBEDTLS_MPI_WINDOW_SIZE ], Apos;
      int neg;
  
      if( mbedtls_mpi_cmp_int( N, 0 ) < 0 || ( N->p[0] & 1 ) == 0 )
          return( MBEDTLS_ERR_MPI_BAD_INPUT_DATA );
  
      if( mbedtls_mpi_cmp_int( E, 0 ) < 0 )
          return( MBEDTLS_ERR_MPI_BAD_INPUT_DATA );
  
      /*
       * Init temps and window size
       */
      mpi_montg_init( &mm, N );
      mbedtls_mpi_init( &RR ); mbedtls_mpi_init( &T );
      mbedtls_mpi_init( &Apos );
      memset( W, 0, sizeof( W ) );
  
      i = mbedtls_mpi_bitlen( E );
  
      wsize = ( i > 671 ) ? 6 : ( i > 239 ) ? 5 :
              ( i >  79 ) ? 4 : ( i >  23 ) ? 3 : 1;
  
      if( wsize > MBEDTLS_MPI_WINDOW_SIZE )
          wsize = MBEDTLS_MPI_WINDOW_SIZE;
  
      j = N->n + 1;
      MBEDTLS_MPI_CHK( mbedtls_mpi_grow( X, j ) );
      MBEDTLS_MPI_CHK( mbedtls_mpi_grow( &W[1],  j ) );
      MBEDTLS_MPI_CHK( mbedtls_mpi_grow( &T, j * 2 ) );
  
      /*
       * Compensate for negative A (and correct at the end)
       */
      neg = ( A->s == -1 );
      if( neg )
      {
          MBEDTLS_MPI_CHK( mbedtls_mpi_copy( &Apos, A ) );
          Apos.s = 1;
          A = &Apos;
      }
  
      /*
       * If 1st call, pre-compute R^2 mod N
       */
      if( _RR == NULL || _RR->p == NULL )
      {
          MBEDTLS_MPI_CHK( mbedtls_mpi_lset( &RR, 1 ) );
          MBEDTLS_MPI_CHK( mbedtls_mpi_shift_l( &RR, N->n * 2 * biL ) );
          MBEDTLS_MPI_CHK( mbedtls_mpi_mod_mpi( &RR, &RR, N ) );
  
          if( _RR != NULL )
              memcpy( _RR, &RR, sizeof( mbedtls_mpi ) );
      }
      else
          memcpy( &RR, _RR, sizeof( mbedtls_mpi ) );
  
      /*
       * W[1] = A * R^2 * R^-1 mod N = A * R mod N
       */
      if( mbedtls_mpi_cmp_mpi( A, N ) >= 0 )
          MBEDTLS_MPI_CHK( mbedtls_mpi_mod_mpi( &W[1], A, N ) );
      else
          MBEDTLS_MPI_CHK( mbedtls_mpi_copy( &W[1], A ) );
  
      mpi_montmul( &W[1], &RR, N, mm, &T );
  
      /*
       * X = R^2 * R^-1 mod N = R mod N
       */
      MBEDTLS_MPI_CHK( mbedtls_mpi_copy( X, &RR ) );
      mpi_montred( X, N, mm, &T );
  
      if( wsize > 1 )
      {
          /*
           * W[1 << (wsize - 1)] = W[1] ^ (wsize - 1)
           */
          j =  one << ( wsize - 1 );
  
          MBEDTLS_MPI_CHK( mbedtls_mpi_grow( &W[j], N->n + 1 ) );
          MBEDTLS_MPI_CHK( mbedtls_mpi_copy( &W[j], &W[1]    ) );
  
          for( i = 0; i < wsize - 1; i++ )
              mpi_montmul( &W[j], &W[j], N, mm, &T );
  
          /*
           * W[i] = W[i - 1] * W[1]
           */
          for( i = j + 1; i < ( one << wsize ); i++ )
          {
              MBEDTLS_MPI_CHK( mbedtls_mpi_grow( &W[i], N->n + 1 ) );
              MBEDTLS_MPI_CHK( mbedtls_mpi_copy( &W[i], &W[i - 1] ) );
  
              mpi_montmul( &W[i], &W[1], N, mm, &T );
          }
      }
  
      nblimbs = E->n;
      bufsize = 0;
      nbits   = 0;
      wbits   = 0;
      state   = 0;
  
      while( 1 )
      {
          if( bufsize == 0 )
          {
              if( nblimbs == 0 )
                  break;
  
              nblimbs--;
  
              bufsize = sizeof( mbedtls_mpi_uint ) << 3;
          }
  
          bufsize--;
  
          ei = (E->p[nblimbs] >> bufsize) & 1;
  
          /*
           * skip leading 0s
           */
          if( ei == 0 && state == 0 )
              continue;
  
          if( ei == 0 && state == 1 )
          {
              /*
               * out of window, square X
               */
              mpi_montmul( X, X, N, mm, &T );
              continue;
          }
  
          /*
           * add ei to current window
           */
          state = 2;
  
          nbits++;
          wbits |= ( ei << ( wsize - nbits ) );
  
          if( nbits == wsize )
          {
              /*
               * X = X^wsize R^-1 mod N
               */
              for( i = 0; i < wsize; i++ )
                  mpi_montmul( X, X, N, mm, &T );
  
              /*
               * X = X * W[wbits] R^-1 mod N
               */
              mpi_montmul( X, &W[wbits], N, mm, &T );
  
              state--;
              nbits = 0;
              wbits = 0;
          }
      }
  
      /*
       * process the remaining bits
       */
      for( i = 0; i < nbits; i++ )
      {
          mpi_montmul( X, X, N, mm, &T );
  
          wbits <<= 1;
  
          if( ( wbits & ( one << wsize ) ) != 0 )
              mpi_montmul( X, &W[1], N, mm, &T );
      }
  
      /*
       * X = A^E * R * R^-1 mod N = A^E mod N
       */
      mpi_montred( X, N, mm, &T );
  
      if( neg )
      {
          X->s = -1;
          MBEDTLS_MPI_CHK( mbedtls_mpi_add_mpi( X, N, X ) );
      }
  
  cleanup:
  
      for( i = ( one << ( wsize - 1 ) ); i < ( one << wsize ); i++ )
          mbedtls_mpi_free( &W[i] );
  
      mbedtls_mpi_free( &W[1] ); mbedtls_mpi_free( &T ); mbedtls_mpi_free( &Apos );
  
      if( _RR == NULL || _RR->p == NULL )
          mbedtls_mpi_free( &RR );
  
      return( ret );
  }
  
  /*
   * Greatest common divisor: G = gcd(A, B)  (HAC 14.54)
   */
  int mbedtls_mpi_gcd( mbedtls_mpi *G, const mbedtls_mpi *A, const mbedtls_mpi *B )
  {
      int ret;
      size_t lz, lzt;
      mbedtls_mpi TG, TA, TB;
  
      mbedtls_mpi_init( &TG ); mbedtls_mpi_init( &TA ); mbedtls_mpi_init( &TB );
  
      MBEDTLS_MPI_CHK( mbedtls_mpi_copy( &TA, A ) );
      MBEDTLS_MPI_CHK( mbedtls_mpi_copy( &TB, B ) );
  
      lz = mbedtls_mpi_lsb( &TA );
      lzt = mbedtls_mpi_lsb( &TB );
  
      if( lzt < lz )
          lz = lzt;
  
      MBEDTLS_MPI_CHK( mbedtls_mpi_shift_r( &TA, lz ) );
      MBEDTLS_MPI_CHK( mbedtls_mpi_shift_r( &TB, lz ) );
  
      TA.s = TB.s = 1;
  
      while( mbedtls_mpi_cmp_int( &TA, 0 ) != 0 )
      {
          MBEDTLS_MPI_CHK( mbedtls_mpi_shift_r( &TA, mbedtls_mpi_lsb( &TA ) ) );
          MBEDTLS_MPI_CHK( mbedtls_mpi_shift_r( &TB, mbedtls_mpi_lsb( &TB ) ) );
  
          if( mbedtls_mpi_cmp_mpi( &TA, &TB ) >= 0 )
          {
              MBEDTLS_MPI_CHK( mbedtls_mpi_sub_abs( &TA, &TA, &TB ) );
              MBEDTLS_MPI_CHK( mbedtls_mpi_shift_r( &TA, 1 ) );
          }
          else
          {
              MBEDTLS_MPI_CHK( mbedtls_mpi_sub_abs( &TB, &TB, &TA ) );
              MBEDTLS_MPI_CHK( mbedtls_mpi_shift_r( &TB, 1 ) );
          }
      }
  
      MBEDTLS_MPI_CHK( mbedtls_mpi_shift_l( &TB, lz ) );
      MBEDTLS_MPI_CHK( mbedtls_mpi_copy( G, &TB ) );
  
  cleanup:
  
      mbedtls_mpi_free( &TG ); mbedtls_mpi_free( &TA ); mbedtls_mpi_free( &TB );
  
      return( ret );
  }
  
  /*
   * Fill X with size bytes of random.
   *
   * Use a temporary bytes representation to make sure the result is the same
   * regardless of the platform endianness (useful when f_rng is actually
   * deterministic, eg for tests).
   */
  int mbedtls_mpi_fill_random( mbedtls_mpi *X, size_t size,
                       int (*f_rng)(void *, unsigned char *, size_t),
                       void *p_rng )
  {
      int ret;
      unsigned char buf[MBEDTLS_MPI_MAX_SIZE];
  
      if( size > MBEDTLS_MPI_MAX_SIZE )
          return( MBEDTLS_ERR_MPI_BAD_INPUT_DATA );
  
      MBEDTLS_MPI_CHK( f_rng( p_rng, buf, size ) );
      MBEDTLS_MPI_CHK( mbedtls_mpi_read_binary( X, buf, size ) );
  
  cleanup:
      return( ret );
  }
  
  /*
   * Modular inverse: X = A^-1 mod N  (HAC 14.61 / 14.64)
   */
  int mbedtls_mpi_inv_mod( mbedtls_mpi *X, const mbedtls_mpi *A, const mbedtls_mpi *N )
  {
      int ret;
      mbedtls_mpi G, TA, TU, U1, U2, TB, TV, V1, V2;
  
      if( mbedtls_mpi_cmp_int( N, 0 ) <= 0 )
          return( MBEDTLS_ERR_MPI_BAD_INPUT_DATA );
  
      mbedtls_mpi_init( &TA ); mbedtls_mpi_init( &TU ); mbedtls_mpi_init( &U1 ); mbedtls_mpi_init( &U2 );
      mbedtls_mpi_init( &G ); mbedtls_mpi_init( &TB ); mbedtls_mpi_init( &TV );
      mbedtls_mpi_init( &V1 ); mbedtls_mpi_init( &V2 );
  
      MBEDTLS_MPI_CHK( mbedtls_mpi_gcd( &G, A, N ) );
  
      if( mbedtls_mpi_cmp_int( &G, 1 ) != 0 )
      {
          ret = MBEDTLS_ERR_MPI_NOT_ACCEPTABLE;
          goto cleanup;
      }
  
      MBEDTLS_MPI_CHK( mbedtls_mpi_mod_mpi( &TA, A, N ) );
      MBEDTLS_MPI_CHK( mbedtls_mpi_copy( &TU, &TA ) );
      MBEDTLS_MPI_CHK( mbedtls_mpi_copy( &TB, N ) );
      MBEDTLS_MPI_CHK( mbedtls_mpi_copy( &TV, N ) );
  
      MBEDTLS_MPI_CHK( mbedtls_mpi_lset( &U1, 1 ) );
      MBEDTLS_MPI_CHK( mbedtls_mpi_lset( &U2, 0 ) );
      MBEDTLS_MPI_CHK( mbedtls_mpi_lset( &V1, 0 ) );
      MBEDTLS_MPI_CHK( mbedtls_mpi_lset( &V2, 1 ) );
  
      do
      {
          while( ( TU.p[0] & 1 ) == 0 )
          {
              MBEDTLS_MPI_CHK( mbedtls_mpi_shift_r( &TU, 1 ) );
  
              if( ( U1.p[0] & 1 ) != 0 || ( U2.p[0] & 1 ) != 0 )
              {
                  MBEDTLS_MPI_CHK( mbedtls_mpi_add_mpi( &U1, &U1, &TB ) );
                  MBEDTLS_MPI_CHK( mbedtls_mpi_sub_mpi( &U2, &U2, &TA ) );
              }
  
              MBEDTLS_MPI_CHK( mbedtls_mpi_shift_r( &U1, 1 ) );
              MBEDTLS_MPI_CHK( mbedtls_mpi_shift_r( &U2, 1 ) );
          }
  
          while( ( TV.p[0] & 1 ) == 0 )
          {
              MBEDTLS_MPI_CHK( mbedtls_mpi_shift_r( &TV, 1 ) );
  
              if( ( V1.p[0] & 1 ) != 0 || ( V2.p[0] & 1 ) != 0 )
              {
                  MBEDTLS_MPI_CHK( mbedtls_mpi_add_mpi( &V1, &V1, &TB ) );
                  MBEDTLS_MPI_CHK( mbedtls_mpi_sub_mpi( &V2, &V2, &TA ) );
              }
  
              MBEDTLS_MPI_CHK( mbedtls_mpi_shift_r( &V1, 1 ) );
              MBEDTLS_MPI_CHK( mbedtls_mpi_shift_r( &V2, 1 ) );
          }
  
          if( mbedtls_mpi_cmp_mpi( &TU, &TV ) >= 0 )
          {
              MBEDTLS_MPI_CHK( mbedtls_mpi_sub_mpi( &TU, &TU, &TV ) );
              MBEDTLS_MPI_CHK( mbedtls_mpi_sub_mpi( &U1, &U1, &V1 ) );
              MBEDTLS_MPI_CHK( mbedtls_mpi_sub_mpi( &U2, &U2, &V2 ) );
          }
          else
          {
              MBEDTLS_MPI_CHK( mbedtls_mpi_sub_mpi( &TV, &TV, &TU ) );
              MBEDTLS_MPI_CHK( mbedtls_mpi_sub_mpi( &V1, &V1, &U1 ) );
              MBEDTLS_MPI_CHK( mbedtls_mpi_sub_mpi( &V2, &V2, &U2 ) );
          }
      }
      while( mbedtls_mpi_cmp_int( &TU, 0 ) != 0 );
  
      while( mbedtls_mpi_cmp_int( &V1, 0 ) < 0 )
          MBEDTLS_MPI_CHK( mbedtls_mpi_add_mpi( &V1, &V1, N ) );
  
      while( mbedtls_mpi_cmp_mpi( &V1, N ) >= 0 )
          MBEDTLS_MPI_CHK( mbedtls_mpi_sub_mpi( &V1, &V1, N ) );
  
      MBEDTLS_MPI_CHK( mbedtls_mpi_copy( X, &V1 ) );
  
  cleanup:
  
      mbedtls_mpi_free( &TA ); mbedtls_mpi_free( &TU ); mbedtls_mpi_free( &U1 ); mbedtls_mpi_free( &U2 );
      mbedtls_mpi_free( &G ); mbedtls_mpi_free( &TB ); mbedtls_mpi_free( &TV );
      mbedtls_mpi_free( &V1 ); mbedtls_mpi_free( &V2 );
  
      return( ret );
  }
  
  #if defined(MBEDTLS_GENPRIME)
  
  static const int small_prime[] =
  {
          3,    5,    7,   11,   13,   17,   19,   23,
         29,   31,   37,   41,   43,   47,   53,   59,
         61,   67,   71,   73,   79,   83,   89,   97,
        101,  103,  107,  109,  113,  127,  131,  137,
        139,  149,  151,  157,  163,  167,  173,  179,
        181,  191,  193,  197,  199,  211,  223,  227,
        229,  233,  239,  241,  251,  257,  263,  269,
        271,  277,  281,  283,  293,  307,  311,  313,
        317,  331,  337,  347,  349,  353,  359,  367,
        373,  379,  383,  389,  397,  401,  409,  419,
        421,  431,  433,  439,  443,  449,  457,  461,
        463,  467,  479,  487,  491,  499,  503,  509,
        521,  523,  541,  547,  557,  563,  569,  571,
        577,  587,  593,  599,  601,  607,  613,  617,
        619,  631,  641,  643,  647,  653,  659,  661,
        673,  677,  683,  691,  701,  709,  719,  727,
        733,  739,  743,  751,  757,  761,  769,  773,
        787,  797,  809,  811,  821,  823,  827,  829,
        839,  853,  857,  859,  863,  877,  881,  883,
        887,  907,  911,  919,  929,  937,  941,  947,
        953,  967,  971,  977,  983,  991,  997, -103
  };
  
  /*
   * Small divisors test (X must be positive)
   *
   * Return values:
   * 0: no small factor (possible prime, more tests needed)
   * 1: certain prime
   * MBEDTLS_ERR_MPI_NOT_ACCEPTABLE: certain non-prime
   * other negative: error
   */
  static int mpi_check_small_factors( const mbedtls_mpi *X )
  {
      int ret = 0;
      size_t i;
      mbedtls_mpi_uint r;
  
      if( ( X->p[0] & 1 ) == 0 )
          return( MBEDTLS_ERR_MPI_NOT_ACCEPTABLE );
  
      for( i = 0; small_prime[i] > 0; i++ )
      {
          if( mbedtls_mpi_cmp_int( X, small_prime[i] ) <= 0 )
              return( 1 );
  
          MBEDTLS_MPI_CHK( mbedtls_mpi_mod_int( &r, X, small_prime[i] ) );
  
          if( r == 0 )
              return( MBEDTLS_ERR_MPI_NOT_ACCEPTABLE );
      }
  
  cleanup:
      return( ret );
  }
  
  /*
   * Miller-Rabin pseudo-primality test  (HAC 4.24)
   */
  static int mpi_miller_rabin( const mbedtls_mpi *X,
                               int (*f_rng)(void *, unsigned char *, size_t),
                               void *p_rng )
  {
      int ret, count;
      size_t i, j, k, n, s;
      mbedtls_mpi W, R, T, A, RR;
  
      mbedtls_mpi_init( &W ); mbedtls_mpi_init( &R ); mbedtls_mpi_init( &T ); mbedtls_mpi_init( &A );
      mbedtls_mpi_init( &RR );
  
      /*
       * W = |X| - 1
       * R = W >> lsb( W )
       */
      MBEDTLS_MPI_CHK( mbedtls_mpi_sub_int( &W, X, 1 ) );
      s = mbedtls_mpi_lsb( &W );
      MBEDTLS_MPI_CHK( mbedtls_mpi_copy( &R, &W ) );
      MBEDTLS_MPI_CHK( mbedtls_mpi_shift_r( &R, s ) );
  
      i = mbedtls_mpi_bitlen( X );
      /*
       * HAC, table 4.4
       */
      n = ( ( i >= 1300 ) ?  2 : ( i >=  850 ) ?  3 :
            ( i >=  650 ) ?  4 : ( i >=  350 ) ?  8 :
            ( i >=  250 ) ? 12 : ( i >=  150 ) ? 18 : 27 );
  
      for( i = 0; i < n; i++ )
      {
          /*
           * pick a random A, 1 < A < |X| - 1
           */
          MBEDTLS_MPI_CHK( mbedtls_mpi_fill_random( &A, X->n * ciL, f_rng, p_rng ) );
  
          if( mbedtls_mpi_cmp_mpi( &A, &W ) >= 0 )
          {
              j = mbedtls_mpi_bitlen( &A ) - mbedtls_mpi_bitlen( &W );
              MBEDTLS_MPI_CHK( mbedtls_mpi_shift_r( &A, j + 1 ) );
          }
          A.p[0] |= 3;
  
          count = 0;
          do {
              MBEDTLS_MPI_CHK( mbedtls_mpi_fill_random( &A, X->n * ciL, f_rng, p_rng ) );
  
              j = mbedtls_mpi_bitlen( &A );
              k = mbedtls_mpi_bitlen( &W );
              if (j > k) {
                  MBEDTLS_MPI_CHK( mbedtls_mpi_shift_r( &A, j - k ) );
              }
  
              if (count++ > 30) {
                  return MBEDTLS_ERR_MPI_NOT_ACCEPTABLE;
              }
  
          } while ( mbedtls_mpi_cmp_mpi( &A, &W ) >= 0 ||
                    mbedtls_mpi_cmp_int( &A, 1 )  <= 0    );
  
          /*
           * A = A^R mod |X|
           */
          MBEDTLS_MPI_CHK( mbedtls_mpi_exp_mod( &A, &A, &R, X, &RR ) );
  
          if( mbedtls_mpi_cmp_mpi( &A, &W ) == 0 ||
              mbedtls_mpi_cmp_int( &A,  1 ) == 0 )
              continue;
  
          j = 1;
          while( j < s && mbedtls_mpi_cmp_mpi( &A, &W ) != 0 )
          {
              /*
               * A = A * A mod |X|
               */
              MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &T, &A, &A ) );
              MBEDTLS_MPI_CHK( mbedtls_mpi_mod_mpi( &A, &T, X  ) );
  
              if( mbedtls_mpi_cmp_int( &A, 1 ) == 0 )
                  break;
  
              j++;
          }
  
          /*
           * not prime if A != |X| - 1 or A == 1
           */
          if( mbedtls_mpi_cmp_mpi( &A, &W ) != 0 ||
              mbedtls_mpi_cmp_int( &A,  1 ) == 0 )
          {
              ret = MBEDTLS_ERR_MPI_NOT_ACCEPTABLE;
              break;
          }
      }
  
  cleanup:
      mbedtls_mpi_free( &W ); mbedtls_mpi_free( &R ); mbedtls_mpi_free( &T ); mbedtls_mpi_free( &A );
      mbedtls_mpi_free( &RR );
  
      return( ret );
  }
  
  /*
   * Pseudo-primality test: small factors, then Miller-Rabin
   */
  int mbedtls_mpi_is_prime( const mbedtls_mpi *X,
                    int (*f_rng)(void *, unsigned char *, size_t),
                    void *p_rng )
  {
      int ret;
      mbedtls_mpi XX;
  
      XX.s = 1;
      XX.n = X->n;
      XX.p = X->p;
  
      if( mbedtls_mpi_cmp_int( &XX, 0 ) == 0 ||
          mbedtls_mpi_cmp_int( &XX, 1 ) == 0 )
          return( MBEDTLS_ERR_MPI_NOT_ACCEPTABLE );
  
      if( mbedtls_mpi_cmp_int( &XX, 2 ) == 0 )
          return( 0 );
  
      if( ( ret = mpi_check_small_factors( &XX ) ) != 0 )
      {
          if( ret == 1 )
              return( 0 );
  
          return( ret );
      }
  
      return( mpi_miller_rabin( &XX, f_rng, p_rng ) );
  }
  
  /*
   * Prime number generation
   */
  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 )
  {
      int ret;
      size_t k, n;
      mbedtls_mpi_uint r;
      mbedtls_mpi Y;
  
      if( nbits < 3 || nbits > MBEDTLS_MPI_MAX_BITS )
          return( MBEDTLS_ERR_MPI_BAD_INPUT_DATA );
  
      mbedtls_mpi_init( &Y );
  
      n = BITS_TO_LIMBS( nbits );
  
      MBEDTLS_MPI_CHK( mbedtls_mpi_fill_random( X, n * ciL, f_rng, p_rng ) );
  
      k = mbedtls_mpi_bitlen( X );
      if( k > nbits ) MBEDTLS_MPI_CHK( mbedtls_mpi_shift_r( X, k - nbits + 1 ) );
  
      mbedtls_mpi_set_bit( X, nbits-1, 1 );
  
      X->p[0] |= 1;
  
      if( dh_flag == 0 )
      {
          while( ( ret = mbedtls_mpi_is_prime( X, f_rng, p_rng ) ) != 0 )
          {
              if( ret != MBEDTLS_ERR_MPI_NOT_ACCEPTABLE )
                  goto cleanup;
  
              MBEDTLS_MPI_CHK( mbedtls_mpi_add_int( X, X, 2 ) );
          }
      }
      else
      {
          /*
           * An necessary condition for Y and X = 2Y + 1 to be prime
           * is X = 2 mod 3 (which is equivalent to Y = 2 mod 3).
           * Make sure it is satisfied, while keeping X = 3 mod 4
           */
  
          X->p[0] |= 2;
  
          MBEDTLS_MPI_CHK( mbedtls_mpi_mod_int( &r, X, 3 ) );
          if( r == 0 )
              MBEDTLS_MPI_CHK( mbedtls_mpi_add_int( X, X, 8 ) );
          else if( r == 1 )
              MBEDTLS_MPI_CHK( mbedtls_mpi_add_int( X, X, 4 ) );
  
          /* Set Y = (X-1) / 2, which is X / 2 because X is odd */
          MBEDTLS_MPI_CHK( mbedtls_mpi_copy( &Y, X ) );
          MBEDTLS_MPI_CHK( mbedtls_mpi_shift_r( &Y, 1 ) );
  
          while( 1 )
          {
              /*
               * First, check small factors for X and Y
               * before doing Miller-Rabin on any of them
               */
              if( ( ret = mpi_check_small_factors(  X         ) ) == 0 &&
                  ( ret = mpi_check_small_factors( &Y         ) ) == 0 &&
                  ( ret = mpi_miller_rabin(  X, f_rng, p_rng  ) ) == 0 &&
                  ( ret = mpi_miller_rabin( &Y, f_rng, p_rng  ) ) == 0 )
              {
                  break;
              }
  
              if( ret != MBEDTLS_ERR_MPI_NOT_ACCEPTABLE )
                  goto cleanup;
  
              /*
               * Next candidates. We want to preserve Y = (X-1) / 2 and
               * Y = 1 mod 2 and Y = 2 mod 3 (eq X = 3 mod 4 and X = 2 mod 3)
               * so up Y by 6 and X by 12.
               */
              MBEDTLS_MPI_CHK( mbedtls_mpi_add_int(  X,  X, 12 ) );
              MBEDTLS_MPI_CHK( mbedtls_mpi_add_int( &Y, &Y, 6  ) );
          }
      }
  
  cleanup:
  
      mbedtls_mpi_free( &Y );
  
      return( ret );
  }
  
  #endif /* MBEDTLS_GENPRIME */
  
  #if defined(MBEDTLS_SELF_TEST)
  
  #define GCD_PAIR_COUNT  3
  
  static const int gcd_pairs[GCD_PAIR_COUNT][3] =
  {
      { 693, 609, 21 },
      { 1764, 868, 28 },
      { 768454923, 542167814, 1 }
  };
  
  /*
   * Checkup routine
   */
  int mbedtls_mpi_self_test( int verbose )
  {
      int ret, i;
      mbedtls_mpi A, E, N, X, Y, U, V;
  
      mbedtls_mpi_init( &A ); mbedtls_mpi_init( &E ); mbedtls_mpi_init( &N ); mbedtls_mpi_init( &X );
      mbedtls_mpi_init( &Y ); mbedtls_mpi_init( &U ); mbedtls_mpi_init( &V );
  
      MBEDTLS_MPI_CHK( mbedtls_mpi_read_string( &A, 16,
          "EFE021C2645FD1DC586E69184AF4A31E" \
          "D5F53E93B5F123FA41680867BA110131" \
          "944FE7952E2517337780CB0DB80E61AA" \
          "E7C8DDC6C5C6AADEB34EB38A2F40D5E6" ) );
  
      MBEDTLS_MPI_CHK( mbedtls_mpi_read_string( &E, 16,
          "B2E7EFD37075B9F03FF989C7C5051C20" \
          "34D2A323810251127E7BF8625A4F49A5" \
          "F3E27F4DA8BD59C47D6DAABA4C8127BD" \
          "5B5C25763222FEFCCFC38B832366C29E" ) );
  
      MBEDTLS_MPI_CHK( mbedtls_mpi_read_string( &N, 16,
          "0066A198186C18C10B2F5ED9B522752A" \
          "9830B69916E535C8F047518A889A43A5" \
          "94B6BED27A168D31D4A52F88925AA8F5" ) );
  
      MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &X, &A, &N ) );
  
      MBEDTLS_MPI_CHK( mbedtls_mpi_read_string( &U, 16,
          "602AB7ECA597A3D6B56FF9829A5E8B85" \
          "9E857EA95A03512E2BAE7391688D264A" \
          "A5663B0341DB9CCFD2C4C5F421FEC814" \
          "8001B72E848A38CAE1C65F78E56ABDEF" \
          "E12D3C039B8A02D6BE593F0BBBDA56F1" \
          "ECF677152EF804370C1A305CAF3B5BF1" \
          "30879B56C61DE584A0F53A2447A51E" ) );
  
      if( verbose != 0 )
          mbedtls_printf( "  MPI test #1 (mul_mpi): " );
  
      if( mbedtls_mpi_cmp_mpi( &X, &U ) != 0 )
      {
          if( verbose != 0 )
              mbedtls_printf( "failed\n" );
  
          ret = 1;
          goto cleanup;
      }
  
      if( verbose != 0 )
          mbedtls_printf( "passed\n" );
  
      MBEDTLS_MPI_CHK( mbedtls_mpi_div_mpi( &X, &Y, &A, &N ) );
  
      MBEDTLS_MPI_CHK( mbedtls_mpi_read_string( &U, 16,
          "256567336059E52CAE22925474705F39A94" ) );
  
      MBEDTLS_MPI_CHK( mbedtls_mpi_read_string( &V, 16,
          "6613F26162223DF488E9CD48CC132C7A" \
          "0AC93C701B001B092E4E5B9F73BCD27B" \
          "9EE50D0657C77F374E903CDFA4C642" ) );
  
      if( verbose != 0 )
          mbedtls_printf( "  MPI test #2 (div_mpi): " );
  
      if( mbedtls_mpi_cmp_mpi( &X, &U ) != 0 ||
          mbedtls_mpi_cmp_mpi( &Y, &V ) != 0 )
      {
          if( verbose != 0 )
              mbedtls_printf( "failed\n" );
  
          ret = 1;
          goto cleanup;
      }
  
      if( verbose != 0 )
          mbedtls_printf( "passed\n" );
  
      MBEDTLS_MPI_CHK( mbedtls_mpi_exp_mod( &X, &A, &E, &N, NULL ) );
  
      MBEDTLS_MPI_CHK( mbedtls_mpi_read_string( &U, 16,
          "36E139AEA55215609D2816998ED020BB" \
          "BD96C37890F65171D948E9BC7CBAA4D9" \
          "325D24D6A3C12710F10A09FA08AB87" ) );
  
      if( verbose != 0 )
          mbedtls_printf( "  MPI test #3 (exp_mod): " );
  
      if( mbedtls_mpi_cmp_mpi( &X, &U ) != 0 )
      {
          if( verbose != 0 )
              mbedtls_printf( "failed\n" );
  
          ret = 1;
          goto cleanup;
      }
  
      if( verbose != 0 )
          mbedtls_printf( "passed\n" );
  
      MBEDTLS_MPI_CHK( mbedtls_mpi_inv_mod( &X, &A, &N ) );
  
      MBEDTLS_MPI_CHK( mbedtls_mpi_read_string( &U, 16,
          "003A0AAEDD7E784FC07D8F9EC6E3BFD5" \
          "C3DBA76456363A10869622EAC2DD84EC" \
          "C5B8A74DAC4D09E03B5E0BE779F2DF61" ) );
  
      if( verbose != 0 )
          mbedtls_printf( "  MPI test #4 (inv_mod): " );
  
      if( mbedtls_mpi_cmp_mpi( &X, &U ) != 0 )
      {
          if( verbose != 0 )
              mbedtls_printf( "failed\n" );
  
          ret = 1;
          goto cleanup;
      }
  
      if( verbose != 0 )
          mbedtls_printf( "passed\n" );
  
      if( verbose != 0 )
          mbedtls_printf( "  MPI test #5 (simple gcd): " );
  
      for( i = 0; i < GCD_PAIR_COUNT; i++ )
      {
          MBEDTLS_MPI_CHK( mbedtls_mpi_lset( &X, gcd_pairs[i][0] ) );
          MBEDTLS_MPI_CHK( mbedtls_mpi_lset( &Y, gcd_pairs[i][1] ) );
  
          MBEDTLS_MPI_CHK( mbedtls_mpi_gcd( &A, &X, &Y ) );
  
          if( mbedtls_mpi_cmp_int( &A, gcd_pairs[i][2] ) != 0 )
          {
              if( verbose != 0 )
                  mbedtls_printf( "failed at %d\n", i );
  
              ret = 1;
              goto cleanup;
          }
      }
  
      if( verbose != 0 )
          mbedtls_printf( "passed\n" );
  
  cleanup:
  
      if( ret != 0 && verbose != 0 )
          mbedtls_printf( "Unexpected error, return code = %08X\n", ret );
  
      mbedtls_mpi_free( &A ); mbedtls_mpi_free( &E ); mbedtls_mpi_free( &N ); mbedtls_mpi_free( &X );
      mbedtls_mpi_free( &Y ); mbedtls_mpi_free( &U ); mbedtls_mpi_free( &V );
  
      if( verbose != 0 )
          mbedtls_printf( "\n" );
  
      return( ret );
  }
  
  #endif /* MBEDTLS_SELF_TEST */
  
  #endif /* MBEDTLS_BIGNUM_C */
  