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  1. /*
  2.  *  Multi-precision integer library
  3.  *
  4.  *  Copyright (C) 2006-2015, ARM Limited, All Rights Reserved
  5.  *  SPDX-License-Identifier: GPL-2.0
  6.  *
  7.  *  This program is free software; you can redistribute it and/or modify
  8.  *  it under the terms of the GNU General Public License as published by
  9.  *  the Free Software Foundation; either version 2 of the License, or
  10.  *  (at your option) any later version.
  11.  *
  12.  *  This program is distributed in the hope that it will be useful,
  13.  *  but WITHOUT ANY WARRANTY; without even the implied warranty of
  14.  *  MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
  15.  *  GNU General Public License for more details.
  16.  *
  17.  *  You should have received a copy of the GNU General Public License along
  18.  *  with this program; if not, write to the Free Software Foundation, Inc.,
  19.  *  51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA.
  20.  *
  21.  *  This file is part of mbed TLS (https://tls.mbed.org)
  22.  */
  23.  
  24. /*
  25.  *  The following sources were referenced in the design of this Multi-precision
  26.  *  Integer library:
  27.  *
  28.  *  [1] Handbook of Applied Cryptography - 1997
  29.  *      Menezes, van Oorschot and Vanstone
  30.  *
  31.  *  [2] Multi-Precision Math
  32.  *      Tom St Denis
  33.  *      https://github.com/libtom/libtommath/blob/develop/tommath.pdf
  34.  *
  35.  *  [3] GNU Multi-Precision Arithmetic Library
  36.  *      https://gmplib.org/manual/index.html
  37.  *
  38.  */
  39.  
  40. #if !defined(MBEDTLS_CONFIG_FILE)
  41. #include "mbedtls/config.h"
  42. #else
  43. #include MBEDTLS_CONFIG_FILE
  44. #endif
  45.  
  46. #if defined(MBEDTLS_BIGNUM_C)
  47.  
  48. #include "mbedtls/bignum.h"
  49. #include "mbedtls/bn_mul.h"
  50. #include "mbedtls/platform_util.h"
  51.  
  52. #include <string.h>
  53.  
  54. #if defined(MBEDTLS_PLATFORM_C)
  55. #include "mbedtls/platform.h"
  56. #else
  57. #include <stdio.h>
  58. #include <stdlib.h>
  59. #define mbedtls_printf     printf
  60. #define mbedtls_calloc    calloc
  61. #define mbedtls_free       free
  62. #endif
  63.  
  64. #define MPI_VALIDATE_RET( cond )                                       \
  65.     MBEDTLS_INTERNAL_VALIDATE_RET( cond, MBEDTLS_ERR_MPI_BAD_INPUT_DATA )
  66. #define MPI_VALIDATE( cond )                                           \
  67.     MBEDTLS_INTERNAL_VALIDATE( cond )
  68.  
  69. #define ciL    (sizeof(mbedtls_mpi_uint))         /* chars in limb  */
  70. #define biL    (ciL << 3)               /* bits  in limb  */
  71. #define biH    (ciL << 2)               /* half limb size */
  72.  
  73. #define MPI_SIZE_T_MAX  ( (size_t) -1 ) /* SIZE_T_MAX is not standard */
  74.  
  75. /*
  76.  * Convert between bits/chars and number of limbs
  77.  * Divide first in order to avoid potential overflows
  78.  */
  79. #define BITS_TO_LIMBS(i)  ( (i) / biL + ( (i) % biL != 0 ) )
  80. #define CHARS_TO_LIMBS(i) ( (i) / ciL + ( (i) % ciL != 0 ) )
  81.  
  82. /* Implementation that should never be optimized out by the compiler */
  83. static void mbedtls_mpi_zeroize( mbedtls_mpi_uint *v, size_t n )
  84. {
  85.     mbedtls_platform_zeroize( v, ciL * n );
  86. }
  87.  
  88. /*
  89.  * Initialize one MPI
  90.  */
  91. void mbedtls_mpi_init( mbedtls_mpi *X )
  92. {
  93.     MPI_VALIDATE( X != NULL );
  94.  
  95.     X->s = 1;
  96.     X->n = 0;
  97.     X->p = NULL;
  98. }
  99.  
  100. /*
  101.  * Unallocate one MPI
  102.  */
  103. void mbedtls_mpi_free( mbedtls_mpi *X )
  104. {
  105.     if( X == NULL )
  106.         return;
  107.  
  108.     if( X->p != NULL )
  109.     {
  110.         mbedtls_mpi_zeroize( X->p, X->n );
  111.         mbedtls_free( X->p );
  112.     }
  113.  
  114.     X->s = 1;
  115.     X->n = 0;
  116.     X->p = NULL;
  117. }
  118.  
  119. /*
  120.  * Enlarge to the specified number of limbs
  121.  */
  122. int mbedtls_mpi_grow( mbedtls_mpi *X, size_t nblimbs )
  123. {
  124.     mbedtls_mpi_uint *p;
  125.     MPI_VALIDATE_RET( X != NULL );
  126.  
  127.     if( nblimbs > MBEDTLS_MPI_MAX_LIMBS )
  128.         return( MBEDTLS_ERR_MPI_ALLOC_FAILED );
  129.  
  130.     if( X->n < nblimbs )
  131.     {
  132.         if( ( p = (mbedtls_mpi_uint*)mbedtls_calloc( nblimbs, ciL ) ) == NULL )
  133.             return( MBEDTLS_ERR_MPI_ALLOC_FAILED );
  134.  
  135.         if( X->p != NULL )
  136.         {
  137.             memcpy( p, X->p, X->n * ciL );
  138.             mbedtls_mpi_zeroize( X->p, X->n );
  139.             mbedtls_free( X->p );
  140.         }
  141.  
  142.         X->n = nblimbs;
  143.         X->p = p;
  144.     }
  145.  
  146.     return( 0 );
  147. }
  148.  
  149. /*
  150.  * Resize down as much as possible,
  151.  * while keeping at least the specified number of limbs
  152.  */
  153. int mbedtls_mpi_shrink( mbedtls_mpi *X, size_t nblimbs )
  154. {
  155.     mbedtls_mpi_uint *p;
  156.     size_t i;
  157.     MPI_VALIDATE_RET( X != NULL );
  158.  
  159.     if( nblimbs > MBEDTLS_MPI_MAX_LIMBS )
  160.         return( MBEDTLS_ERR_MPI_ALLOC_FAILED );
  161.  
  162.     /* Actually resize up if there are currently fewer than nblimbs limbs. */
  163.     if( X->n <= nblimbs )
  164.         return( mbedtls_mpi_grow( X, nblimbs ) );
  165.     /* After this point, then X->n > nblimbs and in particular X->n > 0. */
  166.  
  167.     for( i = X->n - 1; i > 0; i-- )
  168.         if( X->p[i] != 0 )
  169.             break;
  170.     i++;
  171.  
  172.     if( i < nblimbs )
  173.         i = nblimbs;
  174.  
  175.     if( ( p = (mbedtls_mpi_uint*)mbedtls_calloc( i, ciL ) ) == NULL )
  176.         return( MBEDTLS_ERR_MPI_ALLOC_FAILED );
  177.  
  178.     if( X->p != NULL )
  179.     {
  180.         memcpy( p, X->p, i * ciL );
  181.         mbedtls_mpi_zeroize( X->p, X->n );
  182.         mbedtls_free( X->p );
  183.     }
  184.  
  185.     X->n = i;
  186.     X->p = p;
  187.  
  188.     return( 0 );
  189. }
  190.  
  191. /*
  192.  * Copy the contents of Y into X
  193.  */
  194. int mbedtls_mpi_copy( mbedtls_mpi *X, const mbedtls_mpi *Y )
  195. {
  196.     int ret = 0;
  197.     size_t i;
  198.     MPI_VALIDATE_RET( X != NULL );
  199.     MPI_VALIDATE_RET( Y != NULL );
  200.  
  201.     if( X == Y )
  202.         return( 0 );
  203.  
  204.     if( Y->n == 0 )
  205.     {
  206.         mbedtls_mpi_free( X );
  207.         return( 0 );
  208.     }
  209.  
  210.     for( i = Y->n - 1; i > 0; i-- )
  211.         if( Y->p[i] != 0 )
  212.             break;
  213.     i++;
  214.  
  215.     X->s = Y->s;
  216.  
  217.     if( X->n < i )
  218.     {
  219.         MBEDTLS_MPI_CHK( mbedtls_mpi_grow( X, i ) );
  220.     }
  221.     else
  222.     {
  223.         memset( X->p + i, 0, ( X->n - i ) * ciL );
  224.     }
  225.  
  226.     memcpy( X->p, Y->p, i * ciL );
  227.  
  228. cleanup:
  229.  
  230.     return( ret );
  231. }
  232.  
  233. /*
  234.  * Swap the contents of X and Y
  235.  */
  236. void mbedtls_mpi_swap( mbedtls_mpi *X, mbedtls_mpi *Y )
  237. {
  238.     mbedtls_mpi T;
  239.     MPI_VALIDATE( X != NULL );
  240.     MPI_VALIDATE( Y != NULL );
  241.  
  242.     memcpy( &T,  X, sizeof( mbedtls_mpi ) );
  243.     memcpy(  X,  Y, sizeof( mbedtls_mpi ) );
  244.     memcpy(  Y, &T, sizeof( mbedtls_mpi ) );
  245. }
  246.  
  247. /*
  248.  * Conditionally assign X = Y, without leaking information
  249.  * about whether the assignment was made or not.
  250.  * (Leaking information about the respective sizes of X and Y is ok however.)
  251.  */
  252. int mbedtls_mpi_safe_cond_assign( mbedtls_mpi *X, const mbedtls_mpi *Y, unsigned char assign )
  253. {
  254.     int ret = 0;
  255.     size_t i;
  256.     MPI_VALIDATE_RET( X != NULL );
  257.     MPI_VALIDATE_RET( Y != NULL );
  258.  
  259.     /* make sure assign is 0 or 1 in a time-constant manner */
  260.     assign = (assign | (unsigned char)-assign) >> 7;
  261.  
  262.     MBEDTLS_MPI_CHK( mbedtls_mpi_grow( X, Y->n ) );
  263.  
  264.     X->s = X->s * ( 1 - assign ) + Y->s * assign;
  265.  
  266.     for( i = 0; i < Y->n; i++ )
  267.         X->p[i] = X->p[i] * ( 1 - assign ) + Y->p[i] * assign;
  268.  
  269.     for( ; i < X->n; i++ )
  270.         X->p[i] *= ( 1 - assign );
  271.  
  272. cleanup:
  273.     return( ret );
  274. }
  275.  
  276. /*
  277.  * Conditionally swap X and Y, without leaking information
  278.  * about whether the swap was made or not.
  279.  * Here it is not ok to simply swap the pointers, which whould lead to
  280.  * different memory access patterns when X and Y are used afterwards.
  281.  */
  282. int mbedtls_mpi_safe_cond_swap( mbedtls_mpi *X, mbedtls_mpi *Y, unsigned char swap )
  283. {
  284.     int ret, s;
  285.     size_t i;
  286.     mbedtls_mpi_uint tmp;
  287.     MPI_VALIDATE_RET( X != NULL );
  288.     MPI_VALIDATE_RET( Y != NULL );
  289.  
  290.     if( X == Y )
  291.         return( 0 );
  292.  
  293.     /* make sure swap is 0 or 1 in a time-constant manner */
  294.     swap = (swap | (unsigned char)-swap) >> 7;
  295.  
  296.     MBEDTLS_MPI_CHK( mbedtls_mpi_grow( X, Y->n ) );
  297.     MBEDTLS_MPI_CHK( mbedtls_mpi_grow( Y, X->n ) );
  298.  
  299.     s = X->s;
  300.     X->s = X->s * ( 1 - swap ) + Y->s * swap;
  301.     Y->s = Y->s * ( 1 - swap ) +    s * swap;
  302.  
  303.  
  304.     for( i = 0; i < X->n; i++ )
  305.     {
  306.         tmp = X->p[i];
  307.         X->p[i] = X->p[i] * ( 1 - swap ) + Y->p[i] * swap;
  308.         Y->p[i] = Y->p[i] * ( 1 - swap ) +     tmp * swap;
  309.     }
  310.  
  311. cleanup:
  312.     return( ret );
  313. }
  314.  
  315. /*
  316.  * Set value from integer
  317.  */
  318. int mbedtls_mpi_lset( mbedtls_mpi *X, mbedtls_mpi_sint z )
  319. {
  320.     int ret;
  321.     MPI_VALIDATE_RET( X != NULL );
  322.  
  323.     MBEDTLS_MPI_CHK( mbedtls_mpi_grow( X, 1 ) );
  324.     memset( X->p, 0, X->n * ciL );
  325.  
  326.     X->p[0] = ( z < 0 ) ? -z : z;
  327.     X->s    = ( z < 0 ) ? -1 : 1;
  328.  
  329. cleanup:
  330.  
  331.     return( ret );
  332. }
  333.  
  334. /*
  335.  * Get a specific bit
  336.  */
  337. int mbedtls_mpi_get_bit( const mbedtls_mpi *X, size_t pos )
  338. {
  339.     MPI_VALIDATE_RET( X != NULL );
  340.  
  341.     if( X->n * biL <= pos )
  342.         return( 0 );
  343.  
  344.     return( ( X->p[pos / biL] >> ( pos % biL ) ) & 0x01 );
  345. }
  346.  
  347. /* Get a specific byte, without range checks. */
  348. #define GET_BYTE( X, i )                                \
  349.     ( ( ( X )->p[( i ) / ciL] >> ( ( ( i ) % ciL ) * 8 ) ) & 0xff )
  350.  
  351. /*
  352.  * Set a bit to a specific value of 0 or 1
  353.  */
  354. int mbedtls_mpi_set_bit( mbedtls_mpi *X, size_t pos, unsigned char val )
  355. {
  356.     int ret = 0;
  357.     size_t off = pos / biL;
  358.     size_t idx = pos % biL;
  359.     MPI_VALIDATE_RET( X != NULL );
  360.  
  361.     if( val != 0 && val != 1 )
  362.         return( MBEDTLS_ERR_MPI_BAD_INPUT_DATA );
  363.  
  364.     if( X->n * biL <= pos )
  365.     {
  366.         if( val == 0 )
  367.             return( 0 );
  368.  
  369.         MBEDTLS_MPI_CHK( mbedtls_mpi_grow( X, off + 1 ) );
  370.     }
  371.  
  372.     X->p[off] &= ~( (mbedtls_mpi_uint) 0x01 << idx );
  373.     X->p[off] |= (mbedtls_mpi_uint) val << idx;
  374.  
  375. cleanup:
  376.  
  377.     return( ret );
  378. }
  379.  
  380. /*
  381.  * Return the number of less significant zero-bits
  382.  */
  383. size_t mbedtls_mpi_lsb( const mbedtls_mpi *X )
  384. {
  385.     size_t i, j, count = 0;
  386.     MBEDTLS_INTERNAL_VALIDATE_RET( X != NULL, 0 );
  387.  
  388.     for( i = 0; i < X->n; i++ )
  389.         for( j = 0; j < biL; j++, count++ )
  390.             if( ( ( X->p[i] >> j ) & 1 ) != 0 )
  391.                 return( count );
  392.  
  393.     return( 0 );
  394. }
  395.  
  396. /*
  397.  * Count leading zero bits in a given integer
  398.  */
  399. static size_t mbedtls_clz( const mbedtls_mpi_uint x )
  400. {
  401.     size_t j;
  402.     mbedtls_mpi_uint mask = (mbedtls_mpi_uint) 1 << (biL - 1);
  403.  
  404.     for( j = 0; j < biL; j++ )
  405.     {
  406.         if( x & mask ) break;
  407.  
  408.         mask >>= 1;
  409.     }
  410.  
  411.     return j;
  412. }
  413.  
  414. /*
  415.  * Return the number of bits
  416.  */
  417. size_t mbedtls_mpi_bitlen( const mbedtls_mpi *X )
  418. {
  419.     size_t i, j;
  420.  
  421.     if( X->n == 0 )
  422.         return( 0 );
  423.  
  424.     for( i = X->n - 1; i > 0; i-- )
  425.         if( X->p[i] != 0 )
  426.             break;
  427.  
  428.     j = biL - mbedtls_clz( X->p[i] );
  429.  
  430.     return( ( i * biL ) + j );
  431. }
  432.  
  433. /*
  434.  * Return the total size in bytes
  435.  */
  436. size_t mbedtls_mpi_size( const mbedtls_mpi *X )
  437. {
  438.     return( ( mbedtls_mpi_bitlen( X ) + 7 ) >> 3 );
  439. }
  440.  
  441. /*
  442.  * Convert an ASCII character to digit value
  443.  */
  444. static int mpi_get_digit( mbedtls_mpi_uint *d, int radix, char c )
  445. {
  446.     *d = 255;
  447.  
  448.     if( c >= 0x30 && c <= 0x39 ) *d = c - 0x30;
  449.     if( c >= 0x41 && c <= 0x46 ) *d = c - 0x37;
  450.     if( c >= 0x61 && c <= 0x66 ) *d = c - 0x57;
  451.  
  452.     if( *d >= (mbedtls_mpi_uint) radix )
  453.         return( MBEDTLS_ERR_MPI_INVALID_CHARACTER );
  454.  
  455.     return( 0 );
  456. }
  457.  
  458. /*
  459.  * Import from an ASCII string
  460.  */
  461. int mbedtls_mpi_read_string( mbedtls_mpi *X, int radix, const char *s )
  462. {
  463.     int ret;
  464.     size_t i, j, slen, n;
  465.     mbedtls_mpi_uint d;
  466.     mbedtls_mpi T;
  467.     MPI_VALIDATE_RET( X != NULL );
  468.     MPI_VALIDATE_RET( s != NULL );
  469.  
  470.     if( radix < 2 || radix > 16 )
  471.         return( MBEDTLS_ERR_MPI_BAD_INPUT_DATA );
  472.  
  473.     mbedtls_mpi_init( &T );
  474.  
  475.     slen = strlen( s );
  476.  
  477.     if( radix == 16 )
  478.     {
  479.         if( slen > MPI_SIZE_T_MAX >> 2 )
  480.             return( MBEDTLS_ERR_MPI_BAD_INPUT_DATA );
  481.  
  482.         n = BITS_TO_LIMBS( slen << 2 );
  483.  
  484.         MBEDTLS_MPI_CHK( mbedtls_mpi_grow( X, n ) );
  485.         MBEDTLS_MPI_CHK( mbedtls_mpi_lset( X, 0 ) );
  486.  
  487.         for( i = slen, j = 0; i > 0; i--, j++ )
  488.         {
  489.             if( i == 1 && s[i - 1] == '-' )
  490.             {
  491.                 X->s = -1;
  492.                 break;
  493.             }
  494.  
  495.             MBEDTLS_MPI_CHK( mpi_get_digit( &d, radix, s[i - 1] ) );
  496.             X->p[j / ( 2 * ciL )] |= d << ( ( j % ( 2 * ciL ) ) << 2 );
  497.         }
  498.     }
  499.     else
  500.     {
  501.         MBEDTLS_MPI_CHK( mbedtls_mpi_lset( X, 0 ) );
  502.  
  503.         for( i = 0; i < slen; i++ )
  504.         {
  505.             if( i == 0 && s[i] == '-' )
  506.             {
  507.                 X->s = -1;
  508.                 continue;
  509.             }
  510.  
  511.             MBEDTLS_MPI_CHK( mpi_get_digit( &d, radix, s[i] ) );
  512.             MBEDTLS_MPI_CHK( mbedtls_mpi_mul_int( &T, X, radix ) );
  513.  
  514.             if( X->s == 1 )
  515.             {
  516.                 MBEDTLS_MPI_CHK( mbedtls_mpi_add_int( X, &T, d ) );
  517.             }
  518.             else
  519.             {
  520.                 MBEDTLS_MPI_CHK( mbedtls_mpi_sub_int( X, &T, d ) );
  521.             }
  522.         }
  523.     }
  524.  
  525. cleanup:
  526.  
  527.     mbedtls_mpi_free( &T );
  528.  
  529.     return( ret );
  530. }
  531.  
  532. /*
  533.  * Helper to write the digits high-order first.
  534.  */
  535. static int mpi_write_hlp( mbedtls_mpi *X, int radix,
  536.                           char **p, const size_t buflen )
  537. {
  538.     int ret;
  539.     mbedtls_mpi_uint r;
  540.     size_t length = 0;
  541.     char *p_end = *p + buflen;
  542.  
  543.     do
  544.     {
  545.         if( length >= buflen )
  546.         {
  547.             return( MBEDTLS_ERR_MPI_BUFFER_TOO_SMALL );
  548.         }
  549.  
  550.         MBEDTLS_MPI_CHK( mbedtls_mpi_mod_int( &r, X, radix ) );
  551.         MBEDTLS_MPI_CHK( mbedtls_mpi_div_int( X, NULL, X, radix ) );
  552.         /*
  553.          * Write the residue in the current position, as an ASCII character.
  554.          */
  555.         if( r < 0xA )
  556.             *(--p_end) = (char)( '0' + r );
  557.         else
  558.             *(--p_end) = (char)( 'A' + ( r - 0xA ) );
  559.  
  560.         length++;
  561.     } while( mbedtls_mpi_cmp_int( X, 0 ) != 0 );
  562.  
  563.     memmove( *p, p_end, length );
  564.     *p += length;
  565.  
  566. cleanup:
  567.  
  568.     return( ret );
  569. }
  570.  
  571. /*
  572.  * Export into an ASCII string
  573.  */
  574. int mbedtls_mpi_write_string( const mbedtls_mpi *X, int radix,
  575.                               char *buf, size_t buflen, size_t *olen )
  576. {
  577.     int ret = 0;
  578.     size_t n;
  579.     char *p;
  580.     mbedtls_mpi T;
  581.     MPI_VALIDATE_RET( X    != NULL );
  582.     MPI_VALIDATE_RET( olen != NULL );
  583.     MPI_VALIDATE_RET( buflen == 0 || buf != NULL );
  584.  
  585.     if( radix < 2 || radix > 16 )
  586.         return( MBEDTLS_ERR_MPI_BAD_INPUT_DATA );
  587.  
  588.     n = mbedtls_mpi_bitlen( X ); /* Number of bits necessary to present `n`. */
  589.     if( radix >=  4 ) n >>= 1;   /* Number of 4-adic digits necessary to present
  590.                                   * `n`. If radix > 4, this might be a strict
  591.                                   * overapproximation of the number of
  592.                                   * radix-adic digits needed to present `n`. */
  593.     if( radix >= 16 ) n >>= 1;   /* Number of hexadecimal digits necessary to
  594.                                   * present `n`. */
  595.  
  596.     n += 1; /* Terminating null byte */
  597.     n += 1; /* Compensate for the divisions above, which round down `n`
  598.              * in case it's not even. */
  599.     n += 1; /* Potential '-'-sign. */
  600.     n += ( n & 1 ); /* Make n even to have enough space for hexadecimal writing,
  601.                      * which always uses an even number of hex-digits. */
  602.  
  603.     if( buflen < n )
  604.     {
  605.         *olen = n;
  606.         return( MBEDTLS_ERR_MPI_BUFFER_TOO_SMALL );
  607.     }
  608.  
  609.     p = buf;
  610.     mbedtls_mpi_init( &T );
  611.  
  612.     if( X->s == -1 )
  613.     {
  614.         *p++ = '-';
  615.         buflen--;
  616.     }
  617.  
  618.     if( radix == 16 )
  619.     {
  620.         int c;
  621.         size_t i, j, k;
  622.  
  623.         for( i = X->n, k = 0; i > 0; i-- )
  624.         {
  625.             for( j = ciL; j > 0; j-- )
  626.             {
  627.                 c = ( X->p[i - 1] >> ( ( j - 1 ) << 3) ) & 0xFF;
  628.  
  629.                 if( c == 0 && k == 0 && ( i + j ) != 2 )
  630.                     continue;
  631.  
  632.                 *(p++) = "0123456789ABCDEF" [c / 16];
  633.                 *(p++) = "0123456789ABCDEF" [c % 16];
  634.                 k = 1;
  635.             }
  636.         }
  637.     }
  638.     else
  639.     {
  640.         MBEDTLS_MPI_CHK( mbedtls_mpi_copy( &T, X ) );
  641.  
  642.         if( T.s == -1 )
  643.             T.s = 1;
  644.  
  645.         MBEDTLS_MPI_CHK( mpi_write_hlp( &T, radix, &p, buflen ) );
  646.     }
  647.  
  648.     *p++ = '\0';
  649.     *olen = p - buf;
  650.  
  651. cleanup:
  652.  
  653.     mbedtls_mpi_free( &T );
  654.  
  655.     return( ret );
  656. }
  657.  
  658. #if defined(MBEDTLS_FS_IO)
  659. /*
  660.  * Read X from an opened file
  661.  */
  662. int mbedtls_mpi_read_file( mbedtls_mpi *X, int radix, FILE *fin )
  663. {
  664.     mbedtls_mpi_uint d;
  665.     size_t slen;
  666.     char *p;
  667.     /*
  668.      * Buffer should have space for (short) label and decimal formatted MPI,
  669.      * newline characters and '\0'
  670.      */
  671.     char s[ MBEDTLS_MPI_RW_BUFFER_SIZE ];
  672.  
  673.     MPI_VALIDATE_RET( X   != NULL );
  674.     MPI_VALIDATE_RET( fin != NULL );
  675.  
  676.     if( radix < 2 || radix > 16 )
  677.         return( MBEDTLS_ERR_MPI_BAD_INPUT_DATA );
  678.  
  679.     memset( s, 0, sizeof( s ) );
  680.     if( fgets( s, sizeof( s ) - 1, fin ) == NULL )
  681.         return( MBEDTLS_ERR_MPI_FILE_IO_ERROR );
  682.  
  683.     slen = strlen( s );
  684.     if( slen == sizeof( s ) - 2 )
  685.         return( MBEDTLS_ERR_MPI_BUFFER_TOO_SMALL );
  686.  
  687.     if( slen > 0 && s[slen - 1] == '\n' ) { slen--; s[slen] = '\0'; }
  688.     if( slen > 0 && s[slen - 1] == '\r' ) { slen--; s[slen] = '\0'; }
  689.  
  690.     p = s + slen;
  691.     while( p-- > s )
  692.         if( mpi_get_digit( &d, radix, *p ) != 0 )
  693.             break;
  694.  
  695.     return( mbedtls_mpi_read_string( X, radix, p + 1 ) );
  696. }
  697.  
  698. /*
  699.  * Write X into an opened file (or stdout if fout == NULL)
  700.  */
  701. int mbedtls_mpi_write_file( const char *p, const mbedtls_mpi *X, int radix, FILE *fout )
  702. {
  703.     int ret;
  704.     size_t n, slen, plen;
  705.     /*
  706.      * Buffer should have space for (short) label and decimal formatted MPI,
  707.      * newline characters and '\0'
  708.      */
  709.     char s[ MBEDTLS_MPI_RW_BUFFER_SIZE ];
  710.     MPI_VALIDATE_RET( X != NULL );
  711.  
  712.     if( radix < 2 || radix > 16 )
  713.         return( MBEDTLS_ERR_MPI_BAD_INPUT_DATA );
  714.  
  715.     memset( s, 0, sizeof( s ) );
  716.  
  717.     MBEDTLS_MPI_CHK( mbedtls_mpi_write_string( X, radix, s, sizeof( s ) - 2, &n ) );
  718.  
  719.     if( p == NULL ) p = "";
  720.  
  721.     plen = strlen( p );
  722.     slen = strlen( s );
  723.     s[slen++] = '\r';
  724.     s[slen++] = '\n';
  725.  
  726.     if( fout != NULL )
  727.     {
  728.         if( fwrite( p, 1, plen, fout ) != plen ||
  729.             fwrite( s, 1, slen, fout ) != slen )
  730.             return( MBEDTLS_ERR_MPI_FILE_IO_ERROR );
  731.     }
  732.     else
  733.         mbedtls_printf( "%s%s", p, s );
  734.  
  735. cleanup:
  736.  
  737.     return( ret );
  738. }
  739. #endif /* MBEDTLS_FS_IO */
  740.  
  741.  
  742. /* Convert a big-endian byte array aligned to the size of mbedtls_mpi_uint
  743.  * into the storage form used by mbedtls_mpi. */
  744.  
  745. static mbedtls_mpi_uint mpi_uint_bigendian_to_host_c( mbedtls_mpi_uint x )
  746. {
  747.     uint8_t i;
  748.     unsigned char *x_ptr;
  749.     mbedtls_mpi_uint tmp = 0;
  750.  
  751.     for( i = 0, x_ptr = (unsigned char*) &x; i < ciL; i++, x_ptr++ )
  752.     {
  753.         tmp <<= CHAR_BIT;
  754.         tmp |= (mbedtls_mpi_uint) *x_ptr;
  755.     }
  756.  
  757.     return( tmp );
  758. }
  759.  
  760. static mbedtls_mpi_uint mpi_uint_bigendian_to_host( mbedtls_mpi_uint x )
  761. {
  762. #if defined(__BYTE_ORDER__)
  763.  
  764. /* Nothing to do on bigendian systems. */
  765. #if ( __BYTE_ORDER__ == __ORDER_BIG_ENDIAN__ )
  766.     return( x );
  767. #endif /* __BYTE_ORDER__ == __ORDER_BIG_ENDIAN__ */
  768.  
  769. #if ( __BYTE_ORDER__ == __ORDER_LITTLE_ENDIAN__ )
  770.  
  771. /* For GCC and Clang, have builtins for byte swapping. */
  772. #if defined(__GNUC__) && defined(__GNUC_PREREQ)
  773. #if __GNUC_PREREQ(4,3)
  774. #define have_bswap
  775. #endif
  776. #endif
  777.  
  778. #if defined(__clang__) && defined(__has_builtin)
  779. #if __has_builtin(__builtin_bswap32)  &&                 \
  780.     __has_builtin(__builtin_bswap64)
  781. #define have_bswap
  782. #endif
  783. #endif
  784.  
  785. #if defined(have_bswap)
  786.     /* The compiler is hopefully able to statically evaluate this! */
  787.     switch( sizeof(mbedtls_mpi_uint) )
  788.     {
  789.         case 4:
  790.             return( __builtin_bswap32(x) );
  791.         case 8:
  792.             return( __builtin_bswap64(x) );
  793.     }
  794. #endif
  795. #endif /* __BYTE_ORDER__ == __ORDER_LITTLE_ENDIAN__ */
  796. #endif /* __BYTE_ORDER__ */
  797.  
  798.     /* Fall back to C-based reordering if we don't know the byte order
  799.      * or we couldn't use a compiler-specific builtin. */
  800.     return( mpi_uint_bigendian_to_host_c( x ) );
  801. }
  802.  
  803. static void mpi_bigendian_to_host( mbedtls_mpi_uint * const p, size_t limbs )
  804. {
  805.     mbedtls_mpi_uint *cur_limb_left;
  806.     mbedtls_mpi_uint *cur_limb_right;
  807.     if( limbs == 0 )
  808.         return;
  809.  
  810.     /*
  811.      * Traverse limbs and
  812.      * - adapt byte-order in each limb
  813.      * - swap the limbs themselves.
  814.      * For that, simultaneously traverse the limbs from left to right
  815.      * and from right to left, as long as the left index is not bigger
  816.      * than the right index (it's not a problem if limbs is odd and the
  817.      * indices coincide in the last iteration).
  818.      */
  819.     for( cur_limb_left = p, cur_limb_right = p + ( limbs - 1 );
  820.          cur_limb_left <= cur_limb_right;
  821.          cur_limb_left++, cur_limb_right-- )
  822.     {
  823.         mbedtls_mpi_uint tmp;
  824.         /* Note that if cur_limb_left == cur_limb_right,
  825.          * this code effectively swaps the bytes only once. */
  826.         tmp             = mpi_uint_bigendian_to_host( *cur_limb_left  );
  827.         *cur_limb_left  = mpi_uint_bigendian_to_host( *cur_limb_right );
  828.         *cur_limb_right = tmp;
  829.     }
  830. }
  831.  
  832. /*
  833.  * Import X from unsigned binary data, big endian
  834.  */
  835. int mbedtls_mpi_read_binary( mbedtls_mpi *X, const unsigned char *buf, size_t buflen )
  836. {
  837.     int ret;
  838.     size_t const limbs    = CHARS_TO_LIMBS( buflen );
  839.     size_t const overhead = ( limbs * ciL ) - buflen;
  840.     unsigned char *Xp;
  841.  
  842.     MPI_VALIDATE_RET( X != NULL );
  843.     MPI_VALIDATE_RET( buflen == 0 || buf != NULL );
  844.  
  845.     /* Ensure that target MPI has exactly the necessary number of limbs */
  846.     if( X->n != limbs )
  847.     {
  848.         mbedtls_mpi_free( X );
  849.         mbedtls_mpi_init( X );
  850.         MBEDTLS_MPI_CHK( mbedtls_mpi_grow( X, limbs ) );
  851.     }
  852.     MBEDTLS_MPI_CHK( mbedtls_mpi_lset( X, 0 ) );
  853.  
  854.     /* Avoid calling `memcpy` with NULL source argument,
  855.      * even if buflen is 0. */
  856.     if( buf != NULL )
  857.     {
  858.         Xp = (unsigned char*) X->p;
  859.         memcpy( Xp + overhead, buf, buflen );
  860.  
  861.         mpi_bigendian_to_host( X->p, limbs );
  862.     }
  863.  
  864. cleanup:
  865.  
  866.     return( ret );
  867. }
  868.  
  869. /*
  870.  * Export X into unsigned binary data, big endian
  871.  */
  872. int mbedtls_mpi_write_binary( const mbedtls_mpi *X,
  873.                               unsigned char *buf, size_t buflen )
  874. {
  875.     size_t stored_bytes;
  876.     size_t bytes_to_copy;
  877.     unsigned char *p;
  878.     size_t i;
  879.  
  880.     MPI_VALIDATE_RET( X != NULL );
  881.     MPI_VALIDATE_RET( buflen == 0 || buf != NULL );
  882.  
  883.     stored_bytes = X->n * ciL;
  884.  
  885.     if( stored_bytes < buflen )
  886.     {
  887.         /* There is enough space in the output buffer. Write initial
  888.          * null bytes and record the position at which to start
  889.          * writing the significant bytes. In this case, the execution
  890.          * trace of this function does not depend on the value of the
  891.          * number. */
  892.         bytes_to_copy = stored_bytes;
  893.         p = buf + buflen - stored_bytes;
  894.         memset( buf, 0, buflen - stored_bytes );
  895.     }
  896.     else
  897.     {
  898.         /* The output buffer is smaller than the allocated size of X.
  899.          * However X may fit if its leading bytes are zero. */
  900.         bytes_to_copy = buflen;
  901.         p = buf;
  902.         for( i = bytes_to_copy; i < stored_bytes; i++ )
  903.         {
  904.             if( GET_BYTE( X, i ) != 0 )
  905.                 return( MBEDTLS_ERR_MPI_BUFFER_TOO_SMALL );
  906.         }
  907.     }
  908.  
  909.     for( i = 0; i < bytes_to_copy; i++ )
  910.         p[bytes_to_copy - i - 1] = GET_BYTE( X, i );
  911.  
  912.     return( 0 );
  913. }
  914.  
  915. /*
  916.  * Left-shift: X <<= count
  917.  */
  918. int mbedtls_mpi_shift_l( mbedtls_mpi *X, size_t count )
  919. {
  920.     int ret;
  921.     size_t i, v0, t1;
  922.     mbedtls_mpi_uint r0 = 0, r1;
  923.     MPI_VALIDATE_RET( X != NULL );
  924.  
  925.     v0 = count / (biL    );
  926.     t1 = count & (biL - 1);
  927.  
  928.     i = mbedtls_mpi_bitlen( X ) + count;
  929.  
  930.     if( X->n * biL < i )
  931.         MBEDTLS_MPI_CHK( mbedtls_mpi_grow( X, BITS_TO_LIMBS( i ) ) );
  932.  
  933.     ret = 0;
  934.  
  935.     /*
  936.      * shift by count / limb_size
  937.      */
  938.     if( v0 > 0 )
  939.     {
  940.         for( i = X->n; i > v0; i-- )
  941.             X->p[i - 1] = X->p[i - v0 - 1];
  942.  
  943.         for( ; i > 0; i-- )
  944.             X->p[i - 1] = 0;
  945.     }
  946.  
  947.     /*
  948.      * shift by count % limb_size
  949.      */
  950.     if( t1 > 0 )
  951.     {
  952.         for( i = v0; i < X->n; i++ )
  953.         {
  954.             r1 = X->p[i] >> (biL - t1);
  955.             X->p[i] <<= t1;
  956.             X->p[i] |= r0;
  957.             r0 = r1;
  958.         }
  959.     }
  960.  
  961. cleanup:
  962.  
  963.     return( ret );
  964. }
  965.  
  966. /*
  967.  * Right-shift: X >>= count
  968.  */
  969. int mbedtls_mpi_shift_r( mbedtls_mpi *X, size_t count )
  970. {
  971.     size_t i, v0, v1;
  972.     mbedtls_mpi_uint r0 = 0, r1;
  973.     MPI_VALIDATE_RET( X != NULL );
  974.  
  975.     v0 = count /  biL;
  976.     v1 = count & (biL - 1);
  977.  
  978.     if( v0 > X->n || ( v0 == X->n && v1 > 0 ) )
  979.         return mbedtls_mpi_lset( X, 0 );
  980.  
  981.     /*
  982.      * shift by count / limb_size
  983.      */
  984.     if( v0 > 0 )
  985.     {
  986.         for( i = 0; i < X->n - v0; i++ )
  987.             X->p[i] = X->p[i + v0];
  988.  
  989.         for( ; i < X->n; i++ )
  990.             X->p[i] = 0;
  991.     }
  992.  
  993.     /*
  994.      * shift by count % limb_size
  995.      */
  996.     if( v1 > 0 )
  997.     {
  998.         for( i = X->n; i > 0; i-- )
  999.         {
  1000.             r1 = X->p[i - 1] << (biL - v1);
  1001.             X->p[i - 1] >>= v1;
  1002.             X->p[i - 1] |= r0;
  1003.             r0 = r1;
  1004.         }
  1005.     }
  1006.  
  1007.     return( 0 );
  1008. }
  1009.  
  1010. /*
  1011.  * Compare unsigned values
  1012.  */
  1013. int mbedtls_mpi_cmp_abs( const mbedtls_mpi *X, const mbedtls_mpi *Y )
  1014. {
  1015.     size_t i, j;
  1016.     MPI_VALIDATE_RET( X != NULL );
  1017.     MPI_VALIDATE_RET( Y != NULL );
  1018.  
  1019.     for( i = X->n; i > 0; i-- )
  1020.         if( X->p[i - 1] != 0 )
  1021.             break;
  1022.  
  1023.     for( j = Y->n; j > 0; j-- )
  1024.         if( Y->p[j - 1] != 0 )
  1025.             break;
  1026.  
  1027.     if( i == 0 && j == 0 )
  1028.         return( 0 );
  1029.  
  1030.     if( i > j ) return(  1 );
  1031.     if( j > i ) return( -1 );
  1032.  
  1033.     for( ; i > 0; i-- )
  1034.     {
  1035.         if( X->p[i - 1] > Y->p[i - 1] ) return(  1 );
  1036.         if( X->p[i - 1] < Y->p[i - 1] ) return( -1 );
  1037.     }
  1038.  
  1039.     return( 0 );
  1040. }
  1041.  
  1042. /*
  1043.  * Compare signed values
  1044.  */
  1045. int mbedtls_mpi_cmp_mpi( const mbedtls_mpi *X, const mbedtls_mpi *Y )
  1046. {
  1047.     size_t i, j;
  1048.     MPI_VALIDATE_RET( X != NULL );
  1049.     MPI_VALIDATE_RET( Y != NULL );
  1050.  
  1051.     for( i = X->n; i > 0; i-- )
  1052.         if( X->p[i - 1] != 0 )
  1053.             break;
  1054.  
  1055.     for( j = Y->n; j > 0; j-- )
  1056.         if( Y->p[j - 1] != 0 )
  1057.             break;
  1058.  
  1059.     if( i == 0 && j == 0 )
  1060.         return( 0 );
  1061.  
  1062.     if( i > j ) return(  X->s );
  1063.     if( j > i ) return( -Y->s );
  1064.  
  1065.     if( X->s > 0 && Y->s < 0 ) return(  1 );
  1066.     if( Y->s > 0 && X->s < 0 ) return( -1 );
  1067.  
  1068.     for( ; i > 0; i-- )
  1069.     {
  1070.         if( X->p[i - 1] > Y->p[i - 1] ) return(  X->s );
  1071.         if( X->p[i - 1] < Y->p[i - 1] ) return( -X->s );
  1072.     }
  1073.  
  1074.     return( 0 );
  1075. }
  1076.  
  1077. /** Decide if an integer is less than the other, without branches.
  1078.  *
  1079.  * \param x         First integer.
  1080.  * \param y         Second integer.
  1081.  *
  1082.  * \return          1 if \p x is less than \p y, 0 otherwise
  1083.  */
  1084. static unsigned ct_lt_mpi_uint( const mbedtls_mpi_uint x,
  1085.         const mbedtls_mpi_uint y )
  1086. {
  1087.     mbedtls_mpi_uint ret;
  1088.     mbedtls_mpi_uint cond;
  1089.  
  1090.     /*
  1091.      * Check if the most significant bits (MSB) of the operands are different.
  1092.      */
  1093.     cond = ( x ^ y );
  1094.     /*
  1095.      * If the MSB are the same then the difference x-y will be negative (and
  1096.      * have its MSB set to 1 during conversion to unsigned) if and only if x<y.
  1097.      */
  1098.     ret = ( x - y ) & ~cond;
  1099.     /*
  1100.      * If the MSB are different, then the operand with the MSB of 1 is the
  1101.      * bigger. (That is if y has MSB of 1, then x<y is true and it is false if
  1102.      * the MSB of y is 0.)
  1103.      */
  1104.     ret |= y & cond;
  1105.  
  1106.  
  1107.     ret = ret >> ( biL - 1 );
  1108.  
  1109.     return (unsigned) ret;
  1110. }
  1111.  
  1112. /*
  1113.  * Compare signed values in constant time
  1114.  */
  1115. int mbedtls_mpi_lt_mpi_ct( const mbedtls_mpi *X, const mbedtls_mpi *Y,
  1116.         unsigned *ret )
  1117. {
  1118.     size_t i;
  1119.     /* The value of any of these variables is either 0 or 1 at all times. */
  1120.     unsigned cond, done, X_is_negative, Y_is_negative;
  1121.  
  1122.     MPI_VALIDATE_RET( X != NULL );
  1123.     MPI_VALIDATE_RET( Y != NULL );
  1124.     MPI_VALIDATE_RET( ret != NULL );
  1125.  
  1126.     if( X->n != Y->n )
  1127.         return MBEDTLS_ERR_MPI_BAD_INPUT_DATA;
  1128.  
  1129.     /*
  1130.      * Set sign_N to 1 if N >= 0, 0 if N < 0.
  1131.      * We know that N->s == 1 if N >= 0 and N->s == -1 if N < 0.
  1132.      */
  1133.     X_is_negative = ( X->s & 2 ) >> 1;
  1134.     Y_is_negative = ( Y->s & 2 ) >> 1;
  1135.  
  1136.     /*
  1137.      * If the signs are different, then the positive operand is the bigger.
  1138.      * That is if X is negative (X_is_negative == 1), then X < Y is true and it
  1139.      * is false if X is positive (X_is_negative == 0).
  1140.      */
  1141.     cond = ( X_is_negative ^ Y_is_negative );
  1142.     *ret = cond & X_is_negative;
  1143.  
  1144.     /*
  1145.      * This is a constant-time function. We might have the result, but we still
  1146.      * need to go through the loop. Record if we have the result already.
  1147.      */
  1148.     done = cond;
  1149.  
  1150.     for( i = X->n; i > 0; i-- )
  1151.     {
  1152.         /*
  1153.          * If Y->p[i - 1] < X->p[i - 1] then X < Y is true if and only if both
  1154.          * X and Y are negative.
  1155.          *
  1156.          * Again even if we can make a decision, we just mark the result and
  1157.          * the fact that we are done and continue looping.
  1158.          */
  1159.         cond = ct_lt_mpi_uint( Y->p[i - 1], X->p[i - 1] );
  1160.         *ret |= cond & ( 1 - done ) & X_is_negative;
  1161.         done |= cond;
  1162.  
  1163.         /*
  1164.          * If X->p[i - 1] < Y->p[i - 1] then X < Y is true if and only if both
  1165.          * X and Y are positive.
  1166.          *
  1167.          * Again even if we can make a decision, we just mark the result and
  1168.          * the fact that we are done and continue looping.
  1169.          */
  1170.         cond = ct_lt_mpi_uint( X->p[i - 1], Y->p[i - 1] );
  1171.         *ret |= cond & ( 1 - done ) & ( 1 - X_is_negative );
  1172.         done |= cond;
  1173.     }
  1174.  
  1175.     return( 0 );
  1176. }
  1177.  
  1178. /*
  1179.  * Compare signed values
  1180.  */
  1181. int mbedtls_mpi_cmp_int( const mbedtls_mpi *X, mbedtls_mpi_sint z )
  1182. {
  1183.     mbedtls_mpi Y;
  1184.     mbedtls_mpi_uint p[1];
  1185.     MPI_VALIDATE_RET( X != NULL );
  1186.  
  1187.     *p  = ( z < 0 ) ? -z : z;
  1188.     Y.s = ( z < 0 ) ? -1 : 1;
  1189.     Y.n = 1;
  1190.     Y.p = p;
  1191.  
  1192.     return( mbedtls_mpi_cmp_mpi( X, &Y ) );
  1193. }
  1194.  
  1195. /*
  1196.  * Unsigned addition: X = |A| + |B|  (HAC 14.7)
  1197.  */
  1198. int mbedtls_mpi_add_abs( mbedtls_mpi *X, const mbedtls_mpi *A, const mbedtls_mpi *B )
  1199. {
  1200.     int ret;
  1201.     size_t i, j;
  1202.     mbedtls_mpi_uint *o, *p, c, tmp;
  1203.     MPI_VALIDATE_RET( X != NULL );
  1204.     MPI_VALIDATE_RET( A != NULL );
  1205.     MPI_VALIDATE_RET( B != NULL );
  1206.  
  1207.     if( X == B )
  1208.     {
  1209.         const mbedtls_mpi *T = A; A = X; B = T;
  1210.     }
  1211.  
  1212.     if( X != A )
  1213.         MBEDTLS_MPI_CHK( mbedtls_mpi_copy( X, A ) );
  1214.  
  1215.     /*
  1216.      * X should always be positive as a result of unsigned additions.
  1217.      */
  1218.     X->s = 1;
  1219.  
  1220.     for( j = B->n; j > 0; j-- )
  1221.         if( B->p[j - 1] != 0 )
  1222.             break;
  1223.  
  1224.     MBEDTLS_MPI_CHK( mbedtls_mpi_grow( X, j ) );
  1225.  
  1226.     o = B->p; p = X->p; c = 0;
  1227.  
  1228.     /*
  1229.      * tmp is used because it might happen that p == o
  1230.      */
  1231.     for( i = 0; i < j; i++, o++, p++ )
  1232.     {
  1233.         tmp= *o;
  1234.         *p +=  c; c  = ( *p <  c );
  1235.         *p += tmp; c += ( *p < tmp );
  1236.     }
  1237.  
  1238.     while( c != 0 )
  1239.     {
  1240.         if( i >= X->n )
  1241.         {
  1242.             MBEDTLS_MPI_CHK( mbedtls_mpi_grow( X, i + 1 ) );
  1243.             p = X->p + i;
  1244.         }
  1245.  
  1246.         *p += c; c = ( *p < c ); i++; p++;
  1247.     }
  1248.  
  1249. cleanup:
  1250.  
  1251.     return( ret );
  1252. }
  1253.  
  1254. /*
  1255.  * Helper for mbedtls_mpi subtraction
  1256.  */
  1257. static void mpi_sub_hlp( size_t n, mbedtls_mpi_uint *s, mbedtls_mpi_uint *d )
  1258. {
  1259.     size_t i;
  1260.     mbedtls_mpi_uint c, z;
  1261.  
  1262.     for( i = c = 0; i < n; i++, s++, d++ )
  1263.     {
  1264.         z = ( *d <  c );     *d -=  c;
  1265.         c = ( *d < *s ) + z; *d -= *s;
  1266.     }
  1267.  
  1268.     while( c != 0 )
  1269.     {
  1270.         z = ( *d < c ); *d -= c;
  1271.         c = z; d++;
  1272.     }
  1273. }
  1274.  
  1275. /*
  1276.  * Unsigned subtraction: X = |A| - |B|  (HAC 14.9)
  1277.  */
  1278. int mbedtls_mpi_sub_abs( mbedtls_mpi *X, const mbedtls_mpi *A, const mbedtls_mpi *B )
  1279. {
  1280.     mbedtls_mpi TB;
  1281.     int ret;
  1282.     size_t n;
  1283.     MPI_VALIDATE_RET( X != NULL );
  1284.     MPI_VALIDATE_RET( A != NULL );
  1285.     MPI_VALIDATE_RET( B != NULL );
  1286.  
  1287.     if( mbedtls_mpi_cmp_abs( A, B ) < 0 )
  1288.         return( MBEDTLS_ERR_MPI_NEGATIVE_VALUE );
  1289.  
  1290.     mbedtls_mpi_init( &TB );
  1291.  
  1292.     if( X == B )
  1293.     {
  1294.         MBEDTLS_MPI_CHK( mbedtls_mpi_copy( &TB, B ) );
  1295.         B = &TB;
  1296.     }
  1297.  
  1298.     if( X != A )
  1299.         MBEDTLS_MPI_CHK( mbedtls_mpi_copy( X, A ) );
  1300.  
  1301.     /*
  1302.      * X should always be positive as a result of unsigned subtractions.
  1303.      */
  1304.     X->s = 1;
  1305.  
  1306.     ret = 0;
  1307.  
  1308.     for( n = B->n; n > 0; n-- )
  1309.         if( B->p[n - 1] != 0 )
  1310.             break;
  1311.  
  1312.     mpi_sub_hlp( n, B->p, X->p );
  1313.  
  1314. cleanup:
  1315.  
  1316.     mbedtls_mpi_free( &TB );
  1317.  
  1318.     return( ret );
  1319. }
  1320.  
  1321. /*
  1322.  * Signed addition: X = A + B
  1323.  */
  1324. int mbedtls_mpi_add_mpi( mbedtls_mpi *X, const mbedtls_mpi *A, const mbedtls_mpi *B )
  1325. {
  1326.     int ret, s;
  1327.     MPI_VALIDATE_RET( X != NULL );
  1328.     MPI_VALIDATE_RET( A != NULL );
  1329.     MPI_VALIDATE_RET( B != NULL );
  1330.  
  1331.     s = A->s;
  1332.     if( A->s * B->s < 0 )
  1333.     {
  1334.         if( mbedtls_mpi_cmp_abs( A, B ) >= 0 )
  1335.         {
  1336.             MBEDTLS_MPI_CHK( mbedtls_mpi_sub_abs( X, A, B ) );
  1337.             X->s =  s;
  1338.         }
  1339.         else
  1340.         {
  1341.             MBEDTLS_MPI_CHK( mbedtls_mpi_sub_abs( X, B, A ) );
  1342.             X->s = -s;
  1343.         }
  1344.     }
  1345.     else
  1346.     {
  1347.         MBEDTLS_MPI_CHK( mbedtls_mpi_add_abs( X, A, B ) );
  1348.         X->s = s;
  1349.     }
  1350.  
  1351. cleanup:
  1352.  
  1353.     return( ret );
  1354. }
  1355.  
  1356. /*
  1357.  * Signed subtraction: X = A - B
  1358.  */
  1359. int mbedtls_mpi_sub_mpi( mbedtls_mpi *X, const mbedtls_mpi *A, const mbedtls_mpi *B )
  1360. {
  1361.     int ret, s;
  1362.     MPI_VALIDATE_RET( X != NULL );
  1363.     MPI_VALIDATE_RET( A != NULL );
  1364.     MPI_VALIDATE_RET( B != NULL );
  1365.  
  1366.     s = A->s;
  1367.     if( A->s * B->s > 0 )
  1368.     {
  1369.         if( mbedtls_mpi_cmp_abs( A, B ) >= 0 )
  1370.         {
  1371.             MBEDTLS_MPI_CHK( mbedtls_mpi_sub_abs( X, A, B ) );
  1372.             X->s =  s;
  1373.         }
  1374.         else
  1375.         {
  1376.             MBEDTLS_MPI_CHK( mbedtls_mpi_sub_abs( X, B, A ) );
  1377.             X->s = -s;
  1378.         }
  1379.     }
  1380.     else
  1381.     {
  1382.         MBEDTLS_MPI_CHK( mbedtls_mpi_add_abs( X, A, B ) );
  1383.         X->s = s;
  1384.     }
  1385.  
  1386. cleanup:
  1387.  
  1388.     return( ret );
  1389. }
  1390.  
  1391. /*
  1392.  * Signed addition: X = A + b
  1393.  */
  1394. int mbedtls_mpi_add_int( mbedtls_mpi *X, const mbedtls_mpi *A, mbedtls_mpi_sint b )
  1395. {
  1396.     mbedtls_mpi _B;
  1397.     mbedtls_mpi_uint p[1];
  1398.     MPI_VALIDATE_RET( X != NULL );
  1399.     MPI_VALIDATE_RET( A != NULL );
  1400.  
  1401.     p[0] = ( b < 0 ) ? -b : b;
  1402.     _B.s = ( b < 0 ) ? -1 : 1;
  1403.     _B.n = 1;
  1404.     _B.p = p;
  1405.  
  1406.     return( mbedtls_mpi_add_mpi( X, A, &_B ) );
  1407. }
  1408.  
  1409. /*
  1410.  * Signed subtraction: X = A - b
  1411.  */
  1412. int mbedtls_mpi_sub_int( mbedtls_mpi *X, const mbedtls_mpi *A, mbedtls_mpi_sint b )
  1413. {
  1414.     mbedtls_mpi _B;
  1415.     mbedtls_mpi_uint p[1];
  1416.     MPI_VALIDATE_RET( X != NULL );
  1417.     MPI_VALIDATE_RET( A != NULL );
  1418.  
  1419.     p[0] = ( b < 0 ) ? -b : b;
  1420.     _B.s = ( b < 0 ) ? -1 : 1;
  1421.     _B.n = 1;
  1422.     _B.p = p;
  1423.  
  1424.     return( mbedtls_mpi_sub_mpi( X, A, &_B ) );
  1425. }
  1426.  
  1427. /*
  1428.  * Helper for mbedtls_mpi multiplication
  1429.  */
  1430. static
  1431. #if defined(__APPLE__) && defined(__arm__)
  1432. /*
  1433.  * Apple LLVM version 4.2 (clang-425.0.24) (based on LLVM 3.2svn)
  1434.  * appears to need this to prevent bad ARM code generation at -O3.
  1435.  */
  1436. __attribute__ ((noinline))
  1437. #endif
  1438. void mpi_mul_hlp( size_t i, mbedtls_mpi_uint *s, mbedtls_mpi_uint *d, mbedtls_mpi_uint b )
  1439. {
  1440.     mbedtls_mpi_uint c = 0, t = 0;
  1441.  
  1442. #if defined(MULADDC_HUIT)
  1443.     for( ; i >= 8; i -= 8 )
  1444.     {
  1445.         MULADDC_INIT
  1446.         MULADDC_HUIT
  1447.         MULADDC_STOP
  1448.     }
  1449.  
  1450.     for( ; i > 0; i-- )
  1451.     {
  1452.         MULADDC_INIT
  1453.         MULADDC_CORE
  1454.         MULADDC_STOP
  1455.     }
  1456. #else /* MULADDC_HUIT */
  1457.     for( ; i >= 16; i -= 16 )
  1458.     {
  1459.         MULADDC_INIT
  1460.         MULADDC_CORE   MULADDC_CORE
  1461.         MULADDC_CORE   MULADDC_CORE
  1462.         MULADDC_CORE   MULADDC_CORE
  1463.         MULADDC_CORE   MULADDC_CORE
  1464.  
  1465.         MULADDC_CORE   MULADDC_CORE
  1466.         MULADDC_CORE   MULADDC_CORE
  1467.         MULADDC_CORE   MULADDC_CORE
  1468.         MULADDC_CORE   MULADDC_CORE
  1469.         MULADDC_STOP
  1470.     }
  1471.  
  1472.     for( ; i >= 8; i -= 8 )
  1473.     {
  1474.         MULADDC_INIT
  1475.         MULADDC_CORE   MULADDC_CORE
  1476.         MULADDC_CORE   MULADDC_CORE
  1477.  
  1478.         MULADDC_CORE   MULADDC_CORE
  1479.         MULADDC_CORE   MULADDC_CORE
  1480.         MULADDC_STOP
  1481.     }
  1482.  
  1483.     for( ; i > 0; i-- )
  1484.     {
  1485.         MULADDC_INIT
  1486.         MULADDC_CORE
  1487.         MULADDC_STOP
  1488.     }
  1489. #endif /* MULADDC_HUIT */
  1490.  
  1491.     t++;
  1492.  
  1493.     do {
  1494.         *d += c; c = ( *d < c ); d++;
  1495.     }
  1496.     while( c != 0 );
  1497. }
  1498.  
  1499. /*
  1500.  * Baseline multiplication: X = A * B  (HAC 14.12)
  1501.  */
  1502. int mbedtls_mpi_mul_mpi( mbedtls_mpi *X, const mbedtls_mpi *A, const mbedtls_mpi *B )
  1503. {
  1504.     int ret;
  1505.     size_t i, j;
  1506.     mbedtls_mpi TA, TB;
  1507.     MPI_VALIDATE_RET( X != NULL );
  1508.     MPI_VALIDATE_RET( A != NULL );
  1509.     MPI_VALIDATE_RET( B != NULL );
  1510.  
  1511.     mbedtls_mpi_init( &TA ); mbedtls_mpi_init( &TB );
  1512.  
  1513.     if( X == A ) { MBEDTLS_MPI_CHK( mbedtls_mpi_copy( &TA, A ) ); A = &TA; }
  1514.     if( X == B ) { MBEDTLS_MPI_CHK( mbedtls_mpi_copy( &TB, B ) ); B = &TB; }
  1515.  
  1516.     for( i = A->n; i > 0; i-- )
  1517.         if( A->p[i - 1] != 0 )
  1518.             break;
  1519.  
  1520.     for( j = B->n; j > 0; j-- )
  1521.         if( B->p[j - 1] != 0 )
  1522.             break;
  1523.  
  1524.     MBEDTLS_MPI_CHK( mbedtls_mpi_grow( X, i + j ) );
  1525.     MBEDTLS_MPI_CHK( mbedtls_mpi_lset( X, 0 ) );
  1526.  
  1527.     for( ; j > 0; j-- )
  1528.         mpi_mul_hlp( i, A->p, X->p + j - 1, B->p[j - 1] );
  1529.  
  1530.     X->s = A->s * B->s;
  1531.  
  1532. cleanup:
  1533.  
  1534.     mbedtls_mpi_free( &TB ); mbedtls_mpi_free( &TA );
  1535.  
  1536.     return( ret );
  1537. }
  1538.  
  1539. /*
  1540.  * Baseline multiplication: X = A * b
  1541.  */
  1542. int mbedtls_mpi_mul_int( mbedtls_mpi *X, const mbedtls_mpi *A, mbedtls_mpi_uint b )
  1543. {
  1544.     mbedtls_mpi _B;
  1545.     mbedtls_mpi_uint p[1];
  1546.     MPI_VALIDATE_RET( X != NULL );
  1547.     MPI_VALIDATE_RET( A != NULL );
  1548.  
  1549.     _B.s = 1;
  1550.     _B.n = 1;
  1551.     _B.p = p;
  1552.     p[0] = b;
  1553.  
  1554.     return( mbedtls_mpi_mul_mpi( X, A, &_B ) );
  1555. }
  1556.  
  1557. /*
  1558.  * Unsigned integer divide - double mbedtls_mpi_uint dividend, u1/u0, and
  1559.  * mbedtls_mpi_uint divisor, d
  1560.  */
  1561. static mbedtls_mpi_uint mbedtls_int_div_int( mbedtls_mpi_uint u1,
  1562.             mbedtls_mpi_uint u0, mbedtls_mpi_uint d, mbedtls_mpi_uint *r )
  1563. {
  1564. #if defined(MBEDTLS_HAVE_UDBL)
  1565.     mbedtls_t_udbl dividend, quotient;
  1566. #else
  1567.     const mbedtls_mpi_uint radix = (mbedtls_mpi_uint) 1 << biH;
  1568.     const mbedtls_mpi_uint uint_halfword_mask = ( (mbedtls_mpi_uint) 1 << biH ) - 1;
  1569.     mbedtls_mpi_uint d0, d1, q0, q1, rAX, r0, quotient;
  1570.     mbedtls_mpi_uint u0_msw, u0_lsw;
  1571.     size_t s;
  1572. #endif
  1573.  
  1574.     /*
  1575.      * Check for overflow
  1576.      */
  1577.     if( 0 == d || u1 >= d )
  1578.     {
  1579.         if (r != NULL) *r = ~0;
  1580.  
  1581.         return ( ~0 );
  1582.     }
  1583.  
  1584. #if defined(MBEDTLS_HAVE_UDBL)
  1585.     dividend  = (mbedtls_t_udbl) u1 << biL;
  1586.     dividend |= (mbedtls_t_udbl) u0;
  1587.     quotient = dividend / d;
  1588.     if( quotient > ( (mbedtls_t_udbl) 1 << biL ) - 1 )
  1589.         quotient = ( (mbedtls_t_udbl) 1 << biL ) - 1;
  1590.  
  1591.     if( r != NULL )
  1592.         *r = (mbedtls_mpi_uint)( dividend - (quotient * d ) );
  1593.  
  1594.     return (mbedtls_mpi_uint) quotient;
  1595. #else
  1596.  
  1597.     /*
  1598.      * Algorithm D, Section 4.3.1 - The Art of Computer Programming
  1599.      *   Vol. 2 - Seminumerical Algorithms, Knuth
  1600.      */
  1601.  
  1602.     /*
  1603.      * Normalize the divisor, d, and dividend, u0, u1
  1604.      */
  1605.     s = mbedtls_clz( d );
  1606.     d = d << s;
  1607.  
  1608.     u1 = u1 << s;
  1609.     u1 |= ( u0 >> ( biL - s ) ) & ( -(mbedtls_mpi_sint)s >> ( biL - 1 ) );
  1610.     u0 =  u0 << s;
  1611.  
  1612.     d1 = d >> biH;
  1613.     d0 = d & uint_halfword_mask;
  1614.  
  1615.     u0_msw = u0 >> biH;
  1616.     u0_lsw = u0 & uint_halfword_mask;
  1617.  
  1618.     /*
  1619.      * Find the first quotient and remainder
  1620.      */
  1621.     q1 = u1 / d1;
  1622.     r0 = u1 - d1 * q1;
  1623.  
  1624.     while( q1 >= radix || ( q1 * d0 > radix * r0 + u0_msw ) )
  1625.     {
  1626.         q1 -= 1;
  1627.         r0 += d1;
  1628.  
  1629.         if ( r0 >= radix ) break;
  1630.     }
  1631.  
  1632.     rAX = ( u1 * radix ) + ( u0_msw - q1 * d );
  1633.     q0 = rAX / d1;
  1634.     r0 = rAX - q0 * d1;
  1635.  
  1636.     while( q0 >= radix || ( q0 * d0 > radix * r0 + u0_lsw ) )
  1637.     {
  1638.         q0 -= 1;
  1639.         r0 += d1;
  1640.  
  1641.         if ( r0 >= radix ) break;
  1642.     }
  1643.  
  1644.     if (r != NULL)
  1645.         *r = ( rAX * radix + u0_lsw - q0 * d ) >> s;
  1646.  
  1647.     quotient = q1 * radix + q0;
  1648.  
  1649.     return quotient;
  1650. #endif
  1651. }
  1652.  
  1653. /*
  1654.  * Division by mbedtls_mpi: A = Q * B + R  (HAC 14.20)
  1655.  */
  1656. int mbedtls_mpi_div_mpi( mbedtls_mpi *Q, mbedtls_mpi *R, const mbedtls_mpi *A,
  1657.                          const mbedtls_mpi *B )
  1658. {
  1659.     int ret;
  1660.     size_t i, n, t, k;
  1661.     mbedtls_mpi X, Y, Z, T1, T2;
  1662.     MPI_VALIDATE_RET( A != NULL );
  1663.     MPI_VALIDATE_RET( B != NULL );
  1664.  
  1665.     if( mbedtls_mpi_cmp_int( B, 0 ) == 0 )
  1666.         return( MBEDTLS_ERR_MPI_DIVISION_BY_ZERO );
  1667.  
  1668.     mbedtls_mpi_init( &X ); mbedtls_mpi_init( &Y ); mbedtls_mpi_init( &Z );
  1669.     mbedtls_mpi_init( &T1 ); mbedtls_mpi_init( &T2 );
  1670.  
  1671.     if( mbedtls_mpi_cmp_abs( A, B ) < 0 )
  1672.     {
  1673.         if( Q != NULL ) MBEDTLS_MPI_CHK( mbedtls_mpi_lset( Q, 0 ) );
  1674.         if( R != NULL ) MBEDTLS_MPI_CHK( mbedtls_mpi_copy( R, A ) );
  1675.         return( 0 );
  1676.     }
  1677.  
  1678.     MBEDTLS_MPI_CHK( mbedtls_mpi_copy( &X, A ) );
  1679.     MBEDTLS_MPI_CHK( mbedtls_mpi_copy( &Y, B ) );
  1680.     X.s = Y.s = 1;
  1681.  
  1682.     MBEDTLS_MPI_CHK( mbedtls_mpi_grow( &Z, A->n + 2 ) );
  1683.     MBEDTLS_MPI_CHK( mbedtls_mpi_lset( &Z,  0 ) );
  1684.     MBEDTLS_MPI_CHK( mbedtls_mpi_grow( &T1, 2 ) );
  1685.     MBEDTLS_MPI_CHK( mbedtls_mpi_grow( &T2, 3 ) );
  1686.  
  1687.     k = mbedtls_mpi_bitlen( &Y ) % biL;
  1688.     if( k < biL - 1 )
  1689.     {
  1690.         k = biL - 1 - k;
  1691.         MBEDTLS_MPI_CHK( mbedtls_mpi_shift_l( &X, k ) );
  1692.         MBEDTLS_MPI_CHK( mbedtls_mpi_shift_l( &Y, k ) );
  1693.     }
  1694.     else k = 0;
  1695.  
  1696.     n = X.n - 1;
  1697.     t = Y.n - 1;
  1698.     MBEDTLS_MPI_CHK( mbedtls_mpi_shift_l( &Y, biL * ( n - t ) ) );
  1699.  
  1700.     while( mbedtls_mpi_cmp_mpi( &X, &Y ) >= 0 )
  1701.     {
  1702.         Z.p[n - t]++;
  1703.         MBEDTLS_MPI_CHK( mbedtls_mpi_sub_mpi( &X, &X, &Y ) );
  1704.     }
  1705.     MBEDTLS_MPI_CHK( mbedtls_mpi_shift_r( &Y, biL * ( n - t ) ) );
  1706.  
  1707.     for( i = n; i > t ; i-- )
  1708.     {
  1709.         if( X.p[i] >= Y.p[t] )
  1710.             Z.p[i - t - 1] = ~0;
  1711.         else
  1712.         {
  1713.             Z.p[i - t - 1] = mbedtls_int_div_int( X.p[i], X.p[i - 1],
  1714.                                                             Y.p[t], NULL);
  1715.         }
  1716.  
  1717.         Z.p[i - t - 1]++;
  1718.         do
  1719.         {
  1720.             Z.p[i - t - 1]--;
  1721.  
  1722.             MBEDTLS_MPI_CHK( mbedtls_mpi_lset( &T1, 0 ) );
  1723.             T1.p[0] = ( t < 1 ) ? 0 : Y.p[t - 1];
  1724.             T1.p[1] = Y.p[t];
  1725.             MBEDTLS_MPI_CHK( mbedtls_mpi_mul_int( &T1, &T1, Z.p[i - t - 1] ) );
  1726.  
  1727.             MBEDTLS_MPI_CHK( mbedtls_mpi_lset( &T2, 0 ) );
  1728.             T2.p[0] = ( i < 2 ) ? 0 : X.p[i - 2];
  1729.             T2.p[1] = ( i < 1 ) ? 0 : X.p[i - 1];
  1730.             T2.p[2] = X.p[i];
  1731.         }
  1732.         while( mbedtls_mpi_cmp_mpi( &T1, &T2 ) > 0 );
  1733.  
  1734.         MBEDTLS_MPI_CHK( mbedtls_mpi_mul_int( &T1, &Y, Z.p[i - t - 1] ) );
  1735.         MBEDTLS_MPI_CHK( mbedtls_mpi_shift_l( &T1,  biL * ( i - t - 1 ) ) );
  1736.         MBEDTLS_MPI_CHK( mbedtls_mpi_sub_mpi( &X, &X, &T1 ) );
  1737.  
  1738.         if( mbedtls_mpi_cmp_int( &X, 0 ) < 0 )
  1739.         {
  1740.             MBEDTLS_MPI_CHK( mbedtls_mpi_copy( &T1, &Y ) );
  1741.             MBEDTLS_MPI_CHK( mbedtls_mpi_shift_l( &T1, biL * ( i - t - 1 ) ) );
  1742.             MBEDTLS_MPI_CHK( mbedtls_mpi_add_mpi( &X, &X, &T1 ) );
  1743.             Z.p[i - t - 1]--;
  1744.         }
  1745.     }
  1746.  
  1747.     if( Q != NULL )
  1748.     {
  1749.         MBEDTLS_MPI_CHK( mbedtls_mpi_copy( Q, &Z ) );
  1750.         Q->s = A->s * B->s;
  1751.     }
  1752.  
  1753.     if( R != NULL )
  1754.     {
  1755.         MBEDTLS_MPI_CHK( mbedtls_mpi_shift_r( &X, k ) );
  1756.         X.s = A->s;
  1757.         MBEDTLS_MPI_CHK( mbedtls_mpi_copy( R, &X ) );
  1758.  
  1759.         if( mbedtls_mpi_cmp_int( R, 0 ) == 0 )
  1760.             R->s = 1;
  1761.     }
  1762.  
  1763. cleanup:
  1764.  
  1765.     mbedtls_mpi_free( &X ); mbedtls_mpi_free( &Y ); mbedtls_mpi_free( &Z );
  1766.     mbedtls_mpi_free( &T1 ); mbedtls_mpi_free( &T2 );
  1767.  
  1768.     return( ret );
  1769. }
  1770.  
  1771. /*
  1772.  * Division by int: A = Q * b + R
  1773.  */
  1774. int mbedtls_mpi_div_int( mbedtls_mpi *Q, mbedtls_mpi *R,
  1775.                          const mbedtls_mpi *A,
  1776.                          mbedtls_mpi_sint b )
  1777. {
  1778.     mbedtls_mpi _B;
  1779.     mbedtls_mpi_uint p[1];
  1780.     MPI_VALIDATE_RET( A != NULL );
  1781.  
  1782.     p[0] = ( b < 0 ) ? -b : b;
  1783.     _B.s = ( b < 0 ) ? -1 : 1;
  1784.     _B.n = 1;
  1785.     _B.p = p;
  1786.  
  1787.     return( mbedtls_mpi_div_mpi( Q, R, A, &_B ) );
  1788. }
  1789.  
  1790. /*
  1791.  * Modulo: R = A mod B
  1792.  */
  1793. int mbedtls_mpi_mod_mpi( mbedtls_mpi *R, const mbedtls_mpi *A, const mbedtls_mpi *B )
  1794. {
  1795.     int ret;
  1796.     MPI_VALIDATE_RET( R != NULL );
  1797.     MPI_VALIDATE_RET( A != NULL );
  1798.     MPI_VALIDATE_RET( B != NULL );
  1799.  
  1800.     if( mbedtls_mpi_cmp_int( B, 0 ) < 0 )
  1801.         return( MBEDTLS_ERR_MPI_NEGATIVE_VALUE );
  1802.  
  1803.     MBEDTLS_MPI_CHK( mbedtls_mpi_div_mpi( NULL, R, A, B ) );
  1804.  
  1805.     while( mbedtls_mpi_cmp_int( R, 0 ) < 0 )
  1806.       MBEDTLS_MPI_CHK( mbedtls_mpi_add_mpi( R, R, B ) );
  1807.  
  1808.     while( mbedtls_mpi_cmp_mpi( R, B ) >= 0 )
  1809.       MBEDTLS_MPI_CHK( mbedtls_mpi_sub_mpi( R, R, B ) );
  1810.  
  1811. cleanup:
  1812.  
  1813.     return( ret );
  1814. }
  1815.  
  1816. /*
  1817.  * Modulo: r = A mod b
  1818.  */
  1819. int mbedtls_mpi_mod_int( mbedtls_mpi_uint *r, const mbedtls_mpi *A, mbedtls_mpi_sint b )
  1820. {
  1821.     size_t i;
  1822.     mbedtls_mpi_uint x, y, z;
  1823.     MPI_VALIDATE_RET( r != NULL );
  1824.     MPI_VALIDATE_RET( A != NULL );
  1825.  
  1826.     if( b == 0 )
  1827.         return( MBEDTLS_ERR_MPI_DIVISION_BY_ZERO );
  1828.  
  1829.     if( b < 0 )
  1830.         return( MBEDTLS_ERR_MPI_NEGATIVE_VALUE );
  1831.  
  1832.     /*
  1833.      * handle trivial cases
  1834.      */
  1835.     if( b == 1 )
  1836.     {
  1837.         *r = 0;
  1838.         return( 0 );
  1839.     }
  1840.  
  1841.     if( b == 2 )
  1842.     {
  1843.         *r = A->p[0] & 1;
  1844.         return( 0 );
  1845.     }
  1846.  
  1847.     /*
  1848.      * general case
  1849.      */
  1850.     for( i = A->n, y = 0; i > 0; i-- )
  1851.     {
  1852.         x  = A->p[i - 1];
  1853.         y  = ( y << biH ) | ( x >> biH );
  1854.         z  = y / b;
  1855.         y -= z * b;
  1856.  
  1857.         x <<= biH;
  1858.         y  = ( y << biH ) | ( x >> biH );
  1859.         z  = y / b;
  1860.         y -= z * b;
  1861.     }
  1862.  
  1863.     /*
  1864.      * If A is negative, then the current y represents a negative value.
  1865.      * Flipping it to the positive side.
  1866.      */
  1867.     if( A->s < 0 && y != 0 )
  1868.         y = b - y;
  1869.  
  1870.     *r = y;
  1871.  
  1872.     return( 0 );
  1873. }
  1874.  
  1875. /*
  1876.  * Fast Montgomery initialization (thanks to Tom St Denis)
  1877.  */
  1878. static void mpi_montg_init( mbedtls_mpi_uint *mm, const mbedtls_mpi *N )
  1879. {
  1880.     mbedtls_mpi_uint x, m0 = N->p[0];
  1881.     unsigned int i;
  1882.  
  1883.     x  = m0;
  1884.     x += ( ( m0 + 2 ) & 4 ) << 1;
  1885.  
  1886.     for( i = biL; i >= 8; i /= 2 )
  1887.         x *= ( 2 - ( m0 * x ) );
  1888.  
  1889.     *mm = ~x + 1;
  1890. }
  1891.  
  1892. /*
  1893.  * Montgomery multiplication: A = A * B * R^-1 mod N  (HAC 14.36)
  1894.  */
  1895. static int mpi_montmul( mbedtls_mpi *A, const mbedtls_mpi *B, const mbedtls_mpi *N, mbedtls_mpi_uint mm,
  1896.                          const mbedtls_mpi *T )
  1897. {
  1898.     size_t i, n, m;
  1899.     mbedtls_mpi_uint u0, u1, *d;
  1900.  
  1901.     if( T->n < N->n + 1 || T->p == NULL )
  1902.         return( MBEDTLS_ERR_MPI_BAD_INPUT_DATA );
  1903.  
  1904.     memset( T->p, 0, T->n * ciL );
  1905.  
  1906.     d = T->p;
  1907.     n = N->n;
  1908.     m = ( B->n < n ) ? B->n : n;
  1909.  
  1910.     for( i = 0; i < n; i++ )
  1911.     {
  1912.         /*
  1913.          * T = (T + u0*B + u1*N) / 2^biL
  1914.          */
  1915.         u0 = A->p[i];
  1916.         u1 = ( d[0] + u0 * B->p[0] ) * mm;
  1917.  
  1918.         mpi_mul_hlp( m, B->p, d, u0 );
  1919.         mpi_mul_hlp( n, N->p, d, u1 );
  1920.  
  1921.         *d++ = u0; d[n + 1] = 0;
  1922.     }
  1923.  
  1924.     memcpy( A->p, d, ( n + 1 ) * ciL );
  1925.  
  1926.     if( mbedtls_mpi_cmp_abs( A, N ) >= 0 )
  1927.         mpi_sub_hlp( n, N->p, A->p );
  1928.     else
  1929.         /* prevent timing attacks */
  1930.         mpi_sub_hlp( n, A->p, T->p );
  1931.  
  1932.     return( 0 );
  1933. }
  1934.  
  1935. /*
  1936.  * Montgomery reduction: A = A * R^-1 mod N
  1937.  */
  1938. static int mpi_montred( mbedtls_mpi *A, const mbedtls_mpi *N,
  1939.                         mbedtls_mpi_uint mm, const mbedtls_mpi *T )
  1940. {
  1941.     mbedtls_mpi_uint z = 1;
  1942.     mbedtls_mpi U;
  1943.  
  1944.     U.n = U.s = (int) z;
  1945.     U.p = &z;
  1946.  
  1947.     return( mpi_montmul( A, &U, N, mm, T ) );
  1948. }
  1949.  
  1950. /*
  1951.  * Sliding-window exponentiation: X = A^E mod N  (HAC 14.85)
  1952.  */
  1953. int mbedtls_mpi_exp_mod( mbedtls_mpi *X, const mbedtls_mpi *A,
  1954.                          const mbedtls_mpi *E, const mbedtls_mpi *N,
  1955.                          mbedtls_mpi *_RR )
  1956. {
  1957.     int ret;
  1958.     size_t wbits, wsize, one = 1;
  1959.     size_t i, j, nblimbs;
  1960.     size_t bufsize, nbits;
  1961.     mbedtls_mpi_uint ei, mm, state;
  1962.     mbedtls_mpi RR, T, W[ 2 << MBEDTLS_MPI_WINDOW_SIZE ], Apos;
  1963.     int neg;
  1964.  
  1965.     MPI_VALIDATE_RET( X != NULL );
  1966.     MPI_VALIDATE_RET( A != NULL );
  1967.     MPI_VALIDATE_RET( E != NULL );
  1968.     MPI_VALIDATE_RET( N != NULL );
  1969.  
  1970.     if( mbedtls_mpi_cmp_int( N, 0 ) <= 0 || ( N->p[0] & 1 ) == 0 )
  1971.         return( MBEDTLS_ERR_MPI_BAD_INPUT_DATA );
  1972.  
  1973.     if( mbedtls_mpi_cmp_int( E, 0 ) < 0 )
  1974.         return( MBEDTLS_ERR_MPI_BAD_INPUT_DATA );
  1975.  
  1976.     /*
  1977.      * Init temps and window size
  1978.      */
  1979.     mpi_montg_init( &mm, N );
  1980.     mbedtls_mpi_init( &RR ); mbedtls_mpi_init( &T );
  1981.     mbedtls_mpi_init( &Apos );
  1982.     memset( W, 0, sizeof( W ) );
  1983.  
  1984.     i = mbedtls_mpi_bitlen( E );
  1985.  
  1986.     wsize = ( i > 671 ) ? 6 : ( i > 239 ) ? 5 :
  1987.             ( i >  79 ) ? 4 : ( i >  23 ) ? 3 : 1;
  1988.  
  1989. #if( MBEDTLS_MPI_WINDOW_SIZE < 6 )
  1990.     if( wsize > MBEDTLS_MPI_WINDOW_SIZE )
  1991.         wsize = MBEDTLS_MPI_WINDOW_SIZE;
  1992. #endif
  1993.  
  1994.     j = N->n + 1;
  1995.     MBEDTLS_MPI_CHK( mbedtls_mpi_grow( X, j ) );
  1996.     MBEDTLS_MPI_CHK( mbedtls_mpi_grow( &W[1],  j ) );
  1997.     MBEDTLS_MPI_CHK( mbedtls_mpi_grow( &T, j * 2 ) );
  1998.  
  1999.     /*
  2000.      * Compensate for negative A (and correct at the end)
  2001.      */
  2002.     neg = ( A->s == -1 );
  2003.     if( neg )
  2004.     {
  2005.         MBEDTLS_MPI_CHK( mbedtls_mpi_copy( &Apos, A ) );
  2006.         Apos.s = 1;
  2007.         A = &Apos;
  2008.     }
  2009.  
  2010.     /*
  2011.      * If 1st call, pre-compute R^2 mod N
  2012.      */
  2013.     if( _RR == NULL || _RR->p == NULL )
  2014.     {
  2015.         MBEDTLS_MPI_CHK( mbedtls_mpi_lset( &RR, 1 ) );
  2016.         MBEDTLS_MPI_CHK( mbedtls_mpi_shift_l( &RR, N->n * 2 * biL ) );
  2017.         MBEDTLS_MPI_CHK( mbedtls_mpi_mod_mpi( &RR, &RR, N ) );
  2018.  
  2019.         if( _RR != NULL )
  2020.             memcpy( _RR, &RR, sizeof( mbedtls_mpi ) );
  2021.     }
  2022.     else
  2023.         memcpy( &RR, _RR, sizeof( mbedtls_mpi ) );
  2024.  
  2025.     /*
  2026.      * W[1] = A * R^2 * R^-1 mod N = A * R mod N
  2027.      */
  2028.     if( mbedtls_mpi_cmp_mpi( A, N ) >= 0 )
  2029.         MBEDTLS_MPI_CHK( mbedtls_mpi_mod_mpi( &W[1], A, N ) );
  2030.     else
  2031.         MBEDTLS_MPI_CHK( mbedtls_mpi_copy( &W[1], A ) );
  2032.  
  2033.     MBEDTLS_MPI_CHK( mpi_montmul( &W[1], &RR, N, mm, &T ) );
  2034.  
  2035.     /*
  2036.      * X = R^2 * R^-1 mod N = R mod N
  2037.      */
  2038.     MBEDTLS_MPI_CHK( mbedtls_mpi_copy( X, &RR ) );
  2039.     MBEDTLS_MPI_CHK( mpi_montred( X, N, mm, &T ) );
  2040.  
  2041.     if( wsize > 1 )
  2042.     {
  2043.         /*
  2044.          * W[1 << (wsize - 1)] = W[1] ^ (wsize - 1)
  2045.          */
  2046.         j =  one << ( wsize - 1 );
  2047.  
  2048.         MBEDTLS_MPI_CHK( mbedtls_mpi_grow( &W[j], N->n + 1 ) );
  2049.         MBEDTLS_MPI_CHK( mbedtls_mpi_copy( &W[j], &W[1]    ) );
  2050.  
  2051.         for( i = 0; i < wsize - 1; i++ )
  2052.             MBEDTLS_MPI_CHK( mpi_montmul( &W[j], &W[j], N, mm, &T ) );
  2053.  
  2054.         /*
  2055.          * W[i] = W[i - 1] * W[1]
  2056.          */
  2057.         for( i = j + 1; i < ( one << wsize ); i++ )
  2058.         {
  2059.             MBEDTLS_MPI_CHK( mbedtls_mpi_grow( &W[i], N->n + 1 ) );
  2060.             MBEDTLS_MPI_CHK( mbedtls_mpi_copy( &W[i], &W[i - 1] ) );
  2061.  
  2062.             MBEDTLS_MPI_CHK( mpi_montmul( &W[i], &W[1], N, mm, &T ) );
  2063.         }
  2064.     }
  2065.  
  2066.     nblimbs = E->n;
  2067.     bufsize = 0;
  2068.     nbits   = 0;
  2069.     wbits   = 0;
  2070.     state   = 0;
  2071.  
  2072.     while( 1 )
  2073.     {
  2074.         if( bufsize == 0 )
  2075.         {
  2076.             if( nblimbs == 0 )
  2077.                 break;
  2078.  
  2079.             nblimbs--;
  2080.  
  2081.             bufsize = sizeof( mbedtls_mpi_uint ) << 3;
  2082.         }
  2083.  
  2084.         bufsize--;
  2085.  
  2086.         ei = (E->p[nblimbs] >> bufsize) & 1;
  2087.  
  2088.         /*
  2089.          * skip leading 0s
  2090.          */
  2091.         if( ei == 0 && state == 0 )
  2092.             continue;
  2093.  
  2094.         if( ei == 0 && state == 1 )
  2095.         {
  2096.             /*
  2097.              * out of window, square X
  2098.              */
  2099.             MBEDTLS_MPI_CHK( mpi_montmul( X, X, N, mm, &T ) );
  2100.             continue;
  2101.         }
  2102.  
  2103.         /*
  2104.          * add ei to current window
  2105.          */
  2106.         state = 2;
  2107.  
  2108.         nbits++;
  2109.         wbits |= ( ei << ( wsize - nbits ) );
  2110.  
  2111.         if( nbits == wsize )
  2112.         {
  2113.             /*
  2114.              * X = X^wsize R^-1 mod N
  2115.              */
  2116.             for( i = 0; i < wsize; i++ )
  2117.                 MBEDTLS_MPI_CHK( mpi_montmul( X, X, N, mm, &T ) );
  2118.  
  2119.             /*
  2120.              * X = X * W[wbits] R^-1 mod N
  2121.              */
  2122.             MBEDTLS_MPI_CHK( mpi_montmul( X, &W[wbits], N, mm, &T ) );
  2123.  
  2124.             state--;
  2125.             nbits = 0;
  2126.             wbits = 0;
  2127.         }
  2128.     }
  2129.  
  2130.     /*
  2131.      * process the remaining bits
  2132.      */
  2133.     for( i = 0; i < nbits; i++ )
  2134.     {
  2135.         MBEDTLS_MPI_CHK( mpi_montmul( X, X, N, mm, &T ) );
  2136.  
  2137.         wbits <<= 1;
  2138.  
  2139.         if( ( wbits & ( one << wsize ) ) != 0 )
  2140.             MBEDTLS_MPI_CHK( mpi_montmul( X, &W[1], N, mm, &T ) );
  2141.     }
  2142.  
  2143.     /*
  2144.      * X = A^E * R * R^-1 mod N = A^E mod N
  2145.      */
  2146.     MBEDTLS_MPI_CHK( mpi_montred( X, N, mm, &T ) );
  2147.  
  2148.     if( neg && E->n != 0 && ( E->p[0] & 1 ) != 0 )
  2149.     {
  2150.         X->s = -1;
  2151.         MBEDTLS_MPI_CHK( mbedtls_mpi_add_mpi( X, N, X ) );
  2152.     }
  2153.  
  2154. cleanup:
  2155.  
  2156.     for( i = ( one << ( wsize - 1 ) ); i < ( one << wsize ); i++ )
  2157.         mbedtls_mpi_free( &W[i] );
  2158.  
  2159.     mbedtls_mpi_free( &W[1] ); mbedtls_mpi_free( &T ); mbedtls_mpi_free( &Apos );
  2160.  
  2161.     if( _RR == NULL || _RR->p == NULL )
  2162.         mbedtls_mpi_free( &RR );
  2163.  
  2164.     return( ret );
  2165. }
  2166.  
  2167. /*
  2168.  * Greatest common divisor: G = gcd(A, B)  (HAC 14.54)
  2169.  */
  2170. int mbedtls_mpi_gcd( mbedtls_mpi *G, const mbedtls_mpi *A, const mbedtls_mpi *B )
  2171. {
  2172.     int ret;
  2173.     size_t lz, lzt;
  2174.     mbedtls_mpi TG, TA, TB;
  2175.  
  2176.     MPI_VALIDATE_RET( G != NULL );
  2177.     MPI_VALIDATE_RET( A != NULL );
  2178.     MPI_VALIDATE_RET( B != NULL );
  2179.  
  2180.     mbedtls_mpi_init( &TG ); mbedtls_mpi_init( &TA ); mbedtls_mpi_init( &TB );
  2181.  
  2182.     MBEDTLS_MPI_CHK( mbedtls_mpi_copy( &TA, A ) );
  2183.     MBEDTLS_MPI_CHK( mbedtls_mpi_copy( &TB, B ) );
  2184.  
  2185.     lz = mbedtls_mpi_lsb( &TA );
  2186.     lzt = mbedtls_mpi_lsb( &TB );
  2187.  
  2188.     if( lzt < lz )
  2189.         lz = lzt;
  2190.  
  2191.     MBEDTLS_MPI_CHK( mbedtls_mpi_shift_r( &TA, lz ) );
  2192.     MBEDTLS_MPI_CHK( mbedtls_mpi_shift_r( &TB, lz ) );
  2193.  
  2194.     TA.s = TB.s = 1;
  2195.  
  2196.     while( mbedtls_mpi_cmp_int( &TA, 0 ) != 0 )
  2197.     {
  2198.         MBEDTLS_MPI_CHK( mbedtls_mpi_shift_r( &TA, mbedtls_mpi_lsb( &TA ) ) );
  2199.         MBEDTLS_MPI_CHK( mbedtls_mpi_shift_r( &TB, mbedtls_mpi_lsb( &TB ) ) );
  2200.  
  2201.         if( mbedtls_mpi_cmp_mpi( &TA, &TB ) >= 0 )
  2202.         {
  2203.             MBEDTLS_MPI_CHK( mbedtls_mpi_sub_abs( &TA, &TA, &TB ) );
  2204.             MBEDTLS_MPI_CHK( mbedtls_mpi_shift_r( &TA, 1 ) );
  2205.         }
  2206.         else
  2207.         {
  2208.             MBEDTLS_MPI_CHK( mbedtls_mpi_sub_abs( &TB, &TB, &TA ) );
  2209.             MBEDTLS_MPI_CHK( mbedtls_mpi_shift_r( &TB, 1 ) );
  2210.         }
  2211.     }
  2212.  
  2213.     MBEDTLS_MPI_CHK( mbedtls_mpi_shift_l( &TB, lz ) );
  2214.     MBEDTLS_MPI_CHK( mbedtls_mpi_copy( G, &TB ) );
  2215.  
  2216. cleanup:
  2217.  
  2218.     mbedtls_mpi_free( &TG ); mbedtls_mpi_free( &TA ); mbedtls_mpi_free( &TB );
  2219.  
  2220.     return( ret );
  2221. }
  2222.  
  2223. /*
  2224.  * Fill X with size bytes of random.
  2225.  *
  2226.  * Use a temporary bytes representation to make sure the result is the same
  2227.  * regardless of the platform endianness (useful when f_rng is actually
  2228.  * deterministic, eg for tests).
  2229.  */
  2230. int mbedtls_mpi_fill_random( mbedtls_mpi *X, size_t size,
  2231.                      int (*f_rng)(void *, unsigned char *, size_t),
  2232.                      void *p_rng )
  2233. {
  2234.     int ret;
  2235.     size_t const limbs = CHARS_TO_LIMBS( size );
  2236.     size_t const overhead = ( limbs * ciL ) - size;
  2237.     unsigned char *Xp;
  2238.  
  2239.     MPI_VALIDATE_RET( X     != NULL );
  2240.     MPI_VALIDATE_RET( f_rng != NULL );
  2241.  
  2242.     /* Ensure that target MPI has exactly the necessary number of limbs */
  2243.     if( X->n != limbs )
  2244.     {
  2245.         mbedtls_mpi_free( X );
  2246.         mbedtls_mpi_init( X );
  2247.         MBEDTLS_MPI_CHK( mbedtls_mpi_grow( X, limbs ) );
  2248.     }
  2249.     MBEDTLS_MPI_CHK( mbedtls_mpi_lset( X, 0 ) );
  2250.  
  2251.     Xp = (unsigned char*) X->p;
  2252.     f_rng( p_rng, Xp + overhead, size );
  2253.  
  2254.     mpi_bigendian_to_host( X->p, limbs );
  2255.  
  2256. cleanup:
  2257.     return( ret );
  2258. }
  2259.  
  2260. /*
  2261.  * Modular inverse: X = A^-1 mod N  (HAC 14.61 / 14.64)
  2262.  */
  2263. int mbedtls_mpi_inv_mod( mbedtls_mpi *X, const mbedtls_mpi *A, const mbedtls_mpi *N )
  2264. {
  2265.     int ret;
  2266.     mbedtls_mpi G, TA, TU, U1, U2, TB, TV, V1, V2;
  2267.     MPI_VALIDATE_RET( X != NULL );
  2268.     MPI_VALIDATE_RET( A != NULL );
  2269.     MPI_VALIDATE_RET( N != NULL );
  2270.  
  2271.     if( mbedtls_mpi_cmp_int( N, 1 ) <= 0 )
  2272.         return( MBEDTLS_ERR_MPI_BAD_INPUT_DATA );
  2273.  
  2274.     mbedtls_mpi_init( &TA ); mbedtls_mpi_init( &TU ); mbedtls_mpi_init( &U1 ); mbedtls_mpi_init( &U2 );
  2275.     mbedtls_mpi_init( &G ); mbedtls_mpi_init( &TB ); mbedtls_mpi_init( &TV );
  2276.     mbedtls_mpi_init( &V1 ); mbedtls_mpi_init( &V2 );
  2277.  
  2278.     MBEDTLS_MPI_CHK( mbedtls_mpi_gcd( &G, A, N ) );
  2279.  
  2280.     if( mbedtls_mpi_cmp_int( &G, 1 ) != 0 )
  2281.     {
  2282.         ret = MBEDTLS_ERR_MPI_NOT_ACCEPTABLE;
  2283.         goto cleanup;
  2284.     }
  2285.  
  2286.     MBEDTLS_MPI_CHK( mbedtls_mpi_mod_mpi( &TA, A, N ) );
  2287.     MBEDTLS_MPI_CHK( mbedtls_mpi_copy( &TU, &TA ) );
  2288.     MBEDTLS_MPI_CHK( mbedtls_mpi_copy( &TB, N ) );
  2289.     MBEDTLS_MPI_CHK( mbedtls_mpi_copy( &TV, N ) );
  2290.  
  2291.     MBEDTLS_MPI_CHK( mbedtls_mpi_lset( &U1, 1 ) );
  2292.     MBEDTLS_MPI_CHK( mbedtls_mpi_lset( &U2, 0 ) );
  2293.     MBEDTLS_MPI_CHK( mbedtls_mpi_lset( &V1, 0 ) );
  2294.     MBEDTLS_MPI_CHK( mbedtls_mpi_lset( &V2, 1 ) );
  2295.  
  2296.     do
  2297.     {
  2298.         while( ( TU.p[0] & 1 ) == 0 )
  2299.         {
  2300.             MBEDTLS_MPI_CHK( mbedtls_mpi_shift_r( &TU, 1 ) );
  2301.  
  2302.             if( ( U1.p[0] & 1 ) != 0 || ( U2.p[0] & 1 ) != 0 )
  2303.             {
  2304.                 MBEDTLS_MPI_CHK( mbedtls_mpi_add_mpi( &U1, &U1, &TB ) );
  2305.                 MBEDTLS_MPI_CHK( mbedtls_mpi_sub_mpi( &U2, &U2, &TA ) );
  2306.             }
  2307.  
  2308.             MBEDTLS_MPI_CHK( mbedtls_mpi_shift_r( &U1, 1 ) );
  2309.             MBEDTLS_MPI_CHK( mbedtls_mpi_shift_r( &U2, 1 ) );
  2310.         }
  2311.  
  2312.         while( ( TV.p[0] & 1 ) == 0 )
  2313.         {
  2314.             MBEDTLS_MPI_CHK( mbedtls_mpi_shift_r( &TV, 1 ) );
  2315.  
  2316.             if( ( V1.p[0] & 1 ) != 0 || ( V2.p[0] & 1 ) != 0 )
  2317.             {
  2318.                 MBEDTLS_MPI_CHK( mbedtls_mpi_add_mpi( &V1, &V1, &TB ) );
  2319.                 MBEDTLS_MPI_CHK( mbedtls_mpi_sub_mpi( &V2, &V2, &TA ) );
  2320.             }
  2321.  
  2322.             MBEDTLS_MPI_CHK( mbedtls_mpi_shift_r( &V1, 1 ) );
  2323.             MBEDTLS_MPI_CHK( mbedtls_mpi_shift_r( &V2, 1 ) );
  2324.         }
  2325.  
  2326.         if( mbedtls_mpi_cmp_mpi( &TU, &TV ) >= 0 )
  2327.         {
  2328.             MBEDTLS_MPI_CHK( mbedtls_mpi_sub_mpi( &TU, &TU, &TV ) );
  2329.             MBEDTLS_MPI_CHK( mbedtls_mpi_sub_mpi( &U1, &U1, &V1 ) );
  2330.             MBEDTLS_MPI_CHK( mbedtls_mpi_sub_mpi( &U2, &U2, &V2 ) );
  2331.         }
  2332.         else
  2333.         {
  2334.             MBEDTLS_MPI_CHK( mbedtls_mpi_sub_mpi( &TV, &TV, &TU ) );
  2335.             MBEDTLS_MPI_CHK( mbedtls_mpi_sub_mpi( &V1, &V1, &U1 ) );
  2336.             MBEDTLS_MPI_CHK( mbedtls_mpi_sub_mpi( &V2, &V2, &U2 ) );
  2337.         }
  2338.     }
  2339.     while( mbedtls_mpi_cmp_int( &TU, 0 ) != 0 );
  2340.  
  2341.     while( mbedtls_mpi_cmp_int( &V1, 0 ) < 0 )
  2342.         MBEDTLS_MPI_CHK( mbedtls_mpi_add_mpi( &V1, &V1, N ) );
  2343.  
  2344.     while( mbedtls_mpi_cmp_mpi( &V1, N ) >= 0 )
  2345.         MBEDTLS_MPI_CHK( mbedtls_mpi_sub_mpi( &V1, &V1, N ) );
  2346.  
  2347.     MBEDTLS_MPI_CHK( mbedtls_mpi_copy( X, &V1 ) );
  2348.  
  2349. cleanup:
  2350.  
  2351.     mbedtls_mpi_free( &TA ); mbedtls_mpi_free( &TU ); mbedtls_mpi_free( &U1 ); mbedtls_mpi_free( &U2 );
  2352.     mbedtls_mpi_free( &G ); mbedtls_mpi_free( &TB ); mbedtls_mpi_free( &TV );
  2353.     mbedtls_mpi_free( &V1 ); mbedtls_mpi_free( &V2 );
  2354.  
  2355.     return( ret );
  2356. }
  2357.  
  2358. #if defined(MBEDTLS_GENPRIME)
  2359.  
  2360. static const int small_prime[] =
  2361. {
  2362.         3,    5,    7,   11,   13,   17,   19,   23,
  2363.        29,   31,   37,   41,   43,   47,   53,   59,
  2364.        61,   67,   71,   73,   79,   83,   89,   97,
  2365.       101,  103,  107,  109,  113,  127,  131,  137,
  2366.       139,  149,  151,  157,  163,  167,  173,  179,
  2367.       181,  191,  193,  197,  199,  211,  223,  227,
  2368.       229,  233,  239,  241,  251,  257,  263,  269,
  2369.       271,  277,  281,  283,  293,  307,  311,  313,
  2370.       317,  331,  337,  347,  349,  353,  359,  367,
  2371.       373,  379,  383,  389,  397,  401,  409,  419,
  2372.       421,  431,  433,  439,  443,  449,  457,  461,
  2373.       463,  467,  479,  487,  491,  499,  503,  509,
  2374.       521,  523,  541,  547,  557,  563,  569,  571,
  2375.       577,  587,  593,  599,  601,  607,  613,  617,
  2376.       619,  631,  641,  643,  647,  653,  659,  661,
  2377.       673,  677,  683,  691,  701,  709,  719,  727,
  2378.       733,  739,  743,  751,  757,  761,  769,  773,
  2379.       787,  797,  809,  811,  821,  823,  827,  829,
  2380.       839,  853,  857,  859,  863,  877,  881,  883,
  2381.       887,  907,  911,  919,  929,  937,  941,  947,
  2382.       953,  967,  971,  977,  983,  991,  997, -103
  2383. };
  2384.  
  2385. /*
  2386.  * Small divisors test (X must be positive)
  2387.  *
  2388.  * Return values:
  2389.  * 0: no small factor (possible prime, more tests needed)
  2390.  * 1: certain prime
  2391.  * MBEDTLS_ERR_MPI_NOT_ACCEPTABLE: certain non-prime
  2392.  * other negative: error
  2393.  */
  2394. static int mpi_check_small_factors( const mbedtls_mpi *X )
  2395. {
  2396.     int ret = 0;
  2397.     size_t i;
  2398.     mbedtls_mpi_uint r;
  2399.  
  2400.     if( ( X->p[0] & 1 ) == 0 )
  2401.         return( MBEDTLS_ERR_MPI_NOT_ACCEPTABLE );
  2402.  
  2403.     for( i = 0; small_prime[i] > 0; i++ )
  2404.     {
  2405.         if( mbedtls_mpi_cmp_int( X, small_prime[i] ) <= 0 )
  2406.             return( 1 );
  2407.  
  2408.         MBEDTLS_MPI_CHK( mbedtls_mpi_mod_int( &r, X, small_prime[i] ) );
  2409.  
  2410.         if( r == 0 )
  2411.             return( MBEDTLS_ERR_MPI_NOT_ACCEPTABLE );
  2412.     }
  2413.  
  2414. cleanup:
  2415.     return( ret );
  2416. }
  2417.  
  2418. /*
  2419.  * Miller-Rabin pseudo-primality test  (HAC 4.24)
  2420.  */
  2421. static int mpi_miller_rabin( const mbedtls_mpi *X, size_t rounds,
  2422.                              int (*f_rng)(void *, unsigned char *, size_t),
  2423.                              void *p_rng )
  2424. {
  2425.     int ret, count;
  2426.     size_t i, j, k, s;
  2427.     mbedtls_mpi W, R, T, A, RR;
  2428.  
  2429.     MPI_VALIDATE_RET( X     != NULL );
  2430.     MPI_VALIDATE_RET( f_rng != NULL );
  2431.  
  2432.     mbedtls_mpi_init( &W ); mbedtls_mpi_init( &R );
  2433.     mbedtls_mpi_init( &T ); mbedtls_mpi_init( &A );
  2434.     mbedtls_mpi_init( &RR );
  2435.  
  2436.     /*
  2437.      * W = |X| - 1
  2438.      * R = W >> lsb( W )
  2439.      */
  2440.     MBEDTLS_MPI_CHK( mbedtls_mpi_sub_int( &W, X, 1 ) );
  2441.     s = mbedtls_mpi_lsb( &W );
  2442.     MBEDTLS_MPI_CHK( mbedtls_mpi_copy( &R, &W ) );
  2443.     MBEDTLS_MPI_CHK( mbedtls_mpi_shift_r( &R, s ) );
  2444.  
  2445.     for( i = 0; i < rounds; i++ )
  2446.     {
  2447.         /*
  2448.          * pick a random A, 1 < A < |X| - 1
  2449.          */
  2450.         count = 0;
  2451.         do {
  2452.             MBEDTLS_MPI_CHK( mbedtls_mpi_fill_random( &A, X->n * ciL, f_rng, p_rng ) );
  2453.  
  2454.             j = mbedtls_mpi_bitlen( &A );
  2455.             k = mbedtls_mpi_bitlen( &W );
  2456.             if (j > k) {
  2457.                 A.p[A.n - 1] &= ( (mbedtls_mpi_uint) 1 << ( k - ( A.n - 1 ) * biL - 1 ) ) - 1;
  2458.             }
  2459.  
  2460.             if (count++ > 30) {
  2461.                 ret = MBEDTLS_ERR_MPI_NOT_ACCEPTABLE;
  2462.                 goto cleanup;
  2463.             }
  2464.  
  2465.         } while ( mbedtls_mpi_cmp_mpi( &A, &W ) >= 0 ||
  2466.                   mbedtls_mpi_cmp_int( &A, 1 )  <= 0    );
  2467.  
  2468.         /*
  2469.          * A = A^R mod |X|
  2470.          */
  2471.         MBEDTLS_MPI_CHK( mbedtls_mpi_exp_mod( &A, &A, &R, X, &RR ) );
  2472.  
  2473.         if( mbedtls_mpi_cmp_mpi( &A, &W ) == 0 ||
  2474.             mbedtls_mpi_cmp_int( &A,  1 ) == 0 )
  2475.             continue;
  2476.  
  2477.         j = 1;
  2478.         while( j < s && mbedtls_mpi_cmp_mpi( &A, &W ) != 0 )
  2479.         {
  2480.             /*
  2481.              * A = A * A mod |X|
  2482.              */
  2483.             MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &T, &A, &A ) );
  2484.             MBEDTLS_MPI_CHK( mbedtls_mpi_mod_mpi( &A, &T, X  ) );
  2485.  
  2486.             if( mbedtls_mpi_cmp_int( &A, 1 ) == 0 )
  2487.                 break;
  2488.  
  2489.             j++;
  2490.         }
  2491.  
  2492.         /*
  2493.          * not prime if A != |X| - 1 or A == 1
  2494.          */
  2495.         if( mbedtls_mpi_cmp_mpi( &A, &W ) != 0 ||
  2496.             mbedtls_mpi_cmp_int( &A,  1 ) == 0 )
  2497.         {
  2498.             ret = MBEDTLS_ERR_MPI_NOT_ACCEPTABLE;
  2499.             break;
  2500.         }
  2501.     }
  2502.  
  2503. cleanup:
  2504.     mbedtls_mpi_free( &W ); mbedtls_mpi_free( &R );
  2505.     mbedtls_mpi_free( &T ); mbedtls_mpi_free( &A );
  2506.     mbedtls_mpi_free( &RR );
  2507.  
  2508.     return( ret );
  2509. }
  2510.  
  2511. /*
  2512.  * Pseudo-primality test: small factors, then Miller-Rabin
  2513.  */
  2514. int mbedtls_mpi_is_prime_ext( const mbedtls_mpi *X, int rounds,
  2515.                               int (*f_rng)(void *, unsigned char *, size_t),
  2516.                               void *p_rng )
  2517. {
  2518.     int ret;
  2519.     mbedtls_mpi XX;
  2520.     MPI_VALIDATE_RET( X     != NULL );
  2521.     MPI_VALIDATE_RET( f_rng != NULL );
  2522.  
  2523.     XX.s = 1;
  2524.     XX.n = X->n;
  2525.     XX.p = X->p;
  2526.  
  2527.     if( mbedtls_mpi_cmp_int( &XX, 0 ) == 0 ||
  2528.         mbedtls_mpi_cmp_int( &XX, 1 ) == 0 )
  2529.         return( MBEDTLS_ERR_MPI_NOT_ACCEPTABLE );
  2530.  
  2531.     if( mbedtls_mpi_cmp_int( &XX, 2 ) == 0 )
  2532.         return( 0 );
  2533.  
  2534.     if( ( ret = mpi_check_small_factors( &XX ) ) != 0 )
  2535.     {
  2536.         if( ret == 1 )
  2537.             return( 0 );
  2538.  
  2539.         return( ret );
  2540.     }
  2541.  
  2542.     return( mpi_miller_rabin( &XX, rounds, f_rng, p_rng ) );
  2543. }
  2544.  
  2545. #if !defined(MBEDTLS_DEPRECATED_REMOVED)
  2546. /*
  2547.  * Pseudo-primality test, error probability 2^-80
  2548.  */
  2549. int mbedtls_mpi_is_prime( const mbedtls_mpi *X,
  2550.                   int (*f_rng)(void *, unsigned char *, size_t),
  2551.                   void *p_rng )
  2552. {
  2553.     MPI_VALIDATE_RET( X     != NULL );
  2554.     MPI_VALIDATE_RET( f_rng != NULL );
  2555.  
  2556.     /*
  2557.      * In the past our key generation aimed for an error rate of at most
  2558.      * 2^-80. Since this function is deprecated, aim for the same certainty
  2559.      * here as well.
  2560.      */
  2561.     return( mbedtls_mpi_is_prime_ext( X, 40, f_rng, p_rng ) );
  2562. }
  2563. #endif
  2564.  
  2565. /*
  2566.  * Prime number generation
  2567.  *
  2568.  * To generate an RSA key in a way recommended by FIPS 186-4, both primes must
  2569.  * be either 1024 bits or 1536 bits long, and flags must contain
  2570.  * MBEDTLS_MPI_GEN_PRIME_FLAG_LOW_ERR.
  2571.  */
  2572. int mbedtls_mpi_gen_prime( mbedtls_mpi *X, size_t nbits, int flags,
  2573.                    int (*f_rng)(void *, unsigned char *, size_t),
  2574.                    void *p_rng )
  2575. {
  2576. #ifdef MBEDTLS_HAVE_INT64
  2577. // ceil(2^63.5)
  2578. #define CEIL_MAXUINT_DIV_SQRT2 0xb504f333f9de6485ULL
  2579. #else
  2580. // ceil(2^31.5)
  2581. #define CEIL_MAXUINT_DIV_SQRT2 0xb504f334U
  2582. #endif
  2583.     int ret = MBEDTLS_ERR_MPI_NOT_ACCEPTABLE;
  2584.     size_t k, n;
  2585.     int rounds;
  2586.     mbedtls_mpi_uint r;
  2587.     mbedtls_mpi Y;
  2588.  
  2589.     MPI_VALIDATE_RET( X     != NULL );
  2590.     MPI_VALIDATE_RET( f_rng != NULL );
  2591.  
  2592.     if( nbits < 3 || nbits > MBEDTLS_MPI_MAX_BITS )
  2593.         return( MBEDTLS_ERR_MPI_BAD_INPUT_DATA );
  2594.  
  2595.     mbedtls_mpi_init( &Y );
  2596.  
  2597.     n = BITS_TO_LIMBS( nbits );
  2598.  
  2599.     if( ( flags & MBEDTLS_MPI_GEN_PRIME_FLAG_LOW_ERR ) == 0 )
  2600.     {
  2601.         /*
  2602.          * 2^-80 error probability, number of rounds chosen per HAC, table 4.4
  2603.          */
  2604.         rounds = ( ( nbits >= 1300 ) ?  2 : ( nbits >=  850 ) ?  3 :
  2605.                    ( nbits >=  650 ) ?  4 : ( nbits >=  350 ) ?  8 :
  2606.                    ( nbits >=  250 ) ? 12 : ( nbits >=  150 ) ? 18 : 27 );
  2607.     }
  2608.     else
  2609.     {
  2610.         /*
  2611.          * 2^-100 error probability, number of rounds computed based on HAC,
  2612.          * fact 4.48
  2613.          */
  2614.         rounds = ( ( nbits >= 1450 ) ?  4 : ( nbits >=  1150 ) ?  5 :
  2615.                    ( nbits >= 1000 ) ?  6 : ( nbits >=   850 ) ?  7 :
  2616.                    ( nbits >=  750 ) ?  8 : ( nbits >=   500 ) ? 13 :
  2617.                    ( nbits >=  250 ) ? 28 : ( nbits >=   150 ) ? 40 : 51 );
  2618.     }
  2619.  
  2620.     while( 1 )
  2621.     {
  2622.         MBEDTLS_MPI_CHK( mbedtls_mpi_fill_random( X, n * ciL, f_rng, p_rng ) );
  2623.         /* make sure generated number is at least (nbits-1)+0.5 bits (FIPS 186-4 §B.3.3 steps 4.4, 5.5) */
  2624.         if( X->p[n-1] < CEIL_MAXUINT_DIV_SQRT2 ) continue;
  2625.  
  2626.         k = n * biL;
  2627.         if( k > nbits ) MBEDTLS_MPI_CHK( mbedtls_mpi_shift_r( X, k - nbits ) );
  2628.         X->p[0] |= 1;
  2629.  
  2630.         if( ( flags & MBEDTLS_MPI_GEN_PRIME_FLAG_DH ) == 0 )
  2631.         {
  2632.             ret = mbedtls_mpi_is_prime_ext( X, rounds, f_rng, p_rng );
  2633.  
  2634.             if( ret != MBEDTLS_ERR_MPI_NOT_ACCEPTABLE )
  2635.                 goto cleanup;
  2636.         }
  2637.         else
  2638.         {
  2639.             /*
  2640.              * An necessary condition for Y and X = 2Y + 1 to be prime
  2641.              * is X = 2 mod 3 (which is equivalent to Y = 2 mod 3).
  2642.              * Make sure it is satisfied, while keeping X = 3 mod 4
  2643.              */
  2644.  
  2645.             X->p[0] |= 2;
  2646.  
  2647.             MBEDTLS_MPI_CHK( mbedtls_mpi_mod_int( &r, X, 3 ) );
  2648.             if( r == 0 )
  2649.                 MBEDTLS_MPI_CHK( mbedtls_mpi_add_int( X, X, 8 ) );
  2650.             else if( r == 1 )
  2651.                 MBEDTLS_MPI_CHK( mbedtls_mpi_add_int( X, X, 4 ) );
  2652.  
  2653.             /* Set Y = (X-1) / 2, which is X / 2 because X is odd */
  2654.             MBEDTLS_MPI_CHK( mbedtls_mpi_copy( &Y, X ) );
  2655.             MBEDTLS_MPI_CHK( mbedtls_mpi_shift_r( &Y, 1 ) );
  2656.  
  2657.             while( 1 )
  2658.             {
  2659.                 /*
  2660.                  * First, check small factors for X and Y
  2661.                  * before doing Miller-Rabin on any of them
  2662.                  */
  2663.                 if( ( ret = mpi_check_small_factors(  X         ) ) == 0 &&
  2664.                     ( ret = mpi_check_small_factors( &Y         ) ) == 0 &&
  2665.                     ( ret = mpi_miller_rabin(  X, rounds, f_rng, p_rng  ) )
  2666.                                                                     == 0 &&
  2667.                     ( ret = mpi_miller_rabin( &Y, rounds, f_rng, p_rng  ) )
  2668.                                                                     == 0 )
  2669.                     goto cleanup;
  2670.  
  2671.                 if( ret != MBEDTLS_ERR_MPI_NOT_ACCEPTABLE )
  2672.                     goto cleanup;
  2673.  
  2674.                 /*
  2675.                  * Next candidates. We want to preserve Y = (X-1) / 2 and
  2676.                  * Y = 1 mod 2 and Y = 2 mod 3 (eq X = 3 mod 4 and X = 2 mod 3)
  2677.                  * so up Y by 6 and X by 12.
  2678.                  */
  2679.                 MBEDTLS_MPI_CHK( mbedtls_mpi_add_int(  X,  X, 12 ) );
  2680.                 MBEDTLS_MPI_CHK( mbedtls_mpi_add_int( &Y, &Y, 6  ) );
  2681.             }
  2682.         }
  2683.     }
  2684.  
  2685. cleanup:
  2686.  
  2687.     mbedtls_mpi_free( &Y );
  2688.  
  2689.     return( ret );
  2690. }
  2691.  
  2692. #endif /* MBEDTLS_GENPRIME */
  2693.  
  2694. #if defined(MBEDTLS_SELF_TEST)
  2695.  
  2696. #define GCD_PAIR_COUNT  3
  2697.  
  2698. static const int gcd_pairs[GCD_PAIR_COUNT][3] =
  2699. {
  2700.     { 693, 609, 21 },
  2701.     { 1764, 868, 28 },
  2702.     { 768454923, 542167814, 1 }
  2703. };
  2704.  
  2705. /*
  2706.  * Checkup routine
  2707.  */
  2708. int mbedtls_mpi_self_test( int verbose )
  2709. {
  2710.     int ret, i;
  2711.     mbedtls_mpi A, E, N, X, Y, U, V;
  2712.  
  2713.     mbedtls_mpi_init( &A ); mbedtls_mpi_init( &E ); mbedtls_mpi_init( &N ); mbedtls_mpi_init( &X );
  2714.     mbedtls_mpi_init( &Y ); mbedtls_mpi_init( &U ); mbedtls_mpi_init( &V );
  2715.  
  2716.     MBEDTLS_MPI_CHK( mbedtls_mpi_read_string( &A, 16,
  2717.         "EFE021C2645FD1DC586E69184AF4A31E" \
  2718.         "D5F53E93B5F123FA41680867BA110131" \
  2719.         "944FE7952E2517337780CB0DB80E61AA" \
  2720.         "E7C8DDC6C5C6AADEB34EB38A2F40D5E6" ) );
  2721.  
  2722.     MBEDTLS_MPI_CHK( mbedtls_mpi_read_string( &E, 16,
  2723.         "B2E7EFD37075B9F03FF989C7C5051C20" \
  2724.         "34D2A323810251127E7BF8625A4F49A5" \
  2725.         "F3E27F4DA8BD59C47D6DAABA4C8127BD" \
  2726.         "5B5C25763222FEFCCFC38B832366C29E" ) );
  2727.  
  2728.     MBEDTLS_MPI_CHK( mbedtls_mpi_read_string( &N, 16,
  2729.         "0066A198186C18C10B2F5ED9B522752A" \
  2730.         "9830B69916E535C8F047518A889A43A5" \
  2731.         "94B6BED27A168D31D4A52F88925AA8F5" ) );
  2732.  
  2733.     MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &X, &A, &N ) );
  2734.  
  2735.     MBEDTLS_MPI_CHK( mbedtls_mpi_read_string( &U, 16,
  2736.         "602AB7ECA597A3D6B56FF9829A5E8B85" \
  2737.         "9E857EA95A03512E2BAE7391688D264A" \
  2738.         "A5663B0341DB9CCFD2C4C5F421FEC814" \
  2739.         "8001B72E848A38CAE1C65F78E56ABDEF" \
  2740.         "E12D3C039B8A02D6BE593F0BBBDA56F1" \
  2741.         "ECF677152EF804370C1A305CAF3B5BF1" \
  2742.         "30879B56C61DE584A0F53A2447A51E" ) );
  2743.  
  2744.     if( verbose != 0 )
  2745.         mbedtls_printf( "  MPI test #1 (mul_mpi): " );
  2746.  
  2747.     if( mbedtls_mpi_cmp_mpi( &X, &U ) != 0 )
  2748.     {
  2749.         if( verbose != 0 )
  2750.             mbedtls_printf( "failed\n" );
  2751.  
  2752.         ret = 1;
  2753.         goto cleanup;
  2754.     }
  2755.  
  2756.     if( verbose != 0 )
  2757.         mbedtls_printf( "passed\n" );
  2758.  
  2759.     MBEDTLS_MPI_CHK( mbedtls_mpi_div_mpi( &X, &Y, &A, &N ) );
  2760.  
  2761.     MBEDTLS_MPI_CHK( mbedtls_mpi_read_string( &U, 16,
  2762.         "256567336059E52CAE22925474705F39A94" ) );
  2763.  
  2764.     MBEDTLS_MPI_CHK( mbedtls_mpi_read_string( &V, 16,
  2765.         "6613F26162223DF488E9CD48CC132C7A" \
  2766.         "0AC93C701B001B092E4E5B9F73BCD27B" \
  2767.         "9EE50D0657C77F374E903CDFA4C642" ) );
  2768.  
  2769.     if( verbose != 0 )
  2770.         mbedtls_printf( "  MPI test #2 (div_mpi): " );
  2771.  
  2772.     if( mbedtls_mpi_cmp_mpi( &X, &U ) != 0 ||
  2773.         mbedtls_mpi_cmp_mpi( &Y, &V ) != 0 )
  2774.     {
  2775.         if( verbose != 0 )
  2776.             mbedtls_printf( "failed\n" );
  2777.  
  2778.         ret = 1;
  2779.         goto cleanup;
  2780.     }
  2781.  
  2782.     if( verbose != 0 )
  2783.         mbedtls_printf( "passed\n" );
  2784.  
  2785.     MBEDTLS_MPI_CHK( mbedtls_mpi_exp_mod( &X, &A, &E, &N, NULL ) );
  2786.  
  2787.     MBEDTLS_MPI_CHK( mbedtls_mpi_read_string( &U, 16,
  2788.         "36E139AEA55215609D2816998ED020BB" \
  2789.         "BD96C37890F65171D948E9BC7CBAA4D9" \
  2790.         "325D24D6A3C12710F10A09FA08AB87" ) );
  2791.  
  2792.     if( verbose != 0 )
  2793.         mbedtls_printf( "  MPI test #3 (exp_mod): " );
  2794.  
  2795.     if( mbedtls_mpi_cmp_mpi( &X, &U ) != 0 )
  2796.     {
  2797.         if( verbose != 0 )
  2798.             mbedtls_printf( "failed\n" );
  2799.  
  2800.         ret = 1;
  2801.         goto cleanup;
  2802.     }
  2803.  
  2804.     if( verbose != 0 )
  2805.         mbedtls_printf( "passed\n" );
  2806.  
  2807.     MBEDTLS_MPI_CHK( mbedtls_mpi_inv_mod( &X, &A, &N ) );
  2808.  
  2809.     MBEDTLS_MPI_CHK( mbedtls_mpi_read_string( &U, 16,
  2810.         "003A0AAEDD7E784FC07D8F9EC6E3BFD5" \
  2811.         "C3DBA76456363A10869622EAC2DD84EC" \
  2812.         "C5B8A74DAC4D09E03B5E0BE779F2DF61" ) );
  2813.  
  2814.     if( verbose != 0 )
  2815.         mbedtls_printf( "  MPI test #4 (inv_mod): " );
  2816.  
  2817.     if( mbedtls_mpi_cmp_mpi( &X, &U ) != 0 )
  2818.     {
  2819.         if( verbose != 0 )
  2820.             mbedtls_printf( "failed\n" );
  2821.  
  2822.         ret = 1;
  2823.         goto cleanup;
  2824.     }
  2825.  
  2826.     if( verbose != 0 )
  2827.         mbedtls_printf( "passed\n" );
  2828.  
  2829.     if( verbose != 0 )
  2830.         mbedtls_printf( "  MPI test #5 (simple gcd): " );
  2831.  
  2832.     for( i = 0; i < GCD_PAIR_COUNT; i++ )
  2833.     {
  2834.         MBEDTLS_MPI_CHK( mbedtls_mpi_lset( &X, gcd_pairs[i][0] ) );
  2835.         MBEDTLS_MPI_CHK( mbedtls_mpi_lset( &Y, gcd_pairs[i][1] ) );
  2836.  
  2837.         MBEDTLS_MPI_CHK( mbedtls_mpi_gcd( &A, &X, &Y ) );
  2838.  
  2839.         if( mbedtls_mpi_cmp_int( &A, gcd_pairs[i][2] ) != 0 )
  2840.         {
  2841.             if( verbose != 0 )
  2842.                 mbedtls_printf( "failed at %d\n", i );
  2843.  
  2844.             ret = 1;
  2845.             goto cleanup;
  2846.         }
  2847.     }
  2848.  
  2849.     if( verbose != 0 )
  2850.         mbedtls_printf( "passed\n" );
  2851.  
  2852. cleanup:
  2853.  
  2854.     if( ret != 0 && verbose != 0 )
  2855.         mbedtls_printf( "Unexpected error, return code = %08X\n", ret );
  2856.  
  2857.     mbedtls_mpi_free( &A ); mbedtls_mpi_free( &E ); mbedtls_mpi_free( &N ); mbedtls_mpi_free( &X );
  2858.     mbedtls_mpi_free( &Y ); mbedtls_mpi_free( &U ); mbedtls_mpi_free( &V );
  2859.  
  2860.     if( verbose != 0 )
  2861.         mbedtls_printf( "\n" );
  2862.  
  2863.     return( ret );
  2864. }
  2865.  
  2866. #endif /* MBEDTLS_SELF_TEST */
  2867.  
  2868. #endif /* MBEDTLS_BIGNUM_C */
  2869.