+/*
+ * Multi-precision integer library
+ *
+ * Copyright (C) 2006-2010, Brainspark B.V.
+ *
+ * This file is part of PolarSSL (http://www.polarssl.org)
+ * Lead Maintainer: Paul Bakker <polarssl_maintainer at polarssl.org>
+ *
+ * All rights reserved.
+ *
+ * This program is free software; you can redistribute it and/or modify
+ * it under the terms of the GNU General Public License as published by
+ * the Free Software Foundation; either version 2 of the License, or
+ * (at your option) any later version.
+ *
+ * This program is distributed in the hope that it will be useful,
+ * but WITHOUT ANY WARRANTY; without even the implied warranty of
+ * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
+ * GNU General Public License for more details.
+ *
+ * You should have received a copy of the GNU General Public License along
+ * with this program; if not, write to the Free Software Foundation, Inc.,
+ * 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA.
+ */
+/*
+ * This MPI implementation is based on:
+ *
+ * http://www.cacr.math.uwaterloo.ca/hac/about/chap14.pdf
+ * http://www.stillhq.com/extracted/gnupg-api/mpi/
+ * http://math.libtomcrypt.com/files/tommath.pdf
+ */
+
+#include "polarssl_config.h"
+
+#if defined(POLARSSL_BIGNUM_C)
+
+#include "bignum.h"
+#include "bn_mul.h"
+
+#include <stdlib.h>
+
+#define ciL (sizeof(t_uint)) /* chars in limb */
+#define biL (ciL << 3) /* bits in limb */
+#define biH (ciL << 2) /* half limb size */
+
+/*
+ * Convert between bits/chars and number of limbs
+ */
+#define BITS_TO_LIMBS(i) (((i) + biL - 1) / biL)
+#define CHARS_TO_LIMBS(i) (((i) + ciL - 1) / ciL)
+
+/*
+ * Initialize one MPI
+ */
+void mpi_init( mpi *X )
+{
+ if( X == NULL )
+ return;
+
+ X->s = 1;
+ X->n = 0;
+ X->p = NULL;
+}
+
+/*
+ * Unallocate one MPI
+ */
+void mpi_free( mpi *X )
+{
+ if( X == NULL )
+ return;
+
+ if( X->p != NULL )
+ {
+ memset( X->p, 0, X->n * ciL );
+ free( X->p );
+ }
+
+ X->s = 1;
+ X->n = 0;
+ X->p = NULL;
+}
+
+/*
+ * Enlarge to the specified number of limbs
+ */
+int mpi_grow( mpi *X, size_t nblimbs )
+{
+ t_uint *p;
+
+ if( nblimbs > POLARSSL_MPI_MAX_LIMBS )
+ return( POLARSSL_ERR_MPI_MALLOC_FAILED );
+
+ if( X->n < nblimbs )
+ {
+ if( ( p = (t_uint *) malloc( nblimbs * ciL ) ) == NULL )
+ return( POLARSSL_ERR_MPI_MALLOC_FAILED );
+
+ memset( p, 0, nblimbs * ciL );
+
+ if( X->p != NULL )
+ {
+ memcpy( p, X->p, X->n * ciL );
+ memset( X->p, 0, X->n * ciL );
+ free( X->p );
+ }
+
+ X->n = nblimbs;
+ X->p = p;
+ }
+
+ return( 0 );
+}
+
+/*
+ * Copy the contents of Y into X
+ */
+int mpi_copy( mpi *X, const mpi *Y )
+{
+ int ret;
+ size_t i;
+
+ if( X == Y )
+ return( 0 );
+
+ for( i = Y->n - 1; i > 0; i-- )
+ if( Y->p[i] != 0 )
+ break;
+ i++;
+
+ X->s = Y->s;
+
+ MPI_CHK( mpi_grow( X, i ) );
+
+ memset( X->p, 0, X->n * ciL );
+ memcpy( X->p, Y->p, i * ciL );
+
+cleanup:
+
+ return( ret );
+}
+
+/*
+ * Swap the contents of X and Y
+ */
+void mpi_swap( mpi *X, mpi *Y )
+{
+ mpi T;
+
+ memcpy( &T, X, sizeof( mpi ) );
+ memcpy( X, Y, sizeof( mpi ) );
+ memcpy( Y, &T, sizeof( mpi ) );
+}
+
+/*
+ * Set value from integer
+ */
+int mpi_lset( mpi *X, t_sint z )
+{
+ int ret;
+
+ MPI_CHK( mpi_grow( X, 1 ) );
+ memset( X->p, 0, X->n * ciL );
+
+ X->p[0] = ( z < 0 ) ? -z : z;
+ X->s = ( z < 0 ) ? -1 : 1;
+
+cleanup:
+
+ return( ret );
+}
+
+/*
+ * Get a specific bit
+ */
+int mpi_get_bit( const mpi *X, size_t pos )
+{
+ if( X->n * biL <= pos )
+ return( 0 );
+
+ return ( X->p[pos / biL] >> ( pos % biL ) ) & 0x01;
+}
+
+/*
+ * Set a bit to a specific value of 0 or 1
+ */
+int mpi_set_bit( mpi *X, size_t pos, unsigned char val )
+{
+ int ret = 0;
+ size_t off = pos / biL;
+ size_t idx = pos % biL;
+
+ if( val != 0 && val != 1 )
+ return POLARSSL_ERR_MPI_BAD_INPUT_DATA;
+
+ if( X->n * biL <= pos )
+ {
+ if( val == 0 )
+ return ( 0 );
+
+ MPI_CHK( mpi_grow( X, off + 1 ) );
+ }
+
+ X->p[off] = ( X->p[off] & ~( 0x01 << idx ) ) | ( val << idx );
+
+cleanup:
+
+ return( ret );
+}
+
+/*
+ * Return the number of least significant bits
+ */
+size_t mpi_lsb( const mpi *X )
+{
+ size_t i, j, count = 0;
+
+ for( i = 0; i < X->n; i++ )
+ for( j = 0; j < biL; j++, count++ )
+ if( ( ( X->p[i] >> j ) & 1 ) != 0 )
+ return( count );
+
+ return( 0 );
+}
+
+/*
+ * Return the number of most significant bits
+ */
+size_t mpi_msb( const mpi *X )
+{
+ size_t i, j;
+
+ for( i = X->n - 1; i > 0; i-- )
+ if( X->p[i] != 0 )
+ break;
+
+ for( j = biL; j > 0; j-- )
+ if( ( ( X->p[i] >> ( j - 1 ) ) & 1 ) != 0 )
+ break;
+
+ return( ( i * biL ) + j );
+}
+
+/*
+ * Return the total size in bytes
+ */
+size_t mpi_size( const mpi *X )
+{
+ return( ( mpi_msb( X ) + 7 ) >> 3 );
+}
+
+/*
+ * Convert an ASCII character to digit value
+ */
+static int mpi_get_digit( t_uint *d, int radix, char c )
+{
+ *d = 255;
+
+ if( c >= 0x30 && c <= 0x39 ) *d = c - 0x30;
+ if( c >= 0x41 && c <= 0x46 ) *d = c - 0x37;
+ if( c >= 0x61 && c <= 0x66 ) *d = c - 0x57;
+
+ if( *d >= (t_uint) radix )
+ return( POLARSSL_ERR_MPI_INVALID_CHARACTER );
+
+ return( 0 );
+}
+
+/*
+ * Import from an ASCII string
+ */
+int mpi_read_string( mpi *X, int radix, const char *s )
+{
+ int ret;
+ size_t i, j, slen, n;
+ t_uint d;
+ mpi T;
+
+ if( radix < 2 || radix > 16 )
+ return( POLARSSL_ERR_MPI_BAD_INPUT_DATA );
+
+ mpi_init( &T );
+
+ slen = strlen( s );
+
+ if( radix == 16 )
+ {
+ n = BITS_TO_LIMBS( slen << 2 );
+
+ MPI_CHK( mpi_grow( X, n ) );
+ MPI_CHK( mpi_lset( X, 0 ) );
+
+ for( i = slen, j = 0; i > 0; i--, j++ )
+ {
+ if( i == 1 && s[i - 1] == '-' )
+ {
+ X->s = -1;
+ break;
+ }
+
+ MPI_CHK( mpi_get_digit( &d, radix, s[i - 1] ) );
+ X->p[j / (2 * ciL)] |= d << ( (j % (2 * ciL)) << 2 );
+ }
+ }
+ else
+ {
+ MPI_CHK( mpi_lset( X, 0 ) );
+
+ for( i = 0; i < slen; i++ )
+ {
+ if( i == 0 && s[i] == '-' )
+ {
+ X->s = -1;
+ continue;
+ }
+
+ MPI_CHK( mpi_get_digit( &d, radix, s[i] ) );
+ MPI_CHK( mpi_mul_int( &T, X, radix ) );
+
+ if( X->s == 1 )
+ {
+ MPI_CHK( mpi_add_int( X, &T, d ) );
+ }
+ else
+ {
+ MPI_CHK( mpi_sub_int( X, &T, d ) );
+ }
+ }
+ }
+
+cleanup:
+
+ mpi_free( &T );
+
+ return( ret );
+}
+
+/*
+ * Helper to write the digits high-order first
+ */
+static int mpi_write_hlp( mpi *X, int radix, char **p )
+{
+ int ret;
+ t_uint r;
+
+ if( radix < 2 || radix > 16 )
+ return( POLARSSL_ERR_MPI_BAD_INPUT_DATA );
+
+ MPI_CHK( mpi_mod_int( &r, X, radix ) );
+ MPI_CHK( mpi_div_int( X, NULL, X, radix ) );
+
+ if( mpi_cmp_int( X, 0 ) != 0 )
+ MPI_CHK( mpi_write_hlp( X, radix, p ) );
+
+ if( r < 10 )
+ *(*p)++ = (char)( r + 0x30 );
+ else
+ *(*p)++ = (char)( r + 0x37 );
+
+cleanup:
+
+ return( ret );
+}
+
+/*
+ * Export into an ASCII string
+ */
+int mpi_write_string( const mpi *X, int radix, char *s, size_t *slen )
+{
+ int ret = 0;
+ size_t n;
+ char *p;
+ mpi T;
+
+ if( radix < 2 || radix > 16 )
+ return( POLARSSL_ERR_MPI_BAD_INPUT_DATA );
+
+ n = mpi_msb( X );
+ if( radix >= 4 ) n >>= 1;
+ if( radix >= 16 ) n >>= 1;
+ n += 3;
+
+ if( *slen < n )
+ {
+ *slen = n;
+ return( POLARSSL_ERR_MPI_BUFFER_TOO_SMALL );
+ }
+
+ p = s;
+ mpi_init( &T );
+
+ if( X->s == -1 )
+ *p++ = '-';
+
+ if( radix == 16 )
+ {
+ int c;
+ size_t i, j, k;
+
+ for( i = X->n, k = 0; i > 0; i-- )
+ {
+ for( j = ciL; j > 0; j-- )
+ {
+ c = ( X->p[i - 1] >> ( ( j - 1 ) << 3) ) & 0xFF;
+
+ if( c == 0 && k == 0 && ( i + j + 3 ) != 0 )
+ continue;
+
+ *(p++) = "0123456789ABCDEF" [c / 16];
+ *(p++) = "0123456789ABCDEF" [c % 16];
+ k = 1;
+ }
+ }
+ }
+ else
+ {
+ MPI_CHK( mpi_copy( &T, X ) );
+
+ if( T.s == -1 )
+ T.s = 1;
+
+ MPI_CHK( mpi_write_hlp( &T, radix, &p ) );
+ }
+
+ *p++ = '\0';
+ *slen = p - s;
+
+cleanup:
+
+ mpi_free( &T );
+
+ return( ret );
+}
+
+#if defined(POLARSSL_FS_IO)
+/*
+ * Read X from an opened file
+ */
+int mpi_read_file( mpi *X, int radix, FILE *fin )
+{
+ t_uint d;
+ size_t slen;
+ char *p;
+ /*
+ * Buffer should have space for (short) label and decimal formatted MPI,
+ * newline characters and '\0'
+ */
+ char s[ POLARSSL_MPI_RW_BUFFER_SIZE ];
+
+ memset( s, 0, sizeof( s ) );
+ if( fgets( s, sizeof( s ) - 1, fin ) == NULL )
+ return( POLARSSL_ERR_MPI_FILE_IO_ERROR );
+
+ slen = strlen( s );
+ if( slen == sizeof( s ) - 2 )
+ return( POLARSSL_ERR_MPI_BUFFER_TOO_SMALL );
+
+ if( s[slen - 1] == '\n' ) { slen--; s[slen] = '\0'; }
+ if( s[slen - 1] == '\r' ) { slen--; s[slen] = '\0'; }
+
+ p = s + slen;
+ while( --p >= s )
+ if( mpi_get_digit( &d, radix, *p ) != 0 )
+ break;
+
+ return( mpi_read_string( X, radix, p + 1 ) );
+}
+
+/*
+ * Write X into an opened file (or stdout if fout == NULL)
+ */
+int mpi_write_file( const char *p, const mpi *X, int radix, FILE *fout )
+{
+ int ret;
+ size_t n, slen, plen;
+ /*
+ * Buffer should have space for (short) label and decimal formatted MPI,
+ * newline characters and '\0'
+ */
+ char s[ POLARSSL_MPI_RW_BUFFER_SIZE ];
+
+ n = sizeof( s );
+ memset( s, 0, n );
+ n -= 2;
+
+ MPI_CHK( mpi_write_string( X, radix, s, (size_t *) &n ) );
+
+ if( p == NULL ) p = "";
+
+ plen = strlen( p );
+ slen = strlen( s );
+ s[slen++] = '\r';
+ s[slen++] = '\n';
+
+ if( fout != NULL )
+ {
+ if( fwrite( p, 1, plen, fout ) != plen ||
+ fwrite( s, 1, slen, fout ) != slen )
+ return( POLARSSL_ERR_MPI_FILE_IO_ERROR );
+ }
+ else
+ printf( "%s%s", p, s );
+
+cleanup:
+
+ return( ret );
+}
+#endif /* POLARSSL_FS_IO */
+
+/*
+ * Import X from unsigned binary data, big endian
+ */
+int mpi_read_binary( mpi *X, const unsigned char *buf, size_t buflen )
+{
+ int ret;
+ size_t i, j, n;
+
+ for( n = 0; n < buflen; n++ )
+ if( buf[n] != 0 )
+ break;
+
+ MPI_CHK( mpi_grow( X, CHARS_TO_LIMBS( buflen - n ) ) );
+ MPI_CHK( mpi_lset( X, 0 ) );
+
+ for( i = buflen, j = 0; i > n; i--, j++ )
+ X->p[j / ciL] |= ((t_uint) buf[i - 1]) << ((j % ciL) << 3);
+
+cleanup:
+
+ return( ret );
+}
+
+/*
+ * Export X into unsigned binary data, big endian
+ */
+int mpi_write_binary( const mpi *X, unsigned char *buf, size_t buflen )
+{
+ size_t i, j, n;
+
+ n = mpi_size( X );
+
+ if( buflen < n )
+ return( POLARSSL_ERR_MPI_BUFFER_TOO_SMALL );
+
+ memset( buf, 0, buflen );
+
+ for( i = buflen - 1, j = 0; n > 0; i--, j++, n-- )
+ buf[i] = (unsigned char)( X->p[j / ciL] >> ((j % ciL) << 3) );
+
+ return( 0 );
+}
+
+/*
+ * Left-shift: X <<= count
+ */
+int mpi_shift_l( mpi *X, size_t count )
+{
+ int ret;
+ size_t i, v0, t1;
+ t_uint r0 = 0, r1;
+
+ v0 = count / (biL );
+ t1 = count & (biL - 1);
+
+ i = mpi_msb( X ) + count;
+
+ if( X->n * biL < i )
+ MPI_CHK( mpi_grow( X, BITS_TO_LIMBS( i ) ) );
+
+ ret = 0;
+
+ /*
+ * shift by count / limb_size
+ */
+ if( v0 > 0 )
+ {
+ for( i = X->n; i > v0; i-- )
+ X->p[i - 1] = X->p[i - v0 - 1];
+
+ for( ; i > 0; i-- )
+ X->p[i - 1] = 0;
+ }
+
+ /*
+ * shift by count % limb_size
+ */
+ if( t1 > 0 )
+ {
+ for( i = v0; i < X->n; i++ )
+ {
+ r1 = X->p[i] >> (biL - t1);
+ X->p[i] <<= t1;
+ X->p[i] |= r0;
+ r0 = r1;
+ }
+ }
+
+cleanup:
+
+ return( ret );
+}
+
+/*
+ * Right-shift: X >>= count
+ */
+int mpi_shift_r( mpi *X, size_t count )
+{
+ size_t i, v0, v1;
+ t_uint r0 = 0, r1;
+
+ v0 = count / biL;
+ v1 = count & (biL - 1);
+
+ if( v0 > X->n || ( v0 == X->n && v1 > 0 ) )
+ return mpi_lset( X, 0 );
+
+ /*
+ * shift by count / limb_size
+ */
+ if( v0 > 0 )
+ {
+ for( i = 0; i < X->n - v0; i++ )
+ X->p[i] = X->p[i + v0];
+
+ for( ; i < X->n; i++ )
+ X->p[i] = 0;
+ }
+
+ /*
+ * shift by count % limb_size
+ */
+ if( v1 > 0 )
+ {
+ for( i = X->n; i > 0; i-- )
+ {
+ r1 = X->p[i - 1] << (biL - v1);
+ X->p[i - 1] >>= v1;
+ X->p[i - 1] |= r0;
+ r0 = r1;
+ }
+ }
+
+ return( 0 );
+}
+
+/*
+ * Compare unsigned values
+ */
+int mpi_cmp_abs( const mpi *X, const mpi *Y )
+{
+ size_t i, j;
+
+ for( i = X->n; i > 0; i-- )
+ if( X->p[i - 1] != 0 )
+ break;
+
+ for( j = Y->n; j > 0; j-- )
+ if( Y->p[j - 1] != 0 )
+ break;
+
+ if( i == 0 && j == 0 )
+ return( 0 );
+
+ if( i > j ) return( 1 );
+ if( j > i ) return( -1 );
+
+ for( ; i > 0; i-- )
+ {
+ if( X->p[i - 1] > Y->p[i - 1] ) return( 1 );
+ if( X->p[i - 1] < Y->p[i - 1] ) return( -1 );
+ }
+
+ return( 0 );
+}
+
+/*
+ * Compare signed values
+ */
+int mpi_cmp_mpi( const mpi *X, const mpi *Y )
+{
+ size_t i, j;
+
+ for( i = X->n; i > 0; i-- )
+ if( X->p[i - 1] != 0 )
+ break;
+
+ for( j = Y->n; j > 0; j-- )
+ if( Y->p[j - 1] != 0 )
+ break;
+
+ if( i == 0 && j == 0 )
+ return( 0 );
+
+ if( i > j ) return( X->s );
+ if( j > i ) return( -Y->s );
+
+ if( X->s > 0 && Y->s < 0 ) return( 1 );
+ if( Y->s > 0 && X->s < 0 ) return( -1 );
+
+ for( ; i > 0; i-- )
+ {
+ if( X->p[i - 1] > Y->p[i - 1] ) return( X->s );
+ if( X->p[i - 1] < Y->p[i - 1] ) return( -X->s );
+ }
+
+ return( 0 );
+}
+
+/*
+ * Compare signed values
+ */
+int mpi_cmp_int( const mpi *X, t_sint z )
+{
+ mpi Y;
+ t_uint p[1];
+
+ *p = ( z < 0 ) ? -z : z;
+ Y.s = ( z < 0 ) ? -1 : 1;
+ Y.n = 1;
+ Y.p = p;
+
+ return( mpi_cmp_mpi( X, &Y ) );
+}
+
+/*
+ * Unsigned addition: X = |A| + |B| (HAC 14.7)
+ */
+int mpi_add_abs( mpi *X, const mpi *A, const mpi *B )
+{
+ int ret;
+ size_t i, j;
+ t_uint *o, *p, c;
+
+ if( X == B )
+ {
+ const mpi *T = A; A = X; B = T;
+ }
+
+ if( X != A )
+ MPI_CHK( mpi_copy( X, A ) );
+
+ /*
+ * X should always be positive as a result of unsigned additions.
+ */
+ X->s = 1;
+
+ for( j = B->n; j > 0; j-- )
+ if( B->p[j - 1] != 0 )
+ break;
+
+ MPI_CHK( mpi_grow( X, j ) );
+
+ o = B->p; p = X->p; c = 0;
+
+ for( i = 0; i < j; i++, o++, p++ )
+ {
+ *p += c; c = ( *p < c );
+ *p += *o; c += ( *p < *o );
+ }
+
+ while( c != 0 )
+ {
+ if( i >= X->n )
+ {
+ MPI_CHK( mpi_grow( X, i + 1 ) );
+ p = X->p + i;
+ }
+
+ *p += c; c = ( *p < c ); i++; p++;
+ }
+
+cleanup:
+
+ return( ret );
+}
+
+/*
+ * Helper for mpi substraction
+ */
+static void mpi_sub_hlp( size_t n, t_uint *s, t_uint *d )
+{
+ size_t i;
+ t_uint c, z;
+
+ for( i = c = 0; i < n; i++, s++, d++ )
+ {
+ z = ( *d < c ); *d -= c;
+ c = ( *d < *s ) + z; *d -= *s;
+ }
+
+ while( c != 0 )
+ {
+ z = ( *d < c ); *d -= c;
+ c = z; i++; d++;
+ }
+}
+
+/*
+ * Unsigned substraction: X = |A| - |B| (HAC 14.9)
+ */
+int mpi_sub_abs( mpi *X, const mpi *A, const mpi *B )
+{
+ mpi TB;
+ int ret;
+ size_t n;
+
+ if( mpi_cmp_abs( A, B ) < 0 )
+ return( POLARSSL_ERR_MPI_NEGATIVE_VALUE );
+
+ mpi_init( &TB );
+
+ if( X == B )
+ {
+ MPI_CHK( mpi_copy( &TB, B ) );
+ B = &TB;
+ }
+
+ if( X != A )
+ MPI_CHK( mpi_copy( X, A ) );
+
+ /*
+ * X should always be positive as a result of unsigned substractions.
+ */
+ X->s = 1;
+
+ ret = 0;
+
+ for( n = B->n; n > 0; n-- )
+ if( B->p[n - 1] != 0 )
+ break;
+
+ mpi_sub_hlp( n, B->p, X->p );
+
+cleanup:
+
+ mpi_free( &TB );
+
+ return( ret );
+}
+
+/*
+ * Signed addition: X = A + B
+ */
+int mpi_add_mpi( mpi *X, const mpi *A, const mpi *B )
+{
+ int ret, s = A->s;
+
+ if( A->s * B->s < 0 )
+ {
+ if( mpi_cmp_abs( A, B ) >= 0 )
+ {
+ MPI_CHK( mpi_sub_abs( X, A, B ) );
+ X->s = s;
+ }
+ else
+ {
+ MPI_CHK( mpi_sub_abs( X, B, A ) );
+ X->s = -s;
+ }
+ }
+ else
+ {
+ MPI_CHK( mpi_add_abs( X, A, B ) );
+ X->s = s;
+ }
+
+cleanup:
+
+ return( ret );
+}
+
+/*
+ * Signed substraction: X = A - B
+ */
+int mpi_sub_mpi( mpi *X, const mpi *A, const mpi *B )
+{
+ int ret, s = A->s;
+
+ if( A->s * B->s > 0 )
+ {
+ if( mpi_cmp_abs( A, B ) >= 0 )
+ {
+ MPI_CHK( mpi_sub_abs( X, A, B ) );
+ X->s = s;
+ }
+ else
+ {
+ MPI_CHK( mpi_sub_abs( X, B, A ) );
+ X->s = -s;
+ }
+ }
+ else
+ {
+ MPI_CHK( mpi_add_abs( X, A, B ) );
+ X->s = s;
+ }
+
+cleanup:
+
+ return( ret );
+}
+
+/*
+ * Signed addition: X = A + b
+ */
+int mpi_add_int( mpi *X, const mpi *A, t_sint b )
+{
+ mpi _B;
+ t_uint p[1];
+
+ p[0] = ( b < 0 ) ? -b : b;
+ _B.s = ( b < 0 ) ? -1 : 1;
+ _B.n = 1;
+ _B.p = p;
+
+ return( mpi_add_mpi( X, A, &_B ) );
+}
+
+/*
+ * Signed substraction: X = A - b
+ */
+int mpi_sub_int( mpi *X, const mpi *A, t_sint b )
+{
+ mpi _B;
+ t_uint p[1];
+
+ p[0] = ( b < 0 ) ? -b : b;
+ _B.s = ( b < 0 ) ? -1 : 1;
+ _B.n = 1;
+ _B.p = p;
+
+ return( mpi_sub_mpi( X, A, &_B ) );
+}
+
+/*
+ * Helper for mpi multiplication
+ */
+static
+#if defined(__APPLE__) && defined(__arm__)
+/*
+ * Apple LLVM version 4.2 (clang-425.0.24) (based on LLVM 3.2svn)
+ * appears to need this to prevent bad ARM code generation at -O3.
+ */
+__attribute__ ((noinline))
+#endif
+void mpi_mul_hlp( size_t i, t_uint *s, t_uint *d, t_uint b )
+{
+ t_uint c = 0, t = 0;
+
+#if defined(MULADDC_HUIT)
+ for( ; i >= 8; i -= 8 )
+ {
+ MULADDC_INIT
+ MULADDC_HUIT
+ MULADDC_STOP
+ }
+
+ for( ; i > 0; i-- )
+ {
+ MULADDC_INIT
+ MULADDC_CORE
+ MULADDC_STOP
+ }
+#else
+ for( ; i >= 16; i -= 16 )
+ {
+ MULADDC_INIT
+ MULADDC_CORE MULADDC_CORE
+ MULADDC_CORE MULADDC_CORE
+ MULADDC_CORE MULADDC_CORE
+ MULADDC_CORE MULADDC_CORE
+
+ MULADDC_CORE MULADDC_CORE
+ MULADDC_CORE MULADDC_CORE
+ MULADDC_CORE MULADDC_CORE
+ MULADDC_CORE MULADDC_CORE
+ MULADDC_STOP
+ }
+
+ for( ; i >= 8; i -= 8 )
+ {
+ MULADDC_INIT
+ MULADDC_CORE MULADDC_CORE
+ MULADDC_CORE MULADDC_CORE
+
+ MULADDC_CORE MULADDC_CORE
+ MULADDC_CORE MULADDC_CORE
+ MULADDC_STOP
+ }
+
+ for( ; i > 0; i-- )
+ {
+ MULADDC_INIT
+ MULADDC_CORE
+ MULADDC_STOP
+ }
+#endif
+
+ t++;
+
+ do {
+ *d += c; c = ( *d < c ); d++;
+ }
+ while( c != 0 );
+}
+
+/*
+ * Baseline multiplication: X = A * B (HAC 14.12)
+ */
+int mpi_mul_mpi( mpi *X, const mpi *A, const mpi *B )
+{
+ int ret;
+ size_t i, j;
+ mpi TA, TB;
+
+ mpi_init( &TA ); mpi_init( &TB );
+
+ if( X == A ) { MPI_CHK( mpi_copy( &TA, A ) ); A = &TA; }
+ if( X == B ) { MPI_CHK( mpi_copy( &TB, B ) ); B = &TB; }
+
+ for( i = A->n; i > 0; i-- )
+ if( A->p[i - 1] != 0 )
+ break;
+
+ for( j = B->n; j > 0; j-- )
+ if( B->p[j - 1] != 0 )
+ break;
+
+ MPI_CHK( mpi_grow( X, i + j ) );
+ MPI_CHK( mpi_lset( X, 0 ) );
+
+ for( i++; j > 0; j-- )
+ mpi_mul_hlp( i - 1, A->p, X->p + j - 1, B->p[j - 1] );
+
+ X->s = A->s * B->s;
+
+cleanup:
+
+ mpi_free( &TB ); mpi_free( &TA );
+
+ return( ret );
+}
+
+/*
+ * Baseline multiplication: X = A * b
+ */
+int mpi_mul_int( mpi *X, const mpi *A, t_sint b )
+{
+ mpi _B;
+ t_uint p[1];
+
+ _B.s = 1;
+ _B.n = 1;
+ _B.p = p;
+ p[0] = b;
+
+ return( mpi_mul_mpi( X, A, &_B ) );
+}
+
+/*
+ * Division by mpi: A = Q * B + R (HAC 14.20)
+ */
+int mpi_div_mpi( mpi *Q, mpi *R, const mpi *A, const mpi *B )
+{
+ int ret;
+ size_t i, n, t, k;
+ mpi X, Y, Z, T1, T2;
+
+ if( mpi_cmp_int( B, 0 ) == 0 )
+ return( POLARSSL_ERR_MPI_DIVISION_BY_ZERO );
+
+ mpi_init( &X ); mpi_init( &Y ); mpi_init( &Z );
+ mpi_init( &T1 ); mpi_init( &T2 );
+
+ if( mpi_cmp_abs( A, B ) < 0 )
+ {
+ if( Q != NULL ) MPI_CHK( mpi_lset( Q, 0 ) );
+ if( R != NULL ) MPI_CHK( mpi_copy( R, A ) );
+ return( 0 );
+ }
+
+ MPI_CHK( mpi_copy( &X, A ) );
+ MPI_CHK( mpi_copy( &Y, B ) );
+ X.s = Y.s = 1;
+
+ MPI_CHK( mpi_grow( &Z, A->n + 2 ) );
+ MPI_CHK( mpi_lset( &Z, 0 ) );
+ MPI_CHK( mpi_grow( &T1, 2 ) );
+ MPI_CHK( mpi_grow( &T2, 3 ) );
+
+ k = mpi_msb( &Y ) % biL;
+ if( k < biL - 1 )
+ {
+ k = biL - 1 - k;
+ MPI_CHK( mpi_shift_l( &X, k ) );
+ MPI_CHK( mpi_shift_l( &Y, k ) );
+ }
+ else k = 0;
+
+ n = X.n - 1;
+ t = Y.n - 1;
+ MPI_CHK( mpi_shift_l( &Y, biL * (n - t) ) );
+
+ while( mpi_cmp_mpi( &X, &Y ) >= 0 )
+ {
+ Z.p[n - t]++;
+ mpi_sub_mpi( &X, &X, &Y );
+ }
+ mpi_shift_r( &Y, biL * (n - t) );
+
+ for( i = n; i > t ; i-- )
+ {
+ if( X.p[i] >= Y.p[t] )
+ Z.p[i - t - 1] = ~0;
+ else
+ {
+#if defined(POLARSSL_HAVE_UDBL)
+ t_udbl r;
+
+ r = (t_udbl) X.p[i] << biL;
+ r |= (t_udbl) X.p[i - 1];
+ r /= Y.p[t];
+ if( r > ((t_udbl) 1 << biL) - 1)
+ r = ((t_udbl) 1 << biL) - 1;
+
+ Z.p[i - t - 1] = (t_uint) r;
+#else
+ /*
+ * __udiv_qrnnd_c, from gmp/longlong.h
+ */
+ t_uint q0, q1, r0, r1;
+ t_uint d0, d1, d, m;
+
+ d = Y.p[t];
+ d0 = ( d << biH ) >> biH;
+ d1 = ( d >> biH );
+
+ q1 = X.p[i] / d1;
+ r1 = X.p[i] - d1 * q1;
+ r1 <<= biH;
+ r1 |= ( X.p[i - 1] >> biH );
+
+ m = q1 * d0;
+ if( r1 < m )
+ {
+ q1--, r1 += d;
+ while( r1 >= d && r1 < m )
+ q1--, r1 += d;
+ }
+ r1 -= m;
+
+ q0 = r1 / d1;
+ r0 = r1 - d1 * q0;
+ r0 <<= biH;
+ r0 |= ( X.p[i - 1] << biH ) >> biH;
+
+ m = q0 * d0;
+ if( r0 < m )
+ {
+ q0--, r0 += d;
+ while( r0 >= d && r0 < m )
+ q0--, r0 += d;
+ }
+ r0 -= m;
+
+ Z.p[i - t - 1] = ( q1 << biH ) | q0;
+#endif
+ }
+
+ Z.p[i - t - 1]++;
+ do
+ {
+ Z.p[i - t - 1]--;
+
+ MPI_CHK( mpi_lset( &T1, 0 ) );
+ T1.p[0] = (t < 1) ? 0 : Y.p[t - 1];
+ T1.p[1] = Y.p[t];
+ MPI_CHK( mpi_mul_int( &T1, &T1, Z.p[i - t - 1] ) );
+
+ MPI_CHK( mpi_lset( &T2, 0 ) );
+ T2.p[0] = (i < 2) ? 0 : X.p[i - 2];
+ T2.p[1] = (i < 1) ? 0 : X.p[i - 1];
+ T2.p[2] = X.p[i];
+ }
+ while( mpi_cmp_mpi( &T1, &T2 ) > 0 );
+
+ MPI_CHK( mpi_mul_int( &T1, &Y, Z.p[i - t - 1] ) );
+ MPI_CHK( mpi_shift_l( &T1, biL * (i - t - 1) ) );
+ MPI_CHK( mpi_sub_mpi( &X, &X, &T1 ) );
+
+ if( mpi_cmp_int( &X, 0 ) < 0 )
+ {
+ MPI_CHK( mpi_copy( &T1, &Y ) );
+ MPI_CHK( mpi_shift_l( &T1, biL * (i - t - 1) ) );
+ MPI_CHK( mpi_add_mpi( &X, &X, &T1 ) );
+ Z.p[i - t - 1]--;
+ }
+ }
+
+ if( Q != NULL )
+ {
+ mpi_copy( Q, &Z );
+ Q->s = A->s * B->s;
+ }
+
+ if( R != NULL )
+ {
+ mpi_shift_r( &X, k );
+ X.s = A->s;
+ mpi_copy( R, &X );
+
+ if( mpi_cmp_int( R, 0 ) == 0 )
+ R->s = 1;
+ }
+
+cleanup:
+
+ mpi_free( &X ); mpi_free( &Y ); mpi_free( &Z );
+ mpi_free( &T1 ); mpi_free( &T2 );
+
+ return( ret );
+}
+
+/*
+ * Division by int: A = Q * b + R
+ */
+int mpi_div_int( mpi *Q, mpi *R, const mpi *A, t_sint b )
+{
+ mpi _B;
+ t_uint p[1];
+
+ p[0] = ( b < 0 ) ? -b : b;
+ _B.s = ( b < 0 ) ? -1 : 1;
+ _B.n = 1;
+ _B.p = p;
+
+ return( mpi_div_mpi( Q, R, A, &_B ) );
+}
+
+/*
+ * Modulo: R = A mod B
+ */
+int mpi_mod_mpi( mpi *R, const mpi *A, const mpi *B )
+{
+ int ret;
+
+ if( mpi_cmp_int( B, 0 ) < 0 )
+ return POLARSSL_ERR_MPI_NEGATIVE_VALUE;
+
+ MPI_CHK( mpi_div_mpi( NULL, R, A, B ) );
+
+ while( mpi_cmp_int( R, 0 ) < 0 )
+ MPI_CHK( mpi_add_mpi( R, R, B ) );
+
+ while( mpi_cmp_mpi( R, B ) >= 0 )
+ MPI_CHK( mpi_sub_mpi( R, R, B ) );
+
+cleanup:
+
+ return( ret );
+}
+
+/*
+ * Modulo: r = A mod b
+ */
+int mpi_mod_int( t_uint *r, const mpi *A, t_sint b )
+{
+ size_t i;
+ t_uint x, y, z;
+
+ if( b == 0 )
+ return( POLARSSL_ERR_MPI_DIVISION_BY_ZERO );
+
+ if( b < 0 )
+ return POLARSSL_ERR_MPI_NEGATIVE_VALUE;
+
+ /*
+ * handle trivial cases
+ */
+ if( b == 1 )
+ {
+ *r = 0;
+ return( 0 );
+ }
+
+ if( b == 2 )
+ {
+ *r = A->p[0] & 1;
+ return( 0 );
+ }
+
+ /*
+ * general case
+ */
+ for( i = A->n, y = 0; i > 0; i-- )
+ {
+ x = A->p[i - 1];
+ y = ( y << biH ) | ( x >> biH );
+ z = y / b;
+ y -= z * b;
+
+ x <<= biH;
+ y = ( y << biH ) | ( x >> biH );
+ z = y / b;
+ y -= z * b;
+ }
+
+ /*
+ * If A is negative, then the current y represents a negative value.
+ * Flipping it to the positive side.
+ */
+ if( A->s < 0 && y != 0 )
+ y = b - y;
+
+ *r = y;
+
+ return( 0 );
+}
+
+/*
+ * Fast Montgomery initialization (thanks to Tom St Denis)
+ */
+static void mpi_montg_init( t_uint *mm, const mpi *N )
+{
+ t_uint x, m0 = N->p[0];
+
+ x = m0;
+ x += ( ( m0 + 2 ) & 4 ) << 1;
+ x *= ( 2 - ( m0 * x ) );
+
+ if( biL >= 16 ) x *= ( 2 - ( m0 * x ) );
+ if( biL >= 32 ) x *= ( 2 - ( m0 * x ) );
+ if( biL >= 64 ) x *= ( 2 - ( m0 * x ) );
+
+ *mm = ~x + 1;
+}
+
+/*
+ * Montgomery multiplication: A = A * B * R^-1 mod N (HAC 14.36)
+ */
+static void mpi_montmul( mpi *A, const mpi *B, const mpi *N, t_uint mm, const mpi *T )
+{
+ size_t i, n, m;
+ t_uint u0, u1, *d;
+
+ memset( T->p, 0, T->n * ciL );
+
+ d = T->p;
+ n = N->n;
+ m = ( B->n < n ) ? B->n : n;
+
+ for( i = 0; i < n; i++ )
+ {
+ /*
+ * T = (T + u0*B + u1*N) / 2^biL
+ */
+ u0 = A->p[i];
+ u1 = ( d[0] + u0 * B->p[0] ) * mm;
+
+ mpi_mul_hlp( m, B->p, d, u0 );
+ mpi_mul_hlp( n, N->p, d, u1 );
+
+ *d++ = u0; d[n + 1] = 0;
+ }
+
+ memcpy( A->p, d, (n + 1) * ciL );
+
+ if( mpi_cmp_abs( A, N ) >= 0 )
+ mpi_sub_hlp( n, N->p, A->p );
+ else
+ /* prevent timing attacks */
+ mpi_sub_hlp( n, A->p, T->p );
+}
+
+/*
+ * Montgomery reduction: A = A * R^-1 mod N
+ */
+static void mpi_montred( mpi *A, const mpi *N, t_uint mm, const mpi *T )
+{
+ t_uint z = 1;
+ mpi U;
+
+ U.n = U.s = (int) z;
+ U.p = &z;
+
+ mpi_montmul( A, &U, N, mm, T );
+}
+
+/*
+ * Sliding-window exponentiation: X = A^E mod N (HAC 14.85)
+ */
+int mpi_exp_mod( mpi *X, const mpi *A, const mpi *E, const mpi *N, mpi *_RR )
+{
+ int ret;
+ size_t wbits, wsize, one = 1;
+ size_t i, j, nblimbs;
+ size_t bufsize, nbits;
+ t_uint ei, mm, state;
+ mpi RR, T, W[ 2 << POLARSSL_MPI_WINDOW_SIZE ], Apos;
+ int neg;
+
+ if( mpi_cmp_int( N, 0 ) < 0 || ( N->p[0] & 1 ) == 0 )
+ return( POLARSSL_ERR_MPI_BAD_INPUT_DATA );
+
+ if( mpi_cmp_int( E, 0 ) < 0 )
+ return( POLARSSL_ERR_MPI_BAD_INPUT_DATA );
+
+ /*
+ * Init temps and window size
+ */
+ mpi_montg_init( &mm, N );
+ mpi_init( &RR ); mpi_init( &T );
+ memset( W, 0, sizeof( W ) );
+
+ i = mpi_msb( E );
+
+ wsize = ( i > 671 ) ? 6 : ( i > 239 ) ? 5 :
+ ( i > 79 ) ? 4 : ( i > 23 ) ? 3 : 1;
+
+ if( wsize > POLARSSL_MPI_WINDOW_SIZE )
+ wsize = POLARSSL_MPI_WINDOW_SIZE;
+
+ j = N->n + 1;
+ MPI_CHK( mpi_grow( X, j ) );
+ MPI_CHK( mpi_grow( &W[1], j ) );
+ MPI_CHK( mpi_grow( &T, j * 2 ) );
+
+ /*
+ * Compensate for negative A (and correct at the end)
+ */
+ neg = ( A->s == -1 );
+
+ mpi_init( &Apos );
+ if( neg )
+ {
+ MPI_CHK( mpi_copy( &Apos, A ) );
+ Apos.s = 1;
+ A = &Apos;
+ }
+
+ /*
+ * If 1st call, pre-compute R^2 mod N
+ */
+ if( _RR == NULL || _RR->p == NULL )
+ {
+ MPI_CHK( mpi_lset( &RR, 1 ) );
+ MPI_CHK( mpi_shift_l( &RR, N->n * 2 * biL ) );
+ MPI_CHK( mpi_mod_mpi( &RR, &RR, N ) );
+
+ if( _RR != NULL )
+ memcpy( _RR, &RR, sizeof( mpi ) );
+ }
+ else
+ memcpy( &RR, _RR, sizeof( mpi ) );
+
+ /*
+ * W[1] = A * R^2 * R^-1 mod N = A * R mod N
+ */
+ if( mpi_cmp_mpi( A, N ) >= 0 )
+ mpi_mod_mpi( &W[1], A, N );
+ else mpi_copy( &W[1], A );
+
+ mpi_montmul( &W[1], &RR, N, mm, &T );
+
+ /*
+ * X = R^2 * R^-1 mod N = R mod N
+ */
+ MPI_CHK( mpi_copy( X, &RR ) );
+ mpi_montred( X, N, mm, &T );
+
+ if( wsize > 1 )
+ {
+ /*
+ * W[1 << (wsize - 1)] = W[1] ^ (wsize - 1)
+ */
+ j = one << (wsize - 1);
+
+ MPI_CHK( mpi_grow( &W[j], N->n + 1 ) );
+ MPI_CHK( mpi_copy( &W[j], &W[1] ) );
+
+ for( i = 0; i < wsize - 1; i++ )
+ mpi_montmul( &W[j], &W[j], N, mm, &T );
+
+ /*
+ * W[i] = W[i - 1] * W[1]
+ */
+ for( i = j + 1; i < (one << wsize); i++ )
+ {
+ MPI_CHK( mpi_grow( &W[i], N->n + 1 ) );
+ MPI_CHK( mpi_copy( &W[i], &W[i - 1] ) );
+
+ mpi_montmul( &W[i], &W[1], N, mm, &T );
+ }
+ }
+
+ nblimbs = E->n;
+ bufsize = 0;
+ nbits = 0;
+ wbits = 0;
+ state = 0;
+
+ while( 1 )
+ {
+ if( bufsize == 0 )
+ {
+ if( nblimbs-- == 0 )
+ break;
+
+ bufsize = sizeof( t_uint ) << 3;
+ }
+
+ bufsize--;
+
+ ei = (E->p[nblimbs] >> bufsize) & 1;
+
+ /*
+ * skip leading 0s
+ */
+ if( ei == 0 && state == 0 )
+ continue;
+
+ if( ei == 0 && state == 1 )
+ {
+ /*
+ * out of window, square X
+ */
+ mpi_montmul( X, X, N, mm, &T );
+ continue;
+ }
+
+ /*
+ * add ei to current window
+ */
+ state = 2;
+
+ nbits++;
+ wbits |= (ei << (wsize - nbits));
+
+ if( nbits == wsize )
+ {
+ /*
+ * X = X^wsize R^-1 mod N
+ */
+ for( i = 0; i < wsize; i++ )
+ mpi_montmul( X, X, N, mm, &T );
+
+ /*
+ * X = X * W[wbits] R^-1 mod N
+ */
+ mpi_montmul( X, &W[wbits], N, mm, &T );
+
+ state--;
+ nbits = 0;
+ wbits = 0;
+ }
+ }
+
+ /*
+ * process the remaining bits
+ */
+ for( i = 0; i < nbits; i++ )
+ {
+ mpi_montmul( X, X, N, mm, &T );
+
+ wbits <<= 1;
+
+ if( (wbits & (one << wsize)) != 0 )
+ mpi_montmul( X, &W[1], N, mm, &T );
+ }
+
+ /*
+ * X = A^E * R * R^-1 mod N = A^E mod N
+ */
+ mpi_montred( X, N, mm, &T );
+
+ if( neg )
+ {
+ X->s = -1;
+ mpi_add_mpi( X, N, X );
+ }
+
+cleanup:
+
+ for( i = (one << (wsize - 1)); i < (one << wsize); i++ )
+ mpi_free( &W[i] );
+
+ mpi_free( &W[1] ); mpi_free( &T ); mpi_free( &Apos );
+
+ if( _RR == NULL )
+ mpi_free( &RR );
+
+ return( ret );
+}
+
+/*
+ * Greatest common divisor: G = gcd(A, B) (HAC 14.54)
+ */
+int mpi_gcd( mpi *G, const mpi *A, const mpi *B )
+{
+ int ret;
+ size_t lz, lzt;
+ mpi TG, TA, TB;
+
+ mpi_init( &TG ); mpi_init( &TA ); mpi_init( &TB );
+
+ MPI_CHK( mpi_copy( &TA, A ) );
+ MPI_CHK( mpi_copy( &TB, B ) );
+
+ lz = mpi_lsb( &TA );
+ lzt = mpi_lsb( &TB );
+
+ if ( lzt < lz )
+ lz = lzt;
+
+ MPI_CHK( mpi_shift_r( &TA, lz ) );
+ MPI_CHK( mpi_shift_r( &TB, lz ) );
+
+ TA.s = TB.s = 1;
+
+ while( mpi_cmp_int( &TA, 0 ) != 0 )
+ {
+ MPI_CHK( mpi_shift_r( &TA, mpi_lsb( &TA ) ) );
+ MPI_CHK( mpi_shift_r( &TB, mpi_lsb( &TB ) ) );
+
+ if( mpi_cmp_mpi( &TA, &TB ) >= 0 )
+ {
+ MPI_CHK( mpi_sub_abs( &TA, &TA, &TB ) );
+ MPI_CHK( mpi_shift_r( &TA, 1 ) );
+ }
+ else
+ {
+ MPI_CHK( mpi_sub_abs( &TB, &TB, &TA ) );
+ MPI_CHK( mpi_shift_r( &TB, 1 ) );
+ }
+ }
+
+ MPI_CHK( mpi_shift_l( &TB, lz ) );
+ MPI_CHK( mpi_copy( G, &TB ) );
+
+cleanup:
+
+ mpi_free( &TG ); mpi_free( &TA ); mpi_free( &TB );
+
+ return( ret );
+}
+
+int mpi_fill_random( mpi *X, size_t size,
+ int (*f_rng)(void *, unsigned char *, size_t),
+ void *p_rng )
+{
+ int ret;
+
+ MPI_CHK( mpi_grow( X, CHARS_TO_LIMBS( size ) ) );
+ MPI_CHK( mpi_lset( X, 0 ) );
+
+ MPI_CHK( f_rng( p_rng, (unsigned char *) X->p, size ) );
+
+cleanup:
+ return( ret );
+}
+
+/*
+ * Modular inverse: X = A^-1 mod N (HAC 14.61 / 14.64)
+ */
+int mpi_inv_mod( mpi *X, const mpi *A, const mpi *N )
+{
+ int ret;
+ mpi G, TA, TU, U1, U2, TB, TV, V1, V2;
+
+ if( mpi_cmp_int( N, 0 ) <= 0 )
+ return( POLARSSL_ERR_MPI_BAD_INPUT_DATA );
+
+ mpi_init( &TA ); mpi_init( &TU ); mpi_init( &U1 ); mpi_init( &U2 );
+ mpi_init( &G ); mpi_init( &TB ); mpi_init( &TV );
+ mpi_init( &V1 ); mpi_init( &V2 );
+
+ MPI_CHK( mpi_gcd( &G, A, N ) );
+
+ if( mpi_cmp_int( &G, 1 ) != 0 )
+ {
+ ret = POLARSSL_ERR_MPI_NOT_ACCEPTABLE;
+ goto cleanup;
+ }
+
+ MPI_CHK( mpi_mod_mpi( &TA, A, N ) );
+ MPI_CHK( mpi_copy( &TU, &TA ) );
+ MPI_CHK( mpi_copy( &TB, N ) );
+ MPI_CHK( mpi_copy( &TV, N ) );
+
+ MPI_CHK( mpi_lset( &U1, 1 ) );
+ MPI_CHK( mpi_lset( &U2, 0 ) );
+ MPI_CHK( mpi_lset( &V1, 0 ) );
+ MPI_CHK( mpi_lset( &V2, 1 ) );
+
+ do
+ {
+ while( ( TU.p[0] & 1 ) == 0 )
+ {
+ MPI_CHK( mpi_shift_r( &TU, 1 ) );
+
+ if( ( U1.p[0] & 1 ) != 0 || ( U2.p[0] & 1 ) != 0 )
+ {
+ MPI_CHK( mpi_add_mpi( &U1, &U1, &TB ) );
+ MPI_CHK( mpi_sub_mpi( &U2, &U2, &TA ) );
+ }
+
+ MPI_CHK( mpi_shift_r( &U1, 1 ) );
+ MPI_CHK( mpi_shift_r( &U2, 1 ) );
+ }
+
+ while( ( TV.p[0] & 1 ) == 0 )
+ {
+ MPI_CHK( mpi_shift_r( &TV, 1 ) );
+
+ if( ( V1.p[0] & 1 ) != 0 || ( V2.p[0] & 1 ) != 0 )
+ {
+ MPI_CHK( mpi_add_mpi( &V1, &V1, &TB ) );
+ MPI_CHK( mpi_sub_mpi( &V2, &V2, &TA ) );
+ }
+
+ MPI_CHK( mpi_shift_r( &V1, 1 ) );
+ MPI_CHK( mpi_shift_r( &V2, 1 ) );
+ }
+
+ if( mpi_cmp_mpi( &TU, &TV ) >= 0 )
+ {
+ MPI_CHK( mpi_sub_mpi( &TU, &TU, &TV ) );
+ MPI_CHK( mpi_sub_mpi( &U1, &U1, &V1 ) );
+ MPI_CHK( mpi_sub_mpi( &U2, &U2, &V2 ) );
+ }
+ else
+ {
+ MPI_CHK( mpi_sub_mpi( &TV, &TV, &TU ) );
+ MPI_CHK( mpi_sub_mpi( &V1, &V1, &U1 ) );
+ MPI_CHK( mpi_sub_mpi( &V2, &V2, &U2 ) );
+ }
+ }
+ while( mpi_cmp_int( &TU, 0 ) != 0 );
+
+ while( mpi_cmp_int( &V1, 0 ) < 0 )
+ MPI_CHK( mpi_add_mpi( &V1, &V1, N ) );
+
+ while( mpi_cmp_mpi( &V1, N ) >= 0 )
+ MPI_CHK( mpi_sub_mpi( &V1, &V1, N ) );
+
+ MPI_CHK( mpi_copy( X, &V1 ) );
+
+cleanup:
+
+ mpi_free( &TA ); mpi_free( &TU ); mpi_free( &U1 ); mpi_free( &U2 );
+ mpi_free( &G ); mpi_free( &TB ); mpi_free( &TV );
+ mpi_free( &V1 ); mpi_free( &V2 );
+
+ return( ret );
+}
+
+#if defined(POLARSSL_GENPRIME)
+
+static const int small_prime[] =
+{
+ 3, 5, 7, 11, 13, 17, 19, 23,
+ 29, 31, 37, 41, 43, 47, 53, 59,
+ 61, 67, 71, 73, 79, 83, 89, 97,
+ 101, 103, 107, 109, 113, 127, 131, 137,
+ 139, 149, 151, 157, 163, 167, 173, 179,
+ 181, 191, 193, 197, 199, 211, 223, 227,
+ 229, 233, 239, 241, 251, 257, 263, 269,
+ 271, 277, 281, 283, 293, 307, 311, 313,
+ 317, 331, 337, 347, 349, 353, 359, 367,
+ 373, 379, 383, 389, 397, 401, 409, 419,
+ 421, 431, 433, 439, 443, 449, 457, 461,
+ 463, 467, 479, 487, 491, 499, 503, 509,
+ 521, 523, 541, 547, 557, 563, 569, 571,
+ 577, 587, 593, 599, 601, 607, 613, 617,
+ 619, 631, 641, 643, 647, 653, 659, 661,
+ 673, 677, 683, 691, 701, 709, 719, 727,
+ 733, 739, 743, 751, 757, 761, 769, 773,
+ 787, 797, 809, 811, 821, 823, 827, 829,
+ 839, 853, 857, 859, 863, 877, 881, 883,
+ 887, 907, 911, 919, 929, 937, 941, 947,
+ 953, 967, 971, 977, 983, 991, 997, -103
+};
+
+/*
+ * Miller-Rabin primality test (HAC 4.24)
+ */
+int mpi_is_prime( mpi *X,
+ int (*f_rng)(void *, unsigned char *, size_t),
+ void *p_rng )
+{
+ int ret, xs;
+ size_t i, j, n, s;
+ mpi W, R, T, A, RR;
+
+ if( mpi_cmp_int( X, 0 ) == 0 ||
+ mpi_cmp_int( X, 1 ) == 0 )
+ return( POLARSSL_ERR_MPI_NOT_ACCEPTABLE );
+
+ if( mpi_cmp_int( X, 2 ) == 0 )
+ return( 0 );
+
+ mpi_init( &W ); mpi_init( &R ); mpi_init( &T ); mpi_init( &A );
+ mpi_init( &RR );
+
+ xs = X->s; X->s = 1;
+
+ /*
+ * test trivial factors first
+ */
+ if( ( X->p[0] & 1 ) == 0 )
+ return( POLARSSL_ERR_MPI_NOT_ACCEPTABLE );
+
+ for( i = 0; small_prime[i] > 0; i++ )
+ {
+ t_uint r;
+
+ if( mpi_cmp_int( X, small_prime[i] ) <= 0 )
+ return( 0 );
+
+ MPI_CHK( mpi_mod_int( &r, X, small_prime[i] ) );
+
+ if( r == 0 )
+ return( POLARSSL_ERR_MPI_NOT_ACCEPTABLE );
+ }
+
+ /*
+ * W = |X| - 1
+ * R = W >> lsb( W )
+ */
+ MPI_CHK( mpi_sub_int( &W, X, 1 ) );
+ s = mpi_lsb( &W );
+ MPI_CHK( mpi_copy( &R, &W ) );
+ MPI_CHK( mpi_shift_r( &R, s ) );
+
+ i = mpi_msb( X );
+ /*
+ * HAC, table 4.4
+ */
+ n = ( ( i >= 1300 ) ? 2 : ( i >= 850 ) ? 3 :
+ ( i >= 650 ) ? 4 : ( i >= 350 ) ? 8 :
+ ( i >= 250 ) ? 12 : ( i >= 150 ) ? 18 : 27 );
+
+ for( i = 0; i < n; i++ )
+ {
+ /*
+ * pick a random A, 1 < A < |X| - 1
+ */
+ MPI_CHK( mpi_fill_random( &A, X->n * ciL, f_rng, p_rng ) );
+
+ if( mpi_cmp_mpi( &A, &W ) >= 0 )
+ {
+ j = mpi_msb( &A ) - mpi_msb( &W );
+ MPI_CHK( mpi_shift_r( &A, j + 1 ) );
+ }
+ A.p[0] |= 3;
+
+ /*
+ * A = A^R mod |X|
+ */
+ MPI_CHK( mpi_exp_mod( &A, &A, &R, X, &RR ) );
+
+ if( mpi_cmp_mpi( &A, &W ) == 0 ||
+ mpi_cmp_int( &A, 1 ) == 0 )
+ continue;
+
+ j = 1;
+ while( j < s && mpi_cmp_mpi( &A, &W ) != 0 )
+ {
+ /*
+ * A = A * A mod |X|
+ */
+ MPI_CHK( mpi_mul_mpi( &T, &A, &A ) );
+ MPI_CHK( mpi_mod_mpi( &A, &T, X ) );
+
+ if( mpi_cmp_int( &A, 1 ) == 0 )
+ break;
+
+ j++;
+ }
+
+ /*
+ * not prime if A != |X| - 1 or A == 1
+ */
+ if( mpi_cmp_mpi( &A, &W ) != 0 ||
+ mpi_cmp_int( &A, 1 ) == 0 )
+ {
+ ret = POLARSSL_ERR_MPI_NOT_ACCEPTABLE;
+ break;
+ }
+ }
+
+cleanup:
+
+ X->s = xs;
+
+ mpi_free( &W ); mpi_free( &R ); mpi_free( &T ); mpi_free( &A );
+ mpi_free( &RR );
+
+ return( ret );
+}
+
+/*
+ * Prime number generation
+ */
+int mpi_gen_prime( mpi *X, size_t nbits, int dh_flag,
+ int (*f_rng)(void *, unsigned char *, size_t),
+ void *p_rng )
+{
+ int ret;
+ size_t k, n;
+ mpi Y;
+
+ if( nbits < 3 || nbits > POLARSSL_MPI_MAX_BITS )
+ return( POLARSSL_ERR_MPI_BAD_INPUT_DATA );
+
+ mpi_init( &Y );
+
+ n = BITS_TO_LIMBS( nbits );
+
+ MPI_CHK( mpi_fill_random( X, n * ciL, f_rng, p_rng ) );
+
+ k = mpi_msb( X );
+ if( k < nbits ) MPI_CHK( mpi_shift_l( X, nbits - k ) );
+ if( k > nbits ) MPI_CHK( mpi_shift_r( X, k - nbits ) );
+
+ X->p[0] |= 3;
+
+ if( dh_flag == 0 )
+ {
+ while( ( ret = mpi_is_prime( X, f_rng, p_rng ) ) != 0 )
+ {
+ if( ret != POLARSSL_ERR_MPI_NOT_ACCEPTABLE )
+ goto cleanup;
+
+ MPI_CHK( mpi_add_int( X, X, 2 ) );
+ }
+ }
+ else
+ {
+ MPI_CHK( mpi_sub_int( &Y, X, 1 ) );
+ MPI_CHK( mpi_shift_r( &Y, 1 ) );
+
+ while( 1 )
+ {
+ if( ( ret = mpi_is_prime( X, f_rng, p_rng ) ) == 0 )
+ {
+ if( ( ret = mpi_is_prime( &Y, f_rng, p_rng ) ) == 0 )
+ break;
+
+ if( ret != POLARSSL_ERR_MPI_NOT_ACCEPTABLE )
+ goto cleanup;
+ }
+
+ if( ret != POLARSSL_ERR_MPI_NOT_ACCEPTABLE )
+ goto cleanup;
+
+ MPI_CHK( mpi_add_int( &Y, X, 1 ) );
+ MPI_CHK( mpi_add_int( X, X, 2 ) );
+ MPI_CHK( mpi_shift_r( &Y, 1 ) );
+ }
+ }
+
+cleanup:
+
+ mpi_free( &Y );
+
+ return( ret );
+}
+
+#endif
+
+#if defined(POLARSSL_SELF_TEST)
+
+#define GCD_PAIR_COUNT 3
+
+static const int gcd_pairs[GCD_PAIR_COUNT][3] =
+{
+ { 693, 609, 21 },
+ { 1764, 868, 28 },
+ { 768454923, 542167814, 1 }
+};
+
+/*
+ * Checkup routine
+ */
+int mpi_self_test( int verbose )
+{
+ int ret, i;
+ mpi A, E, N, X, Y, U, V;
+
+ mpi_init( &A ); mpi_init( &E ); mpi_init( &N ); mpi_init( &X );
+ mpi_init( &Y ); mpi_init( &U ); mpi_init( &V );
+
+ MPI_CHK( mpi_read_string( &A, 16,
+ "EFE021C2645FD1DC586E69184AF4A31E" \
+ "D5F53E93B5F123FA41680867BA110131" \
+ "944FE7952E2517337780CB0DB80E61AA" \
+ "E7C8DDC6C5C6AADEB34EB38A2F40D5E6" ) );
+
+ MPI_CHK( mpi_read_string( &E, 16,
+ "B2E7EFD37075B9F03FF989C7C5051C20" \
+ "34D2A323810251127E7BF8625A4F49A5" \
+ "F3E27F4DA8BD59C47D6DAABA4C8127BD" \
+ "5B5C25763222FEFCCFC38B832366C29E" ) );
+
+ MPI_CHK( mpi_read_string( &N, 16,
+ "0066A198186C18C10B2F5ED9B522752A" \
+ "9830B69916E535C8F047518A889A43A5" \
+ "94B6BED27A168D31D4A52F88925AA8F5" ) );
+
+ MPI_CHK( mpi_mul_mpi( &X, &A, &N ) );
+
+ MPI_CHK( mpi_read_string( &U, 16,
+ "602AB7ECA597A3D6B56FF9829A5E8B85" \
+ "9E857EA95A03512E2BAE7391688D264A" \
+ "A5663B0341DB9CCFD2C4C5F421FEC814" \
+ "8001B72E848A38CAE1C65F78E56ABDEF" \
+ "E12D3C039B8A02D6BE593F0BBBDA56F1" \
+ "ECF677152EF804370C1A305CAF3B5BF1" \
+ "30879B56C61DE584A0F53A2447A51E" ) );
+
+ if( verbose != 0 )
+ printf( " MPI test #1 (mul_mpi): " );
+
+ if( mpi_cmp_mpi( &X, &U ) != 0 )
+ {
+ if( verbose != 0 )
+ printf( "failed\n" );
+
+ return( 1 );
+ }
+
+ if( verbose != 0 )
+ printf( "passed\n" );
+
+ MPI_CHK( mpi_div_mpi( &X, &Y, &A, &N ) );
+
+ MPI_CHK( mpi_read_string( &U, 16,
+ "256567336059E52CAE22925474705F39A94" ) );
+
+ MPI_CHK( mpi_read_string( &V, 16,
+ "6613F26162223DF488E9CD48CC132C7A" \
+ "0AC93C701B001B092E4E5B9F73BCD27B" \
+ "9EE50D0657C77F374E903CDFA4C642" ) );
+
+ if( verbose != 0 )
+ printf( " MPI test #2 (div_mpi): " );
+
+ if( mpi_cmp_mpi( &X, &U ) != 0 ||
+ mpi_cmp_mpi( &Y, &V ) != 0 )
+ {
+ if( verbose != 0 )
+ printf( "failed\n" );
+
+ return( 1 );
+ }
+
+ if( verbose != 0 )
+ printf( "passed\n" );
+
+ MPI_CHK( mpi_exp_mod( &X, &A, &E, &N, NULL ) );
+
+ MPI_CHK( mpi_read_string( &U, 16,
+ "36E139AEA55215609D2816998ED020BB" \
+ "BD96C37890F65171D948E9BC7CBAA4D9" \
+ "325D24D6A3C12710F10A09FA08AB87" ) );
+
+ if( verbose != 0 )
+ printf( " MPI test #3 (exp_mod): " );
+
+ if( mpi_cmp_mpi( &X, &U ) != 0 )
+ {
+ if( verbose != 0 )
+ printf( "failed\n" );
+
+ return( 1 );
+ }
+
+ if( verbose != 0 )
+ printf( "passed\n" );
+
+#if defined(POLARSSL_GENPRIME)
+ MPI_CHK( mpi_inv_mod( &X, &A, &N ) );
+
+ MPI_CHK( mpi_read_string( &U, 16,
+ "003A0AAEDD7E784FC07D8F9EC6E3BFD5" \
+ "C3DBA76456363A10869622EAC2DD84EC" \
+ "C5B8A74DAC4D09E03B5E0BE779F2DF61" ) );
+
+ if( verbose != 0 )
+ printf( " MPI test #4 (inv_mod): " );
+
+ if( mpi_cmp_mpi( &X, &U ) != 0 )
+ {
+ if( verbose != 0 )
+ printf( "failed\n" );
+
+ return( 1 );
+ }
+
+ if( verbose != 0 )
+ printf( "passed\n" );
+#endif
+
+ if( verbose != 0 )
+ printf( " MPI test #5 (simple gcd): " );
+
+ for ( i = 0; i < GCD_PAIR_COUNT; i++)
+ {
+ MPI_CHK( mpi_lset( &X, gcd_pairs[i][0] ) );
+ MPI_CHK( mpi_lset( &Y, gcd_pairs[i][1] ) );
+
+ MPI_CHK( mpi_gcd( &A, &X, &Y ) );
+
+ if( mpi_cmp_int( &A, gcd_pairs[i][2] ) != 0 )
+ {
+ if( verbose != 0 )
+ printf( "failed at %d\n", i );
+
+ return( 1 );
+ }
+ }
+
+ if( verbose != 0 )
+ printf( "passed\n" );
+
+cleanup:
+
+ if( ret != 0 && verbose != 0 )
+ printf( "Unexpected error, return code = %08X\n", ret );
+
+ mpi_free( &A ); mpi_free( &E ); mpi_free( &N ); mpi_free( &X );
+ mpi_free( &Y ); mpi_free( &U ); mpi_free( &V );
+
+ if( verbose != 0 )
+ printf( "\n" );
+
+ return( ret );
+}
+
+#endif
+
+#endif
projects / proxmark3-svn / commitdiff