add px5g (moved from LuCI trunk)

SVN-Revision: 20429

1 files changed, 2010 insertions, 0 deletions

diff --git a/package/px5g/src/library/bignum.c b/package/px5g/src/library/bignum.c
new file mode 100644
index 0000000000..8b7c12ff00
--- /dev/null
+++ b/package/px5g/src/library/bignum.c
@@ -0,0 +1,2010 @@
+/*
+ *  Multi-precision integer library
+ *
+ *  Based on XySSL: Copyright (C) 2006-2008  Christophe Devine
+ *
+ *  Copyright (C) 2009  Paul Bakker <polarssl_maintainer at polarssl dot org>
+ *
+ *  All rights reserved.
+ *
+ *  Redistribution and use in source and binary forms, with or without
+ *  modification, are permitted provided that the following conditions
+ *  are met:
+ *  
+ *    * Redistributions of source code must retain the above copyright
+ *      notice, this list of conditions and the following disclaimer.
+ *    * Redistributions in binary form must reproduce the above copyright
+ *      notice, this list of conditions and the following disclaimer in the
+ *      documentation and/or other materials provided with the distribution.
+ *    * Neither the names of PolarSSL or XySSL nor the names of its contributors
+ *      may be used to endorse or promote products derived from this software
+ *      without specific prior written permission.
+ *  
+ *  THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
+ *  "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
+ *  LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS
+ *  FOR A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT
+ *  OWNER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL,
+ *  SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED
+ *  TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR
+ *  PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF
+ *  LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING
+ *  NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS
+ *  SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
+ */
+/*
+ *  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 "polarssl/bignum.h"
+#include "polarssl/bn_mul.h"
+
+#include <string.h>
+#include <stdlib.h>
+#include <stdarg.h>
+
+#define ciL    ((int) sizeof(t_int))    /* 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 or more mpi
+ */
+void mpi_init( mpi *X, ... )
+{
+    va_list args;
+
+    va_start( args, X );
+
+    while( X != NULL )
+    {
+        X->s = 1;
+        X->n = 0;
+        X->p = NULL;
+
+        X = va_arg( args, mpi* );
+    }
+
+    va_end( args );
+}
+
+/*
+ * Unallocate one or more mpi
+ */
+void mpi_free( mpi *X, ... )
+{
+    va_list args;
+
+    va_start( args, X );
+
+    while( X != NULL )
+    {
+        if( X->p != NULL )
+        {
+            memset( X->p, 0, X->n * ciL );
+            free( X->p );
+        }
+
+        X->s = 1;
+        X->n = 0;
+        X->p = NULL;
+
+        X = va_arg( args, mpi* );
+    }
+
+    va_end( args );
+}
+
+/*
+ * Enlarge to the specified number of limbs
+ */
+int mpi_grow( mpi *X, int nblimbs )
+{
+    t_int *p;
+
+    if( X->n < nblimbs )
+    {
+        if( ( p = (t_int *) malloc( nblimbs * ciL ) ) == NULL )
+            return( 1 );
+
+        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, mpi *Y )
+{
+    int ret, 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, int 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 );
+}
+
+/*
+ * Return the number of least significant bits
+ */
+int mpi_lsb( mpi *X )
+{
+    int i, j, count = 0;
+
+    for( i = 0; i < X->n; i++ )
+        for( j = 0; j < (int) biL; j++, count++ )
+            if( ( ( X->p[i] >> j ) & 1 ) != 0 )
+                return( count );
+
+    return( 0 );
+}
+
+/*
+ * Return the number of most significant bits
+ */
+int mpi_msb( mpi *X )
+{
+    int i, j;
+
+    for( i = X->n - 1; i > 0; i-- )
+        if( X->p[i] != 0 )
+            break;
+
+    for( j = biL - 1; j >= 0; j-- )
+        if( ( ( X->p[i] >> j ) & 1 ) != 0 )
+            break;
+
+    return( ( i * biL ) + j + 1 );
+}
+
+/*
+ * Return the total size in bytes
+ */
+int mpi_size( mpi *X )
+{
+    return( ( mpi_msb( X ) + 7 ) >> 3 );
+}
+
+/*
+ * Convert an ASCII character to digit value
+ */
+static int mpi_get_digit( t_int *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_int) radix )
+        return( POLARSSL_ERR_MPI_INVALID_CHARACTER );
+
+    return( 0 );
+}
+
+/*
+ * Import from an ASCII string
+ */
+int mpi_read_string( mpi *X, int radix, char *s )
+{
+    int ret, i, j, n;
+    t_int d;
+    mpi T;
+
+    if( radix < 2 || radix > 16 )
+        return( POLARSSL_ERR_MPI_BAD_INPUT_DATA );
+
+    mpi_init( &T, NULL );
+
+    if( radix == 16 )
+    {
+        n = BITS_TO_LIMBS( strlen( s ) << 2 );
+
+        MPI_CHK( mpi_grow( X, n ) );
+        MPI_CHK( mpi_lset( X, 0 ) );
+
+        for( i = strlen( s ) - 1, j = 0; i >= 0; i--, j++ )
+        {
+            if( i == 0 && s[i] == '-' )
+            {
+                X->s = -1;
+                break;
+            }
+
+            MPI_CHK( mpi_get_digit( &d, radix, s[i] ) );
+            X->p[j / (2 * ciL)] |= d << ( (j % (2 * ciL)) << 2 );
+        }
+    }
+    else
+    {
+        MPI_CHK( mpi_lset( X, 0 ) );
+
+        for( i = 0; i < (int) strlen( s ); 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 ) );
+            MPI_CHK( mpi_add_int( X, &T, d ) );
+        }
+    }
+
+cleanup:
+
+    mpi_free( &T, NULL );
+
+    return( ret );
+}
+
+/*
+ * Helper to write the digits high-order first
+ */
+static int mpi_write_hlp( mpi *X, int radix, char **p )
+{
+    int ret;
+    t_int 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( mpi *X, int radix, char *s, int *slen )
+{
+    int ret = 0, 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, NULL );
+
+    if( X->s == -1 )
+        *p++ = '-';
+
+    if( radix == 16 )
+    {
+        int c, i, j, k;
+
+        for( i = X->n - 1, k = 0; i >= 0; i-- )
+        {
+            for( j = ciL - 1; j >= 0; j-- )
+            {
+                c = ( X->p[i] >> (j << 3) ) & 0xFF;
+
+                if( c == 0 && k == 0 && (i + j) != 0 )
+                    continue;
+
+                p += sprintf( p, "%02X", c );
+                k = 1;
+            }
+        }
+    }
+    else
+    {
+        MPI_CHK( mpi_copy( &T, X ) );
+        MPI_CHK( mpi_write_hlp( &T, radix, &p ) );
+    }
+
+    *p++ = '\0';
+    *slen = p - s;
+
+cleanup:
+
+    mpi_free( &T, NULL );
+
+    return( ret );
+}
+
+/*
+ * Read X from an opened file
+ */
+int mpi_read_file( mpi *X, int radix, FILE *fin )
+{
+    t_int d;
+    int slen;
+    char *p;
+    char s[1024];
+
+    memset( s, 0, sizeof( s ) );
+    if( fgets( s, sizeof( s ) - 1, fin ) == NULL )
+        return( POLARSSL_ERR_MPI_FILE_IO_ERROR );
+
+    slen = strlen( s );
+    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( char *p, mpi *X, int radix, FILE *fout )
+{
+    int n, ret;
+    size_t slen;
+    size_t plen;
+    char s[1024];
+
+    n = sizeof( s );
+    memset( s, 0, n );
+    n -= 2;
+
+    MPI_CHK( mpi_write_string( X, radix, s, (int *) &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 );
+}
+
+/*
+ * Import X from unsigned binary data, big endian
+ */
+int mpi_read_binary( mpi *X, unsigned char *buf, int buflen )
+{
+    int ret, 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 - 1, j = 0; i >= n; i--, j++ )
+        X->p[j / ciL] |= ((t_int) buf[i]) << ((j % ciL) << 3);
+
+cleanup:
+
+    return( ret );
+}
+
+/*
+ * Export X into unsigned binary data, big endian
+ */
+int mpi_write_binary( mpi *X, unsigned char *buf, int buflen )
+{
+    int 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, int count )
+{
+    int ret, i, v0, t1;
+    t_int r0 = 0, r1;
+
+    v0 = count / (biL    );
+    t1 = count & (biL - 1);
+
+    i = mpi_msb( X ) + count;
+
+    if( X->n * (int) 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 - 1; i >= v0; i-- )
+            X->p[i] = X->p[i - v0];
+
+        for( ; i >= 0; i-- )
+            X->p[i] = 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, int count )
+{
+    int i, v0, v1;
+    t_int r0 = 0, r1;
+
+    v0 = count /  biL;
+    v1 = count & (biL - 1);
+
+    /*
+     * 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 - 1; i >= 0; i-- )
+        {
+            r1 = X->p[i] << (biL - v1);
+            X->p[i] >>= v1;
+            X->p[i] |= r0;
+            r0 = r1;
+        }
+    }
+
+    return( 0 );
+}
+
+/*
+ * Compare unsigned values
+ */
+int mpi_cmp_abs( mpi *X, mpi *Y )
+{
+    int i, j;
+
+    for( i = X->n - 1; i >= 0; i-- )
+        if( X->p[i] != 0 )
+            break;
+
+    for( j = Y->n - 1; j >= 0; j-- )
+        if( Y->p[j] != 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] > Y->p[i] ) return(  1 );
+        if( X->p[i] < Y->p[i] ) return( -1 );
+    }
+
+    return( 0 );
+}
+
+/*
+ * Compare signed values
+ */
+int mpi_cmp_mpi( mpi *X, mpi *Y )
+{
+    int i, j;
+
+    for( i = X->n - 1; i >= 0; i-- )
+        if( X->p[i] != 0 )
+            break;
+
+    for( j = Y->n - 1; j >= 0; j-- )
+        if( Y->p[j] != 0 )
+            break;
+
+    if( i < 0 && j < 0 )
+        return( 0 );
+
+    if( i > j ) return(  X->s );
+    if( j > i ) return( -X->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] > Y->p[i] ) return(  X->s );
+        if( X->p[i] < Y->p[i] ) return( -X->s );
+    }
+
+    return( 0 );
+}
+
+/*
+ * Compare signed values
+ */
+int mpi_cmp_int( mpi *X, int z )
+{
+    mpi Y;
+    t_int 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, mpi *A, mpi *B )
+{
+    int ret, i, j;
+    t_int *o, *p, c;
+
+    if( X == B )
+    {
+        mpi *T = A; A = X; B = T;
+    }
+
+    if( X != A )
+        MPI_CHK( mpi_copy( X, A ) );
+
+    for( j = B->n - 1; j >= 0; j-- )
+        if( B->p[j] != 0 )
+            break;
+
+    MPI_CHK( mpi_grow( X, j + 1 ) );
+
+    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++;
+    }
+
+cleanup:
+
+    return( ret );
+}
+
+/*
+ * Helper for mpi substraction
+ */
+static void mpi_sub_hlp( int n, t_int *s, t_int *d )
+{
+    int i;
+    t_int 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, mpi *A, mpi *B )
+{
+    mpi TB;
+    int ret, n;
+
+    if( mpi_cmp_abs( A, B ) < 0 )
+        return( POLARSSL_ERR_MPI_NEGATIVE_VALUE );
+
+    mpi_init( &TB, NULL );
+
+    if( X == B )
+    {
+        MPI_CHK( mpi_copy( &TB, B ) );
+        B = &TB;
+    }
+
+    if( X != A )
+        MPI_CHK( mpi_copy( X, A ) );
+
+    ret = 0;
+
+    for( n = B->n - 1; n >= 0; n-- )
+        if( B->p[n] != 0 )
+            break;
+
+    mpi_sub_hlp( n + 1, B->p, X->p );
+
+cleanup:
+
+    mpi_free( &TB, NULL );
+
+    return( ret );
+}
+
+/*
+ * Signed addition: X = A + B
+ */
+int mpi_add_mpi( mpi *X, mpi *A, 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, mpi *A, 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, mpi *A, int b )
+{
+    mpi _B;
+    t_int 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, mpi *A, int b )
+{
+    mpi _B;
+    t_int 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 void mpi_mul_hlp( int i, t_int *s, t_int *d, t_int b )
+{
+    t_int 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, mpi *A, mpi *B )
+{
+    int ret, i, j;
+    mpi TA, TB;
+
+    mpi_init( &TA, &TB, NULL );
+
+    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 - 1; i >= 0; i-- )
+        if( A->p[i] != 0 )
+            break;
+
+    for( j = B->n - 1; j >= 0; j-- )
+        if( B->p[j] != 0 )
+            break;
+
+    MPI_CHK( mpi_grow( X, i + j + 2 ) );
+    MPI_CHK( mpi_lset( X, 0 ) );
+
+    for( i++; j >= 0; j-- )
+        mpi_mul_hlp( i, A->p, X->p + j, B->p[j] );
+
+    X->s = A->s * B->s;
+
+cleanup:
+
+    mpi_free( &TB, &TA, NULL );
+
+    return( ret );
+}
+
+/*
+ * Baseline multiplication: X = A * b
+ */
+int mpi_mul_int( mpi *X, mpi *A, t_int b )
+{
+    mpi _B;
+    t_int 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, mpi *A, mpi *B )
+{
+    int ret, 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, &Y, &Z, &T1, &T2, NULL );
+
+    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 < (int) 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_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_LONGLONG)
+            t_dbl r;
+
+            r  = (t_dbl) X.p[i] << biL;
+            r |= (t_dbl) X.p[i - 1];
+            r /= Y.p[t];
+            if( r > ((t_dbl) 1 << biL) - 1)
+                r = ((t_dbl) 1 << biL) - 1;
+
+            Z.p[i - t - 1] = (t_int) r;
+#else
+            /*
+             * __udiv_qrnnd_c, from gmp/longlong.h
+             */
+            t_int q0, q1, r0, r1;
+            t_int 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 );
+        mpi_copy( R, &X );
+
+        R->s = A->s;
+        if( mpi_cmp_int( R, 0 ) == 0 )
+            R->s = 1;
+    }
+
+cleanup:
+
+    mpi_free( &X, &Y, &Z, &T1, &T2, NULL );
+
+    return( ret );
+}
+
+/*
+ * Division by int: A = Q * b + R
+ *
+ * Returns 0 if successful
+ *         1 if memory allocation failed
+ *         POLARSSL_ERR_MPI_DIVISION_BY_ZERO if b == 0
+ */
+int mpi_div_int( mpi *Q, mpi *R, mpi *A, int b )
+{
+    mpi _B;
+    t_int 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, mpi *A, mpi *B )
+{
+    int ret;
+
+    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_int *r, mpi *A, int b )
+{
+    int i;
+    t_int x, y, z;
+
+    if( b == 0 )
+        return( POLARSSL_ERR_MPI_DIVISION_BY_ZERO );
+
+    if( b < 0 )
+        b = -b;
+
+    /*
+     * 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 - 1, y = 0; i >= 0; i-- )
+    {
+        x  = A->p[i];
+        y  = ( y << biH ) | ( x >> biH );
+        z  = y / b;
+        y -= z * b;
+
+        x <<= biH;
+        y  = ( y << biH ) | ( x >> biH );
+        z  = y / b;
+        y -= z * b;
+    }
+
+    *r = y;
+
+    return( 0 );
+}
+
+/*
+ * Fast Montgomery initialization (thanks to Tom St Denis)
+ */
+static void mpi_montg_init( t_int *mm, mpi *N )
+{
+    t_int 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, mpi *B, mpi *N, t_int mm, mpi *T )
+{
+    int i, n, m;
+    t_int 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, mpi *N, t_int mm, mpi *T )
+{
+    t_int z = 1;
+    mpi U;
+
+    U.n = U.s = 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, mpi *A, mpi *E, mpi *N, mpi *_RR )
+{
+    int ret, i, j, wsize, wbits;
+    int bufsize, nblimbs, nbits;
+    t_int ei, mm, state;
+    mpi RR, T, W[64];
+
+    if( mpi_cmp_int( N, 0 ) < 0 || ( N->p[0] & 1 ) == 0 )
+        return( POLARSSL_ERR_MPI_BAD_INPUT_DATA );
+
+    /*
+     * Init temps and window size
+     */
+    mpi_montg_init( &mm, N );
+    mpi_init( &RR, &T, NULL );
+    memset( W, 0, sizeof( W ) );
+
+    i = mpi_msb( E );
+
+    wsize = ( i > 671 ) ? 6 : ( i > 239 ) ? 5 :
+            ( i >  79 ) ? 4 : ( i >  23 ) ? 3 : 1;
+
+    j = N->n + 1;
+    MPI_CHK( mpi_grow( X, j ) );
+    MPI_CHK( mpi_grow( &W[1],  j ) );
+    MPI_CHK( mpi_grow( &T, j * 2 ) );
+
+    /*
+     * 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 =  1 << (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 < (1 << 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_int ) << 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 & (1 << 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 );
+
+cleanup:
+
+    for( i = (1 << (wsize - 1)); i < (1 << wsize); i++ )
+        mpi_free( &W[i], NULL );
+
+    if( _RR != NULL )
+         mpi_free( &W[1], &T, NULL );
+    else mpi_free( &W[1], &T, &RR, NULL );
+
+    return( ret );
+}
+
+/*
+ * Greatest common divisor: G = gcd(A, B)  (HAC 14.54)
+ */
+int mpi_gcd( mpi *G, mpi *A, mpi *B )
+{
+    int ret, lz, lzt;
+    mpi TG, TA, TB;
+
+    mpi_init( &TG, &TA, &TB, NULL );
+
+    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( &TB, &TA, &TG, NULL );
+
+    return( ret );
+}
+
+#if defined(POLARSSL_GENPRIME)
+
+/*
+ * Modular inverse: X = A^-1 mod N  (HAC 14.61 / 14.64)
+ */
+int mpi_inv_mod( mpi *X, mpi *A, 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, &TU, &U1, &U2, &G,
+              &TB, &TV, &V1, &V2, NULL );
+
+    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( &V2, &V1, &TV, &TB, &G,
+              &U2, &U1, &TU, &TA, NULL );
+
+    return( ret );
+}
+
+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 *), void *p_rng )
+{
+    int ret, i, j, n, s, xs;
+    mpi W, R, T, A, RR;
+    unsigned char *p;
+
+    if( mpi_cmp_int( X, 0 ) == 0 )
+        return( 0 );
+
+    mpi_init( &W, &R, &T, &A, &RR, NULL );
+
+    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_int 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 )
+     */
+    s = mpi_lsb( &W );
+    MPI_CHK( mpi_sub_int( &W, X, 1 ) );
+    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_grow( &A, X->n ) );
+
+        p = (unsigned char *) A.p;
+        for( j = 0; j < A.n * ciL; j++ )
+            *p++ = (unsigned char) f_rng( p_rng );
+
+        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( &RR, &A, &T, &R, &W, NULL );
+
+    return( ret );
+}
+
+/*
+ * Prime number generation
+ */
+int mpi_gen_prime( mpi *X, int nbits, int dh_flag,
+                   int (*f_rng)(void *), void *p_rng )
+{
+    int ret, k, n;
+    unsigned char *p;
+    mpi Y;
+
+    if( nbits < 3 )
+        return( POLARSSL_ERR_MPI_BAD_INPUT_DATA );
+
+    mpi_init( &Y, NULL );
+
+    n = BITS_TO_LIMBS( nbits );
+
+    MPI_CHK( mpi_grow( X, n ) );
+    MPI_CHK( mpi_lset( X, 0 ) );
+
+    p = (unsigned char *) X->p;
+    for( k = 0; k < X->n * ciL; k++ )
+        *p++ = (unsigned char) 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, NULL );
+
+    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, &E, &N, &X, &Y, &U, &V, NULL );
+
+    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" );
+
+    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" );
+
+    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( &V, &U, &Y, &X, &N, &E, &A, NULL );
+
+    if( verbose != 0 )
+        printf( "\n" );
+
+    return( ret );
+}
+
+#endif
+
+#endif