/*
 *  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 "common.h"
#include <string.h>
#include <rsa_config.h>
#include <stdio.h>


#if defined(POLARSSL_BIGNUM_C)

#include "bignum.h"
#include "bn_mul.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)


#define CONFIG_MALLOC_MAX	(128 * 1024)

//char malloc_buffer[CONFIG_MALLOC_MAX];
//static unsigned char * malloc_buffer = (unsigned char *)(0x10400000);
static int malloc_addr = 0;

void *mymalloc(int size)
{
	void *p;

	if (malloc_addr + size > CONFIG_MALLOC_MAX)
		p = NULL;
	else
		//p = (char *)&malloc_buffer[0] + malloc_addr;
		p = (char *)(unsigned long)(0x1700000+ malloc_addr);

	if (p)
		malloc_addr += size;
	//ss_printf("malloc size %d/%d addr %p\n", size, malloc_addr, p);

	//printf("aml log : malloc_buffer=%p malloc_addr=0x%x p=%p size=%d\n",
	//	malloc_buffer,malloc_addr,p,size);

	return p;
}

void myfree(void *ptr)
{
}

void mymallocreset()
{
	malloc_addr = 0;
}


/*
 * 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 );
        myfree( 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 *) mymalloc( 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 );
            myfree( 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 );
}


/*
 * 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 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 );
}
/*
 * 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 );
}

#endif