140 lines
4.8 KiB
C
140 lines
4.8 KiB
C
/*
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* Copyright (C) 2012 Michael Brown <mbrown@fensystems.co.uk>.
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*
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* This program is free software; you can redistribute it and/or
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* modify it under the terms of the GNU General Public License as
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* published by the Free Software Foundation; either version 2 of the
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* License, or any later version.
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*
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* This program is distributed in the hope that it will be useful, but
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* WITHOUT ANY WARRANTY; without even the implied warranty of
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* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
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* General Public License for more details.
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*
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* You should have received a copy of the GNU General Public License
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* along with this program; if not, write to the Free Software
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* Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA
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* 02110-1301, USA.
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*
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* You can also choose to distribute this program under the terms of
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* the Unmodified Binary Distribution Licence (as given in the file
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* COPYING.UBDL), provided that you have satisfied its requirements.
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*/
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FILE_LICENCE ( GPL2_OR_LATER_OR_UBDL );
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#include <stdint.h>
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#include <string.h>
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#include <assert.h>
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#include <ipxe/bigint.h>
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/** @file
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*
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* Big integer support
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*/
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/**
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* Perform modular multiplication of big integers
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*
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* @v multiplicand0 Element 0 of big integer to be multiplied
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* @v multiplier0 Element 0 of big integer to be multiplied
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* @v modulus0 Element 0 of big integer modulus
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* @v result0 Element 0 of big integer to hold result
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* @v size Number of elements in base, modulus, and result
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* @v tmp Temporary working space
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*/
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void bigint_mod_multiply_raw ( const bigint_element_t *multiplicand0,
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const bigint_element_t *multiplier0,
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const bigint_element_t *modulus0,
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bigint_element_t *result0,
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unsigned int size, void *tmp ) {
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const bigint_t ( size ) __attribute__ (( may_alias )) *multiplicand =
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( ( const void * ) multiplicand0 );
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const bigint_t ( size ) __attribute__ (( may_alias )) *multiplier =
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( ( const void * ) multiplier0 );
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const bigint_t ( size ) __attribute__ (( may_alias )) *modulus =
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( ( const void * ) modulus0 );
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bigint_t ( size ) __attribute__ (( may_alias )) *result =
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( ( void * ) result0 );
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struct {
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bigint_t ( size * 2 ) result;
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bigint_t ( size * 2 ) modulus;
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} *temp = tmp;
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int rotation;
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int i;
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/* Sanity check */
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assert ( sizeof ( *temp ) == bigint_mod_multiply_tmp_len ( modulus ) );
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/* Perform multiplication */
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bigint_multiply ( multiplicand, multiplier, &temp->result );
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/* Rescale modulus to match result */
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bigint_grow ( modulus, &temp->modulus );
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rotation = ( bigint_max_set_bit ( &temp->result ) -
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bigint_max_set_bit ( &temp->modulus ) );
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for ( i = 0 ; i < rotation ; i++ )
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bigint_rol ( &temp->modulus );
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/* Subtract multiples of modulus */
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for ( i = 0 ; i <= rotation ; i++ ) {
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if ( bigint_is_geq ( &temp->result, &temp->modulus ) )
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bigint_subtract ( &temp->modulus, &temp->result );
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bigint_ror ( &temp->modulus );
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}
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/* Resize result */
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bigint_shrink ( &temp->result, result );
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/* Sanity check */
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assert ( bigint_is_geq ( modulus, result ) );
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}
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/**
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* Perform modular exponentiation of big integers
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*
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* @v base0 Element 0 of big integer base
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* @v modulus0 Element 0 of big integer modulus
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* @v exponent0 Element 0 of big integer exponent
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* @v result0 Element 0 of big integer to hold result
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* @v size Number of elements in base, modulus, and result
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* @v exponent_size Number of elements in exponent
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* @v tmp Temporary working space
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*/
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void bigint_mod_exp_raw ( const bigint_element_t *base0,
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const bigint_element_t *modulus0,
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const bigint_element_t *exponent0,
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bigint_element_t *result0,
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unsigned int size, unsigned int exponent_size,
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void *tmp ) {
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const bigint_t ( size ) __attribute__ (( may_alias )) *base =
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( ( const void * ) base0 );
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const bigint_t ( size ) __attribute__ (( may_alias )) *modulus =
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( ( const void * ) modulus0 );
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const bigint_t ( exponent_size ) __attribute__ (( may_alias ))
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*exponent = ( ( const void * ) exponent0 );
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bigint_t ( size ) __attribute__ (( may_alias )) *result =
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( ( void * ) result0 );
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size_t mod_multiply_len = bigint_mod_multiply_tmp_len ( modulus );
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struct {
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bigint_t ( size ) base;
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bigint_t ( exponent_size ) exponent;
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uint8_t mod_multiply[mod_multiply_len];
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} *temp = tmp;
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static const uint8_t start[1] = { 0x01 };
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memcpy ( &temp->base, base, sizeof ( temp->base ) );
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memcpy ( &temp->exponent, exponent, sizeof ( temp->exponent ) );
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bigint_init ( result, start, sizeof ( start ) );
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while ( ! bigint_is_zero ( &temp->exponent ) ) {
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if ( bigint_bit_is_set ( &temp->exponent, 0 ) ) {
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bigint_mod_multiply ( result, &temp->base, modulus,
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result, temp->mod_multiply );
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}
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bigint_ror ( &temp->exponent );
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bigint_mod_multiply ( &temp->base, &temp->base, modulus,
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&temp->base, temp->mod_multiply );
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}
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}
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