bigint.c

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/*
 * Copyright (C) 2012 Michael Brown <mbrown@fensystems.co.uk>.
 *
 * 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 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.
 *
 * You can also choose to distribute this program under the terms of
 * the Unmodified Binary Distribution Licence (as given in the file
 * COPYING.UBDL), provided that you have satisfied its requirements.
 */

FILE_LICENCE ( GPL2_OR_LATER_OR_UBDL );

#include <stdint.h>
#include <string.h>
#include <assert.h>
#include <ipxe/profile.h>
#include <ipxe/bigint.h>

/** @file
 *
 * Big integer support
 */

/** Modular multiplication overall profiler */
static struct profiler bigint_mod_multiply_profiler __profiler =
        { .name = "bigint_mod_multiply" };

/** Modular multiplication multiply step profiler */
static struct profiler bigint_mod_multiply_multiply_profiler __profiler =
        { .name = "bigint_mod_multiply.multiply" };

/** Modular multiplication rescale step profiler */
static struct profiler bigint_mod_multiply_rescale_profiler __profiler =
        { .name = "bigint_mod_multiply.rescale" };

/** Modular multiplication subtract step profiler */
static struct profiler bigint_mod_multiply_subtract_profiler __profiler =
        { .name = "bigint_mod_multiply.subtract" };

/**
 * Conditionally swap big integers (in constant time)
 *
 * @v first0            Element 0 of big integer to be conditionally swapped
 * @v second0           Element 0 of big integer to be conditionally swapped
 * @v size              Number of elements in big integers
 * @v swap              Swap first and second big integers
 */
void bigint_swap_raw ( bigint_element_t *first0, bigint_element_t *second0,
                       unsigned int size, int swap ) {
        bigint_element_t mask;
        bigint_element_t xor;
        unsigned int i;

        /* Construct mask */
        mask = ( ( bigint_element_t ) ( ! swap ) - 1 );

        /* Conditionally swap elements */
        for ( i = 0 ; i < size ; i++ ) {
                xor = ( mask & ( first0[i] ^ second0[i] ) );
                first0[i] ^= xor;
                second0[i] ^= xor;
        }
}

/**
 * Perform modular multiplication of big integers
 *
 * @v multiplicand0     Element 0 of big integer to be multiplied
 * @v multiplier0       Element 0 of big integer to be multiplied
 * @v modulus0          Element 0 of big integer modulus
 * @v result0           Element 0 of big integer to hold result
 * @v size              Number of elements in base, modulus, and result
 * @v tmp               Temporary working space
 */
void bigint_mod_multiply_raw ( const bigint_element_t *multiplicand0,
                               const bigint_element_t *multiplier0,
                               const bigint_element_t *modulus0,
                               bigint_element_t *result0,
                               unsigned int size, void *tmp ) {
        const bigint_t ( size ) __attribute__ (( may_alias )) *multiplicand =
                ( ( const void * ) multiplicand0 );
        const bigint_t ( size ) __attribute__ (( may_alias )) *multiplier =
                ( ( const void * ) multiplier0 );
        const bigint_t ( size ) __attribute__ (( may_alias )) *modulus =
                ( ( const void * ) modulus0 );
        bigint_t ( size ) __attribute__ (( may_alias )) *result =
                ( ( void * ) result0 );
        struct {
                bigint_t ( size * 2 ) result;
                bigint_t ( size * 2 ) modulus;
        } *temp = tmp;
        int rotation;
        int i;

        /* Start profiling */
        profile_start ( &bigint_mod_multiply_profiler );

        /* Sanity check */
        assert ( sizeof ( *temp ) == bigint_mod_multiply_tmp_len ( modulus ) );

        /* Perform multiplication */
        profile_start ( &bigint_mod_multiply_multiply_profiler );
        bigint_multiply ( multiplicand, multiplier, &temp->result );
        profile_stop ( &bigint_mod_multiply_multiply_profiler );

        /* Rescale modulus to match result */
        profile_start ( &bigint_mod_multiply_rescale_profiler );
        bigint_grow ( modulus, &temp->modulus );
        rotation = ( bigint_max_set_bit ( &temp->result ) -
                     bigint_max_set_bit ( &temp->modulus ) );
        for ( i = 0 ; i < rotation ; i++ )
                bigint_rol ( &temp->modulus );
        profile_stop ( &bigint_mod_multiply_rescale_profiler );

        /* Subtract multiples of modulus */
        profile_start ( &bigint_mod_multiply_subtract_profiler );
        for ( i = 0 ; i <= rotation ; i++ ) {
                if ( bigint_is_geq ( &temp->result, &temp->modulus ) )
                        bigint_subtract ( &temp->modulus, &temp->result );
                bigint_ror ( &temp->modulus );
        }
        profile_stop ( &bigint_mod_multiply_subtract_profiler );

        /* Resize result */
        bigint_shrink ( &temp->result, result );

        /* Sanity check */
        assert ( bigint_is_geq ( modulus, result ) );

        /* Stop profiling */
        profile_stop ( &bigint_mod_multiply_profiler );
}

/**
 * Perform modular exponentiation of big integers
 *
 * @v base0             Element 0 of big integer base
 * @v modulus0          Element 0 of big integer modulus
 * @v exponent0         Element 0 of big integer exponent
 * @v result0           Element 0 of big integer to hold result
 * @v size              Number of elements in base, modulus, and result
 * @v exponent_size     Number of elements in exponent
 * @v tmp               Temporary working space
 */
void bigint_mod_exp_raw ( const bigint_element_t *base0,
                          const bigint_element_t *modulus0,
                          const bigint_element_t *exponent0,
                          bigint_element_t *result0,
                          unsigned int size, unsigned int exponent_size,
                          void *tmp ) {
        const bigint_t ( size ) __attribute__ (( may_alias )) *base =
                ( ( const void * ) base0 );
        const bigint_t ( size ) __attribute__ (( may_alias )) *modulus =
                ( ( const void * ) modulus0 );
        const bigint_t ( exponent_size ) __attribute__ (( may_alias ))
                *exponent = ( ( const void * ) exponent0 );
        bigint_t ( size ) __attribute__ (( may_alias )) *result =
                ( ( void * ) result0 );
        size_t mod_multiply_len = bigint_mod_multiply_tmp_len ( modulus );
        struct {
                bigint_t ( size ) base;
                bigint_t ( exponent_size ) exponent;
                uint8_t mod_multiply[mod_multiply_len];
        } *temp = tmp;
        static const uint8_t start[1] = { 0x01 };

        memcpy ( &temp->base, base, sizeof ( temp->base ) );
        memcpy ( &temp->exponent, exponent, sizeof ( temp->exponent ) );
        bigint_init ( result, start, sizeof ( start ) );

        while ( ! bigint_is_zero ( &temp->exponent ) ) {
                if ( bigint_bit_is_set ( &temp->exponent, 0 ) ) {
                        bigint_mod_multiply ( result, &temp->base, modulus,
                                              result, temp->mod_multiply );
                }
                bigint_ror ( &temp->exponent );
                bigint_mod_multiply ( &temp->base, &temp->base, modulus,
                                      &temp->base, temp->mod_multiply );
        }
}