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/* mpi-inv.c - MPI functions
* Copyright (c) 1997 by Werner Koch (dd9jn)
*
* This file is part of G10.
*
* G10 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.
*
* G10 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., 59 Temple Place - Suite 330, Boston, MA 02111-1307, USA
*/
#include <config.h>
#include <stdio.h>
#include <stdlib.h>
#include "mpi-internal.h"
/****************
* Calculate the multiplicative inverse X of U mod V
* That is: Find the solution for
* 1 = (u*x) mod v
* This has only a unique solution if U and V are relatively prime.
* Returns 0 if a solution was found.
*/
int
mpi_inv_mod( MPI x, MPI u, MPI v )
{
#if 0
/* Extended Euclid's algorithm (See TAOPC Vol II, 4.52. Alg X) */
MPI u1, u2, u3, v1, v2, v3, q, t1, t2, t3;
u1 = mpi_alloc_set_ui(1);
u2 = mpi_alloc_set_ui(0);
u3 = mpi_copy(u);
v1 = mpi_alloc_set_ui(0);
v2 = mpi_alloc_set_ui(1);
v3 = mpi_copy(v);
q = mpi_alloc( mpi_get_nlimbs(u) );
t1 = mpi_alloc( mpi_get_nlimbs(u) );
t2 = mpi_alloc( mpi_get_nlimbs(u) );
t3 = mpi_alloc( mpi_get_nlimbs(u) );
while( mpi_cmp_ui( v3, 0 ) ) {
/*log_debug("----------------------\n");
log_mpidump("q =", u1);
log_mpidump("u1=", u1);
log_mpidump("u2=", u2);
log_mpidump("u3=", u3);
log_mpidump("v1=", v1);
log_mpidump("v2=", v2);
log_mpidump("v3=", v3); */
mpi_fdiv_q( q, u3, v3 );
mpi_mul(t1, v1, q); mpi_mul(t2, v2, q); mpi_mul(t3, v3, q);
mpi_sub(t1, u1, t1); mpi_sub(t2, u2, t2); mpi_sub(t3, u3, t3);
mpi_set(u1, v1); mpi_set(u2, v2); mpi_set(u3, v3);
mpi_set(v1, t1); mpi_set(v2, t2); mpi_set(v3, t3);
}
mpi_set(x, u3);
mpi_free(u1);
mpi_free(u2);
mpi_free(u3);
mpi_free(v1);
mpi_free(v2);
mpi_free(v3);
mpi_free(q);
mpi_free(t1);
mpi_free(t2);
mpi_free(t3);
#endif
/*****************************
* 1. Init: g0 = u g1 = v v0 = 0 v1 = 1
* 2. Test: if g1 is 0 terminate. Result = v0 < 0: v0 + n
* else: v0
* 3. Divide: div,rem = g0 / g1
* t1 = v0 - div * v1
* v0 = v1
* v1 = t1
* g0 = g1
* g1 = rem
* continue with step 2.
*/
MPI g0, g1, v0, v1, div, rem, t1;
g0 = mpi_copy(v);
g1 = mpi_copy(u);
v0 = mpi_alloc_set_ui( 0 );
v1 = mpi_alloc_set_ui( 1 );
div = mpi_alloc(mpi_get_nlimbs(v));
rem = mpi_alloc(mpi_get_nlimbs(v));
t1 = mpi_alloc(mpi_get_nlimbs(v));
while( mpi_cmp_ui( g1, 0) ) {
mpi_fdiv_qr(div, rem, g0, g1);
mpi_mul(t1, div, v1);
mpi_sub(t1, v0, t1);
mpi_set(v0, v1);
mpi_set(v1, t1);
mpi_set(g0, g1);
mpi_set(g1, rem);
}
if( mpi_cmp_ui( v0, 0) < 0 )
mpi_add( x, v0, v);
else
mpi_set( x, v0);
mpi_free(g0);
mpi_free(g1);
mpi_free(v0);
mpi_free(v1);
mpi_free(div);
mpi_free(rem);
mpi_free(t1);
return 0;
}
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