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267 lines
6.3 KiB
C
267 lines
6.3 KiB
C
/* mpi-inv.c - MPI functions
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* Copyright (C) 1998, 1999, 2000, 2001 Free Software Foundation, Inc.
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*
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* This file is part of GnuPG.
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*
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* GnuPG is free software; you can redistribute it and/or modify
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* it under the terms of the GNU General Public License as published by
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* the Free Software Foundation; either version 3 of the License, or
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* (at your option) any later version.
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*
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* GnuPG is distributed in the hope that it will be useful,
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* but WITHOUT ANY WARRANTY; without even the implied warranty of
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* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
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* GNU 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, see <http://www.gnu.org/licenses/>.
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*/
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#include <config.h>
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#include <stdio.h>
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#include <stdlib.h>
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#include "mpi-internal.h"
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/****************
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* Calculate the multiplicative inverse X of A mod N
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* That is: Find the solution x for
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* 1 = (a*x) mod n
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*/
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void
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mpi_invm( MPI x, MPI a, MPI n )
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{
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#if 0
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MPI u, v, u1, u2, u3, v1, v2, v3, q, t1, t2, t3;
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MPI ta, tb, tc;
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u = mpi_copy(a);
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v = mpi_copy(n);
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u1 = mpi_alloc_set_ui(1);
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u2 = mpi_alloc_set_ui(0);
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u3 = mpi_copy(u);
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v1 = mpi_alloc_set_ui(0);
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v2 = mpi_alloc_set_ui(1);
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v3 = mpi_copy(v);
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q = mpi_alloc( mpi_get_nlimbs(u)+1 );
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t1 = mpi_alloc( mpi_get_nlimbs(u)+1 );
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t2 = mpi_alloc( mpi_get_nlimbs(u)+1 );
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t3 = mpi_alloc( mpi_get_nlimbs(u)+1 );
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while( mpi_cmp_ui( v3, 0 ) ) {
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mpi_fdiv_q( q, u3, v3 );
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mpi_mul(t1, v1, q); mpi_mul(t2, v2, q); mpi_mul(t3, v3, q);
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mpi_sub(t1, u1, t1); mpi_sub(t2, u2, t2); mpi_sub(t3, u3, t3);
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mpi_set(u1, v1); mpi_set(u2, v2); mpi_set(u3, v3);
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mpi_set(v1, t1); mpi_set(v2, t2); mpi_set(v3, t3);
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}
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/* log_debug("result:\n");
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log_mpidump("q =", q );
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log_mpidump("u1=", u1);
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log_mpidump("u2=", u2);
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log_mpidump("u3=", u3);
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log_mpidump("v1=", v1);
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log_mpidump("v2=", v2); */
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mpi_set(x, u1);
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mpi_free(u1);
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mpi_free(u2);
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mpi_free(u3);
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mpi_free(v1);
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mpi_free(v2);
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mpi_free(v3);
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mpi_free(q);
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mpi_free(t1);
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mpi_free(t2);
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mpi_free(t3);
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mpi_free(u);
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mpi_free(v);
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#elif 0
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/* Extended Euclid's algorithm (See TAOPC Vol II, 4.5.2, Alg X)
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* modified according to Michael Penk's solution for Exercice 35 */
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/* FIXME: we can simplify this in most cases (see Knuth) */
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MPI u, v, u1, u2, u3, v1, v2, v3, t1, t2, t3;
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unsigned k;
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int sign;
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u = mpi_copy(a);
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v = mpi_copy(n);
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for(k=0; !mpi_test_bit(u,0) && !mpi_test_bit(v,0); k++ ) {
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mpi_rshift(u, u, 1);
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mpi_rshift(v, v, 1);
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}
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u1 = mpi_alloc_set_ui(1);
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u2 = mpi_alloc_set_ui(0);
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u3 = mpi_copy(u);
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v1 = mpi_copy(v); /* !-- used as const 1 */
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v2 = mpi_alloc( mpi_get_nlimbs(u) ); mpi_sub( v2, u1, u );
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v3 = mpi_copy(v);
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if( mpi_test_bit(u, 0) ) { /* u is odd */
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t1 = mpi_alloc_set_ui(0);
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t2 = mpi_alloc_set_ui(1); t2->sign = 1;
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t3 = mpi_copy(v); t3->sign = !t3->sign;
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goto Y4;
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}
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else {
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t1 = mpi_alloc_set_ui(1);
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t2 = mpi_alloc_set_ui(0);
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t3 = mpi_copy(u);
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}
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do {
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do {
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if( mpi_test_bit(t1, 0) || mpi_test_bit(t2, 0) ) { /* one is odd */
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mpi_add(t1, t1, v);
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mpi_sub(t2, t2, u);
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}
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mpi_rshift(t1, t1, 1);
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mpi_rshift(t2, t2, 1);
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mpi_rshift(t3, t3, 1);
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Y4:
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;
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} while( !mpi_test_bit( t3, 0 ) ); /* while t3 is even */
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if( !t3->sign ) {
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mpi_set(u1, t1);
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mpi_set(u2, t2);
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mpi_set(u3, t3);
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}
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else {
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mpi_sub(v1, v, t1);
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sign = u->sign; u->sign = !u->sign;
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mpi_sub(v2, u, t2);
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u->sign = sign;
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sign = t3->sign; t3->sign = !t3->sign;
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mpi_set(v3, t3);
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t3->sign = sign;
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}
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mpi_sub(t1, u1, v1);
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mpi_sub(t2, u2, v2);
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mpi_sub(t3, u3, v3);
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if( t1->sign ) {
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mpi_add(t1, t1, v);
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mpi_sub(t2, t2, u);
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}
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} while( mpi_cmp_ui( t3, 0 ) ); /* while t3 != 0 */
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/* mpi_lshift( u3, k ); */
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mpi_set(x, u1);
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mpi_free(u1);
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mpi_free(u2);
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mpi_free(u3);
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mpi_free(v1);
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mpi_free(v2);
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mpi_free(v3);
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mpi_free(t1);
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mpi_free(t2);
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mpi_free(t3);
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#else
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/* Extended Euclid's algorithm (See TAOPC Vol II, 4.5.2, Alg X)
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* modified according to Michael Penk's solution for Exercice 35
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* with further enhancement */
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MPI u, v, u1, u2=NULL, u3, v1, v2=NULL, v3, t1, t2=NULL, t3;
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unsigned k;
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int sign;
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int odd ;
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u = mpi_copy(a);
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v = mpi_copy(n);
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for(k=0; !mpi_test_bit(u,0) && !mpi_test_bit(v,0); k++ ) {
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mpi_rshift(u, u, 1);
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mpi_rshift(v, v, 1);
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}
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odd = mpi_test_bit(v,0);
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u1 = mpi_alloc_set_ui(1);
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if( !odd )
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u2 = mpi_alloc_set_ui(0);
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u3 = mpi_copy(u);
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v1 = mpi_copy(v);
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if( !odd ) {
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v2 = mpi_alloc( mpi_get_nlimbs(u) );
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mpi_sub( v2, u1, u ); /* U is used as const 1 */
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}
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v3 = mpi_copy(v);
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if( mpi_test_bit(u, 0) ) { /* u is odd */
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t1 = mpi_alloc_set_ui(0);
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if( !odd ) {
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t2 = mpi_alloc_set_ui(1); t2->sign = 1;
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}
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t3 = mpi_copy(v); t3->sign = !t3->sign;
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goto Y4;
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}
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else {
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t1 = mpi_alloc_set_ui(1);
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if( !odd )
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t2 = mpi_alloc_set_ui(0);
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t3 = mpi_copy(u);
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}
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do {
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do {
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if( !odd ) {
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if( mpi_test_bit(t1, 0) || mpi_test_bit(t2, 0) ) { /* one is odd */
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mpi_add(t1, t1, v);
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mpi_sub(t2, t2, u);
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}
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mpi_rshift(t1, t1, 1);
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mpi_rshift(t2, t2, 1);
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mpi_rshift(t3, t3, 1);
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}
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else {
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if( mpi_test_bit(t1, 0) )
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mpi_add(t1, t1, v);
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mpi_rshift(t1, t1, 1);
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mpi_rshift(t3, t3, 1);
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}
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Y4:
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;
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} while( !mpi_test_bit( t3, 0 ) ); /* while t3 is even */
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if( !t3->sign ) {
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mpi_set(u1, t1);
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if( !odd )
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mpi_set(u2, t2);
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mpi_set(u3, t3);
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}
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else {
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mpi_sub(v1, v, t1);
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sign = u->sign; u->sign = !u->sign;
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if( !odd )
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mpi_sub(v2, u, t2);
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u->sign = sign;
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sign = t3->sign; t3->sign = !t3->sign;
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mpi_set(v3, t3);
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t3->sign = sign;
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}
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mpi_sub(t1, u1, v1);
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if( !odd )
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mpi_sub(t2, u2, v2);
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mpi_sub(t3, u3, v3);
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if( t1->sign ) {
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mpi_add(t1, t1, v);
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if( !odd )
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mpi_sub(t2, t2, u);
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}
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} while( mpi_cmp_ui( t3, 0 ) ); /* while t3 != 0 */
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/* mpi_lshift( u3, k ); */
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mpi_set(x, u1);
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mpi_free(u1);
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mpi_free(v1);
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mpi_free(t1);
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if( !odd ) {
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mpi_free(u2);
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mpi_free(v2);
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mpi_free(t2);
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}
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mpi_free(u3);
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mpi_free(v3);
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mpi_free(t3);
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mpi_free(u);
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mpi_free(v);
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#endif
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}
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