/* mpi-inv.c - MPI functions
* Copyright (C) 1998, 2001, 2002, 2003 Free Software Foundation, Inc.
*
* This file is part of Libgcrypt.
*
* Libgcrypt is free software; you can redistribute it and/or modify
* it under the terms of the GNU Lesser General Public License as
* published by the Free Software Foundation; either version 2.1 of
* the License, or (at your option) any later version.
*
* Libgcrypt 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 Lesser General Public License for more details.
*
* You should have received a copy of the GNU Lesser General Public
* License along with this program; if not, see .
*/
#include
#include
#include
#include "mpi-internal.h"
#include "g10lib.h"
/****************
* Calculate the multiplicative inverse X of A mod N
* That is: Find the solution x for
* 1 = (a*x) mod n
*/
int
_gcry_mpi_invm (gcry_mpi_t x, gcry_mpi_t a, gcry_mpi_t n)
{
#if 0
gcry_mpi_t u, v, u1, u2, u3, v1, v2, v3, q, t1, t2, t3;
gcry_mpi_t ta, tb, tc;
u = mpi_copy(a);
v = mpi_copy(n);
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)+1 );
t1 = mpi_alloc( mpi_get_nlimbs(u)+1 );
t2 = mpi_alloc( mpi_get_nlimbs(u)+1 );
t3 = mpi_alloc( mpi_get_nlimbs(u)+1 );
while( mpi_cmp_ui( v3, 0 ) ) {
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);
}
/* log_debug("result:\n");
log_mpidump("q =", q );
log_mpidump("u1=", u1);
log_mpidump("u2=", u2);
log_mpidump("u3=", u3);
log_mpidump("v1=", v1);
log_mpidump("v2=", v2); */
mpi_set(x, u1);
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);
mpi_free(u);
mpi_free(v);
#elif 0
/* Extended Euclid's algorithm (See TAOCP Vol II, 4.5.2, Alg X)
* modified according to Michael Penk's solution for Exercise 35 */
/* FIXME: we can simplify this in most cases (see Knuth) */
gcry_mpi_t u, v, u1, u2, u3, v1, v2, v3, t1, t2, t3;
unsigned k;
int sign;
u = mpi_copy(a);
v = mpi_copy(n);
for(k=0; !mpi_test_bit(u,0) && !mpi_test_bit(v,0); k++ ) {
mpi_rshift(u, u, 1);
mpi_rshift(v, v, 1);
}
u1 = mpi_alloc_set_ui(1);
u2 = mpi_alloc_set_ui(0);
u3 = mpi_copy(u);
v1 = mpi_copy(v); /* !-- used as const 1 */
v2 = mpi_alloc( mpi_get_nlimbs(u) ); mpi_sub( v2, u1, u );
v3 = mpi_copy(v);
if( mpi_test_bit(u, 0) ) { /* u is odd */
t1 = mpi_alloc_set_ui(0);
t2 = mpi_alloc_set_ui(1); t2->sign = 1;
t3 = mpi_copy(v); t3->sign = !t3->sign;
goto Y4;
}
else {
t1 = mpi_alloc_set_ui(1);
t2 = mpi_alloc_set_ui(0);
t3 = mpi_copy(u);
}
do {
do {
if( mpi_test_bit(t1, 0) || mpi_test_bit(t2, 0) ) { /* one is odd */
mpi_add(t1, t1, v);
mpi_sub(t2, t2, u);
}
mpi_rshift(t1, t1, 1);
mpi_rshift(t2, t2, 1);
mpi_rshift(t3, t3, 1);
Y4:
;
} while( !mpi_test_bit( t3, 0 ) ); /* while t3 is even */
if( !t3->sign ) {
mpi_set(u1, t1);
mpi_set(u2, t2);
mpi_set(u3, t3);
}
else {
mpi_sub(v1, v, t1);
sign = u->sign; u->sign = !u->sign;
mpi_sub(v2, u, t2);
u->sign = sign;
sign = t3->sign; t3->sign = !t3->sign;
mpi_set(v3, t3);
t3->sign = sign;
}
mpi_sub(t1, u1, v1);
mpi_sub(t2, u2, v2);
mpi_sub(t3, u3, v3);
if( t1->sign ) {
mpi_add(t1, t1, v);
mpi_sub(t2, t2, u);
}
} while( mpi_cmp_ui( t3, 0 ) ); /* while t3 != 0 */
/* mpi_lshift( u3, k ); */
mpi_set(x, u1);
mpi_free(u1);
mpi_free(u2);
mpi_free(u3);
mpi_free(v1);
mpi_free(v2);
mpi_free(v3);
mpi_free(t1);
mpi_free(t2);
mpi_free(t3);
#else
/* Extended Euclid's algorithm (See TAOCP Vol II, 4.5.2, Alg X)
* modified according to Michael Penk's solution for Exercise 35
* with further enhancement */
gcry_mpi_t u, v, u1, u2=NULL, u3, v1, v2=NULL, v3, t1, t2=NULL, t3;
unsigned k;
int sign;
int odd ;
if (!mpi_cmp_ui (a, 0))
return 0; /* Inverse does not exists. */
if (!mpi_cmp_ui (n, 1))
return 0; /* Inverse does not exists. */
u = mpi_copy(a);
v = mpi_copy(n);
for(k=0; !mpi_test_bit(u,0) && !mpi_test_bit(v,0); k++ ) {
mpi_rshift(u, u, 1);
mpi_rshift(v, v, 1);
}
odd = mpi_test_bit(v,0);
u1 = mpi_alloc_set_ui(1);
if( !odd )
u2 = mpi_alloc_set_ui(0);
u3 = mpi_copy(u);
v1 = mpi_copy(v);
if( !odd ) {
v2 = mpi_alloc( mpi_get_nlimbs(u) );
mpi_sub( v2, u1, u ); /* U is used as const 1 */
}
v3 = mpi_copy(v);
if( mpi_test_bit(u, 0) ) { /* u is odd */
t1 = mpi_alloc_set_ui(0);
if( !odd ) {
t2 = mpi_alloc_set_ui(1); t2->sign = 1;
}
t3 = mpi_copy(v); t3->sign = !t3->sign;
goto Y4;
}
else {
t1 = mpi_alloc_set_ui(1);
if( !odd )
t2 = mpi_alloc_set_ui(0);
t3 = mpi_copy(u);
}
do {
do {
if( !odd ) {
if( mpi_test_bit(t1, 0) || mpi_test_bit(t2, 0) ) { /* one is odd */
mpi_add(t1, t1, v);
mpi_sub(t2, t2, u);
}
mpi_rshift(t1, t1, 1);
mpi_rshift(t2, t2, 1);
mpi_rshift(t3, t3, 1);
}
else {
if( mpi_test_bit(t1, 0) )
mpi_add(t1, t1, v);
mpi_rshift(t1, t1, 1);
mpi_rshift(t3, t3, 1);
}
Y4:
;
} while( !mpi_test_bit( t3, 0 ) ); /* while t3 is even */
if( !t3->sign ) {
mpi_set(u1, t1);
if( !odd )
mpi_set(u2, t2);
mpi_set(u3, t3);
}
else {
mpi_sub(v1, v, t1);
sign = u->sign; u->sign = !u->sign;
if( !odd )
mpi_sub(v2, u, t2);
u->sign = sign;
sign = t3->sign; t3->sign = !t3->sign;
mpi_set(v3, t3);
t3->sign = sign;
}
mpi_sub(t1, u1, v1);
if( !odd )
mpi_sub(t2, u2, v2);
mpi_sub(t3, u3, v3);
if( t1->sign ) {
mpi_add(t1, t1, v);
if( !odd )
mpi_sub(t2, t2, u);
}
} while( mpi_cmp_ui( t3, 0 ) ); /* while t3 != 0 */
/* mpi_lshift( u3, k ); */
mpi_set(x, u1);
mpi_free(u1);
mpi_free(v1);
mpi_free(t1);
if( !odd ) {
mpi_free(u2);
mpi_free(v2);
mpi_free(t2);
}
mpi_free(u3);
mpi_free(v3);
mpi_free(t3);
mpi_free(u);
mpi_free(v);
#endif
return 1;
}