mpi-inv.c
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/* 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 <http://www.gnu.org/licenses/>.
*/
#include "mpi-internal.h"
/****************
* Calculate the multiplicative inverse X of A mod N
* That is: Find the solution x for
* 1 = (a*x) mod n
*/
int mpi_invm(MPI x, MPI a, MPI n)
{
/* 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
*/
MPI u, v, u1, u2 = NULL, u3, v1, v2 = NULL, v3, t1, t2 = NULL, t3;
unsigned int 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);
return 1;
}
EXPORT_SYMBOL_GPL(mpi_invm);