lib/mpi/mpi-inv.c

/* mpi-inv.c  -  MPI functions
 * Copyright (C) 1998, 1999, 2000, 2001 Free Software Foundation, Inc.
 *
 * This file is part of GnuPG.
 *
 * GnuPG 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.
 *
 * GnuPG 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 "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, const MPI a, const MPI n)
{
	/* Extended Euclid's algorithm (See TAOPC Vol II, 4.5.2, Alg X)
	 * modified according to Michael Penk's solution for Exercice 35
	 * with further enhancement */
	MPI u = NULL, v = NULL;
	MPI u1 = NULL, u2 = NULL, u3 = NULL;
	MPI v1 = NULL, v2 = NULL, v3 = NULL;
	MPI t1 = NULL, t2 = NULL, t3 = NULL;
	unsigned k;
	int sign;
	int odd = 0;
	int rc = -ENOMEM;

	if (mpi_copy(&u, a) < 0)
		goto cleanup;
	if (mpi_copy(&v, n) < 0)
		goto cleanup;

	for (k = 0; !mpi_test_bit(u, 0) && !mpi_test_bit(v, 0); k++) {
		if (mpi_rshift(u, u, 1) < 0)
			goto cleanup;
		if (mpi_rshift(v, v, 1) < 0)
			goto cleanup;
	}
	odd = mpi_test_bit(v, 0);

	u1 = mpi_alloc_set_ui(1);
	if (!u1)
		goto cleanup;
	if (!odd) {
		u2 = mpi_alloc_set_ui(0);
		if (!u2)
			goto cleanup;
	}
	if (mpi_copy(&u3, u) < 0)
		goto cleanup;
	if (mpi_copy(&v1, v) < 0)
		goto cleanup;
	if (!odd) {
		v2 = mpi_alloc(mpi_get_nlimbs(u));
		if (!v2)
			goto cleanup;
		if (mpi_sub(v2, u1, u) < 0)
			goto cleanup;	/* U is used as const 1 */
	}
	if (mpi_copy(&v3, v) < 0)
		goto cleanup;
	if (mpi_test_bit(u, 0)) {	/* u is odd */
		t1 = mpi_alloc_set_ui(0);
		if (!t1)
			goto cleanup;
		if (!odd) {
			t2 = mpi_alloc_set_ui(1);
			if (!t2)
				goto cleanup;
			t2->sign = 1;
		}
		if (mpi_copy(&t3, v) < 0)
			goto cleanup;
		t3->sign = !t3->sign;
		goto Y4;
	} else {
		t1 = mpi_alloc_set_ui(1);
		if (!t1)
			goto cleanup;
		if (!odd) {
			t2 = mpi_alloc_set_ui(0);
			if (!t2)
				goto cleanup;
		}
		if (mpi_copy(&t3, u) < 0)
			goto cleanup;
	}
	do {
		do {
			if (!odd) {
				if (mpi_test_bit(t1, 0) || mpi_test_bit(t2, 0)) {	/* one is odd */
					if (mpi_add(t1, t1, v) < 0)
						goto cleanup;
					if (mpi_sub(t2, t2, u) < 0)
						goto cleanup;
				}
				if (mpi_rshift(t1, t1, 1) < 0)
					goto cleanup;
				if (mpi_rshift(t2, t2, 1) < 0)
					goto cleanup;
				if (mpi_rshift(t3, t3, 1) < 0)
					goto cleanup;
			} else {
				if (mpi_test_bit(t1, 0))
					if (mpi_add(t1, t1, v) < 0)
						goto cleanup;
				if (mpi_rshift(t1, t1, 1) < 0)
					goto cleanup;
				if (mpi_rshift(t3, t3, 1) < 0)
					goto cleanup;
			}
Y4:
			;
		} while (!mpi_test_bit(t3, 0));	/* while t3 is even */

		if (!t3->sign) {
			if (mpi_set(u1, t1) < 0)
				goto cleanup;
			if (!odd)
				if (mpi_set(u2, t2) < 0)
					goto cleanup;
			if (mpi_set(u3, t3) < 0)
				goto cleanup;
		} else {
			if (mpi_sub(v1, v, t1) < 0)
				goto cleanup;
			sign = u->sign;
			u->sign = !u->sign;
			if (!odd)
				if (mpi_sub(v2, u, t2) < 0)
					goto cleanup;
			u->sign = sign;
			sign = t3->sign;
			t3->sign = !t3->sign;
			if (mpi_set(v3, t3) < 0)
				goto cleanup;
			t3->sign = sign;
		}
		if (mpi_sub(t1, u1, v1) < 0)
			goto cleanup;
		if (!odd)
			if (mpi_sub(t2, u2, v2) < 0)
				goto cleanup;
		if (mpi_sub(t3, u3, v3) < 0)
			goto cleanup;
		if (t1->sign) {
			if (mpi_add(t1, t1, v) < 0)
				goto cleanup;
			if (!odd)
				if (mpi_sub(t2, t2, u) < 0)
					goto cleanup;
		}
	} while (mpi_cmp_ui(t3, 0));	/* while t3 != 0 */
	/* mpi_lshift( u3, k ); */
	rc = mpi_set(x, u1);

cleanup:
	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 rc;
}