1/* mpi-inv.c  -  MPI functions
  2 *	Copyright (C) 1998, 2001, 2002, 2003 Free Software Foundation, Inc.
  3 *
  4 * This file is part of Libgcrypt.
  5 *
  6 * Libgcrypt is free software; you can redistribute it and/or modify
  7 * it under the terms of the GNU Lesser General Public License as
  8 * published by the Free Software Foundation; either version 2.1 of
  9 * the License, or (at your option) any later version.
 10 *
 11 * Libgcrypt is distributed in the hope that it will be useful,
 12 * but WITHOUT ANY WARRANTY; without even the implied warranty of
 13 * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
 14 * GNU Lesser General Public License for more details.
 15 *
 16 * You should have received a copy of the GNU Lesser General Public
 17 * License along with this program; if not, see <http://www.gnu.org/licenses/>.
 18 */
 19
 20#include "mpi-internal.h"
 21
 22/****************
 23 * Calculate the multiplicative inverse X of A mod N
 24 * That is: Find the solution x for
 25 *		1 = (a*x) mod n
 26 */
 27int mpi_invm(MPI x, MPI a, MPI n)
 28{
 29	/* Extended Euclid's algorithm (See TAOCP Vol II, 4.5.2, Alg X)
 30	 * modified according to Michael Penk's solution for Exercise 35
 31	 * with further enhancement
 32	 */
 33	MPI u, v, u1, u2 = NULL, u3, v1, v2 = NULL, v3, t1, t2 = NULL, t3;
 34	unsigned int k;
 35	int sign;
 36	int odd;
 37
 38	if (!mpi_cmp_ui(a, 0))
 39		return 0; /* Inverse does not exists.  */
 40	if (!mpi_cmp_ui(n, 1))
 41		return 0; /* Inverse does not exists.  */
 42
 43	u = mpi_copy(a);
 44	v = mpi_copy(n);
 45
 46	for (k = 0; !mpi_test_bit(u, 0) && !mpi_test_bit(v, 0); k++) {
 47		mpi_rshift(u, u, 1);
 48		mpi_rshift(v, v, 1);
 49	}
 50	odd = mpi_test_bit(v, 0);
 51
 52	u1 = mpi_alloc_set_ui(1);
 53	if (!odd)
 54		u2 = mpi_alloc_set_ui(0);
 55	u3 = mpi_copy(u);
 56	v1 = mpi_copy(v);
 57	if (!odd) {
 58		v2 = mpi_alloc(mpi_get_nlimbs(u));
 59		mpi_sub(v2, u1, u); /* U is used as const 1 */
 60	}
 61	v3 = mpi_copy(v);
 62	if (mpi_test_bit(u, 0)) { /* u is odd */
 63		t1 = mpi_alloc_set_ui(0);
 64		if (!odd) {
 65			t2 = mpi_alloc_set_ui(1);
 66			t2->sign = 1;
 67		}
 68		t3 = mpi_copy(v);
 69		t3->sign = !t3->sign;
 70		goto Y4;
 71	} else {
 72		t1 = mpi_alloc_set_ui(1);
 73		if (!odd)
 74			t2 = mpi_alloc_set_ui(0);
 75		t3 = mpi_copy(u);
 76	}
 77
 78	do {
 79		do {
 80			if (!odd) {
 81				if (mpi_test_bit(t1, 0) || mpi_test_bit(t2, 0)) {
 82					/* one is odd */
 83					mpi_add(t1, t1, v);
 84					mpi_sub(t2, t2, u);
 85				}
 86				mpi_rshift(t1, t1, 1);
 87				mpi_rshift(t2, t2, 1);
 88				mpi_rshift(t3, t3, 1);
 89			} else {
 90				if (mpi_test_bit(t1, 0))
 91					mpi_add(t1, t1, v);
 92				mpi_rshift(t1, t1, 1);
 93				mpi_rshift(t3, t3, 1);
 94			}
 95Y4:
 96			;
 97		} while (!mpi_test_bit(t3, 0)); /* while t3 is even */
 98
 99		if (!t3->sign) {
100			mpi_set(u1, t1);
101			if (!odd)
102				mpi_set(u2, t2);
103			mpi_set(u3, t3);
104		} else {
105			mpi_sub(v1, v, t1);
106			sign = u->sign; u->sign = !u->sign;
107			if (!odd)
108				mpi_sub(v2, u, t2);
109			u->sign = sign;
110			sign = t3->sign; t3->sign = !t3->sign;
111			mpi_set(v3, t3);
112			t3->sign = sign;
113		}
114		mpi_sub(t1, u1, v1);
115		if (!odd)
116			mpi_sub(t2, u2, v2);
117		mpi_sub(t3, u3, v3);
118		if (t1->sign) {
119			mpi_add(t1, t1, v);
120			if (!odd)
121				mpi_sub(t2, t2, u);
122		}
123	} while (mpi_cmp_ui(t3, 0)); /* while t3 != 0 */
124	/* mpi_lshift( u3, k ); */
125	mpi_set(x, u1);
126
127	mpi_free(u1);
128	mpi_free(v1);
129	mpi_free(t1);
130	if (!odd) {
131		mpi_free(u2);
132		mpi_free(v2);
133		mpi_free(t2);
134	}
135	mpi_free(u3);
136	mpi_free(v3);
137	mpi_free(t3);
138
139	mpi_free(u);
140	mpi_free(v);
141	return 1;
142}
143EXPORT_SYMBOL_GPL(mpi_invm);