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  1/* mpi-inv.c  -  MPI functions
  2 * Copyright (C) 1998, 1999, 2000, 2001 Free Software Foundation, Inc.
  3 *
  4 * This file is part of GnuPG.
  5 *
  6 * GnuPG is free software; you can redistribute it and/or modify
  7 * it under the terms of the GNU General Public License as published by
  8 * the Free Software Foundation; either version 2 of the License, or
  9 * (at your option) any later version.
 10 *
 11 * GnuPG 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 General Public License for more details.
 15 *
 16 * You should have received a copy of the GNU General Public License
 17 * along with this program; if not, write to the Free Software
 18 * Foundation, Inc., 59 Temple Place - Suite 330, Boston, MA 02111-1307, USA
 19 */
 20
 21#include "mpi-internal.h"
 22
 23/****************
 24 * Calculate the multiplicative inverse X of A mod N
 25 * That is: Find the solution x for
 26 *		1 = (a*x) mod n
 27 */
 28int mpi_invm(MPI x, const MPI a, const MPI n)
 29{
 30	/* Extended Euclid's algorithm (See TAOPC Vol II, 4.5.2, Alg X)
 31	 * modified according to Michael Penk's solution for Exercice 35
 32	 * with further enhancement */
 33	MPI u = NULL, v = NULL;
 34	MPI u1 = NULL, u2 = NULL, u3 = NULL;
 35	MPI v1 = NULL, v2 = NULL, v3 = NULL;
 36	MPI t1 = NULL, t2 = NULL, t3 = NULL;
 37	unsigned k;
 38	int sign;
 39	int odd = 0;
 40	int rc = -ENOMEM;
 41
 42	if (mpi_copy(&u, a) < 0)
 43		goto cleanup;
 44	if (mpi_copy(&v, n) < 0)
 45		goto cleanup;
 46
 47	for (k = 0; !mpi_test_bit(u, 0) && !mpi_test_bit(v, 0); k++) {
 48		if (mpi_rshift(u, u, 1) < 0)
 49			goto cleanup;
 50		if (mpi_rshift(v, v, 1) < 0)
 51			goto cleanup;
 52	}
 53	odd = mpi_test_bit(v, 0);
 54
 55	u1 = mpi_alloc_set_ui(1);
 56	if (!u1)
 57		goto cleanup;
 58	if (!odd) {
 59		u2 = mpi_alloc_set_ui(0);
 60		if (!u2)
 61			goto cleanup;
 62	}
 63	if (mpi_copy(&u3, u) < 0)
 64		goto cleanup;
 65	if (mpi_copy(&v1, v) < 0)
 66		goto cleanup;
 67	if (!odd) {
 68		v2 = mpi_alloc(mpi_get_nlimbs(u));
 69		if (!v2)
 70			goto cleanup;
 71		if (mpi_sub(v2, u1, u) < 0)
 72			goto cleanup;	/* U is used as const 1 */
 73	}
 74	if (mpi_copy(&v3, v) < 0)
 75		goto cleanup;
 76	if (mpi_test_bit(u, 0)) {	/* u is odd */
 77		t1 = mpi_alloc_set_ui(0);
 78		if (!t1)
 79			goto cleanup;
 80		if (!odd) {
 81			t2 = mpi_alloc_set_ui(1);
 82			if (!t2)
 83				goto cleanup;
 84			t2->sign = 1;
 85		}
 86		if (mpi_copy(&t3, v) < 0)
 87			goto cleanup;
 88		t3->sign = !t3->sign;
 89		goto Y4;
 90	} else {
 91		t1 = mpi_alloc_set_ui(1);
 92		if (!t1)
 93			goto cleanup;
 94		if (!odd) {
 95			t2 = mpi_alloc_set_ui(0);
 96			if (!t2)
 97				goto cleanup;
 98		}
 99		if (mpi_copy(&t3, u) < 0)
100			goto cleanup;
101	}
102	do {
103		do {
104			if (!odd) {
105				if (mpi_test_bit(t1, 0) || mpi_test_bit(t2, 0)) {	/* one is odd */
106					if (mpi_add(t1, t1, v) < 0)
107						goto cleanup;
108					if (mpi_sub(t2, t2, u) < 0)
109						goto cleanup;
110				}
111				if (mpi_rshift(t1, t1, 1) < 0)
112					goto cleanup;
113				if (mpi_rshift(t2, t2, 1) < 0)
114					goto cleanup;
115				if (mpi_rshift(t3, t3, 1) < 0)
116					goto cleanup;
117			} else {
118				if (mpi_test_bit(t1, 0))
119					if (mpi_add(t1, t1, v) < 0)
120						goto cleanup;
121				if (mpi_rshift(t1, t1, 1) < 0)
122					goto cleanup;
123				if (mpi_rshift(t3, t3, 1) < 0)
124					goto cleanup;
125			}
126Y4:
127			;
128		} while (!mpi_test_bit(t3, 0));	/* while t3 is even */
129
130		if (!t3->sign) {
131			if (mpi_set(u1, t1) < 0)
132				goto cleanup;
133			if (!odd)
134				if (mpi_set(u2, t2) < 0)
135					goto cleanup;
136			if (mpi_set(u3, t3) < 0)
137				goto cleanup;
138		} else {
139			if (mpi_sub(v1, v, t1) < 0)
140				goto cleanup;
141			sign = u->sign;
142			u->sign = !u->sign;
143			if (!odd)
144				if (mpi_sub(v2, u, t2) < 0)
145					goto cleanup;
146			u->sign = sign;
147			sign = t3->sign;
148			t3->sign = !t3->sign;
149			if (mpi_set(v3, t3) < 0)
150				goto cleanup;
151			t3->sign = sign;
152		}
153		if (mpi_sub(t1, u1, v1) < 0)
154			goto cleanup;
155		if (!odd)
156			if (mpi_sub(t2, u2, v2) < 0)
157				goto cleanup;
158		if (mpi_sub(t3, u3, v3) < 0)
159			goto cleanup;
160		if (t1->sign) {
161			if (mpi_add(t1, t1, v) < 0)
162				goto cleanup;
163			if (!odd)
164				if (mpi_sub(t2, t2, u) < 0)
165					goto cleanup;
166		}
167	} while (mpi_cmp_ui(t3, 0));	/* while t3 != 0 */
168	/* mpi_lshift( u3, k ); */
169	rc = mpi_set(x, u1);
170
171cleanup:
172	mpi_free(u1);
173	mpi_free(v1);
174	mpi_free(t1);
175	if (!odd) {
176		mpi_free(u2);
177		mpi_free(v2);
178		mpi_free(t2);
179	}
180	mpi_free(u3);
181	mpi_free(v3);
182	mpi_free(t3);
183
184	mpi_free(u);
185	mpi_free(v);
186	return rc;
187}