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  */
mpi_invm(MPI x,MPI a,MPI n)27 int 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 			}
95 Y4:
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 }
143 EXPORT_SYMBOL_GPL(mpi_invm);
144