144 lines
3.3 KiB
C
144 lines
3.3 KiB
C
/* mpi-inv.c - MPI functions
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* Copyright (C) 1998, 2001, 2002, 2003 Free Software Foundation, Inc.
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*
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* This file is part of Libgcrypt.
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*
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* Libgcrypt is free software; you can redistribute it and/or modify
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* it under the terms of the GNU Lesser General Public License as
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* published by the Free Software Foundation; either version 2.1 of
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* the License, or (at your option) any later version.
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*
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* Libgcrypt is distributed in the hope that it will be useful,
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* but WITHOUT ANY WARRANTY; without even the implied warranty of
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* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
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* GNU Lesser General Public License for more details.
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*
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* You should have received a copy of the GNU Lesser General Public
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* License along with this program; if not, see <http://www.gnu.org/licenses/>.
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*/
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#include "mpi-internal.h"
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/****************
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* Calculate the multiplicative inverse X of A mod N
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* That is: Find the solution x for
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* 1 = (a*x) mod n
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*/
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int mpi_invm(MPI x, MPI a, MPI n)
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{
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/* Extended Euclid's algorithm (See TAOCP Vol II, 4.5.2, Alg X)
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* modified according to Michael Penk's solution for Exercise 35
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* with further enhancement
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*/
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MPI u, v, u1, u2 = NULL, u3, v1, v2 = NULL, v3, t1, t2 = NULL, t3;
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unsigned int k;
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int sign;
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int odd;
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if (!mpi_cmp_ui(a, 0))
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return 0; /* Inverse does not exists. */
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if (!mpi_cmp_ui(n, 1))
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return 0; /* Inverse does not exists. */
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u = mpi_copy(a);
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v = mpi_copy(n);
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for (k = 0; !mpi_test_bit(u, 0) && !mpi_test_bit(v, 0); k++) {
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mpi_rshift(u, u, 1);
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mpi_rshift(v, v, 1);
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}
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odd = mpi_test_bit(v, 0);
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u1 = mpi_alloc_set_ui(1);
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if (!odd)
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u2 = mpi_alloc_set_ui(0);
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u3 = mpi_copy(u);
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v1 = mpi_copy(v);
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if (!odd) {
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v2 = mpi_alloc(mpi_get_nlimbs(u));
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mpi_sub(v2, u1, u); /* U is used as const 1 */
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}
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v3 = mpi_copy(v);
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if (mpi_test_bit(u, 0)) { /* u is odd */
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t1 = mpi_alloc_set_ui(0);
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if (!odd) {
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t2 = mpi_alloc_set_ui(1);
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t2->sign = 1;
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}
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t3 = mpi_copy(v);
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t3->sign = !t3->sign;
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goto Y4;
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} else {
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t1 = mpi_alloc_set_ui(1);
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if (!odd)
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t2 = mpi_alloc_set_ui(0);
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t3 = mpi_copy(u);
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}
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do {
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do {
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if (!odd) {
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if (mpi_test_bit(t1, 0) || mpi_test_bit(t2, 0)) {
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/* one is odd */
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mpi_add(t1, t1, v);
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mpi_sub(t2, t2, u);
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}
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mpi_rshift(t1, t1, 1);
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mpi_rshift(t2, t2, 1);
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mpi_rshift(t3, t3, 1);
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} else {
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if (mpi_test_bit(t1, 0))
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mpi_add(t1, t1, v);
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mpi_rshift(t1, t1, 1);
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mpi_rshift(t3, t3, 1);
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}
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Y4:
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;
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} while (!mpi_test_bit(t3, 0)); /* while t3 is even */
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if (!t3->sign) {
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mpi_set(u1, t1);
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if (!odd)
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mpi_set(u2, t2);
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mpi_set(u3, t3);
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} else {
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mpi_sub(v1, v, t1);
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sign = u->sign; u->sign = !u->sign;
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if (!odd)
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mpi_sub(v2, u, t2);
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u->sign = sign;
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sign = t3->sign; t3->sign = !t3->sign;
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mpi_set(v3, t3);
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t3->sign = sign;
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}
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mpi_sub(t1, u1, v1);
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if (!odd)
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mpi_sub(t2, u2, v2);
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mpi_sub(t3, u3, v3);
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if (t1->sign) {
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mpi_add(t1, t1, v);
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if (!odd)
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mpi_sub(t2, t2, u);
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}
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} while (mpi_cmp_ui(t3, 0)); /* while t3 != 0 */
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/* mpi_lshift( u3, k ); */
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mpi_set(x, u1);
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mpi_free(u1);
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mpi_free(v1);
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mpi_free(t1);
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if (!odd) {
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mpi_free(u2);
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mpi_free(v2);
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mpi_free(t2);
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}
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mpi_free(u3);
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mpi_free(v3);
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mpi_free(t3);
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mpi_free(u);
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mpi_free(v);
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return 1;
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}
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EXPORT_SYMBOL_GPL(mpi_invm);
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