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143 lines
3.3 KiB
143 lines
3.3 KiB
/* 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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