/* mpi-inv.c - MPI functions * Copyright (c) 1997 by Werner Koch (dd9jn) * * This file is part of G10. * * G10 is free software; you can redistribute it and/or modify * it under the terms of the GNU General Public License as published by * the Free Software Foundation; either version 2 of the License, or * (at your option) any later version. * * G10 is distributed in the hope that it will be useful, * but WITHOUT ANY WARRANTY; without even the implied warranty of * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the * GNU General Public License for more details. * * You should have received a copy of the GNU General Public License * along with this program; if not, write to the Free Software * Foundation, Inc., 59 Temple Place - Suite 330, Boston, MA 02111-1307, USA */ #include #include #include #include "mpi-internal.h" /**************** * Calculate the multiplicative inverse X of U mod V * That is: Find the solution for * 1 = (u*x) mod v * This has only a unique solution if U and V are relatively prime. * Returns 0 if a solution was found. */ int mpi_inv_mod( MPI x, MPI u, MPI v ) { #if 0 /* Extended Euclid's algorithm (See TAOPC Vol II, 4.52. Alg X) */ MPI u1, u2, u3, v1, v2, v3, q, t1, t2, t3; u1 = mpi_alloc_set_ui(1); u2 = mpi_alloc_set_ui(0); u3 = mpi_copy(u); v1 = mpi_alloc_set_ui(0); v2 = mpi_alloc_set_ui(1); v3 = mpi_copy(v); q = mpi_alloc( mpi_get_nlimbs(u) ); t1 = mpi_alloc( mpi_get_nlimbs(u) ); t2 = mpi_alloc( mpi_get_nlimbs(u) ); t3 = mpi_alloc( mpi_get_nlimbs(u) ); while( mpi_cmp_ui( v3, 0 ) ) { /*log_debug("----------------------\n"); log_mpidump("q =", u1); log_mpidump("u1=", u1); log_mpidump("u2=", u2); log_mpidump("u3=", u3); log_mpidump("v1=", v1); log_mpidump("v2=", v2); log_mpidump("v3=", v3); */ mpi_fdiv_q( q, u3, v3 ); mpi_mul(t1, v1, q); mpi_mul(t2, v2, q); mpi_mul(t3, v3, q); mpi_sub(t1, u1, t1); mpi_sub(t2, u2, t2); mpi_sub(t3, u3, t3); mpi_set(u1, v1); mpi_set(u2, v2); mpi_set(u3, v3); mpi_set(v1, t1); mpi_set(v2, t2); mpi_set(v3, t3); } mpi_set(x, u3); mpi_free(u1); mpi_free(u2); mpi_free(u3); mpi_free(v1); mpi_free(v2); mpi_free(v3); mpi_free(q); mpi_free(t1); mpi_free(t2); mpi_free(t3); #endif /***************************** * 1. Init: g0 = u g1 = v v0 = 0 v1 = 1 * 2. Test: if g1 is 0 terminate. Result = v0 < 0: v0 + n * else: v0 * 3. Divide: div,rem = g0 / g1 * t1 = v0 - div * v1 * v0 = v1 * v1 = t1 * g0 = g1 * g1 = rem * continue with step 2. */ MPI g0, g1, v0, v1, div, rem, t1; g0 = mpi_copy(v); g1 = mpi_copy(u); v0 = mpi_alloc_set_ui( 0 ); v1 = mpi_alloc_set_ui( 1 ); div = mpi_alloc(mpi_get_nlimbs(v)); rem = mpi_alloc(mpi_get_nlimbs(v)); t1 = mpi_alloc(mpi_get_nlimbs(v)); while( mpi_cmp_ui( g1, 0) ) { mpi_fdiv_qr(div, rem, g0, g1); mpi_mul(t1, div, v1); mpi_sub(t1, v0, t1); mpi_set(v0, v1); mpi_set(v1, t1); mpi_set(g0, g1); mpi_set(g1, rem); } if( mpi_cmp_ui( v0, 0) < 0 ) mpi_add( x, v0, v); else mpi_set( x, v0); mpi_free(g0); mpi_free(g1); mpi_free(v0); mpi_free(v1); mpi_free(div); mpi_free(rem); mpi_free(t1); return 0; }