mpi-genesis 1
mpi-genesis 2 * Copyright (C) 1998, 1999, 2000, 2001 Free Software Foundation, Inc.
mpi-genesis 3 *
mpi-genesis 4 * This file is part of GnuPG.
mpi-genesis 5 *
mpi-genesis 6 * GnuPG is free software; you can redistribute it and/or modify
mpi-genesis 7 * it under the terms of the GNU General Public License as published by
mpi-genesis 8 * the Free Software Foundation; either version 3 of the License, or
mpi-genesis 9 * (at your option) any later version.
mpi-genesis 10 *
mpi-genesis 11 * GnuPG is distributed in the hope that it will be useful,
mpi-genesis 12 * but WITHOUT ANY WARRANTY; without even the implied warranty of
mpi-genesis 13 * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
mpi-genesis 14 * GNU General Public License for more details.
mpi-genesis 15 *
mpi-genesis 16 * You should have received a copy of the GNU General Public License
mpi-genesis 17 * along with this program; if not, see <http:
mpi-genesis 18 */
mpi-genesis 19
mpi-genesis 20 #include <config.h>
mpi-genesis 21 #include <stdio.h>
mpi-genesis 22 #include <stdlib.h>
mpi-genesis 23 #include "mpi-internal.h"
mpi-genesis 24
mpi-genesis 25
mpi-genesis 26
mpi-genesis 27 * Calculate the multiplicative inverse X of A mod N
mpi-genesis 28 * That is: Find the solution x for
mpi-genesis 29 * 1 = (a*x) mod n
mpi-genesis 30 */
mpi-genesis 31 void
mpi-genesis 32 mpi_invm( MPI x, MPI a, MPI n )
mpi-genesis 33 {
mpi-genesis 34 #if 0
mpi-genesis 35 MPI u, v, u1, u2, u3, v1, v2, v3, q, t1, t2, t3;
mpi-genesis 36 MPI ta, tb, tc;
mpi-genesis 37
mpi-genesis 38 u = mpi_copy(a);
mpi-genesis 39 v = mpi_copy(n);
mpi-genesis 40 u1 = mpi_alloc_set_ui(1);
mpi-genesis 41 u2 = mpi_alloc_set_ui(0);
mpi-genesis 42 u3 = mpi_copy(u);
mpi-genesis 43 v1 = mpi_alloc_set_ui(0);
mpi-genesis 44 v2 = mpi_alloc_set_ui(1);
mpi-genesis 45 v3 = mpi_copy(v);
mpi-genesis 46 q = mpi_alloc( mpi_get_nlimbs(u)+1 );
mpi-genesis 47 t1 = mpi_alloc( mpi_get_nlimbs(u)+1 );
mpi-genesis 48 t2 = mpi_alloc( mpi_get_nlimbs(u)+1 );
mpi-genesis 49 t3 = mpi_alloc( mpi_get_nlimbs(u)+1 );
mpi-genesis 50 while( mpi_cmp_ui( v3, 0 ) ) {
mpi-genesis 51 mpi_fdiv_q( q, u3, v3 );
mpi-genesis 52 mpi_mul(t1, v1, q); mpi_mul(t2, v2, q); mpi_mul(t3, v3, q);
mpi-genesis 53 mpi_sub(t1, u1, t1); mpi_sub(t2, u2, t2); mpi_sub(t3, u3, t3);
mpi-genesis 54 mpi_set(u1, v1); mpi_set(u2, v2); mpi_set(u3, v3);
mpi-genesis 55 mpi_set(v1, t1); mpi_set(v2, t2); mpi_set(v3, t3);
mpi-genesis 56 }
mpi-genesis 57
mpi-genesis 58 log_mpidump("q =", q );
mpi-genesis 59 log_mpidump("u1=", u1);
mpi-genesis 60 log_mpidump("u2=", u2);
mpi-genesis 61 log_mpidump("u3=", u3);
mpi-genesis 62 log_mpidump("v1=", v1);
mpi-genesis 63 log_mpidump("v2=", v2); */
mpi-genesis 64 mpi_set(x, u1);
mpi-genesis 65
mpi-genesis 66 mpi_free(u1);
mpi-genesis 67 mpi_free(u2);
mpi-genesis 68 mpi_free(u3);
mpi-genesis 69 mpi_free(v1);
mpi-genesis 70 mpi_free(v2);
mpi-genesis 71 mpi_free(v3);
mpi-genesis 72 mpi_free(q);
mpi-genesis 73 mpi_free(t1);
mpi-genesis 74 mpi_free(t2);
mpi-genesis 75 mpi_free(t3);
mpi-genesis 76 mpi_free(u);
mpi-genesis 77 mpi_free(v);
mpi-genesis 78 #elif 0
mpi-genesis 79
mpi-genesis 80 * modified according to Michael Penk's solution for Exercice 35 */
mpi-genesis 81
mpi-genesis 82
mpi-genesis 83 MPI u, v, u1, u2, u3, v1, v2, v3, t1, t2, t3;
mpi-genesis 84 unsigned k;
mpi-genesis 85 int sign;
mpi-genesis 86
mpi-genesis 87 u = mpi_copy(a);
mpi-genesis 88 v = mpi_copy(n);
mpi-genesis 89 for(k=0; !mpi_test_bit(u,0) && !mpi_test_bit(v,0); k++ ) {
mpi-genesis 90 mpi_rshift(u, u, 1);
mpi-genesis 91 mpi_rshift(v, v, 1);
mpi-genesis 92 }
mpi-genesis 93
mpi-genesis 94
mpi-genesis 95 u1 = mpi_alloc_set_ui(1);
mpi-genesis 96 u2 = mpi_alloc_set_ui(0);
mpi-genesis 97 u3 = mpi_copy(u);
mpi-genesis 98 v1 = mpi_copy(v);
mpi-genesis 99 v2 = mpi_alloc( mpi_get_nlimbs(u) ); mpi_sub( v2, u1, u );
mpi-genesis 100 v3 = mpi_copy(v);
mpi-genesis 101 if( mpi_test_bit(u, 0) ) {
mpi-genesis 102 t1 = mpi_alloc_set_ui(0);
mpi-genesis 103 t2 = mpi_alloc_set_ui(1); t2->sign = 1;
mpi-genesis 104 t3 = mpi_copy(v); t3->sign = !t3->sign;
mpi-genesis 105 goto Y4;
mpi-genesis 106 }
mpi-genesis 107 else {
mpi-genesis 108 t1 = mpi_alloc_set_ui(1);
mpi-genesis 109 t2 = mpi_alloc_set_ui(0);
mpi-genesis 110 t3 = mpi_copy(u);
mpi-genesis 111 }
mpi-genesis 112 do {
mpi-genesis 113 do {
mpi-genesis 114 if( mpi_test_bit(t1, 0) || mpi_test_bit(t2, 0) ) {
mpi-genesis 115 mpi_add(t1, t1, v);
mpi-genesis 116 mpi_sub(t2, t2, u);
mpi-genesis 117 }
mpi-genesis 118 mpi_rshift(t1, t1, 1);
mpi-genesis 119 mpi_rshift(t2, t2, 1);
mpi-genesis 120 mpi_rshift(t3, t3, 1);
mpi-genesis 121 Y4:
mpi-genesis 122 ;
mpi-genesis 123 } while( !mpi_test_bit( t3, 0 ) );
mpi-genesis 124
mpi-genesis 125 if( !t3->sign ) {
mpi-genesis 126 mpi_set(u1, t1);
mpi-genesis 127 mpi_set(u2, t2);
mpi-genesis 128 mpi_set(u3, t3);
mpi-genesis 129 }
mpi-genesis 130 else {
mpi-genesis 131 mpi_sub(v1, v, t1);
mpi-genesis 132 sign = u->sign; u->sign = !u->sign;
mpi-genesis 133 mpi_sub(v2, u, t2);
mpi-genesis 134 u->sign = sign;
mpi-genesis 135 sign = t3->sign; t3->sign = !t3->sign;
mpi-genesis 136 mpi_set(v3, t3);
mpi-genesis 137 t3->sign = sign;
mpi-genesis 138 }
mpi-genesis 139 mpi_sub(t1, u1, v1);
mpi-genesis 140 mpi_sub(t2, u2, v2);
mpi-genesis 141 mpi_sub(t3, u3, v3);
mpi-genesis 142 if( t1->sign ) {
mpi-genesis 143 mpi_add(t1, t1, v);
mpi-genesis 144 mpi_sub(t2, t2, u);
mpi-genesis 145 }
mpi-genesis 146 } while( mpi_cmp_ui( t3, 0 ) );
mpi-genesis 147
mpi-genesis 148 mpi_set(x, u1);
mpi-genesis 149
mpi-genesis 150 mpi_free(u1);
mpi-genesis 151 mpi_free(u2);
mpi-genesis 152 mpi_free(u3);
mpi-genesis 153 mpi_free(v1);
mpi-genesis 154 mpi_free(v2);
mpi-genesis 155 mpi_free(v3);
mpi-genesis 156 mpi_free(t1);
mpi-genesis 157 mpi_free(t2);
mpi-genesis 158 mpi_free(t3);
mpi-genesis 159 #else
mpi-genesis 160
mpi-genesis 161 * modified according to Michael Penk's solution for Exercice 35
mpi-genesis 162 * with further enhancement */
mpi-genesis 163 MPI u, v, u1, u2=NULL, u3, v1, v2=NULL, v3, t1, t2=NULL, t3;
mpi-genesis 164 unsigned k;
mpi-genesis 165 int sign;
mpi-genesis 166 int odd ;
mpi-genesis 167
mpi-genesis 168 u = mpi_copy(a);
mpi-genesis 169 v = mpi_copy(n);
mpi-genesis 170
mpi-genesis 171 for(k=0; !mpi_test_bit(u,0) && !mpi_test_bit(v,0); k++ ) {
mpi-genesis 172 mpi_rshift(u, u, 1);
mpi-genesis 173 mpi_rshift(v, v, 1);
mpi-genesis 174 }
mpi-genesis 175 odd = mpi_test_bit(v,0);
mpi-genesis 176
mpi-genesis 177 u1 = mpi_alloc_set_ui(1);
mpi-genesis 178 if( !odd )
mpi-genesis 179 u2 = mpi_alloc_set_ui(0);
mpi-genesis 180 u3 = mpi_copy(u);
mpi-genesis 181 v1 = mpi_copy(v);
mpi-genesis 182 if( !odd ) {
mpi-genesis 183 v2 = mpi_alloc( mpi_get_nlimbs(u) );
mpi-genesis 184 mpi_sub( v2, u1, u );
mpi-genesis 185 }
mpi-genesis 186 v3 = mpi_copy(v);
mpi-genesis 187 if( mpi_test_bit(u, 0) ) {
mpi-genesis 188 t1 = mpi_alloc_set_ui(0);
mpi-genesis 189 if( !odd ) {
mpi-genesis 190 t2 = mpi_alloc_set_ui(1); t2->sign = 1;
mpi-genesis 191 }
mpi-genesis 192 t3 = mpi_copy(v); t3->sign = !t3->sign;
mpi-genesis 193 goto Y4;
mpi-genesis 194 }
mpi-genesis 195 else {
mpi-genesis 196 t1 = mpi_alloc_set_ui(1);
mpi-genesis 197 if( !odd )
mpi-genesis 198 t2 = mpi_alloc_set_ui(0);
mpi-genesis 199 t3 = mpi_copy(u);
mpi-genesis 200 }
mpi-genesis 201 do {
mpi-genesis 202 do {
mpi-genesis 203 if( !odd ) {
mpi-genesis 204 if( mpi_test_bit(t1, 0) || mpi_test_bit(t2, 0) ) {
mpi-genesis 205 mpi_add(t1, t1, v);
mpi-genesis 206 mpi_sub(t2, t2, u);
mpi-genesis 207 }
mpi-genesis 208 mpi_rshift(t1, t1, 1);
mpi-genesis 209 mpi_rshift(t2, t2, 1);
mpi-genesis 210 mpi_rshift(t3, t3, 1);
mpi-genesis 211 }
mpi-genesis 212 else {
mpi-genesis 213 if( mpi_test_bit(t1, 0) )
mpi-genesis 214 mpi_add(t1, t1, v);
mpi-genesis 215 mpi_rshift(t1, t1, 1);
mpi-genesis 216 mpi_rshift(t3, t3, 1);
mpi-genesis 217 }
mpi-genesis 218 Y4:
mpi-genesis 219 ;
mpi-genesis 220 } while( !mpi_test_bit( t3, 0 ) );
mpi-genesis 221
mpi-genesis 222 if( !t3->sign ) {
mpi-genesis 223 mpi_set(u1, t1);
mpi-genesis 224 if( !odd )
mpi-genesis 225 mpi_set(u2, t2);
mpi-genesis 226 mpi_set(u3, t3);
mpi-genesis 227 }
mpi-genesis 228 else {
mpi-genesis 229 mpi_sub(v1, v, t1);
mpi-genesis 230 sign = u->sign; u->sign = !u->sign;
mpi-genesis 231 if( !odd )
mpi-genesis 232 mpi_sub(v2, u, t2);
mpi-genesis 233 u->sign = sign;
mpi-genesis 234 sign = t3->sign; t3->sign = !t3->sign;
mpi-genesis 235 mpi_set(v3, t3);
mpi-genesis 236 t3->sign = sign;
mpi-genesis 237 }
mpi-genesis 238 mpi_sub(t1, u1, v1);
mpi-genesis 239 if( !odd )
mpi-genesis 240 mpi_sub(t2, u2, v2);
mpi-genesis 241 mpi_sub(t3, u3, v3);
mpi-genesis 242 if( t1->sign ) {
mpi-genesis 243 mpi_add(t1, t1, v);
mpi-genesis 244 if( !odd )
mpi-genesis 245 mpi_sub(t2, t2, u);
mpi-genesis 246 }
mpi-genesis 247 } while( mpi_cmp_ui( t3, 0 ) );
mpi-genesis 248
mpi-genesis 249 mpi_set(x, u1);
mpi-genesis 250
mpi-genesis 251 mpi_free(u1);
mpi-genesis 252 mpi_free(v1);
mpi-genesis 253 mpi_free(t1);
mpi-genesis 254 if( !odd ) {
mpi-genesis 255 mpi_free(u2);
mpi-genesis 256 mpi_free(v2);
mpi-genesis 257 mpi_free(t2);
mpi-genesis 258 }
mpi-genesis 259 mpi_free(u3);
mpi-genesis 260 mpi_free(v3);
mpi-genesis 261 mpi_free(t3);
mpi-genesis 262
mpi-genesis 263 mpi_free(u);
mpi-genesis 264 mpi_free(v);
mpi-genesis 265 #endif
mpi-genesis 266 }