mpi-genesis~ 1
mpi-genesis~ 2 * Copyright (C) 1994, 1996, 1998, 2000 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 * Note: This code is heavily based on the GNU MP Library.
mpi-genesis~ 20 * Actually it's the same code with only minor changes in the
mpi-genesis~ 21 * way the data is stored; this is to support the abstraction
mpi-genesis~ 22 * of an optional secure memory allocation which may be used
mpi-genesis~ 23 * to avoid revealing of sensitive data due to paging etc.
mpi-genesis~ 24 * The GNU MP Library itself is published under the LGPL;
mpi-genesis~ 25 * however I decided to publish this code under the plain GPL.
mpi-genesis~ 26 */
mpi-genesis~ 27
mpi-genesis~ 28 #include <config.h>
mpi-genesis~ 29 #include <stdio.h>
mpi-genesis~ 30 #include <stdlib.h>
mpi-genesis~ 31 #include <string.h>
mpi-genesis~ 32 #include "mpi-internal.h"
mpi-genesis~ 33 #include "longlong.h"
mpi-genesis~ 34 #include <assert.h>
mpi-genesis~ 35
mpi-genesis~ 36
mpi-genesis~ 37
mpi-genesis~ 38 * RES = BASE ^ EXP mod MOD
mpi-genesis~ 39 */
mpi-genesis~ 40 void
mpi-genesis~ 41 mpi_powm( MPI res, MPI base, MPI exponent, MPI mod)
mpi-genesis~ 42 {
mpi-genesis~ 43 mpi_ptr_t rp, ep, mp, bp;
mpi-genesis~ 44 mpi_size_t esize, msize, bsize, rsize;
mpi-genesis~ 45 int esign, msign, bsign, rsign;
mpi-genesis~ 46 int esec, msec, bsec, rsec;
mpi-genesis~ 47 mpi_size_t size;
mpi-genesis~ 48 int mod_shift_cnt;
mpi-genesis~ 49 int negative_result;
mpi-genesis~ 50 mpi_ptr_t mp_marker=NULL, bp_marker=NULL, ep_marker=NULL;
mpi-genesis~ 51 mpi_ptr_t xp_marker=NULL;
mpi-genesis~ 52 int assign_rp=0;
mpi-genesis~ 53 mpi_ptr_t tspace = NULL;
mpi-genesis~ 54 mpi_size_t tsize=0;
mpi-genesis~ 55
mpi-genesis~ 56
mpi-genesis~ 57 esize = exponent->nlimbs;
mpi-genesis~ 58 msize = mod->nlimbs;
mpi-genesis~ 59 size = 2 * msize;
mpi-genesis~ 60 esign = exponent->sign;
mpi-genesis~ 61 msign = mod->sign;
mpi-genesis~ 62
mpi-genesis~ 63 esec = mpi_is_secure(exponent);
mpi-genesis~ 64 msec = mpi_is_secure(mod);
mpi-genesis~ 65 bsec = mpi_is_secure(base);
mpi-genesis~ 66 rsec = mpi_is_secure(res);
mpi-genesis~ 67
mpi-genesis~ 68 rp = res->d;
mpi-genesis~ 69 ep = exponent->d;
mpi-genesis~ 70
mpi-genesis~ 71 if( !msize )
mpi-genesis~ 72 msize = 1 / msize;
mpi-genesis~ 73
mpi-genesis~ 74 if( !esize ) {
mpi-genesis~ 75
mpi-genesis~ 76 * depending on if MOD equals 1. */
mpi-genesis~ 77 rp[0] = 1;
mpi-genesis~ 78 res->nlimbs = (msize == 1 && mod->d[0] == 1) ? 0 : 1;
mpi-genesis~ 79 res->sign = 0;
mpi-genesis~ 80 goto leave;
mpi-genesis~ 81 }
mpi-genesis~ 82
mpi-genesis~ 83
mpi-genesis~ 84 * mpn_divrem. This will make the intermediate values in the calculation
mpi-genesis~ 85 * slightly larger, but the correct result is obtained after a final
mpi-genesis~ 86 * reduction using the original MOD value. */
mpi-genesis~ 87 mp = mp_marker = mpi_alloc_limb_space(msize, msec);
mpi-genesis~ 88 count_leading_zeros( mod_shift_cnt, mod->d[msize-1] );
mpi-genesis~ 89 if( mod_shift_cnt )
mpi-genesis~ 90 mpihelp_lshift( mp, mod->d, msize, mod_shift_cnt );
mpi-genesis~ 91 else
mpi-genesis~ 92 MPN_COPY( mp, mod->d, msize );
mpi-genesis~ 93
mpi-genesis~ 94 bsize = base->nlimbs;
mpi-genesis~ 95 bsign = base->sign;
mpi-genesis~ 96 if( bsize > msize ) {
mpi-genesis~ 97
mpi-genesis~ 98 * (The quotient is (bsize - msize + 1) limbs.) */
mpi-genesis~ 99 bp = bp_marker = mpi_alloc_limb_space( bsize + 1, bsec );
mpi-genesis~ 100 MPN_COPY( bp, base->d, bsize );
mpi-genesis~ 101
mpi-genesis~ 102 * at BP + MSIZE. */
mpi-genesis~ 103 mpihelp_divrem( bp + msize, 0, bp, bsize, mp, msize );
mpi-genesis~ 104 bsize = msize;
mpi-genesis~ 105
mpi-genesis~ 106 * quite a few times. */
mpi-genesis~ 107 MPN_NORMALIZE( bp, bsize );
mpi-genesis~ 108 }
mpi-genesis~ 109 else
mpi-genesis~ 110 bp = base->d;
mpi-genesis~ 111
mpi-genesis~ 112 if( !bsize ) {
mpi-genesis~ 113 res->nlimbs = 0;
mpi-genesis~ 114 res->sign = 0;
mpi-genesis~ 115 goto leave;
mpi-genesis~ 116 }
mpi-genesis~ 117
mpi-genesis~ 118 if( res->alloced < size ) {
mpi-genesis~ 119
mpi-genesis~ 120 * parameters are identical to RES, defer deallocation of the old
mpi-genesis~ 121 * space. */
mpi-genesis~ 122 if( rp == ep || rp == mp || rp == bp ) {
mpi-genesis~ 123 rp = mpi_alloc_limb_space( size, rsec );
mpi-genesis~ 124 assign_rp = 1;
mpi-genesis~ 125 }
mpi-genesis~ 126 else {
mpi-genesis~ 127 mpi_resize( res, size );
mpi-genesis~ 128 rp = res->d;
mpi-genesis~ 129 }
mpi-genesis~ 130 }
mpi-genesis~ 131 else {
mpi-genesis~ 132 if( rp == bp ) {
mpi-genesis~ 133
mpi-genesis~ 134 assert( !bp_marker );
mpi-genesis~ 135 bp = bp_marker = mpi_alloc_limb_space( bsize, bsec );
mpi-genesis~ 136 MPN_COPY(bp, rp, bsize);
mpi-genesis~ 137 }
mpi-genesis~ 138 if( rp == ep ) {
mpi-genesis~ 139
mpi-genesis~ 140 Allocate temp. space for EXPONENT. */
mpi-genesis~ 141 ep = ep_marker = mpi_alloc_limb_space( esize, esec );
mpi-genesis~ 142 MPN_COPY(ep, rp, esize);
mpi-genesis~ 143 }
mpi-genesis~ 144 if( rp == mp ) {
mpi-genesis~ 145
mpi-genesis~ 146 assert( !mp_marker );
mpi-genesis~ 147 mp = mp_marker = mpi_alloc_limb_space( msize, msec );
mpi-genesis~ 148 MPN_COPY(mp, rp, msize);
mpi-genesis~ 149 }
mpi-genesis~ 150 }
mpi-genesis~ 151
mpi-genesis~ 152 MPN_COPY( rp, bp, bsize );
mpi-genesis~ 153 rsize = bsize;
mpi-genesis~ 154 rsign = bsign;
mpi-genesis~ 155
mpi-genesis~ 156 {
mpi-genesis~ 157 mpi_size_t i;
mpi-genesis~ 158 mpi_ptr_t xp = xp_marker = mpi_alloc_limb_space( 2 * (msize + 1), msec );
mpi-genesis~ 159 int c;
mpi-genesis~ 160 mpi_limb_t e;
mpi-genesis~ 161 mpi_limb_t carry_limb;
mpi-genesis~ 162 struct karatsuba_ctx karactx;
mpi-genesis~ 163
mpi-genesis~ 164 memset( &karactx, 0, sizeof karactx );
mpi-genesis~ 165 negative_result = (ep[0] & 1) && base->sign;
mpi-genesis~ 166
mpi-genesis~ 167 i = esize - 1;
mpi-genesis~ 168 e = ep[i];
mpi-genesis~ 169 count_leading_zeros (c, e);
mpi-genesis~ 170 e = (e << c) << 1;
mpi-genesis~ 171 c = BITS_PER_MPI_LIMB - 1 - c;
mpi-genesis~ 172
mpi-genesis~ 173
mpi-genesis~ 174 *
mpi-genesis~ 175 * Make the result be pointed to alternately by XP and RP. This
mpi-genesis~ 176 * helps us avoid block copying, which would otherwise be necessary
mpi-genesis~ 177 * with the overlap restrictions of mpihelp_divmod. With 50% probability
mpi-genesis~ 178 * the result after this loop will be in the area originally pointed
mpi-genesis~ 179 * by RP (==RES->d), and with 50% probability in the area originally
mpi-genesis~ 180 * pointed to by XP.
mpi-genesis~ 181 */
mpi-genesis~ 182
mpi-genesis~ 183 for(;;) {
mpi-genesis~ 184 while( c ) {
mpi-genesis~ 185 mpi_ptr_t tp;
mpi-genesis~ 186 mpi_size_t xsize;
mpi-genesis~ 187
mpi-genesis~ 188
mpi-genesis~ 189 if( rsize < KARATSUBA_THRESHOLD )
mpi-genesis~ 190 mpih_sqr_n_basecase( xp, rp, rsize );
mpi-genesis~ 191 else {
mpi-genesis~ 192 if( !tspace ) {
mpi-genesis~ 193 tsize = 2 * rsize;
mpi-genesis~ 194 tspace = mpi_alloc_limb_space( tsize, 0 );
mpi-genesis~ 195 }
mpi-genesis~ 196 else if( tsize < (2*rsize) ) {
mpi-genesis~ 197 mpi_free_limb_space( tspace );
mpi-genesis~ 198 tsize = 2 * rsize;
mpi-genesis~ 199 tspace = mpi_alloc_limb_space( tsize, 0 );
mpi-genesis~ 200 }
mpi-genesis~ 201 mpih_sqr_n( xp, rp, rsize, tspace );
mpi-genesis~ 202 }
mpi-genesis~ 203
mpi-genesis~ 204 xsize = 2 * rsize;
mpi-genesis~ 205 if( xsize > msize ) {
mpi-genesis~ 206 mpihelp_divrem(xp + msize, 0, xp, xsize, mp, msize);
mpi-genesis~ 207 xsize = msize;
mpi-genesis~ 208 }
mpi-genesis~ 209
mpi-genesis~ 210 tp = rp; rp = xp; xp = tp;
mpi-genesis~ 211 rsize = xsize;
mpi-genesis~ 212
mpi-genesis~ 213 if( (mpi_limb_signed_t)e < 0 ) {
mpi-genesis~ 214
mpi-genesis~ 215 if( bsize < KARATSUBA_THRESHOLD ) {
mpi-genesis~ 216 mpihelp_mul( xp, rp, rsize, bp, bsize );
mpi-genesis~ 217 }
mpi-genesis~ 218 else {
mpi-genesis~ 219 mpihelp_mul_karatsuba_case(
mpi-genesis~ 220 xp, rp, rsize, bp, bsize, &karactx );
mpi-genesis~ 221 }
mpi-genesis~ 222
mpi-genesis~ 223 xsize = rsize + bsize;
mpi-genesis~ 224 if( xsize > msize ) {
mpi-genesis~ 225 mpihelp_divrem(xp + msize, 0, xp, xsize, mp, msize);
mpi-genesis~ 226 xsize = msize;
mpi-genesis~ 227 }
mpi-genesis~ 228
mpi-genesis~ 229 tp = rp; rp = xp; xp = tp;
mpi-genesis~ 230 rsize = xsize;
mpi-genesis~ 231 }
mpi-genesis~ 232 e <<= 1;
mpi-genesis~ 233 c--;
mpi-genesis~ 234 }
mpi-genesis~ 235
mpi-genesis~ 236 i--;
mpi-genesis~ 237 if( i < 0 )
mpi-genesis~ 238 break;
mpi-genesis~ 239 e = ep[i];
mpi-genesis~ 240 c = BITS_PER_MPI_LIMB;
mpi-genesis~ 241 }
mpi-genesis~ 242
mpi-genesis~ 243
mpi-genesis~ 244 * steps. Adjust the result by reducing it with the original MOD.
mpi-genesis~ 245 *
mpi-genesis~ 246 * Also make sure the result is put in RES->d (where it already
mpi-genesis~ 247 * might be, see above).
mpi-genesis~ 248 */
mpi-genesis~ 249 if( mod_shift_cnt ) {
mpi-genesis~ 250 carry_limb = mpihelp_lshift( res->d, rp, rsize, mod_shift_cnt);
mpi-genesis~ 251 rp = res->d;
mpi-genesis~ 252 if( carry_limb ) {
mpi-genesis~ 253 rp[rsize] = carry_limb;
mpi-genesis~ 254 rsize++;
mpi-genesis~ 255 }
mpi-genesis~ 256 }
mpi-genesis~ 257 else {
mpi-genesis~ 258 MPN_COPY( res->d, rp, rsize);
mpi-genesis~ 259 rp = res->d;
mpi-genesis~ 260 }
mpi-genesis~ 261
mpi-genesis~ 262 if( rsize >= msize ) {
mpi-genesis~ 263 mpihelp_divrem(rp + msize, 0, rp, rsize, mp, msize);
mpi-genesis~ 264 rsize = msize;
mpi-genesis~ 265 }
mpi-genesis~ 266
mpi-genesis~ 267
mpi-genesis~ 268 if( mod_shift_cnt )
mpi-genesis~ 269 mpihelp_rshift( rp, rp, rsize, mod_shift_cnt);
mpi-genesis~ 270 MPN_NORMALIZE (rp, rsize);
mpi-genesis~ 271
mpi-genesis~ 272 mpihelp_release_karatsuba_ctx( &karactx );
mpi-genesis~ 273 }
mpi-genesis~ 274
mpi-genesis~ 275 if( negative_result && rsize ) {
mpi-genesis~ 276 if( mod_shift_cnt )
mpi-genesis~ 277 mpihelp_rshift( mp, mp, msize, mod_shift_cnt);
mpi-genesis~ 278 mpihelp_sub( rp, mp, msize, rp, rsize);
mpi-genesis~ 279 rsize = msize;
mpi-genesis~ 280 rsign = msign;
mpi-genesis~ 281 MPN_NORMALIZE(rp, rsize);
mpi-genesis~ 282 }
mpi-genesis~ 283 res->nlimbs = rsize;
mpi-genesis~ 284 res->sign = rsign;
mpi-genesis~ 285
mpi-genesis~ 286 leave:
mpi-genesis~ 287 if( assign_rp ) mpi_assign_limb_space( res, rp, size );
mpi-genesis~ 288 if( mp_marker ) mpi_free_limb_space( mp_marker );
mpi-genesis~ 289 if( bp_marker ) mpi_free_limb_space( bp_marker );
mpi-genesis~ 290 if( ep_marker ) mpi_free_limb_space( ep_marker );
mpi-genesis~ 291 if( xp_marker ) mpi_free_limb_space( xp_marker );
mpi-genesis~ 292 if( tspace ) mpi_free_limb_space( tspace );
mpi-genesis~ 293 }
mpi-genesis~ 294