lib/mpi/mpi-pow.c

   1 /* mpi-pow.c  -  MPI functions
   2  *      Copyright (C) 1994, 1996, 1998, 2000 Free Software Foundation, Inc.
   3  *
   4  * This file is part of GnuPG.
   5  *
   6  * GnuPG is free software; you can redistribute it and/or modify
   7  * it under the terms of the GNU General Public License as published by
   8  * the Free Software Foundation; either version 2 of the License, or
   9  * (at your option) any later version.
  10  *
  11  * GnuPG is distributed in the hope that it will be useful,
  12  * but WITHOUT ANY WARRANTY; without even the implied warranty of
  13  * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
  14  * GNU General Public License for more details.
  15  *
  16  * You should have received a copy of the GNU General Public License
  17  * along with this program; if not, write to the Free Software
  18  * Foundation, Inc., 59 Temple Place - Suite 330, Boston, MA 02111-1307, USA
  19  *
  20  * Note: This code is heavily based on the GNU MP Library.
  21  *       Actually it's the same code with only minor changes in the
  22  *       way the data is stored; this is to support the abstraction
  23  *       of an optional secure memory allocation which may be used
  24  *       to avoid revealing of sensitive data due to paging etc.
  25  *       The GNU MP Library itself is published under the LGPL;
  26  *       however I decided to publish this code under the plain GPL.
  27  */
  28
  29 #include <linux/string.h>
  30 #include "mpi-internal.h"
  31 #include "longlong.h"
  32
  33 /****************
  34  * RES = BASE ^ EXP mod MOD
  35  */
  36 int mpi_powm(MPI res, MPI base, MPI exp, MPI mod)
  37 {
  38         mpi_ptr_t mp_marker = NULL, bp_marker = NULL, ep_marker = NULL;
  39         mpi_ptr_t xp_marker = NULL;
  40         mpi_ptr_t tspace = NULL;
  41         mpi_ptr_t rp, ep, mp, bp;
  42         mpi_size_t esize, msize, bsize, rsize;
  43         int esign, msign, bsign, rsign;
  44         mpi_size_t size;
  45         int mod_shift_cnt;
  46         int negative_result;
  47         int assign_rp = 0;
  48         mpi_size_t tsize = 0;   /* to avoid compiler warning */
  49         /* fixme: we should check that the warning is void */
  50         int rc = -ENOMEM;
  51
  52         esize = exp->nlimbs;
  53         msize = mod->nlimbs;
  54         size = 2 * msize;
  55         esign = exp->sign;
  56         msign = mod->sign;
  57
  58         rp = res->d;
  59         ep = exp->d;
  60
  61         if (!msize)
  62                 return -EINVAL;
  63
  64         if (!esize) {
  65                 /* Exponent is zero, result is 1 mod MOD, i.e., 1 or 0
  66                  * depending on if MOD equals 1.  */
  67                 rp[0] = 1;
  68                 res->nlimbs = (msize == 1 && mod->d[0] == 1) ? 0 : 1;
  69                 res->sign = 0;
  70                 goto leave;
  71         }
  72
  73         /* Normalize MOD (i.e. make its most significant bit set) as required by
  74          * mpn_divrem.  This will make the intermediate values in the calculation
  75          * slightly larger, but the correct result is obtained after a final
  76          * reduction using the original MOD value.  */
  77         mp = mp_marker = mpi_alloc_limb_space(msize);
  78         if (!mp)
  79                 goto enomem;
  80         mod_shift_cnt = count_leading_zeros(mod->d[msize - 1]);
  81         if (mod_shift_cnt)
  82                 mpihelp_lshift(mp, mod->d, msize, mod_shift_cnt);
  83         else
  84                 MPN_COPY(mp, mod->d, msize);
  85
  86         bsize = base->nlimbs;
  87         bsign = base->sign;
  88         if (bsize > msize) {    /* The base is larger than the module. Reduce it. */
  89                 /* Allocate (BSIZE + 1) with space for remainder and quotient.
  90                  * (The quotient is (bsize - msize + 1) limbs.)  */
  91                 bp = bp_marker = mpi_alloc_limb_space(bsize + 1);
  92                 if (!bp)
  93                         goto enomem;
  94                 MPN_COPY(bp, base->d, bsize);
  95                 /* We don't care about the quotient, store it above the remainder,
  96                  * at BP + MSIZE.  */
  97                 mpihelp_divrem(bp + msize, 0, bp, bsize, mp, msize);
  98                 bsize = msize;
  99                 /* Canonicalize the base, since we are going to multiply with it
 100                  * quite a few times.  */
 101                 MPN_NORMALIZE(bp, bsize);
 102         } else
 103                 bp = base->d;
 104
 105         if (!bsize) {
 106                 res->nlimbs = 0;
 107                 res->sign = 0;
 108                 goto leave;
 109         }
 110
 111         if (res->alloced < size) {
 112                 /* We have to allocate more space for RES.  If any of the input
 113                  * parameters are identical to RES, defer deallocation of the old
 114                  * space.  */
 115                 if (rp == ep || rp == mp || rp == bp) {
 116                         rp = mpi_alloc_limb_space(size);
 117                         if (!rp)
 118                                 goto enomem;
 119                         assign_rp = 1;
 120                 } else {
 121                         if (mpi_resize(res, size) < 0)
 122                                 goto enomem;
 123                         rp = res->d;
 124                 }
 125         } else {                /* Make BASE, EXP and MOD not overlap with RES.  */
 126                 if (rp == bp) {
 127                         /* RES and BASE are identical.  Allocate temp. space for BASE.  */
 128                         BUG_ON(bp_marker);
 129                         bp = bp_marker = mpi_alloc_limb_space(bsize);
 130                         if (!bp)
 131                                 goto enomem;
 132                         MPN_COPY(bp, rp, bsize);
 133                 }
 134                 if (rp == ep) {
 135                         /* RES and EXP are identical.  Allocate temp. space for EXP.  */
 136                         ep = ep_marker = mpi_alloc_limb_space(esize);
 137                         if (!ep)
 138                                 goto enomem;
 139                         MPN_COPY(ep, rp, esize);
 140                 }
 141                 if (rp == mp) {
 142                         /* RES and MOD are identical.  Allocate temporary space for MOD. */
 143                         BUG_ON(mp_marker);
 144                         mp = mp_marker = mpi_alloc_limb_space(msize);
 145                         if (!mp)
 146                                 goto enomem;
 147                         MPN_COPY(mp, rp, msize);
 148                 }
 149         }
 150
 151         MPN_COPY(rp, bp, bsize);
 152         rsize = bsize;
 153         rsign = bsign;
 154
 155         {
 156                 mpi_size_t i;
 157                 mpi_ptr_t xp;
 158                 int c;
 159                 mpi_limb_t e;
 160                 mpi_limb_t carry_limb;
 161                 struct karatsuba_ctx karactx;
 162
 163                 xp = xp_marker = mpi_alloc_limb_space(2 * (msize + 1));
 164                 if (!xp)
 165                         goto enomem;
 166
 167                 memset(&karactx, 0, sizeof karactx);
 168                 negative_result = (ep[0] & 1) && base->sign;
 169
 170                 i = esize - 1;
 171                 e = ep[i];
 172                 c = count_leading_zeros(e);
 173                 e = (e << c) << 1;      /* shift the exp bits to the left, lose msb */
 174                 c = BITS_PER_MPI_LIMB - 1 - c;
 175
 176                 /* Main loop.
 177                  *
 178                  * Make the result be pointed to alternately by XP and RP.  This
 179                  * helps us avoid block copying, which would otherwise be necessary
 180                  * with the overlap restrictions of mpihelp_divmod. With 50% probability
 181                  * the result after this loop will be in the area originally pointed
 182                  * by RP (==RES->d), and with 50% probability in the area originally
 183                  * pointed to by XP.
 184                  */
 185
 186                 for (;;) {
 187                         while (c) {
 188                                 mpi_ptr_t tp;
 189                                 mpi_size_t xsize;
 190
 191                                 /*if (mpihelp_mul_n(xp, rp, rp, rsize) < 0) goto enomem */
 192                                 if (rsize < KARATSUBA_THRESHOLD)
 193                                         mpih_sqr_n_basecase(xp, rp, rsize);
 194                                 else {
 195                                         if (!tspace) {
 196                                                 tsize = 2 * rsize;
 197                                                 tspace =
 198                                                     mpi_alloc_limb_space(tsize);
 199                                                 if (!tspace)
 200                                                         goto enomem;
 201                                         } else if (tsize < (2 * rsize)) {
 202                                                 mpi_free_limb_space(tspace);
 203                                                 tsize = 2 * rsize;
 204                                                 tspace =
 205                                                     mpi_alloc_limb_space(tsize);
 206                                                 if (!tspace)
 207                                                         goto enomem;
 208                                         }
 209                                         mpih_sqr_n(xp, rp, rsize, tspace);
 210                                 }
 211
 212                                 xsize = 2 * rsize;
 213                                 if (xsize > msize) {
 214                                         mpihelp_divrem(xp + msize, 0, xp, xsize,
 215                                                        mp, msize);
 216                                         xsize = msize;
 217                                 }
 218
 219                                 tp = rp;
 220                                 rp = xp;
 221                                 xp = tp;
 222                                 rsize = xsize;
 223
 224                                 if ((mpi_limb_signed_t) e < 0) {
 225                                         /*mpihelp_mul( xp, rp, rsize, bp, bsize ); */
 226                                         if (bsize < KARATSUBA_THRESHOLD) {
 227                                                 mpi_limb_t tmp;
 228                                                 if (mpihelp_mul
 229                                                     (xp, rp, rsize, bp, bsize,
 230                                                      &tmp) < 0)
 231                                                         goto enomem;
 232                                         } else {
 233                                                 if (mpihelp_mul_karatsuba_case
 234                                                     (xp, rp, rsize, bp, bsize,
 235                                                      &karactx) < 0)
 236                                                         goto enomem;
 237                                         }
 238
 239                                         xsize = rsize + bsize;
 240                                         if (xsize > msize) {
 241                                                 mpihelp_divrem(xp + msize, 0,
 242                                                                xp, xsize, mp,
 243                                                                msize);
 244                                                 xsize = msize;
 245                                         }
 246
 247                                         tp = rp;
 248                                         rp = xp;
 249                                         xp = tp;
 250                                         rsize = xsize;
 251                                 }
 252                                 e <<= 1;
 253                                 c--;
 254                         }
 255
 256                         i--;
 257                         if (i < 0)
 258                                 break;
 259                         e = ep[i];
 260                         c = BITS_PER_MPI_LIMB;
 261                 }
 262
 263                 /* We shifted MOD, the modulo reduction argument, left MOD_SHIFT_CNT
 264                  * steps.  Adjust the result by reducing it with the original MOD.
 265                  *
 266                  * Also make sure the result is put in RES->d (where it already
 267                  * might be, see above).
 268                  */
 269                 if (mod_shift_cnt) {
 270                         carry_limb =
 271                             mpihelp_lshift(res->d, rp, rsize, mod_shift_cnt);
 272                         rp = res->d;
 273                         if (carry_limb) {
 274                                 rp[rsize] = carry_limb;
 275                                 rsize++;
 276                         }
 277                 } else {
 278                         MPN_COPY(res->d, rp, rsize);
 279                         rp = res->d;
 280                 }
 281
 282                 if (rsize >= msize) {
 283                         mpihelp_divrem(rp + msize, 0, rp, rsize, mp, msize);
 284                         rsize = msize;
 285                 }
 286
 287                 /* Remove any leading zero words from the result.  */
 288                 if (mod_shift_cnt)
 289                         mpihelp_rshift(rp, rp, rsize, mod_shift_cnt);
 290                 MPN_NORMALIZE(rp, rsize);
 291
 292                 mpihelp_release_karatsuba_ctx(&karactx);
 293         }
 294
 295         if (negative_result && rsize) {
 296                 if (mod_shift_cnt)
 297                         mpihelp_rshift(mp, mp, msize, mod_shift_cnt);
 298                 mpihelp_sub(rp, mp, msize, rp, rsize);
 299                 rsize = msize;
 300                 rsign = msign;
 301                 MPN_NORMALIZE(rp, rsize);
 302         }
 303         res->nlimbs = rsize;
 304         res->sign = rsign;
 305
 306 leave:
 307         rc = 0;
 308 enomem:
 309         if (assign_rp)
 310                 mpi_assign_limb_space(res, rp, size);
 311         if (mp_marker)
 312                 mpi_free_limb_space(mp_marker);
 313         if (bp_marker)
 314                 mpi_free_limb_space(bp_marker);
 315         if (ep_marker)
 316                 mpi_free_limb_space(ep_marker);
 317         if (xp_marker)
 318                 mpi_free_limb_space(xp_marker);
 319         if (tspace)
 320                 mpi_free_limb_space(tspace);
 321         return rc;
 322 }
 323 EXPORT_SYMBOL_GPL(mpi_powm);