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/sched.h>
  30 #include <linux/string.h>
  31 #include "mpi-internal.h"
  32 #include "longlong.h"
  33
  34 /****************
  35  * RES = BASE ^ EXP mod MOD
  36  */
  37 int mpi_powm(MPI res, MPI base, MPI exp, MPI mod)
  38 {
  39         mpi_ptr_t mp_marker = NULL, bp_marker = NULL, ep_marker = NULL;
  40         mpi_ptr_t xp_marker = NULL;
  41         mpi_ptr_t tspace = NULL;
  42         mpi_ptr_t rp, ep, mp, bp;
  43         mpi_size_t esize, msize, bsize, rsize;
  44         int esign, msign, bsign, rsign;
  45         mpi_size_t size;
  46         int mod_shift_cnt;
  47         int negative_result;
  48         int assign_rp = 0;
  49         mpi_size_t tsize = 0;   /* to avoid compiler warning */
  50         /* fixme: we should check that the warning is void */
  51         int rc = -ENOMEM;
  52
  53         esize = exp->nlimbs;
  54         msize = mod->nlimbs;
  55         size = 2 * msize;
  56         esign = exp->sign;
  57         msign = mod->sign;
  58
  59         rp = res->d;
  60         ep = exp->d;
  61
  62         if (!msize)
  63                 return -EINVAL;
  64
  65         if (!esize) {
  66                 /* Exponent is zero, result is 1 mod MOD, i.e., 1 or 0
  67                  * depending on if MOD equals 1.  */
  68                 res->nlimbs = (msize == 1 && mod->d[0] == 1) ? 0 : 1;
  69                 if (res->nlimbs) {
  70                         if (mpi_resize(res, 1) < 0)
  71                                 goto enomem;
  72                         rp = res->d;
  73                         rp[0] = 1;
  74                 }
  75                 res->sign = 0;
  76                 goto leave;
  77         }
  78
  79         /* Normalize MOD (i.e. make its most significant bit set) as required by
  80          * mpn_divrem.  This will make the intermediate values in the calculation
  81          * slightly larger, but the correct result is obtained after a final
  82          * reduction using the original MOD value.  */
  83         mp = mp_marker = mpi_alloc_limb_space(msize);
  84         if (!mp)
  85                 goto enomem;
  86         mod_shift_cnt = count_leading_zeros(mod->d[msize - 1]);
  87         if (mod_shift_cnt)
  88                 mpihelp_lshift(mp, mod->d, msize, mod_shift_cnt);
  89         else
  90                 MPN_COPY(mp, mod->d, msize);
  91
  92         bsize = base->nlimbs;
  93         bsign = base->sign;
  94         if (bsize > msize) {    /* The base is larger than the module. Reduce it. */
  95                 /* Allocate (BSIZE + 1) with space for remainder and quotient.
  96                  * (The quotient is (bsize - msize + 1) limbs.)  */
  97                 bp = bp_marker = mpi_alloc_limb_space(bsize + 1);
  98                 if (!bp)
  99                         goto enomem;
 100                 MPN_COPY(bp, base->d, bsize);
 101                 /* We don't care about the quotient, store it above the remainder,
 102                  * at BP + MSIZE.  */
 103                 mpihelp_divrem(bp + msize, 0, bp, bsize, mp, msize);
 104                 bsize = msize;
 105                 /* Canonicalize the base, since we are going to multiply with it
 106                  * quite a few times.  */
 107                 MPN_NORMALIZE(bp, bsize);
 108         } else
 109                 bp = base->d;
 110
 111         if (!bsize) {
 112                 res->nlimbs = 0;
 113                 res->sign = 0;
 114                 goto leave;
 115         }
 116
 117         if (res->alloced < size) {
 118                 /* We have to allocate more space for RES.  If any of the input
 119                  * parameters are identical to RES, defer deallocation of the old
 120                  * space.  */
 121                 if (rp == ep || rp == mp || rp == bp) {
 122                         rp = mpi_alloc_limb_space(size);
 123                         if (!rp)
 124                                 goto enomem;
 125                         assign_rp = 1;
 126                 } else {
 127                         if (mpi_resize(res, size) < 0)
 128                                 goto enomem;
 129                         rp = res->d;
 130                 }
 131         } else {                /* Make BASE, EXP and MOD not overlap with RES.  */
 132                 if (rp == bp) {
 133                         /* RES and BASE are identical.  Allocate temp. space for BASE.  */
 134                         BUG_ON(bp_marker);
 135                         bp = bp_marker = mpi_alloc_limb_space(bsize);
 136                         if (!bp)
 137                                 goto enomem;
 138                         MPN_COPY(bp, rp, bsize);
 139                 }
 140                 if (rp == ep) {
 141                         /* RES and EXP are identical.  Allocate temp. space for EXP.  */
 142                         ep = ep_marker = mpi_alloc_limb_space(esize);
 143                         if (!ep)
 144                                 goto enomem;
 145                         MPN_COPY(ep, rp, esize);
 146                 }
 147                 if (rp == mp) {
 148                         /* RES and MOD are identical.  Allocate temporary space for MOD. */
 149                         BUG_ON(mp_marker);
 150                         mp = mp_marker = mpi_alloc_limb_space(msize);
 151                         if (!mp)
 152                                 goto enomem;
 153                         MPN_COPY(mp, rp, msize);
 154                 }
 155         }
 156
 157         MPN_COPY(rp, bp, bsize);
 158         rsize = bsize;
 159         rsign = bsign;
 160
 161         {
 162                 mpi_size_t i;
 163                 mpi_ptr_t xp;
 164                 int c;
 165                 mpi_limb_t e;
 166                 mpi_limb_t carry_limb;
 167                 struct karatsuba_ctx karactx;
 168
 169                 xp = xp_marker = mpi_alloc_limb_space(2 * (msize + 1));
 170                 if (!xp)
 171                         goto enomem;
 172
 173                 memset(&karactx, 0, sizeof karactx);
 174                 negative_result = (ep[0] & 1) && base->sign;
 175
 176                 i = esize - 1;
 177                 e = ep[i];
 178                 c = count_leading_zeros(e);
 179                 e = (e << c) << 1;      /* shift the exp bits to the left, lose msb */
 180                 c = BITS_PER_MPI_LIMB - 1 - c;
 181
 182                 /* Main loop.
 183                  *
 184                  * Make the result be pointed to alternately by XP and RP.  This
 185                  * helps us avoid block copying, which would otherwise be necessary
 186                  * with the overlap restrictions of mpihelp_divmod. With 50% probability
 187                  * the result after this loop will be in the area originally pointed
 188                  * by RP (==RES->d), and with 50% probability in the area originally
 189                  * pointed to by XP.
 190                  */
 191
 192                 for (;;) {
 193                         while (c) {
 194                                 mpi_ptr_t tp;
 195                                 mpi_size_t xsize;
 196
 197                                 /*if (mpihelp_mul_n(xp, rp, rp, rsize) < 0) goto enomem */
 198                                 if (rsize < KARATSUBA_THRESHOLD)
 199                                         mpih_sqr_n_basecase(xp, rp, rsize);
 200                                 else {
 201                                         if (!tspace) {
 202                                                 tsize = 2 * rsize;
 203                                                 tspace =
 204                                                     mpi_alloc_limb_space(tsize);
 205                                                 if (!tspace)
 206                                                         goto enomem;
 207                                         } else if (tsize < (2 * rsize)) {
 208                                                 mpi_free_limb_space(tspace);
 209                                                 tsize = 2 * rsize;
 210                                                 tspace =
 211                                                     mpi_alloc_limb_space(tsize);
 212                                                 if (!tspace)
 213                                                         goto enomem;
 214                                         }
 215                                         mpih_sqr_n(xp, rp, rsize, tspace);
 216                                 }
 217
 218                                 xsize = 2 * rsize;
 219                                 if (xsize > msize) {
 220                                         mpihelp_divrem(xp + msize, 0, xp, xsize,
 221                                                        mp, msize);
 222                                         xsize = msize;
 223                                 }
 224
 225                                 tp = rp;
 226                                 rp = xp;
 227                                 xp = tp;
 228                                 rsize = xsize;
 229
 230                                 if ((mpi_limb_signed_t) e < 0) {
 231                                         /*mpihelp_mul( xp, rp, rsize, bp, bsize ); */
 232                                         if (bsize < KARATSUBA_THRESHOLD) {
 233                                                 mpi_limb_t tmp;
 234                                                 if (mpihelp_mul
 235                                                     (xp, rp, rsize, bp, bsize,
 236                                                      &tmp) < 0)
 237                                                         goto enomem;
 238                                         } else {
 239                                                 if (mpihelp_mul_karatsuba_case
 240                                                     (xp, rp, rsize, bp, bsize,
 241                                                      &karactx) < 0)
 242                                                         goto enomem;
 243                                         }
 244
 245                                         xsize = rsize + bsize;
 246                                         if (xsize > msize) {
 247                                                 mpihelp_divrem(xp + msize, 0,
 248                                                                xp, xsize, mp,
 249                                                                msize);
 250                                                 xsize = msize;
 251                                         }
 252
 253                                         tp = rp;
 254                                         rp = xp;
 255                                         xp = tp;
 256                                         rsize = xsize;
 257                                 }
 258                                 e <<= 1;
 259                                 c--;
 260                                 cond_resched();
 261                         }
 262
 263                         i--;
 264                         if (i < 0)
 265                                 break;
 266                         e = ep[i];
 267                         c = BITS_PER_MPI_LIMB;
 268                 }
 269
 270                 /* We shifted MOD, the modulo reduction argument, left MOD_SHIFT_CNT
 271                  * steps.  Adjust the result by reducing it with the original MOD.
 272                  *
 273                  * Also make sure the result is put in RES->d (where it already
 274                  * might be, see above).
 275                  */
 276                 if (mod_shift_cnt) {
 277                         carry_limb =
 278                             mpihelp_lshift(res->d, rp, rsize, mod_shift_cnt);
 279                         rp = res->d;
 280                         if (carry_limb) {
 281                                 rp[rsize] = carry_limb;
 282                                 rsize++;
 283                         }
 284                 } else {
 285                         MPN_COPY(res->d, rp, rsize);
 286                         rp = res->d;
 287                 }
 288
 289                 if (rsize >= msize) {
 290                         mpihelp_divrem(rp + msize, 0, rp, rsize, mp, msize);
 291                         rsize = msize;
 292                 }
 293
 294                 /* Remove any leading zero words from the result.  */
 295                 if (mod_shift_cnt)
 296                         mpihelp_rshift(rp, rp, rsize, mod_shift_cnt);
 297                 MPN_NORMALIZE(rp, rsize);
 298
 299                 mpihelp_release_karatsuba_ctx(&karactx);
 300         }
 301
 302         if (negative_result && rsize) {
 303                 if (mod_shift_cnt)
 304                         mpihelp_rshift(mp, mp, msize, mod_shift_cnt);
 305                 mpihelp_sub(rp, mp, msize, rp, rsize);
 306                 rsize = msize;
 307                 rsign = msign;
 308                 MPN_NORMALIZE(rp, rsize);
 309         }
 310         res->nlimbs = rsize;
 311         res->sign = rsign;
 312
 313 leave:
 314         rc = 0;
 315 enomem:
 316         if (assign_rp)
 317                 mpi_assign_limb_space(res, rp, size);
 318         if (mp_marker)
 319                 mpi_free_limb_space(mp_marker);
 320         if (bp_marker)
 321                 mpi_free_limb_space(bp_marker);
 322         if (ep_marker)
 323                 mpi_free_limb_space(ep_marker);
 324         if (xp_marker)
 325                 mpi_free_limb_space(xp_marker);
 326         if (tspace)
 327                 mpi_free_limb_space(tspace);
 328         return rc;
 329 }
 330 EXPORT_SYMBOL_GPL(mpi_powm);