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