lib/mpi/mpi-pow.c

   1 // SPDX-License-Identifier: GPL-2.0-or-later
   2 /* mpi-pow.c  -  MPI functions
   3  *      Copyright (C) 1994, 1996, 1998, 2000 Free Software Foundation, Inc.
   4  *
   5  * This file is part of GnuPG.
   6  *
   7  * Note: This code is heavily based on the GNU MP Library.
   8  *       Actually it's the same code with only minor changes in the
   9  *       way the data is stored; this is to support the abstraction
  10  *       of an optional secure memory allocation which may be used
  11  *       to avoid revealing of sensitive data due to paging etc.
  12  *       The GNU MP Library itself is published under the LGPL;
  13  *       however I decided to publish this code under the plain GPL.
  14  */
  15
  16 #include <linux/sched.h>
  17 #include <linux/string.h>
  18 #include "mpi-internal.h"
  19 #include "longlong.h"
  20
  21 /****************
  22  * RES = BASE ^ EXP mod MOD
  23  */
  24 int mpi_powm(MPI res, MPI base, MPI exp, MPI mod)
  25 {
  26         mpi_ptr_t mp_marker = NULL, bp_marker = NULL, ep_marker = NULL;
  27         struct karatsuba_ctx karactx = {};
  28         mpi_ptr_t xp_marker = NULL;
  29         mpi_ptr_t tspace = NULL;
  30         mpi_ptr_t rp, ep, mp, bp;
  31         mpi_size_t esize, msize, bsize, rsize;
  32         int msign, bsign, rsign;
  33         mpi_size_t size;
  34         int mod_shift_cnt;
  35         int negative_result;
  36         int assign_rp = 0;
  37         mpi_size_t tsize = 0;   /* to avoid compiler warning */
  38         /* fixme: we should check that the warning is void */
  39         int rc = -ENOMEM;
  40
  41         esize = exp->nlimbs;
  42         msize = mod->nlimbs;
  43         size = 2 * msize;
  44         msign = mod->sign;
  45
  46         rp = res->d;
  47         ep = exp->d;
  48
  49         if (!msize)
  50                 return -EINVAL;
  51
  52         if (!esize) {
  53                 /* Exponent is zero, result is 1 mod MOD, i.e., 1 or 0
  54                  * depending on if MOD equals 1.  */
  55                 res->nlimbs = (msize == 1 && mod->d[0] == 1) ? 0 : 1;
  56                 if (res->nlimbs) {
  57                         if (mpi_resize(res, 1) < 0)
  58                                 goto enomem;
  59                         rp = res->d;
  60                         rp[0] = 1;
  61                 }
  62                 res->sign = 0;
  63                 goto leave;
  64         }
  65
  66         /* Normalize MOD (i.e. make its most significant bit set) as required by
  67          * mpn_divrem.  This will make the intermediate values in the calculation
  68          * slightly larger, but the correct result is obtained after a final
  69          * reduction using the original MOD value.  */
  70         mp = mp_marker = mpi_alloc_limb_space(msize);
  71         if (!mp)
  72                 goto enomem;
  73         mod_shift_cnt = count_leading_zeros(mod->d[msize - 1]);
  74         if (mod_shift_cnt)
  75                 mpihelp_lshift(mp, mod->d, msize, mod_shift_cnt);
  76         else
  77                 MPN_COPY(mp, mod->d, msize);
  78
  79         bsize = base->nlimbs;
  80         bsign = base->sign;
  81         if (bsize > msize) {    /* The base is larger than the module. Reduce it. */
  82                 /* Allocate (BSIZE + 1) with space for remainder and quotient.
  83                  * (The quotient is (bsize - msize + 1) limbs.)  */
  84                 bp = bp_marker = mpi_alloc_limb_space(bsize + 1);
  85                 if (!bp)
  86                         goto enomem;
  87                 MPN_COPY(bp, base->d, bsize);
  88                 /* We don't care about the quotient, store it above the remainder,
  89                  * at BP + MSIZE.  */
  90                 mpihelp_divrem(bp + msize, 0, bp, bsize, mp, msize);
  91                 bsize = msize;
  92                 /* Canonicalize the base, since we are going to multiply with it
  93                  * quite a few times.  */
  94                 MPN_NORMALIZE(bp, bsize);
  95         } else
  96                 bp = base->d;
  97
  98         if (!bsize) {
  99                 res->nlimbs = 0;
 100                 res->sign = 0;
 101                 goto leave;
 102         }
 103
 104         if (res->alloced < size) {
 105                 /* We have to allocate more space for RES.  If any of the input
 106                  * parameters are identical to RES, defer deallocation of the old
 107                  * space.  */
 108                 if (rp == ep || rp == mp || rp == bp) {
 109                         rp = mpi_alloc_limb_space(size);
 110                         if (!rp)
 111                                 goto enomem;
 112                         assign_rp = 1;
 113                 } else {
 114                         if (mpi_resize(res, size) < 0)
 115                                 goto enomem;
 116                         rp = res->d;
 117                 }
 118         } else {                /* Make BASE, EXP and MOD not overlap with RES.  */
 119                 if (rp == bp) {
 120                         /* RES and BASE are identical.  Allocate temp. space for BASE.  */
 121                         BUG_ON(bp_marker);
 122                         bp = bp_marker = mpi_alloc_limb_space(bsize);
 123                         if (!bp)
 124                                 goto enomem;
 125                         MPN_COPY(bp, rp, bsize);
 126                 }
 127                 if (rp == ep) {
 128                         /* RES and EXP are identical.  Allocate temp. space for EXP.  */
 129                         ep = ep_marker = mpi_alloc_limb_space(esize);
 130                         if (!ep)
 131                                 goto enomem;
 132                         MPN_COPY(ep, rp, esize);
 133                 }
 134                 if (rp == mp) {
 135                         /* RES and MOD are identical.  Allocate temporary space for MOD. */
 136                         BUG_ON(mp_marker);
 137                         mp = mp_marker = mpi_alloc_limb_space(msize);
 138                         if (!mp)
 139                                 goto enomem;
 140                         MPN_COPY(mp, rp, msize);
 141                 }
 142         }
 143
 144         MPN_COPY(rp, bp, bsize);
 145         rsize = bsize;
 146         rsign = bsign;
 147
 148         {
 149                 mpi_size_t i;
 150                 mpi_ptr_t xp;
 151                 int c;
 152                 mpi_limb_t e;
 153                 mpi_limb_t carry_limb;
 154
 155                 xp = xp_marker = mpi_alloc_limb_space(2 * (msize + 1));
 156                 if (!xp)
 157                         goto enomem;
 158
 159                 negative_result = (ep[0] & 1) && base->sign;
 160
 161                 i = esize - 1;
 162                 e = ep[i];
 163                 c = count_leading_zeros(e);
 164                 e = (e << c) << 1;      /* shift the exp bits to the left, lose msb */
 165                 c = BITS_PER_MPI_LIMB - 1 - c;
 166
 167                 /* Main loop.
 168                  *
 169                  * Make the result be pointed to alternately by XP and RP.  This
 170                  * helps us avoid block copying, which would otherwise be necessary
 171                  * with the overlap restrictions of mpihelp_divmod. With 50% probability
 172                  * the result after this loop will be in the area originally pointed
 173                  * by RP (==RES->d), and with 50% probability in the area originally
 174                  * pointed to by XP.
 175                  */
 176
 177                 for (;;) {
 178                         while (c) {
 179                                 mpi_ptr_t tp;
 180                                 mpi_size_t xsize;
 181
 182                                 /*if (mpihelp_mul_n(xp, rp, rp, rsize) < 0) goto enomem */
 183                                 if (rsize < KARATSUBA_THRESHOLD)
 184                                         mpih_sqr_n_basecase(xp, rp, rsize);
 185                                 else {
 186                                         if (!tspace) {
 187                                                 tsize = 2 * rsize;
 188                                                 tspace =
 189                                                     mpi_alloc_limb_space(tsize);
 190                                                 if (!tspace)
 191                                                         goto enomem;
 192                                         } else if (tsize < (2 * rsize)) {
 193                                                 mpi_free_limb_space(tspace);
 194                                                 tsize = 2 * rsize;
 195                                                 tspace =
 196                                                     mpi_alloc_limb_space(tsize);
 197                                                 if (!tspace)
 198                                                         goto enomem;
 199                                         }
 200                                         mpih_sqr_n(xp, rp, rsize, tspace);
 201                                 }
 202
 203                                 xsize = 2 * rsize;
 204                                 if (xsize > msize) {
 205                                         mpihelp_divrem(xp + msize, 0, xp, xsize,
 206                                                        mp, msize);
 207                                         xsize = msize;
 208                                 }
 209
 210                                 tp = rp;
 211                                 rp = xp;
 212                                 xp = tp;
 213                                 rsize = xsize;
 214
 215                                 if ((mpi_limb_signed_t) e < 0) {
 216                                         /*mpihelp_mul( xp, rp, rsize, bp, bsize ); */
 217                                         if (bsize < KARATSUBA_THRESHOLD) {
 218                                                 mpi_limb_t tmp;
 219                                                 if (mpihelp_mul
 220                                                     (xp, rp, rsize, bp, bsize,
 221                                                      &tmp) < 0)
 222                                                         goto enomem;
 223                                         } else {
 224                                                 if (mpihelp_mul_karatsuba_case
 225                                                     (xp, rp, rsize, bp, bsize,
 226                                                      &karactx) < 0)
 227                                                         goto enomem;
 228                                         }
 229
 230                                         xsize = rsize + bsize;
 231                                         if (xsize > msize) {
 232                                                 mpihelp_divrem(xp + msize, 0,
 233                                                                xp, xsize, mp,
 234                                                                msize);
 235                                                 xsize = msize;
 236                                         }
 237
 238                                         tp = rp;
 239                                         rp = xp;
 240                                         xp = tp;
 241                                         rsize = xsize;
 242                                 }
 243                                 e <<= 1;
 244                                 c--;
 245                                 cond_resched();
 246                         }
 247
 248                         i--;
 249                         if (i < 0)
 250                                 break;
 251                         e = ep[i];
 252                         c = BITS_PER_MPI_LIMB;
 253                 }
 254
 255                 /* We shifted MOD, the modulo reduction argument, left MOD_SHIFT_CNT
 256                  * steps.  Adjust the result by reducing it with the original MOD.
 257                  *
 258                  * Also make sure the result is put in RES->d (where it already
 259                  * might be, see above).
 260                  */
 261                 if (mod_shift_cnt) {
 262                         carry_limb =
 263                             mpihelp_lshift(res->d, rp, rsize, mod_shift_cnt);
 264                         rp = res->d;
 265                         if (carry_limb) {
 266                                 rp[rsize] = carry_limb;
 267                                 rsize++;
 268                         }
 269                 } else {
 270                         MPN_COPY(res->d, rp, rsize);
 271                         rp = res->d;
 272                 }
 273
 274                 if (rsize >= msize) {
 275                         mpihelp_divrem(rp + msize, 0, rp, rsize, mp, msize);
 276                         rsize = msize;
 277                 }
 278
 279                 /* Remove any leading zero words from the result.  */
 280                 if (mod_shift_cnt)
 281                         mpihelp_rshift(rp, rp, rsize, mod_shift_cnt);
 282                 MPN_NORMALIZE(rp, rsize);
 283         }
 284
 285         if (negative_result && rsize) {
 286                 if (mod_shift_cnt)
 287                         mpihelp_rshift(mp, mp, msize, mod_shift_cnt);
 288                 mpihelp_sub(rp, mp, msize, rp, rsize);
 289                 rsize = msize;
 290                 rsign = msign;
 291                 MPN_NORMALIZE(rp, rsize);
 292         }
 293         res->nlimbs = rsize;
 294         res->sign = rsign;
 295
 296 leave:
 297         rc = 0;
 298 enomem:
 299         mpihelp_release_karatsuba_ctx(&karactx);
 300         if (assign_rp)
 301                 mpi_assign_limb_space(res, rp, size);
 302         if (mp_marker)
 303                 mpi_free_limb_space(mp_marker);
 304         if (bp_marker)
 305                 mpi_free_limb_space(bp_marker);
 306         if (ep_marker)
 307                 mpi_free_limb_space(ep_marker);
 308         if (xp_marker)
 309                 mpi_free_limb_space(xp_marker);
 310         if (tspace)
 311                 mpi_free_limb_space(tspace);
 312         return rc;
 313 }
 314 EXPORT_SYMBOL_GPL(mpi_powm);