linux/lib/mpi/mpi-pow.c
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   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 */
  36int 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        count_leading_zeros(mod_shift_cnt, 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                count_leading_zeros(c, 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
 306leave:
 307        rc = 0;
 308enomem:
 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}
 323EXPORT_SYMBOL_GPL(mpi_powm);
 324
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