Root/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 */
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    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
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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