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 */
mpi_powm(MPI res,MPI base,MPI exp,MPI mod)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 struct karatsuba_ctx karactx = {};
41 mpi_ptr_t xp_marker = NULL;
42 mpi_ptr_t tspace = NULL;
43 mpi_ptr_t rp, ep, mp, bp;
44 mpi_size_t esize, msize, bsize, rsize;
45 int msign, bsign, rsign;
46 mpi_size_t size;
47 int mod_shift_cnt;
48 int negative_result;
49 int assign_rp = 0;
50 mpi_size_t tsize = 0; /* to avoid compiler warning */
51 /* fixme: we should check that the warning is void */
52 int rc = -ENOMEM;
53
54 esize = exp->nlimbs;
55 msize = mod->nlimbs;
56 size = 2 * msize;
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
168 xp = xp_marker = mpi_alloc_limb_space(2 * (msize + 1));
169 if (!xp)
170 goto enomem;
171
172 negative_result = (ep[0] & 1) && base->sign;
173
174 i = esize - 1;
175 e = ep[i];
176 c = count_leading_zeros(e);
177 e = (e << c) << 1; /* shift the exp bits to the left, lose msb */
178 c = BITS_PER_MPI_LIMB - 1 - c;
179
180 /* Main loop.
181 *
182 * Make the result be pointed to alternately by XP and RP. This
183 * helps us avoid block copying, which would otherwise be necessary
184 * with the overlap restrictions of mpihelp_divmod. With 50% probability
185 * the result after this loop will be in the area originally pointed
186 * by RP (==RES->d), and with 50% probability in the area originally
187 * pointed to by XP.
188 */
189
190 for (;;) {
191 while (c) {
192 mpi_ptr_t tp;
193 mpi_size_t xsize;
194
195 /*if (mpihelp_mul_n(xp, rp, rp, rsize) < 0) goto enomem */
196 if (rsize < KARATSUBA_THRESHOLD)
197 mpih_sqr_n_basecase(xp, rp, rsize);
198 else {
199 if (!tspace) {
200 tsize = 2 * rsize;
201 tspace =
202 mpi_alloc_limb_space(tsize);
203 if (!tspace)
204 goto enomem;
205 } else if (tsize < (2 * rsize)) {
206 mpi_free_limb_space(tspace);
207 tsize = 2 * rsize;
208 tspace =
209 mpi_alloc_limb_space(tsize);
210 if (!tspace)
211 goto enomem;
212 }
213 mpih_sqr_n(xp, rp, rsize, tspace);
214 }
215
216 xsize = 2 * rsize;
217 if (xsize > msize) {
218 mpihelp_divrem(xp + msize, 0, xp, xsize,
219 mp, msize);
220 xsize = msize;
221 }
222
223 tp = rp;
224 rp = xp;
225 xp = tp;
226 rsize = xsize;
227
228 if ((mpi_limb_signed_t) e < 0) {
229 /*mpihelp_mul( xp, rp, rsize, bp, bsize ); */
230 if (bsize < KARATSUBA_THRESHOLD) {
231 mpi_limb_t tmp;
232 if (mpihelp_mul
233 (xp, rp, rsize, bp, bsize,
234 &tmp) < 0)
235 goto enomem;
236 } else {
237 if (mpihelp_mul_karatsuba_case
238 (xp, rp, rsize, bp, bsize,
239 &karactx) < 0)
240 goto enomem;
241 }
242
243 xsize = rsize + bsize;
244 if (xsize > msize) {
245 mpihelp_divrem(xp + msize, 0,
246 xp, xsize, mp,
247 msize);
248 xsize = msize;
249 }
250
251 tp = rp;
252 rp = xp;
253 xp = tp;
254 rsize = xsize;
255 }
256 e <<= 1;
257 c--;
258 cond_resched();
259 }
260
261 i--;
262 if (i < 0)
263 break;
264 e = ep[i];
265 c = BITS_PER_MPI_LIMB;
266 }
267
268 /* We shifted MOD, the modulo reduction argument, left MOD_SHIFT_CNT
269 * steps. Adjust the result by reducing it with the original MOD.
270 *
271 * Also make sure the result is put in RES->d (where it already
272 * might be, see above).
273 */
274 if (mod_shift_cnt) {
275 carry_limb =
276 mpihelp_lshift(res->d, rp, rsize, mod_shift_cnt);
277 rp = res->d;
278 if (carry_limb) {
279 rp[rsize] = carry_limb;
280 rsize++;
281 }
282 } else {
283 MPN_COPY(res->d, rp, rsize);
284 rp = res->d;
285 }
286
287 if (rsize >= msize) {
288 mpihelp_divrem(rp + msize, 0, rp, rsize, mp, msize);
289 rsize = msize;
290 }
291
292 /* Remove any leading zero words from the result. */
293 if (mod_shift_cnt)
294 mpihelp_rshift(rp, rp, rsize, mod_shift_cnt);
295 MPN_NORMALIZE(rp, rsize);
296 }
297
298 if (negative_result && rsize) {
299 if (mod_shift_cnt)
300 mpihelp_rshift(mp, mp, msize, mod_shift_cnt);
301 mpihelp_sub(rp, mp, msize, rp, rsize);
302 rsize = msize;
303 rsign = msign;
304 MPN_NORMALIZE(rp, rsize);
305 }
306 res->nlimbs = rsize;
307 res->sign = rsign;
308
309 leave:
310 rc = 0;
311 enomem:
312 mpihelp_release_karatsuba_ctx(&karactx);
313 if (assign_rp)
314 mpi_assign_limb_space(res, rp, size);
315 if (mp_marker)
316 mpi_free_limb_space(mp_marker);
317 if (bp_marker)
318 mpi_free_limb_space(bp_marker);
319 if (ep_marker)
320 mpi_free_limb_space(ep_marker);
321 if (xp_marker)
322 mpi_free_limb_space(xp_marker);
323 if (tspace)
324 mpi_free_limb_space(tspace);
325 return rc;
326 }
327 EXPORT_SYMBOL_GPL(mpi_powm);
328