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 */
mpi_powm(MPI res,MPI base,MPI exp,MPI mod)36 int 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
306 leave:
307 rc = 0;
308 enomem:
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 }
323 EXPORT_SYMBOL_GPL(mpi_powm);
324