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Use the generic exponentiation functions.
[u/mdw/catacomb] / mpbarrett.c
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21a7c4b1 1/* -*-c-*-
2 *
4640a0dd 3 * $Id: mpbarrett.c,v 1.8 2001/06/16 13:00:20 mdw Exp $
21a7c4b1 4 *
5 * Barrett modular reduction
6 *
7 * (c) 1999 Straylight/Edgeware
8 */
9
10/*----- Licensing notice --------------------------------------------------*
11 *
12 * This file is part of Catacomb.
13 *
14 * Catacomb is free software; you can redistribute it and/or modify
15 * it under the terms of the GNU Library General Public License as
16 * published by the Free Software Foundation; either version 2 of the
17 * License, or (at your option) any later version.
18 *
19 * Catacomb is distributed in the hope that it will be useful,
20 * but WITHOUT ANY WARRANTY; without even the implied warranty of
21 * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
22 * GNU Library General Public License for more details.
23 *
24 * You should have received a copy of the GNU Library General Public
25 * License along with Catacomb; if not, write to the Free
26 * Software Foundation, Inc., 59 Temple Place - Suite 330, Boston,
27 * MA 02111-1307, USA.
28 */
29
30/*----- Revision history --------------------------------------------------*
31 *
32 * $Log: mpbarrett.c,v $
4640a0dd 33 * Revision 1.8 2001/06/16 13:00:20 mdw
34 * Use the generic exponentiation functions.
35 *
1ba69a1e 36 * Revision 1.7 2001/04/19 18:25:26 mdw
37 * Use sliding-window exponentiation.
38 *
30cbe7a7 39 * Revision 1.6 2000/10/08 12:03:44 mdw
40 * (mpbarrett_reduce): Cope with negative numbers.
41 *
419d33ed 42 * Revision 1.5 2000/07/29 17:04:33 mdw
43 * Change to use left-to-right bitwise exponentiation. This will improve
44 * performance when the base is small.
45 *
d34decd2 46 * Revision 1.4 2000/06/17 11:45:09 mdw
47 * Major memory management overhaul. Added arena support. Use the secure
48 * arena for secret integers. Replace and improve the MP management macros
49 * (e.g., replace MP_MODIFY by MP_DEST).
50 *
0a5d0bc7 51 * Revision 1.3 1999/12/12 15:08:52 mdw
52 * Don't bother shifting %$q$% in @mpbarrett_reduce@, just skip the least
53 * significant digits.
54 *
ed6d1bd2 55 * Revision 1.2 1999/12/11 01:50:56 mdw
56 * Improve initialization slightly.
57 *
21a7c4b1 58 * Revision 1.1 1999/12/10 23:21:59 mdw
59 * Barrett reduction support: works with even moduli.
60 *
61 */
62
63/*----- Header files ------------------------------------------------------*/
64
65#include "mp.h"
66#include "mpbarrett.h"
4640a0dd 67#include "mpbarrett-exp.h"
21a7c4b1 68
69/*----- Main code ---------------------------------------------------------*/
70
71/* --- @mpbarrett_create@ --- *
72 *
73 * Arguments: @mpbarrett *mb@ = pointer to Barrett reduction context
74 * @mp *m@ = modulus to work to
75 *
76 *
77 * Returns: ---
78 *
79 * Use: Initializes a Barrett reduction context ready for use.
80 */
81
82void mpbarrett_create(mpbarrett *mb, mp *m)
83{
84 mp *b;
85
86 /* --- Validate the arguments --- */
87
88 assert(((void)"Barrett modulus must be positive", (m->f & MP_NEG) == 0));
89
90 /* --- Compute %$\mu$% --- */
91
92 mp_shrink(m);
93 mb->k = MP_LEN(m);
94 mb->m = MP_COPY(m);
d34decd2 95 b = mp_new(2 * mb->k + 1, 0);
ed6d1bd2 96 MPX_ZERO(b->v, b->vl - 1);
97 b->vl[-1] = 1;
21a7c4b1 98 mp_div(&b, 0, b, m);
99 mb->mu = b;
100}
101
102/* --- @mpbarrett_destroy@ --- *
103 *
104 * Arguments: @mpbarrett *mb@ = pointer to Barrett reduction context
105 *
106 * Returns: ---
107 *
108 * Use: Destroys a Barrett reduction context releasing any resources
109 * claimed.
110 */
111
112void mpbarrett_destroy(mpbarrett *mb)
113{
114 mp_drop(mb->m);
115 mp_drop(mb->mu);
116}
117
118/* --- @mpbarrett_reduce@ --- *
119 *
120 * Arguments: @mpbarrett *mb@ = pointer to Barrett reduction context
121 * @mp *d@ = destination for result
122 * @mp *m@ = number to reduce
123 *
124 * Returns: The residue of @m@ modulo the number in the reduction
125 * context.
126 *
30cbe7a7 127 * Use: Performs an efficient modular reduction.
21a7c4b1 128 */
129
130mp *mpbarrett_reduce(mpbarrett *mb, mp *d, mp *m)
131{
132 mp *q;
133 size_t k = mb->k;
134
135 /* --- Special case if @m@ is too small --- */
136
137 if (MP_LEN(m) < k) {
138 m = MP_COPY(m);
d34decd2 139 if (d)
140 MP_DROP(d);
21a7c4b1 141 return (m);
142 }
143
144 /* --- First stage --- */
145
146 {
147 mp qq;
148 mp_build(&qq, m->v + (k - 1), m->vl);
149 q = mp_mul(MP_NEW, &qq, mb->mu);
0a5d0bc7 150 if (MP_LEN(q) <= k) {
151 m = MP_COPY(m);
d34decd2 152 if (d)
153 MP_DROP(d);
0a5d0bc7 154 return (m);
155 }
21a7c4b1 156 }
157
158 /* --- Second stage --- */
159
160 {
161 mp *r;
162 mpw *mvl;
163
164 MP_COPY(m);
165 if (MP_LEN(m) <= k + 1)
166 mvl = m->vl;
167 else
168 mvl = m->v + k + 1;
d34decd2 169 r = mp_new(k + 1, (q->f | mb->m->f) & MP_BURN);
0a5d0bc7 170 mpx_umul(r->v, r->vl, q->v + k + 1, q->vl, mb->m->v, mb->m->vl);
d34decd2 171 MP_DEST(d, k + 1, r->f);
21a7c4b1 172 mpx_usub(d->v, d->vl, m->v, mvl, r->v, r->vl);
30cbe7a7 173 d->f = (m->f | r->f) & (MP_BURN | MP_NEG);
21a7c4b1 174 MP_DROP(r);
175 MP_DROP(q);
176 MP_DROP(m);
177 }
178
179 /* --- Final stage --- */
180
181 MP_SHRINK(d);
182 while (MPX_UCMP(d->v, d->vl, >=, mb->m->v, mb->m->vl))
183 mpx_usub(d->v, d->vl, d->v, d->vl, mb->m->v, mb->m->vl);
184
30cbe7a7 185 /* --- Fix up the sign --- */
186
187 if (d->f & MP_NEG) {
188 mpx_usub(d->v, d->vl, mb->m->v, mb->m->vl, d->v, d->vl);
189 d->f &= ~MP_NEG;
190 }
191
21a7c4b1 192 MP_SHRINK(d);
193 return (d);
194}
195
196/* --- @mpbarrett_exp@ --- *
197 *
198 * Arguments: @mpbarrett *mb@ = pointer to Barrett reduction context
199 * @mp *d@ = fake destination
200 * @mp *a@ = base
201 * @mp *e@ = exponent
202 *
203 * Returns: Result, %$a^e \bmod m$%.
204 */
205
1ba69a1e 206mp *mpbarrett_exp(mpbarrett *mb, mp *d, mp *a, mp *e)
207{
1ba69a1e 208 mp *x = MP_ONE;
4640a0dd 209 mp *spare = (e->f & MP_BURN) ? MP_NEWSEC : MP_NEW;
1ba69a1e 210
211 MP_SHRINK(e);
4640a0dd 212 if (!MP_LEN(e))
213 ;
214 else if (MP_LEN(e) < EXP_THRESH)
215 EXP_SIMPLE(x, a, e);
216 else
217 EXP_WINDOW(x, a, e);
1ba69a1e 218 mp_drop(d);
219 mp_drop(spare);
220 return (x);
221}
222
21a7c4b1 223/*----- Test rig ----------------------------------------------------------*/
224
225#ifdef TEST_RIG
226
227static int vmod(dstr *v)
228{
229 mp *x = *(mp **)v[0].buf;
230 mp *n = *(mp **)v[1].buf;
231 mp *r = *(mp **)v[2].buf;
232 mp *s;
233 mpbarrett mb;
234 int ok = 1;
235
236 mpbarrett_create(&mb, n);
237 s = mpbarrett_reduce(&mb, MP_NEW, x);
238
30cbe7a7 239 if (!MP_EQ(s, r)) {
21a7c4b1 240 fputs("\n*** barrett reduction failure\n", stderr);
241 fputs("x = ", stderr); mp_writefile(x, stderr, 10); fputc('\n', stderr);
242 fputs("n = ", stderr); mp_writefile(n, stderr, 10); fputc('\n', stderr);
243 fputs("r = ", stderr); mp_writefile(r, stderr, 10); fputc('\n', stderr);
244 fputs("s = ", stderr); mp_writefile(s, stderr, 10); fputc('\n', stderr);
245 ok = 0;
246 }
247
248 mpbarrett_destroy(&mb);
249 mp_drop(x);
250 mp_drop(n);
251 mp_drop(r);
252 mp_drop(s);
253 assert(mparena_count(MPARENA_GLOBAL) == 0);
254 return (ok);
255}
256
257static int vexp(dstr *v)
258{
259 mp *m = *(mp **)v[0].buf;
260 mp *a = *(mp **)v[1].buf;
261 mp *b = *(mp **)v[2].buf;
262 mp *r = *(mp **)v[3].buf;
263 mp *mr;
264 int ok = 1;
265
266 mpbarrett mb;
267 mpbarrett_create(&mb, m);
268
269 mr = mpbarrett_exp(&mb, MP_NEW, a, b);
270
30cbe7a7 271 if (!MP_EQ(mr, r)) {
21a7c4b1 272 fputs("\n*** barrett modexp failed", stderr);
273 fputs("\n m = ", stderr); mp_writefile(m, stderr, 10);
274 fputs("\n a = ", stderr); mp_writefile(a, stderr, 10);
275 fputs("\n e = ", stderr); mp_writefile(b, stderr, 10);
276 fputs("\n r = ", stderr); mp_writefile(r, stderr, 10);
277 fputs("\nmr = ", stderr); mp_writefile(mr, stderr, 10);
278 fputc('\n', stderr);
279 ok = 0;
280 }
281
282 mp_drop(m);
283 mp_drop(a);
284 mp_drop(b);
285 mp_drop(r);
286 mp_drop(mr);
287 mpbarrett_destroy(&mb);
288 assert(mparena_count(MPARENA_GLOBAL) == 0);
289 return ok;
290}
291
292static test_chunk tests[] = {
293 { "mpbarrett-reduce", vmod, { &type_mp, &type_mp, &type_mp, 0 } },
294 { "mpbarrett-exp", vexp, { &type_mp, &type_mp, &type_mp, &type_mp, 0 } },
295 { 0, 0, { 0 } }
296};
297
298int main(int argc, char *argv[])
299{
300 sub_init();
301 test_run(argc, argv, tests, SRCDIR "/tests/mpbarrett");
302 return (0);
303}
304
305#endif
306
307/*----- That's all, folks -------------------------------------------------*/
Catacomb cryptographic library (downstream of http://git.distorted.org.uk/~mdw/catacomb/)