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Provide @mp_eq@ and @MP_EQ@ for rapidly testing equality of two
[u/mdw/catacomb] / mpbarrett.c
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21a7c4b1 1/* -*-c-*-
2 *
419d33ed 3 * $Id: mpbarrett.c,v 1.5 2000/07/29 17:04:33 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 $
419d33ed 33 * Revision 1.5 2000/07/29 17:04:33 mdw
34 * Change to use left-to-right bitwise exponentiation. This will improve
35 * performance when the base is small.
36 *
d34decd2 37 * Revision 1.4 2000/06/17 11:45:09 mdw
38 * Major memory management overhaul. Added arena support. Use the secure
39 * arena for secret integers. Replace and improve the MP management macros
40 * (e.g., replace MP_MODIFY by MP_DEST).
41 *
0a5d0bc7 42 * Revision 1.3 1999/12/12 15:08:52 mdw
43 * Don't bother shifting %$q$% in @mpbarrett_reduce@, just skip the least
44 * significant digits.
45 *
ed6d1bd2 46 * Revision 1.2 1999/12/11 01:50:56 mdw
47 * Improve initialization slightly.
48 *
21a7c4b1 49 * Revision 1.1 1999/12/10 23:21:59 mdw
50 * Barrett reduction support: works with even moduli.
51 *
52 */
53
54/*----- Header files ------------------------------------------------------*/
55
56#include "mp.h"
57#include "mpbarrett.h"
58
59/*----- Main code ---------------------------------------------------------*/
60
61/* --- @mpbarrett_create@ --- *
62 *
63 * Arguments: @mpbarrett *mb@ = pointer to Barrett reduction context
64 * @mp *m@ = modulus to work to
65 *
66 *
67 * Returns: ---
68 *
69 * Use: Initializes a Barrett reduction context ready for use.
70 */
71
72void mpbarrett_create(mpbarrett *mb, mp *m)
73{
74 mp *b;
75
76 /* --- Validate the arguments --- */
77
78 assert(((void)"Barrett modulus must be positive", (m->f & MP_NEG) == 0));
79
80 /* --- Compute %$\mu$% --- */
81
82 mp_shrink(m);
83 mb->k = MP_LEN(m);
84 mb->m = MP_COPY(m);
d34decd2 85 b = mp_new(2 * mb->k + 1, 0);
ed6d1bd2 86 MPX_ZERO(b->v, b->vl - 1);
87 b->vl[-1] = 1;
21a7c4b1 88 mp_div(&b, 0, b, m);
89 mb->mu = b;
90}
91
92/* --- @mpbarrett_destroy@ --- *
93 *
94 * Arguments: @mpbarrett *mb@ = pointer to Barrett reduction context
95 *
96 * Returns: ---
97 *
98 * Use: Destroys a Barrett reduction context releasing any resources
99 * claimed.
100 */
101
102void mpbarrett_destroy(mpbarrett *mb)
103{
104 mp_drop(mb->m);
105 mp_drop(mb->mu);
106}
107
108/* --- @mpbarrett_reduce@ --- *
109 *
110 * Arguments: @mpbarrett *mb@ = pointer to Barrett reduction context
111 * @mp *d@ = destination for result
112 * @mp *m@ = number to reduce
113 *
114 * Returns: The residue of @m@ modulo the number in the reduction
115 * context.
116 *
117 * Use: Performs an efficient modular reduction. The argument is
118 * assumed to be positive.
119 */
120
121mp *mpbarrett_reduce(mpbarrett *mb, mp *d, mp *m)
122{
123 mp *q;
124 size_t k = mb->k;
125
126 /* --- Special case if @m@ is too small --- */
127
128 if (MP_LEN(m) < k) {
129 m = MP_COPY(m);
d34decd2 130 if (d)
131 MP_DROP(d);
21a7c4b1 132 return (m);
133 }
134
135 /* --- First stage --- */
136
137 {
138 mp qq;
139 mp_build(&qq, m->v + (k - 1), m->vl);
140 q = mp_mul(MP_NEW, &qq, mb->mu);
0a5d0bc7 141 if (MP_LEN(q) <= k) {
142 m = MP_COPY(m);
d34decd2 143 if (d)
144 MP_DROP(d);
0a5d0bc7 145 return (m);
146 }
21a7c4b1 147 }
148
149 /* --- Second stage --- */
150
151 {
152 mp *r;
153 mpw *mvl;
154
155 MP_COPY(m);
156 if (MP_LEN(m) <= k + 1)
157 mvl = m->vl;
158 else
159 mvl = m->v + k + 1;
d34decd2 160 r = mp_new(k + 1, (q->f | mb->m->f) & MP_BURN);
0a5d0bc7 161 mpx_umul(r->v, r->vl, q->v + k + 1, q->vl, mb->m->v, mb->m->vl);
d34decd2 162 MP_DEST(d, k + 1, r->f);
21a7c4b1 163 mpx_usub(d->v, d->vl, m->v, mvl, r->v, r->vl);
164 d->f = (m->f | r->f) & MP_BURN;
165 MP_DROP(r);
166 MP_DROP(q);
167 MP_DROP(m);
168 }
169
170 /* --- Final stage --- */
171
172 MP_SHRINK(d);
173 while (MPX_UCMP(d->v, d->vl, >=, mb->m->v, mb->m->vl))
174 mpx_usub(d->v, d->vl, d->v, d->vl, mb->m->v, mb->m->vl);
175
176 MP_SHRINK(d);
177 return (d);
178}
179
180/* --- @mpbarrett_exp@ --- *
181 *
182 * Arguments: @mpbarrett *mb@ = pointer to Barrett reduction context
183 * @mp *d@ = fake destination
184 * @mp *a@ = base
185 * @mp *e@ = exponent
186 *
187 * Returns: Result, %$a^e \bmod m$%.
188 */
189
190mp *mpbarrett_exp(mpbarrett *mb, mp *d, mp *a, mp *e)
191{
192 mpscan sc;
193 mp *x = MP_ONE;
419d33ed 194 mp *spare = (e->f & MP_BURN) ? MP_NEWSEC : MP_NEW;
195 unsigned sq = 0;
21a7c4b1 196
197 a = MP_COPY(a);
419d33ed 198 mp_rscan(&sc, e);
199 if (!MP_RSTEP(&sc))
200 goto exit;
201 while (!MP_RBIT(&sc))
202 MP_RSTEP(&sc);
203
204 /* --- Do the main body of the work --- */
205
206 for (;;) {
207 sq++;
208 while (sq) {
209 mp *y;
210 y = mp_sqr(spare, x);
211 y = mpbarrett_reduce(mb, y, y);
212 spare = x; x = y;
213 sq--;
214 }
215 {
216 mp *y = mp_mul(spare, x, a);
217 y = mpbarrett_reduce(mb, y, y);
218 spare = x; x = y;
219 }
21a7c4b1 220 for (;;) {
419d33ed 221 if (!MP_RSTEP(&sc))
222 goto done;
223 if (MP_RBIT(&sc))
224 break;
21a7c4b1 225 sq++;
21a7c4b1 226 }
227 }
228
419d33ed 229 /* --- Do a final round of squaring --- */
230
231done:
232 while (sq) {
233 mp *y;
234 y = mp_sqr(spare, x);
235 y = mpbarrett_reduce(mb, y, y);
236 spare = x; x = y;
237 sq--;
238 }
239
240exit:
21a7c4b1 241 MP_DROP(a);
242 if (spare != MP_NEW)
243 MP_DROP(spare);
244 if (d != MP_NEW)
245 MP_DROP(d);
246 return (x);
247}
248
249/*----- Test rig ----------------------------------------------------------*/
250
251#ifdef TEST_RIG
252
253static int vmod(dstr *v)
254{
255 mp *x = *(mp **)v[0].buf;
256 mp *n = *(mp **)v[1].buf;
257 mp *r = *(mp **)v[2].buf;
258 mp *s;
259 mpbarrett mb;
260 int ok = 1;
261
262 mpbarrett_create(&mb, n);
263 s = mpbarrett_reduce(&mb, MP_NEW, x);
264
265 if (MP_CMP(s, !=, r)) {
266 fputs("\n*** barrett reduction failure\n", stderr);
267 fputs("x = ", stderr); mp_writefile(x, stderr, 10); fputc('\n', stderr);
268 fputs("n = ", stderr); mp_writefile(n, stderr, 10); fputc('\n', stderr);
269 fputs("r = ", stderr); mp_writefile(r, stderr, 10); fputc('\n', stderr);
270 fputs("s = ", stderr); mp_writefile(s, stderr, 10); fputc('\n', stderr);
271 ok = 0;
272 }
273
274 mpbarrett_destroy(&mb);
275 mp_drop(x);
276 mp_drop(n);
277 mp_drop(r);
278 mp_drop(s);
279 assert(mparena_count(MPARENA_GLOBAL) == 0);
280 return (ok);
281}
282
283static int vexp(dstr *v)
284{
285 mp *m = *(mp **)v[0].buf;
286 mp *a = *(mp **)v[1].buf;
287 mp *b = *(mp **)v[2].buf;
288 mp *r = *(mp **)v[3].buf;
289 mp *mr;
290 int ok = 1;
291
292 mpbarrett mb;
293 mpbarrett_create(&mb, m);
294
295 mr = mpbarrett_exp(&mb, MP_NEW, a, b);
296
297 if (MP_CMP(mr, !=, r)) {
298 fputs("\n*** barrett modexp failed", stderr);
299 fputs("\n m = ", stderr); mp_writefile(m, stderr, 10);
300 fputs("\n a = ", stderr); mp_writefile(a, stderr, 10);
301 fputs("\n e = ", stderr); mp_writefile(b, stderr, 10);
302 fputs("\n r = ", stderr); mp_writefile(r, stderr, 10);
303 fputs("\nmr = ", stderr); mp_writefile(mr, stderr, 10);
304 fputc('\n', stderr);
305 ok = 0;
306 }
307
308 mp_drop(m);
309 mp_drop(a);
310 mp_drop(b);
311 mp_drop(r);
312 mp_drop(mr);
313 mpbarrett_destroy(&mb);
314 assert(mparena_count(MPARENA_GLOBAL) == 0);
315 return ok;
316}
317
318static test_chunk tests[] = {
319 { "mpbarrett-reduce", vmod, { &type_mp, &type_mp, &type_mp, 0 } },
320 { "mpbarrett-exp", vexp, { &type_mp, &type_mp, &type_mp, &type_mp, 0 } },
321 { 0, 0, { 0 } }
322};
323
324int main(int argc, char *argv[])
325{
326 sub_init();
327 test_run(argc, argv, tests, SRCDIR "/tests/mpbarrett");
328 return (0);
329}
330
331#endif
332
333/*----- That's all, folks -------------------------------------------------*/
Catacomb cryptographic library (downstream of http://git.distorted.org.uk/~mdw/catacomb/)