21a7c4b1 |
1 | /* -*-c-*- |
2 | * |
1ba69a1e |
3 | * $Id: mpbarrett.c,v 1.7 2001/04/19 18:25:26 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 $ |
1ba69a1e |
33 | * Revision 1.7 2001/04/19 18:25:26 mdw |
34 | * Use sliding-window exponentiation. |
35 | * |
30cbe7a7 |
36 | * Revision 1.6 2000/10/08 12:03:44 mdw |
37 | * (mpbarrett_reduce): Cope with negative numbers. |
38 | * |
419d33ed |
39 | * Revision 1.5 2000/07/29 17:04:33 mdw |
40 | * Change to use left-to-right bitwise exponentiation. This will improve |
41 | * performance when the base is small. |
42 | * |
d34decd2 |
43 | * Revision 1.4 2000/06/17 11:45:09 mdw |
44 | * Major memory management overhaul. Added arena support. Use the secure |
45 | * arena for secret integers. Replace and improve the MP management macros |
46 | * (e.g., replace MP_MODIFY by MP_DEST). |
47 | * |
0a5d0bc7 |
48 | * Revision 1.3 1999/12/12 15:08:52 mdw |
49 | * Don't bother shifting %$q$% in @mpbarrett_reduce@, just skip the least |
50 | * significant digits. |
51 | * |
ed6d1bd2 |
52 | * Revision 1.2 1999/12/11 01:50:56 mdw |
53 | * Improve initialization slightly. |
54 | * |
21a7c4b1 |
55 | * Revision 1.1 1999/12/10 23:21:59 mdw |
56 | * Barrett reduction support: works with even moduli. |
57 | * |
58 | */ |
59 | |
60 | /*----- Header files ------------------------------------------------------*/ |
61 | |
62 | #include "mp.h" |
63 | #include "mpbarrett.h" |
64 | |
65 | /*----- Main code ---------------------------------------------------------*/ |
66 | |
67 | /* --- @mpbarrett_create@ --- * |
68 | * |
69 | * Arguments: @mpbarrett *mb@ = pointer to Barrett reduction context |
70 | * @mp *m@ = modulus to work to |
71 | * |
72 | * |
73 | * Returns: --- |
74 | * |
75 | * Use: Initializes a Barrett reduction context ready for use. |
76 | */ |
77 | |
78 | void mpbarrett_create(mpbarrett *mb, mp *m) |
79 | { |
80 | mp *b; |
81 | |
82 | /* --- Validate the arguments --- */ |
83 | |
84 | assert(((void)"Barrett modulus must be positive", (m->f & MP_NEG) == 0)); |
85 | |
86 | /* --- Compute %$\mu$% --- */ |
87 | |
88 | mp_shrink(m); |
89 | mb->k = MP_LEN(m); |
90 | mb->m = MP_COPY(m); |
d34decd2 |
91 | b = mp_new(2 * mb->k + 1, 0); |
ed6d1bd2 |
92 | MPX_ZERO(b->v, b->vl - 1); |
93 | b->vl[-1] = 1; |
21a7c4b1 |
94 | mp_div(&b, 0, b, m); |
95 | mb->mu = b; |
96 | } |
97 | |
98 | /* --- @mpbarrett_destroy@ --- * |
99 | * |
100 | * Arguments: @mpbarrett *mb@ = pointer to Barrett reduction context |
101 | * |
102 | * Returns: --- |
103 | * |
104 | * Use: Destroys a Barrett reduction context releasing any resources |
105 | * claimed. |
106 | */ |
107 | |
108 | void mpbarrett_destroy(mpbarrett *mb) |
109 | { |
110 | mp_drop(mb->m); |
111 | mp_drop(mb->mu); |
112 | } |
113 | |
114 | /* --- @mpbarrett_reduce@ --- * |
115 | * |
116 | * Arguments: @mpbarrett *mb@ = pointer to Barrett reduction context |
117 | * @mp *d@ = destination for result |
118 | * @mp *m@ = number to reduce |
119 | * |
120 | * Returns: The residue of @m@ modulo the number in the reduction |
121 | * context. |
122 | * |
30cbe7a7 |
123 | * Use: Performs an efficient modular reduction. |
21a7c4b1 |
124 | */ |
125 | |
126 | mp *mpbarrett_reduce(mpbarrett *mb, mp *d, mp *m) |
127 | { |
128 | mp *q; |
129 | size_t k = mb->k; |
130 | |
131 | /* --- Special case if @m@ is too small --- */ |
132 | |
133 | if (MP_LEN(m) < k) { |
134 | m = MP_COPY(m); |
d34decd2 |
135 | if (d) |
136 | MP_DROP(d); |
21a7c4b1 |
137 | return (m); |
138 | } |
139 | |
140 | /* --- First stage --- */ |
141 | |
142 | { |
143 | mp qq; |
144 | mp_build(&qq, m->v + (k - 1), m->vl); |
145 | q = mp_mul(MP_NEW, &qq, mb->mu); |
0a5d0bc7 |
146 | if (MP_LEN(q) <= k) { |
147 | m = MP_COPY(m); |
d34decd2 |
148 | if (d) |
149 | MP_DROP(d); |
0a5d0bc7 |
150 | return (m); |
151 | } |
21a7c4b1 |
152 | } |
153 | |
154 | /* --- Second stage --- */ |
155 | |
156 | { |
157 | mp *r; |
158 | mpw *mvl; |
159 | |
160 | MP_COPY(m); |
161 | if (MP_LEN(m) <= k + 1) |
162 | mvl = m->vl; |
163 | else |
164 | mvl = m->v + k + 1; |
d34decd2 |
165 | r = mp_new(k + 1, (q->f | mb->m->f) & MP_BURN); |
0a5d0bc7 |
166 | mpx_umul(r->v, r->vl, q->v + k + 1, q->vl, mb->m->v, mb->m->vl); |
d34decd2 |
167 | MP_DEST(d, k + 1, r->f); |
21a7c4b1 |
168 | mpx_usub(d->v, d->vl, m->v, mvl, r->v, r->vl); |
30cbe7a7 |
169 | d->f = (m->f | r->f) & (MP_BURN | MP_NEG); |
21a7c4b1 |
170 | MP_DROP(r); |
171 | MP_DROP(q); |
172 | MP_DROP(m); |
173 | } |
174 | |
175 | /* --- Final stage --- */ |
176 | |
177 | MP_SHRINK(d); |
178 | while (MPX_UCMP(d->v, d->vl, >=, mb->m->v, mb->m->vl)) |
179 | mpx_usub(d->v, d->vl, d->v, d->vl, mb->m->v, mb->m->vl); |
180 | |
30cbe7a7 |
181 | /* --- Fix up the sign --- */ |
182 | |
183 | if (d->f & MP_NEG) { |
184 | mpx_usub(d->v, d->vl, mb->m->v, mb->m->vl, d->v, d->vl); |
185 | d->f &= ~MP_NEG; |
186 | } |
187 | |
21a7c4b1 |
188 | MP_SHRINK(d); |
189 | return (d); |
190 | } |
191 | |
192 | /* --- @mpbarrett_exp@ --- * |
193 | * |
194 | * Arguments: @mpbarrett *mb@ = pointer to Barrett reduction context |
195 | * @mp *d@ = fake destination |
196 | * @mp *a@ = base |
197 | * @mp *e@ = exponent |
198 | * |
199 | * Returns: Result, %$a^e \bmod m$%. |
200 | */ |
201 | |
1ba69a1e |
202 | #define WINSZ 5 |
203 | #define TABSZ (1 << (WINSZ - 1)) |
204 | |
205 | #define THRESH (((MPW_BITS / WINSZ) << 2) + 1) |
206 | |
207 | static mp *exp_simple(mpbarrett *mb, mp *d, mp *a, mp *e) |
21a7c4b1 |
208 | { |
209 | mpscan sc; |
210 | mp *x = MP_ONE; |
419d33ed |
211 | mp *spare = (e->f & MP_BURN) ? MP_NEWSEC : MP_NEW; |
212 | unsigned sq = 0; |
21a7c4b1 |
213 | |
214 | a = MP_COPY(a); |
419d33ed |
215 | mp_rscan(&sc, e); |
216 | if (!MP_RSTEP(&sc)) |
217 | goto exit; |
218 | while (!MP_RBIT(&sc)) |
219 | MP_RSTEP(&sc); |
220 | |
221 | /* --- Do the main body of the work --- */ |
222 | |
223 | for (;;) { |
224 | sq++; |
225 | while (sq) { |
226 | mp *y; |
227 | y = mp_sqr(spare, x); |
228 | y = mpbarrett_reduce(mb, y, y); |
229 | spare = x; x = y; |
230 | sq--; |
231 | } |
232 | { |
233 | mp *y = mp_mul(spare, x, a); |
234 | y = mpbarrett_reduce(mb, y, y); |
235 | spare = x; x = y; |
236 | } |
21a7c4b1 |
237 | for (;;) { |
419d33ed |
238 | if (!MP_RSTEP(&sc)) |
239 | goto done; |
240 | if (MP_RBIT(&sc)) |
241 | break; |
21a7c4b1 |
242 | sq++; |
21a7c4b1 |
243 | } |
244 | } |
245 | |
419d33ed |
246 | /* --- Do a final round of squaring --- */ |
247 | |
248 | done: |
249 | while (sq) { |
250 | mp *y; |
251 | y = mp_sqr(spare, x); |
252 | y = mpbarrett_reduce(mb, y, y); |
253 | spare = x; x = y; |
254 | sq--; |
255 | } |
256 | |
257 | exit: |
21a7c4b1 |
258 | MP_DROP(a); |
259 | if (spare != MP_NEW) |
260 | MP_DROP(spare); |
261 | if (d != MP_NEW) |
262 | MP_DROP(d); |
263 | return (x); |
264 | } |
265 | |
1ba69a1e |
266 | mp *mpbarrett_exp(mpbarrett *mb, mp *d, mp *a, mp *e) |
267 | { |
268 | mp **tab; |
269 | mp *a2; |
270 | mp *spare = (e->f & MP_BURN) ? MP_NEWSEC : MP_NEW; |
271 | mp *x = MP_ONE; |
272 | unsigned i, sq = 0; |
273 | mpscan sc; |
274 | |
275 | /* --- Do we bother? --- */ |
276 | |
277 | MP_SHRINK(e); |
278 | if (MP_LEN(e) == 0) |
279 | goto exit; |
280 | if (MP_LEN(e) < THRESH) { |
281 | x->ref--; |
282 | return (exp_simple(mb, d, a, e)); |
283 | } |
284 | |
285 | /* --- Do the precomputation --- */ |
286 | |
287 | a2 = mp_sqr(MP_NEW, a); |
288 | a2 = mpbarrett_reduce(mb, a2, a2); |
289 | tab = xmalloc(TABSZ * sizeof(mp *)); |
290 | tab[0] = MP_COPY(a); |
291 | for (i = 1; i < TABSZ; i++) { |
292 | mp *x = mp_mul(MP_NEW, tab[i - 1], a2); |
293 | tab[i] = mpbarrett_reduce(mb, x, x); |
294 | } |
295 | mp_drop(a2); |
296 | mp_rscan(&sc, e); |
297 | |
298 | /* --- Skip top-end zero bits --- * |
299 | * |
300 | * If the initial step worked, there must be a set bit somewhere, so keep |
301 | * stepping until I find it. |
302 | */ |
303 | |
304 | MP_RSTEP(&sc); |
305 | while (!MP_RBIT(&sc)) |
306 | MP_RSTEP(&sc); |
307 | |
308 | /* --- Now for the main work --- */ |
309 | |
310 | for (;;) { |
311 | unsigned l = 0; |
312 | unsigned z = 0; |
313 | |
314 | /* --- The next bit is set, so read a window index --- * |
315 | * |
316 | * Reset @i@ to zero and increment @sq@. Then, until either I read |
317 | * @WINSZ@ bits or I run out of bits, scan in a bit: if it's clear, bump |
318 | * the @z@ counter; if it's set, push a set bit into @i@, shift it over |
319 | * by @z@ bits, bump @sq@ by @z + 1@ and clear @z@. By the end of this |
320 | * palaver, @i@ is an index to the precomputed value in @tab@. |
321 | */ |
322 | |
323 | i = 0; |
324 | sq++; |
325 | for (;;) { |
326 | l++; |
327 | if (l >= WINSZ || !MP_RSTEP(&sc)) |
328 | break; |
329 | if (!MP_RBIT(&sc)) |
330 | z++; |
331 | else { |
332 | i = ((i << 1) | 1) << z; |
333 | sq += z + 1; |
334 | z = 0; |
335 | } |
336 | } |
337 | |
338 | /* --- Do the squaring --- * |
339 | * |
340 | * Remember that @sq@ carries over from the zero-skipping stuff below. |
341 | */ |
342 | |
343 | while (sq) { |
344 | mp *y; |
345 | y = mp_sqr(spare, x); |
346 | y = mpbarrett_reduce(mb, y, y); |
347 | spare = x; x = y; |
348 | sq--; |
349 | } |
350 | |
351 | /* --- Do the multiply --- */ |
352 | |
353 | { mp *y = mp_mul(spare, x, tab[i]); spare = x; |
354 | x = mpbarrett_reduce(mb, y, y); } |
355 | |
356 | /* --- Now grind along through the rest of the bits --- */ |
357 | |
358 | sq = z; |
359 | for (;;) { |
360 | if (!MP_RSTEP(&sc)) |
361 | goto done; |
362 | if (MP_RBIT(&sc)) |
363 | break; |
364 | sq++; |
365 | } |
366 | } |
367 | |
368 | /* --- Do a final round of squaring --- */ |
369 | |
370 | done: |
371 | while (sq) { |
372 | mp *y; |
373 | y = mp_sqr(spare, x); |
374 | y = mpbarrett_reduce(mb, y, y); |
375 | spare = x; x = y; |
376 | sq--; |
377 | } |
378 | |
379 | /* --- Done --- */ |
380 | |
381 | for (i = 0; i < TABSZ; i++) |
382 | mp_drop(tab[i]); |
383 | xfree(tab); |
384 | exit: |
385 | mp_drop(d); |
386 | mp_drop(spare); |
387 | return (x); |
388 | } |
389 | |
21a7c4b1 |
390 | /*----- Test rig ----------------------------------------------------------*/ |
391 | |
392 | #ifdef TEST_RIG |
393 | |
394 | static int vmod(dstr *v) |
395 | { |
396 | mp *x = *(mp **)v[0].buf; |
397 | mp *n = *(mp **)v[1].buf; |
398 | mp *r = *(mp **)v[2].buf; |
399 | mp *s; |
400 | mpbarrett mb; |
401 | int ok = 1; |
402 | |
403 | mpbarrett_create(&mb, n); |
404 | s = mpbarrett_reduce(&mb, MP_NEW, x); |
405 | |
30cbe7a7 |
406 | if (!MP_EQ(s, r)) { |
21a7c4b1 |
407 | fputs("\n*** barrett reduction failure\n", stderr); |
408 | fputs("x = ", stderr); mp_writefile(x, stderr, 10); fputc('\n', stderr); |
409 | fputs("n = ", stderr); mp_writefile(n, stderr, 10); fputc('\n', stderr); |
410 | fputs("r = ", stderr); mp_writefile(r, stderr, 10); fputc('\n', stderr); |
411 | fputs("s = ", stderr); mp_writefile(s, stderr, 10); fputc('\n', stderr); |
412 | ok = 0; |
413 | } |
414 | |
415 | mpbarrett_destroy(&mb); |
416 | mp_drop(x); |
417 | mp_drop(n); |
418 | mp_drop(r); |
419 | mp_drop(s); |
420 | assert(mparena_count(MPARENA_GLOBAL) == 0); |
421 | return (ok); |
422 | } |
423 | |
424 | static int vexp(dstr *v) |
425 | { |
426 | mp *m = *(mp **)v[0].buf; |
427 | mp *a = *(mp **)v[1].buf; |
428 | mp *b = *(mp **)v[2].buf; |
429 | mp *r = *(mp **)v[3].buf; |
430 | mp *mr; |
431 | int ok = 1; |
432 | |
433 | mpbarrett mb; |
434 | mpbarrett_create(&mb, m); |
435 | |
436 | mr = mpbarrett_exp(&mb, MP_NEW, a, b); |
437 | |
30cbe7a7 |
438 | if (!MP_EQ(mr, r)) { |
21a7c4b1 |
439 | fputs("\n*** barrett modexp failed", stderr); |
440 | fputs("\n m = ", stderr); mp_writefile(m, stderr, 10); |
441 | fputs("\n a = ", stderr); mp_writefile(a, stderr, 10); |
442 | fputs("\n e = ", stderr); mp_writefile(b, stderr, 10); |
443 | fputs("\n r = ", stderr); mp_writefile(r, stderr, 10); |
444 | fputs("\nmr = ", stderr); mp_writefile(mr, stderr, 10); |
445 | fputc('\n', stderr); |
446 | ok = 0; |
447 | } |
448 | |
449 | mp_drop(m); |
450 | mp_drop(a); |
451 | mp_drop(b); |
452 | mp_drop(r); |
453 | mp_drop(mr); |
454 | mpbarrett_destroy(&mb); |
455 | assert(mparena_count(MPARENA_GLOBAL) == 0); |
456 | return ok; |
457 | } |
458 | |
459 | static test_chunk tests[] = { |
460 | { "mpbarrett-reduce", vmod, { &type_mp, &type_mp, &type_mp, 0 } }, |
461 | { "mpbarrett-exp", vexp, { &type_mp, &type_mp, &type_mp, &type_mp, 0 } }, |
462 | { 0, 0, { 0 } } |
463 | }; |
464 | |
465 | int main(int argc, char *argv[]) |
466 | { |
467 | sub_init(); |
468 | test_run(argc, argv, tests, SRCDIR "/tests/mpbarrett"); |
469 | return (0); |
470 | } |
471 | |
472 | #endif |
473 | |
474 | /*----- That's all, folks -------------------------------------------------*/ |