d3409d5e |
1 | /* -*-c-*- |
2 | * |
ef5f4810 |
3 | * $Id: mpmont.c,v 1.6 1999/12/10 23:18:39 mdw Exp $ |
d3409d5e |
4 | * |
5 | * Montgomery 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: mpmont.c,v $ |
ef5f4810 |
33 | * Revision 1.6 1999/12/10 23:18:39 mdw |
34 | * Change interface for suggested destinations. |
35 | * |
52e4b041 |
36 | * Revision 1.5 1999/11/22 13:58:40 mdw |
37 | * Add an option to disable Montgomery reduction, so that performance |
38 | * comparisons can be done. |
39 | * |
93feaa6e |
40 | * Revision 1.4 1999/11/21 12:27:06 mdw |
41 | * Remove a division from the Montgomery setup by calculating |
42 | * %$R^2 \bmod m$% first and then %$R \bmod m$% by Montgomery reduction of |
43 | * %$R^2$%. |
44 | * |
79a34029 |
45 | * Revision 1.3 1999/11/21 11:35:10 mdw |
46 | * Performance improvement: use @mp_sqr@ and @mpmont_reduce@ instead of |
47 | * @mpmont_mul@ for squaring in exponentiation. |
48 | * |
17ad212e |
49 | * Revision 1.2 1999/11/19 13:17:26 mdw |
50 | * Add extra interface to exponentiation which returns a Montgomerized |
51 | * result. |
52 | * |
d3409d5e |
53 | * Revision 1.1 1999/11/17 18:02:16 mdw |
54 | * New multiprecision integer arithmetic suite. |
55 | * |
56 | */ |
57 | |
58 | /*----- Header files ------------------------------------------------------*/ |
59 | |
60 | #include "mp.h" |
61 | #include "mpmont.h" |
62 | |
52e4b041 |
63 | /*----- Tweakables --------------------------------------------------------*/ |
64 | |
65 | /* --- @MPMONT_DISABLE@ --- * |
66 | * |
67 | * Replace all the clever Montgomery reduction with good old-fashioned long |
68 | * division. |
69 | */ |
70 | |
71 | /* #define MPMONT_DISABLE */ |
72 | |
d3409d5e |
73 | /*----- Main code ---------------------------------------------------------*/ |
74 | |
75 | /* --- @mpmont_create@ --- * |
76 | * |
77 | * Arguments: @mpmont *mm@ = pointer to Montgomery reduction context |
78 | * @mp *m@ = modulus to use |
79 | * |
80 | * Returns: --- |
81 | * |
82 | * Use: Initializes a Montgomery reduction context ready for use. |
ef5f4810 |
83 | * The argument @m@ must be a positive odd integer. |
d3409d5e |
84 | */ |
85 | |
52e4b041 |
86 | #ifdef MPMONT_DISABLE |
87 | |
88 | void mpmont_create(mpmont *mm, mp *m) |
89 | { |
90 | mp_shrink(m); |
91 | mm->m = MP_COPY(m); |
92 | mm->r = MP_ONE; |
93 | mm->r2 = MP_ONE; |
94 | } |
95 | |
96 | #else |
97 | |
d3409d5e |
98 | void mpmont_create(mpmont *mm, mp *m) |
99 | { |
ef5f4810 |
100 | /* --- Validate the arguments --- */ |
101 | |
102 | assert(((void)"Montgomery modulus must be positive", |
103 | (m->f & MP_NEG) == 0)); |
104 | assert(((void)"Montgomery modulus must be odd", m->v[0] & 1)); |
105 | |
d3409d5e |
106 | /* --- Take a copy of the modulus --- */ |
107 | |
108 | mp_shrink(m); |
109 | mm->m = MP_COPY(m); |
110 | |
111 | /* --- Find the magic value @mi@ --- * |
112 | * |
113 | * This is a slightly grungy way of solving the problem, but it does work. |
114 | */ |
115 | |
116 | { |
117 | mpw av[2] = { 0, 1 }; |
118 | mp a, b; |
ef5f4810 |
119 | mp *i = MP_NEW; |
d3409d5e |
120 | mpw mi; |
121 | |
122 | mp_build(&a, av, av + 2); |
123 | mp_build(&b, m->v, m->v + 1); |
124 | mp_gcd(0, 0, &i, &a, &b); |
125 | mi = i->v[0]; |
126 | if (!(i->f & MP_NEG)) |
127 | mi = MPW(-mi); |
128 | mm->mi = mi; |
129 | MP_DROP(i); |
130 | } |
131 | |
132 | /* --- Discover the values %$R \bmod m$% and %$R^2 \bmod m$% --- */ |
133 | |
134 | { |
135 | size_t l = MP_LEN(m); |
93feaa6e |
136 | mp *r = mp_create(2 * l + 1); |
d3409d5e |
137 | |
138 | mm->shift = l * MPW_BITS; |
139 | MPX_ZERO(r->v, r->vl - 1); |
140 | r->vl[-1] = 1; |
93feaa6e |
141 | mm->r2 = MP_NEW; |
d3409d5e |
142 | mp_div(0, &mm->r2, r, m); |
93feaa6e |
143 | mm->r = mpmont_reduce(mm, MP_NEW, mm->r2); |
d3409d5e |
144 | MP_DROP(r); |
145 | } |
146 | } |
147 | |
52e4b041 |
148 | #endif |
149 | |
d3409d5e |
150 | /* --- @mpmont_destroy@ --- * |
151 | * |
152 | * Arguments: @mpmont *mm@ = pointer to a Montgomery reduction context |
153 | * |
154 | * Returns: --- |
155 | * |
156 | * Use: Disposes of a context when it's no longer of any use to |
157 | * anyone. |
158 | */ |
159 | |
160 | void mpmont_destroy(mpmont *mm) |
161 | { |
162 | MP_DROP(mm->m); |
163 | MP_DROP(mm->r); |
164 | MP_DROP(mm->r2); |
165 | } |
166 | |
167 | /* --- @mpmont_reduce@ --- * |
168 | * |
169 | * Arguments: @mpmont *mm@ = pointer to Montgomery reduction context |
170 | * @mp *d@ = destination |
ef5f4810 |
171 | * @mp *a@ = source, assumed positive |
d3409d5e |
172 | * |
173 | * Returns: Result, %$a R^{-1} \bmod m$%. |
174 | */ |
175 | |
52e4b041 |
176 | #ifdef MPMONT_DISABLE |
177 | |
ef5f4810 |
178 | mp *mpmont_reduce(mpmont *mm, mp *d, mp *a) |
52e4b041 |
179 | { |
180 | mp_div(0, &d, a, mm->m); |
181 | return (d); |
182 | } |
183 | |
184 | #else |
185 | |
ef5f4810 |
186 | mp *mpmont_reduce(mpmont *mm, mp *d, mp *a) |
d3409d5e |
187 | { |
188 | mpw *dv, *dvl; |
ef5f4810 |
189 | mpw *mv, *mvl; |
d3409d5e |
190 | size_t n; |
191 | |
192 | /* --- Initial conditioning of the arguments --- */ |
193 | |
194 | n = MP_LEN(mm->m); |
195 | |
196 | if (d == a) |
79a34029 |
197 | MP_MODIFY(d, 2 * n + 1); |
d3409d5e |
198 | else { |
79a34029 |
199 | MP_MODIFY(d, 2 * n + 1); |
d3409d5e |
200 | memcpy(d->v, a->v, MPWS(MP_LEN(a))); |
201 | memset(d->v + MP_LEN(a), 0, MPWS(MP_LEN(d) - MP_LEN(a))); |
202 | } |
203 | |
204 | dv = d->v; dvl = d->vl; |
205 | mv = mm->m->v; mvl = mm->m->vl; |
206 | |
207 | /* --- Let's go to work --- */ |
208 | |
209 | while (n--) { |
210 | mpw u = MPW(*dv * mm->mi); |
211 | MPX_UMLAN(dv, dvl, mv, mvl, u); |
212 | dv++; |
213 | } |
214 | |
215 | /* --- Done --- */ |
216 | |
217 | memmove(d->v, dv, MPWS(dvl - dv)); |
218 | d->vl -= dv - d->v; |
219 | MP_SHRINK(d); |
220 | d->f = a->f & MP_BURN; |
17ad212e |
221 | if (MP_CMP(d, >=, mm->m)) |
222 | d = mp_sub(d, d, mm->m); |
d3409d5e |
223 | return (d); |
224 | } |
225 | |
52e4b041 |
226 | #endif |
227 | |
d3409d5e |
228 | /* --- @mpmont_mul@ --- * |
229 | * |
230 | * Arguments: @mpmont *mm@ = pointer to Montgomery reduction context |
231 | * @mp *d@ = destination |
ef5f4810 |
232 | * @mp *a, *b@ = sources, assumed positive |
d3409d5e |
233 | * |
234 | * Returns: Result, %$a b R^{-1} \bmod m$%. |
235 | */ |
236 | |
52e4b041 |
237 | #ifdef MPMONT_DISABLE |
238 | |
ef5f4810 |
239 | mp *mpmont_mul(mpmont *mm, mp *d, mp *a, mp *b) |
52e4b041 |
240 | { |
241 | d = mp_mul(d, a, b); |
242 | mp_div(0, &d, d, mm->m); |
243 | return (d); |
244 | } |
245 | |
246 | #else |
247 | |
ef5f4810 |
248 | mp *mpmont_mul(mpmont *mm, mp *d, mp *a, mp *b) |
d3409d5e |
249 | { |
ef5f4810 |
250 | if (MP_LEN(a) > KARATSUBA_CUTOFF && MP_LEN(b) > KARATSUBA_CUTOFF) { |
251 | d = mp_mul(d, a, b); |
252 | d = mpmont_reduce(mm, d, d); |
253 | } else { |
254 | mpw *dv, *dvl; |
255 | mpw *av, *avl; |
256 | mpw *bv, *bvl; |
257 | mpw *mv, *mvl; |
258 | mpw y; |
259 | size_t n, i; |
260 | |
261 | /* --- Initial conditioning of the arguments --- */ |
262 | |
263 | if (MP_LEN(a) > MP_LEN(b)) { |
264 | mp *t = a; a = b; b = t; |
265 | } |
266 | n = MP_LEN(mm->m); |
d3409d5e |
267 | |
ef5f4810 |
268 | a = MP_COPY(a); |
269 | b = MP_COPY(b); |
270 | MP_MODIFY(d, 2 * n + 1); |
271 | dv = d->v; dvl = d->vl; |
272 | MPX_ZERO(dv, dvl); |
273 | av = a->v; avl = a->vl; |
274 | bv = b->v; bvl = b->vl; |
275 | mv = mm->m->v; mvl = mm->m->vl; |
276 | y = *bv; |
277 | |
278 | /* --- Montgomery multiplication phase --- */ |
279 | |
280 | i = 0; |
281 | while (i < n && av < avl) { |
282 | mpw x = *av++; |
283 | mpw u = MPW((*dv + x * y) * mm->mi); |
284 | MPX_UMLAN(dv, dvl, bv, bvl, x); |
285 | MPX_UMLAN(dv, dvl, mv, mvl, u); |
286 | dv++; |
287 | i++; |
288 | } |
d3409d5e |
289 | |
ef5f4810 |
290 | /* --- Simpler Montgomery reduction phase --- */ |
d3409d5e |
291 | |
ef5f4810 |
292 | while (i < n) { |
293 | mpw u = MPW(*dv * mm->mi); |
294 | MPX_UMLAN(dv, dvl, mv, mvl, u); |
295 | dv++; |
296 | i++; |
297 | } |
d3409d5e |
298 | |
ef5f4810 |
299 | /* --- Done --- */ |
d3409d5e |
300 | |
ef5f4810 |
301 | memmove(d->v, dv, MPWS(dvl - dv)); |
302 | d->vl -= dv - d->v; |
303 | MP_SHRINK(d); |
304 | d->f = (a->f | b->f) & MP_BURN; |
305 | if (MP_CMP(d, >=, mm->m)) |
306 | d = mp_sub(d, d, mm->m); |
307 | MP_DROP(a); |
308 | MP_DROP(b); |
d3409d5e |
309 | } |
310 | |
d3409d5e |
311 | return (d); |
312 | } |
313 | |
52e4b041 |
314 | #endif |
315 | |
17ad212e |
316 | /* --- @mpmont_expr@ --- * |
d3409d5e |
317 | * |
318 | * Arguments: @mpmont *mm@ = pointer to Montgomery reduction context |
ef5f4810 |
319 | * @mp *d@ = fake destination |
320 | * @mp *a@ = base |
321 | * @mp *e@ = exponent |
d3409d5e |
322 | * |
17ad212e |
323 | * Returns: Result, %$a^e R \bmod m$%. |
d3409d5e |
324 | */ |
325 | |
ef5f4810 |
326 | mp *mpmont_expr(mpmont *mm, mp *d, mp *a, mp *e) |
d3409d5e |
327 | { |
328 | mpscan sc; |
329 | mp *ar = mpmont_mul(mm, MP_NEW, a, mm->r2); |
ef5f4810 |
330 | mp *x = MP_COPY(mm->r); |
17ad212e |
331 | mp *spare = MP_NEW; |
d3409d5e |
332 | |
333 | mp_scan(&sc, e); |
334 | |
335 | if (MP_STEP(&sc)) { |
17ad212e |
336 | size_t sq = 0; |
d3409d5e |
337 | for (;;) { |
338 | mp *dd; |
339 | if (MP_BIT(&sc)) { |
17ad212e |
340 | while (sq) { |
79a34029 |
341 | dd = mp_sqr(spare, ar); |
342 | dd = mpmont_reduce(mm, dd, dd); |
17ad212e |
343 | spare = ar; ar = dd; |
344 | sq--; |
345 | } |
ef5f4810 |
346 | dd = mpmont_mul(mm, spare, x, ar); |
347 | spare = x; x = dd; |
d3409d5e |
348 | } |
17ad212e |
349 | sq++; |
d3409d5e |
350 | if (!MP_STEP(&sc)) |
351 | break; |
d3409d5e |
352 | } |
353 | } |
354 | MP_DROP(ar); |
17ad212e |
355 | if (spare != MP_NEW) |
356 | MP_DROP(spare); |
ef5f4810 |
357 | if (d != MP_NEW) |
358 | MP_DROP(d); |
359 | return (x); |
17ad212e |
360 | } |
361 | |
362 | /* --- @mpmont_exp@ --- * |
363 | * |
364 | * Arguments: @mpmont *mm@ = pointer to Montgomery reduction context |
ef5f4810 |
365 | * @mp *d@ = fake destination |
366 | * @mp *a@ = base |
367 | * @mp *e@ = exponent |
17ad212e |
368 | * |
369 | * Returns: Result, %$a^e \bmod m$%. |
370 | */ |
371 | |
ef5f4810 |
372 | mp *mpmont_exp(mpmont *mm, mp *d, mp *a, mp *e) |
17ad212e |
373 | { |
ef5f4810 |
374 | d = mpmont_expr(mm, d, a, e); |
17ad212e |
375 | d = mpmont_reduce(mm, d, d); |
376 | return (d); |
d3409d5e |
377 | } |
378 | |
379 | /*----- Test rig ----------------------------------------------------------*/ |
380 | |
381 | #ifdef TEST_RIG |
382 | |
383 | static int tcreate(dstr *v) |
384 | { |
385 | mp *m = *(mp **)v[0].buf; |
386 | mp *mi = *(mp **)v[1].buf; |
387 | mp *r = *(mp **)v[2].buf; |
388 | mp *r2 = *(mp **)v[3].buf; |
389 | |
390 | mpmont mm; |
391 | int ok = 1; |
392 | |
393 | mpmont_create(&mm, m); |
394 | |
395 | if (mm.mi != mi->v[0]) { |
396 | fprintf(stderr, "\n*** bad mi: found %lu, expected %lu", |
397 | (unsigned long)mm.mi, (unsigned long)mi->v[0]); |
398 | fputs("\nm = ", stderr); mp_writefile(m, stderr, 10); |
399 | fputc('\n', stderr); |
400 | ok = 0; |
401 | } |
402 | |
403 | if (MP_CMP(mm.r, !=, r)) { |
404 | fputs("\n*** bad r", stderr); |
405 | fputs("\nm = ", stderr); mp_writefile(m, stderr, 10); |
406 | fputs("\nexpected ", stderr); mp_writefile(r, stderr, 10); |
17ad212e |
407 | fputs("\n found ", stderr); mp_writefile(mm.r, stderr, 10); |
d3409d5e |
408 | fputc('\n', stderr); |
409 | ok = 0; |
410 | } |
411 | |
412 | if (MP_CMP(mm.r2, !=, r2)) { |
413 | fputs("\n*** bad r2", stderr); |
414 | fputs("\nm = ", stderr); mp_writefile(m, stderr, 10); |
415 | fputs("\nexpected ", stderr); mp_writefile(r2, stderr, 10); |
17ad212e |
416 | fputs("\n found ", stderr); mp_writefile(mm.r2, stderr, 10); |
d3409d5e |
417 | fputc('\n', stderr); |
418 | ok = 0; |
419 | } |
420 | |
421 | MP_DROP(m); |
422 | MP_DROP(mi); |
423 | MP_DROP(r); |
424 | MP_DROP(r2); |
425 | mpmont_destroy(&mm); |
ef5f4810 |
426 | assert(mparena_count(MPARENA_GLOBAL) == 0); |
d3409d5e |
427 | return (ok); |
428 | } |
429 | |
430 | static int tmul(dstr *v) |
431 | { |
432 | mp *m = *(mp **)v[0].buf; |
433 | mp *a = *(mp **)v[1].buf; |
434 | mp *b = *(mp **)v[2].buf; |
435 | mp *r = *(mp **)v[3].buf; |
d3409d5e |
436 | int ok = 1; |
437 | |
438 | mpmont mm; |
439 | mpmont_create(&mm, m); |
440 | |
441 | { |
79a34029 |
442 | mp *qr = mp_mul(MP_NEW, a, b); |
443 | mp_div(0, &qr, qr, m); |
444 | |
445 | if (MP_CMP(qr, !=, r)) { |
446 | fputs("\n*** classical modmul failed", stderr); |
447 | fputs("\n m = ", stderr); mp_writefile(m, stderr, 10); |
448 | fputs("\n a = ", stderr); mp_writefile(a, stderr, 10); |
449 | fputs("\n b = ", stderr); mp_writefile(b, stderr, 10); |
450 | fputs("\n r = ", stderr); mp_writefile(r, stderr, 10); |
451 | fputs("\nqr = ", stderr); mp_writefile(qr, stderr, 10); |
452 | fputc('\n', stderr); |
453 | ok = 0; |
454 | } |
455 | |
456 | mp_drop(qr); |
457 | } |
458 | |
459 | { |
d3409d5e |
460 | mp *ar = mpmont_mul(&mm, MP_NEW, a, mm.r2); |
461 | mp *br = mpmont_mul(&mm, MP_NEW, b, mm.r2); |
79a34029 |
462 | mp *mr = mpmont_mul(&mm, MP_NEW, ar, br); |
d3409d5e |
463 | mr = mpmont_reduce(&mm, mr, mr); |
79a34029 |
464 | if (MP_CMP(mr, !=, r)) { |
465 | fputs("\n*** montgomery modmul failed", stderr); |
466 | fputs("\n m = ", stderr); mp_writefile(m, stderr, 10); |
467 | fputs("\n a = ", stderr); mp_writefile(a, stderr, 10); |
468 | fputs("\n b = ", stderr); mp_writefile(b, stderr, 10); |
469 | fputs("\n r = ", stderr); mp_writefile(r, stderr, 10); |
470 | fputs("\nmr = ", stderr); mp_writefile(mr, stderr, 10); |
471 | fputc('\n', stderr); |
472 | ok = 0; |
473 | } |
d3409d5e |
474 | MP_DROP(ar); MP_DROP(br); |
79a34029 |
475 | mp_drop(mr); |
d3409d5e |
476 | } |
477 | |
d3409d5e |
478 | |
479 | MP_DROP(m); |
480 | MP_DROP(a); |
481 | MP_DROP(b); |
482 | MP_DROP(r); |
d3409d5e |
483 | mpmont_destroy(&mm); |
ef5f4810 |
484 | assert(mparena_count(MPARENA_GLOBAL) == 0); |
d3409d5e |
485 | return ok; |
486 | } |
487 | |
488 | static int texp(dstr *v) |
489 | { |
490 | mp *m = *(mp **)v[0].buf; |
491 | mp *a = *(mp **)v[1].buf; |
492 | mp *b = *(mp **)v[2].buf; |
493 | mp *r = *(mp **)v[3].buf; |
494 | mp *mr; |
495 | int ok = 1; |
496 | |
497 | mpmont mm; |
498 | mpmont_create(&mm, m); |
499 | |
ef5f4810 |
500 | mr = mpmont_exp(&mm, MP_NEW, a, b); |
d3409d5e |
501 | |
502 | if (MP_CMP(mr, !=, r)) { |
503 | fputs("\n*** montgomery modexp failed", stderr); |
504 | fputs("\n m = ", stderr); mp_writefile(m, stderr, 10); |
505 | fputs("\n a = ", stderr); mp_writefile(a, stderr, 10); |
506 | fputs("\n e = ", stderr); mp_writefile(b, stderr, 10); |
507 | fputs("\n r = ", stderr); mp_writefile(r, stderr, 10); |
508 | fputs("\nmr = ", stderr); mp_writefile(mr, stderr, 10); |
509 | fputc('\n', stderr); |
510 | ok = 0; |
511 | } |
512 | |
513 | MP_DROP(m); |
514 | MP_DROP(a); |
515 | MP_DROP(b); |
516 | MP_DROP(r); |
517 | MP_DROP(mr); |
518 | mpmont_destroy(&mm); |
ef5f4810 |
519 | assert(mparena_count(MPARENA_GLOBAL) == 0); |
d3409d5e |
520 | return ok; |
521 | } |
522 | |
523 | |
524 | static test_chunk tests[] = { |
ef5f4810 |
525 | { "create", tcreate, { &type_mp, &type_mp, &type_mp, &type_mp, 0 } }, |
526 | { "mul", tmul, { &type_mp, &type_mp, &type_mp, &type_mp, 0 } }, |
527 | { "exp", texp, { &type_mp, &type_mp, &type_mp, &type_mp, 0 } }, |
d3409d5e |
528 | { 0, 0, { 0 } }, |
529 | }; |
530 | |
531 | int main(int argc, char *argv[]) |
532 | { |
533 | sub_init(); |
534 | test_run(argc, argv, tests, SRCDIR "/tests/mpmont"); |
535 | return (0); |
536 | } |
537 | |
538 | #endif |
539 | |
540 | /*----- That's all, folks -------------------------------------------------*/ |