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