d3409d5e |
1 | /* -*-c-*- |
2 | * |
b096ec7f |
3 | * $Id: mpmont.c,v 1.14 2001/02/22 09:04:26 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 $ |
b096ec7f |
33 | * Revision 1.14 2001/02/22 09:04:26 mdw |
34 | * Cosmetic fix. |
35 | * |
f1140c41 |
36 | * Revision 1.13 2001/02/03 12:00:29 mdw |
37 | * Now @mp_drop@ checks its argument is non-NULL before attempting to free |
38 | * it. Note that the macro version @MP_DROP@ doesn't do this. |
39 | * |
52cdaca9 |
40 | * Revision 1.12 2000/10/08 15:48:35 mdw |
41 | * Rename Karatsuba constants now that we have @gfx_kmul@ too. |
42 | * |
032099d1 |
43 | * Revision 1.11 2000/10/08 12:04:27 mdw |
44 | * (mpmont_reduce, mpmont_mul): Cope with negative numbers. |
45 | * |
c9d4c30b |
46 | * Revision 1.10 2000/07/29 17:05:43 mdw |
47 | * (mpmont_expr): Use sliding window exponentiation, with a drop-through |
48 | * for small exponents to use a simple left-to-right bitwise routine. This |
49 | * can reduce modexp times by up to a quarter. |
50 | * |
d34decd2 |
51 | * Revision 1.9 2000/06/17 11:45:09 mdw |
52 | * Major memory management overhaul. Added arena support. Use the secure |
53 | * arena for secret integers. Replace and improve the MP management macros |
54 | * (e.g., replace MP_MODIFY by MP_DEST). |
55 | * |
01f6ed1a |
56 | * Revision 1.8 1999/12/22 15:55:00 mdw |
57 | * Adjust Karatsuba parameters. |
58 | * |
f5f35081 |
59 | * Revision 1.7 1999/12/11 01:51:14 mdw |
60 | * Use a Karatsuba-based reduction for large moduli. |
61 | * |
ef5f4810 |
62 | * Revision 1.6 1999/12/10 23:18:39 mdw |
63 | * Change interface for suggested destinations. |
64 | * |
52e4b041 |
65 | * Revision 1.5 1999/11/22 13:58:40 mdw |
66 | * Add an option to disable Montgomery reduction, so that performance |
67 | * comparisons can be done. |
68 | * |
93feaa6e |
69 | * Revision 1.4 1999/11/21 12:27:06 mdw |
70 | * Remove a division from the Montgomery setup by calculating |
71 | * %$R^2 \bmod m$% first and then %$R \bmod m$% by Montgomery reduction of |
72 | * %$R^2$%. |
73 | * |
79a34029 |
74 | * Revision 1.3 1999/11/21 11:35:10 mdw |
75 | * Performance improvement: use @mp_sqr@ and @mpmont_reduce@ instead of |
76 | * @mpmont_mul@ for squaring in exponentiation. |
77 | * |
17ad212e |
78 | * Revision 1.2 1999/11/19 13:17:26 mdw |
79 | * Add extra interface to exponentiation which returns a Montgomerized |
80 | * result. |
81 | * |
d3409d5e |
82 | * Revision 1.1 1999/11/17 18:02:16 mdw |
83 | * New multiprecision integer arithmetic suite. |
84 | * |
85 | */ |
86 | |
87 | /*----- Header files ------------------------------------------------------*/ |
88 | |
89 | #include "mp.h" |
90 | #include "mpmont.h" |
91 | |
52e4b041 |
92 | /*----- Tweakables --------------------------------------------------------*/ |
93 | |
94 | /* --- @MPMONT_DISABLE@ --- * |
95 | * |
96 | * Replace all the clever Montgomery reduction with good old-fashioned long |
97 | * division. |
98 | */ |
99 | |
100 | /* #define MPMONT_DISABLE */ |
101 | |
d3409d5e |
102 | /*----- Main code ---------------------------------------------------------*/ |
103 | |
104 | /* --- @mpmont_create@ --- * |
105 | * |
106 | * Arguments: @mpmont *mm@ = pointer to Montgomery reduction context |
107 | * @mp *m@ = modulus to use |
108 | * |
109 | * Returns: --- |
110 | * |
111 | * Use: Initializes a Montgomery reduction context ready for use. |
ef5f4810 |
112 | * The argument @m@ must be a positive odd integer. |
d3409d5e |
113 | */ |
114 | |
52e4b041 |
115 | #ifdef MPMONT_DISABLE |
116 | |
117 | void mpmont_create(mpmont *mm, mp *m) |
118 | { |
119 | mp_shrink(m); |
120 | mm->m = MP_COPY(m); |
121 | mm->r = MP_ONE; |
122 | mm->r2 = MP_ONE; |
f5f35081 |
123 | mm->mi = MP_ONE; |
52e4b041 |
124 | } |
125 | |
126 | #else |
127 | |
d3409d5e |
128 | void mpmont_create(mpmont *mm, mp *m) |
129 | { |
f5f35081 |
130 | size_t n = MP_LEN(m); |
d34decd2 |
131 | mp *r2 = mp_new(2 * n + 1, 0); |
f5f35081 |
132 | mp r; |
133 | |
ef5f4810 |
134 | /* --- Validate the arguments --- */ |
135 | |
136 | assert(((void)"Montgomery modulus must be positive", |
137 | (m->f & MP_NEG) == 0)); |
138 | assert(((void)"Montgomery modulus must be odd", m->v[0] & 1)); |
139 | |
d3409d5e |
140 | /* --- Take a copy of the modulus --- */ |
141 | |
142 | mp_shrink(m); |
143 | mm->m = MP_COPY(m); |
144 | |
f5f35081 |
145 | /* --- Determine %$R^2$% --- */ |
d3409d5e |
146 | |
f5f35081 |
147 | mm->n = n; |
148 | MPX_ZERO(r2->v, r2->vl - 1); |
149 | r2->vl[-1] = 1; |
d3409d5e |
150 | |
f5f35081 |
151 | /* --- Find the magic value @mi@ --- */ |
152 | |
153 | mp_build(&r, r2->v + n, r2->vl); |
154 | mm->mi = MP_NEW; |
155 | mp_gcd(0, 0, &mm->mi, &r, m); |
156 | mm->mi = mp_sub(mm->mi, &r, mm->mi); |
d3409d5e |
157 | |
158 | /* --- Discover the values %$R \bmod m$% and %$R^2 \bmod m$% --- */ |
159 | |
f5f35081 |
160 | mm->r2 = MP_NEW; |
161 | mp_div(0, &mm->r2, r2, m); |
162 | mm->r = mpmont_reduce(mm, MP_NEW, mm->r2); |
163 | MP_DROP(r2); |
d3409d5e |
164 | } |
165 | |
52e4b041 |
166 | #endif |
167 | |
d3409d5e |
168 | /* --- @mpmont_destroy@ --- * |
169 | * |
170 | * Arguments: @mpmont *mm@ = pointer to a Montgomery reduction context |
171 | * |
172 | * Returns: --- |
173 | * |
174 | * Use: Disposes of a context when it's no longer of any use to |
175 | * anyone. |
176 | */ |
177 | |
178 | void mpmont_destroy(mpmont *mm) |
179 | { |
180 | MP_DROP(mm->m); |
181 | MP_DROP(mm->r); |
182 | MP_DROP(mm->r2); |
f5f35081 |
183 | MP_DROP(mm->mi); |
d3409d5e |
184 | } |
185 | |
186 | /* --- @mpmont_reduce@ --- * |
187 | * |
188 | * Arguments: @mpmont *mm@ = pointer to Montgomery reduction context |
189 | * @mp *d@ = destination |
ef5f4810 |
190 | * @mp *a@ = source, assumed positive |
d3409d5e |
191 | * |
192 | * Returns: Result, %$a R^{-1} \bmod m$%. |
193 | */ |
194 | |
52e4b041 |
195 | #ifdef MPMONT_DISABLE |
196 | |
ef5f4810 |
197 | mp *mpmont_reduce(mpmont *mm, mp *d, mp *a) |
52e4b041 |
198 | { |
199 | mp_div(0, &d, a, mm->m); |
200 | return (d); |
201 | } |
202 | |
203 | #else |
204 | |
ef5f4810 |
205 | mp *mpmont_reduce(mpmont *mm, mp *d, mp *a) |
d3409d5e |
206 | { |
f5f35081 |
207 | size_t n = mm->n; |
208 | |
209 | /* --- Check for serious Karatsuba reduction --- */ |
210 | |
52cdaca9 |
211 | if (n > MPK_THRESH * 3) { |
f5f35081 |
212 | mp al; |
213 | mpw *vl; |
214 | mp *u; |
215 | |
216 | if (MP_LEN(a) >= n) |
217 | vl = a->v + n; |
218 | else |
219 | vl = a->vl; |
220 | mp_build(&al, a->v, vl); |
221 | u = mp_mul(MP_NEW, &al, mm->mi); |
222 | if (MP_LEN(u) > n) |
223 | u->vl = u->v + n; |
224 | u = mp_mul(u, u, mm->m); |
225 | d = mp_add(d, a, u); |
226 | mp_drop(u); |
227 | } |
d3409d5e |
228 | |
f5f35081 |
229 | /* --- Otherwise do it the hard way --- */ |
d3409d5e |
230 | |
d3409d5e |
231 | else { |
f5f35081 |
232 | mpw *dv, *dvl; |
233 | mpw *mv, *mvl; |
234 | mpw mi; |
235 | size_t k = n; |
236 | |
237 | /* --- Initial conditioning of the arguments --- */ |
238 | |
d34decd2 |
239 | a = MP_COPY(a); |
240 | if (d) |
241 | MP_DROP(d); |
242 | d = a; |
243 | MP_DEST(d, 2 * n + 1, a->f); |
244 | |
f5f35081 |
245 | dv = d->v; dvl = d->vl; |
246 | mv = mm->m->v; mvl = mm->m->vl; |
d3409d5e |
247 | |
f5f35081 |
248 | /* --- Let's go to work --- */ |
d3409d5e |
249 | |
f5f35081 |
250 | mi = mm->mi->v[0]; |
251 | while (k--) { |
252 | mpw u = MPW(*dv * mi); |
253 | MPX_UMLAN(dv, dvl, mv, mvl, u); |
254 | dv++; |
255 | } |
d3409d5e |
256 | } |
257 | |
f5f35081 |
258 | /* --- Wrap everything up --- */ |
d3409d5e |
259 | |
f5f35081 |
260 | memmove(d->v, d->v + n, MPWS(MP_LEN(d) - n)); |
261 | d->vl -= n; |
032099d1 |
262 | if (MPX_UCMP(d->v, d->vl, >=, mm->m->v, mm->m->vl)) |
263 | mpx_usub(d->v, d->vl, d->v, d->vl, mm->m->v, mm->m->vl); |
264 | if (d->f & MP_NEG) { |
265 | mpx_usub(d->v, d->vl, mm->m->v, mm->m->vl, d->v, d->vl); |
266 | d->f &= ~MP_NEG; |
267 | } |
f5f35081 |
268 | MP_SHRINK(d); |
d3409d5e |
269 | return (d); |
270 | } |
271 | |
52e4b041 |
272 | #endif |
273 | |
d3409d5e |
274 | /* --- @mpmont_mul@ --- * |
275 | * |
276 | * Arguments: @mpmont *mm@ = pointer to Montgomery reduction context |
277 | * @mp *d@ = destination |
ef5f4810 |
278 | * @mp *a, *b@ = sources, assumed positive |
d3409d5e |
279 | * |
280 | * Returns: Result, %$a b R^{-1} \bmod m$%. |
281 | */ |
282 | |
52e4b041 |
283 | #ifdef MPMONT_DISABLE |
284 | |
ef5f4810 |
285 | mp *mpmont_mul(mpmont *mm, mp *d, mp *a, mp *b) |
52e4b041 |
286 | { |
287 | d = mp_mul(d, a, b); |
288 | mp_div(0, &d, d, mm->m); |
289 | return (d); |
290 | } |
291 | |
292 | #else |
293 | |
ef5f4810 |
294 | mp *mpmont_mul(mpmont *mm, mp *d, mp *a, mp *b) |
d3409d5e |
295 | { |
52cdaca9 |
296 | if (mm->n > MPK_THRESH * 3) { |
ef5f4810 |
297 | d = mp_mul(d, a, b); |
298 | d = mpmont_reduce(mm, d, d); |
299 | } else { |
300 | mpw *dv, *dvl; |
301 | mpw *av, *avl; |
302 | mpw *bv, *bvl; |
303 | mpw *mv, *mvl; |
304 | mpw y; |
305 | size_t n, i; |
f5f35081 |
306 | mpw mi; |
ef5f4810 |
307 | |
308 | /* --- Initial conditioning of the arguments --- */ |
309 | |
310 | if (MP_LEN(a) > MP_LEN(b)) { |
311 | mp *t = a; a = b; b = t; |
312 | } |
313 | n = MP_LEN(mm->m); |
d3409d5e |
314 | |
ef5f4810 |
315 | a = MP_COPY(a); |
316 | b = MP_COPY(b); |
d34decd2 |
317 | MP_DEST(d, 2 * n + 1, a->f | b->f | MP_UNDEF); |
ef5f4810 |
318 | dv = d->v; dvl = d->vl; |
319 | MPX_ZERO(dv, dvl); |
320 | av = a->v; avl = a->vl; |
321 | bv = b->v; bvl = b->vl; |
322 | mv = mm->m->v; mvl = mm->m->vl; |
323 | y = *bv; |
324 | |
325 | /* --- Montgomery multiplication phase --- */ |
326 | |
327 | i = 0; |
f5f35081 |
328 | mi = mm->mi->v[0]; |
ef5f4810 |
329 | while (i < n && av < avl) { |
330 | mpw x = *av++; |
f5f35081 |
331 | mpw u = MPW((*dv + x * y) * mi); |
ef5f4810 |
332 | MPX_UMLAN(dv, dvl, bv, bvl, x); |
333 | MPX_UMLAN(dv, dvl, mv, mvl, u); |
334 | dv++; |
335 | i++; |
336 | } |
d3409d5e |
337 | |
ef5f4810 |
338 | /* --- Simpler Montgomery reduction phase --- */ |
d3409d5e |
339 | |
ef5f4810 |
340 | while (i < n) { |
f5f35081 |
341 | mpw u = MPW(*dv * mi); |
ef5f4810 |
342 | MPX_UMLAN(dv, dvl, mv, mvl, u); |
343 | dv++; |
344 | i++; |
345 | } |
d3409d5e |
346 | |
ef5f4810 |
347 | /* --- Done --- */ |
d3409d5e |
348 | |
ef5f4810 |
349 | memmove(d->v, dv, MPWS(dvl - dv)); |
350 | d->vl -= dv - d->v; |
032099d1 |
351 | if (MPX_UCMP(d->v, d->vl, >=, mm->m->v, mm->m->vl)) |
352 | mpx_usub(d->v, d->vl, d->v, d->vl, mm->m->v, mm->m->vl); |
353 | if ((a->f ^ b->f) & MP_NEG) |
354 | mpx_usub(d->v, d->vl, mm->m->v, mm->m->vl, d->v, d->vl); |
ef5f4810 |
355 | MP_SHRINK(d); |
356 | d->f = (a->f | b->f) & MP_BURN; |
ef5f4810 |
357 | MP_DROP(a); |
358 | MP_DROP(b); |
d3409d5e |
359 | } |
360 | |
d3409d5e |
361 | return (d); |
362 | } |
363 | |
52e4b041 |
364 | #endif |
365 | |
17ad212e |
366 | /* --- @mpmont_expr@ --- * |
d3409d5e |
367 | * |
368 | * Arguments: @mpmont *mm@ = pointer to Montgomery reduction context |
ef5f4810 |
369 | * @mp *d@ = fake destination |
370 | * @mp *a@ = base |
371 | * @mp *e@ = exponent |
d3409d5e |
372 | * |
17ad212e |
373 | * Returns: Result, %$a^e R \bmod m$%. |
d3409d5e |
374 | */ |
375 | |
c9d4c30b |
376 | #define WINSZ 5 |
377 | #define TABSZ (1 << (WINSZ - 1)) |
378 | |
379 | #define THRESH (((MPW_BITS / WINSZ) << 2) + 1) |
380 | |
381 | static mp *exp_simple(mpmont *mm, mp *d, mp *a, mp *e) |
d3409d5e |
382 | { |
383 | mpscan sc; |
c9d4c30b |
384 | mp *ar; |
ef5f4810 |
385 | mp *x = MP_COPY(mm->r); |
d34decd2 |
386 | mp *spare = (e->f & MP_BURN) ? MP_NEWSEC : MP_NEW; |
c9d4c30b |
387 | unsigned sq = 0; |
388 | |
389 | mp_rscan(&sc, e); |
390 | if (!MP_RSTEP(&sc)) |
391 | goto exit; |
392 | while (!MP_RBIT(&sc)) |
393 | MP_RSTEP(&sc); |
394 | |
395 | /* --- Do the main body of the work --- */ |
396 | |
397 | ar = mpmont_mul(mm, MP_NEW, a, mm->r2); |
398 | for (;;) { |
399 | sq++; |
400 | while (sq) { |
401 | mp *y; |
402 | y = mp_sqr(spare, x); |
403 | y = mpmont_reduce(mm, y, y); |
404 | spare = x; x = y; |
405 | sq--; |
406 | } |
407 | { mp *y = mpmont_mul(mm, spare, x, ar); spare = x; x = y; } |
408 | sq = 0; |
d3409d5e |
409 | for (;;) { |
c9d4c30b |
410 | if (!MP_RSTEP(&sc)) |
411 | goto done; |
412 | if (MP_RBIT(&sc)) |
d3409d5e |
413 | break; |
c9d4c30b |
414 | sq++; |
d3409d5e |
415 | } |
416 | } |
c9d4c30b |
417 | |
418 | /* --- Do a final round of squaring --- */ |
419 | |
420 | done: |
421 | while (sq) { |
422 | mp *y; |
423 | y = mp_sqr(spare, x); |
424 | y = mpmont_reduce(mm, y, y); |
425 | spare = x; x = y; |
426 | sq--; |
427 | } |
428 | |
429 | /* --- Done --- */ |
430 | |
d3409d5e |
431 | MP_DROP(ar); |
c9d4c30b |
432 | exit: |
17ad212e |
433 | if (spare != MP_NEW) |
434 | MP_DROP(spare); |
ef5f4810 |
435 | if (d != MP_NEW) |
436 | MP_DROP(d); |
437 | return (x); |
17ad212e |
438 | } |
439 | |
c9d4c30b |
440 | mp *mpmont_expr(mpmont *mm, mp *d, mp *a, mp *e) |
441 | { |
442 | mp **tab; |
443 | mp *ar, *a2; |
444 | mp *spare = (e->f & MP_BURN) ? MP_NEWSEC : MP_NEW; |
445 | mp *x = MP_COPY(mm->r); |
446 | unsigned i, sq = 0; |
447 | mpscan sc; |
448 | |
449 | /* --- Do we bother? --- */ |
450 | |
451 | MP_SHRINK(e); |
452 | if (MP_LEN(e) == 0) |
453 | goto exit; |
454 | if (MP_LEN(e) < THRESH) { |
455 | x->ref--; |
456 | return (exp_simple(mm, d, a, e)); |
457 | } |
458 | |
459 | /* --- Do the precomputation --- */ |
460 | |
461 | ar = mpmont_mul(mm, MP_NEW, a, mm->r2); |
462 | a2 = mp_sqr(MP_NEW, ar); |
463 | a2 = mpmont_reduce(mm, a2, a2); |
464 | tab = xmalloc(TABSZ * sizeof(mp *)); |
465 | tab[0] = ar; |
466 | for (i = 1; i < TABSZ; i++) |
467 | tab[i] = mpmont_mul(mm, MP_NEW, tab[i - 1], a2); |
468 | mp_drop(a2); |
469 | mp_rscan(&sc, e); |
470 | |
471 | /* --- Skip top-end zero bits --- * |
472 | * |
473 | * If the initial step worked, there must be a set bit somewhere, so keep |
474 | * stepping until I find it. |
475 | */ |
476 | |
477 | MP_RSTEP(&sc); |
b096ec7f |
478 | while (!MP_RBIT(&sc)) |
c9d4c30b |
479 | MP_RSTEP(&sc); |
c9d4c30b |
480 | |
481 | /* --- Now for the main work --- */ |
482 | |
483 | for (;;) { |
484 | unsigned l = 0; |
485 | unsigned z = 0; |
486 | |
487 | /* --- The next bit is set, so read a window index --- * |
488 | * |
489 | * Reset @i@ to zero and increment @sq@. Then, until either I read |
490 | * @WINSZ@ bits or I run out of bits, scan in a bit: if it's clear, bump |
491 | * the @z@ counter; if it's set, push a set bit into @i@, shift it over |
492 | * by @z@ bits, bump @sq@ by @z + 1@ and clear @z@. By the end of this |
493 | * palaver, @i@ is an index to the precomputed value in @tab@. |
494 | */ |
495 | |
496 | i = 0; |
497 | sq++; |
498 | for (;;) { |
499 | l++; |
500 | if (l >= WINSZ || !MP_RSTEP(&sc)) |
501 | break; |
502 | if (!MP_RBIT(&sc)) |
503 | z++; |
504 | else { |
505 | i = ((i << 1) | 1) << z; |
506 | sq += z + 1; |
507 | z = 0; |
508 | } |
509 | } |
510 | |
511 | /* --- Do the squaring --- * |
512 | * |
513 | * Remember that @sq@ carries over from the zero-skipping stuff below. |
514 | */ |
515 | |
516 | while (sq) { |
517 | mp *y; |
518 | y = mp_sqr(spare, x); |
519 | y = mpmont_reduce(mm, y, y); |
520 | spare = x; x = y; |
521 | sq--; |
522 | } |
523 | |
524 | /* --- Do the multiply --- */ |
525 | |
526 | { mp *y = mpmont_mul(mm, spare, x, tab[i]); spare = x; x = y; } |
527 | |
528 | /* --- Now grind along through the rest of the bits --- */ |
529 | |
530 | sq = z; |
531 | for (;;) { |
532 | if (!MP_RSTEP(&sc)) |
533 | goto done; |
534 | if (MP_RBIT(&sc)) |
535 | break; |
536 | sq++; |
537 | } |
538 | } |
539 | |
540 | /* --- Do a final round of squaring --- */ |
541 | |
542 | done: |
543 | while (sq) { |
544 | mp *y; |
545 | y = mp_sqr(spare, x); |
546 | y = mpmont_reduce(mm, y, y); |
547 | spare = x; x = y; |
548 | sq--; |
549 | } |
550 | |
551 | /* --- Done --- */ |
552 | |
553 | for (i = 0; i < TABSZ; i++) |
554 | mp_drop(tab[i]); |
555 | xfree(tab); |
556 | exit: |
f1140c41 |
557 | mp_drop(d); |
558 | mp_drop(spare); |
c9d4c30b |
559 | return (x); |
560 | } |
561 | |
17ad212e |
562 | /* --- @mpmont_exp@ --- * |
563 | * |
564 | * Arguments: @mpmont *mm@ = pointer to Montgomery reduction context |
ef5f4810 |
565 | * @mp *d@ = fake destination |
566 | * @mp *a@ = base |
567 | * @mp *e@ = exponent |
17ad212e |
568 | * |
569 | * Returns: Result, %$a^e \bmod m$%. |
570 | */ |
571 | |
ef5f4810 |
572 | mp *mpmont_exp(mpmont *mm, mp *d, mp *a, mp *e) |
17ad212e |
573 | { |
ef5f4810 |
574 | d = mpmont_expr(mm, d, a, e); |
17ad212e |
575 | d = mpmont_reduce(mm, d, d); |
576 | return (d); |
d3409d5e |
577 | } |
578 | |
579 | /*----- Test rig ----------------------------------------------------------*/ |
580 | |
581 | #ifdef TEST_RIG |
582 | |
583 | static int tcreate(dstr *v) |
584 | { |
585 | mp *m = *(mp **)v[0].buf; |
586 | mp *mi = *(mp **)v[1].buf; |
587 | mp *r = *(mp **)v[2].buf; |
588 | mp *r2 = *(mp **)v[3].buf; |
589 | |
590 | mpmont mm; |
591 | int ok = 1; |
592 | |
593 | mpmont_create(&mm, m); |
594 | |
f5f35081 |
595 | if (mm.mi->v[0] != mi->v[0]) { |
d3409d5e |
596 | fprintf(stderr, "\n*** bad mi: found %lu, expected %lu", |
f5f35081 |
597 | (unsigned long)mm.mi->v[0], (unsigned long)mi->v[0]); |
d3409d5e |
598 | fputs("\nm = ", stderr); mp_writefile(m, stderr, 10); |
599 | fputc('\n', stderr); |
600 | ok = 0; |
601 | } |
602 | |
032099d1 |
603 | if (!MP_EQ(mm.r, r)) { |
d3409d5e |
604 | fputs("\n*** bad r", stderr); |
605 | fputs("\nm = ", stderr); mp_writefile(m, stderr, 10); |
606 | fputs("\nexpected ", stderr); mp_writefile(r, stderr, 10); |
17ad212e |
607 | fputs("\n found ", stderr); mp_writefile(mm.r, stderr, 10); |
d3409d5e |
608 | fputc('\n', stderr); |
609 | ok = 0; |
610 | } |
611 | |
032099d1 |
612 | if (!MP_EQ(mm.r2, r2)) { |
d3409d5e |
613 | fputs("\n*** bad r2", stderr); |
614 | fputs("\nm = ", stderr); mp_writefile(m, stderr, 10); |
615 | fputs("\nexpected ", stderr); mp_writefile(r2, stderr, 10); |
17ad212e |
616 | fputs("\n found ", stderr); mp_writefile(mm.r2, stderr, 10); |
d3409d5e |
617 | fputc('\n', stderr); |
618 | ok = 0; |
619 | } |
620 | |
621 | MP_DROP(m); |
622 | MP_DROP(mi); |
623 | MP_DROP(r); |
624 | MP_DROP(r2); |
625 | mpmont_destroy(&mm); |
ef5f4810 |
626 | assert(mparena_count(MPARENA_GLOBAL) == 0); |
d3409d5e |
627 | return (ok); |
628 | } |
629 | |
630 | static int tmul(dstr *v) |
631 | { |
632 | mp *m = *(mp **)v[0].buf; |
633 | mp *a = *(mp **)v[1].buf; |
634 | mp *b = *(mp **)v[2].buf; |
635 | mp *r = *(mp **)v[3].buf; |
d3409d5e |
636 | int ok = 1; |
637 | |
638 | mpmont mm; |
639 | mpmont_create(&mm, m); |
640 | |
641 | { |
79a34029 |
642 | mp *qr = mp_mul(MP_NEW, a, b); |
643 | mp_div(0, &qr, qr, m); |
644 | |
032099d1 |
645 | if (!MP_EQ(qr, r)) { |
79a34029 |
646 | fputs("\n*** classical modmul failed", stderr); |
647 | fputs("\n m = ", stderr); mp_writefile(m, stderr, 10); |
648 | fputs("\n a = ", stderr); mp_writefile(a, stderr, 10); |
649 | fputs("\n b = ", stderr); mp_writefile(b, stderr, 10); |
650 | fputs("\n r = ", stderr); mp_writefile(r, stderr, 10); |
651 | fputs("\nqr = ", stderr); mp_writefile(qr, stderr, 10); |
652 | fputc('\n', stderr); |
653 | ok = 0; |
654 | } |
655 | |
656 | mp_drop(qr); |
657 | } |
658 | |
659 | { |
d3409d5e |
660 | mp *ar = mpmont_mul(&mm, MP_NEW, a, mm.r2); |
661 | mp *br = mpmont_mul(&mm, MP_NEW, b, mm.r2); |
79a34029 |
662 | mp *mr = mpmont_mul(&mm, MP_NEW, ar, br); |
d3409d5e |
663 | mr = mpmont_reduce(&mm, mr, mr); |
032099d1 |
664 | if (!MP_EQ(mr, r)) { |
79a34029 |
665 | fputs("\n*** montgomery modmul failed", stderr); |
666 | fputs("\n m = ", stderr); mp_writefile(m, stderr, 10); |
667 | fputs("\n a = ", stderr); mp_writefile(a, stderr, 10); |
668 | fputs("\n b = ", stderr); mp_writefile(b, stderr, 10); |
669 | fputs("\n r = ", stderr); mp_writefile(r, stderr, 10); |
670 | fputs("\nmr = ", stderr); mp_writefile(mr, stderr, 10); |
671 | fputc('\n', stderr); |
672 | ok = 0; |
673 | } |
d3409d5e |
674 | MP_DROP(ar); MP_DROP(br); |
79a34029 |
675 | mp_drop(mr); |
d3409d5e |
676 | } |
677 | |
d3409d5e |
678 | |
679 | MP_DROP(m); |
680 | MP_DROP(a); |
681 | MP_DROP(b); |
682 | MP_DROP(r); |
d3409d5e |
683 | mpmont_destroy(&mm); |
ef5f4810 |
684 | assert(mparena_count(MPARENA_GLOBAL) == 0); |
d3409d5e |
685 | return ok; |
686 | } |
687 | |
688 | static int texp(dstr *v) |
689 | { |
690 | mp *m = *(mp **)v[0].buf; |
691 | mp *a = *(mp **)v[1].buf; |
692 | mp *b = *(mp **)v[2].buf; |
693 | mp *r = *(mp **)v[3].buf; |
694 | mp *mr; |
695 | int ok = 1; |
696 | |
697 | mpmont mm; |
698 | mpmont_create(&mm, m); |
699 | |
ef5f4810 |
700 | mr = mpmont_exp(&mm, MP_NEW, a, b); |
d3409d5e |
701 | |
032099d1 |
702 | if (!MP_EQ(mr, r)) { |
d3409d5e |
703 | fputs("\n*** montgomery modexp failed", stderr); |
704 | fputs("\n m = ", stderr); mp_writefile(m, stderr, 10); |
705 | fputs("\n a = ", stderr); mp_writefile(a, stderr, 10); |
706 | fputs("\n e = ", stderr); mp_writefile(b, stderr, 10); |
707 | fputs("\n r = ", stderr); mp_writefile(r, stderr, 10); |
708 | fputs("\nmr = ", stderr); mp_writefile(mr, stderr, 10); |
709 | fputc('\n', stderr); |
710 | ok = 0; |
711 | } |
712 | |
713 | MP_DROP(m); |
714 | MP_DROP(a); |
715 | MP_DROP(b); |
716 | MP_DROP(r); |
717 | MP_DROP(mr); |
718 | mpmont_destroy(&mm); |
ef5f4810 |
719 | assert(mparena_count(MPARENA_GLOBAL) == 0); |
d3409d5e |
720 | return ok; |
721 | } |
722 | |
723 | |
724 | static test_chunk tests[] = { |
ef5f4810 |
725 | { "create", tcreate, { &type_mp, &type_mp, &type_mp, &type_mp, 0 } }, |
726 | { "mul", tmul, { &type_mp, &type_mp, &type_mp, &type_mp, 0 } }, |
727 | { "exp", texp, { &type_mp, &type_mp, &type_mp, &type_mp, 0 } }, |
d3409d5e |
728 | { 0, 0, { 0 } }, |
729 | }; |
730 | |
731 | int main(int argc, char *argv[]) |
732 | { |
733 | sub_init(); |
734 | test_run(argc, argv, tests, SRCDIR "/tests/mpmont"); |
735 | return (0); |
736 | } |
737 | |
738 | #endif |
739 | |
740 | /*----- That's all, folks -------------------------------------------------*/ |