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Use the generic exponentiation functions.
[u/mdw/catacomb] / mpmont.c
1 /* -*-c-*-
2 *
3 * $Id: mpmont.c,v 1.15 2001/06/16 13:00:20 mdw Exp $
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 $
33 * Revision 1.15 2001/06/16 13:00:20 mdw
34 * Use the generic exponentiation functions.
35 *
36 * Revision 1.14 2001/02/22 09:04:26 mdw
37 * Cosmetic fix.
38 *
39 * Revision 1.13 2001/02/03 12:00:29 mdw
40 * Now @mp_drop@ checks its argument is non-NULL before attempting to free
41 * it. Note that the macro version @MP_DROP@ doesn't do this.
42 *
43 * Revision 1.12 2000/10/08 15:48:35 mdw
44 * Rename Karatsuba constants now that we have @gfx_kmul@ too.
45 *
46 * Revision 1.11 2000/10/08 12:04:27 mdw
47 * (mpmont_reduce, mpmont_mul): Cope with negative numbers.
48 *
49 * Revision 1.10 2000/07/29 17:05:43 mdw
50 * (mpmont_expr): Use sliding window exponentiation, with a drop-through
51 * for small exponents to use a simple left-to-right bitwise routine. This
52 * can reduce modexp times by up to a quarter.
53 *
54 * Revision 1.9 2000/06/17 11:45:09 mdw
55 * Major memory management overhaul. Added arena support. Use the secure
56 * arena for secret integers. Replace and improve the MP management macros
57 * (e.g., replace MP_MODIFY by MP_DEST).
58 *
59 * Revision 1.8 1999/12/22 15:55:00 mdw
60 * Adjust Karatsuba parameters.
61 *
62 * Revision 1.7 1999/12/11 01:51:14 mdw
63 * Use a Karatsuba-based reduction for large moduli.
64 *
65 * Revision 1.6 1999/12/10 23:18:39 mdw
66 * Change interface for suggested destinations.
67 *
68 * Revision 1.5 1999/11/22 13:58:40 mdw
69 * Add an option to disable Montgomery reduction, so that performance
70 * comparisons can be done.
71 *
72 * Revision 1.4 1999/11/21 12:27:06 mdw
73 * Remove a division from the Montgomery setup by calculating
74 * %$R^2 \bmod m$% first and then %$R \bmod m$% by Montgomery reduction of
75 * %$R^2$%.
76 *
77 * Revision 1.3 1999/11/21 11:35:10 mdw
78 * Performance improvement: use @mp_sqr@ and @mpmont_reduce@ instead of
79 * @mpmont_mul@ for squaring in exponentiation.
80 *
81 * Revision 1.2 1999/11/19 13:17:26 mdw
82 * Add extra interface to exponentiation which returns a Montgomerized
83 * result.
84 *
85 * Revision 1.1 1999/11/17 18:02:16 mdw
86 * New multiprecision integer arithmetic suite.
87 *
88 */
89
90 /*----- Header files ------------------------------------------------------*/
91
92 #include "mp.h"
93 #include "mpmont.h"
94 #include "mpmont-exp.h"
95
96 /*----- Tweakables --------------------------------------------------------*/
97
98 /* --- @MPMONT_DISABLE@ --- *
99 *
100 * Replace all the clever Montgomery reduction with good old-fashioned long
101 * division.
102 */
103
104 /* #define MPMONT_DISABLE */
105
106 /*----- Reduction and multiplication --------------------------------------*/
107
108 /* --- @mpmont_create@ --- *
109 *
110 * Arguments: @mpmont *mm@ = pointer to Montgomery reduction context
111 * @mp *m@ = modulus to use
112 *
113 * Returns: ---
114 *
115 * Use: Initializes a Montgomery reduction context ready for use.
116 * The argument @m@ must be a positive odd integer.
117 */
118
119 #ifdef MPMONT_DISABLE
120
121 void mpmont_create(mpmont *mm, mp *m)
122 {
123 mp_shrink(m);
124 mm->m = MP_COPY(m);
125 mm->r = MP_ONE;
126 mm->r2 = MP_ONE;
127 mm->mi = MP_ONE;
128 }
129
130 #else
131
132 void mpmont_create(mpmont *mm, mp *m)
133 {
134 size_t n = MP_LEN(m);
135 mp *r2 = mp_new(2 * n + 1, 0);
136 mp r;
137
138 /* --- Validate the arguments --- */
139
140 assert(((void)"Montgomery modulus must be positive",
141 (m->f & MP_NEG) == 0));
142 assert(((void)"Montgomery modulus must be odd", m->v[0] & 1));
143
144 /* --- Take a copy of the modulus --- */
145
146 mp_shrink(m);
147 mm->m = MP_COPY(m);
148
149 /* --- Determine %$R^2$% --- */
150
151 mm->n = n;
152 MPX_ZERO(r2->v, r2->vl - 1);
153 r2->vl[-1] = 1;
154
155 /* --- Find the magic value @mi@ --- */
156
157 mp_build(&r, r2->v + n, r2->vl);
158 mm->mi = MP_NEW;
159 mp_gcd(0, 0, &mm->mi, &r, m);
160 mm->mi = mp_sub(mm->mi, &r, mm->mi);
161
162 /* --- Discover the values %$R \bmod m$% and %$R^2 \bmod m$% --- */
163
164 mm->r2 = MP_NEW;
165 mp_div(0, &mm->r2, r2, m);
166 mm->r = mpmont_reduce(mm, MP_NEW, mm->r2);
167 MP_DROP(r2);
168 }
169
170 #endif
171
172 /* --- @mpmont_destroy@ --- *
173 *
174 * Arguments: @mpmont *mm@ = pointer to a Montgomery reduction context
175 *
176 * Returns: ---
177 *
178 * Use: Disposes of a context when it's no longer of any use to
179 * anyone.
180 */
181
182 void mpmont_destroy(mpmont *mm)
183 {
184 MP_DROP(mm->m);
185 MP_DROP(mm->r);
186 MP_DROP(mm->r2);
187 MP_DROP(mm->mi);
188 }
189
190 /* --- @mpmont_reduce@ --- *
191 *
192 * Arguments: @mpmont *mm@ = pointer to Montgomery reduction context
193 * @mp *d@ = destination
194 * @mp *a@ = source, assumed positive
195 *
196 * Returns: Result, %$a R^{-1} \bmod m$%.
197 */
198
199 #ifdef MPMONT_DISABLE
200
201 mp *mpmont_reduce(mpmont *mm, mp *d, mp *a)
202 {
203 mp_div(0, &d, a, mm->m);
204 return (d);
205 }
206
207 #else
208
209 mp *mpmont_reduce(mpmont *mm, mp *d, mp *a)
210 {
211 size_t n = mm->n;
212
213 /* --- Check for serious Karatsuba reduction --- */
214
215 if (n > MPK_THRESH * 3) {
216 mp al;
217 mpw *vl;
218 mp *u;
219
220 if (MP_LEN(a) >= n)
221 vl = a->v + n;
222 else
223 vl = a->vl;
224 mp_build(&al, a->v, vl);
225 u = mp_mul(MP_NEW, &al, mm->mi);
226 if (MP_LEN(u) > n)
227 u->vl = u->v + n;
228 u = mp_mul(u, u, mm->m);
229 d = mp_add(d, a, u);
230 mp_drop(u);
231 }
232
233 /* --- Otherwise do it the hard way --- */
234
235 else {
236 mpw *dv, *dvl;
237 mpw *mv, *mvl;
238 mpw mi;
239 size_t k = n;
240
241 /* --- Initial conditioning of the arguments --- */
242
243 a = MP_COPY(a);
244 if (d)
245 MP_DROP(d);
246 d = a;
247 MP_DEST(d, 2 * n + 1, a->f);
248
249 dv = d->v; dvl = d->vl;
250 mv = mm->m->v; mvl = mm->m->vl;
251
252 /* --- Let's go to work --- */
253
254 mi = mm->mi->v[0];
255 while (k--) {
256 mpw u = MPW(*dv * mi);
257 MPX_UMLAN(dv, dvl, mv, mvl, u);
258 dv++;
259 }
260 }
261
262 /* --- Wrap everything up --- */
263
264 memmove(d->v, d->v + n, MPWS(MP_LEN(d) - n));
265 d->vl -= n;
266 if (MPX_UCMP(d->v, d->vl, >=, mm->m->v, mm->m->vl))
267 mpx_usub(d->v, d->vl, d->v, d->vl, mm->m->v, mm->m->vl);
268 if (d->f & MP_NEG) {
269 mpx_usub(d->v, d->vl, mm->m->v, mm->m->vl, d->v, d->vl);
270 d->f &= ~MP_NEG;
271 }
272 MP_SHRINK(d);
273 return (d);
274 }
275
276 #endif
277
278 /* --- @mpmont_mul@ --- *
279 *
280 * Arguments: @mpmont *mm@ = pointer to Montgomery reduction context
281 * @mp *d@ = destination
282 * @mp *a, *b@ = sources, assumed positive
283 *
284 * Returns: Result, %$a b R^{-1} \bmod m$%.
285 */
286
287 #ifdef MPMONT_DISABLE
288
289 mp *mpmont_mul(mpmont *mm, mp *d, mp *a, mp *b)
290 {
291 d = mp_mul(d, a, b);
292 mp_div(0, &d, d, mm->m);
293 return (d);
294 }
295
296 #else
297
298 mp *mpmont_mul(mpmont *mm, mp *d, mp *a, mp *b)
299 {
300 if (mm->n > MPK_THRESH * 3) {
301 d = mp_mul(d, a, b);
302 d = mpmont_reduce(mm, d, d);
303 } else {
304 mpw *dv, *dvl;
305 mpw *av, *avl;
306 mpw *bv, *bvl;
307 mpw *mv, *mvl;
308 mpw y;
309 size_t n, i;
310 mpw mi;
311
312 /* --- Initial conditioning of the arguments --- */
313
314 if (MP_LEN(a) > MP_LEN(b)) {
315 mp *t = a; a = b; b = t;
316 }
317 n = MP_LEN(mm->m);
318
319 a = MP_COPY(a);
320 b = MP_COPY(b);
321 MP_DEST(d, 2 * n + 1, a->f | b->f | MP_UNDEF);
322 dv = d->v; dvl = d->vl;
323 MPX_ZERO(dv, dvl);
324 av = a->v; avl = a->vl;
325 bv = b->v; bvl = b->vl;
326 mv = mm->m->v; mvl = mm->m->vl;
327 y = *bv;
328
329 /* --- Montgomery multiplication phase --- */
330
331 i = 0;
332 mi = mm->mi->v[0];
333 while (i < n && av < avl) {
334 mpw x = *av++;
335 mpw u = MPW((*dv + x * y) * mi);
336 MPX_UMLAN(dv, dvl, bv, bvl, x);
337 MPX_UMLAN(dv, dvl, mv, mvl, u);
338 dv++;
339 i++;
340 }
341
342 /* --- Simpler Montgomery reduction phase --- */
343
344 while (i < n) {
345 mpw u = MPW(*dv * mi);
346 MPX_UMLAN(dv, dvl, mv, mvl, u);
347 dv++;
348 i++;
349 }
350
351 /* --- Done --- */
352
353 memmove(d->v, dv, MPWS(dvl - dv));
354 d->vl -= dv - d->v;
355 if (MPX_UCMP(d->v, d->vl, >=, mm->m->v, mm->m->vl))
356 mpx_usub(d->v, d->vl, d->v, d->vl, mm->m->v, mm->m->vl);
357 if ((a->f ^ b->f) & MP_NEG)
358 mpx_usub(d->v, d->vl, mm->m->v, mm->m->vl, d->v, d->vl);
359 MP_SHRINK(d);
360 d->f = (a->f | b->f) & MP_BURN;
361 MP_DROP(a);
362 MP_DROP(b);
363 }
364
365 return (d);
366 }
367
368 #endif
369
370 /*----- Exponentiation ----------------------------------------------------*/
371
372 /* --- @mpmont_expr@ --- *
373 *
374 * Arguments: @mpmont *mm@ = pointer to Montgomery reduction context
375 * @mp *d@ = fake destination
376 * @mp *a@ = base
377 * @mp *e@ = exponent
378 *
379 * Returns: Result, %$(a R^{-1})^e R \bmod m$%.
380 */
381
382 mp *mpmont_expr(mpmont *mm, mp *d, mp *a, mp *e)
383 {
384 mp *x = MP_COPY(mm->r);
385 mp *spare = (e->f & MP_BURN) ? MP_NEWSEC : MP_NEW;
386
387 MP_SHRINK(e);
388 if (MP_LEN(e) == 0)
389 ;
390 else if (MP_LEN(e) < EXP_THRESH)
391 EXP_SIMPLE(x, a, e);
392 else
393 EXP_WINDOW(x, a, e);
394 mp_drop(d);
395 mp_drop(spare);
396 return (x);
397 }
398
399 /* --- @mpmont_exp@ --- *
400 *
401 * Arguments: @mpmont *mm@ = pointer to Montgomery reduction context
402 * @mp *d@ = fake destination
403 * @mp *a@ = base
404 * @mp *e@ = exponent
405 *
406 * Returns: Result, %$a^e \bmod m$%.
407 */
408
409 mp *mpmont_exp(mpmont *mm, mp *d, mp *a, mp *e)
410 {
411 d = mpmont_mul(mm, d, a, mm->r2);
412 d = mpmont_expr(mm, d, d, e);
413 d = mpmont_reduce(mm, d, d);
414 return (d);
415 }
416
417 /*----- Test rig ----------------------------------------------------------*/
418
419 #ifdef TEST_RIG
420
421 static int tcreate(dstr *v)
422 {
423 mp *m = *(mp **)v[0].buf;
424 mp *mi = *(mp **)v[1].buf;
425 mp *r = *(mp **)v[2].buf;
426 mp *r2 = *(mp **)v[3].buf;
427
428 mpmont mm;
429 int ok = 1;
430
431 mpmont_create(&mm, m);
432
433 if (mm.mi->v[0] != mi->v[0]) {
434 fprintf(stderr, "\n*** bad mi: found %lu, expected %lu",
435 (unsigned long)mm.mi->v[0], (unsigned long)mi->v[0]);
436 fputs("\nm = ", stderr); mp_writefile(m, stderr, 10);
437 fputc('\n', stderr);
438 ok = 0;
439 }
440
441 if (!MP_EQ(mm.r, r)) {
442 fputs("\n*** bad r", stderr);
443 fputs("\nm = ", stderr); mp_writefile(m, stderr, 10);
444 fputs("\nexpected ", stderr); mp_writefile(r, stderr, 10);
445 fputs("\n found ", stderr); mp_writefile(mm.r, stderr, 10);
446 fputc('\n', stderr);
447 ok = 0;
448 }
449
450 if (!MP_EQ(mm.r2, r2)) {
451 fputs("\n*** bad r2", stderr);
452 fputs("\nm = ", stderr); mp_writefile(m, stderr, 10);
453 fputs("\nexpected ", stderr); mp_writefile(r2, stderr, 10);
454 fputs("\n found ", stderr); mp_writefile(mm.r2, stderr, 10);
455 fputc('\n', stderr);
456 ok = 0;
457 }
458
459 MP_DROP(m);
460 MP_DROP(mi);
461 MP_DROP(r);
462 MP_DROP(r2);
463 mpmont_destroy(&mm);
464 assert(mparena_count(MPARENA_GLOBAL) == 0);
465 return (ok);
466 }
467
468 static int tmul(dstr *v)
469 {
470 mp *m = *(mp **)v[0].buf;
471 mp *a = *(mp **)v[1].buf;
472 mp *b = *(mp **)v[2].buf;
473 mp *r = *(mp **)v[3].buf;
474 int ok = 1;
475
476 mpmont mm;
477 mpmont_create(&mm, m);
478
479 {
480 mp *qr = mp_mul(MP_NEW, a, b);
481 mp_div(0, &qr, qr, m);
482
483 if (!MP_EQ(qr, r)) {
484 fputs("\n*** classical modmul failed", stderr);
485 fputs("\n m = ", stderr); mp_writefile(m, stderr, 10);
486 fputs("\n a = ", stderr); mp_writefile(a, stderr, 10);
487 fputs("\n b = ", stderr); mp_writefile(b, stderr, 10);
488 fputs("\n r = ", stderr); mp_writefile(r, stderr, 10);
489 fputs("\nqr = ", stderr); mp_writefile(qr, stderr, 10);
490 fputc('\n', stderr);
491 ok = 0;
492 }
493
494 mp_drop(qr);
495 }
496
497 {
498 mp *ar = mpmont_mul(&mm, MP_NEW, a, mm.r2);
499 mp *br = mpmont_mul(&mm, MP_NEW, b, mm.r2);
500 mp *mr = mpmont_mul(&mm, MP_NEW, ar, br);
501 mr = mpmont_reduce(&mm, mr, mr);
502 if (!MP_EQ(mr, r)) {
503 fputs("\n*** montgomery modmul 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 b = ", 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 MP_DROP(ar); MP_DROP(br);
513 mp_drop(mr);
514 }
515
516
517 MP_DROP(m);
518 MP_DROP(a);
519 MP_DROP(b);
520 MP_DROP(r);
521 mpmont_destroy(&mm);
522 assert(mparena_count(MPARENA_GLOBAL) == 0);
523 return ok;
524 }
525
526 static int texp(dstr *v)
527 {
528 mp *m = *(mp **)v[0].buf;
529 mp *a = *(mp **)v[1].buf;
530 mp *b = *(mp **)v[2].buf;
531 mp *r = *(mp **)v[3].buf;
532 mp *mr;
533 int ok = 1;
534
535 mpmont mm;
536 mpmont_create(&mm, m);
537
538 mr = mpmont_exp(&mm, MP_NEW, a, b);
539
540 if (!MP_EQ(mr, r)) {
541 fputs("\n*** montgomery modexp failed", stderr);
542 fputs("\n m = ", stderr); mp_writefile(m, stderr, 10);
543 fputs("\n a = ", stderr); mp_writefile(a, stderr, 10);
544 fputs("\n e = ", stderr); mp_writefile(b, stderr, 10);
545 fputs("\n r = ", stderr); mp_writefile(r, stderr, 10);
546 fputs("\nmr = ", stderr); mp_writefile(mr, stderr, 10);
547 fputc('\n', stderr);
548 ok = 0;
549 }
550
551 MP_DROP(m);
552 MP_DROP(a);
553 MP_DROP(b);
554 MP_DROP(r);
555 MP_DROP(mr);
556 mpmont_destroy(&mm);
557 assert(mparena_count(MPARENA_GLOBAL) == 0);
558 return ok;
559 }
560
561
562 static test_chunk tests[] = {
563 { "create", tcreate, { &type_mp, &type_mp, &type_mp, &type_mp, 0 } },
564 { "mul", tmul, { &type_mp, &type_mp, &type_mp, &type_mp, 0 } },
565 { "exp", texp, { &type_mp, &type_mp, &type_mp, &type_mp, 0 } },
566 { 0, 0, { 0 } },
567 };
568
569 int main(int argc, char *argv[])
570 {
571 sub_init();
572 test_run(argc, argv, tests, SRCDIR "/tests/mpmont");
573 return (0);
574 }
575
576 #endif
577
578 /*----- That's all, folks -------------------------------------------------*/
Catacomb cryptographic library (downstream of http://git.distorted.org.uk/~mdw/catacomb/)