projects / u / mdw / catacomb / blob
? search:
summary | shortlog | log | commit | commitdiff | tree
blame | history | raw | HEAD
General robustification.
[u/mdw/catacomb] / mpmont.c
1 /* -*-c-*-
2 *
3 * $Id: mpmont.c,v 1.18 2004/04/03 03:32:05 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 1.18 2004/04/03 03:32:05 mdw
34 * General robustification.
35 *
36 * Revision 1.17 2004/04/01 12:50:09 mdw
37 * Add cyclic group abstraction, with test code. Separate off exponentation
38 * functions for better static linking. Fix a buttload of bugs on the way.
39 * Generally ensure that negative exponents do inversion correctly. Add
40 * table of standard prime-field subgroups. (Binary field subgroups are
41 * currently unimplemented but easy to add if anyone ever finds a good one.)
42 *
43 * Revision 1.16 2002/01/13 13:40:31 mdw
44 * Avoid trashing arguments before we've used them.
45 *
46 * Revision 1.15 2001/06/16 13:00:20 mdw
47 * Use the generic exponentiation functions.
48 *
49 * Revision 1.14 2001/02/22 09:04:26 mdw
50 * Cosmetic fix.
51 *
52 * Revision 1.13 2001/02/03 12:00:29 mdw
53 * Now @mp_drop@ checks its argument is non-NULL before attempting to free
54 * it. Note that the macro version @MP_DROP@ doesn't do this.
55 *
56 * Revision 1.12 2000/10/08 15:48:35 mdw
57 * Rename Karatsuba constants now that we have @gfx_kmul@ too.
58 *
59 * Revision 1.11 2000/10/08 12:04:27 mdw
60 * (mpmont_reduce, mpmont_mul): Cope with negative numbers.
61 *
62 * Revision 1.10 2000/07/29 17:05:43 mdw
63 * (mpmont_expr): Use sliding window exponentiation, with a drop-through
64 * for small exponents to use a simple left-to-right bitwise routine. This
65 * can reduce modexp times by up to a quarter.
66 *
67 * Revision 1.9 2000/06/17 11:45:09 mdw
68 * Major memory management overhaul. Added arena support. Use the secure
69 * arena for secret integers. Replace and improve the MP management macros
70 * (e.g., replace MP_MODIFY by MP_DEST).
71 *
72 * Revision 1.8 1999/12/22 15:55:00 mdw
73 * Adjust Karatsuba parameters.
74 *
75 * Revision 1.7 1999/12/11 01:51:14 mdw
76 * Use a Karatsuba-based reduction for large moduli.
77 *
78 * Revision 1.6 1999/12/10 23:18:39 mdw
79 * Change interface for suggested destinations.
80 *
81 * Revision 1.5 1999/11/22 13:58:40 mdw
82 * Add an option to disable Montgomery reduction, so that performance
83 * comparisons can be done.
84 *
85 * Revision 1.4 1999/11/21 12:27:06 mdw
86 * Remove a division from the Montgomery setup by calculating
87 * %$R^2 \bmod m$% first and then %$R \bmod m$% by Montgomery reduction of
88 * %$R^2$%.
89 *
90 * Revision 1.3 1999/11/21 11:35:10 mdw
91 * Performance improvement: use @mp_sqr@ and @mpmont_reduce@ instead of
92 * @mpmont_mul@ for squaring in exponentiation.
93 *
94 * Revision 1.2 1999/11/19 13:17:26 mdw
95 * Add extra interface to exponentiation which returns a Montgomerized
96 * result.
97 *
98 * Revision 1.1 1999/11/17 18:02:16 mdw
99 * New multiprecision integer arithmetic suite.
100 *
101 */
102
103 /*----- Header files ------------------------------------------------------*/
104
105 #include "mp.h"
106 #include "mpmont.h"
107
108 /*----- Tweakables --------------------------------------------------------*/
109
110 /* --- @MPMONT_DISABLE@ --- *
111 *
112 * Replace all the clever Montgomery reduction with good old-fashioned long
113 * division.
114 */
115
116 /* #define MPMONT_DISABLE */
117
118 /*----- Reduction and multiplication --------------------------------------*/
119
120 /* --- @mpmont_create@ --- *
121 *
122 * Arguments: @mpmont *mm@ = pointer to Montgomery reduction context
123 * @mp *m@ = modulus to use
124 *
125 * Returns: ---
126 *
127 * Use: Initializes a Montgomery reduction context ready for use.
128 * The argument @m@ must be a positive odd integer.
129 */
130
131 #ifdef MPMONT_DISABLE
132
133 void mpmont_create(mpmont *mm, mp *m)
134 {
135 mp_shrink(m);
136 mm->m = MP_COPY(m);
137 mm->r = MP_ONE;
138 mm->r2 = MP_ONE;
139 mm->mi = MP_ONE;
140 }
141
142 #else
143
144 void mpmont_create(mpmont *mm, mp *m)
145 {
146 size_t n = MP_LEN(m);
147 mp *r2 = mp_new(2 * n + 1, 0);
148 mp r;
149
150 /* --- Take a copy of the modulus --- */
151
152 assert(MP_ISPOS(m) && MP_ISODD(m));
153 mm->m = MP_COPY(m);
154
155 /* --- Determine %$R^2$% --- */
156
157 mm->n = n;
158 MPX_ZERO(r2->v, r2->vl - 1);
159 r2->vl[-1] = 1;
160
161 /* --- Find the magic value @mi@ --- */
162
163 mp_build(&r, r2->v + n, r2->vl);
164 mm->mi = MP_NEW;
165 mp_gcd(0, 0, &mm->mi, &r, m);
166 mm->mi = mp_sub(mm->mi, &r, mm->mi);
167
168 /* --- Discover the values %$R \bmod m$% and %$R^2 \bmod m$% --- */
169
170 mm->r2 = MP_NEW;
171 mp_div(0, &mm->r2, r2, m);
172 mm->r = mpmont_reduce(mm, MP_NEW, mm->r2);
173 MP_DROP(r2);
174 }
175
176 #endif
177
178 /* --- @mpmont_destroy@ --- *
179 *
180 * Arguments: @mpmont *mm@ = pointer to a Montgomery reduction context
181 *
182 * Returns: ---
183 *
184 * Use: Disposes of a context when it's no longer of any use to
185 * anyone.
186 */
187
188 void mpmont_destroy(mpmont *mm)
189 {
190 MP_DROP(mm->m);
191 MP_DROP(mm->r);
192 MP_DROP(mm->r2);
193 MP_DROP(mm->mi);
194 }
195
196 /* --- @mpmont_reduce@ --- *
197 *
198 * Arguments: @mpmont *mm@ = pointer to Montgomery reduction context
199 * @mp *d@ = destination
200 * @mp *a@ = source, assumed positive
201 *
202 * Returns: Result, %$a R^{-1} \bmod m$%.
203 */
204
205 #ifdef MPMONT_DISABLE
206
207 mp *mpmont_reduce(mpmont *mm, mp *d, mp *a)
208 {
209 mp_div(0, &d, a, mm->m);
210 return (d);
211 }
212
213 #else
214
215 mp *mpmont_reduce(mpmont *mm, mp *d, mp *a)
216 {
217 size_t n = mm->n;
218
219 /* --- Check for serious Karatsuba reduction --- */
220
221 if (n > MPK_THRESH * 3) {
222 mp al;
223 mpw *vl;
224 mp *u;
225
226 if (MP_LEN(a) >= n)
227 vl = a->v + n;
228 else
229 vl = a->vl;
230 mp_build(&al, a->v, vl);
231 u = mp_mul(MP_NEW, &al, mm->mi);
232 if (MP_LEN(u) > n)
233 u->vl = u->v + n;
234 u = mp_mul(u, u, mm->m);
235 d = mp_add(d, a, u);
236 mp_drop(u);
237 }
238
239 /* --- Otherwise do it the hard way --- */
240
241 else {
242 mpw *dv, *dvl;
243 mpw *mv, *mvl;
244 mpw mi;
245 size_t k = n;
246
247 /* --- Initial conditioning of the arguments --- */
248
249 a = MP_COPY(a);
250 if (d)
251 MP_DROP(d);
252 d = a;
253 MP_DEST(d, 2 * n + 1, a->f);
254
255 dv = d->v; dvl = d->vl;
256 mv = mm->m->v; mvl = mm->m->vl;
257
258 /* --- Let's go to work --- */
259
260 mi = mm->mi->v[0];
261 while (k--) {
262 mpw u = MPW(*dv * mi);
263 MPX_UMLAN(dv, dvl, mv, mvl, u);
264 dv++;
265 }
266 }
267
268 /* --- Wrap everything up --- */
269
270 memmove(d->v, d->v + n, MPWS(MP_LEN(d) - n));
271 d->vl -= n;
272 if (MPX_UCMP(d->v, d->vl, >=, mm->m->v, mm->m->vl))
273 mpx_usub(d->v, d->vl, d->v, d->vl, mm->m->v, mm->m->vl);
274 if (d->f & MP_NEG) {
275 mpx_usub(d->v, d->vl, mm->m->v, mm->m->vl, d->v, d->vl);
276 d->f &= ~MP_NEG;
277 }
278 MP_SHRINK(d);
279 return (d);
280 }
281
282 #endif
283
284 /* --- @mpmont_mul@ --- *
285 *
286 * Arguments: @mpmont *mm@ = pointer to Montgomery reduction context
287 * @mp *d@ = destination
288 * @mp *a, *b@ = sources, assumed positive
289 *
290 * Returns: Result, %$a b R^{-1} \bmod m$%.
291 */
292
293 #ifdef MPMONT_DISABLE
294
295 mp *mpmont_mul(mpmont *mm, mp *d, mp *a, mp *b)
296 {
297 d = mp_mul(d, a, b);
298 mp_div(0, &d, d, mm->m);
299 return (d);
300 }
301
302 #else
303
304 mp *mpmont_mul(mpmont *mm, mp *d, mp *a, mp *b)
305 {
306 if (mm->n > MPK_THRESH * 3) {
307 d = mp_mul(d, a, b);
308 d = mpmont_reduce(mm, d, d);
309 } else {
310 mpw *dv, *dvl;
311 mpw *av, *avl;
312 mpw *bv, *bvl;
313 mpw *mv, *mvl;
314 mpw y;
315 size_t n, i;
316 mpw mi;
317
318 /* --- Initial conditioning of the arguments --- */
319
320 if (MP_LEN(a) > MP_LEN(b)) {
321 mp *t = a; a = b; b = t;
322 }
323 n = MP_LEN(mm->m);
324
325 a = MP_COPY(a);
326 b = MP_COPY(b);
327 MP_DEST(d, 2 * n + 1, a->f | b->f | MP_UNDEF);
328 dv = d->v; dvl = d->vl;
329 MPX_ZERO(dv, dvl);
330 av = a->v; avl = a->vl;
331 bv = b->v; bvl = b->vl;
332 mv = mm->m->v; mvl = mm->m->vl;
333 y = *bv;
334
335 /* --- Montgomery multiplication phase --- */
336
337 i = 0;
338 mi = mm->mi->v[0];
339 while (i < n && av < avl) {
340 mpw x = *av++;
341 mpw u = MPW((*dv + x * y) * mi);
342 MPX_UMLAN(dv, dvl, bv, bvl, x);
343 MPX_UMLAN(dv, dvl, mv, mvl, u);
344 dv++;
345 i++;
346 }
347
348 /* --- Simpler Montgomery reduction phase --- */
349
350 while (i < n) {
351 mpw u = MPW(*dv * mi);
352 MPX_UMLAN(dv, dvl, mv, mvl, u);
353 dv++;
354 i++;
355 }
356
357 /* --- Done --- */
358
359 memmove(d->v, dv, MPWS(dvl - dv));
360 d->vl -= dv - d->v;
361 if (MPX_UCMP(d->v, d->vl, >=, mm->m->v, mm->m->vl))
362 mpx_usub(d->v, d->vl, d->v, d->vl, mm->m->v, mm->m->vl);
363 if ((a->f ^ b->f) & MP_NEG)
364 mpx_usub(d->v, d->vl, mm->m->v, mm->m->vl, d->v, d->vl);
365 MP_SHRINK(d);
366 d->f = (a->f | b->f) & MP_BURN;
367 MP_DROP(a);
368 MP_DROP(b);
369 }
370
371 return (d);
372 }
373
374 #endif
375
376 /*----- Test rig ----------------------------------------------------------*/
377
378 #ifdef TEST_RIG
379
380 static int tcreate(dstr *v)
381 {
382 mp *m = *(mp **)v[0].buf;
383 mp *mi = *(mp **)v[1].buf;
384 mp *r = *(mp **)v[2].buf;
385 mp *r2 = *(mp **)v[3].buf;
386
387 mpmont mm;
388 int ok = 1;
389
390 mpmont_create(&mm, m);
391
392 if (mm.mi->v[0] != mi->v[0]) {
393 fprintf(stderr, "\n*** bad mi: found %lu, expected %lu",
394 (unsigned long)mm.mi->v[0], (unsigned long)mi->v[0]);
395 fputs("\nm = ", stderr); mp_writefile(m, stderr, 10);
396 fputc('\n', stderr);
397 ok = 0;
398 }
399
400 if (!MP_EQ(mm.r, r)) {
401 fputs("\n*** bad r", stderr);
402 fputs("\nm = ", stderr); mp_writefile(m, stderr, 10);
403 fputs("\nexpected ", stderr); mp_writefile(r, stderr, 10);
404 fputs("\n found ", stderr); mp_writefile(mm.r, stderr, 10);
405 fputc('\n', stderr);
406 ok = 0;
407 }
408
409 if (!MP_EQ(mm.r2, r2)) {
410 fputs("\n*** bad r2", stderr);
411 fputs("\nm = ", stderr); mp_writefile(m, stderr, 10);
412 fputs("\nexpected ", stderr); mp_writefile(r2, stderr, 10);
413 fputs("\n found ", stderr); mp_writefile(mm.r2, stderr, 10);
414 fputc('\n', stderr);
415 ok = 0;
416 }
417
418 MP_DROP(m);
419 MP_DROP(mi);
420 MP_DROP(r);
421 MP_DROP(r2);
422 mpmont_destroy(&mm);
423 assert(mparena_count(MPARENA_GLOBAL) == 0);
424 return (ok);
425 }
426
427 static int tmul(dstr *v)
428 {
429 mp *m = *(mp **)v[0].buf;
430 mp *a = *(mp **)v[1].buf;
431 mp *b = *(mp **)v[2].buf;
432 mp *r = *(mp **)v[3].buf;
433 int ok = 1;
434
435 mpmont mm;
436 mpmont_create(&mm, m);
437
438 {
439 mp *qr = mp_mul(MP_NEW, a, b);
440 mp_div(0, &qr, qr, m);
441
442 if (!MP_EQ(qr, r)) {
443 fputs("\n*** classical modmul failed", stderr);
444 fputs("\n m = ", stderr); mp_writefile(m, stderr, 10);
445 fputs("\n a = ", stderr); mp_writefile(a, stderr, 10);
446 fputs("\n b = ", stderr); mp_writefile(b, stderr, 10);
447 fputs("\n r = ", stderr); mp_writefile(r, stderr, 10);
448 fputs("\nqr = ", stderr); mp_writefile(qr, stderr, 10);
449 fputc('\n', stderr);
450 ok = 0;
451 }
452
453 mp_drop(qr);
454 }
455
456 {
457 mp *ar = mpmont_mul(&mm, MP_NEW, a, mm.r2);
458 mp *br = mpmont_mul(&mm, MP_NEW, b, mm.r2);
459 mp *mr = mpmont_mul(&mm, MP_NEW, ar, br);
460 mr = mpmont_reduce(&mm, mr, mr);
461 if (!MP_EQ(mr, r)) {
462 fputs("\n*** montgomery modmul failed", stderr);
463 fputs("\n m = ", stderr); mp_writefile(m, stderr, 10);
464 fputs("\n a = ", stderr); mp_writefile(a, stderr, 10);
465 fputs("\n b = ", stderr); mp_writefile(b, stderr, 10);
466 fputs("\n r = ", stderr); mp_writefile(r, stderr, 10);
467 fputs("\nmr = ", stderr); mp_writefile(mr, stderr, 10);
468 fputc('\n', stderr);
469 ok = 0;
470 }
471 MP_DROP(ar); MP_DROP(br);
472 mp_drop(mr);
473 }
474
475
476 MP_DROP(m);
477 MP_DROP(a);
478 MP_DROP(b);
479 MP_DROP(r);
480 mpmont_destroy(&mm);
481 assert(mparena_count(MPARENA_GLOBAL) == 0);
482 return ok;
483 }
484
485 static test_chunk tests[] = {
486 { "create", tcreate, { &type_mp, &type_mp, &type_mp, &type_mp, 0 } },
487 { "mul", tmul, { &type_mp, &type_mp, &type_mp, &type_mp, 0 } },
488 { 0, 0, { 0 } },
489 };
490
491 int main(int argc, char *argv[])
492 {
493 sub_init();
494 test_run(argc, argv, tests, SRCDIR "/tests/mpmont");
495 return (0);
496 }
497
498 #endif
499
500 /*----- That's all, folks -------------------------------------------------*/
Catacomb cryptographic library (downstream of http://git.distorted.org.uk/~mdw/catacomb/)