d3409d5e |
1 | /* -*-c-*- |
2 | * |
34e4f738 |
3 | * $Id: mpmont.c,v 1.17 2004/04/01 12:50:09 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 $ |
34e4f738 |
33 | * Revision 1.17 2004/04/01 12:50:09 mdw |
34 | * Add cyclic group abstraction, with test code. Separate off exponentation |
35 | * functions for better static linking. Fix a buttload of bugs on the way. |
36 | * Generally ensure that negative exponents do inversion correctly. Add |
37 | * table of standard prime-field subgroups. (Binary field subgroups are |
38 | * currently unimplemented but easy to add if anyone ever finds a good one.) |
39 | * |
97490e68 |
40 | * Revision 1.16 2002/01/13 13:40:31 mdw |
41 | * Avoid trashing arguments before we've used them. |
42 | * |
4640a0dd |
43 | * Revision 1.15 2001/06/16 13:00:20 mdw |
44 | * Use the generic exponentiation functions. |
45 | * |
b096ec7f |
46 | * Revision 1.14 2001/02/22 09:04:26 mdw |
47 | * Cosmetic fix. |
48 | * |
f1140c41 |
49 | * Revision 1.13 2001/02/03 12:00:29 mdw |
50 | * Now @mp_drop@ checks its argument is non-NULL before attempting to free |
51 | * it. Note that the macro version @MP_DROP@ doesn't do this. |
52 | * |
52cdaca9 |
53 | * Revision 1.12 2000/10/08 15:48:35 mdw |
54 | * Rename Karatsuba constants now that we have @gfx_kmul@ too. |
55 | * |
032099d1 |
56 | * Revision 1.11 2000/10/08 12:04:27 mdw |
57 | * (mpmont_reduce, mpmont_mul): Cope with negative numbers. |
58 | * |
c9d4c30b |
59 | * Revision 1.10 2000/07/29 17:05:43 mdw |
60 | * (mpmont_expr): Use sliding window exponentiation, with a drop-through |
61 | * for small exponents to use a simple left-to-right bitwise routine. This |
62 | * can reduce modexp times by up to a quarter. |
63 | * |
d34decd2 |
64 | * Revision 1.9 2000/06/17 11:45:09 mdw |
65 | * Major memory management overhaul. Added arena support. Use the secure |
66 | * arena for secret integers. Replace and improve the MP management macros |
67 | * (e.g., replace MP_MODIFY by MP_DEST). |
68 | * |
01f6ed1a |
69 | * Revision 1.8 1999/12/22 15:55:00 mdw |
70 | * Adjust Karatsuba parameters. |
71 | * |
f5f35081 |
72 | * Revision 1.7 1999/12/11 01:51:14 mdw |
73 | * Use a Karatsuba-based reduction for large moduli. |
74 | * |
ef5f4810 |
75 | * Revision 1.6 1999/12/10 23:18:39 mdw |
76 | * Change interface for suggested destinations. |
77 | * |
52e4b041 |
78 | * Revision 1.5 1999/11/22 13:58:40 mdw |
79 | * Add an option to disable Montgomery reduction, so that performance |
80 | * comparisons can be done. |
81 | * |
93feaa6e |
82 | * Revision 1.4 1999/11/21 12:27:06 mdw |
83 | * Remove a division from the Montgomery setup by calculating |
84 | * %$R^2 \bmod m$% first and then %$R \bmod m$% by Montgomery reduction of |
85 | * %$R^2$%. |
86 | * |
79a34029 |
87 | * Revision 1.3 1999/11/21 11:35:10 mdw |
88 | * Performance improvement: use @mp_sqr@ and @mpmont_reduce@ instead of |
89 | * @mpmont_mul@ for squaring in exponentiation. |
90 | * |
17ad212e |
91 | * Revision 1.2 1999/11/19 13:17:26 mdw |
92 | * Add extra interface to exponentiation which returns a Montgomerized |
93 | * result. |
94 | * |
d3409d5e |
95 | * Revision 1.1 1999/11/17 18:02:16 mdw |
96 | * New multiprecision integer arithmetic suite. |
97 | * |
98 | */ |
99 | |
100 | /*----- Header files ------------------------------------------------------*/ |
101 | |
102 | #include "mp.h" |
103 | #include "mpmont.h" |
104 | |
52e4b041 |
105 | /*----- Tweakables --------------------------------------------------------*/ |
106 | |
107 | /* --- @MPMONT_DISABLE@ --- * |
108 | * |
109 | * Replace all the clever Montgomery reduction with good old-fashioned long |
110 | * division. |
111 | */ |
112 | |
113 | /* #define MPMONT_DISABLE */ |
114 | |
4640a0dd |
115 | /*----- Reduction and multiplication --------------------------------------*/ |
d3409d5e |
116 | |
117 | /* --- @mpmont_create@ --- * |
118 | * |
119 | * Arguments: @mpmont *mm@ = pointer to Montgomery reduction context |
120 | * @mp *m@ = modulus to use |
121 | * |
122 | * Returns: --- |
123 | * |
124 | * Use: Initializes a Montgomery reduction context ready for use. |
ef5f4810 |
125 | * The argument @m@ must be a positive odd integer. |
d3409d5e |
126 | */ |
127 | |
52e4b041 |
128 | #ifdef MPMONT_DISABLE |
129 | |
130 | void mpmont_create(mpmont *mm, mp *m) |
131 | { |
132 | mp_shrink(m); |
133 | mm->m = MP_COPY(m); |
134 | mm->r = MP_ONE; |
135 | mm->r2 = MP_ONE; |
f5f35081 |
136 | mm->mi = MP_ONE; |
52e4b041 |
137 | } |
138 | |
139 | #else |
140 | |
d3409d5e |
141 | void mpmont_create(mpmont *mm, mp *m) |
142 | { |
f5f35081 |
143 | size_t n = MP_LEN(m); |
d34decd2 |
144 | mp *r2 = mp_new(2 * n + 1, 0); |
f5f35081 |
145 | mp r; |
146 | |
ef5f4810 |
147 | /* --- Validate the arguments --- */ |
148 | |
149 | assert(((void)"Montgomery modulus must be positive", |
150 | (m->f & MP_NEG) == 0)); |
151 | assert(((void)"Montgomery modulus must be odd", m->v[0] & 1)); |
152 | |
d3409d5e |
153 | /* --- Take a copy of the modulus --- */ |
154 | |
155 | mp_shrink(m); |
156 | mm->m = MP_COPY(m); |
157 | |
f5f35081 |
158 | /* --- Determine %$R^2$% --- */ |
d3409d5e |
159 | |
f5f35081 |
160 | mm->n = n; |
161 | MPX_ZERO(r2->v, r2->vl - 1); |
162 | r2->vl[-1] = 1; |
d3409d5e |
163 | |
f5f35081 |
164 | /* --- Find the magic value @mi@ --- */ |
165 | |
166 | mp_build(&r, r2->v + n, r2->vl); |
167 | mm->mi = MP_NEW; |
168 | mp_gcd(0, 0, &mm->mi, &r, m); |
169 | mm->mi = mp_sub(mm->mi, &r, mm->mi); |
d3409d5e |
170 | |
171 | /* --- Discover the values %$R \bmod m$% and %$R^2 \bmod m$% --- */ |
172 | |
f5f35081 |
173 | mm->r2 = MP_NEW; |
174 | mp_div(0, &mm->r2, r2, m); |
175 | mm->r = mpmont_reduce(mm, MP_NEW, mm->r2); |
176 | MP_DROP(r2); |
d3409d5e |
177 | } |
178 | |
52e4b041 |
179 | #endif |
180 | |
d3409d5e |
181 | /* --- @mpmont_destroy@ --- * |
182 | * |
183 | * Arguments: @mpmont *mm@ = pointer to a Montgomery reduction context |
184 | * |
185 | * Returns: --- |
186 | * |
187 | * Use: Disposes of a context when it's no longer of any use to |
188 | * anyone. |
189 | */ |
190 | |
191 | void mpmont_destroy(mpmont *mm) |
192 | { |
193 | MP_DROP(mm->m); |
194 | MP_DROP(mm->r); |
195 | MP_DROP(mm->r2); |
f5f35081 |
196 | MP_DROP(mm->mi); |
d3409d5e |
197 | } |
198 | |
199 | /* --- @mpmont_reduce@ --- * |
200 | * |
201 | * Arguments: @mpmont *mm@ = pointer to Montgomery reduction context |
202 | * @mp *d@ = destination |
ef5f4810 |
203 | * @mp *a@ = source, assumed positive |
d3409d5e |
204 | * |
205 | * Returns: Result, %$a R^{-1} \bmod m$%. |
206 | */ |
207 | |
52e4b041 |
208 | #ifdef MPMONT_DISABLE |
209 | |
ef5f4810 |
210 | mp *mpmont_reduce(mpmont *mm, mp *d, mp *a) |
52e4b041 |
211 | { |
212 | mp_div(0, &d, a, mm->m); |
213 | return (d); |
214 | } |
215 | |
216 | #else |
217 | |
ef5f4810 |
218 | mp *mpmont_reduce(mpmont *mm, mp *d, mp *a) |
d3409d5e |
219 | { |
f5f35081 |
220 | size_t n = mm->n; |
221 | |
222 | /* --- Check for serious Karatsuba reduction --- */ |
223 | |
52cdaca9 |
224 | if (n > MPK_THRESH * 3) { |
f5f35081 |
225 | mp al; |
226 | mpw *vl; |
227 | mp *u; |
228 | |
229 | if (MP_LEN(a) >= n) |
230 | vl = a->v + n; |
231 | else |
232 | vl = a->vl; |
233 | mp_build(&al, a->v, vl); |
234 | u = mp_mul(MP_NEW, &al, mm->mi); |
235 | if (MP_LEN(u) > n) |
236 | u->vl = u->v + n; |
237 | u = mp_mul(u, u, mm->m); |
238 | d = mp_add(d, a, u); |
239 | mp_drop(u); |
240 | } |
d3409d5e |
241 | |
f5f35081 |
242 | /* --- Otherwise do it the hard way --- */ |
d3409d5e |
243 | |
d3409d5e |
244 | else { |
f5f35081 |
245 | mpw *dv, *dvl; |
246 | mpw *mv, *mvl; |
247 | mpw mi; |
248 | size_t k = n; |
249 | |
250 | /* --- Initial conditioning of the arguments --- */ |
251 | |
d34decd2 |
252 | a = MP_COPY(a); |
253 | if (d) |
254 | MP_DROP(d); |
255 | d = a; |
256 | MP_DEST(d, 2 * n + 1, a->f); |
257 | |
f5f35081 |
258 | dv = d->v; dvl = d->vl; |
259 | mv = mm->m->v; mvl = mm->m->vl; |
d3409d5e |
260 | |
f5f35081 |
261 | /* --- Let's go to work --- */ |
d3409d5e |
262 | |
f5f35081 |
263 | mi = mm->mi->v[0]; |
264 | while (k--) { |
265 | mpw u = MPW(*dv * mi); |
266 | MPX_UMLAN(dv, dvl, mv, mvl, u); |
267 | dv++; |
268 | } |
d3409d5e |
269 | } |
270 | |
f5f35081 |
271 | /* --- Wrap everything up --- */ |
d3409d5e |
272 | |
f5f35081 |
273 | memmove(d->v, d->v + n, MPWS(MP_LEN(d) - n)); |
274 | d->vl -= n; |
032099d1 |
275 | if (MPX_UCMP(d->v, d->vl, >=, mm->m->v, mm->m->vl)) |
276 | mpx_usub(d->v, d->vl, d->v, d->vl, mm->m->v, mm->m->vl); |
277 | if (d->f & MP_NEG) { |
278 | mpx_usub(d->v, d->vl, mm->m->v, mm->m->vl, d->v, d->vl); |
279 | d->f &= ~MP_NEG; |
280 | } |
f5f35081 |
281 | MP_SHRINK(d); |
d3409d5e |
282 | return (d); |
283 | } |
284 | |
52e4b041 |
285 | #endif |
286 | |
d3409d5e |
287 | /* --- @mpmont_mul@ --- * |
288 | * |
289 | * Arguments: @mpmont *mm@ = pointer to Montgomery reduction context |
290 | * @mp *d@ = destination |
ef5f4810 |
291 | * @mp *a, *b@ = sources, assumed positive |
d3409d5e |
292 | * |
293 | * Returns: Result, %$a b R^{-1} \bmod m$%. |
294 | */ |
295 | |
52e4b041 |
296 | #ifdef MPMONT_DISABLE |
297 | |
ef5f4810 |
298 | mp *mpmont_mul(mpmont *mm, mp *d, mp *a, mp *b) |
52e4b041 |
299 | { |
300 | d = mp_mul(d, a, b); |
301 | mp_div(0, &d, d, mm->m); |
302 | return (d); |
303 | } |
304 | |
305 | #else |
306 | |
ef5f4810 |
307 | mp *mpmont_mul(mpmont *mm, mp *d, mp *a, mp *b) |
d3409d5e |
308 | { |
52cdaca9 |
309 | if (mm->n > MPK_THRESH * 3) { |
ef5f4810 |
310 | d = mp_mul(d, a, b); |
311 | d = mpmont_reduce(mm, d, d); |
312 | } else { |
313 | mpw *dv, *dvl; |
314 | mpw *av, *avl; |
315 | mpw *bv, *bvl; |
316 | mpw *mv, *mvl; |
317 | mpw y; |
318 | size_t n, i; |
f5f35081 |
319 | mpw mi; |
ef5f4810 |
320 | |
321 | /* --- Initial conditioning of the arguments --- */ |
322 | |
323 | if (MP_LEN(a) > MP_LEN(b)) { |
324 | mp *t = a; a = b; b = t; |
325 | } |
326 | n = MP_LEN(mm->m); |
d3409d5e |
327 | |
ef5f4810 |
328 | a = MP_COPY(a); |
329 | b = MP_COPY(b); |
d34decd2 |
330 | MP_DEST(d, 2 * n + 1, a->f | b->f | MP_UNDEF); |
ef5f4810 |
331 | dv = d->v; dvl = d->vl; |
332 | MPX_ZERO(dv, dvl); |
333 | av = a->v; avl = a->vl; |
334 | bv = b->v; bvl = b->vl; |
335 | mv = mm->m->v; mvl = mm->m->vl; |
336 | y = *bv; |
337 | |
338 | /* --- Montgomery multiplication phase --- */ |
339 | |
340 | i = 0; |
f5f35081 |
341 | mi = mm->mi->v[0]; |
ef5f4810 |
342 | while (i < n && av < avl) { |
343 | mpw x = *av++; |
f5f35081 |
344 | mpw u = MPW((*dv + x * y) * mi); |
ef5f4810 |
345 | MPX_UMLAN(dv, dvl, bv, bvl, x); |
346 | MPX_UMLAN(dv, dvl, mv, mvl, u); |
347 | dv++; |
348 | i++; |
349 | } |
d3409d5e |
350 | |
ef5f4810 |
351 | /* --- Simpler Montgomery reduction phase --- */ |
d3409d5e |
352 | |
ef5f4810 |
353 | while (i < n) { |
f5f35081 |
354 | mpw u = MPW(*dv * mi); |
ef5f4810 |
355 | MPX_UMLAN(dv, dvl, mv, mvl, u); |
356 | dv++; |
357 | i++; |
358 | } |
d3409d5e |
359 | |
ef5f4810 |
360 | /* --- Done --- */ |
d3409d5e |
361 | |
ef5f4810 |
362 | memmove(d->v, dv, MPWS(dvl - dv)); |
363 | d->vl -= dv - d->v; |
032099d1 |
364 | if (MPX_UCMP(d->v, d->vl, >=, mm->m->v, mm->m->vl)) |
365 | mpx_usub(d->v, d->vl, d->v, d->vl, mm->m->v, mm->m->vl); |
366 | if ((a->f ^ b->f) & MP_NEG) |
367 | mpx_usub(d->v, d->vl, mm->m->v, mm->m->vl, d->v, d->vl); |
ef5f4810 |
368 | MP_SHRINK(d); |
369 | d->f = (a->f | b->f) & MP_BURN; |
ef5f4810 |
370 | MP_DROP(a); |
371 | MP_DROP(b); |
d3409d5e |
372 | } |
373 | |
d3409d5e |
374 | return (d); |
375 | } |
376 | |
52e4b041 |
377 | #endif |
378 | |
d3409d5e |
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 | |
f5f35081 |
395 | if (mm.mi->v[0] != mi->v[0]) { |
d3409d5e |
396 | fprintf(stderr, "\n*** bad mi: found %lu, expected %lu", |
f5f35081 |
397 | (unsigned long)mm.mi->v[0], (unsigned long)mi->v[0]); |
d3409d5e |
398 | fputs("\nm = ", stderr); mp_writefile(m, stderr, 10); |
399 | fputc('\n', stderr); |
400 | ok = 0; |
401 | } |
402 | |
032099d1 |
403 | if (!MP_EQ(mm.r, r)) { |
d3409d5e |
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 | |
032099d1 |
412 | if (!MP_EQ(mm.r2, r2)) { |
d3409d5e |
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 | |
032099d1 |
445 | if (!MP_EQ(qr, r)) { |
79a34029 |
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); |
032099d1 |
464 | if (!MP_EQ(mr, r)) { |
79a34029 |
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 | |
d3409d5e |
488 | static test_chunk tests[] = { |
ef5f4810 |
489 | { "create", tcreate, { &type_mp, &type_mp, &type_mp, &type_mp, 0 } }, |
490 | { "mul", tmul, { &type_mp, &type_mp, &type_mp, &type_mp, 0 } }, |
d3409d5e |
491 | { 0, 0, { 0 } }, |
492 | }; |
493 | |
494 | int main(int argc, char *argv[]) |
495 | { |
496 | sub_init(); |
497 | test_run(argc, argv, tests, SRCDIR "/tests/mpmont"); |
498 | return (0); |
499 | } |
500 | |
501 | #endif |
502 | |
503 | /*----- That's all, folks -------------------------------------------------*/ |