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