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