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