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