d3409d5e |
1 | /* -*-c-*- |
2 | * |
b817bfc6 |
3 | * $Id: mpmont.c,v 1.19 2004/04/08 01:36:15 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 | |
d3409d5e |
30 | /*----- Header files ------------------------------------------------------*/ |
31 | |
32 | #include "mp.h" |
33 | #include "mpmont.h" |
34 | |
52e4b041 |
35 | /*----- Tweakables --------------------------------------------------------*/ |
36 | |
37 | /* --- @MPMONT_DISABLE@ --- * |
38 | * |
39 | * Replace all the clever Montgomery reduction with good old-fashioned long |
40 | * division. |
41 | */ |
42 | |
43 | /* #define MPMONT_DISABLE */ |
44 | |
4640a0dd |
45 | /*----- Reduction and multiplication --------------------------------------*/ |
d3409d5e |
46 | |
47 | /* --- @mpmont_create@ --- * |
48 | * |
49 | * Arguments: @mpmont *mm@ = pointer to Montgomery reduction context |
50 | * @mp *m@ = modulus to use |
51 | * |
52 | * Returns: --- |
53 | * |
54 | * Use: Initializes a Montgomery reduction context ready for use. |
ef5f4810 |
55 | * The argument @m@ must be a positive odd integer. |
d3409d5e |
56 | */ |
57 | |
52e4b041 |
58 | #ifdef MPMONT_DISABLE |
59 | |
60 | void mpmont_create(mpmont *mm, mp *m) |
61 | { |
62 | mp_shrink(m); |
63 | mm->m = MP_COPY(m); |
64 | mm->r = MP_ONE; |
65 | mm->r2 = MP_ONE; |
f5f35081 |
66 | mm->mi = MP_ONE; |
52e4b041 |
67 | } |
68 | |
69 | #else |
70 | |
d3409d5e |
71 | void mpmont_create(mpmont *mm, mp *m) |
72 | { |
f5f35081 |
73 | size_t n = MP_LEN(m); |
d34decd2 |
74 | mp *r2 = mp_new(2 * n + 1, 0); |
f5f35081 |
75 | mp r; |
76 | |
d3409d5e |
77 | /* --- Take a copy of the modulus --- */ |
78 | |
02d7884d |
79 | assert(MP_ISPOS(m) && MP_ISODD(m)); |
d3409d5e |
80 | mm->m = MP_COPY(m); |
81 | |
f5f35081 |
82 | /* --- Determine %$R^2$% --- */ |
d3409d5e |
83 | |
f5f35081 |
84 | mm->n = n; |
85 | MPX_ZERO(r2->v, r2->vl - 1); |
86 | r2->vl[-1] = 1; |
d3409d5e |
87 | |
f5f35081 |
88 | /* --- Find the magic value @mi@ --- */ |
89 | |
90 | mp_build(&r, r2->v + n, r2->vl); |
b817bfc6 |
91 | mm->mi = mp_modinv(MP_NEW, m, &r); |
f5f35081 |
92 | mm->mi = mp_sub(mm->mi, &r, mm->mi); |
d3409d5e |
93 | |
94 | /* --- Discover the values %$R \bmod m$% and %$R^2 \bmod m$% --- */ |
95 | |
f5f35081 |
96 | mm->r2 = MP_NEW; |
97 | mp_div(0, &mm->r2, r2, m); |
98 | mm->r = mpmont_reduce(mm, MP_NEW, mm->r2); |
99 | MP_DROP(r2); |
d3409d5e |
100 | } |
101 | |
52e4b041 |
102 | #endif |
103 | |
d3409d5e |
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); |
f5f35081 |
119 | MP_DROP(mm->mi); |
d3409d5e |
120 | } |
121 | |
122 | /* --- @mpmont_reduce@ --- * |
123 | * |
124 | * Arguments: @mpmont *mm@ = pointer to Montgomery reduction context |
125 | * @mp *d@ = destination |
ef5f4810 |
126 | * @mp *a@ = source, assumed positive |
d3409d5e |
127 | * |
128 | * Returns: Result, %$a R^{-1} \bmod m$%. |
129 | */ |
130 | |
52e4b041 |
131 | #ifdef MPMONT_DISABLE |
132 | |
ef5f4810 |
133 | mp *mpmont_reduce(mpmont *mm, mp *d, mp *a) |
52e4b041 |
134 | { |
135 | mp_div(0, &d, a, mm->m); |
136 | return (d); |
137 | } |
138 | |
139 | #else |
140 | |
ef5f4810 |
141 | mp *mpmont_reduce(mpmont *mm, mp *d, mp *a) |
d3409d5e |
142 | { |
f5f35081 |
143 | size_t n = mm->n; |
144 | |
145 | /* --- Check for serious Karatsuba reduction --- */ |
146 | |
52cdaca9 |
147 | if (n > MPK_THRESH * 3) { |
f5f35081 |
148 | mp al; |
149 | mpw *vl; |
150 | mp *u; |
151 | |
152 | if (MP_LEN(a) >= n) |
153 | vl = a->v + n; |
154 | else |
155 | vl = a->vl; |
156 | mp_build(&al, a->v, vl); |
157 | u = mp_mul(MP_NEW, &al, mm->mi); |
158 | if (MP_LEN(u) > n) |
159 | u->vl = u->v + n; |
160 | u = mp_mul(u, u, mm->m); |
161 | d = mp_add(d, a, u); |
162 | mp_drop(u); |
163 | } |
d3409d5e |
164 | |
f5f35081 |
165 | /* --- Otherwise do it the hard way --- */ |
d3409d5e |
166 | |
d3409d5e |
167 | else { |
f5f35081 |
168 | mpw *dv, *dvl; |
169 | mpw *mv, *mvl; |
170 | mpw mi; |
171 | size_t k = n; |
172 | |
173 | /* --- Initial conditioning of the arguments --- */ |
174 | |
d34decd2 |
175 | a = MP_COPY(a); |
176 | if (d) |
177 | MP_DROP(d); |
178 | d = a; |
179 | MP_DEST(d, 2 * n + 1, a->f); |
180 | |
f5f35081 |
181 | dv = d->v; dvl = d->vl; |
182 | mv = mm->m->v; mvl = mm->m->vl; |
d3409d5e |
183 | |
f5f35081 |
184 | /* --- Let's go to work --- */ |
d3409d5e |
185 | |
f5f35081 |
186 | mi = mm->mi->v[0]; |
187 | while (k--) { |
188 | mpw u = MPW(*dv * mi); |
189 | MPX_UMLAN(dv, dvl, mv, mvl, u); |
190 | dv++; |
191 | } |
d3409d5e |
192 | } |
193 | |
f5f35081 |
194 | /* --- Wrap everything up --- */ |
d3409d5e |
195 | |
f5f35081 |
196 | memmove(d->v, d->v + n, MPWS(MP_LEN(d) - n)); |
197 | d->vl -= n; |
032099d1 |
198 | if (MPX_UCMP(d->v, d->vl, >=, mm->m->v, mm->m->vl)) |
199 | mpx_usub(d->v, d->vl, d->v, d->vl, mm->m->v, mm->m->vl); |
200 | if (d->f & MP_NEG) { |
201 | mpx_usub(d->v, d->vl, mm->m->v, mm->m->vl, d->v, d->vl); |
202 | d->f &= ~MP_NEG; |
203 | } |
f5f35081 |
204 | MP_SHRINK(d); |
d3409d5e |
205 | return (d); |
206 | } |
207 | |
52e4b041 |
208 | #endif |
209 | |
d3409d5e |
210 | /* --- @mpmont_mul@ --- * |
211 | * |
212 | * Arguments: @mpmont *mm@ = pointer to Montgomery reduction context |
213 | * @mp *d@ = destination |
ef5f4810 |
214 | * @mp *a, *b@ = sources, assumed positive |
d3409d5e |
215 | * |
216 | * Returns: Result, %$a b R^{-1} \bmod m$%. |
217 | */ |
218 | |
52e4b041 |
219 | #ifdef MPMONT_DISABLE |
220 | |
ef5f4810 |
221 | mp *mpmont_mul(mpmont *mm, mp *d, mp *a, mp *b) |
52e4b041 |
222 | { |
223 | d = mp_mul(d, a, b); |
224 | mp_div(0, &d, d, mm->m); |
225 | return (d); |
226 | } |
227 | |
228 | #else |
229 | |
ef5f4810 |
230 | mp *mpmont_mul(mpmont *mm, mp *d, mp *a, mp *b) |
d3409d5e |
231 | { |
52cdaca9 |
232 | if (mm->n > MPK_THRESH * 3) { |
ef5f4810 |
233 | d = mp_mul(d, a, b); |
234 | d = mpmont_reduce(mm, d, d); |
235 | } else { |
236 | mpw *dv, *dvl; |
237 | mpw *av, *avl; |
238 | mpw *bv, *bvl; |
239 | mpw *mv, *mvl; |
240 | mpw y; |
241 | size_t n, i; |
f5f35081 |
242 | mpw mi; |
ef5f4810 |
243 | |
244 | /* --- Initial conditioning of the arguments --- */ |
245 | |
246 | if (MP_LEN(a) > MP_LEN(b)) { |
247 | mp *t = a; a = b; b = t; |
248 | } |
249 | n = MP_LEN(mm->m); |
d3409d5e |
250 | |
ef5f4810 |
251 | a = MP_COPY(a); |
252 | b = MP_COPY(b); |
d34decd2 |
253 | MP_DEST(d, 2 * n + 1, a->f | b->f | MP_UNDEF); |
ef5f4810 |
254 | dv = d->v; dvl = d->vl; |
255 | MPX_ZERO(dv, dvl); |
256 | av = a->v; avl = a->vl; |
257 | bv = b->v; bvl = b->vl; |
258 | mv = mm->m->v; mvl = mm->m->vl; |
259 | y = *bv; |
260 | |
261 | /* --- Montgomery multiplication phase --- */ |
262 | |
263 | i = 0; |
f5f35081 |
264 | mi = mm->mi->v[0]; |
ef5f4810 |
265 | while (i < n && av < avl) { |
266 | mpw x = *av++; |
f5f35081 |
267 | mpw u = MPW((*dv + x * y) * mi); |
ef5f4810 |
268 | MPX_UMLAN(dv, dvl, bv, bvl, x); |
269 | MPX_UMLAN(dv, dvl, mv, mvl, u); |
270 | dv++; |
271 | i++; |
272 | } |
d3409d5e |
273 | |
ef5f4810 |
274 | /* --- Simpler Montgomery reduction phase --- */ |
d3409d5e |
275 | |
ef5f4810 |
276 | while (i < n) { |
f5f35081 |
277 | mpw u = MPW(*dv * mi); |
ef5f4810 |
278 | MPX_UMLAN(dv, dvl, mv, mvl, u); |
279 | dv++; |
280 | i++; |
281 | } |
d3409d5e |
282 | |
ef5f4810 |
283 | /* --- Done --- */ |
d3409d5e |
284 | |
ef5f4810 |
285 | memmove(d->v, dv, MPWS(dvl - dv)); |
286 | d->vl -= dv - d->v; |
032099d1 |
287 | if (MPX_UCMP(d->v, d->vl, >=, mm->m->v, mm->m->vl)) |
288 | mpx_usub(d->v, d->vl, d->v, d->vl, mm->m->v, mm->m->vl); |
289 | if ((a->f ^ b->f) & MP_NEG) |
290 | mpx_usub(d->v, d->vl, mm->m->v, mm->m->vl, d->v, d->vl); |
ef5f4810 |
291 | MP_SHRINK(d); |
292 | d->f = (a->f | b->f) & MP_BURN; |
ef5f4810 |
293 | MP_DROP(a); |
294 | MP_DROP(b); |
d3409d5e |
295 | } |
296 | |
d3409d5e |
297 | return (d); |
298 | } |
299 | |
52e4b041 |
300 | #endif |
301 | |
d3409d5e |
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 | |
f5f35081 |
318 | if (mm.mi->v[0] != mi->v[0]) { |
d3409d5e |
319 | fprintf(stderr, "\n*** bad mi: found %lu, expected %lu", |
f5f35081 |
320 | (unsigned long)mm.mi->v[0], (unsigned long)mi->v[0]); |
d3409d5e |
321 | fputs("\nm = ", stderr); mp_writefile(m, stderr, 10); |
322 | fputc('\n', stderr); |
323 | ok = 0; |
324 | } |
325 | |
032099d1 |
326 | if (!MP_EQ(mm.r, r)) { |
d3409d5e |
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 | |
032099d1 |
335 | if (!MP_EQ(mm.r2, r2)) { |
d3409d5e |
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); |
ef5f4810 |
349 | assert(mparena_count(MPARENA_GLOBAL) == 0); |
d3409d5e |
350 | return (ok); |
351 | } |
352 | |
353 | static int tmul(dstr *v) |
354 | { |
355 | mp *m = *(mp **)v[0].buf; |
356 | mp *a = *(mp **)v[1].buf; |
357 | mp *b = *(mp **)v[2].buf; |
358 | mp *r = *(mp **)v[3].buf; |
d3409d5e |
359 | int ok = 1; |
360 | |
361 | mpmont mm; |
362 | mpmont_create(&mm, m); |
363 | |
364 | { |
79a34029 |
365 | mp *qr = mp_mul(MP_NEW, a, b); |
366 | mp_div(0, &qr, qr, m); |
367 | |
032099d1 |
368 | if (!MP_EQ(qr, r)) { |
79a34029 |
369 | fputs("\n*** classical modmul failed", stderr); |
370 | fputs("\n m = ", stderr); mp_writefile(m, stderr, 10); |
371 | fputs("\n a = ", stderr); mp_writefile(a, stderr, 10); |
372 | fputs("\n b = ", stderr); mp_writefile(b, stderr, 10); |
373 | fputs("\n r = ", stderr); mp_writefile(r, stderr, 10); |
374 | fputs("\nqr = ", stderr); mp_writefile(qr, stderr, 10); |
375 | fputc('\n', stderr); |
376 | ok = 0; |
377 | } |
378 | |
379 | mp_drop(qr); |
380 | } |
381 | |
382 | { |
d3409d5e |
383 | mp *ar = mpmont_mul(&mm, MP_NEW, a, mm.r2); |
384 | mp *br = mpmont_mul(&mm, MP_NEW, b, mm.r2); |
79a34029 |
385 | mp *mr = mpmont_mul(&mm, MP_NEW, ar, br); |
d3409d5e |
386 | mr = mpmont_reduce(&mm, mr, mr); |
032099d1 |
387 | if (!MP_EQ(mr, r)) { |
79a34029 |
388 | fputs("\n*** montgomery modmul failed", stderr); |
389 | fputs("\n m = ", stderr); mp_writefile(m, stderr, 10); |
390 | fputs("\n a = ", stderr); mp_writefile(a, stderr, 10); |
391 | fputs("\n b = ", stderr); mp_writefile(b, stderr, 10); |
392 | fputs("\n r = ", stderr); mp_writefile(r, stderr, 10); |
393 | fputs("\nmr = ", stderr); mp_writefile(mr, stderr, 10); |
394 | fputc('\n', stderr); |
395 | ok = 0; |
396 | } |
d3409d5e |
397 | MP_DROP(ar); MP_DROP(br); |
79a34029 |
398 | mp_drop(mr); |
d3409d5e |
399 | } |
400 | |
d3409d5e |
401 | |
402 | MP_DROP(m); |
403 | MP_DROP(a); |
404 | MP_DROP(b); |
405 | MP_DROP(r); |
d3409d5e |
406 | mpmont_destroy(&mm); |
ef5f4810 |
407 | assert(mparena_count(MPARENA_GLOBAL) == 0); |
d3409d5e |
408 | return ok; |
409 | } |
410 | |
d3409d5e |
411 | static test_chunk tests[] = { |
ef5f4810 |
412 | { "create", tcreate, { &type_mp, &type_mp, &type_mp, &type_mp, 0 } }, |
413 | { "mul", tmul, { &type_mp, &type_mp, &type_mp, &type_mp, 0 } }, |
d3409d5e |
414 | { 0, 0, { 0 } }, |
415 | }; |
416 | |
417 | int main(int argc, char *argv[]) |
418 | { |
419 | sub_init(); |
420 | test_run(argc, argv, tests, SRCDIR "/tests/mpmont"); |
421 | return (0); |
422 | } |
423 | |
424 | #endif |
425 | |
426 | /*----- That's all, folks -------------------------------------------------*/ |