d3409d5e |
1 | /* -*-c-*- |
2 | * |
a69a3efd |
3 | * $Id$ |
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 | * |
f4535c64 |
52 | * Returns: Zero on success, nonzero on error. |
d3409d5e |
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 | |
f4535c64 |
60 | int mpmont_create(mpmont *mm, mp *m) |
52e4b041 |
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; |
f4535c64 |
67 | return (0); |
52e4b041 |
68 | } |
69 | |
70 | #else |
71 | |
f4535c64 |
72 | int mpmont_create(mpmont *mm, mp *m) |
d3409d5e |
73 | { |
f5f35081 |
74 | size_t n = MP_LEN(m); |
d34decd2 |
75 | mp *r2 = mp_new(2 * n + 1, 0); |
f5f35081 |
76 | mp r; |
77 | |
d3409d5e |
78 | /* --- Take a copy of the modulus --- */ |
79 | |
f4535c64 |
80 | if (!MP_POSP(m) || !MP_ODDP(m)) |
81 | return (-1); |
d3409d5e |
82 | mm->m = MP_COPY(m); |
83 | |
f5f35081 |
84 | /* --- Determine %$R^2$% --- */ |
d3409d5e |
85 | |
f5f35081 |
86 | mm->n = n; |
87 | MPX_ZERO(r2->v, r2->vl - 1); |
88 | r2->vl[-1] = 1; |
d3409d5e |
89 | |
f5f35081 |
90 | /* --- Find the magic value @mi@ --- */ |
91 | |
92 | mp_build(&r, r2->v + n, r2->vl); |
b817bfc6 |
93 | mm->mi = mp_modinv(MP_NEW, m, &r); |
f5f35081 |
94 | mm->mi = mp_sub(mm->mi, &r, mm->mi); |
d3409d5e |
95 | |
96 | /* --- Discover the values %$R \bmod m$% and %$R^2 \bmod m$% --- */ |
97 | |
f5f35081 |
98 | mm->r2 = MP_NEW; |
99 | mp_div(0, &mm->r2, r2, m); |
100 | mm->r = mpmont_reduce(mm, MP_NEW, mm->r2); |
101 | MP_DROP(r2); |
f4535c64 |
102 | return (0); |
d3409d5e |
103 | } |
104 | |
52e4b041 |
105 | #endif |
106 | |
d3409d5e |
107 | /* --- @mpmont_destroy@ --- * |
108 | * |
109 | * Arguments: @mpmont *mm@ = pointer to a Montgomery reduction context |
110 | * |
111 | * Returns: --- |
112 | * |
113 | * Use: Disposes of a context when it's no longer of any use to |
114 | * anyone. |
115 | */ |
116 | |
117 | void mpmont_destroy(mpmont *mm) |
118 | { |
119 | MP_DROP(mm->m); |
120 | MP_DROP(mm->r); |
121 | MP_DROP(mm->r2); |
f5f35081 |
122 | MP_DROP(mm->mi); |
d3409d5e |
123 | } |
124 | |
125 | /* --- @mpmont_reduce@ --- * |
126 | * |
127 | * Arguments: @mpmont *mm@ = pointer to Montgomery reduction context |
128 | * @mp *d@ = destination |
ef5f4810 |
129 | * @mp *a@ = source, assumed positive |
d3409d5e |
130 | * |
131 | * Returns: Result, %$a R^{-1} \bmod m$%. |
132 | */ |
133 | |
52e4b041 |
134 | #ifdef MPMONT_DISABLE |
135 | |
ef5f4810 |
136 | mp *mpmont_reduce(mpmont *mm, mp *d, mp *a) |
52e4b041 |
137 | { |
138 | mp_div(0, &d, a, mm->m); |
139 | return (d); |
140 | } |
141 | |
142 | #else |
143 | |
ef5f4810 |
144 | mp *mpmont_reduce(mpmont *mm, mp *d, mp *a) |
d3409d5e |
145 | { |
f5f35081 |
146 | size_t n = mm->n; |
147 | |
148 | /* --- Check for serious Karatsuba reduction --- */ |
149 | |
52cdaca9 |
150 | if (n > MPK_THRESH * 3) { |
f5f35081 |
151 | mp al; |
152 | mpw *vl; |
153 | mp *u; |
154 | |
155 | if (MP_LEN(a) >= n) |
156 | vl = a->v + n; |
157 | else |
158 | vl = a->vl; |
159 | mp_build(&al, a->v, vl); |
160 | u = mp_mul(MP_NEW, &al, mm->mi); |
161 | if (MP_LEN(u) > n) |
162 | u->vl = u->v + n; |
163 | u = mp_mul(u, u, mm->m); |
164 | d = mp_add(d, a, u); |
165 | mp_drop(u); |
166 | } |
d3409d5e |
167 | |
f5f35081 |
168 | /* --- Otherwise do it the hard way --- */ |
d3409d5e |
169 | |
d3409d5e |
170 | else { |
f5f35081 |
171 | mpw *dv, *dvl; |
172 | mpw *mv, *mvl; |
173 | mpw mi; |
174 | size_t k = n; |
175 | |
176 | /* --- Initial conditioning of the arguments --- */ |
177 | |
d34decd2 |
178 | a = MP_COPY(a); |
179 | if (d) |
180 | MP_DROP(d); |
181 | d = a; |
182 | MP_DEST(d, 2 * n + 1, a->f); |
183 | |
f5f35081 |
184 | dv = d->v; dvl = d->vl; |
185 | mv = mm->m->v; mvl = mm->m->vl; |
d3409d5e |
186 | |
f5f35081 |
187 | /* --- Let's go to work --- */ |
d3409d5e |
188 | |
f5f35081 |
189 | mi = mm->mi->v[0]; |
190 | while (k--) { |
191 | mpw u = MPW(*dv * mi); |
192 | MPX_UMLAN(dv, dvl, mv, mvl, u); |
193 | dv++; |
194 | } |
d3409d5e |
195 | } |
196 | |
f5f35081 |
197 | /* --- Wrap everything up --- */ |
d3409d5e |
198 | |
f5f35081 |
199 | memmove(d->v, d->v + n, MPWS(MP_LEN(d) - n)); |
200 | d->vl -= n; |
032099d1 |
201 | if (MPX_UCMP(d->v, d->vl, >=, mm->m->v, mm->m->vl)) |
202 | mpx_usub(d->v, d->vl, d->v, d->vl, mm->m->v, mm->m->vl); |
203 | if (d->f & MP_NEG) { |
204 | mpx_usub(d->v, d->vl, mm->m->v, mm->m->vl, d->v, d->vl); |
205 | d->f &= ~MP_NEG; |
206 | } |
f5f35081 |
207 | MP_SHRINK(d); |
d3409d5e |
208 | return (d); |
209 | } |
210 | |
52e4b041 |
211 | #endif |
212 | |
d3409d5e |
213 | /* --- @mpmont_mul@ --- * |
214 | * |
215 | * Arguments: @mpmont *mm@ = pointer to Montgomery reduction context |
216 | * @mp *d@ = destination |
ef5f4810 |
217 | * @mp *a, *b@ = sources, assumed positive |
d3409d5e |
218 | * |
219 | * Returns: Result, %$a b R^{-1} \bmod m$%. |
220 | */ |
221 | |
52e4b041 |
222 | #ifdef MPMONT_DISABLE |
223 | |
ef5f4810 |
224 | mp *mpmont_mul(mpmont *mm, mp *d, mp *a, mp *b) |
52e4b041 |
225 | { |
226 | d = mp_mul(d, a, b); |
227 | mp_div(0, &d, d, mm->m); |
228 | return (d); |
229 | } |
230 | |
231 | #else |
232 | |
ef5f4810 |
233 | mp *mpmont_mul(mpmont *mm, mp *d, mp *a, mp *b) |
d3409d5e |
234 | { |
52cdaca9 |
235 | if (mm->n > MPK_THRESH * 3) { |
ef5f4810 |
236 | d = mp_mul(d, a, b); |
237 | d = mpmont_reduce(mm, d, d); |
238 | } else { |
239 | mpw *dv, *dvl; |
240 | mpw *av, *avl; |
241 | mpw *bv, *bvl; |
242 | mpw *mv, *mvl; |
243 | mpw y; |
244 | size_t n, i; |
f5f35081 |
245 | mpw mi; |
ef5f4810 |
246 | |
247 | /* --- Initial conditioning of the arguments --- */ |
248 | |
249 | if (MP_LEN(a) > MP_LEN(b)) { |
250 | mp *t = a; a = b; b = t; |
251 | } |
252 | n = MP_LEN(mm->m); |
d3409d5e |
253 | |
ef5f4810 |
254 | a = MP_COPY(a); |
255 | b = MP_COPY(b); |
d34decd2 |
256 | MP_DEST(d, 2 * n + 1, a->f | b->f | MP_UNDEF); |
ef5f4810 |
257 | dv = d->v; dvl = d->vl; |
258 | MPX_ZERO(dv, dvl); |
259 | av = a->v; avl = a->vl; |
260 | bv = b->v; bvl = b->vl; |
261 | mv = mm->m->v; mvl = mm->m->vl; |
262 | y = *bv; |
263 | |
264 | /* --- Montgomery multiplication phase --- */ |
265 | |
266 | i = 0; |
f5f35081 |
267 | mi = mm->mi->v[0]; |
ef5f4810 |
268 | while (i < n && av < avl) { |
269 | mpw x = *av++; |
f5f35081 |
270 | mpw u = MPW((*dv + x * y) * mi); |
ef5f4810 |
271 | MPX_UMLAN(dv, dvl, bv, bvl, x); |
272 | MPX_UMLAN(dv, dvl, mv, mvl, u); |
273 | dv++; |
274 | i++; |
275 | } |
d3409d5e |
276 | |
ef5f4810 |
277 | /* --- Simpler Montgomery reduction phase --- */ |
d3409d5e |
278 | |
ef5f4810 |
279 | while (i < n) { |
f5f35081 |
280 | mpw u = MPW(*dv * mi); |
ef5f4810 |
281 | MPX_UMLAN(dv, dvl, mv, mvl, u); |
282 | dv++; |
283 | i++; |
284 | } |
d3409d5e |
285 | |
ef5f4810 |
286 | /* --- Done --- */ |
d3409d5e |
287 | |
ef5f4810 |
288 | memmove(d->v, dv, MPWS(dvl - dv)); |
289 | d->vl -= dv - d->v; |
032099d1 |
290 | if (MPX_UCMP(d->v, d->vl, >=, mm->m->v, mm->m->vl)) |
291 | mpx_usub(d->v, d->vl, d->v, d->vl, mm->m->v, mm->m->vl); |
292 | if ((a->f ^ b->f) & MP_NEG) |
293 | mpx_usub(d->v, d->vl, mm->m->v, mm->m->vl, d->v, d->vl); |
ef5f4810 |
294 | MP_SHRINK(d); |
295 | d->f = (a->f | b->f) & MP_BURN; |
ef5f4810 |
296 | MP_DROP(a); |
297 | MP_DROP(b); |
d3409d5e |
298 | } |
299 | |
d3409d5e |
300 | return (d); |
301 | } |
302 | |
52e4b041 |
303 | #endif |
304 | |
d3409d5e |
305 | /*----- Test rig ----------------------------------------------------------*/ |
306 | |
307 | #ifdef TEST_RIG |
308 | |
309 | static int tcreate(dstr *v) |
310 | { |
311 | mp *m = *(mp **)v[0].buf; |
312 | mp *mi = *(mp **)v[1].buf; |
313 | mp *r = *(mp **)v[2].buf; |
314 | mp *r2 = *(mp **)v[3].buf; |
315 | |
316 | mpmont mm; |
317 | int ok = 1; |
318 | |
319 | mpmont_create(&mm, m); |
320 | |
f5f35081 |
321 | if (mm.mi->v[0] != mi->v[0]) { |
d3409d5e |
322 | fprintf(stderr, "\n*** bad mi: found %lu, expected %lu", |
f5f35081 |
323 | (unsigned long)mm.mi->v[0], (unsigned long)mi->v[0]); |
d3409d5e |
324 | fputs("\nm = ", stderr); mp_writefile(m, stderr, 10); |
325 | fputc('\n', stderr); |
326 | ok = 0; |
327 | } |
328 | |
032099d1 |
329 | if (!MP_EQ(mm.r, r)) { |
d3409d5e |
330 | fputs("\n*** bad r", stderr); |
331 | fputs("\nm = ", stderr); mp_writefile(m, stderr, 10); |
332 | fputs("\nexpected ", stderr); mp_writefile(r, stderr, 10); |
17ad212e |
333 | fputs("\n found ", stderr); mp_writefile(mm.r, stderr, 10); |
d3409d5e |
334 | fputc('\n', stderr); |
335 | ok = 0; |
336 | } |
337 | |
032099d1 |
338 | if (!MP_EQ(mm.r2, r2)) { |
d3409d5e |
339 | fputs("\n*** bad r2", stderr); |
340 | fputs("\nm = ", stderr); mp_writefile(m, stderr, 10); |
341 | fputs("\nexpected ", stderr); mp_writefile(r2, stderr, 10); |
17ad212e |
342 | fputs("\n found ", stderr); mp_writefile(mm.r2, stderr, 10); |
d3409d5e |
343 | fputc('\n', stderr); |
344 | ok = 0; |
345 | } |
346 | |
347 | MP_DROP(m); |
348 | MP_DROP(mi); |
349 | MP_DROP(r); |
350 | MP_DROP(r2); |
351 | mpmont_destroy(&mm); |
ef5f4810 |
352 | assert(mparena_count(MPARENA_GLOBAL) == 0); |
d3409d5e |
353 | return (ok); |
354 | } |
355 | |
356 | static int tmul(dstr *v) |
357 | { |
358 | mp *m = *(mp **)v[0].buf; |
359 | mp *a = *(mp **)v[1].buf; |
360 | mp *b = *(mp **)v[2].buf; |
361 | mp *r = *(mp **)v[3].buf; |
d3409d5e |
362 | int ok = 1; |
363 | |
364 | mpmont mm; |
365 | mpmont_create(&mm, m); |
366 | |
367 | { |
79a34029 |
368 | mp *qr = mp_mul(MP_NEW, a, b); |
369 | mp_div(0, &qr, qr, m); |
370 | |
032099d1 |
371 | if (!MP_EQ(qr, r)) { |
79a34029 |
372 | fputs("\n*** classical modmul failed", stderr); |
373 | fputs("\n m = ", stderr); mp_writefile(m, stderr, 10); |
374 | fputs("\n a = ", stderr); mp_writefile(a, stderr, 10); |
375 | fputs("\n b = ", stderr); mp_writefile(b, stderr, 10); |
376 | fputs("\n r = ", stderr); mp_writefile(r, stderr, 10); |
377 | fputs("\nqr = ", stderr); mp_writefile(qr, stderr, 10); |
378 | fputc('\n', stderr); |
379 | ok = 0; |
380 | } |
381 | |
382 | mp_drop(qr); |
383 | } |
384 | |
385 | { |
d3409d5e |
386 | mp *ar = mpmont_mul(&mm, MP_NEW, a, mm.r2); |
387 | mp *br = mpmont_mul(&mm, MP_NEW, b, mm.r2); |
79a34029 |
388 | mp *mr = mpmont_mul(&mm, MP_NEW, ar, br); |
d3409d5e |
389 | mr = mpmont_reduce(&mm, mr, mr); |
032099d1 |
390 | if (!MP_EQ(mr, r)) { |
79a34029 |
391 | fputs("\n*** montgomery modmul failed", stderr); |
392 | fputs("\n m = ", stderr); mp_writefile(m, stderr, 10); |
393 | fputs("\n a = ", stderr); mp_writefile(a, stderr, 10); |
394 | fputs("\n b = ", stderr); mp_writefile(b, stderr, 10); |
395 | fputs("\n r = ", stderr); mp_writefile(r, stderr, 10); |
396 | fputs("\nmr = ", stderr); mp_writefile(mr, stderr, 10); |
397 | fputc('\n', stderr); |
398 | ok = 0; |
399 | } |
d3409d5e |
400 | MP_DROP(ar); MP_DROP(br); |
79a34029 |
401 | mp_drop(mr); |
d3409d5e |
402 | } |
403 | |
d3409d5e |
404 | |
405 | MP_DROP(m); |
406 | MP_DROP(a); |
407 | MP_DROP(b); |
408 | MP_DROP(r); |
d3409d5e |
409 | mpmont_destroy(&mm); |
ef5f4810 |
410 | assert(mparena_count(MPARENA_GLOBAL) == 0); |
d3409d5e |
411 | return ok; |
412 | } |
413 | |
d3409d5e |
414 | static test_chunk tests[] = { |
ef5f4810 |
415 | { "create", tcreate, { &type_mp, &type_mp, &type_mp, &type_mp, 0 } }, |
416 | { "mul", tmul, { &type_mp, &type_mp, &type_mp, &type_mp, 0 } }, |
d3409d5e |
417 | { 0, 0, { 0 } }, |
418 | }; |
419 | |
420 | int main(int argc, char *argv[]) |
421 | { |
422 | sub_init(); |
423 | test_run(argc, argv, tests, SRCDIR "/tests/mpmont"); |
424 | return (0); |
425 | } |
426 | |
427 | #endif |
428 | |
429 | /*----- That's all, folks -------------------------------------------------*/ |