d3409d5e |
1 | /* -*-c-*- |
2 | * |
d3409d5e |
3 | * Montgomery reduction |
4 | * |
5 | * (c) 1999 Straylight/Edgeware |
6 | */ |
7 | |
45c0fd36 |
8 | /*----- Licensing notice --------------------------------------------------* |
d3409d5e |
9 | * |
10 | * This file is part of Catacomb. |
11 | * |
12 | * Catacomb is free software; you can redistribute it and/or modify |
13 | * it under the terms of the GNU Library General Public License as |
14 | * published by the Free Software Foundation; either version 2 of the |
15 | * License, or (at your option) any later version. |
45c0fd36 |
16 | * |
d3409d5e |
17 | * Catacomb is distributed in the hope that it will be useful, |
18 | * but WITHOUT ANY WARRANTY; without even the implied warranty of |
19 | * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the |
20 | * GNU Library General Public License for more details. |
45c0fd36 |
21 | * |
d3409d5e |
22 | * You should have received a copy of the GNU Library General Public |
23 | * License along with Catacomb; if not, write to the Free |
24 | * Software Foundation, Inc., 59 Temple Place - Suite 330, Boston, |
25 | * MA 02111-1307, USA. |
26 | */ |
27 | |
d3409d5e |
28 | /*----- Header files ------------------------------------------------------*/ |
29 | |
30 | #include "mp.h" |
31 | #include "mpmont.h" |
32 | |
52e4b041 |
33 | /*----- Tweakables --------------------------------------------------------*/ |
34 | |
35 | /* --- @MPMONT_DISABLE@ --- * |
36 | * |
37 | * Replace all the clever Montgomery reduction with good old-fashioned long |
38 | * division. |
39 | */ |
40 | |
41 | /* #define MPMONT_DISABLE */ |
42 | |
4640a0dd |
43 | /*----- Reduction and multiplication --------------------------------------*/ |
d3409d5e |
44 | |
45 | /* --- @mpmont_create@ --- * |
46 | * |
47 | * Arguments: @mpmont *mm@ = pointer to Montgomery reduction context |
48 | * @mp *m@ = modulus to use |
49 | * |
f4535c64 |
50 | * Returns: Zero on success, nonzero on error. |
d3409d5e |
51 | * |
52 | * Use: Initializes a Montgomery reduction context ready for use. |
ef5f4810 |
53 | * The argument @m@ must be a positive odd integer. |
d3409d5e |
54 | */ |
55 | |
52e4b041 |
56 | #ifdef MPMONT_DISABLE |
57 | |
f4535c64 |
58 | int mpmont_create(mpmont *mm, mp *m) |
52e4b041 |
59 | { |
60 | mp_shrink(m); |
61 | mm->m = MP_COPY(m); |
62 | mm->r = MP_ONE; |
63 | mm->r2 = MP_ONE; |
f5f35081 |
64 | mm->mi = MP_ONE; |
f4535c64 |
65 | return (0); |
52e4b041 |
66 | } |
67 | |
68 | #else |
69 | |
f4535c64 |
70 | int mpmont_create(mpmont *mm, mp *m) |
d3409d5e |
71 | { |
f5f35081 |
72 | size_t n = MP_LEN(m); |
d34decd2 |
73 | mp *r2 = mp_new(2 * n + 1, 0); |
f5f35081 |
74 | mp r; |
75 | |
d3409d5e |
76 | /* --- Take a copy of the modulus --- */ |
77 | |
f4535c64 |
78 | if (!MP_POSP(m) || !MP_ODDP(m)) |
79 | return (-1); |
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); |
f4535c64 |
100 | return (0); |
d3409d5e |
101 | } |
102 | |
52e4b041 |
103 | #endif |
104 | |
d3409d5e |
105 | /* --- @mpmont_destroy@ --- * |
106 | * |
107 | * Arguments: @mpmont *mm@ = pointer to a Montgomery reduction context |
108 | * |
109 | * Returns: --- |
110 | * |
111 | * Use: Disposes of a context when it's no longer of any use to |
112 | * anyone. |
113 | */ |
114 | |
115 | void mpmont_destroy(mpmont *mm) |
116 | { |
117 | MP_DROP(mm->m); |
118 | MP_DROP(mm->r); |
119 | MP_DROP(mm->r2); |
f5f35081 |
120 | MP_DROP(mm->mi); |
d3409d5e |
121 | } |
122 | |
123 | /* --- @mpmont_reduce@ --- * |
124 | * |
125 | * Arguments: @mpmont *mm@ = pointer to Montgomery reduction context |
126 | * @mp *d@ = destination |
ef5f4810 |
127 | * @mp *a@ = source, assumed positive |
d3409d5e |
128 | * |
129 | * Returns: Result, %$a R^{-1} \bmod m$%. |
130 | */ |
131 | |
52e4b041 |
132 | #ifdef MPMONT_DISABLE |
133 | |
ef5f4810 |
134 | mp *mpmont_reduce(mpmont *mm, mp *d, mp *a) |
52e4b041 |
135 | { |
136 | mp_div(0, &d, a, mm->m); |
137 | return (d); |
138 | } |
139 | |
140 | #else |
141 | |
ef5f4810 |
142 | mp *mpmont_reduce(mpmont *mm, mp *d, mp *a) |
d3409d5e |
143 | { |
f5f35081 |
144 | size_t n = mm->n; |
145 | |
146 | /* --- Check for serious Karatsuba reduction --- */ |
147 | |
52cdaca9 |
148 | if (n > MPK_THRESH * 3) { |
f5f35081 |
149 | mp al; |
150 | mpw *vl; |
151 | mp *u; |
152 | |
153 | if (MP_LEN(a) >= n) |
154 | vl = a->v + n; |
155 | else |
156 | vl = a->vl; |
157 | mp_build(&al, a->v, vl); |
158 | u = mp_mul(MP_NEW, &al, mm->mi); |
159 | if (MP_LEN(u) > n) |
160 | u->vl = u->v + n; |
161 | u = mp_mul(u, u, mm->m); |
162 | d = mp_add(d, a, u); |
163 | mp_drop(u); |
164 | } |
d3409d5e |
165 | |
f5f35081 |
166 | /* --- Otherwise do it the hard way --- */ |
d3409d5e |
167 | |
d3409d5e |
168 | else { |
f5f35081 |
169 | mpw *dv, *dvl; |
170 | mpw *mv, *mvl; |
171 | mpw mi; |
172 | size_t k = n; |
173 | |
174 | /* --- Initial conditioning of the arguments --- */ |
175 | |
d34decd2 |
176 | a = MP_COPY(a); |
177 | if (d) |
178 | MP_DROP(d); |
179 | d = a; |
180 | MP_DEST(d, 2 * n + 1, a->f); |
181 | |
f5f35081 |
182 | dv = d->v; dvl = d->vl; |
183 | mv = mm->m->v; mvl = mm->m->vl; |
d3409d5e |
184 | |
f5f35081 |
185 | /* --- Let's go to work --- */ |
d3409d5e |
186 | |
f5f35081 |
187 | mi = mm->mi->v[0]; |
188 | while (k--) { |
189 | mpw u = MPW(*dv * mi); |
190 | MPX_UMLAN(dv, dvl, mv, mvl, u); |
191 | dv++; |
192 | } |
d3409d5e |
193 | } |
194 | |
f5f35081 |
195 | /* --- Wrap everything up --- */ |
d3409d5e |
196 | |
f5f35081 |
197 | memmove(d->v, d->v + n, MPWS(MP_LEN(d) - n)); |
198 | d->vl -= n; |
032099d1 |
199 | if (MPX_UCMP(d->v, d->vl, >=, mm->m->v, mm->m->vl)) |
200 | mpx_usub(d->v, d->vl, d->v, d->vl, mm->m->v, mm->m->vl); |
201 | if (d->f & MP_NEG) { |
202 | mpx_usub(d->v, d->vl, mm->m->v, mm->m->vl, d->v, d->vl); |
203 | d->f &= ~MP_NEG; |
204 | } |
f5f35081 |
205 | MP_SHRINK(d); |
d3409d5e |
206 | return (d); |
207 | } |
208 | |
52e4b041 |
209 | #endif |
210 | |
d3409d5e |
211 | /* --- @mpmont_mul@ --- * |
212 | * |
213 | * Arguments: @mpmont *mm@ = pointer to Montgomery reduction context |
214 | * @mp *d@ = destination |
ef5f4810 |
215 | * @mp *a, *b@ = sources, assumed positive |
d3409d5e |
216 | * |
217 | * Returns: Result, %$a b R^{-1} \bmod m$%. |
218 | */ |
219 | |
52e4b041 |
220 | #ifdef MPMONT_DISABLE |
221 | |
ef5f4810 |
222 | mp *mpmont_mul(mpmont *mm, mp *d, mp *a, mp *b) |
52e4b041 |
223 | { |
224 | d = mp_mul(d, a, b); |
225 | mp_div(0, &d, d, mm->m); |
226 | return (d); |
227 | } |
228 | |
229 | #else |
230 | |
ef5f4810 |
231 | mp *mpmont_mul(mpmont *mm, mp *d, mp *a, mp *b) |
d3409d5e |
232 | { |
52cdaca9 |
233 | if (mm->n > MPK_THRESH * 3) { |
ef5f4810 |
234 | d = mp_mul(d, a, b); |
235 | d = mpmont_reduce(mm, d, d); |
236 | } else { |
237 | mpw *dv, *dvl; |
238 | mpw *av, *avl; |
239 | mpw *bv, *bvl; |
240 | mpw *mv, *mvl; |
241 | mpw y; |
242 | size_t n, i; |
f5f35081 |
243 | mpw mi; |
ef5f4810 |
244 | |
245 | /* --- Initial conditioning of the arguments --- */ |
246 | |
247 | if (MP_LEN(a) > MP_LEN(b)) { |
248 | mp *t = a; a = b; b = t; |
249 | } |
250 | n = MP_LEN(mm->m); |
d3409d5e |
251 | |
ef5f4810 |
252 | a = MP_COPY(a); |
253 | b = MP_COPY(b); |
d34decd2 |
254 | MP_DEST(d, 2 * n + 1, a->f | b->f | MP_UNDEF); |
ef5f4810 |
255 | dv = d->v; dvl = d->vl; |
256 | MPX_ZERO(dv, dvl); |
257 | av = a->v; avl = a->vl; |
258 | bv = b->v; bvl = b->vl; |
259 | mv = mm->m->v; mvl = mm->m->vl; |
260 | y = *bv; |
261 | |
262 | /* --- Montgomery multiplication phase --- */ |
263 | |
264 | i = 0; |
f5f35081 |
265 | mi = mm->mi->v[0]; |
ef5f4810 |
266 | while (i < n && av < avl) { |
267 | mpw x = *av++; |
f5f35081 |
268 | mpw u = MPW((*dv + x * y) * mi); |
ef5f4810 |
269 | MPX_UMLAN(dv, dvl, bv, bvl, x); |
270 | MPX_UMLAN(dv, dvl, mv, mvl, u); |
271 | dv++; |
272 | i++; |
273 | } |
d3409d5e |
274 | |
ef5f4810 |
275 | /* --- Simpler Montgomery reduction phase --- */ |
d3409d5e |
276 | |
ef5f4810 |
277 | while (i < n) { |
f5f35081 |
278 | mpw u = MPW(*dv * mi); |
ef5f4810 |
279 | MPX_UMLAN(dv, dvl, mv, mvl, u); |
280 | dv++; |
281 | i++; |
282 | } |
d3409d5e |
283 | |
ef5f4810 |
284 | /* --- Done --- */ |
d3409d5e |
285 | |
ef5f4810 |
286 | memmove(d->v, dv, MPWS(dvl - dv)); |
287 | d->vl -= dv - d->v; |
032099d1 |
288 | if (MPX_UCMP(d->v, d->vl, >=, mm->m->v, mm->m->vl)) |
289 | mpx_usub(d->v, d->vl, d->v, d->vl, mm->m->v, mm->m->vl); |
290 | if ((a->f ^ b->f) & MP_NEG) |
291 | mpx_usub(d->v, d->vl, mm->m->v, mm->m->vl, d->v, d->vl); |
ef5f4810 |
292 | MP_SHRINK(d); |
293 | d->f = (a->f | b->f) & MP_BURN; |
ef5f4810 |
294 | MP_DROP(a); |
295 | MP_DROP(b); |
d3409d5e |
296 | } |
297 | |
d3409d5e |
298 | return (d); |
299 | } |
300 | |
52e4b041 |
301 | #endif |
302 | |
d3409d5e |
303 | /*----- Test rig ----------------------------------------------------------*/ |
304 | |
305 | #ifdef TEST_RIG |
306 | |
307 | static int tcreate(dstr *v) |
308 | { |
309 | mp *m = *(mp **)v[0].buf; |
310 | mp *mi = *(mp **)v[1].buf; |
311 | mp *r = *(mp **)v[2].buf; |
312 | mp *r2 = *(mp **)v[3].buf; |
313 | |
314 | mpmont mm; |
315 | int ok = 1; |
316 | |
317 | mpmont_create(&mm, m); |
318 | |
f5f35081 |
319 | if (mm.mi->v[0] != mi->v[0]) { |
d3409d5e |
320 | fprintf(stderr, "\n*** bad mi: found %lu, expected %lu", |
f5f35081 |
321 | (unsigned long)mm.mi->v[0], (unsigned long)mi->v[0]); |
d3409d5e |
322 | fputs("\nm = ", stderr); mp_writefile(m, stderr, 10); |
323 | fputc('\n', stderr); |
324 | ok = 0; |
325 | } |
326 | |
032099d1 |
327 | if (!MP_EQ(mm.r, r)) { |
d3409d5e |
328 | fputs("\n*** bad r", stderr); |
329 | fputs("\nm = ", stderr); mp_writefile(m, stderr, 10); |
330 | fputs("\nexpected ", stderr); mp_writefile(r, stderr, 10); |
45c0fd36 |
331 | fputs("\n found ", stderr); mp_writefile(mm.r, stderr, 10); |
d3409d5e |
332 | fputc('\n', stderr); |
333 | ok = 0; |
334 | } |
335 | |
032099d1 |
336 | if (!MP_EQ(mm.r2, r2)) { |
d3409d5e |
337 | fputs("\n*** bad r2", stderr); |
338 | fputs("\nm = ", stderr); mp_writefile(m, stderr, 10); |
339 | fputs("\nexpected ", stderr); mp_writefile(r2, stderr, 10); |
45c0fd36 |
340 | fputs("\n found ", stderr); mp_writefile(mm.r2, stderr, 10); |
d3409d5e |
341 | fputc('\n', stderr); |
342 | ok = 0; |
343 | } |
344 | |
345 | MP_DROP(m); |
346 | MP_DROP(mi); |
347 | MP_DROP(r); |
348 | MP_DROP(r2); |
349 | mpmont_destroy(&mm); |
ef5f4810 |
350 | assert(mparena_count(MPARENA_GLOBAL) == 0); |
d3409d5e |
351 | return (ok); |
352 | } |
353 | |
354 | static int tmul(dstr *v) |
355 | { |
356 | mp *m = *(mp **)v[0].buf; |
357 | mp *a = *(mp **)v[1].buf; |
358 | mp *b = *(mp **)v[2].buf; |
359 | mp *r = *(mp **)v[3].buf; |
d3409d5e |
360 | int ok = 1; |
361 | |
362 | mpmont mm; |
363 | mpmont_create(&mm, m); |
364 | |
365 | { |
79a34029 |
366 | mp *qr = mp_mul(MP_NEW, a, b); |
367 | mp_div(0, &qr, qr, m); |
368 | |
032099d1 |
369 | if (!MP_EQ(qr, r)) { |
79a34029 |
370 | fputs("\n*** classical modmul failed", stderr); |
371 | fputs("\n m = ", stderr); mp_writefile(m, stderr, 10); |
372 | fputs("\n a = ", stderr); mp_writefile(a, stderr, 10); |
373 | fputs("\n b = ", stderr); mp_writefile(b, stderr, 10); |
374 | fputs("\n r = ", stderr); mp_writefile(r, stderr, 10); |
375 | fputs("\nqr = ", stderr); mp_writefile(qr, stderr, 10); |
376 | fputc('\n', stderr); |
377 | ok = 0; |
378 | } |
379 | |
380 | mp_drop(qr); |
381 | } |
382 | |
383 | { |
d3409d5e |
384 | mp *ar = mpmont_mul(&mm, MP_NEW, a, mm.r2); |
385 | mp *br = mpmont_mul(&mm, MP_NEW, b, mm.r2); |
79a34029 |
386 | mp *mr = mpmont_mul(&mm, MP_NEW, ar, br); |
d3409d5e |
387 | mr = mpmont_reduce(&mm, mr, mr); |
032099d1 |
388 | if (!MP_EQ(mr, r)) { |
79a34029 |
389 | fputs("\n*** montgomery modmul failed", stderr); |
390 | fputs("\n m = ", stderr); mp_writefile(m, stderr, 10); |
391 | fputs("\n a = ", stderr); mp_writefile(a, stderr, 10); |
392 | fputs("\n b = ", stderr); mp_writefile(b, stderr, 10); |
393 | fputs("\n r = ", stderr); mp_writefile(r, stderr, 10); |
394 | fputs("\nmr = ", stderr); mp_writefile(mr, stderr, 10); |
395 | fputc('\n', stderr); |
396 | ok = 0; |
397 | } |
d3409d5e |
398 | MP_DROP(ar); MP_DROP(br); |
79a34029 |
399 | mp_drop(mr); |
d3409d5e |
400 | } |
401 | |
d3409d5e |
402 | |
403 | MP_DROP(m); |
404 | MP_DROP(a); |
405 | MP_DROP(b); |
406 | MP_DROP(r); |
d3409d5e |
407 | mpmont_destroy(&mm); |
ef5f4810 |
408 | assert(mparena_count(MPARENA_GLOBAL) == 0); |
d3409d5e |
409 | return ok; |
410 | } |
411 | |
d3409d5e |
412 | static test_chunk tests[] = { |
ef5f4810 |
413 | { "create", tcreate, { &type_mp, &type_mp, &type_mp, &type_mp, 0 } }, |
414 | { "mul", tmul, { &type_mp, &type_mp, &type_mp, &type_mp, 0 } }, |
d3409d5e |
415 | { 0, 0, { 0 } }, |
416 | }; |
417 | |
418 | int main(int argc, char *argv[]) |
419 | { |
420 | sub_init(); |
0f00dc4c |
421 | test_run(argc, argv, tests, SRCDIR "/t/mpmont"); |
d3409d5e |
422 | return (0); |
423 | } |
424 | |
425 | #endif |
426 | |
427 | /*----- That's all, folks -------------------------------------------------*/ |