Commit | Line | Data |
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d3409d5e | 1 | /* -*-c-*- |
d3409d5e | 2 | * |
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 | ||
0e70bd46 MW |
43 | /*----- Low-level implementation ------------------------------------------*/ |
44 | ||
45 | #ifndef MPMONT_DISABLE | |
46 | ||
47 | /* --- @redccore@ --- * | |
48 | * | |
49 | * Arguments: @mpw *dv, *dvl@ = base and limit of source/destination | |
50 | * @const mpw *mv@ = base of modulus %$m$% | |
51 | * @size_t n@ = length of modulus | |
52 | * @const mpw *mi@ = base of REDC coefficient %$m'$% | |
53 | * | |
54 | * Returns: --- | |
55 | * | |
56 | * Use: Let %$a$% be the input operand. Store in %$d$% the value | |
57 | * %$a + (m' a \bmod R) m$%. The destination has space for at | |
58 | * least %$2 n + 1$% words of result. | |
59 | */ | |
60 | ||
61 | static void redccore(mpw *dv, mpw *dvl, const mpw *mv, | |
62 | size_t n, const mpw *mi) | |
63 | { | |
64 | mpw mi0 = *mi; | |
65 | size_t i; | |
66 | ||
67 | for (i = 0; i < n; i++) { | |
68 | MPX_UMLAN(dv, dvl, mv, mv + n, MPW(*dv*mi0)); | |
69 | dv++; | |
70 | } | |
71 | } | |
72 | ||
73 | /* --- @redccore@ --- * | |
74 | * | |
75 | * Arguments: @mpw *dv, *dvl@ = base and limit of source/destination | |
76 | * @const mpw *av, *avl@ = base and limit of first multiplicand | |
77 | * @const mpw *bv, *bvl@ = base and limit of second multiplicand | |
78 | * @const mpw *mv@ = base of modulus %$m$% | |
79 | * @size_t n@ = length of modulus | |
80 | * @const mpw *mi@ = base of REDC coefficient %$m'$% | |
81 | * | |
82 | * Returns: --- | |
83 | * | |
84 | * Use: Let %$a$% and %$b$% be the multiplicands. Let %$w = a b$%. | |
85 | * Store in %$d$% the value %$a b + (m' a b \bmod R) m$%. | |
86 | */ | |
87 | ||
88 | static void mulcore(mpw *dv, mpw *dvl, | |
89 | const mpw *av, const mpw *avl, | |
90 | const mpw *bv, const mpw *bvl, | |
91 | const mpw *mv, size_t n, const mpw *mi) | |
92 | { | |
93 | mpw ai, b0, y, mi0 = *mi; | |
94 | const mpw *tv, *tvl; | |
95 | const mpw *mvl = mv + n; | |
96 | size_t i = 0; | |
97 | ||
98 | /* --- Initial setup --- */ | |
99 | ||
100 | MPX_ZERO(dv, dvl); | |
101 | if (avl - av > bvl - bv) { | |
102 | tv = av; av = bv; bv = tv; | |
103 | tvl = avl; avl = bvl; bvl = tvl; | |
104 | } | |
105 | b0 = *bv; | |
106 | ||
107 | /* --- Multiply, until we run out of multiplicand --- */ | |
108 | ||
109 | while (i < n && av < avl) { | |
110 | ai = *av++; | |
111 | y = MPW((*dv + ai*b0)*mi0); | |
112 | MPX_UMLAN(dv, dvl, bv, bvl, ai); | |
113 | MPX_UMLAN(dv, dvl, mv, mvl, y); | |
114 | dv++; i++; | |
115 | } | |
116 | ||
117 | /* --- Continue reducing until we run out of modulus --- */ | |
118 | ||
119 | while (i < n) { | |
120 | y = MPW(*dv*mi0); | |
121 | MPX_UMLAN(dv, dvl, mv, mvl, y); | |
122 | dv++; i++; | |
123 | } | |
124 | } | |
125 | ||
126 | /* --- @finish@ --- * | |
127 | * | |
128 | * Arguments: @mpmont *mm@ = pointer to a Montgomery reduction context | |
129 | * *mp *d@ = pointer to mostly-reduced operand | |
130 | * | |
131 | * Returns: --- | |
132 | * | |
133 | * Use: Applies the finishing touches to Montgomery reduction. The | |
134 | * operand @d@ is a multiple of %$R%$ at this point, so it needs | |
135 | * to be shifted down; the result might need a further | |
136 | * subtraction to get it into the right interval; and we may | |
137 | * need to do an additional subtraction if %$d$% is negative. | |
138 | */ | |
139 | ||
140 | static void finish(mpmont *mm, mp *d) | |
141 | { | |
142 | mpw *dv = d->v, *dvl = d->vl; | |
143 | size_t n = mm->n; | |
144 | ||
145 | memmove(dv, dv + n, MPWS(dvl - (dv + n))); | |
146 | dvl -= n; | |
147 | ||
148 | if (MPX_UCMP(dv, dvl, >=, mm->m->v, mm->m->vl)) | |
149 | mpx_usub(dv, dvl, dv, dvl, mm->m->v, mm->m->vl); | |
150 | ||
151 | if (d->f & MP_NEG) { | |
152 | mpx_usub(dv, dvl, mm->m->v, mm->m->vl, dv, dvl); | |
153 | d->f &= ~MP_NEG; | |
154 | } | |
155 | ||
156 | d->vl = dvl; | |
157 | MP_SHRINK(d); | |
158 | } | |
159 | ||
160 | #endif | |
161 | ||
4640a0dd | 162 | /*----- Reduction and multiplication --------------------------------------*/ |
d3409d5e | 163 | |
164 | /* --- @mpmont_create@ --- * | |
165 | * | |
166 | * Arguments: @mpmont *mm@ = pointer to Montgomery reduction context | |
167 | * @mp *m@ = modulus to use | |
168 | * | |
f4535c64 | 169 | * Returns: Zero on success, nonzero on error. |
d3409d5e | 170 | * |
171 | * Use: Initializes a Montgomery reduction context ready for use. | |
ef5f4810 | 172 | * The argument @m@ must be a positive odd integer. |
d3409d5e | 173 | */ |
174 | ||
52e4b041 | 175 | #ifdef MPMONT_DISABLE |
176 | ||
f4535c64 | 177 | int mpmont_create(mpmont *mm, mp *m) |
52e4b041 | 178 | { |
179 | mp_shrink(m); | |
180 | mm->m = MP_COPY(m); | |
181 | mm->r = MP_ONE; | |
182 | mm->r2 = MP_ONE; | |
f5f35081 | 183 | mm->mi = MP_ONE; |
f4535c64 | 184 | return (0); |
52e4b041 | 185 | } |
186 | ||
187 | #else | |
188 | ||
f4535c64 | 189 | int mpmont_create(mpmont *mm, mp *m) |
d3409d5e | 190 | { |
f5f35081 | 191 | size_t n = MP_LEN(m); |
d34decd2 | 192 | mp *r2 = mp_new(2 * n + 1, 0); |
f5f35081 | 193 | mp r; |
194 | ||
d3409d5e | 195 | /* --- Take a copy of the modulus --- */ |
196 | ||
f4535c64 | 197 | if (!MP_POSP(m) || !MP_ODDP(m)) |
198 | return (-1); | |
d3409d5e | 199 | mm->m = MP_COPY(m); |
200 | ||
f5f35081 | 201 | /* --- Determine %$R^2$% --- */ |
d3409d5e | 202 | |
f5f35081 | 203 | mm->n = n; |
204 | MPX_ZERO(r2->v, r2->vl - 1); | |
205 | r2->vl[-1] = 1; | |
d3409d5e | 206 | |
f5f35081 | 207 | /* --- Find the magic value @mi@ --- */ |
208 | ||
209 | mp_build(&r, r2->v + n, r2->vl); | |
b817bfc6 | 210 | mm->mi = mp_modinv(MP_NEW, m, &r); |
f5f35081 | 211 | mm->mi = mp_sub(mm->mi, &r, mm->mi); |
362c3d18 | 212 | MP_ENSURE(mm->mi, n); |
d3409d5e | 213 | |
214 | /* --- Discover the values %$R \bmod m$% and %$R^2 \bmod m$% --- */ | |
215 | ||
f5f35081 | 216 | mm->r2 = MP_NEW; |
217 | mp_div(0, &mm->r2, r2, m); | |
218 | mm->r = mpmont_reduce(mm, MP_NEW, mm->r2); | |
219 | MP_DROP(r2); | |
f4535c64 | 220 | return (0); |
d3409d5e | 221 | } |
222 | ||
52e4b041 | 223 | #endif |
224 | ||
d3409d5e | 225 | /* --- @mpmont_destroy@ --- * |
226 | * | |
227 | * Arguments: @mpmont *mm@ = pointer to a Montgomery reduction context | |
228 | * | |
229 | * Returns: --- | |
230 | * | |
231 | * Use: Disposes of a context when it's no longer of any use to | |
232 | * anyone. | |
233 | */ | |
234 | ||
235 | void mpmont_destroy(mpmont *mm) | |
236 | { | |
237 | MP_DROP(mm->m); | |
238 | MP_DROP(mm->r); | |
239 | MP_DROP(mm->r2); | |
f5f35081 | 240 | MP_DROP(mm->mi); |
d3409d5e | 241 | } |
242 | ||
243 | /* --- @mpmont_reduce@ --- * | |
244 | * | |
245 | * Arguments: @mpmont *mm@ = pointer to Montgomery reduction context | |
246 | * @mp *d@ = destination | |
ef5f4810 | 247 | * @mp *a@ = source, assumed positive |
d3409d5e | 248 | * |
249 | * Returns: Result, %$a R^{-1} \bmod m$%. | |
250 | */ | |
251 | ||
52e4b041 | 252 | #ifdef MPMONT_DISABLE |
253 | ||
ef5f4810 | 254 | mp *mpmont_reduce(mpmont *mm, mp *d, mp *a) |
52e4b041 | 255 | { |
256 | mp_div(0, &d, a, mm->m); | |
257 | return (d); | |
258 | } | |
259 | ||
260 | #else | |
261 | ||
ef5f4810 | 262 | mp *mpmont_reduce(mpmont *mm, mp *d, mp *a) |
d3409d5e | 263 | { |
f5f35081 | 264 | size_t n = mm->n; |
265 | ||
266 | /* --- Check for serious Karatsuba reduction --- */ | |
267 | ||
52cdaca9 | 268 | if (n > MPK_THRESH * 3) { |
f5f35081 | 269 | mp al; |
270 | mpw *vl; | |
271 | mp *u; | |
272 | ||
0e70bd46 MW |
273 | if (MP_LEN(a) >= n) vl = a->v + n; |
274 | else vl = a->vl; | |
f5f35081 | 275 | mp_build(&al, a->v, vl); |
276 | u = mp_mul(MP_NEW, &al, mm->mi); | |
0e70bd46 | 277 | if (MP_LEN(u) > n) u->vl = u->v + n; |
f5f35081 | 278 | u = mp_mul(u, u, mm->m); |
279 | d = mp_add(d, a, u); | |
366e9701 | 280 | MP_ENSURE(d, n); |
f5f35081 | 281 | mp_drop(u); |
282 | } | |
d3409d5e | 283 | |
f5f35081 | 284 | /* --- Otherwise do it the hard way --- */ |
d3409d5e | 285 | |
d3409d5e | 286 | else { |
d34decd2 | 287 | a = MP_COPY(a); |
0e70bd46 | 288 | if (d) MP_DROP(d); |
d34decd2 | 289 | d = a; |
0e70bd46 MW |
290 | MP_DEST(d, 2*mm->n + 1, a->f); |
291 | redccore(d->v, d->vl, mm->m->v, mm->n, mm->mi->v); | |
d3409d5e | 292 | } |
293 | ||
f5f35081 | 294 | /* --- Wrap everything up --- */ |
d3409d5e | 295 | |
0e70bd46 | 296 | finish(mm, d); |
d3409d5e | 297 | return (d); |
298 | } | |
299 | ||
52e4b041 | 300 | #endif |
301 | ||
d3409d5e | 302 | /* --- @mpmont_mul@ --- * |
303 | * | |
304 | * Arguments: @mpmont *mm@ = pointer to Montgomery reduction context | |
305 | * @mp *d@ = destination | |
ef5f4810 | 306 | * @mp *a, *b@ = sources, assumed positive |
d3409d5e | 307 | * |
308 | * Returns: Result, %$a b R^{-1} \bmod m$%. | |
309 | */ | |
310 | ||
52e4b041 | 311 | #ifdef MPMONT_DISABLE |
312 | ||
ef5f4810 | 313 | mp *mpmont_mul(mpmont *mm, mp *d, mp *a, mp *b) |
52e4b041 | 314 | { |
315 | d = mp_mul(d, a, b); | |
316 | mp_div(0, &d, d, mm->m); | |
317 | return (d); | |
318 | } | |
319 | ||
320 | #else | |
321 | ||
ef5f4810 | 322 | mp *mpmont_mul(mpmont *mm, mp *d, mp *a, mp *b) |
d3409d5e | 323 | { |
52cdaca9 | 324 | if (mm->n > MPK_THRESH * 3) { |
ef5f4810 | 325 | d = mp_mul(d, a, b); |
326 | d = mpmont_reduce(mm, d, d); | |
327 | } else { | |
ef5f4810 | 328 | a = MP_COPY(a); |
329 | b = MP_COPY(b); | |
0e70bd46 MW |
330 | MP_DEST(d, 2*mm->n + 1, a->f | b->f | MP_UNDEF); |
331 | mulcore(d->v, d->vl, a->v, a->vl, b->v, b->vl, | |
332 | mm->m->v, mm->n, mm->mi->v); | |
333 | d->f = ((a->f | b->f) & MP_BURN) | ((a->f ^ b->f) & MP_NEG); | |
334 | finish(mm, d); | |
335 | MP_DROP(a); MP_DROP(b); | |
d3409d5e | 336 | } |
337 | ||
d3409d5e | 338 | return (d); |
339 | } | |
340 | ||
52e4b041 | 341 | #endif |
342 | ||
d3409d5e | 343 | /*----- Test rig ----------------------------------------------------------*/ |
344 | ||
345 | #ifdef TEST_RIG | |
346 | ||
347 | static int tcreate(dstr *v) | |
348 | { | |
349 | mp *m = *(mp **)v[0].buf; | |
350 | mp *mi = *(mp **)v[1].buf; | |
351 | mp *r = *(mp **)v[2].buf; | |
352 | mp *r2 = *(mp **)v[3].buf; | |
353 | ||
354 | mpmont mm; | |
355 | int ok = 1; | |
356 | ||
357 | mpmont_create(&mm, m); | |
358 | ||
f5f35081 | 359 | if (mm.mi->v[0] != mi->v[0]) { |
d3409d5e | 360 | fprintf(stderr, "\n*** bad mi: found %lu, expected %lu", |
f5f35081 | 361 | (unsigned long)mm.mi->v[0], (unsigned long)mi->v[0]); |
d3409d5e | 362 | fputs("\nm = ", stderr); mp_writefile(m, stderr, 10); |
363 | fputc('\n', stderr); | |
364 | ok = 0; | |
365 | } | |
366 | ||
032099d1 | 367 | if (!MP_EQ(mm.r, r)) { |
d3409d5e | 368 | fputs("\n*** bad r", stderr); |
369 | fputs("\nm = ", stderr); mp_writefile(m, stderr, 10); | |
370 | fputs("\nexpected ", stderr); mp_writefile(r, stderr, 10); | |
45c0fd36 | 371 | fputs("\n found ", stderr); mp_writefile(mm.r, stderr, 10); |
d3409d5e | 372 | fputc('\n', stderr); |
373 | ok = 0; | |
374 | } | |
375 | ||
032099d1 | 376 | if (!MP_EQ(mm.r2, r2)) { |
d3409d5e | 377 | fputs("\n*** bad r2", stderr); |
378 | fputs("\nm = ", stderr); mp_writefile(m, stderr, 10); | |
379 | fputs("\nexpected ", stderr); mp_writefile(r2, stderr, 10); | |
45c0fd36 | 380 | fputs("\n found ", stderr); mp_writefile(mm.r2, stderr, 10); |
d3409d5e | 381 | fputc('\n', stderr); |
382 | ok = 0; | |
383 | } | |
384 | ||
385 | MP_DROP(m); | |
386 | MP_DROP(mi); | |
387 | MP_DROP(r); | |
388 | MP_DROP(r2); | |
389 | mpmont_destroy(&mm); | |
ef5f4810 | 390 | assert(mparena_count(MPARENA_GLOBAL) == 0); |
d3409d5e | 391 | return (ok); |
392 | } | |
393 | ||
394 | static int tmul(dstr *v) | |
395 | { | |
396 | mp *m = *(mp **)v[0].buf; | |
397 | mp *a = *(mp **)v[1].buf; | |
398 | mp *b = *(mp **)v[2].buf; | |
399 | mp *r = *(mp **)v[3].buf; | |
d3409d5e | 400 | int ok = 1; |
401 | ||
402 | mpmont mm; | |
403 | mpmont_create(&mm, m); | |
404 | ||
79a34029 | 405 | { |
406 | mp *qr = mp_mul(MP_NEW, a, b); | |
407 | mp_div(0, &qr, qr, m); | |
408 | ||
032099d1 | 409 | if (!MP_EQ(qr, r)) { |
79a34029 | 410 | fputs("\n*** classical modmul failed", stderr); |
411 | fputs("\n m = ", stderr); mp_writefile(m, stderr, 10); | |
412 | fputs("\n a = ", stderr); mp_writefile(a, stderr, 10); | |
413 | fputs("\n b = ", stderr); mp_writefile(b, stderr, 10); | |
414 | fputs("\n r = ", stderr); mp_writefile(r, stderr, 10); | |
415 | fputs("\nqr = ", stderr); mp_writefile(qr, stderr, 10); | |
416 | fputc('\n', stderr); | |
417 | ok = 0; | |
418 | } | |
419 | ||
420 | mp_drop(qr); | |
421 | } | |
422 | ||
d3409d5e | 423 | { |
424 | mp *ar = mpmont_mul(&mm, MP_NEW, a, mm.r2); | |
425 | mp *br = mpmont_mul(&mm, MP_NEW, b, mm.r2); | |
79a34029 | 426 | mp *mr = mpmont_mul(&mm, MP_NEW, ar, br); |
d3409d5e | 427 | mr = mpmont_reduce(&mm, mr, mr); |
032099d1 | 428 | if (!MP_EQ(mr, r)) { |
79a34029 | 429 | fputs("\n*** montgomery modmul failed", stderr); |
430 | fputs("\n m = ", stderr); mp_writefile(m, stderr, 10); | |
431 | fputs("\n a = ", stderr); mp_writefile(a, stderr, 10); | |
432 | fputs("\n b = ", stderr); mp_writefile(b, stderr, 10); | |
433 | fputs("\n r = ", stderr); mp_writefile(r, stderr, 10); | |
434 | fputs("\nmr = ", stderr); mp_writefile(mr, stderr, 10); | |
435 | fputc('\n', stderr); | |
436 | ok = 0; | |
437 | } | |
d3409d5e | 438 | MP_DROP(ar); MP_DROP(br); |
79a34029 | 439 | mp_drop(mr); |
d3409d5e | 440 | } |
441 | ||
d3409d5e | 442 | |
443 | MP_DROP(m); | |
444 | MP_DROP(a); | |
445 | MP_DROP(b); | |
446 | MP_DROP(r); | |
d3409d5e | 447 | mpmont_destroy(&mm); |
ef5f4810 | 448 | assert(mparena_count(MPARENA_GLOBAL) == 0); |
d3409d5e | 449 | return ok; |
450 | } | |
451 | ||
d3409d5e | 452 | static test_chunk tests[] = { |
ef5f4810 | 453 | { "create", tcreate, { &type_mp, &type_mp, &type_mp, &type_mp, 0 } }, |
454 | { "mul", tmul, { &type_mp, &type_mp, &type_mp, &type_mp, 0 } }, | |
d3409d5e | 455 | { 0, 0, { 0 } }, |
456 | }; | |
457 | ||
458 | int main(int argc, char *argv[]) | |
459 | { | |
460 | sub_init(); | |
0f00dc4c | 461 | test_run(argc, argv, tests, SRCDIR "/t/mpmont"); |
d3409d5e | 462 | return (0); |
463 | } | |
464 | ||
465 | #endif | |
466 | ||
467 | /*----- That's all, folks -------------------------------------------------*/ |