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1 | /* -*-c-*- |
2 | * |
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3 | * $Id$ |
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4 | * |
5 | * Efficient reduction modulo nice primes |
6 | * |
7 | * (c) 2004 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 | |
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30 | /*----- Header files ------------------------------------------------------*/ |
31 | |
32 | #include <mLib/darray.h> |
33 | #include <mLib/macros.h> |
34 | |
35 | #include "mp.h" |
36 | #include "mpreduce.h" |
37 | #include "mpreduce-exp.h" |
38 | |
39 | /*----- Data structures ---------------------------------------------------*/ |
40 | |
41 | DA_DECL(instr_v, mpreduce_instr); |
42 | |
43 | /*----- Main code ---------------------------------------------------------*/ |
44 | |
45 | /* --- @mpreduce_create@ --- * |
46 | * |
47 | * Arguments: @gfreduce *r@ = structure to fill in |
48 | * @mp *x@ = an integer |
49 | * |
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50 | * Returns: Zero if successful; nonzero on failure. |
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51 | * |
52 | * Use: Initializes a context structure for reduction. |
53 | */ |
54 | |
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55 | int mpreduce_create(mpreduce *r, mp *p) |
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56 | { |
57 | mpscan sc; |
58 | enum { Z = 0, Z1 = 2, X = 4, X0 = 6 }; |
59 | unsigned st = Z; |
60 | instr_v iv = DA_INIT; |
61 | unsigned long d, i; |
62 | unsigned op; |
63 | size_t w, b; |
64 | |
65 | /* --- Fill in the easy stuff --- */ |
66 | |
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67 | if (!MP_POSP(p)) |
68 | return (-1); |
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69 | d = mp_bits(p); |
70 | r->lim = d/MPW_BITS; |
71 | r->s = d%MPW_BITS; |
72 | if (r->s) |
73 | r->lim++; |
74 | r->p = mp_copy(p); |
75 | |
76 | /* --- Stash a new instruction --- */ |
77 | |
78 | #define INSTR(op_, argx_, argy_) do { \ |
79 | DA_ENSURE(&iv, 1); \ |
80 | DA(&iv)[DA_LEN(&iv)].op = (op_); \ |
81 | DA(&iv)[DA_LEN(&iv)].argx = (argx_); \ |
82 | DA(&iv)[DA_LEN(&iv)].argy = (argy_); \ |
83 | DA_EXTEND(&iv, 1); \ |
84 | } while (0) |
85 | |
86 | /* --- Main loop --- * |
87 | * |
88 | * A simple state machine decomposes @p@ conveniently into positive and |
89 | * negative powers of 2. The pure form of the state machine is left below |
90 | * for reference (and in case I need inspiration for a NAF exponentiator). |
91 | */ |
92 | |
93 | #ifdef DEBUG |
94 | for (i = 0, mp_scan(&sc, p); mp_step(&sc); i++) { |
95 | switch (st | mp_bit(&sc)) { |
96 | case Z | 1: st = Z1; break; |
97 | case Z1 | 0: st = Z; printf("+ %lu\n", i - 1); break; |
98 | case Z1 | 1: st = X; printf("- %lu\n", i - 1); break; |
99 | case X | 0: st = X0; break; |
100 | case X0 | 1: st = X; printf("- %lu\n", i - 1); break; |
101 | case X0 | 0: st = Z; printf("+ %lu\n", i - 1); break; |
102 | } |
103 | } |
104 | if (st >= X) printf("+ %lu\n", i); |
105 | #endif |
106 | |
107 | for (i = 0, mp_scan(&sc, p); i < d - 1 && mp_step(&sc); i++) { |
108 | switch (st | mp_bit(&sc)) { |
109 | case Z | 1: st = Z1; break; |
110 | case Z1 | 0: st = Z; op = MPRI_SUB; goto instr; |
111 | case Z1 | 1: st = X; op = MPRI_ADD; goto instr; |
112 | case X | 0: st = X0; break; |
113 | case X0 | 1: st = X; op = MPRI_ADD; goto instr; |
114 | case X0 | 0: st = Z; op = MPRI_SUB; goto instr; |
115 | instr: |
116 | w = (d - i)/MPW_BITS + 1; |
117 | b = (MPW_BITS + i - d - 1)%MPW_BITS; |
118 | INSTR(op | !!b, w, b); |
119 | } |
120 | } |
121 | if ((DA(&iv)[DA_LEN(&iv) - 1].op & ~1u) == MPRI_SUB) { |
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122 | mp_drop(r->p); |
123 | DA_DESTROY(&iv); |
124 | return (-1); |
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125 | } |
126 | |
127 | #undef INSTR |
128 | |
129 | /* --- Wrap up --- */ |
130 | |
131 | r->in = DA_LEN(&iv); |
132 | if (!r->s) { |
133 | r->iv = xmalloc(r->in * sizeof(mpreduce_instr)); |
134 | memcpy(r->iv, DA(&iv), r->in * sizeof(mpreduce_instr)); |
135 | } else { |
136 | r->iv = xmalloc(r->in * 2 * sizeof(mpreduce_instr)); |
137 | for (i = 0; i < r->in; i++) { |
138 | r->iv[i] = DA(&iv)[i]; |
139 | op = r->iv[i].op & ~1u; |
140 | w = r->iv[i].argx; |
141 | b = r->iv[i].argy; |
142 | b += r->s; |
143 | if (b >= MPW_BITS) { |
144 | b -= MPW_BITS; |
145 | w--; |
146 | } |
147 | if (b) op |= 1; |
148 | r->iv[i + r->in].op = op; |
149 | r->iv[i + r->in].argx = w; |
150 | r->iv[i + r->in].argy = b; |
151 | } |
152 | } |
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153 | DA_DESTROY(&iv); |
154 | return (0); |
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155 | } |
156 | |
157 | /* --- @mpreduce_destroy@ --- * |
158 | * |
159 | * Arguments: @mpreduce *r@ = structure to free |
160 | * |
161 | * Returns: --- |
162 | * |
163 | * Use: Reclaims the resources from a reduction context. |
164 | */ |
165 | |
166 | void mpreduce_destroy(mpreduce *r) |
167 | { |
168 | mp_drop(r->p); |
169 | xfree(r->iv); |
170 | } |
171 | |
172 | /* --- @mpreduce_dump@ --- * |
173 | * |
174 | * Arguments: @mpreduce *r@ = structure to dump |
175 | * @FILE *fp@ = file to dump on |
176 | * |
177 | * Returns: --- |
178 | * |
179 | * Use: Dumps a reduction context. |
180 | */ |
181 | |
182 | void mpreduce_dump(mpreduce *r, FILE *fp) |
183 | { |
184 | size_t i; |
185 | static const char *opname[] = { "add", "addshift", "sub", "subshift" }; |
186 | |
187 | fprintf(fp, "mod = "); mp_writefile(r->p, fp, 16); |
188 | fprintf(fp, "\n lim = %lu; s = %d\n", (unsigned long)r->lim, r->s); |
189 | for (i = 0; i < r->in; i++) { |
190 | assert(r->iv[i].op < N(opname)); |
191 | fprintf(fp, " %s %lu %lu\n", |
192 | opname[r->iv[i].op], |
193 | (unsigned long)r->iv[i].argx, |
194 | (unsigned long)r->iv[i].argy); |
195 | } |
196 | if (r->s) { |
197 | fprintf(fp, "tail end charlie\n"); |
198 | for (i = r->in; i < 2 * r->in; i++) { |
199 | assert(r->iv[i].op < N(opname)); |
200 | fprintf(fp, " %s %lu %lu\n", |
201 | opname[r->iv[i].op], |
202 | (unsigned long)r->iv[i].argx, |
203 | (unsigned long)r->iv[i].argy); |
204 | } |
205 | } |
206 | } |
207 | |
208 | /* --- @mpreduce_do@ --- * |
209 | * |
210 | * Arguments: @mpreduce *r@ = reduction context |
211 | * @mp *d@ = destination |
212 | * @mp *x@ = source |
213 | * |
214 | * Returns: Destination, @x@ reduced modulo the reduction poly. |
215 | */ |
216 | |
217 | static void run(const mpreduce_instr *i, const mpreduce_instr *il, |
218 | mpw *v, mpw z) |
219 | { |
220 | for (; i < il; i++) { |
221 | #ifdef DEBUG |
222 | mp vv; |
223 | mp_build(&vv, v - i->argx, v + 1); |
224 | printf(" 0x"); mp_writefile(&vv, stdout, 16); |
225 | printf(" %c (0x%lx << %u) == 0x", |
226 | (i->op & ~1u) == MPRI_ADD ? '+' : '-', |
227 | (unsigned long)z, |
228 | i->argy); |
229 | #endif |
230 | switch (i->op) { |
231 | case MPRI_ADD: MPX_UADDN(v - i->argx, v + 1, z); break; |
232 | case MPRI_ADDLSL: mpx_uaddnlsl(v - i->argx, v + 1, z, i->argy); break; |
233 | case MPRI_SUB: MPX_USUBN(v - i->argx, v + 1, z); break; |
234 | case MPRI_SUBLSL: mpx_usubnlsl(v - i->argx, v + 1, z, i->argy); break; |
235 | default: |
236 | abort(); |
237 | } |
238 | #ifdef DEBUG |
239 | mp_build(&vv, v - i->argx, v + 1); |
240 | mp_writefile(&vv, stdout, 16); |
241 | printf("\n"); |
242 | #endif |
243 | } |
244 | } |
245 | |
246 | mp *mpreduce_do(mpreduce *r, mp *d, mp *x) |
247 | { |
248 | mpw *v, *vl; |
249 | const mpreduce_instr *il; |
250 | mpw z; |
251 | |
252 | #ifdef DEBUG |
253 | mp *_r = 0, *_rr = 0; |
254 | #endif |
255 | |
256 | /* --- If source is negative, divide --- */ |
257 | |
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258 | if (MP_NEGP(x)) { |
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259 | mp_div(0, &d, x, r->p); |
260 | return (d); |
261 | } |
262 | |
263 | /* --- Try to reuse the source's space --- */ |
264 | |
265 | MP_COPY(x); |
266 | if (d) MP_DROP(d); |
267 | MP_DEST(x, MP_LEN(x), x->f); |
268 | |
269 | /* --- Do the reduction --- */ |
270 | |
271 | #ifdef DEBUG |
272 | _r = MP_NEW; |
273 | mp_div(0, &_r, x, r->p); |
274 | MP_PRINTX("x", x); |
275 | _rr = 0; |
276 | #endif |
277 | |
278 | il = r->iv + r->in; |
279 | if (MP_LEN(x) >= r->lim) { |
280 | v = x->v + r->lim; |
281 | vl = x->vl; |
282 | while (vl-- > v) { |
283 | while (*vl) { |
284 | z = *vl; |
285 | *vl = 0; |
286 | run(r->iv, il, vl, z); |
287 | #ifdef DEBUG |
288 | MP_PRINTX("x", x); |
289 | mp_div(0, &_rr, x, r->p); |
290 | assert(MP_EQ(_r, _rr)); |
291 | #endif |
292 | } |
293 | } |
294 | if (r->s) { |
295 | while (*vl >> r->s) { |
296 | z = *vl >> r->s; |
297 | *vl &= ((1 << r->s) - 1); |
298 | run(r->iv + r->in, il + r->in, vl, z); |
299 | #ifdef DEBUG |
300 | MP_PRINTX("x", x); |
301 | mp_div(0, &_rr, x, r->p); |
302 | assert(MP_EQ(_r, _rr)); |
303 | #endif |
304 | } |
305 | } |
306 | } |
307 | |
308 | /* --- Finishing touches --- */ |
309 | |
310 | MP_SHRINK(x); |
311 | if (MP_CMP(x, >=, r->p)) |
312 | x = mp_sub(x, x, r->p); |
313 | |
314 | /* --- Done --- */ |
315 | |
316 | #ifdef DEBUG |
317 | assert(MP_EQ(_r, x)); |
318 | mp_drop(_r); |
319 | mp_drop(_rr); |
320 | #endif |
321 | return (x); |
322 | } |
323 | |
324 | /* --- @mpreduce_exp@ --- * |
325 | * |
326 | * Arguments: @mpreduce *mr@ = pointer to reduction context |
327 | * @mp *d@ = fake destination |
328 | * @mp *a@ = base |
329 | * @mp *e@ = exponent |
330 | * |
331 | * Returns: Result, %$a^e \bmod m$%. |
332 | */ |
333 | |
334 | mp *mpreduce_exp(mpreduce *mr, mp *d, mp *a, mp *e) |
335 | { |
336 | mp *x = MP_ONE; |
337 | mp *spare = (e->f & MP_BURN) ? MP_NEWSEC : MP_NEW; |
338 | |
339 | MP_SHRINK(e); |
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340 | MP_COPY(a); |
341 | if (MP_ZEROP(e)) |
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342 | ; |
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343 | else { |
344 | if (MP_NEGP(e)) |
345 | a = mp_modinv(a, a, mr->p); |
346 | if (MP_LEN(e) < EXP_THRESH) |
347 | EXP_SIMPLE(x, a, e); |
348 | else |
349 | EXP_WINDOW(x, a, e); |
350 | } |
351 | mp_drop(a); |
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352 | mp_drop(d); |
353 | mp_drop(spare); |
354 | return (x); |
355 | } |
356 | |
357 | /*----- Test rig ----------------------------------------------------------*/ |
358 | |
359 | |
360 | #ifdef TEST_RIG |
361 | |
362 | #define MP(x) mp_readstring(MP_NEW, #x, 0, 0) |
363 | |
364 | static int vreduce(dstr *v) |
365 | { |
366 | mp *d = *(mp **)v[0].buf; |
367 | mp *n = *(mp **)v[1].buf; |
368 | mp *r = *(mp **)v[2].buf; |
369 | mp *c; |
370 | int ok = 1; |
371 | mpreduce rr; |
372 | |
373 | mpreduce_create(&rr, d); |
374 | c = mpreduce_do(&rr, MP_NEW, n); |
375 | if (!MP_EQ(c, r)) { |
376 | fprintf(stderr, "\n*** reduction failed\n*** "); |
377 | mpreduce_dump(&rr, stderr); |
378 | fprintf(stderr, "\n*** n = "); mp_writefile(n, stderr, 10); |
379 | fprintf(stderr, "\n*** r = "); mp_writefile(r, stderr, 10); |
380 | fprintf(stderr, "\n*** c = "); mp_writefile(c, stderr, 10); |
381 | fprintf(stderr, "\n"); |
382 | ok = 0; |
383 | } |
384 | mpreduce_destroy(&rr); |
385 | mp_drop(n); mp_drop(d); mp_drop(r); mp_drop(c); |
386 | assert(mparena_count(MPARENA_GLOBAL) == 0); |
387 | return (ok); |
388 | } |
389 | |
390 | static int vmodexp(dstr *v) |
391 | { |
392 | mp *p = *(mp **)v[0].buf; |
393 | mp *g = *(mp **)v[1].buf; |
394 | mp *x = *(mp **)v[2].buf; |
395 | mp *r = *(mp **)v[3].buf; |
396 | mp *c; |
397 | int ok = 1; |
398 | mpreduce rr; |
399 | |
400 | mpreduce_create(&rr, p); |
401 | c = mpreduce_exp(&rr, MP_NEW, g, x); |
402 | if (!MP_EQ(c, r)) { |
403 | fprintf(stderr, "\n*** modexp failed\n*** "); |
404 | fprintf(stderr, "\n*** p = "); mp_writefile(p, stderr, 10); |
405 | fprintf(stderr, "\n*** g = "); mp_writefile(g, stderr, 10); |
406 | fprintf(stderr, "\n*** x = "); mp_writefile(x, stderr, 10); |
407 | fprintf(stderr, "\n*** c = "); mp_writefile(c, stderr, 10); |
408 | fprintf(stderr, "\n*** r = "); mp_writefile(r, stderr, 10); |
409 | fprintf(stderr, "\n"); |
410 | ok = 0; |
411 | } |
412 | mpreduce_destroy(&rr); |
413 | mp_drop(p); mp_drop(g); mp_drop(r); mp_drop(x); mp_drop(c); |
414 | assert(mparena_count(MPARENA_GLOBAL) == 0); |
415 | return (ok); |
416 | } |
417 | |
418 | static test_chunk defs[] = { |
419 | { "reduce", vreduce, { &type_mp, &type_mp, &type_mp, 0 } }, |
420 | { "modexp", vmodexp, { &type_mp, &type_mp, &type_mp, &type_mp, 0 } }, |
421 | { 0, 0, { 0 } } |
422 | }; |
423 | |
424 | int main(int argc, char *argv[]) |
425 | { |
426 | test_run(argc, argv, defs, SRCDIR"/tests/mpreduce"); |
427 | return (0); |
428 | } |
429 | |
430 | #endif |
431 | |
432 | /*----- That's all, folks -------------------------------------------------*/ |