432c4e18 |
1 | /* -*-c-*- |
2 | * |
3 | * $Id: ec-info.c,v 1.1 2004/03/27 17:54:11 mdw Exp $ |
4 | * |
5 | * Elliptic curve information management |
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 | |
30 | /*----- Revision history --------------------------------------------------* |
31 | * |
32 | * $Log: ec-info.c,v $ |
33 | * Revision 1.1 2004/03/27 17:54:11 mdw |
34 | * Standard curves and curve checking. |
35 | * |
36 | */ |
37 | |
38 | /*----- Header files ------------------------------------------------------*/ |
39 | |
40 | #include "ec.h" |
41 | #include "ectab.h" |
42 | #include "gf.h" |
43 | #include "pgen.h" |
44 | #include "mprand.h" |
45 | #include "rabin.h" |
46 | |
47 | /*----- Main code ---------------------------------------------------------*/ |
48 | |
49 | /* --- @ec_curveparse@ --- * |
50 | * |
51 | * Arguments: @qd_parse *qd@ = parser context |
52 | * |
53 | * Returns: Elliptic curve pointer if OK, or null. |
54 | * |
55 | * Use: Parses an elliptic curve description, which has the form |
56 | * |
57 | * * a field description |
58 | * * an optional `/' |
59 | * * `prime', `primeproj', `bin', or `binproj' |
60 | * * an optional `:' |
61 | * * the %$a$% parameter |
62 | * * an optional `,' |
63 | * * the %$b$% parameter |
64 | */ |
65 | |
66 | ec_curve *ec_curveparse(qd_parse *qd) |
67 | { |
68 | mp *a = MP_NEW, *b = MP_NEW; |
69 | ec_curve *c; |
70 | field *f; |
71 | |
72 | if ((f = field_parse(qd)) == 0) goto fail; |
73 | qd_delim(qd, '/'); |
74 | switch (qd_enum(qd, "prime,primeproj,bin,binproj")) { |
75 | case 0: |
76 | if (F_TYPE(f) != FTY_PRIME) { |
77 | qd->e = "field not prime"; |
78 | goto fail; |
79 | } |
80 | qd_delim(qd, ':'); |
81 | if ((a = qd_getmp(qd)) == 0) goto fail; |
82 | qd_delim(qd, ','); |
83 | if ((b = qd_getmp(qd)) == 0) goto fail; |
84 | c = ec_prime(f, a, b); |
85 | break; |
86 | case 1: |
87 | if (F_TYPE(f) != FTY_PRIME) { |
88 | qd->e = "field not prime"; |
89 | goto fail; |
90 | } |
91 | qd_delim(qd, ':'); |
92 | if ((a = qd_getmp(qd)) == 0) goto fail; |
93 | qd_delim(qd, ','); |
94 | if ((b = qd_getmp(qd)) == 0) goto fail; |
95 | c = ec_primeproj(f, a, b); |
96 | break; |
97 | case 2: |
98 | if (F_TYPE(f) != FTY_BINARY) { |
99 | qd->e = "field not binary"; |
100 | goto fail; |
101 | } |
102 | qd_delim(qd, ':'); |
103 | if ((a = qd_getmp(qd)) == 0) goto fail; |
104 | qd_delim(qd, ','); |
105 | if ((b = qd_getmp(qd)) == 0) goto fail; |
106 | c = ec_bin(f, a, b); |
107 | break; |
108 | case 3: |
109 | if (F_TYPE(f) != FTY_BINARY) { |
110 | qd->e = "field not binary"; |
111 | goto fail; |
112 | } |
113 | qd_delim(qd, ':'); |
114 | if ((a = qd_getmp(qd)) == 0) goto fail; |
115 | qd_delim(qd, ','); |
116 | if ((b = qd_getmp(qd)) == 0) goto fail; |
117 | c = ec_binproj(f, a, b); |
118 | break; |
119 | default: |
120 | goto fail; |
121 | } |
122 | if (a) MP_DROP(a); |
123 | if (b) MP_DROP(b); |
124 | return (c); |
125 | |
126 | fail: |
127 | if (f) F_DESTROY(f); |
128 | if (a) MP_DROP(a); |
129 | if (b) MP_DROP(b); |
130 | return (0); |
131 | } |
132 | |
133 | /* --- @ec_ptparse@ --- * |
134 | * |
135 | * Arguments: @qd_parse *qd@ = parser context |
136 | * @ec *p@ = where to put the point |
137 | * |
138 | * Returns: The point address, or null. |
139 | * |
140 | * Use: Parses an elliptic curve point. This has the form |
141 | * |
142 | * * %$x$%-coordinate |
143 | * * optional `,' |
144 | * * %$y$%-coordinate |
145 | */ |
146 | |
147 | ec *ec_ptparse(qd_parse *qd, ec *p) |
148 | { |
149 | mp *x = MP_NEW, *y = MP_NEW; |
150 | |
151 | if (qd_enum(qd, "inf") >= 0) { |
152 | EC_SETINF(p); |
153 | return (p); |
154 | } |
155 | if ((x = qd_getmp(qd)) == 0) goto fail; |
156 | qd_delim(qd, ','); |
157 | if ((y = qd_getmp(qd)) == 0) goto fail; |
158 | EC_DESTROY(p); |
159 | p->x = x; |
160 | p->y = y; |
161 | p->z = 0; |
162 | return (p); |
163 | |
164 | fail: |
165 | if (x) MP_DROP(x); |
166 | if (y) MP_DROP(y); |
167 | return (0); |
168 | } |
169 | |
170 | /* --- @ec_infoparse@ --- * |
171 | * |
172 | * Arguments: @qd_parse *qd@ = parser context |
173 | * @ec_info *ei@ = curve information block, currently |
174 | * uninitialized |
175 | * |
176 | * Returns: Zero on success, nonzero on failure. |
177 | * |
178 | * Use: Parses an elliptic curve information string, and stores the |
179 | * information in @ei@. This has the form |
180 | * |
181 | * * elliptic curve description |
182 | * * optional `/' |
183 | * * common point |
184 | * * optional `:' |
185 | * * group order |
186 | * * optional `*' |
187 | * * cofactor |
188 | */ |
189 | |
190 | int ec_infoparse(qd_parse *qd, ec_info *ei) |
191 | { |
192 | ec_curve *c = 0; |
193 | field *f; |
194 | ec g = EC_INIT; |
195 | mp *r = MP_NEW, *h = MP_NEW; |
196 | |
197 | if ((c = ec_curveparse(qd)) == 0) goto fail; |
198 | qd_delim(qd, '/'); if (!ec_ptparse(qd, &g)) goto fail; |
199 | qd_delim(qd, ':'); if ((r = qd_getmp(qd)) == 0) goto fail; |
200 | qd_delim(qd, '*'); if ((h = qd_getmp(qd)) == 0) goto fail; |
201 | |
202 | ei->c = c; ei->g = g; ei->r = r; ei->h = h; |
203 | return (0); |
204 | |
205 | fail: |
206 | EC_DESTROY(&g); |
207 | if (r) MP_DROP(r); |
208 | if (h) MP_DROP(h); |
209 | if (c) { f = c->f; ec_destroycurve(c); F_DESTROY(f); } |
210 | return (-1); |
211 | } |
212 | |
213 | /* --- @getinfo@ --- * |
214 | * |
215 | * Arguments: @ec_info *ei@ = where to write the information |
216 | * @const ecdata *ed@ = raw data |
217 | * |
218 | * Returns: --- |
219 | * |
220 | * Use: Loads elliptic curve information about one of the standard |
221 | * curves. |
222 | */ |
223 | |
224 | static mp *getmp(const mpw *v, size_t n) |
225 | { |
226 | mp *x = mp_new(n, 0); |
227 | memcpy(x->v, v, MPWS(n)); |
228 | return (x); |
229 | } |
230 | |
231 | static void getinfo(ec_info *ei, const ecdata *ed) |
232 | { |
233 | field *f; |
234 | mp *p = 0, *a = 0, *b = 0; |
235 | |
236 | switch (ed->ftag) { |
237 | case FTAG_PRIME: |
238 | p = getmp(ed->p, ed->psz); |
239 | f = field_prime(p); |
240 | a = getmp(ed->a, ed->asz); b = getmp(ed->b, ed->bsz); |
241 | ei->c = ec_primeproj(f, a, b); |
242 | break; |
243 | case FTAG_NICEPRIME: |
244 | p = getmp(ed->p, ed->psz); |
245 | f = field_niceprime(p); |
246 | a = getmp(ed->a, ed->asz); b = getmp(ed->b, ed->bsz); |
247 | ei->c = ec_primeproj(f, a, b); |
248 | break; |
249 | case FTAG_BINPOLY: |
250 | p = getmp(ed->p, ed->psz); |
251 | f = field_binpoly(p); |
252 | a = getmp(ed->a, ed->asz); b = getmp(ed->b, ed->bsz); |
253 | ei->c = ec_binproj(f, a, b); |
254 | break; |
255 | default: |
256 | abort(); |
257 | } |
258 | |
259 | EC_CREATE(&ei->g); |
260 | ei->g.x = getmp(ed->gx, ed->gxsz); |
261 | ei->g.y = getmp(ed->gy, ed->gysz); |
262 | ei->g.z = 0; |
263 | ei->r = getmp(ed->r, ed->rsz); |
264 | ei->h = getmp(ed->h, ed->hsz); |
265 | |
266 | MP_DROP(p); |
267 | MP_DROP(a); |
268 | MP_DROP(b); |
269 | } |
270 | |
271 | /* --- @ec_getinfo@ --- * |
272 | * |
273 | * Arguments: @ec_info *ei@ = where to write the information |
274 | * @const char *p@ = string describing a curve |
275 | * |
276 | * Returns: Null on success, or a pointer to an error message. |
277 | * |
278 | * Use: Parses out information about a curve. The string is either a |
279 | * standard curve name, or a curve info string. |
280 | */ |
281 | |
282 | const char *ec_getinfo(ec_info *ei, const char *p) |
283 | { |
284 | qd_parse qd; |
285 | const ecentry *ee; |
286 | |
287 | qd.p = p; |
288 | qd.e = 0; |
289 | for (ee = ectab; ee->name; ee++) { |
290 | if (qd_enum(&qd, ee->name) >= 0) { |
291 | getinfo(ei, ee->data); |
292 | goto found; |
293 | } |
294 | } |
295 | if (ec_infoparse(&qd, ei)) |
296 | return (qd.e); |
297 | found: |
298 | if (!qd_eofp(&qd)) { |
299 | ec_freeinfo(ei); |
300 | return ("junk found at end of string"); |
301 | } |
302 | return (0); |
303 | } |
304 | |
305 | /* --- @ec_freeinfo@ --- * |
306 | * |
307 | * Arguments: @ec_info *ei@ = elliptic curve information block to free |
308 | * |
309 | * Returns: --- |
310 | * |
311 | * Use: Frees the information block. |
312 | */ |
313 | |
314 | void ec_freeinfo(ec_info *ei) |
315 | { |
316 | field *f; |
317 | |
318 | EC_DESTROY(&ei->g); |
319 | MP_DROP(ei->r); |
320 | MP_DROP(ei->h); |
321 | f = ei->c->f; ec_destroycurve(ei->c); F_DESTROY(f); |
322 | } |
323 | |
324 | /* --- @ec_checkinfo@ --- * |
325 | * |
326 | * Arguments: @const ec_info *ei@ = elliptic curve information block |
327 | * |
328 | * Returns: Null if OK, or pointer to error message. |
329 | * |
330 | * Use: Checks an elliptic curve according to the rules in SEC1. |
331 | */ |
332 | |
333 | static int primep(mp *p, grand *gr) |
334 | { |
335 | int i = rabin_iters(mp_bits(p)); |
336 | rabin r; |
337 | mp *x = MP_NEW; |
338 | |
339 | switch (pfilt_smallfactor(p)) { |
340 | case PGEN_DONE: return (1); |
341 | case PGEN_FAIL: return (0); |
342 | } |
343 | rabin_create(&r, p); |
344 | while (i) { |
345 | x = mprand_range(x, p, gr, 0); |
346 | if (rabin_rtest(&r, x) == PGEN_FAIL) |
347 | break; |
348 | i--; |
349 | } |
350 | MP_DROP(x); |
351 | rabin_destroy(&r); |
352 | return (!i); |
353 | } |
354 | |
355 | static int primeeltp(mp *x, field *f) |
356 | { |
357 | return (!MP_ISNEG(x) && MP_CMP(x, <, f->m)); |
358 | } |
359 | |
360 | static const char *primecheck(const ec_info *ei, grand *gr) |
361 | { |
362 | ec_curve *c = ei->c; |
363 | field *f = c->f; |
364 | int i; |
365 | mp *x, *y; |
366 | ec p; |
367 | int rc; |
368 | |
369 | /* --- Check %$p$% is an odd prime --- */ |
370 | |
371 | if (!primep(f->m, gr)) return ("p not prime"); |
372 | |
373 | /* --- Check %$a$%, %$b$%, %$G_x$% and %$G_y$% are in %$[0, p)$% --- */ |
374 | |
375 | if (!primeeltp(c->a, f)) return ("a out of range"); |
376 | if (!primeeltp(c->b, f)) return ("b out of range"); |
377 | if (!primeeltp(ei->g.x, f)) return ("G_x out of range"); |
378 | if (!primeeltp(ei->g.x, f)) return ("G_y out of range"); |
379 | |
380 | /* --- Check %$4 a^3 + 27 b^2 \not\equiv 0 \pmod{p}$% --- */ |
381 | |
382 | x = F_SQR(f, MP_NEW, c->a); |
383 | x = F_MUL(f, x, x, c->a); |
384 | x = F_QDL(f, x, x); |
385 | y = F_SQR(f, MP_NEW, c->b); |
386 | y = F_TPL(f, y, y); |
387 | y = F_TPL(f, y, y); |
388 | y = F_TPL(f, y, y); |
389 | x = F_ADD(f, x, x, y); |
390 | rc = F_ZEROP(f, x); |
391 | MP_DROP(x); |
392 | MP_DROP(y); |
393 | if (rc) return ("not an elliptic curve"); |
394 | |
395 | /* --- Check %$G \in E$% --- */ |
396 | |
397 | if (EC_ATINF(&ei->g)) return ("generator at infinity"); |
398 | if (ec_check(c, &ei->g)) return ("generator not on curve"); |
399 | |
400 | /* --- Check %$r$% is prime --- */ |
401 | |
402 | if (!primep(ei->r, gr)) return ("generator order not prime"); |
403 | |
404 | /* --- Check %$0 < h \le 4$% --- */ |
405 | |
406 | if (MP_CMP(ei->h, <, MP_ONE) || MP_CMP(ei->h, >, MP_FOUR)) |
407 | return ("cofactor out of range"); |
408 | |
409 | /* --- Check %$h = \lfloor (\sqrt{p} + 1)^2/r \rlfoor$% --- * |
410 | * |
411 | * This seems to work with the approximate-sqrt in the library, but might |
412 | * not be so good in some cases. Throw in some extra significate figures |
413 | * for good measure. |
414 | */ |
415 | |
416 | x = mp_lsl(MP_NEW, f->m, 128); |
417 | x = mp_sqrt(x, x); |
418 | y = mp_lsl(MP_NEW, MP_ONE, 64); |
419 | x = mp_add(x, x, y); |
420 | x = mp_sqr(x, x); |
421 | mp_div(&x, 0, x, ei->r); |
422 | x = mp_lsr(x, x, 128); |
423 | rc = MP_EQ(x, ei->h); |
424 | MP_DROP(x); |
425 | MP_DROP(y); |
426 | if (!rc) return ("incorrect cofactor"); |
427 | |
428 | /* --- Check %$n G = O$% --- */ |
429 | |
430 | EC_CREATE(&p); |
431 | ec_mul(c, &p, &ei->g, ei->r); |
432 | rc = EC_ATINF(&p); |
433 | EC_DESTROY(&p); |
434 | if (!rc) return ("incorrect group order"); |
435 | |
436 | /* --- Check that %$p^B \not\equiv 1 \pmod{r}$% for %$1 \le B < 20$% --- * |
437 | * |
438 | * The spec says %$q$%, not %$p$%, but I think that's a misprint. |
439 | */ |
440 | |
441 | x = MP_NEW; |
442 | mp_div(0, &x, f->m, ei->r); |
443 | i = 20; |
444 | while (i) { |
445 | if (MP_EQ(x, MP_ONE)) break; |
446 | x = mp_mul(x, x, f->m); |
447 | mp_div(0, &x, x, ei->r); |
448 | i--; |
449 | } |
450 | MP_DROP(x); |
451 | if (i) return ("curve is weak"); |
452 | |
453 | /* --- Done --- */ |
454 | |
455 | return (0); |
456 | } |
457 | |
458 | static const char *bincheck(const ec_info *ei, grand *gr) |
459 | { |
460 | ec_curve *c = ei->c; |
461 | field *f = c->f; |
462 | int i; |
463 | mp *x, *y; |
464 | ec p; |
465 | int rc; |
466 | |
467 | /* --- Check that %$p$% is irreducible --- */ |
468 | |
469 | if (!gf_irreduciblep(f->m)) return ("p not irreducible"); |
470 | |
471 | /* --- Check that %$a, b, G_x, G_y$% have degree less than %$p$% --- */ |
472 | |
473 | if (mp_bits(c->a) > f->nbits) return ("a out of range"); |
474 | if (mp_bits(c->b) > f->nbits) return ("a out of range"); |
475 | if (mp_bits(ei->g.x) > f->nbits) return ("G_x out of range"); |
476 | if (mp_bits(ei->g.y) > f->nbits) return ("G_y out of range"); |
477 | |
478 | /* --- Check that %$b \ne 0$% --- */ |
479 | |
480 | if (F_ZEROP(f, c->b)) return ("b is zero"); |
481 | |
482 | /* --- Check that %$G \in E$% --- */ |
483 | |
484 | if (EC_ATINF(&ei->g)) return ("generator at infinity"); |
485 | if (ec_check(c, &ei->g)) return ("generator not on curve"); |
486 | |
487 | /* --- Check %$r$% is prime --- */ |
488 | |
489 | if (!primep(ei->r, gr)) return ("generator order not prime"); |
490 | |
491 | /* --- Check %$0 < h \le 4$% --- */ |
492 | |
493 | if (MP_CMP(ei->h, <, MP_ONE) || MP_CMP(ei->h, >, MP_FOUR)) |
494 | return ("cofactor out of range"); |
495 | |
496 | /* --- Check %$h = \lfloor (\sqrt{2^m} + 1)^2/r \rlfoor$% --- * |
497 | * |
498 | * This seems to work with the approximate-sqrt in the library, but might |
499 | * not be so good in some cases. Throw in some extra significate figures |
500 | * for good measure. |
501 | */ |
502 | |
503 | x = mp_lsl(MP_NEW, MP_ONE, f->nbits + 128); |
504 | x = mp_sqrt(x, x); |
505 | y = mp_lsl(MP_NEW, MP_ONE, 64); |
506 | x = mp_add(x, x, y); |
507 | x = mp_sqr(x, x); |
508 | mp_div(&x, 0, x, ei->r); |
509 | x = mp_lsr(x, x, 128); |
510 | rc = MP_EQ(x, ei->h); |
511 | MP_DROP(x); |
512 | MP_DROP(y); |
513 | if (!rc) return ("incorrect cofactor"); |
514 | |
515 | /* --- Check %$n G = O$% --- */ |
516 | |
517 | EC_CREATE(&p); |
518 | ec_mul(c, &p, &ei->g, ei->r); |
519 | rc = EC_ATINF(&p); |
520 | EC_DESTROY(&p); |
521 | if (!rc) return ("incorrect group order"); |
522 | |
523 | /* --- Check %$2^{m B} \not\equiv 1 \pmod{r}$% for %$1 \le B < 20$% --- */ |
524 | |
525 | x = mp_lsl(MP_NEW, MP_ONE, f->nbits); |
526 | mp_div(0, &x, x, ei->r); |
527 | i = 20; |
528 | while (i) { |
529 | if (MP_EQ(x, MP_ONE)) break; |
530 | x = mp_mul(x, x, f->m); |
531 | mp_div(0, &x, x, ei->r); |
532 | i--; |
533 | } |
534 | MP_DROP(x); |
535 | if (i) return ("curve is weak"); |
536 | |
537 | /* --- Done --- */ |
538 | |
539 | return (0); |
540 | } |
541 | |
542 | const char *ec_checkinfo(const ec_info *ei, grand *gr) |
543 | { |
544 | switch (F_TYPE(ei->c->f)) { |
545 | case FTY_PRIME: return (primecheck(ei, gr)); break; |
546 | case FTY_BINARY: return (bincheck(ei, gr)); break; |
547 | } |
548 | return ("unknown curve type"); |
549 | } |
550 | |
551 | /*----- Test rig ----------------------------------------------------------*/ |
552 | |
553 | #ifdef TEST_RIG |
554 | |
555 | #include "fibrand.h" |
556 | |
557 | int main(void) |
558 | { |
559 | const ecentry *ee; |
560 | const char *e; |
561 | int ok = 1; |
562 | grand *gr; |
563 | |
564 | gr = fibrand_create(0); |
565 | fputs("checking standard curves: ", stdout); |
566 | for (ee = ectab; ee->name; ee++) { |
567 | ec_info ei; |
568 | getinfo(&ei, ee->data); |
569 | e = ec_checkinfo(&ei, gr); |
570 | ec_freeinfo(&ei); |
571 | if (e) { |
572 | fprintf(stderr, "\n*** curve %s fails: %s\n", ee->name, e); |
573 | ok = 0; |
574 | } |
575 | putchar('.'); |
576 | fflush(stdout); |
577 | } |
578 | gr->ops->destroy(gr); |
579 | fputs(ok ? " ok\n" : " failed\n", stdout); |
580 | return (!ok); |
581 | } |
582 | |
583 | #endif |
584 | |
585 | /*----- That's all, folks -------------------------------------------------*/ |