432c4e18 |
1 | /* -*-c-*- |
2 | * |
5c3f75ec |
3 | * $Id: ec-info.c,v 1.7 2004/04/17 09:58:37 mdw Exp $ |
432c4e18 |
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 | |
432c4e18 |
30 | /*----- Header files ------------------------------------------------------*/ |
31 | |
32 | #include "ec.h" |
33 | #include "ectab.h" |
34 | #include "gf.h" |
35 | #include "pgen.h" |
36 | #include "mprand.h" |
37 | #include "rabin.h" |
38 | |
39 | /*----- Main code ---------------------------------------------------------*/ |
40 | |
41 | /* --- @ec_curveparse@ --- * |
42 | * |
43 | * Arguments: @qd_parse *qd@ = parser context |
44 | * |
45 | * Returns: Elliptic curve pointer if OK, or null. |
46 | * |
47 | * Use: Parses an elliptic curve description, which has the form |
48 | * |
49 | * * a field description |
50 | * * an optional `/' |
51 | * * `prime', `primeproj', `bin', or `binproj' |
52 | * * an optional `:' |
53 | * * the %$a$% parameter |
54 | * * an optional `,' |
55 | * * the %$b$% parameter |
56 | */ |
57 | |
58 | ec_curve *ec_curveparse(qd_parse *qd) |
59 | { |
60 | mp *a = MP_NEW, *b = MP_NEW; |
61 | ec_curve *c; |
62 | field *f; |
63 | |
64 | if ((f = field_parse(qd)) == 0) goto fail; |
65 | qd_delim(qd, '/'); |
66 | switch (qd_enum(qd, "prime,primeproj,bin,binproj")) { |
67 | case 0: |
68 | if (F_TYPE(f) != FTY_PRIME) { |
69 | qd->e = "field not prime"; |
70 | goto fail; |
71 | } |
72 | qd_delim(qd, ':'); |
73 | if ((a = qd_getmp(qd)) == 0) goto fail; |
74 | qd_delim(qd, ','); |
75 | if ((b = qd_getmp(qd)) == 0) goto fail; |
76 | c = ec_prime(f, a, b); |
77 | break; |
78 | case 1: |
79 | if (F_TYPE(f) != FTY_PRIME) { |
80 | qd->e = "field not prime"; |
81 | goto fail; |
82 | } |
83 | qd_delim(qd, ':'); |
84 | if ((a = qd_getmp(qd)) == 0) goto fail; |
85 | qd_delim(qd, ','); |
86 | if ((b = qd_getmp(qd)) == 0) goto fail; |
87 | c = ec_primeproj(f, a, b); |
88 | break; |
89 | case 2: |
90 | if (F_TYPE(f) != FTY_BINARY) { |
91 | qd->e = "field not binary"; |
92 | goto fail; |
93 | } |
94 | qd_delim(qd, ':'); |
95 | if ((a = qd_getmp(qd)) == 0) goto fail; |
96 | qd_delim(qd, ','); |
97 | if ((b = qd_getmp(qd)) == 0) goto fail; |
98 | c = ec_bin(f, a, b); |
99 | break; |
100 | case 3: |
101 | if (F_TYPE(f) != FTY_BINARY) { |
102 | qd->e = "field not binary"; |
103 | goto fail; |
104 | } |
105 | qd_delim(qd, ':'); |
106 | if ((a = qd_getmp(qd)) == 0) goto fail; |
107 | qd_delim(qd, ','); |
108 | if ((b = qd_getmp(qd)) == 0) goto fail; |
109 | c = ec_binproj(f, a, b); |
110 | break; |
111 | default: |
112 | goto fail; |
113 | } |
02d7884d |
114 | if (!c) { |
115 | qd->e = "bad curve parameters"; |
116 | goto fail; |
117 | } |
432c4e18 |
118 | if (a) MP_DROP(a); |
119 | if (b) MP_DROP(b); |
120 | return (c); |
121 | |
122 | fail: |
123 | if (f) F_DESTROY(f); |
124 | if (a) MP_DROP(a); |
125 | if (b) MP_DROP(b); |
126 | return (0); |
127 | } |
128 | |
129 | /* --- @ec_ptparse@ --- * |
130 | * |
131 | * Arguments: @qd_parse *qd@ = parser context |
132 | * @ec *p@ = where to put the point |
133 | * |
134 | * Returns: The point address, or null. |
135 | * |
136 | * Use: Parses an elliptic curve point. This has the form |
137 | * |
138 | * * %$x$%-coordinate |
139 | * * optional `,' |
140 | * * %$y$%-coordinate |
141 | */ |
142 | |
143 | ec *ec_ptparse(qd_parse *qd, ec *p) |
144 | { |
145 | mp *x = MP_NEW, *y = MP_NEW; |
146 | |
147 | if (qd_enum(qd, "inf") >= 0) { |
148 | EC_SETINF(p); |
149 | return (p); |
150 | } |
151 | if ((x = qd_getmp(qd)) == 0) goto fail; |
152 | qd_delim(qd, ','); |
153 | if ((y = qd_getmp(qd)) == 0) goto fail; |
154 | EC_DESTROY(p); |
155 | p->x = x; |
156 | p->y = y; |
157 | p->z = 0; |
158 | return (p); |
159 | |
160 | fail: |
161 | if (x) MP_DROP(x); |
162 | if (y) MP_DROP(y); |
163 | return (0); |
164 | } |
165 | |
34e4f738 |
166 | /* --- @getinfo@ --- * |
167 | * |
168 | * Arguments: @ec_info *ei@ = where to write the information |
169 | * @ecdata *ed@ = raw data |
170 | * |
171 | * Returns: --- |
172 | * |
173 | * Use: Loads elliptic curve information about one of the standard |
174 | * curves. |
175 | */ |
176 | |
177 | static void getinfo(ec_info *ei, ecdata *ed) |
178 | { |
179 | field *f; |
180 | |
181 | switch (ed->ftag) { |
182 | case FTAG_PRIME: |
183 | f = field_prime(&ed->p); |
184 | ei->c = ec_primeproj(f, &ed->a, &ed->b); |
185 | break; |
186 | case FTAG_NICEPRIME: |
187 | f = field_niceprime(&ed->p); |
188 | ei->c = ec_primeproj(f, &ed->a, &ed->b); |
189 | break; |
190 | case FTAG_BINPOLY: |
191 | f = field_binpoly(&ed->p); |
192 | ei->c = ec_binproj(f, &ed->a, &ed->b); |
193 | break; |
4edc47b8 |
194 | case FTAG_BINNORM: |
195 | f = field_binnorm(&ed->p, &ed->beta); |
196 | ei->c = ec_binproj(f, &ed->a, &ed->b); |
197 | break; |
34e4f738 |
198 | default: |
199 | abort(); |
200 | } |
201 | |
02d7884d |
202 | assert(f); assert(ei->c); |
34e4f738 |
203 | EC_CREATE(&ei->g); ei->g.x = &ed->gx; ei->g.y = &ed->gy; ei->g.z = 0; |
204 | ei->r = &ed->r; ei->h = &ed->h; |
205 | } |
206 | |
432c4e18 |
207 | /* --- @ec_infoparse@ --- * |
208 | * |
209 | * Arguments: @qd_parse *qd@ = parser context |
210 | * @ec_info *ei@ = curve information block, currently |
211 | * uninitialized |
212 | * |
213 | * Returns: Zero on success, nonzero on failure. |
214 | * |
215 | * Use: Parses an elliptic curve information string, and stores the |
34e4f738 |
216 | * information in @ei@. This is either the name of a standard |
217 | * curve, or it has the form |
432c4e18 |
218 | * |
219 | * * elliptic curve description |
220 | * * optional `/' |
221 | * * common point |
222 | * * optional `:' |
223 | * * group order |
224 | * * optional `*' |
225 | * * cofactor |
226 | */ |
227 | |
228 | int ec_infoparse(qd_parse *qd, ec_info *ei) |
229 | { |
230 | ec_curve *c = 0; |
231 | field *f; |
232 | ec g = EC_INIT; |
34e4f738 |
233 | const ecentry *ee; |
432c4e18 |
234 | mp *r = MP_NEW, *h = MP_NEW; |
235 | |
02d7884d |
236 | for (ee = ectab; ee->name; ee++) |
237 | if (qd_enum(qd, ee->name) >= 0) { getinfo(ei, ee->data); goto found; } |
238 | |
432c4e18 |
239 | if ((c = ec_curveparse(qd)) == 0) goto fail; |
240 | qd_delim(qd, '/'); if (!ec_ptparse(qd, &g)) goto fail; |
241 | qd_delim(qd, ':'); if ((r = qd_getmp(qd)) == 0) goto fail; |
242 | qd_delim(qd, '*'); if ((h = qd_getmp(qd)) == 0) goto fail; |
432c4e18 |
243 | ei->c = c; ei->g = g; ei->r = r; ei->h = h; |
34e4f738 |
244 | |
245 | found: |
432c4e18 |
246 | return (0); |
247 | |
248 | fail: |
249 | EC_DESTROY(&g); |
250 | if (r) MP_DROP(r); |
251 | if (h) MP_DROP(h); |
252 | if (c) { f = c->f; ec_destroycurve(c); F_DESTROY(f); } |
253 | return (-1); |
254 | } |
255 | |
432c4e18 |
256 | /* --- @ec_getinfo@ --- * |
257 | * |
258 | * Arguments: @ec_info *ei@ = where to write the information |
259 | * @const char *p@ = string describing a curve |
260 | * |
261 | * Returns: Null on success, or a pointer to an error message. |
262 | * |
263 | * Use: Parses out information about a curve. The string is either a |
264 | * standard curve name, or a curve info string. |
265 | */ |
266 | |
267 | const char *ec_getinfo(ec_info *ei, const char *p) |
268 | { |
269 | qd_parse qd; |
432c4e18 |
270 | |
271 | qd.p = p; |
272 | qd.e = 0; |
432c4e18 |
273 | if (ec_infoparse(&qd, ei)) |
274 | return (qd.e); |
432c4e18 |
275 | if (!qd_eofp(&qd)) { |
276 | ec_freeinfo(ei); |
277 | return ("junk found at end of string"); |
278 | } |
279 | return (0); |
280 | } |
281 | |
34e4f738 |
282 | /* --- @ec_sameinfop@ --- * |
283 | * |
284 | * Arguments: @ec_info *ei, *ej@ = two elliptic curve parameter sets |
285 | * |
286 | * Returns: Nonzero if the curves are identical (not just isomorphic). |
287 | * |
288 | * Use: Checks for sameness of curve parameters. |
289 | */ |
290 | |
291 | int ec_sameinfop(ec_info *ei, ec_info *ej) |
292 | { |
293 | return (ec_samep(ei->c, ej->c) && |
294 | MP_EQ(ei->r, ej->r) && MP_EQ(ei->h, ej->h) && |
295 | EC_EQ(&ei->g, &ej->g)); |
296 | } |
297 | |
432c4e18 |
298 | /* --- @ec_freeinfo@ --- * |
299 | * |
300 | * Arguments: @ec_info *ei@ = elliptic curve information block to free |
301 | * |
302 | * Returns: --- |
303 | * |
304 | * Use: Frees the information block. |
305 | */ |
306 | |
307 | void ec_freeinfo(ec_info *ei) |
308 | { |
309 | field *f; |
310 | |
311 | EC_DESTROY(&ei->g); |
312 | MP_DROP(ei->r); |
313 | MP_DROP(ei->h); |
314 | f = ei->c->f; ec_destroycurve(ei->c); F_DESTROY(f); |
315 | } |
316 | |
317 | /* --- @ec_checkinfo@ --- * |
318 | * |
319 | * Arguments: @const ec_info *ei@ = elliptic curve information block |
320 | * |
321 | * Returns: Null if OK, or pointer to error message. |
322 | * |
323 | * Use: Checks an elliptic curve according to the rules in SEC1. |
324 | */ |
325 | |
432c4e18 |
326 | static int primeeltp(mp *x, field *f) |
327 | { |
328 | return (!MP_ISNEG(x) && MP_CMP(x, <, f->m)); |
329 | } |
330 | |
331 | static const char *primecheck(const ec_info *ei, grand *gr) |
332 | { |
333 | ec_curve *c = ei->c; |
334 | field *f = c->f; |
335 | int i; |
336 | mp *x, *y; |
337 | ec p; |
338 | int rc; |
339 | |
340 | /* --- Check %$p$% is an odd prime --- */ |
341 | |
34e4f738 |
342 | if (!pgen_primep(f->m, gr)) return ("p not prime"); |
432c4e18 |
343 | |
344 | /* --- Check %$a$%, %$b$%, %$G_x$% and %$G_y$% are in %$[0, p)$% --- */ |
345 | |
346 | if (!primeeltp(c->a, f)) return ("a out of range"); |
347 | if (!primeeltp(c->b, f)) return ("b out of range"); |
348 | if (!primeeltp(ei->g.x, f)) return ("G_x out of range"); |
349 | if (!primeeltp(ei->g.x, f)) return ("G_y out of range"); |
350 | |
351 | /* --- Check %$4 a^3 + 27 b^2 \not\equiv 0 \pmod{p}$% --- */ |
352 | |
353 | x = F_SQR(f, MP_NEW, c->a); |
354 | x = F_MUL(f, x, x, c->a); |
355 | x = F_QDL(f, x, x); |
356 | y = F_SQR(f, MP_NEW, c->b); |
357 | y = F_TPL(f, y, y); |
358 | y = F_TPL(f, y, y); |
359 | y = F_TPL(f, y, y); |
360 | x = F_ADD(f, x, x, y); |
361 | rc = F_ZEROP(f, x); |
362 | MP_DROP(x); |
363 | MP_DROP(y); |
364 | if (rc) return ("not an elliptic curve"); |
365 | |
366 | /* --- Check %$G \in E$% --- */ |
367 | |
368 | if (EC_ATINF(&ei->g)) return ("generator at infinity"); |
369 | if (ec_check(c, &ei->g)) return ("generator not on curve"); |
370 | |
371 | /* --- Check %$r$% is prime --- */ |
372 | |
34e4f738 |
373 | if (!pgen_primep(ei->r, gr)) return ("generator order not prime"); |
432c4e18 |
374 | |
432c4e18 |
375 | /* --- Check %$h = \lfloor (\sqrt{p} + 1)^2/r \rlfoor$% --- * |
376 | * |
377 | * This seems to work with the approximate-sqrt in the library, but might |
378 | * not be so good in some cases. Throw in some extra significate figures |
379 | * for good measure. |
380 | */ |
381 | |
382 | x = mp_lsl(MP_NEW, f->m, 128); |
383 | x = mp_sqrt(x, x); |
384 | y = mp_lsl(MP_NEW, MP_ONE, 64); |
385 | x = mp_add(x, x, y); |
386 | x = mp_sqr(x, x); |
387 | mp_div(&x, 0, x, ei->r); |
388 | x = mp_lsr(x, x, 128); |
389 | rc = MP_EQ(x, ei->h); |
390 | MP_DROP(x); |
391 | MP_DROP(y); |
392 | if (!rc) return ("incorrect cofactor"); |
393 | |
394 | /* --- Check %$n G = O$% --- */ |
395 | |
396 | EC_CREATE(&p); |
397 | ec_mul(c, &p, &ei->g, ei->r); |
398 | rc = EC_ATINF(&p); |
399 | EC_DESTROY(&p); |
400 | if (!rc) return ("incorrect group order"); |
401 | |
402 | /* --- Check that %$p^B \not\equiv 1 \pmod{r}$% for %$1 \le B < 20$% --- * |
403 | * |
404 | * The spec says %$q$%, not %$p$%, but I think that's a misprint. |
405 | */ |
406 | |
407 | x = MP_NEW; |
408 | mp_div(0, &x, f->m, ei->r); |
409 | i = 20; |
410 | while (i) { |
411 | if (MP_EQ(x, MP_ONE)) break; |
412 | x = mp_mul(x, x, f->m); |
413 | mp_div(0, &x, x, ei->r); |
414 | i--; |
415 | } |
416 | MP_DROP(x); |
417 | if (i) return ("curve is weak"); |
418 | |
5c3f75ec |
419 | /* --- Check %$0 < h \le 4$% --- */ |
420 | |
421 | if (MP_CMP(ei->h, <, MP_ONE) || MP_CMP(ei->h, >, MP_FOUR)) |
422 | return ("cofactor out of range"); |
423 | |
432c4e18 |
424 | /* --- Done --- */ |
425 | |
426 | return (0); |
427 | } |
428 | |
429 | static const char *bincheck(const ec_info *ei, grand *gr) |
430 | { |
431 | ec_curve *c = ei->c; |
432 | field *f = c->f; |
433 | int i; |
434 | mp *x, *y; |
435 | ec p; |
436 | int rc; |
437 | |
438 | /* --- Check that %$p$% is irreducible --- */ |
439 | |
440 | if (!gf_irreduciblep(f->m)) return ("p not irreducible"); |
441 | |
442 | /* --- Check that %$a, b, G_x, G_y$% have degree less than %$p$% --- */ |
443 | |
444 | if (mp_bits(c->a) > f->nbits) return ("a out of range"); |
445 | if (mp_bits(c->b) > f->nbits) return ("a out of range"); |
446 | if (mp_bits(ei->g.x) > f->nbits) return ("G_x out of range"); |
447 | if (mp_bits(ei->g.y) > f->nbits) return ("G_y out of range"); |
448 | |
449 | /* --- Check that %$b \ne 0$% --- */ |
450 | |
451 | if (F_ZEROP(f, c->b)) return ("b is zero"); |
452 | |
453 | /* --- Check that %$G \in E$% --- */ |
454 | |
455 | if (EC_ATINF(&ei->g)) return ("generator at infinity"); |
456 | if (ec_check(c, &ei->g)) return ("generator not on curve"); |
457 | |
458 | /* --- Check %$r$% is prime --- */ |
459 | |
34e4f738 |
460 | if (!pgen_primep(ei->r, gr)) return ("generator order not prime"); |
432c4e18 |
461 | |
432c4e18 |
462 | /* --- Check %$h = \lfloor (\sqrt{2^m} + 1)^2/r \rlfoor$% --- * |
463 | * |
464 | * This seems to work with the approximate-sqrt in the library, but might |
465 | * not be so good in some cases. Throw in some extra significate figures |
466 | * for good measure. |
467 | */ |
468 | |
469 | x = mp_lsl(MP_NEW, MP_ONE, f->nbits + 128); |
470 | x = mp_sqrt(x, x); |
471 | y = mp_lsl(MP_NEW, MP_ONE, 64); |
472 | x = mp_add(x, x, y); |
473 | x = mp_sqr(x, x); |
474 | mp_div(&x, 0, x, ei->r); |
475 | x = mp_lsr(x, x, 128); |
476 | rc = MP_EQ(x, ei->h); |
477 | MP_DROP(x); |
478 | MP_DROP(y); |
479 | if (!rc) return ("incorrect cofactor"); |
480 | |
481 | /* --- Check %$n G = O$% --- */ |
482 | |
483 | EC_CREATE(&p); |
484 | ec_mul(c, &p, &ei->g, ei->r); |
485 | rc = EC_ATINF(&p); |
486 | EC_DESTROY(&p); |
487 | if (!rc) return ("incorrect group order"); |
488 | |
489 | /* --- Check %$2^{m B} \not\equiv 1 \pmod{r}$% for %$1 \le B < 20$% --- */ |
490 | |
491 | x = mp_lsl(MP_NEW, MP_ONE, f->nbits); |
492 | mp_div(0, &x, x, ei->r); |
493 | i = 20; |
494 | while (i) { |
495 | if (MP_EQ(x, MP_ONE)) break; |
496 | x = mp_mul(x, x, f->m); |
497 | mp_div(0, &x, x, ei->r); |
498 | i--; |
499 | } |
500 | MP_DROP(x); |
501 | if (i) return ("curve is weak"); |
502 | |
5c3f75ec |
503 | /* --- Check %$0 < h \le 4$% --- */ |
504 | |
505 | if (MP_CMP(ei->h, <, MP_ONE) || MP_CMP(ei->h, >, MP_FOUR)) |
506 | return ("cofactor out of range"); |
507 | |
432c4e18 |
508 | /* --- Done --- */ |
509 | |
510 | return (0); |
511 | } |
512 | |
513 | const char *ec_checkinfo(const ec_info *ei, grand *gr) |
514 | { |
515 | switch (F_TYPE(ei->c->f)) { |
516 | case FTY_PRIME: return (primecheck(ei, gr)); break; |
517 | case FTY_BINARY: return (bincheck(ei, gr)); break; |
518 | } |
519 | return ("unknown curve type"); |
520 | } |
521 | |
522 | /*----- Test rig ----------------------------------------------------------*/ |
523 | |
524 | #ifdef TEST_RIG |
525 | |
526 | #include "fibrand.h" |
527 | |
53cbeae3 |
528 | int main(int argc, char *argv[]) |
432c4e18 |
529 | { |
530 | const ecentry *ee; |
531 | const char *e; |
532 | int ok = 1; |
53cbeae3 |
533 | int i; |
432c4e18 |
534 | grand *gr; |
535 | |
536 | gr = fibrand_create(0); |
53cbeae3 |
537 | if (argc > 1) { |
538 | for (i = 1; i < argc; i++) { |
539 | ec_info ei; |
540 | if ((e = ec_getinfo(&ei, argv[i])) != 0) |
541 | fprintf(stderr, "bad curve spec `%s': %s", argv[i], e); |
542 | else { |
543 | e = ec_checkinfo(&ei, gr); |
544 | ec_freeinfo(&ei); |
545 | if (!e) |
546 | printf("OK %s\n", argv[i]); |
547 | else { |
548 | printf("BAD %s: %s\n", argv[i], e); |
549 | ok = 0; |
550 | } |
551 | } |
552 | } |
553 | } else { |
554 | fputs("checking standard curves: ", stdout); |
555 | for (ee = ectab; ee->name; ee++) { |
556 | ec_info ei; |
557 | getinfo(&ei, ee->data); |
558 | e = ec_checkinfo(&ei, gr); |
559 | ec_freeinfo(&ei); |
560 | if (e) { |
561 | fprintf(stderr, "\n*** curve %s fails: %s\n", ee->name, e); |
562 | ok = 0; |
563 | } |
564 | putchar('.'); |
565 | fflush(stdout); |
432c4e18 |
566 | } |
53cbeae3 |
567 | fputs(ok ? " ok\n" : " failed\n", stdout); |
432c4e18 |
568 | } |
569 | gr->ops->destroy(gr); |
432c4e18 |
570 | return (!ok); |
571 | } |
572 | |
573 | #endif |
574 | |
575 | /*----- That's all, folks -------------------------------------------------*/ |