432c4e18 |
1 | /* -*-c-*- |
2 | * |
02d7884d |
3 | * $Id: ec-info.c,v 1.4 2004/04/03 03:32:05 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 | |
30 | /*----- Revision history --------------------------------------------------* |
31 | * |
32 | * $Log: ec-info.c,v $ |
02d7884d |
33 | * Revision 1.4 2004/04/03 03:32:05 mdw |
34 | * General robustification. |
35 | * |
4edc47b8 |
36 | * Revision 1.3 2004/04/01 21:28:41 mdw |
37 | * Normal basis support (translates to poly basis internally). Rewrite |
38 | * EC and prime group table generators in awk, so that they can reuse data |
39 | * for repeated constants. |
40 | * |
34e4f738 |
41 | * Revision 1.2 2004/04/01 12:50:09 mdw |
42 | * Add cyclic group abstraction, with test code. Separate off exponentation |
43 | * functions for better static linking. Fix a buttload of bugs on the way. |
44 | * Generally ensure that negative exponents do inversion correctly. Add |
45 | * table of standard prime-field subgroups. (Binary field subgroups are |
46 | * currently unimplemented but easy to add if anyone ever finds a good one.) |
47 | * |
432c4e18 |
48 | * Revision 1.1 2004/03/27 17:54:11 mdw |
49 | * Standard curves and curve checking. |
50 | * |
51 | */ |
52 | |
53 | /*----- Header files ------------------------------------------------------*/ |
54 | |
55 | #include "ec.h" |
56 | #include "ectab.h" |
57 | #include "gf.h" |
58 | #include "pgen.h" |
59 | #include "mprand.h" |
60 | #include "rabin.h" |
61 | |
62 | /*----- Main code ---------------------------------------------------------*/ |
63 | |
64 | /* --- @ec_curveparse@ --- * |
65 | * |
66 | * Arguments: @qd_parse *qd@ = parser context |
67 | * |
68 | * Returns: Elliptic curve pointer if OK, or null. |
69 | * |
70 | * Use: Parses an elliptic curve description, which has the form |
71 | * |
72 | * * a field description |
73 | * * an optional `/' |
74 | * * `prime', `primeproj', `bin', or `binproj' |
75 | * * an optional `:' |
76 | * * the %$a$% parameter |
77 | * * an optional `,' |
78 | * * the %$b$% parameter |
79 | */ |
80 | |
81 | ec_curve *ec_curveparse(qd_parse *qd) |
82 | { |
83 | mp *a = MP_NEW, *b = MP_NEW; |
84 | ec_curve *c; |
85 | field *f; |
86 | |
87 | if ((f = field_parse(qd)) == 0) goto fail; |
88 | qd_delim(qd, '/'); |
89 | switch (qd_enum(qd, "prime,primeproj,bin,binproj")) { |
90 | case 0: |
91 | if (F_TYPE(f) != FTY_PRIME) { |
92 | qd->e = "field not prime"; |
93 | goto fail; |
94 | } |
95 | qd_delim(qd, ':'); |
96 | if ((a = qd_getmp(qd)) == 0) goto fail; |
97 | qd_delim(qd, ','); |
98 | if ((b = qd_getmp(qd)) == 0) goto fail; |
99 | c = ec_prime(f, a, b); |
100 | break; |
101 | case 1: |
102 | if (F_TYPE(f) != FTY_PRIME) { |
103 | qd->e = "field not prime"; |
104 | goto fail; |
105 | } |
106 | qd_delim(qd, ':'); |
107 | if ((a = qd_getmp(qd)) == 0) goto fail; |
108 | qd_delim(qd, ','); |
109 | if ((b = qd_getmp(qd)) == 0) goto fail; |
110 | c = ec_primeproj(f, a, b); |
111 | break; |
112 | case 2: |
113 | if (F_TYPE(f) != FTY_BINARY) { |
114 | qd->e = "field not binary"; |
115 | goto fail; |
116 | } |
117 | qd_delim(qd, ':'); |
118 | if ((a = qd_getmp(qd)) == 0) goto fail; |
119 | qd_delim(qd, ','); |
120 | if ((b = qd_getmp(qd)) == 0) goto fail; |
121 | c = ec_bin(f, a, b); |
122 | break; |
123 | case 3: |
124 | if (F_TYPE(f) != FTY_BINARY) { |
125 | qd->e = "field not binary"; |
126 | goto fail; |
127 | } |
128 | qd_delim(qd, ':'); |
129 | if ((a = qd_getmp(qd)) == 0) goto fail; |
130 | qd_delim(qd, ','); |
131 | if ((b = qd_getmp(qd)) == 0) goto fail; |
132 | c = ec_binproj(f, a, b); |
133 | break; |
134 | default: |
135 | goto fail; |
136 | } |
02d7884d |
137 | if (!c) { |
138 | qd->e = "bad curve parameters"; |
139 | goto fail; |
140 | } |
432c4e18 |
141 | if (a) MP_DROP(a); |
142 | if (b) MP_DROP(b); |
143 | return (c); |
144 | |
145 | fail: |
146 | if (f) F_DESTROY(f); |
147 | if (a) MP_DROP(a); |
148 | if (b) MP_DROP(b); |
149 | return (0); |
150 | } |
151 | |
152 | /* --- @ec_ptparse@ --- * |
153 | * |
154 | * Arguments: @qd_parse *qd@ = parser context |
155 | * @ec *p@ = where to put the point |
156 | * |
157 | * Returns: The point address, or null. |
158 | * |
159 | * Use: Parses an elliptic curve point. This has the form |
160 | * |
161 | * * %$x$%-coordinate |
162 | * * optional `,' |
163 | * * %$y$%-coordinate |
164 | */ |
165 | |
166 | ec *ec_ptparse(qd_parse *qd, ec *p) |
167 | { |
168 | mp *x = MP_NEW, *y = MP_NEW; |
169 | |
170 | if (qd_enum(qd, "inf") >= 0) { |
171 | EC_SETINF(p); |
172 | return (p); |
173 | } |
174 | if ((x = qd_getmp(qd)) == 0) goto fail; |
175 | qd_delim(qd, ','); |
176 | if ((y = qd_getmp(qd)) == 0) goto fail; |
177 | EC_DESTROY(p); |
178 | p->x = x; |
179 | p->y = y; |
180 | p->z = 0; |
181 | return (p); |
182 | |
183 | fail: |
184 | if (x) MP_DROP(x); |
185 | if (y) MP_DROP(y); |
186 | return (0); |
187 | } |
188 | |
34e4f738 |
189 | /* --- @getinfo@ --- * |
190 | * |
191 | * Arguments: @ec_info *ei@ = where to write the information |
192 | * @ecdata *ed@ = raw data |
193 | * |
194 | * Returns: --- |
195 | * |
196 | * Use: Loads elliptic curve information about one of the standard |
197 | * curves. |
198 | */ |
199 | |
200 | static void getinfo(ec_info *ei, ecdata *ed) |
201 | { |
202 | field *f; |
203 | |
204 | switch (ed->ftag) { |
205 | case FTAG_PRIME: |
206 | f = field_prime(&ed->p); |
207 | ei->c = ec_primeproj(f, &ed->a, &ed->b); |
208 | break; |
209 | case FTAG_NICEPRIME: |
210 | f = field_niceprime(&ed->p); |
211 | ei->c = ec_primeproj(f, &ed->a, &ed->b); |
212 | break; |
213 | case FTAG_BINPOLY: |
214 | f = field_binpoly(&ed->p); |
215 | ei->c = ec_binproj(f, &ed->a, &ed->b); |
216 | break; |
4edc47b8 |
217 | case FTAG_BINNORM: |
218 | f = field_binnorm(&ed->p, &ed->beta); |
219 | ei->c = ec_binproj(f, &ed->a, &ed->b); |
220 | break; |
34e4f738 |
221 | default: |
222 | abort(); |
223 | } |
224 | |
02d7884d |
225 | assert(f); assert(ei->c); |
34e4f738 |
226 | EC_CREATE(&ei->g); ei->g.x = &ed->gx; ei->g.y = &ed->gy; ei->g.z = 0; |
227 | ei->r = &ed->r; ei->h = &ed->h; |
228 | } |
229 | |
432c4e18 |
230 | /* --- @ec_infoparse@ --- * |
231 | * |
232 | * Arguments: @qd_parse *qd@ = parser context |
233 | * @ec_info *ei@ = curve information block, currently |
234 | * uninitialized |
235 | * |
236 | * Returns: Zero on success, nonzero on failure. |
237 | * |
238 | * Use: Parses an elliptic curve information string, and stores the |
34e4f738 |
239 | * information in @ei@. This is either the name of a standard |
240 | * curve, or it has the form |
432c4e18 |
241 | * |
242 | * * elliptic curve description |
243 | * * optional `/' |
244 | * * common point |
245 | * * optional `:' |
246 | * * group order |
247 | * * optional `*' |
248 | * * cofactor |
249 | */ |
250 | |
251 | int ec_infoparse(qd_parse *qd, ec_info *ei) |
252 | { |
253 | ec_curve *c = 0; |
254 | field *f; |
255 | ec g = EC_INIT; |
34e4f738 |
256 | const ecentry *ee; |
432c4e18 |
257 | mp *r = MP_NEW, *h = MP_NEW; |
258 | |
02d7884d |
259 | for (ee = ectab; ee->name; ee++) |
260 | if (qd_enum(qd, ee->name) >= 0) { getinfo(ei, ee->data); goto found; } |
261 | |
432c4e18 |
262 | if ((c = ec_curveparse(qd)) == 0) goto fail; |
263 | qd_delim(qd, '/'); if (!ec_ptparse(qd, &g)) goto fail; |
264 | qd_delim(qd, ':'); if ((r = qd_getmp(qd)) == 0) goto fail; |
265 | qd_delim(qd, '*'); if ((h = qd_getmp(qd)) == 0) goto fail; |
432c4e18 |
266 | ei->c = c; ei->g = g; ei->r = r; ei->h = h; |
34e4f738 |
267 | |
268 | found: |
432c4e18 |
269 | return (0); |
270 | |
271 | fail: |
272 | EC_DESTROY(&g); |
273 | if (r) MP_DROP(r); |
274 | if (h) MP_DROP(h); |
275 | if (c) { f = c->f; ec_destroycurve(c); F_DESTROY(f); } |
276 | return (-1); |
277 | } |
278 | |
432c4e18 |
279 | /* --- @ec_getinfo@ --- * |
280 | * |
281 | * Arguments: @ec_info *ei@ = where to write the information |
282 | * @const char *p@ = string describing a curve |
283 | * |
284 | * Returns: Null on success, or a pointer to an error message. |
285 | * |
286 | * Use: Parses out information about a curve. The string is either a |
287 | * standard curve name, or a curve info string. |
288 | */ |
289 | |
290 | const char *ec_getinfo(ec_info *ei, const char *p) |
291 | { |
292 | qd_parse qd; |
432c4e18 |
293 | |
294 | qd.p = p; |
295 | qd.e = 0; |
432c4e18 |
296 | if (ec_infoparse(&qd, ei)) |
297 | return (qd.e); |
432c4e18 |
298 | if (!qd_eofp(&qd)) { |
299 | ec_freeinfo(ei); |
300 | return ("junk found at end of string"); |
301 | } |
302 | return (0); |
303 | } |
304 | |
34e4f738 |
305 | /* --- @ec_sameinfop@ --- * |
306 | * |
307 | * Arguments: @ec_info *ei, *ej@ = two elliptic curve parameter sets |
308 | * |
309 | * Returns: Nonzero if the curves are identical (not just isomorphic). |
310 | * |
311 | * Use: Checks for sameness of curve parameters. |
312 | */ |
313 | |
314 | int ec_sameinfop(ec_info *ei, ec_info *ej) |
315 | { |
316 | return (ec_samep(ei->c, ej->c) && |
317 | MP_EQ(ei->r, ej->r) && MP_EQ(ei->h, ej->h) && |
318 | EC_EQ(&ei->g, &ej->g)); |
319 | } |
320 | |
432c4e18 |
321 | /* --- @ec_freeinfo@ --- * |
322 | * |
323 | * Arguments: @ec_info *ei@ = elliptic curve information block to free |
324 | * |
325 | * Returns: --- |
326 | * |
327 | * Use: Frees the information block. |
328 | */ |
329 | |
330 | void ec_freeinfo(ec_info *ei) |
331 | { |
332 | field *f; |
333 | |
334 | EC_DESTROY(&ei->g); |
335 | MP_DROP(ei->r); |
336 | MP_DROP(ei->h); |
337 | f = ei->c->f; ec_destroycurve(ei->c); F_DESTROY(f); |
338 | } |
339 | |
340 | /* --- @ec_checkinfo@ --- * |
341 | * |
342 | * Arguments: @const ec_info *ei@ = elliptic curve information block |
343 | * |
344 | * Returns: Null if OK, or pointer to error message. |
345 | * |
346 | * Use: Checks an elliptic curve according to the rules in SEC1. |
347 | */ |
348 | |
432c4e18 |
349 | static int primeeltp(mp *x, field *f) |
350 | { |
351 | return (!MP_ISNEG(x) && MP_CMP(x, <, f->m)); |
352 | } |
353 | |
354 | static const char *primecheck(const ec_info *ei, grand *gr) |
355 | { |
356 | ec_curve *c = ei->c; |
357 | field *f = c->f; |
358 | int i; |
359 | mp *x, *y; |
360 | ec p; |
361 | int rc; |
362 | |
363 | /* --- Check %$p$% is an odd prime --- */ |
364 | |
34e4f738 |
365 | if (!pgen_primep(f->m, gr)) return ("p not prime"); |
432c4e18 |
366 | |
367 | /* --- Check %$a$%, %$b$%, %$G_x$% and %$G_y$% are in %$[0, p)$% --- */ |
368 | |
369 | if (!primeeltp(c->a, f)) return ("a out of range"); |
370 | if (!primeeltp(c->b, f)) return ("b out of range"); |
371 | if (!primeeltp(ei->g.x, f)) return ("G_x out of range"); |
372 | if (!primeeltp(ei->g.x, f)) return ("G_y out of range"); |
373 | |
374 | /* --- Check %$4 a^3 + 27 b^2 \not\equiv 0 \pmod{p}$% --- */ |
375 | |
376 | x = F_SQR(f, MP_NEW, c->a); |
377 | x = F_MUL(f, x, x, c->a); |
378 | x = F_QDL(f, x, x); |
379 | y = F_SQR(f, MP_NEW, c->b); |
380 | y = F_TPL(f, y, y); |
381 | y = F_TPL(f, y, y); |
382 | y = F_TPL(f, y, y); |
383 | x = F_ADD(f, x, x, y); |
384 | rc = F_ZEROP(f, x); |
385 | MP_DROP(x); |
386 | MP_DROP(y); |
387 | if (rc) return ("not an elliptic curve"); |
388 | |
389 | /* --- Check %$G \in E$% --- */ |
390 | |
391 | if (EC_ATINF(&ei->g)) return ("generator at infinity"); |
392 | if (ec_check(c, &ei->g)) return ("generator not on curve"); |
393 | |
394 | /* --- Check %$r$% is prime --- */ |
395 | |
34e4f738 |
396 | if (!pgen_primep(ei->r, gr)) return ("generator order not prime"); |
432c4e18 |
397 | |
398 | /* --- Check %$0 < h \le 4$% --- */ |
399 | |
400 | if (MP_CMP(ei->h, <, MP_ONE) || MP_CMP(ei->h, >, MP_FOUR)) |
401 | return ("cofactor out of range"); |
402 | |
403 | /* --- Check %$h = \lfloor (\sqrt{p} + 1)^2/r \rlfoor$% --- * |
404 | * |
405 | * This seems to work with the approximate-sqrt in the library, but might |
406 | * not be so good in some cases. Throw in some extra significate figures |
407 | * for good measure. |
408 | */ |
409 | |
410 | x = mp_lsl(MP_NEW, f->m, 128); |
411 | x = mp_sqrt(x, x); |
412 | y = mp_lsl(MP_NEW, MP_ONE, 64); |
413 | x = mp_add(x, x, y); |
414 | x = mp_sqr(x, x); |
415 | mp_div(&x, 0, x, ei->r); |
416 | x = mp_lsr(x, x, 128); |
417 | rc = MP_EQ(x, ei->h); |
418 | MP_DROP(x); |
419 | MP_DROP(y); |
420 | if (!rc) return ("incorrect cofactor"); |
421 | |
422 | /* --- Check %$n G = O$% --- */ |
423 | |
424 | EC_CREATE(&p); |
425 | ec_mul(c, &p, &ei->g, ei->r); |
426 | rc = EC_ATINF(&p); |
427 | EC_DESTROY(&p); |
428 | if (!rc) return ("incorrect group order"); |
429 | |
430 | /* --- Check that %$p^B \not\equiv 1 \pmod{r}$% for %$1 \le B < 20$% --- * |
431 | * |
432 | * The spec says %$q$%, not %$p$%, but I think that's a misprint. |
433 | */ |
434 | |
435 | x = MP_NEW; |
436 | mp_div(0, &x, f->m, ei->r); |
437 | i = 20; |
438 | while (i) { |
439 | if (MP_EQ(x, MP_ONE)) break; |
440 | x = mp_mul(x, x, f->m); |
441 | mp_div(0, &x, x, ei->r); |
442 | i--; |
443 | } |
444 | MP_DROP(x); |
445 | if (i) return ("curve is weak"); |
446 | |
447 | /* --- Done --- */ |
448 | |
449 | return (0); |
450 | } |
451 | |
452 | static const char *bincheck(const ec_info *ei, grand *gr) |
453 | { |
454 | ec_curve *c = ei->c; |
455 | field *f = c->f; |
456 | int i; |
457 | mp *x, *y; |
458 | ec p; |
459 | int rc; |
460 | |
461 | /* --- Check that %$p$% is irreducible --- */ |
462 | |
463 | if (!gf_irreduciblep(f->m)) return ("p not irreducible"); |
464 | |
465 | /* --- Check that %$a, b, G_x, G_y$% have degree less than %$p$% --- */ |
466 | |
467 | if (mp_bits(c->a) > f->nbits) return ("a out of range"); |
468 | if (mp_bits(c->b) > f->nbits) return ("a out of range"); |
469 | if (mp_bits(ei->g.x) > f->nbits) return ("G_x out of range"); |
470 | if (mp_bits(ei->g.y) > f->nbits) return ("G_y out of range"); |
471 | |
472 | /* --- Check that %$b \ne 0$% --- */ |
473 | |
474 | if (F_ZEROP(f, c->b)) return ("b is zero"); |
475 | |
476 | /* --- Check that %$G \in E$% --- */ |
477 | |
478 | if (EC_ATINF(&ei->g)) return ("generator at infinity"); |
479 | if (ec_check(c, &ei->g)) return ("generator not on curve"); |
480 | |
481 | /* --- Check %$r$% is prime --- */ |
482 | |
34e4f738 |
483 | if (!pgen_primep(ei->r, gr)) return ("generator order not prime"); |
432c4e18 |
484 | |
485 | /* --- Check %$0 < h \le 4$% --- */ |
486 | |
487 | if (MP_CMP(ei->h, <, MP_ONE) || MP_CMP(ei->h, >, MP_FOUR)) |
488 | return ("cofactor out of range"); |
489 | |
490 | /* --- Check %$h = \lfloor (\sqrt{2^m} + 1)^2/r \rlfoor$% --- * |
491 | * |
492 | * This seems to work with the approximate-sqrt in the library, but might |
493 | * not be so good in some cases. Throw in some extra significate figures |
494 | * for good measure. |
495 | */ |
496 | |
497 | x = mp_lsl(MP_NEW, MP_ONE, f->nbits + 128); |
498 | x = mp_sqrt(x, x); |
499 | y = mp_lsl(MP_NEW, MP_ONE, 64); |
500 | x = mp_add(x, x, y); |
501 | x = mp_sqr(x, x); |
502 | mp_div(&x, 0, x, ei->r); |
503 | x = mp_lsr(x, x, 128); |
504 | rc = MP_EQ(x, ei->h); |
505 | MP_DROP(x); |
506 | MP_DROP(y); |
507 | if (!rc) return ("incorrect cofactor"); |
508 | |
509 | /* --- Check %$n G = O$% --- */ |
510 | |
511 | EC_CREATE(&p); |
512 | ec_mul(c, &p, &ei->g, ei->r); |
513 | rc = EC_ATINF(&p); |
514 | EC_DESTROY(&p); |
515 | if (!rc) return ("incorrect group order"); |
516 | |
517 | /* --- Check %$2^{m B} \not\equiv 1 \pmod{r}$% for %$1 \le B < 20$% --- */ |
518 | |
519 | x = mp_lsl(MP_NEW, MP_ONE, f->nbits); |
520 | mp_div(0, &x, x, ei->r); |
521 | i = 20; |
522 | while (i) { |
523 | if (MP_EQ(x, MP_ONE)) break; |
524 | x = mp_mul(x, x, f->m); |
525 | mp_div(0, &x, x, ei->r); |
526 | i--; |
527 | } |
528 | MP_DROP(x); |
529 | if (i) return ("curve is weak"); |
530 | |
531 | /* --- Done --- */ |
532 | |
533 | return (0); |
534 | } |
535 | |
536 | const char *ec_checkinfo(const ec_info *ei, grand *gr) |
537 | { |
538 | switch (F_TYPE(ei->c->f)) { |
539 | case FTY_PRIME: return (primecheck(ei, gr)); break; |
540 | case FTY_BINARY: return (bincheck(ei, gr)); break; |
541 | } |
542 | return ("unknown curve type"); |
543 | } |
544 | |
545 | /*----- Test rig ----------------------------------------------------------*/ |
546 | |
547 | #ifdef TEST_RIG |
548 | |
549 | #include "fibrand.h" |
550 | |
551 | int main(void) |
552 | { |
553 | const ecentry *ee; |
554 | const char *e; |
555 | int ok = 1; |
556 | grand *gr; |
557 | |
558 | gr = fibrand_create(0); |
559 | fputs("checking standard curves: ", stdout); |
560 | for (ee = ectab; ee->name; ee++) { |
561 | ec_info ei; |
562 | getinfo(&ei, ee->data); |
563 | e = ec_checkinfo(&ei, gr); |
564 | ec_freeinfo(&ei); |
565 | if (e) { |
566 | fprintf(stderr, "\n*** curve %s fails: %s\n", ee->name, e); |
567 | ok = 0; |
568 | } |
569 | putchar('.'); |
570 | fflush(stdout); |
571 | } |
572 | gr->ops->destroy(gr); |
573 | fputs(ok ? " ok\n" : " failed\n", stdout); |
574 | return (!ok); |
575 | } |
576 | |
577 | #endif |
578 | |
579 | /*----- That's all, folks -------------------------------------------------*/ |