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