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