3 * $Id: ec-info.c,v 1.5 2004/04/08 01:36:15 mdw Exp $
5 * Elliptic curve information management
7 * (c) 2004 Straylight/Edgeware
10 /*----- Licensing notice --------------------------------------------------*
12 * This file is part of Catacomb.
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.
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.
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,
30 /*----- Header files ------------------------------------------------------*/
39 /*----- Main code ---------------------------------------------------------*/
41 /* --- @ec_curveparse@ --- *
43 * Arguments: @qd_parse *qd@ = parser context
45 * Returns: Elliptic curve pointer if OK, or null.
47 * Use: Parses an elliptic curve description, which has the form
49 * * a field description
51 * * `prime', `primeproj', `bin', or `binproj'
53 * * the %$a$% parameter
55 * * the %$b$% parameter
58 ec_curve *ec_curveparse(qd_parse *qd)
60 mp *a = MP_NEW, *b = MP_NEW;
64 if ((f = field_parse(qd)) == 0) goto fail;
66 switch (qd_enum(qd, "prime,primeproj,bin,binproj")) {
68 if (F_TYPE(f) != FTY_PRIME) {
69 qd->e = "field not prime";
73 if ((a = qd_getmp(qd)) == 0) goto fail;
75 if ((b = qd_getmp(qd)) == 0) goto fail;
76 c = ec_prime(f, a, b);
79 if (F_TYPE(f) != FTY_PRIME) {
80 qd->e = "field not prime";
84 if ((a = qd_getmp(qd)) == 0) goto fail;
86 if ((b = qd_getmp(qd)) == 0) goto fail;
87 c = ec_primeproj(f, a, b);
90 if (F_TYPE(f) != FTY_BINARY) {
91 qd->e = "field not binary";
95 if ((a = qd_getmp(qd)) == 0) goto fail;
97 if ((b = qd_getmp(qd)) == 0) goto fail;
101 if (F_TYPE(f) != FTY_BINARY) {
102 qd->e = "field not binary";
106 if ((a = qd_getmp(qd)) == 0) goto fail;
108 if ((b = qd_getmp(qd)) == 0) goto fail;
109 c = ec_binproj(f, a, b);
115 qd->e = "bad curve parameters";
129 /* --- @ec_ptparse@ --- *
131 * Arguments: @qd_parse *qd@ = parser context
132 * @ec *p@ = where to put the point
134 * Returns: The point address, or null.
136 * Use: Parses an elliptic curve point. This has the form
143 ec *ec_ptparse(qd_parse *qd, ec *p)
145 mp *x = MP_NEW, *y = MP_NEW;
147 if (qd_enum(qd, "inf") >= 0) {
151 if ((x = qd_getmp(qd)) == 0) goto fail;
153 if ((y = qd_getmp(qd)) == 0) goto fail;
166 /* --- @getinfo@ --- *
168 * Arguments: @ec_info *ei@ = where to write the information
169 * @ecdata *ed@ = raw data
173 * Use: Loads elliptic curve information about one of the standard
177 static void getinfo(ec_info *ei, ecdata *ed)
183 f = field_prime(&ed->p);
184 ei->c = ec_primeproj(f, &ed->a, &ed->b);
187 f = field_niceprime(&ed->p);
188 ei->c = ec_primeproj(f, &ed->a, &ed->b);
191 f = field_binpoly(&ed->p);
192 ei->c = ec_binproj(f, &ed->a, &ed->b);
195 f = field_binnorm(&ed->p, &ed->beta);
196 ei->c = ec_binproj(f, &ed->a, &ed->b);
202 assert(f); assert(ei->c);
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;
207 /* --- @ec_infoparse@ --- *
209 * Arguments: @qd_parse *qd@ = parser context
210 * @ec_info *ei@ = curve information block, currently
213 * Returns: Zero on success, nonzero on failure.
215 * Use: Parses an elliptic curve information string, and stores the
216 * information in @ei@. This is either the name of a standard
217 * curve, or it has the form
219 * * elliptic curve description
228 int ec_infoparse(qd_parse *qd, ec_info *ei)
234 mp *r = MP_NEW, *h = MP_NEW;
236 for (ee = ectab; ee->name; ee++)
237 if (qd_enum(qd, ee->name) >= 0) { getinfo(ei, ee->data); goto found; }
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;
243 ei->c = c; ei->g = g; ei->r = r; ei->h = h;
252 if (c) { f = c->f; ec_destroycurve(c); F_DESTROY(f); }
256 /* --- @ec_getinfo@ --- *
258 * Arguments: @ec_info *ei@ = where to write the information
259 * @const char *p@ = string describing a curve
261 * Returns: Null on success, or a pointer to an error message.
263 * Use: Parses out information about a curve. The string is either a
264 * standard curve name, or a curve info string.
267 const char *ec_getinfo(ec_info *ei, const char *p)
273 if (ec_infoparse(&qd, ei))
277 return ("junk found at end of string");
282 /* --- @ec_sameinfop@ --- *
284 * Arguments: @ec_info *ei, *ej@ = two elliptic curve parameter sets
286 * Returns: Nonzero if the curves are identical (not just isomorphic).
288 * Use: Checks for sameness of curve parameters.
291 int ec_sameinfop(ec_info *ei, ec_info *ej)
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));
298 /* --- @ec_freeinfo@ --- *
300 * Arguments: @ec_info *ei@ = elliptic curve information block to free
304 * Use: Frees the information block.
307 void ec_freeinfo(ec_info *ei)
314 f = ei->c->f; ec_destroycurve(ei->c); F_DESTROY(f);
317 /* --- @ec_checkinfo@ --- *
319 * Arguments: @const ec_info *ei@ = elliptic curve information block
321 * Returns: Null if OK, or pointer to error message.
323 * Use: Checks an elliptic curve according to the rules in SEC1.
326 static int primeeltp(mp *x, field *f)
328 return (!MP_ISNEG(x) && MP_CMP(x, <, f->m));
331 static const char *primecheck(const ec_info *ei, grand *gr)
340 /* --- Check %$p$% is an odd prime --- */
342 if (!pgen_primep(f->m, gr)) return ("p not prime");
344 /* --- Check %$a$%, %$b$%, %$G_x$% and %$G_y$% are in %$[0, p)$% --- */
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");
351 /* --- Check %$4 a^3 + 27 b^2 \not\equiv 0 \pmod{p}$% --- */
353 x = F_SQR(f, MP_NEW, c->a);
354 x = F_MUL(f, x, x, c->a);
356 y = F_SQR(f, MP_NEW, c->b);
360 x = F_ADD(f, x, x, y);
364 if (rc) return ("not an elliptic curve");
366 /* --- Check %$G \in E$% --- */
368 if (EC_ATINF(&ei->g)) return ("generator at infinity");
369 if (ec_check(c, &ei->g)) return ("generator not on curve");
371 /* --- Check %$r$% is prime --- */
373 if (!pgen_primep(ei->r, gr)) return ("generator order not prime");
375 /* --- Check %$0 < h \le 4$% --- */
377 if (MP_CMP(ei->h, <, MP_ONE) || MP_CMP(ei->h, >, MP_FOUR))
378 return ("cofactor out of range");
380 /* --- Check %$h = \lfloor (\sqrt{p} + 1)^2/r \rlfoor$% --- *
382 * This seems to work with the approximate-sqrt in the library, but might
383 * not be so good in some cases. Throw in some extra significate figures
387 x = mp_lsl(MP_NEW, f->m, 128);
389 y = mp_lsl(MP_NEW, MP_ONE, 64);
392 mp_div(&x, 0, x, ei->r);
393 x = mp_lsr(x, x, 128);
394 rc = MP_EQ(x, ei->h);
397 if (!rc) return ("incorrect cofactor");
399 /* --- Check %$n G = O$% --- */
402 ec_mul(c, &p, &ei->g, ei->r);
405 if (!rc) return ("incorrect group order");
407 /* --- Check that %$p^B \not\equiv 1 \pmod{r}$% for %$1 \le B < 20$% --- *
409 * The spec says %$q$%, not %$p$%, but I think that's a misprint.
413 mp_div(0, &x, f->m, ei->r);
416 if (MP_EQ(x, MP_ONE)) break;
417 x = mp_mul(x, x, f->m);
418 mp_div(0, &x, x, ei->r);
422 if (i) return ("curve is weak");
429 static const char *bincheck(const ec_info *ei, grand *gr)
438 /* --- Check that %$p$% is irreducible --- */
440 if (!gf_irreduciblep(f->m)) return ("p not irreducible");
442 /* --- Check that %$a, b, G_x, G_y$% have degree less than %$p$% --- */
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");
449 /* --- Check that %$b \ne 0$% --- */
451 if (F_ZEROP(f, c->b)) return ("b is zero");
453 /* --- Check that %$G \in E$% --- */
455 if (EC_ATINF(&ei->g)) return ("generator at infinity");
456 if (ec_check(c, &ei->g)) return ("generator not on curve");
458 /* --- Check %$r$% is prime --- */
460 if (!pgen_primep(ei->r, gr)) return ("generator order not prime");
462 /* --- Check %$0 < h \le 4$% --- */
464 if (MP_CMP(ei->h, <, MP_ONE) || MP_CMP(ei->h, >, MP_FOUR))
465 return ("cofactor out of range");
467 /* --- Check %$h = \lfloor (\sqrt{2^m} + 1)^2/r \rlfoor$% --- *
469 * This seems to work with the approximate-sqrt in the library, but might
470 * not be so good in some cases. Throw in some extra significate figures
474 x = mp_lsl(MP_NEW, MP_ONE, f->nbits + 128);
476 y = mp_lsl(MP_NEW, MP_ONE, 64);
479 mp_div(&x, 0, x, ei->r);
480 x = mp_lsr(x, x, 128);
481 rc = MP_EQ(x, ei->h);
484 if (!rc) return ("incorrect cofactor");
486 /* --- Check %$n G = O$% --- */
489 ec_mul(c, &p, &ei->g, ei->r);
492 if (!rc) return ("incorrect group order");
494 /* --- Check %$2^{m B} \not\equiv 1 \pmod{r}$% for %$1 \le B < 20$% --- */
496 x = mp_lsl(MP_NEW, MP_ONE, f->nbits);
497 mp_div(0, &x, x, ei->r);
500 if (MP_EQ(x, MP_ONE)) break;
501 x = mp_mul(x, x, f->m);
502 mp_div(0, &x, x, ei->r);
506 if (i) return ("curve is weak");
513 const char *ec_checkinfo(const ec_info *ei, grand *gr)
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;
519 return ("unknown curve type");
522 /*----- Test rig ----------------------------------------------------------*/
535 gr = fibrand_create(0);
536 fputs("checking standard curves: ", stdout);
537 for (ee = ectab; ee->name; ee++) {
539 getinfo(&ei, ee->data);
540 e = ec_checkinfo(&ei, gr);
543 fprintf(stderr, "\n*** curve %s fails: %s\n", ee->name, e);
549 gr->ops->destroy(gr);
550 fputs(ok ? " ok\n" : " failed\n", stdout);
556 /*----- That's all, folks -------------------------------------------------*/