3 * $Id: ec-info.c,v 1.1 2004/03/27 17:54:11 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 /*----- Revision history --------------------------------------------------*
33 * Revision 1.1 2004/03/27 17:54:11 mdw
34 * Standard curves and curve checking.
38 /*----- Header files ------------------------------------------------------*/
47 /*----- Main code ---------------------------------------------------------*/
49 /* --- @ec_curveparse@ --- *
51 * Arguments: @qd_parse *qd@ = parser context
53 * Returns: Elliptic curve pointer if OK, or null.
55 * Use: Parses an elliptic curve description, which has the form
57 * * a field description
59 * * `prime', `primeproj', `bin', or `binproj'
61 * * the %$a$% parameter
63 * * the %$b$% parameter
66 ec_curve *ec_curveparse(qd_parse *qd)
68 mp *a = MP_NEW, *b = MP_NEW;
72 if ((f = field_parse(qd)) == 0) goto fail;
74 switch (qd_enum(qd, "prime,primeproj,bin,binproj")) {
76 if (F_TYPE(f) != FTY_PRIME) {
77 qd->e = "field not prime";
81 if ((a = qd_getmp(qd)) == 0) goto fail;
83 if ((b = qd_getmp(qd)) == 0) goto fail;
84 c = ec_prime(f, a, b);
87 if (F_TYPE(f) != FTY_PRIME) {
88 qd->e = "field not prime";
92 if ((a = qd_getmp(qd)) == 0) goto fail;
94 if ((b = qd_getmp(qd)) == 0) goto fail;
95 c = ec_primeproj(f, a, b);
98 if (F_TYPE(f) != FTY_BINARY) {
99 qd->e = "field not binary";
103 if ((a = qd_getmp(qd)) == 0) goto fail;
105 if ((b = qd_getmp(qd)) == 0) goto fail;
109 if (F_TYPE(f) != FTY_BINARY) {
110 qd->e = "field not binary";
114 if ((a = qd_getmp(qd)) == 0) goto fail;
116 if ((b = qd_getmp(qd)) == 0) goto fail;
117 c = ec_binproj(f, a, b);
133 /* --- @ec_ptparse@ --- *
135 * Arguments: @qd_parse *qd@ = parser context
136 * @ec *p@ = where to put the point
138 * Returns: The point address, or null.
140 * Use: Parses an elliptic curve point. This has the form
147 ec *ec_ptparse(qd_parse *qd, ec *p)
149 mp *x = MP_NEW, *y = MP_NEW;
151 if (qd_enum(qd, "inf") >= 0) {
155 if ((x = qd_getmp(qd)) == 0) goto fail;
157 if ((y = qd_getmp(qd)) == 0) goto fail;
170 /* --- @ec_infoparse@ --- *
172 * Arguments: @qd_parse *qd@ = parser context
173 * @ec_info *ei@ = curve information block, currently
176 * Returns: Zero on success, nonzero on failure.
178 * Use: Parses an elliptic curve information string, and stores the
179 * information in @ei@. This has the form
181 * * elliptic curve description
190 int ec_infoparse(qd_parse *qd, ec_info *ei)
195 mp *r = MP_NEW, *h = MP_NEW;
197 if ((c = ec_curveparse(qd)) == 0) goto fail;
198 qd_delim(qd, '/'); if (!ec_ptparse(qd, &g)) goto fail;
199 qd_delim(qd, ':'); if ((r = qd_getmp(qd)) == 0) goto fail;
200 qd_delim(qd, '*'); if ((h = qd_getmp(qd)) == 0) goto fail;
202 ei->c = c; ei->g = g; ei->r = r; ei->h = h;
209 if (c) { f = c->f; ec_destroycurve(c); F_DESTROY(f); }
213 /* --- @getinfo@ --- *
215 * Arguments: @ec_info *ei@ = where to write the information
216 * @const ecdata *ed@ = raw data
220 * Use: Loads elliptic curve information about one of the standard
224 static mp *getmp(const mpw *v, size_t n)
226 mp *x = mp_new(n, 0);
227 memcpy(x->v, v, MPWS(n));
231 static void getinfo(ec_info *ei, const ecdata *ed)
234 mp *p = 0, *a = 0, *b = 0;
238 p = getmp(ed->p, ed->psz);
240 a = getmp(ed->a, ed->asz); b = getmp(ed->b, ed->bsz);
241 ei->c = ec_primeproj(f, a, b);
244 p = getmp(ed->p, ed->psz);
245 f = field_niceprime(p);
246 a = getmp(ed->a, ed->asz); b = getmp(ed->b, ed->bsz);
247 ei->c = ec_primeproj(f, a, b);
250 p = getmp(ed->p, ed->psz);
251 f = field_binpoly(p);
252 a = getmp(ed->a, ed->asz); b = getmp(ed->b, ed->bsz);
253 ei->c = ec_binproj(f, a, b);
260 ei->g.x = getmp(ed->gx, ed->gxsz);
261 ei->g.y = getmp(ed->gy, ed->gysz);
263 ei->r = getmp(ed->r, ed->rsz);
264 ei->h = getmp(ed->h, ed->hsz);
271 /* --- @ec_getinfo@ --- *
273 * Arguments: @ec_info *ei@ = where to write the information
274 * @const char *p@ = string describing a curve
276 * Returns: Null on success, or a pointer to an error message.
278 * Use: Parses out information about a curve. The string is either a
279 * standard curve name, or a curve info string.
282 const char *ec_getinfo(ec_info *ei, const char *p)
289 for (ee = ectab; ee->name; ee++) {
290 if (qd_enum(&qd, ee->name) >= 0) {
291 getinfo(ei, ee->data);
295 if (ec_infoparse(&qd, ei))
300 return ("junk found at end of string");
305 /* --- @ec_freeinfo@ --- *
307 * Arguments: @ec_info *ei@ = elliptic curve information block to free
311 * Use: Frees the information block.
314 void ec_freeinfo(ec_info *ei)
321 f = ei->c->f; ec_destroycurve(ei->c); F_DESTROY(f);
324 /* --- @ec_checkinfo@ --- *
326 * Arguments: @const ec_info *ei@ = elliptic curve information block
328 * Returns: Null if OK, or pointer to error message.
330 * Use: Checks an elliptic curve according to the rules in SEC1.
333 static int primep(mp *p, grand *gr)
335 int i = rabin_iters(mp_bits(p));
339 switch (pfilt_smallfactor(p)) {
340 case PGEN_DONE: return (1);
341 case PGEN_FAIL: return (0);
345 x = mprand_range(x, p, gr, 0);
346 if (rabin_rtest(&r, x) == PGEN_FAIL)
355 static int primeeltp(mp *x, field *f)
357 return (!MP_ISNEG(x) && MP_CMP(x, <, f->m));
360 static const char *primecheck(const ec_info *ei, grand *gr)
369 /* --- Check %$p$% is an odd prime --- */
371 if (!primep(f->m, gr)) return ("p not prime");
373 /* --- Check %$a$%, %$b$%, %$G_x$% and %$G_y$% are in %$[0, p)$% --- */
375 if (!primeeltp(c->a, f)) return ("a out of range");
376 if (!primeeltp(c->b, f)) return ("b out of range");
377 if (!primeeltp(ei->g.x, f)) return ("G_x out of range");
378 if (!primeeltp(ei->g.x, f)) return ("G_y out of range");
380 /* --- Check %$4 a^3 + 27 b^2 \not\equiv 0 \pmod{p}$% --- */
382 x = F_SQR(f, MP_NEW, c->a);
383 x = F_MUL(f, x, x, c->a);
385 y = F_SQR(f, MP_NEW, c->b);
389 x = F_ADD(f, x, x, y);
393 if (rc) return ("not an elliptic curve");
395 /* --- Check %$G \in E$% --- */
397 if (EC_ATINF(&ei->g)) return ("generator at infinity");
398 if (ec_check(c, &ei->g)) return ("generator not on curve");
400 /* --- Check %$r$% is prime --- */
402 if (!primep(ei->r, gr)) return ("generator order not prime");
404 /* --- Check %$0 < h \le 4$% --- */
406 if (MP_CMP(ei->h, <, MP_ONE) || MP_CMP(ei->h, >, MP_FOUR))
407 return ("cofactor out of range");
409 /* --- Check %$h = \lfloor (\sqrt{p} + 1)^2/r \rlfoor$% --- *
411 * This seems to work with the approximate-sqrt in the library, but might
412 * not be so good in some cases. Throw in some extra significate figures
416 x = mp_lsl(MP_NEW, f->m, 128);
418 y = mp_lsl(MP_NEW, MP_ONE, 64);
421 mp_div(&x, 0, x, ei->r);
422 x = mp_lsr(x, x, 128);
423 rc = MP_EQ(x, ei->h);
426 if (!rc) return ("incorrect cofactor");
428 /* --- Check %$n G = O$% --- */
431 ec_mul(c, &p, &ei->g, ei->r);
434 if (!rc) return ("incorrect group order");
436 /* --- Check that %$p^B \not\equiv 1 \pmod{r}$% for %$1 \le B < 20$% --- *
438 * The spec says %$q$%, not %$p$%, but I think that's a misprint.
442 mp_div(0, &x, f->m, ei->r);
445 if (MP_EQ(x, MP_ONE)) break;
446 x = mp_mul(x, x, f->m);
447 mp_div(0, &x, x, ei->r);
451 if (i) return ("curve is weak");
458 static const char *bincheck(const ec_info *ei, grand *gr)
467 /* --- Check that %$p$% is irreducible --- */
469 if (!gf_irreduciblep(f->m)) return ("p not irreducible");
471 /* --- Check that %$a, b, G_x, G_y$% have degree less than %$p$% --- */
473 if (mp_bits(c->a) > f->nbits) return ("a out of range");
474 if (mp_bits(c->b) > f->nbits) return ("a out of range");
475 if (mp_bits(ei->g.x) > f->nbits) return ("G_x out of range");
476 if (mp_bits(ei->g.y) > f->nbits) return ("G_y out of range");
478 /* --- Check that %$b \ne 0$% --- */
480 if (F_ZEROP(f, c->b)) return ("b is zero");
482 /* --- Check that %$G \in E$% --- */
484 if (EC_ATINF(&ei->g)) return ("generator at infinity");
485 if (ec_check(c, &ei->g)) return ("generator not on curve");
487 /* --- Check %$r$% is prime --- */
489 if (!primep(ei->r, gr)) return ("generator order not prime");
491 /* --- Check %$0 < h \le 4$% --- */
493 if (MP_CMP(ei->h, <, MP_ONE) || MP_CMP(ei->h, >, MP_FOUR))
494 return ("cofactor out of range");
496 /* --- Check %$h = \lfloor (\sqrt{2^m} + 1)^2/r \rlfoor$% --- *
498 * This seems to work with the approximate-sqrt in the library, but might
499 * not be so good in some cases. Throw in some extra significate figures
503 x = mp_lsl(MP_NEW, MP_ONE, f->nbits + 128);
505 y = mp_lsl(MP_NEW, MP_ONE, 64);
508 mp_div(&x, 0, x, ei->r);
509 x = mp_lsr(x, x, 128);
510 rc = MP_EQ(x, ei->h);
513 if (!rc) return ("incorrect cofactor");
515 /* --- Check %$n G = O$% --- */
518 ec_mul(c, &p, &ei->g, ei->r);
521 if (!rc) return ("incorrect group order");
523 /* --- Check %$2^{m B} \not\equiv 1 \pmod{r}$% for %$1 \le B < 20$% --- */
525 x = mp_lsl(MP_NEW, MP_ONE, f->nbits);
526 mp_div(0, &x, x, ei->r);
529 if (MP_EQ(x, MP_ONE)) break;
530 x = mp_mul(x, x, f->m);
531 mp_div(0, &x, x, ei->r);
535 if (i) return ("curve is weak");
542 const char *ec_checkinfo(const ec_info *ei, grand *gr)
544 switch (F_TYPE(ei->c->f)) {
545 case FTY_PRIME: return (primecheck(ei, gr)); break;
546 case FTY_BINARY: return (bincheck(ei, gr)); break;
548 return ("unknown curve type");
551 /*----- Test rig ----------------------------------------------------------*/
564 gr = fibrand_create(0);
565 fputs("checking standard curves: ", stdout);
566 for (ee = ectab; ee->name; ee++) {
568 getinfo(&ei, ee->data);
569 e = ec_checkinfo(&ei, gr);
572 fprintf(stderr, "\n*** curve %s fails: %s\n", ee->name, e);
578 gr->ops->destroy(gr);
579 fputs(ok ? " ok\n" : " failed\n", stdout);
585 /*----- That's all, folks -------------------------------------------------*/