3 * $Id: ec-info.c,v 1.4 2004/04/03 03:32:05 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 1.4 2004/04/03 03:32:05 mdw
34 * General robustification.
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.
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.)
48 * Revision 1.1 2004/03/27 17:54:11 mdw
49 * Standard curves and curve checking.
53 /*----- Header files ------------------------------------------------------*/
62 /*----- Main code ---------------------------------------------------------*/
64 /* --- @ec_curveparse@ --- *
66 * Arguments: @qd_parse *qd@ = parser context
68 * Returns: Elliptic curve pointer if OK, or null.
70 * Use: Parses an elliptic curve description, which has the form
72 * * a field description
74 * * `prime', `primeproj', `bin', or `binproj'
76 * * the %$a$% parameter
78 * * the %$b$% parameter
81 ec_curve
*ec_curveparse(qd_parse
*qd
)
83 mp
*a
= MP_NEW
, *b
= MP_NEW
;
87 if ((f
= field_parse(qd
)) == 0) goto fail
;
89 switch (qd_enum(qd
, "prime,primeproj,bin,binproj")) {
91 if (F_TYPE(f
) != FTY_PRIME
) {
92 qd
->e
= "field not prime";
96 if ((a
= qd_getmp(qd
)) == 0) goto fail
;
98 if ((b
= qd_getmp(qd
)) == 0) goto fail
;
99 c
= ec_prime(f
, a
, b
);
102 if (F_TYPE(f
) != FTY_PRIME
) {
103 qd
->e
= "field not prime";
107 if ((a
= qd_getmp(qd
)) == 0) goto fail
;
109 if ((b
= qd_getmp(qd
)) == 0) goto fail
;
110 c
= ec_primeproj(f
, a
, b
);
113 if (F_TYPE(f
) != FTY_BINARY
) {
114 qd
->e
= "field not binary";
118 if ((a
= qd_getmp(qd
)) == 0) goto fail
;
120 if ((b
= qd_getmp(qd
)) == 0) goto fail
;
124 if (F_TYPE(f
) != FTY_BINARY
) {
125 qd
->e
= "field not binary";
129 if ((a
= qd_getmp(qd
)) == 0) goto fail
;
131 if ((b
= qd_getmp(qd
)) == 0) goto fail
;
132 c
= ec_binproj(f
, a
, b
);
138 qd
->e
= "bad curve parameters";
152 /* --- @ec_ptparse@ --- *
154 * Arguments: @qd_parse *qd@ = parser context
155 * @ec *p@ = where to put the point
157 * Returns: The point address, or null.
159 * Use: Parses an elliptic curve point. This has the form
166 ec
*ec_ptparse(qd_parse
*qd
, ec
*p
)
168 mp
*x
= MP_NEW
, *y
= MP_NEW
;
170 if (qd_enum(qd
, "inf") >= 0) {
174 if ((x
= qd_getmp(qd
)) == 0) goto fail
;
176 if ((y
= qd_getmp(qd
)) == 0) goto fail
;
189 /* --- @getinfo@ --- *
191 * Arguments: @ec_info *ei@ = where to write the information
192 * @ecdata *ed@ = raw data
196 * Use: Loads elliptic curve information about one of the standard
200 static void getinfo(ec_info
*ei
, ecdata
*ed
)
206 f
= field_prime(&ed
->p
);
207 ei
->c
= ec_primeproj(f
, &ed
->a
, &ed
->b
);
210 f
= field_niceprime(&ed
->p
);
211 ei
->c
= ec_primeproj(f
, &ed
->a
, &ed
->b
);
214 f
= field_binpoly(&ed
->p
);
215 ei
->c
= ec_binproj(f
, &ed
->a
, &ed
->b
);
218 f
= field_binnorm(&ed
->p
, &ed
->beta
);
219 ei
->c
= ec_binproj(f
, &ed
->a
, &ed
->b
);
225 assert(f
); assert(ei
->c
);
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
;
230 /* --- @ec_infoparse@ --- *
232 * Arguments: @qd_parse *qd@ = parser context
233 * @ec_info *ei@ = curve information block, currently
236 * Returns: Zero on success, nonzero on failure.
238 * Use: Parses an elliptic curve information string, and stores the
239 * information in @ei@. This is either the name of a standard
240 * curve, or it has the form
242 * * elliptic curve description
251 int ec_infoparse(qd_parse
*qd
, ec_info
*ei
)
257 mp
*r
= MP_NEW
, *h
= MP_NEW
;
259 for (ee
= ectab
; ee
->name
; ee
++)
260 if (qd_enum(qd
, ee
->name
) >= 0) { getinfo(ei
, ee
->data
); goto found
; }
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
;
266 ei
->c
= c
; ei
->g
= g
; ei
->r
= r
; ei
->h
= h
;
275 if (c
) { f
= c
->f
; ec_destroycurve(c
); F_DESTROY(f
); }
279 /* --- @ec_getinfo@ --- *
281 * Arguments: @ec_info *ei@ = where to write the information
282 * @const char *p@ = string describing a curve
284 * Returns: Null on success, or a pointer to an error message.
286 * Use: Parses out information about a curve. The string is either a
287 * standard curve name, or a curve info string.
290 const char *ec_getinfo(ec_info
*ei
, const char *p
)
296 if (ec_infoparse(&qd
, ei
))
300 return ("junk found at end of string");
305 /* --- @ec_sameinfop@ --- *
307 * Arguments: @ec_info *ei, *ej@ = two elliptic curve parameter sets
309 * Returns: Nonzero if the curves are identical (not just isomorphic).
311 * Use: Checks for sameness of curve parameters.
314 int ec_sameinfop(ec_info
*ei
, ec_info
*ej
)
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
));
321 /* --- @ec_freeinfo@ --- *
323 * Arguments: @ec_info *ei@ = elliptic curve information block to free
327 * Use: Frees the information block.
330 void ec_freeinfo(ec_info
*ei
)
337 f
= ei
->c
->f
; ec_destroycurve(ei
->c
); F_DESTROY(f
);
340 /* --- @ec_checkinfo@ --- *
342 * Arguments: @const ec_info *ei@ = elliptic curve information block
344 * Returns: Null if OK, or pointer to error message.
346 * Use: Checks an elliptic curve according to the rules in SEC1.
349 static int primeeltp(mp
*x
, field
*f
)
351 return (!MP_ISNEG(x
) && MP_CMP(x
, <, f
->m
));
354 static const char *primecheck(const ec_info
*ei
, grand
*gr
)
363 /* --- Check %$p$% is an odd prime --- */
365 if (!pgen_primep(f
->m
, gr
)) return ("p not prime");
367 /* --- Check %$a$%, %$b$%, %$G_x$% and %$G_y$% are in %$[0, p)$% --- */
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");
374 /* --- Check %$4 a^3 + 27 b^2 \not\equiv 0 \pmod{p}$% --- */
376 x
= F_SQR(f
, MP_NEW
, c
->a
);
377 x
= F_MUL(f
, x
, x
, c
->a
);
379 y
= F_SQR(f
, MP_NEW
, c
->b
);
383 x
= F_ADD(f
, x
, x
, y
);
387 if (rc
) return ("not an elliptic curve");
389 /* --- Check %$G \in E$% --- */
391 if (EC_ATINF(&ei
->g
)) return ("generator at infinity");
392 if (ec_check(c
, &ei
->g
)) return ("generator not on curve");
394 /* --- Check %$r$% is prime --- */
396 if (!pgen_primep(ei
->r
, gr
)) return ("generator order not prime");
398 /* --- Check %$0 < h \le 4$% --- */
400 if (MP_CMP(ei
->h
, <, MP_ONE
) || MP_CMP(ei
->h
, >, MP_FOUR
))
401 return ("cofactor out of range");
403 /* --- Check %$h = \lfloor (\sqrt{p} + 1)^2/r \rlfoor$% --- *
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
410 x
= mp_lsl(MP_NEW
, f
->m
, 128);
412 y
= mp_lsl(MP_NEW
, MP_ONE
, 64);
415 mp_div(&x
, 0, x
, ei
->r
);
416 x
= mp_lsr(x
, x
, 128);
417 rc
= MP_EQ(x
, ei
->h
);
420 if (!rc
) return ("incorrect cofactor");
422 /* --- Check %$n G = O$% --- */
425 ec_mul(c
, &p
, &ei
->g
, ei
->r
);
428 if (!rc
) return ("incorrect group order");
430 /* --- Check that %$p^B \not\equiv 1 \pmod{r}$% for %$1 \le B < 20$% --- *
432 * The spec says %$q$%, not %$p$%, but I think that's a misprint.
436 mp_div(0, &x
, f
->m
, ei
->r
);
439 if (MP_EQ(x
, MP_ONE
)) break;
440 x
= mp_mul(x
, x
, f
->m
);
441 mp_div(0, &x
, x
, ei
->r
);
445 if (i
) return ("curve is weak");
452 static const char *bincheck(const ec_info
*ei
, grand
*gr
)
461 /* --- Check that %$p$% is irreducible --- */
463 if (!gf_irreduciblep(f
->m
)) return ("p not irreducible");
465 /* --- Check that %$a, b, G_x, G_y$% have degree less than %$p$% --- */
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");
472 /* --- Check that %$b \ne 0$% --- */
474 if (F_ZEROP(f
, c
->b
)) return ("b is zero");
476 /* --- Check that %$G \in E$% --- */
478 if (EC_ATINF(&ei
->g
)) return ("generator at infinity");
479 if (ec_check(c
, &ei
->g
)) return ("generator not on curve");
481 /* --- Check %$r$% is prime --- */
483 if (!pgen_primep(ei
->r
, gr
)) return ("generator order not prime");
485 /* --- Check %$0 < h \le 4$% --- */
487 if (MP_CMP(ei
->h
, <, MP_ONE
) || MP_CMP(ei
->h
, >, MP_FOUR
))
488 return ("cofactor out of range");
490 /* --- Check %$h = \lfloor (\sqrt{2^m} + 1)^2/r \rlfoor$% --- *
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
497 x
= mp_lsl(MP_NEW
, MP_ONE
, f
->nbits
+ 128);
499 y
= mp_lsl(MP_NEW
, MP_ONE
, 64);
502 mp_div(&x
, 0, x
, ei
->r
);
503 x
= mp_lsr(x
, x
, 128);
504 rc
= MP_EQ(x
, ei
->h
);
507 if (!rc
) return ("incorrect cofactor");
509 /* --- Check %$n G = O$% --- */
512 ec_mul(c
, &p
, &ei
->g
, ei
->r
);
515 if (!rc
) return ("incorrect group order");
517 /* --- Check %$2^{m B} \not\equiv 1 \pmod{r}$% for %$1 \le B < 20$% --- */
519 x
= mp_lsl(MP_NEW
, MP_ONE
, f
->nbits
);
520 mp_div(0, &x
, x
, ei
->r
);
523 if (MP_EQ(x
, MP_ONE
)) break;
524 x
= mp_mul(x
, x
, f
->m
);
525 mp_div(0, &x
, x
, ei
->r
);
529 if (i
) return ("curve is weak");
536 const char *ec_checkinfo(const ec_info
*ei
, grand
*gr
)
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;
542 return ("unknown curve type");
545 /*----- Test rig ----------------------------------------------------------*/
558 gr
= fibrand_create(0);
559 fputs("checking standard curves: ", stdout
);
560 for (ee
= ectab
; ee
->name
; ee
++) {
562 getinfo(&ei
, ee
->data
);
563 e
= ec_checkinfo(&ei
, gr
);
566 fprintf(stderr
, "\n*** curve %s fails: %s\n", ee
->name
, e
);
572 gr
->ops
->destroy(gr
);
573 fputs(ok ?
" ok\n" : " failed\n", stdout
);
579 /*----- That's all, folks -------------------------------------------------*/