3 * $Id: ec-info.c,v 1.2 2004/04/01 12:50:09 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 1.2 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.)
40 * Revision 1.1 2004/03/27 17:54:11 mdw
41 * Standard curves and curve checking.
45 /*----- Header files ------------------------------------------------------*/
54 /*----- Main code ---------------------------------------------------------*/
56 /* --- @ec_curveparse@ --- *
58 * Arguments: @qd_parse *qd@ = parser context
60 * Returns: Elliptic curve pointer if OK, or null.
62 * Use: Parses an elliptic curve description, which has the form
64 * * a field description
66 * * `prime', `primeproj', `bin', or `binproj'
68 * * the %$a$% parameter
70 * * the %$b$% parameter
73 ec_curve
*ec_curveparse(qd_parse
*qd
)
75 mp
*a
= MP_NEW
, *b
= MP_NEW
;
79 if ((f
= field_parse(qd
)) == 0) goto fail
;
81 switch (qd_enum(qd
, "prime,primeproj,bin,binproj")) {
83 if (F_TYPE(f
) != FTY_PRIME
) {
84 qd
->e
= "field not prime";
88 if ((a
= qd_getmp(qd
)) == 0) goto fail
;
90 if ((b
= qd_getmp(qd
)) == 0) goto fail
;
91 c
= ec_prime(f
, a
, b
);
94 if (F_TYPE(f
) != FTY_PRIME
) {
95 qd
->e
= "field not prime";
99 if ((a
= qd_getmp(qd
)) == 0) goto fail
;
101 if ((b
= qd_getmp(qd
)) == 0) goto fail
;
102 c
= ec_primeproj(f
, a
, b
);
105 if (F_TYPE(f
) != FTY_BINARY
) {
106 qd
->e
= "field not binary";
110 if ((a
= qd_getmp(qd
)) == 0) goto fail
;
112 if ((b
= qd_getmp(qd
)) == 0) goto fail
;
116 if (F_TYPE(f
) != FTY_BINARY
) {
117 qd
->e
= "field not binary";
121 if ((a
= qd_getmp(qd
)) == 0) goto fail
;
123 if ((b
= qd_getmp(qd
)) == 0) goto fail
;
124 c
= ec_binproj(f
, a
, b
);
140 /* --- @ec_ptparse@ --- *
142 * Arguments: @qd_parse *qd@ = parser context
143 * @ec *p@ = where to put the point
145 * Returns: The point address, or null.
147 * Use: Parses an elliptic curve point. This has the form
154 ec
*ec_ptparse(qd_parse
*qd
, ec
*p
)
156 mp
*x
= MP_NEW
, *y
= MP_NEW
;
158 if (qd_enum(qd
, "inf") >= 0) {
162 if ((x
= qd_getmp(qd
)) == 0) goto fail
;
164 if ((y
= qd_getmp(qd
)) == 0) goto fail
;
177 /* --- @getinfo@ --- *
179 * Arguments: @ec_info *ei@ = where to write the information
180 * @ecdata *ed@ = raw data
184 * Use: Loads elliptic curve information about one of the standard
188 static void getinfo(ec_info
*ei
, ecdata
*ed
)
194 f
= field_prime(&ed
->p
);
195 ei
->c
= ec_primeproj(f
, &ed
->a
, &ed
->b
);
198 f
= field_niceprime(&ed
->p
);
199 ei
->c
= ec_primeproj(f
, &ed
->a
, &ed
->b
);
202 f
= field_binpoly(&ed
->p
);
203 ei
->c
= ec_binproj(f
, &ed
->a
, &ed
->b
);
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
;
213 /* --- @ec_infoparse@ --- *
215 * Arguments: @qd_parse *qd@ = parser context
216 * @ec_info *ei@ = curve information block, currently
219 * Returns: Zero on success, nonzero on failure.
221 * Use: Parses an elliptic curve information string, and stores the
222 * information in @ei@. This is either the name of a standard
223 * curve, or it has the form
225 * * elliptic curve description
234 int ec_infoparse(qd_parse
*qd
, ec_info
*ei
)
240 mp
*r
= MP_NEW
, *h
= MP_NEW
;
242 for (ee
= ectab
; ee
->name
; ee
++) {
243 if (qd_enum(qd
, ee
->name
) >= 0) {
244 getinfo(ei
, ee
->data
);
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
;
252 ei
->c
= c
; ei
->g
= g
; ei
->r
= r
; ei
->h
= h
;
261 if (c
) { f
= c
->f
; ec_destroycurve(c
); F_DESTROY(f
); }
265 /* --- @ec_getinfo@ --- *
267 * Arguments: @ec_info *ei@ = where to write the information
268 * @const char *p@ = string describing a curve
270 * Returns: Null on success, or a pointer to an error message.
272 * Use: Parses out information about a curve. The string is either a
273 * standard curve name, or a curve info string.
276 const char *ec_getinfo(ec_info
*ei
, const char *p
)
282 if (ec_infoparse(&qd
, ei
))
286 return ("junk found at end of string");
291 /* --- @ec_sameinfop@ --- *
293 * Arguments: @ec_info *ei, *ej@ = two elliptic curve parameter sets
295 * Returns: Nonzero if the curves are identical (not just isomorphic).
297 * Use: Checks for sameness of curve parameters.
300 int ec_sameinfop(ec_info
*ei
, ec_info
*ej
)
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
));
307 /* --- @ec_freeinfo@ --- *
309 * Arguments: @ec_info *ei@ = elliptic curve information block to free
313 * Use: Frees the information block.
316 void ec_freeinfo(ec_info
*ei
)
323 f
= ei
->c
->f
; ec_destroycurve(ei
->c
); F_DESTROY(f
);
326 /* --- @ec_checkinfo@ --- *
328 * Arguments: @const ec_info *ei@ = elliptic curve information block
330 * Returns: Null if OK, or pointer to error message.
332 * Use: Checks an elliptic curve according to the rules in SEC1.
335 static int primeeltp(mp
*x
, field
*f
)
337 return (!MP_ISNEG(x
) && MP_CMP(x
, <, f
->m
));
340 static const char *primecheck(const ec_info
*ei
, grand
*gr
)
349 /* --- Check %$p$% is an odd prime --- */
351 if (!pgen_primep(f
->m
, gr
)) return ("p not prime");
353 /* --- Check %$a$%, %$b$%, %$G_x$% and %$G_y$% are in %$[0, p)$% --- */
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");
360 /* --- Check %$4 a^3 + 27 b^2 \not\equiv 0 \pmod{p}$% --- */
362 x
= F_SQR(f
, MP_NEW
, c
->a
);
363 x
= F_MUL(f
, x
, x
, c
->a
);
365 y
= F_SQR(f
, MP_NEW
, c
->b
);
369 x
= F_ADD(f
, x
, x
, y
);
373 if (rc
) return ("not an elliptic curve");
375 /* --- Check %$G \in E$% --- */
377 if (EC_ATINF(&ei
->g
)) return ("generator at infinity");
378 if (ec_check(c
, &ei
->g
)) return ("generator not on curve");
380 /* --- Check %$r$% is prime --- */
382 if (!pgen_primep(ei
->r
, gr
)) return ("generator order not prime");
384 /* --- Check %$0 < h \le 4$% --- */
386 if (MP_CMP(ei
->h
, <, MP_ONE
) || MP_CMP(ei
->h
, >, MP_FOUR
))
387 return ("cofactor out of range");
389 /* --- Check %$h = \lfloor (\sqrt{p} + 1)^2/r \rlfoor$% --- *
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
396 x
= mp_lsl(MP_NEW
, f
->m
, 128);
398 y
= mp_lsl(MP_NEW
, MP_ONE
, 64);
401 mp_div(&x
, 0, x
, ei
->r
);
402 x
= mp_lsr(x
, x
, 128);
403 rc
= MP_EQ(x
, ei
->h
);
406 if (!rc
) return ("incorrect cofactor");
408 /* --- Check %$n G = O$% --- */
411 ec_mul(c
, &p
, &ei
->g
, ei
->r
);
414 if (!rc
) return ("incorrect group order");
416 /* --- Check that %$p^B \not\equiv 1 \pmod{r}$% for %$1 \le B < 20$% --- *
418 * The spec says %$q$%, not %$p$%, but I think that's a misprint.
422 mp_div(0, &x
, f
->m
, ei
->r
);
425 if (MP_EQ(x
, MP_ONE
)) break;
426 x
= mp_mul(x
, x
, f
->m
);
427 mp_div(0, &x
, x
, ei
->r
);
431 if (i
) return ("curve is weak");
438 static const char *bincheck(const ec_info
*ei
, grand
*gr
)
447 /* --- Check that %$p$% is irreducible --- */
449 if (!gf_irreduciblep(f
->m
)) return ("p not irreducible");
451 /* --- Check that %$a, b, G_x, G_y$% have degree less than %$p$% --- */
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");
458 /* --- Check that %$b \ne 0$% --- */
460 if (F_ZEROP(f
, c
->b
)) return ("b is zero");
462 /* --- Check that %$G \in E$% --- */
464 if (EC_ATINF(&ei
->g
)) return ("generator at infinity");
465 if (ec_check(c
, &ei
->g
)) return ("generator not on curve");
467 /* --- Check %$r$% is prime --- */
469 if (!pgen_primep(ei
->r
, gr
)) return ("generator order not prime");
471 /* --- Check %$0 < h \le 4$% --- */
473 if (MP_CMP(ei
->h
, <, MP_ONE
) || MP_CMP(ei
->h
, >, MP_FOUR
))
474 return ("cofactor out of range");
476 /* --- Check %$h = \lfloor (\sqrt{2^m} + 1)^2/r \rlfoor$% --- *
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
483 x
= mp_lsl(MP_NEW
, MP_ONE
, f
->nbits
+ 128);
485 y
= mp_lsl(MP_NEW
, MP_ONE
, 64);
488 mp_div(&x
, 0, x
, ei
->r
);
489 x
= mp_lsr(x
, x
, 128);
490 rc
= MP_EQ(x
, ei
->h
);
493 if (!rc
) return ("incorrect cofactor");
495 /* --- Check %$n G = O$% --- */
498 ec_mul(c
, &p
, &ei
->g
, ei
->r
);
501 if (!rc
) return ("incorrect group order");
503 /* --- Check %$2^{m B} \not\equiv 1 \pmod{r}$% for %$1 \le B < 20$% --- */
505 x
= mp_lsl(MP_NEW
, MP_ONE
, f
->nbits
);
506 mp_div(0, &x
, x
, ei
->r
);
509 if (MP_EQ(x
, MP_ONE
)) break;
510 x
= mp_mul(x
, x
, f
->m
);
511 mp_div(0, &x
, x
, ei
->r
);
515 if (i
) return ("curve is weak");
522 const char *ec_checkinfo(const ec_info
*ei
, grand
*gr
)
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;
528 return ("unknown curve type");
531 /*----- Test rig ----------------------------------------------------------*/
544 gr
= fibrand_create(0);
545 fputs("checking standard curves: ", stdout
);
546 for (ee
= ectab
; ee
->name
; ee
++) {
548 getinfo(&ei
, ee
->data
);
549 e
= ec_checkinfo(&ei
, gr
);
552 fprintf(stderr
, "\n*** curve %s fails: %s\n", ee
->name
, e
);
558 gr
->ops
->destroy(gr
);
559 fputs(ok ?
" ok\n" : " failed\n", stdout
);
565 /*----- That's all, folks -------------------------------------------------*/