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 ------------------------------------------------------*/
40 /*----- Main code ---------------------------------------------------------*/
42 /* --- @ec_curveparse@ --- *
44 * Arguments: @qd_parse *qd@ = parser context
46 * Returns: Elliptic curve pointer if OK, or null.
48 * Use: Parses an elliptic curve description, which has the form
50 * * a field description
52 * * `prime', `primeproj', `bin', or `binproj'
54 * * the %$a$% parameter
56 * * the %$b$% parameter
59 ec_curve
*ec_curveparse(qd_parse
*qd
)
61 mp
*a
= MP_NEW
, *b
= MP_NEW
;
65 if ((f
= field_parse(qd
)) == 0) goto fail
;
67 switch (qd_enum(qd
, "prime,primeproj,bin,binproj")) {
69 if (F_TYPE(f
) != FTY_PRIME
) {
70 qd
->e
= "field not prime";
74 if ((a
= qd_getmp(qd
)) == 0) goto fail
;
76 if ((b
= qd_getmp(qd
)) == 0) goto fail
;
77 c
= ec_prime(f
, a
, b
);
80 if (F_TYPE(f
) != FTY_PRIME
) {
81 qd
->e
= "field not prime";
85 if ((a
= qd_getmp(qd
)) == 0) goto fail
;
87 if ((b
= qd_getmp(qd
)) == 0) goto fail
;
88 c
= ec_primeproj(f
, a
, b
);
91 if (F_TYPE(f
) != FTY_BINARY
) {
92 qd
->e
= "field not binary";
96 if ((a
= qd_getmp(qd
)) == 0) goto fail
;
98 if ((b
= qd_getmp(qd
)) == 0) goto fail
;
102 if (F_TYPE(f
) != FTY_BINARY
) {
103 qd
->e
= "field not binary";
107 if ((a
= qd_getmp(qd
)) == 0) goto fail
;
109 if ((b
= qd_getmp(qd
)) == 0) goto fail
;
110 c
= ec_binproj(f
, a
, b
);
116 qd
->e
= "bad curve parameters";
130 /* --- @ec_ptparse@ --- *
132 * Arguments: @qd_parse *qd@ = parser context
133 * @ec *p@ = where to put the point
135 * Returns: The point address, or null.
137 * Use: Parses an elliptic curve point. This has the form
144 ec
*ec_ptparse(qd_parse
*qd
, ec
*p
)
146 mp
*x
= MP_NEW
, *y
= MP_NEW
;
148 if (qd_enum(qd
, "inf") >= 0) {
152 if ((x
= qd_getmp(qd
)) == 0) goto fail
;
154 if ((y
= qd_getmp(qd
)) == 0) goto fail
;
167 /* --- @getinfo@ --- *
169 * Arguments: @ec_info *ei@ = where to write the information
170 * @ecdata *ed@ = raw data
174 * Use: Loads elliptic curve information about one of the standard
178 static void getinfo(ec_info
*ei
, ecdata
*ed
)
184 f
= field_prime(&ed
->p
);
185 ei
->c
= ec_primeproj(f
, &ed
->a
, &ed
->b
);
188 f
= field_niceprime(&ed
->p
);
189 ei
->c
= ec_primeproj(f
, &ed
->a
, &ed
->b
);
192 f
= field_binpoly(&ed
->p
);
193 ei
->c
= ec_binproj(f
, &ed
->a
, &ed
->b
);
196 f
= field_binnorm(&ed
->p
, &ed
->beta
);
197 ei
->c
= ec_binproj(f
, &ed
->a
, &ed
->b
);
203 assert(f
); assert(ei
->c
);
204 EC_CREATE(&ei
->g
); ei
->g
.x
= &ed
->gx
; ei
->g
.y
= &ed
->gy
; ei
->g
.z
= 0;
205 ei
->r
= &ed
->r
; ei
->h
= &ed
->h
;
208 /* --- @ec_infoparse@ --- *
210 * Arguments: @qd_parse *qd@ = parser context
211 * @ec_info *ei@ = curve information block, currently
214 * Returns: Zero on success, nonzero on failure.
216 * Use: Parses an elliptic curve information string, and stores the
217 * information in @ei@. This is either the name of a standard
218 * curve, or it has the form
220 * * elliptic curve description
229 int ec_infoparse(qd_parse
*qd
, ec_info
*ei
)
235 mp
*r
= MP_NEW
, *h
= MP_NEW
;
237 for (ee
= ectab
; ee
->name
; ee
++)
238 if (qd_enum(qd
, ee
->name
) >= 0) { getinfo(ei
, ee
->data
); goto found
; }
240 if ((c
= ec_curveparse(qd
)) == 0) goto fail
;
241 qd_delim(qd
, '/'); if (!ec_ptparse(qd
, &g
)) goto fail
;
242 qd_delim(qd
, ':'); if ((r
= qd_getmp(qd
)) == 0) goto fail
;
243 qd_delim(qd
, '*'); if ((h
= qd_getmp(qd
)) == 0) goto fail
;
244 ei
->c
= c
; ei
->g
= g
; ei
->r
= r
; ei
->h
= h
;
253 if (c
) { f
= c
->f
; ec_destroycurve(c
); F_DESTROY(f
); }
257 /* --- @ec_getinfo@ --- *
259 * Arguments: @ec_info *ei@ = where to write the information
260 * @const char *p@ = string describing a curve
262 * Returns: Null on success, or a pointer to an error message.
264 * Use: Parses out information about a curve. The string is either a
265 * standard curve name, or a curve info string.
268 const char *ec_getinfo(ec_info
*ei
, const char *p
)
274 if (ec_infoparse(&qd
, ei
))
278 return ("junk found at end of string");
283 /* --- @ec_sameinfop@ --- *
285 * Arguments: @ec_info *ei, *ej@ = two elliptic curve parameter sets
287 * Returns: Nonzero if the curves are identical (not just isomorphic).
289 * Use: Checks for sameness of curve parameters.
292 int ec_sameinfop(ec_info
*ei
, ec_info
*ej
)
294 return (ec_samep(ei
->c
, ej
->c
) &&
295 MP_EQ(ei
->r
, ej
->r
) && MP_EQ(ei
->h
, ej
->h
) &&
296 EC_EQ(&ei
->g
, &ej
->g
));
299 /* --- @ec_freeinfo@ --- *
301 * Arguments: @ec_info *ei@ = elliptic curve information block to free
305 * Use: Frees the information block.
308 void ec_freeinfo(ec_info
*ei
)
315 f
= ei
->c
->f
; ec_destroycurve(ei
->c
); F_DESTROY(f
);
318 /* --- @ec_checkinfo@ --- *
320 * Arguments: @const ec_info *ei@ = elliptic curve information block
322 * Returns: Null if OK, or pointer to error message.
324 * Use: Checks an elliptic curve according to the rules in SEC1.
327 static int primeeltp(mp
*x
, field
*f
)
329 return (!MP_NEGP(x
) && MP_CMP(x
, <, f
->m
));
332 static const char *primecheck(const ec_info
*ei
, grand
*gr
)
341 /* --- Check %$p$% is an odd prime --- */
343 if (!pgen_primep(f
->m
, gr
)) return ("p not prime");
345 /* --- Check %$a$%, %$b$%, %$G_x$% and %$G_y$% are in %$[0, p)$% --- */
347 if (!primeeltp(c
->a
, f
)) return ("a out of range");
348 if (!primeeltp(c
->b
, f
)) return ("b out of range");
349 if (!primeeltp(ei
->g
.x
, f
)) return ("G_x out of range");
350 if (!primeeltp(ei
->g
.x
, f
)) return ("G_y out of range");
352 /* --- Check %$4 a^3 + 27 b^2 \not\equiv 0 \pmod{p}$% --- */
354 x
= F_SQR(f
, MP_NEW
, c
->a
);
355 x
= F_MUL(f
, x
, x
, c
->a
);
357 y
= F_SQR(f
, MP_NEW
, c
->b
);
361 x
= F_ADD(f
, x
, x
, y
);
365 if (rc
) return ("not an elliptic curve");
367 /* --- Check %$G \in E$% --- */
369 if (EC_ATINF(&ei
->g
)) return ("generator at infinity");
370 if (ec_check(c
, &ei
->g
)) return ("generator not on curve");
372 /* --- Check %$r$% is prime --- */
374 if (!pgen_primep(ei
->r
, gr
)) return ("generator order not prime");
376 /* --- Check %$h = \lfloor (\sqrt{p} + 1)^2/r \rlfoor$% --- *
378 * This seems to work with the approximate-sqrt in the library, but might
379 * not be so good in some cases. Throw in some extra significate figures
383 x
= mp_lsl(MP_NEW
, f
->m
, 128);
385 y
= mp_lsl(MP_NEW
, MP_ONE
, 64);
388 mp_div(&x
, 0, x
, ei
->r
);
389 x
= mp_lsr(x
, x
, 128);
390 rc
= MP_EQ(x
, ei
->h
);
393 if (!rc
) return ("incorrect cofactor");
395 /* --- Check %$n G = O$% --- */
398 ec_mul(c
, &p
, &ei
->g
, ei
->r
);
401 if (!rc
) return ("incorrect group order");
403 /* --- Check that %$p^B \not\equiv 1 \pmod{r}$% for %$1 \le B < 20$% --- *
405 * The spec says %$q$%, not %$p$%, but I think that's a misprint.
409 mp_div(0, &x
, f
->m
, ei
->r
);
412 if (MP_EQ(x
, MP_ONE
)) break;
413 x
= mp_mul(x
, x
, f
->m
);
414 mp_div(0, &x
, x
, ei
->r
);
418 if (i
) return ("curve is weak");
420 /* --- Check %$0 < h \le 4$% --- */
422 if (MP_CMP(ei
->h
, <, MP_ONE
) || MP_CMP(ei
->h
, >, MP_FOUR
))
423 return ("cofactor out of range");
430 static const char *bincheck(const ec_info
*ei
, grand
*gr
)
439 /* --- Check that %$m$% is prime --- */
441 x
= mp_fromuint(MP_NEW
, f
->nbits
);
442 rc
= pfilt_smallfactor(x
);
444 if (rc
!= PGEN_DONE
) return ("degree not prime");
446 /* --- Check that %$p$% is irreducible --- */
448 if (!gf_irreduciblep(f
->m
)) return ("p not irreducible");
450 /* --- Check that %$a, b, G_x, G_y$% have degree less than %$p$% --- */
452 if (mp_bits(c
->a
) > f
->nbits
) return ("a out of range");
453 if (mp_bits(c
->b
) > f
->nbits
) return ("a out of range");
454 if (mp_bits(ei
->g
.x
) > f
->nbits
) return ("G_x out of range");
455 if (mp_bits(ei
->g
.y
) > f
->nbits
) return ("G_y out of range");
457 /* --- Check that %$b \ne 0$% --- */
459 if (F_ZEROP(f
, c
->b
)) return ("b is zero");
461 /* --- Check that %$G \in E$% --- */
463 if (EC_ATINF(&ei
->g
)) return ("generator at infinity");
464 if (ec_check(c
, &ei
->g
)) return ("generator not on curve");
466 /* --- Check %$r$% is prime --- */
468 if (!pgen_primep(ei
->r
, gr
)) return ("generator order not prime");
470 /* --- Check %$h = \lfloor (\sqrt{2^m} + 1)^2/r \rlfoor$% --- *
472 * This seems to work with the approximate-sqrt in the library, but might
473 * not be so good in some cases. Throw in some extra significate figures
477 x
= mp_lsl(MP_NEW
, MP_ONE
, f
->nbits
+ 128);
479 y
= mp_lsl(MP_NEW
, MP_ONE
, 64);
482 mp_div(&x
, 0, x
, ei
->r
);
483 x
= mp_lsr(x
, x
, 128);
484 rc
= MP_EQ(x
, ei
->h
);
487 if (!rc
) return ("incorrect cofactor");
489 /* --- Check %$n G = O$% --- */
492 ec_mul(c
, &p
, &ei
->g
, ei
->r
);
495 if (!rc
) return ("incorrect group order");
497 /* --- Check %$2^{m B} \not\equiv 1 \pmod{r}$% for %$1 \le B < 20$% --- */
499 x
= mp_lsl(MP_NEW
, MP_ONE
, f
->nbits
);
500 mp_div(0, &x
, x
, ei
->r
);
503 if (MP_EQ(x
, MP_ONE
)) break;
504 x
= mp_mul(x
, x
, f
->m
);
505 mp_div(0, &x
, x
, ei
->r
);
509 if (i
) return ("curve is weak");
511 /* --- Check %$0 < h \le 4$% --- */
513 if (MP_CMP(ei
->h
, <, MP_ONE
) || MP_CMP(ei
->h
, >, MP_FOUR
))
514 return ("cofactor out of range");
521 const char *ec_checkinfo(const ec_info
*ei
, grand
*gr
)
523 switch (F_TYPE(ei
->c
->f
)) {
524 case FTY_PRIME
: return (primecheck(ei
, gr
)); break;
525 case FTY_BINARY
: return (bincheck(ei
, gr
)); break;
527 return ("unknown curve type");
530 /*----- Test rig ----------------------------------------------------------*/
536 int main(int argc
, char *argv
[])
544 gr
= fibrand_create(0);
546 for (i
= 1; i
< argc
; i
++) {
548 if ((e
= ec_getinfo(&ei
, argv
[i
])) != 0)
549 fprintf(stderr
, "bad curve spec `%s': %s", argv
[i
], e
);
551 e
= ec_checkinfo(&ei
, gr
);
554 printf("OK %s\n", argv
[i
]);
556 printf("BAD %s: %s\n", argv
[i
], e
);
562 fputs("checking standard curves...\n", stdout
);
563 for (ee
= ectab
; ee
->name
; ee
++) {
565 printf(" %s: ", ee
->name
);
567 getinfo(&ei
, ee
->data
);
568 e
= ec_checkinfo(&ei
, gr
);
571 printf("fails: %s\n", e
);
574 fputs("ok\n", stdout
);
578 fputs("all ok\n", stdout
);
580 gr
->ops
->destroy(gr
);
586 /*----- That's all, folks -------------------------------------------------*/