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 /* --- @ec_infofromdata@ --- *
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 void ec_infofromdata(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) {
239 ec_infofromdata(ei
, ee
->data
);
244 if ((c
= ec_curveparse(qd
)) == 0) goto fail
;
245 qd_delim(qd
, ';'); if (!ec_ptparse(qd
, &g
)) goto fail
;
246 qd_delim(qd
, ':'); if ((r
= qd_getmp(qd
)) == 0) goto fail
;
247 qd_delim(qd
, '*'); if ((h
= qd_getmp(qd
)) == 0) goto fail
;
248 ei
->c
= c
; ei
->g
= g
; ei
->r
= r
; ei
->h
= h
;
257 if (c
) { f
= c
->f
; ec_destroycurve(c
); F_DESTROY(f
); }
261 /* --- @ec_getinfo@ --- *
263 * Arguments: @ec_info *ei@ = where to write the information
264 * @const char *p@ = string describing a curve
266 * Returns: Null on success, or a pointer to an error message.
268 * Use: Parses out information about a curve. The string is either a
269 * standard curve name, or a curve info string.
272 const char *ec_getinfo(ec_info
*ei
, const char *p
)
278 if (ec_infoparse(&qd
, ei
))
282 return ("junk found at end of string");
287 /* --- @ec_sameinfop@ --- *
289 * Arguments: @ec_info *ei, *ej@ = two elliptic curve parameter sets
291 * Returns: Nonzero if the curves are identical (not just isomorphic).
293 * Use: Checks for sameness of curve parameters.
296 int ec_sameinfop(ec_info
*ei
, ec_info
*ej
)
298 return (ec_samep(ei
->c
, ej
->c
) &&
299 MP_EQ(ei
->r
, ej
->r
) && MP_EQ(ei
->h
, ej
->h
) &&
300 EC_EQ(&ei
->g
, &ej
->g
));
303 /* --- @ec_freeinfo@ --- *
305 * Arguments: @ec_info *ei@ = elliptic curve information block to free
309 * Use: Frees the information block.
312 void ec_freeinfo(ec_info
*ei
)
319 f
= ei
->c
->f
; ec_destroycurve(ei
->c
); F_DESTROY(f
);
322 /* --- @ec_checkinfo@ --- *
324 * Arguments: @const ec_info *ei@ = elliptic curve information block
326 * Returns: Null if OK, or pointer to error message.
328 * Use: Checks an elliptic curve according to the rules in SEC1.
331 static const char *gencheck(const ec_info
*ei
, grand
*gr
, mp
*q
)
342 /* --- Check %$G \in E$% --- */
344 if (EC_ATINF(&ei
->g
)) return ("generator at infinity");
345 if (ec_check(c
, &ei
->g
)) return ("generator not on curve");
347 /* --- Check %$r$% is prime --- */
349 if (!pgen_primep(ei
->r
, gr
)) return ("generator order not prime");
351 /* --- Check that the cofactor is correct --- *
353 * Let %$q$% be the size of the field, and let %$n = h r = \#E(\gf{q})$% be
354 * the number of %$\gf{q}$%-rational points on our curve. Hasse's theorem
357 * %$|q + 1 - n| \le 2\sqrt{q}$%
359 * or, if we square both sides,
361 * %$(q + 1 - n)^2 \le 4 q$%.
363 * We'd like the cofactor to be uniquely determined by this equation, which
364 * is possible as long as it's not too big. (If it is, we have to mess
365 * about with Weil pairings, which is no fun.) For this, we need the
366 * following inequalities:
368 * * %$A = (q + 1 - n)^2 \le 4 q$% (both lower and upper bounds from
371 * * %$B = (q + 1 - n - r)^2 > 4 q$% (check %$h - 1$% isn't possible);
374 * * %$C = (q + 1 - n + r)^2 > 4 q$% (check %$h + 1$% isn't possible).
378 qq
= mp_add(MP_NEW
, q
, MP_ONE
);
379 nn
= mp_mul(MP_NEW
, ei
->r
, ei
->h
);
380 nn
= mp_sub(nn
, qq
, nn
);
381 qq
= mp_lsl(qq
, q
, 2);
383 y
= mp_sqr(MP_NEW
, nn
);
384 if (MP_CMP(y
, >, qq
)) rc
= 0;
386 x
= mp_sub(MP_NEW
, nn
, ei
->r
);
388 if (MP_CMP(y
, <=, qq
)) rc
= 0;
390 x
= mp_add(x
, nn
, ei
->r
);
392 if (MP_CMP(y
, <=, qq
)) rc
= 0;
398 if (!rc
) return ("incorrect or ambiguous cofactor");
400 /* --- Check %$n G = O$% --- */
403 ec_mul(c
, &p
, &ei
->g
, ei
->r
);
406 if (!rc
) return ("incorrect group order");
408 /* --- Check %$q^B \not\equiv 1 \pmod{r}$% for %$1 \le B < 20$% --- *
410 * Actually, give up if %$q^B \ge 2^{2000}$% because that's probably
411 * good enough for jazz.
415 mp_div(0, &x
, q
, ei
->r
);
416 n
= mp_bits(ei
->r
) - 1;
417 for (i
= 0, j
= n
; i
< 20; i
++, j
+= n
) {
420 if (MP_EQ(x
, MP_ONE
)) {
422 return("curve embedding degree too low");
424 x
= mp_mul(x
, x
, f
->m
);
425 mp_div(0, &x
, x
, ei
->r
);
434 static int primeeltp(mp
*x
, field
*f
)
435 { return (!MP_NEGP(x
) && MP_CMP(x
, <, f
->m
)); }
437 static const char *primecheck(const ec_info
*ei
, grand
*gr
)
445 /* --- Check %$p$% is an odd prime --- */
447 if (!pgen_primep(f
->m
, gr
)) return ("p not prime");
449 /* --- Check %$a$%, %$b$%, %$G_x$% and %$G_y$% are in %$[0, p)$% --- */
451 if (!primeeltp(c
->a
, f
)) return ("a out of range");
452 if (!primeeltp(c
->b
, f
)) return ("b out of range");
453 if (!primeeltp(ei
->g
.x
, f
)) return ("G_x out of range");
454 if (!primeeltp(ei
->g
.x
, f
)) return ("G_y out of range");
456 /* --- Check %$4 a^3 + 27 b^2 \not\equiv 0 \pmod{p}$% --- */
458 x
= F_SQR(f
, MP_NEW
, c
->a
);
459 x
= F_MUL(f
, x
, x
, c
->a
);
461 y
= F_SQR(f
, MP_NEW
, c
->b
);
465 x
= F_ADD(f
, x
, x
, y
);
469 if (rc
) return ("not an elliptic curve");
471 /* --- Now do the general checks --- */
473 err
= gencheck(ei
, gr
, f
->m
);
477 static const char *bincheck(const ec_info
*ei
, grand
*gr
)
485 /* --- Check that %$m$% is prime --- */
487 x
= mp_fromuint(MP_NEW
, f
->nbits
);
488 rc
= pfilt_smallfactor(x
);
490 if (rc
!= PGEN_DONE
) return ("degree not prime");
492 /* --- Check that %$p$% is irreducible --- */
494 if (!gf_irreduciblep(f
->m
)) return ("p not irreducible");
496 /* --- Check that %$a, b, G_x, G_y$% have degree less than %$p$% --- */
498 if (mp_bits(c
->a
) > f
->nbits
) return ("a out of range");
499 if (mp_bits(c
->b
) > f
->nbits
) return ("a out of range");
500 if (mp_bits(ei
->g
.x
) > f
->nbits
) return ("G_x out of range");
501 if (mp_bits(ei
->g
.y
) > f
->nbits
) return ("G_y out of range");
503 /* --- Check that %$b \ne 0$% --- */
505 if (F_ZEROP(f
, c
->b
)) return ("b is zero");
507 /* --- Now do the general checks --- */
509 x
= mp_lsl(MP_NEW
, MP_ONE
, f
->nbits
);
510 err
= gencheck(ei
, gr
, x
);
515 const char *ec_checkinfo(const ec_info
*ei
, grand
*gr
)
517 switch (F_TYPE(ei
->c
->f
)) {
518 case FTY_PRIME
: return (primecheck(ei
, gr
)); break;
519 case FTY_BINARY
: return (bincheck(ei
, gr
)); break;
521 return ("unknown curve type");
524 /*----- Test rig ----------------------------------------------------------*/
530 int main(int argc
, char *argv
[])
538 gr
= fibrand_create(0);
540 for (i
= 1; i
< argc
; i
++) {
542 if ((e
= ec_getinfo(&ei
, argv
[i
])) != 0)
543 fprintf(stderr
, "bad curve spec `%s': %s", argv
[i
], e
);
545 e
= ec_checkinfo(&ei
, gr
);
548 printf("OK %s\n", argv
[i
]);
550 printf("BAD %s: %s\n", argv
[i
], e
);
554 assert(mparena_count(MPARENA_GLOBAL
) == 0);
557 fputs("checking standard curves:", stdout
);
559 for (ee
= ectab
; ee
->name
; ee
++) {
561 ec_infofromdata(&ei
, ee
->data
);
562 e
= ec_checkinfo(&ei
, gr
);
565 printf(" [%s fails: %s]", ee
->name
, e
);
568 printf(" %s", ee
->name
);
570 assert(mparena_count(MPARENA_GLOBAL
) == 0);
572 fputs(ok ?
" ok\n" : " failed\n", stdout
);
574 gr
->ops
->destroy(gr
);
580 /*----- That's all, folks -------------------------------------------------*/