/* -*-c-*-
*
- * $Id: ec-prime.c,v 1.3.4.3 2004/03/21 22:39:46 mdw Exp $
+ * $Id: ec-prime.c,v 1.11 2004/04/08 01:36:15 mdw Exp $
*
* Elliptic curves over prime fields
*
* MA 02111-1307, USA.
*/
-/*----- Revision history --------------------------------------------------*
- *
- * $Log: ec-prime.c,v $
- * Revision 1.3.4.3 2004/03/21 22:39:46 mdw
- * Elliptic curves on binary fields work.
- *
- * Revision 1.3.4.2 2004/03/20 00:13:31 mdw
- * Projective coordinates for prime curves
- *
- * Revision 1.3.4.1 2003/06/10 13:43:53 mdw
- * Simple (non-projective) curves over prime fields now seem to work.
- *
- * Revision 1.3 2003/05/15 23:25:59 mdw
- * Make elliptic curve stuff build.
- *
- * Revision 1.2 2002/01/13 13:48:44 mdw
- * Further progress.
- *
- * Revision 1.1 2001/04/29 18:12:33 mdw
- * Prototype version.
- *
- */
-
/*----- Header files ------------------------------------------------------*/
#include <mLib/sub.h>
#include "ec.h"
-/*----- Data structures ---------------------------------------------------*/
-
-typedef struct ecctx {
- ec_curve c;
- mp *a, *b;
-} ecctx;
-
/*----- Simple prime curves -----------------------------------------------*/
static const ec_ops ec_primeops, ec_primeprojops, ec_primeprojxops;
static ec *ecfind(ec_curve *c, ec *d, mp *x)
{
mp *p, *q;
- ecctx *cc = (ecctx *)c;
field *f = c->f;
q = F_SQR(f, MP_NEW, x);
p = F_MUL(f, MP_NEW, x, q);
- q = F_MUL(f, q, x, cc->a);
+ q = F_MUL(f, q, x, c->a);
p = F_ADD(f, p, p, q);
- p = F_ADD(f, p, p, cc->b);
+ p = F_ADD(f, p, p, c->b);
MP_DROP(q);
p = F_SQRT(f, p, p);
if (!p)
EC_COPY(d, a);
else {
field *f = c->f;
- ecctx *cc = (ecctx *)c;
mp *lambda;
mp *dy, *dx;
dx = F_SQR(f, MP_NEW, a->x); /* %$x^2$% */
dy = F_DBL(f, MP_NEW, a->y); /* %$2 y$% */
dx = F_TPL(f, dx, dx); /* %$3 x^2$% */
- dx = F_ADD(f, dx, dx, cc->a); /* %$3 x^2 + A$% */
+ dx = F_ADD(f, dx, dx, c->a); /* %$3 x^2 + A$% */
dy = F_INV(f, dy, dy); /* %$(2 y)^{-1}$% */
lambda = F_MUL(f, MP_NEW, dx, dy); /* %$\lambda = (3 x^2 + A)/(2 y)$% */
EC_COPY(d, a);
else {
field *f = c->f;
- ecctx *cc = (ecctx *)c;
mp *p, *q, *m, *s, *dx, *dy, *dz;
p = F_SQR(f, MP_NEW, a->z); /* %$z^2$% */
q = F_SQR(f, MP_NEW, p); /* %$z^4$% */
- p = F_MUL(f, p, q, cc->a); /* %$A z^4$% */
+ p = F_MUL(f, p, q, c->a); /* %$A z^4$% */
m = F_SQR(f, MP_NEW, a->x); /* %$x^2$% */
m = F_TPL(f, m, m); /* %$3 x^2$% */
m = F_ADD(f, m, m, p); /* %$m = 3 x^2 + A z^4$% */
EC_SETINF(d);
return (d);
} else {
- ecctx *cc = (ecctx *)c;
dx = F_SQR(f, MP_NEW, a->x); /* %$x_0^2$% */
dx = F_TPL(f, dx, dx); /* %$3 x_0^2$% */
- dx = F_ADD(f, dx, dx, cc->a); /* %$3 x_0^2 + A$% */
+ dx = F_ADD(f, dx, dx, c->a); /* %$3 x_0^2 + A$% */
dy = F_DBL(f, MP_NEW, a->y); /* %$2 y_0$% */
dy = F_INV(f, dy, dy); /* %$(2 y_0)^{-1}$% */
lambda = F_MUL(f, MP_NEW, dx, dy);
EC_COPY(d, a);
else {
field *f = c->f;
- mp *p, *q, *r, *w, *u, *s, *dx, *dy, *dz;
+ mp *p, *q, *r, *w, *u, *uu, *s, *ss, *dx, *dy, *dz;
q = F_SQR(f, MP_NEW, a->z); /* %$z_0^2$% */
u = F_MUL(f, MP_NEW, q, b->x); /* %$u = x_1 z_0^2$% */
p = F_MUL(f, MP_NEW, q, b->y); /* %$y_1 z_0^2$% */
s = F_MUL(f, q, p, a->z); /* %$s = y_1 z_0^3$% */
- w = F_SUB(f, p, a->x, u); /* %$w = x_0 - u$% */
- r = F_SUB(f, MP_NEW, a->y, s); /* %$r = y_0 - s$% */
+ q = F_SQR(f, MP_NEW, b->z); /* %$z_1^2$% */
+ uu = F_MUL(f, MP_NEW, q, a->x); /* %$uu = x_0 z_1^2$%*/
+ p = F_MUL(f, p, q, a->y); /* %$y_0 z_1^2$% */
+ ss = F_MUL(f, q, p, b->z); /* %$ss = y_0 z_1^3$% */
+
+ w = F_SUB(f, p, uu, u); /* %$w = uu - u$% */
+ r = F_SUB(f, MP_NEW, ss, s); /* %$r = ss - s$% */
if (F_ZEROP(f, w)) {
MP_DROP(w);
MP_DROP(u);
MP_DROP(s);
+ MP_DROP(uu);
+ MP_DROP(ss);
if (F_ZEROP(f, r)) {
MP_DROP(r);
return (c->ops->dbl(c, d, a));
return (d);
}
}
- u = F_ADD(f, u, u, a->x); /* %$t = x_0 + u$% */
- s = F_ADD(f, s, s, a->y); /* %$m = y_0 + r$% */
+ u = F_ADD(f, u, u, uu); /* %$t = uu + u$% */
+ s = F_ADD(f, s, s, ss); /* %$m = ss + r$% */
- dz = F_MUL(f, MP_NEW, a->z, w); /* %$z' = z_0 w$% */
+ uu = F_MUL(f, uu, a->z, w); /* %$z_0 w$% */
+ dz = F_MUL(f, ss, uu, b->z); /* %$z' = z_0 z_1 w$% */
- p = F_SQR(f, MP_NEW, w); /* %$w^2$% */
+ p = F_SQR(f, uu, w); /* %$w^2$% */
q = F_MUL(f, MP_NEW, p, u); /* %$t w^2$% */
u = F_MUL(f, u, p, w); /* %$w^3$% */
p = F_MUL(f, p, u, s); /* %$m w^3$% */
static int eccheck(ec_curve *c, const ec *p)
{
- ecctx *cc = (ecctx *)c;
field *f = c->f;
+ mp *l, *x, *r;
int rc;
- mp *l = F_SQR(f, MP_NEW, p->y);
- mp *x = F_SQR(f, MP_NEW, p->x);
- mp *r = F_MUL(f, MP_NEW, x, p->x);
- x = F_MUL(f, x, cc->a, p->x);
+ if (EC_ATINF(p)) return (0);
+ l = F_SQR(f, MP_NEW, p->y);
+ x = F_SQR(f, MP_NEW, p->x);
+ r = F_MUL(f, MP_NEW, x, p->x);
+ x = F_MUL(f, x, c->a, p->x);
r = F_ADD(f, r, r, x);
- r = F_ADD(f, r, r, cc->b);
+ r = F_ADD(f, r, r, c->b);
rc = MP_EQ(l, r) ? 0 : -1;
mp_drop(l);
mp_drop(x);
static void ecdestroy(ec_curve *c)
{
- ecctx *cc = (ecctx *)c;
- MP_DROP(cc->a);
- MP_DROP(cc->b);
- DESTROY(cc);
+ MP_DROP(c->a);
+ MP_DROP(c->b);
+ DESTROY(c);
}
/* --- @ec_prime@, @ec_primeproj@ --- *
* Arguments: @field *f@ = the underlying field for this elliptic curve
* @mp *a, *b@ = the coefficients for this curve
*
- * Returns: A pointer to the curve.
+ * Returns: A pointer to the curve, or null.
*
* Use: Creates a curve structure for an elliptic curve defined over
* a prime field. The @primeproj@ variant uses projective
extern ec_curve *ec_prime(field *f, mp *a, mp *b)
{
- ecctx *cc = CREATE(ecctx);
- cc->c.ops = &ec_primeops;
- cc->c.f = f;
- cc->a = F_IN(f, MP_NEW, a);
- cc->b = F_IN(f, MP_NEW, b);
- return (&cc->c);
+ ec_curve *c = CREATE(ec_curve);
+ c->ops = &ec_primeops;
+ c->f = f;
+ c->a = F_IN(f, MP_NEW, a);
+ c->b = F_IN(f, MP_NEW, b);
+ return (c);
}
extern ec_curve *ec_primeproj(field *f, mp *a, mp *b)
{
- ecctx *cc = CREATE(ecctx);
+ ec_curve *c = CREATE(ec_curve);
mp *ax;
ax = mp_add(MP_NEW, a, MP_THREE);
ax = F_IN(f, ax, ax);
if (F_ZEROP(f, ax))
- cc->c.ops = &ec_primeprojxops;
+ c->ops = &ec_primeprojxops;
else
- cc->c.ops = &ec_primeprojops;
+ c->ops = &ec_primeprojops;
MP_DROP(ax);
- cc->c.f = f;
- cc->a = F_IN(f, MP_NEW, a);
- cc->b = F_IN(f, MP_NEW, b);
- return (&cc->c);
+ c->f = f;
+ c->a = F_IN(f, MP_NEW, a);
+ c->b = F_IN(f, MP_NEW, b);
+ return (c);
}
static const ec_ops ec_primeops = {
- ecdestroy, ec_idin, ec_idout, ec_idfix,
- 0, ecneg, ecadd, ec_stdsub, ecdbl, eccheck
+ ecdestroy, ec_stdsamep, ec_idin, ec_idout, ec_idfix,
+ ecfind, ecneg, ecadd, ec_stdsub, ecdbl, eccheck
};
static const ec_ops ec_primeprojops = {
- ecdestroy, ec_projin, ec_projout, ec_projfix,
- 0, ecneg, ecprojadd, ec_stdsub, ecprojdbl, ecprojcheck
+ ecdestroy, ec_stdsamep, ec_projin, ec_projout, ec_projfix,
+ ecfind, ecneg, ecprojadd, ec_stdsub, ecprojdbl, ecprojcheck
};
static const ec_ops ec_primeprojxops = {
- ecdestroy, ec_projin, ec_projout, ec_projfix,
- 0, ecneg, ecprojadd, ec_stdsub, ecprojxdbl, ecprojcheck
+ ecdestroy, ec_stdsamep, ec_projin, ec_projout, ec_projfix,
+ ecfind, ecneg, ecprojadd, ec_stdsub, ecprojxdbl, ecprojcheck
};
/*----- Test rig ----------------------------------------------------------*/
printf("ec-prime: ");
fflush(stdout);
a = MP(-3);
- b = MP(0x64210519e59c80e70fa7e9ab72243049feb8deecc146b9b1);
- p = MP(6277101735386680763835789423207666416083908700390324961279);
- r = MP(6277101735386680763835789423176059013767194773182842284080);
+ b = MP(0xb3312fa7e23ee7e4988e056be3f82d19181d9c6efe8141120314088f5013875ac656398d8a2ed19d2a85c8edd3ec2aef);
+ p = MP(39402006196394479212279040100143613805079739270465446667948293404245721771496870329047266088258938001861606973112319);
+ r = MP(39402006196394479212279040100143613805079739270465446667946905279627659399113263569398956308152294913554433653942642);
- f = field_prime(p);
+ f = field_niceprime(p);
c = ec_primeproj(f, a, b);
- g.x = MP(0x188da80eb03090f67cbf20eb43a18800f4ff0afd82ff1012);
- g.y = MP(0x07192b95ffc8da78631011ed6b24cdd573f977a11e794811);
+ g.x = MP(0xaa87ca22be8b05378eb1c71ef320ad746e1d3b628ba79b9859f741e082542a385502f25dbf55296c3a545e3872760ab7);
+ g.y = MP(0x3617de4a96262c6f5d9e98bf9292dc29f8f41dbd289a147ce9da3113b5f0b8c00a60b1ce1d7e819d7a431d7c90ea0e5f);
for (i = 0; i < n; i++) {
ec_mul(c, &d, &g, r);
projects / u / mdw / catacomb / blobdiff