/* -*-c-*-
*
- * $Id: ec-bin.c,v 1.3 2004/03/22 02:19:09 mdw Exp $
+ * $Id: ec-bin.c,v 1.9 2004/04/08 01:36:15 mdw Exp $
*
* Arithmetic for elliptic curves over binary fields
*
* MA 02111-1307, USA.
*/
-/*----- Revision history --------------------------------------------------*
- *
- * $Log: ec-bin.c,v $
- * Revision 1.3 2004/03/22 02:19:09 mdw
- * Rationalise the sliding-window threshold. Drop guarantee that right
- * arguments to EC @add@ are canonical, and fix up projective implementations
- * to cope.
- *
- * Revision 1.2 2004/03/21 22:52:06 mdw
- * Merge and close elliptic curve branch.
- *
- * Revision 1.1.2.1 2004/03/21 22:39:46 mdw
- * Elliptic curves on binary fields work.
- *
- */
-
/*----- Header files ------------------------------------------------------*/
#include <mLib/sub.h>
typedef struct ecctx {
ec_curve c;
- mp *a, *b;
mp *bb;
} ecctx;
static ec *ecfind(ec_curve *c, ec *d, mp *x)
{
- /* write me */
- return (0);
+ field *f = c->f;
+ mp *y, *u, *v;
+
+ if (F_ZEROP(f, x))
+ y = F_SQRT(f, MP_NEW, c->b);
+ else {
+ u = F_SQR(f, MP_NEW, x); /* %$x^2$% */
+ y = F_MUL(f, MP_NEW, u, c->a); /* %$a x^2$% */
+ y = F_ADD(f, y, y, c->b); /* %$a x^2 + b$% */
+ v = F_MUL(f, MP_NEW, u, x); /* %$x^3$% */
+ y = F_ADD(f, y, y, v); /* %$A = x^3 + a x^2 + b$% */
+ if (!F_ZEROP(f, y)) {
+ u = F_INV(f, u, u); /* %$x^{-2}$% */
+ v = F_MUL(f, v, u, y); /* %$B = A x^{-2} = x + a + b x^{-2}$% */
+ y = F_QUADSOLVE(f, y, v); /* %$z^2 + z = B$% */
+ if (y) y = F_MUL(f, y, y, x); /* %$y = z x$% */
+ }
+ MP_DROP(u);
+ MP_DROP(v);
+ }
+ if (!y) return (0);
+ EC_DESTROY(d);
+ d->x = MP_COPY(x);
+ d->y = y;
+ d->z = MP_COPY(f->one);
+ return (d);
}
static ec *ecdbl(ec_curve *c, ec *d, const ec *a)
EC_SETINF(d);
else {
field *f = c->f;
- ecctx *cc = (ecctx *)c;
mp *lambda;
mp *dx, *dy;
dx = F_SQR(f, dx, lambda); /* %$\lambda^2$% */
dx = F_ADD(f, dx, dx, lambda); /* %$\lambda^2 + \lambda$% */
- dx = F_ADD(f, dx, dx, cc->a); /* %$x' = a + \lambda^2 + \lambda$% */
+ dx = F_ADD(f, dx, dx, c->a); /* %$x' = a + \lambda^2 + \lambda$% */
dy = F_ADD(f, MP_NEW, a->x, dx); /* %$ x + x' $% */
dy = F_MUL(f, dy, dy, lambda); /* %$ (x + x') \lambda$% */
d->z = dz;
MP_DROP(u);
MP_DROP(v);
- assert(!(d->x->f & MP_DESTROYED));
- assert(!(d->y->f & MP_DESTROYED));
- assert(!(d->z->f & MP_DESTROYED));
}
return (d);
}
EC_COPY(d, a);
else {
field *f = c->f;
- ecctx *cc = (ecctx *)c;
mp *lambda;
mp *dx, *dy;
dx = F_SQR(f, dx, lambda); /* %$\lambda^2$% */
dx = F_ADD(f, dx, dx, lambda); /* %$\lambda^2 + \lambda$% */
- dx = F_ADD(f, dx, dx, cc->a); /* %$a + \lambda^2 + \lambda$% */
+ dx = F_ADD(f, dx, dx, c->a); /* %$a + \lambda^2 + \lambda$% */
dx = F_ADD(f, dx, dx, a->x); /* %$a + \lambda^2 + \lambda + x_0$% */
dx = F_ADD(f, dx, dx, b->x);
/* %$x' = a + \lambda^2 + \lambda + x_0 + x_1$% */
dx = F_SQR(f, dx, lambda); /* %$\lambda^2$% */
dx = F_ADD(f, dx, dx, lambda); /* %$\lambda^2 + \lambda$% */
- dx = F_ADD(f, dx, dx, cc->a); /* %$x' = a + \lambda^2 + \lambda$% */
+ dx = F_ADD(f, dx, dx, c->a); /* %$x' = a + \lambda^2 + \lambda$% */
dy = MP_NEW;
}
EC_COPY(d, a);
else {
field *f = c->f;
- ecctx *cc = (ecctx *)c;
mp *dx, *dy, *dz, *u, *uu, *v, *t, *s, *ss, *r, *w, *l;
dz = F_SQR(f, MP_NEW, b->z); /* %$z_1^2$% */
t = F_ADD(f, t, r, dz); /* %$t = r + z'$% */
uu = F_SQR(f, MP_NEW, dz); /* %$z'^2$% */
- dx = F_MUL(f, MP_NEW, uu, cc->a); /* %$a z'^2$% */
+ dx = F_MUL(f, MP_NEW, uu, c->a); /* %$a z'^2$% */
uu = F_MUL(f, uu, t, r); /* %$t r$% */
dx = F_ADD(f, dx, dx, uu); /* %$a z'^2 + t r$% */
r = F_SQR(f, r, w); /* %$w^2$% */
static int eccheck(ec_curve *c, const ec *p)
{
- ecctx *cc = (ecctx *)c;
field *f = c->f;
int rc;
mp *u, *v;
+ if (EC_ATINF(p)) return (0);
v = F_SQR(f, MP_NEW, p->x);
u = F_MUL(f, MP_NEW, v, p->x);
- v = F_MUL(f, v, v, cc->a);
+ v = F_MUL(f, v, v, c->a);
u = F_ADD(f, u, u, v);
- u = F_ADD(f, u, u, cc->b);
+ u = F_ADD(f, u, u, c->b);
v = F_MUL(f, v, p->x, p->y);
u = F_ADD(f, u, u, v);
v = F_SQR(f, v, p->y);
u = F_ADD(f, u, u, v);
- rc = F_ZEROP(f, u);
+ rc = F_ZEROP(f, u) ? 0 : -1;
mp_drop(u);
mp_drop(v);
return (rc);
static void ecdestroy(ec_curve *c)
{
ecctx *cc = (ecctx *)c;
- MP_DROP(cc->a);
- MP_DROP(cc->b);
+ MP_DROP(cc->c.a);
+ MP_DROP(cc->c.b);
if (cc->bb) MP_DROP(cc->bb);
DESTROY(cc);
}
* 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 binary field. The @binproj@ variant uses projective
ecctx *cc = CREATE(ecctx);
cc->c.ops = &ec_binops;
cc->c.f = f;
- cc->a = F_IN(f, MP_NEW, a);
- cc->b = F_IN(f, MP_NEW, b);
+ cc->c.a = F_IN(f, MP_NEW, a);
+ cc->c.b = F_IN(f, MP_NEW, b);
cc->bb = 0;
return (&cc->c);
}
ecctx *cc = CREATE(ecctx);
cc->c.ops = &ec_binprojops;
cc->c.f = f;
- cc->a = F_IN(f, MP_NEW, a);
- cc->b = F_IN(f, MP_NEW, b);
- cc->bb = F_SQRT(f, MP_NEW, b);
- cc->bb = F_SQRT(f, cc->bb, cc->bb);
+ cc->c.a = F_IN(f, MP_NEW, a);
+ cc->c.b = F_IN(f, MP_NEW, b);
+ cc->bb = F_SQRT(f, MP_NEW, cc->c.b);
+ if (cc->bb)
+ cc->bb = F_SQRT(f, cc->bb, cc->bb);
+ if (!cc->bb) {
+ MP_DROP(cc->c.a);
+ MP_DROP(cc->c.b);
+ DESTROY(cc);
+ return (0);
+ }
return (&cc->c);
}
static const ec_ops ec_binops = {
- 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_binprojops = {
- ecdestroy, ec_projin, ec_projout, ec_projfix,
- 0, ecprojneg, ecprojadd, ec_stdsub, ecprojdbl, ecprojcheck
+ ecdestroy, ec_stdsamep, ec_projin, ec_projout, ec_projfix,
+ ecfind, ecprojneg, ecprojadd, ec_stdsub, ecprojdbl, ecprojcheck
};
/*----- Test rig ----------------------------------------------------------*/
field *f;
ec_curve *c;
ec g = EC_INIT, d = EC_INIT;
- mp *p, *a, *b, *r;
+ mp *p, *a, *b, *r, *beta;
int i, n = argc == 1 ? 1 : atoi(argv[1]);
printf("ec-bin: ");
fflush(stdout);
- a = MP(1);
- b = MP(0x066647ede6c332c7f8c0923bb58213b333b20e9ce4281fe115f7d8f90ad);
- p = MP(0x20000000000000000000000000000000000000004000000000000000001);
- r =
- MP(6901746346790563787434755862277025555839812737345013555379383634485462);
+ a = MP(0x7ffffffffffffffffffffffffffffffffffffffff);
+ b = MP(0x6645f3cacf1638e139c6cd13ef61734fbc9e3d9fb);
+ p = MP(0x800000000000000000000000000000000000000c9);
+ beta = MP(0x715169c109c612e390d347c748342bcd3b02a0bef);
+ r = MP(0x040000000000000000000292fe77e70c12a4234c32);
- f = field_binpoly(p);
+ f = field_binnorm(p, beta);
c = ec_binproj(f, a, b);
-
- g.x = MP(0x0fac9dfcbac8313bb2139f1bb755fef65bc391f8b36f8f8eb7371fd558b);
- g.y = MP(0x1006a08a41903350678e58528bebf8a0beff867a7ca36716f7e01f81052);
+ g.x = MP(0x0311103c17167564ace77ccb09c681f886ba54ee8);
+ g.y = MP(0x333ac13c6447f2e67613bf7009daf98c87bb50c7f);
for (i = 0; i < n; i++) {
ec_mul(c, &d, &g, r);
ec_destroy(&g);
ec_destroycurve(c);
F_DESTROY(f);
- MP_DROP(p); MP_DROP(a); MP_DROP(b); MP_DROP(r);
+ MP_DROP(p); MP_DROP(a); MP_DROP(b); MP_DROP(r); MP_DROP(beta);
assert(!mparena_count(&mparena_global));
printf("ok\n");
return (0);
projects / u / mdw / catacomb / blobdiff