/* -*-c-*-
*
- * $Id: ec-bin.c,v 1.2 2004/03/21 22:52:06 mdw Exp $
+ * $Id: ec-bin.c,v 1.3 2004/03/22 02:19:09 mdw Exp $
*
* Arithmetic for elliptic curves over binary fields
*
/*----- 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.
*
fprintf(stderr, "didn't reach zero\n");
MP_EPRINTX("d.x", d.x);
MP_EPRINTX("d.y", d.y);
- MP_EPRINTX("d.z", d.y);
return (1);
}
ec_destroy(&d);
/* -*-c-*-
*
- * $Id: ec-exp.h,v 1.3 2004/03/21 22:52:06 mdw Exp $
+ * $Id: ec-exp.h,v 1.4 2004/03/22 02:19:10 mdw Exp $
*
* Exponentiation operations for elliptic curves
*
/*----- Revision history --------------------------------------------------*
*
* $Log: ec-exp.h,v $
+ * Revision 1.4 2004/03/22 02:19:10 mdw
+ * Rationalise the sliding-window threshold. Drop guarantee that right
+ * arguments to EC @add@ are canonical, and fix up projective implementations
+ * to cope.
+ *
* Revision 1.3 2004/03/21 22:52:06 mdw
* Merge and close elliptic curve branch.
*
#define EXP_MUL(a, x) EC_ADD(c, &(a), &(a), &(x))
#define EXP_SQR(a) EC_DBL(c, &(a), &(a));
-#define EXP_FIX(x) EC_FIX(c, &(x), &(x));
+#define EXP_FIX(x)
#define EXP_SETMUL(d, x, y) do { \
EC_CREATE(&(d)); \
/* -*-c-*-
*
- * $Id: ec-prime.c,v 1.4 2004/03/21 22:52:06 mdw Exp $
+ * $Id: ec-prime.c,v 1.5 2004/03/22 02:19:10 mdw Exp $
*
* Elliptic curves over prime fields
*
/*----- Revision history --------------------------------------------------*
*
* $Log: ec-prime.c,v $
+ * Revision 1.5 2004/03/22 02:19:10 mdw
+ * Rationalise the sliding-window threshold. Drop guarantee that right
+ * arguments to EC @add@ are canonical, and fix up projective implementations
+ * to cope.
+ *
* Revision 1.4 2004/03/21 22:52:06 mdw
* Merge and close elliptic curve branch.
*
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); /* %$m w^3$% */
/* -*-c-*-
*
- * $Id: ec.h,v 1.5 2004/03/21 22:52:06 mdw Exp $
+ * $Id: ec.h,v 1.6 2004/03/22 02:19:10 mdw Exp $
*
* Elliptic curve definitions
*
/*----- Revision history --------------------------------------------------*
*
* $Log: ec.h,v $
+ * Revision 1.6 2004/03/22 02:19:10 mdw
+ * Rationalise the sliding-window threshold. Drop guarantee that right
+ * arguments to EC @add@ are canonical, and fix up projective implementations
+ * to cope.
+ *
* Revision 1.5 2004/03/21 22:52:06 mdw
* Merge and close elliptic curve branch.
*
/* --- Elliptic curve operations --- *
*
* All operations (apart from @destroy@ and @in@) are guaranteed to be
- * performed on internal representations of points. Moreover, the second
- * argument to @add@ and @mul@ is guaranteed to be the output of @in@ or
- * @fix@.
+ * performed on internal representations of points.
+ *
+ * (Historical note. We used to guarantee that the second to @add@ and @mul@
+ * was the output of @in@ or @fix@, but this canonification turned out to
+ * make the precomputation in @ec_exp@ too slow. Projective implementations
+ * must therefore cope with a pair of arbitrary points.)
*/
typedef struct ec_ops {
/* -*-c-*-
*
- * $Id: exp.h,v 1.2 2004/03/21 22:52:06 mdw Exp $
+ * $Id: exp.h,v 1.3 2004/03/22 02:19:10 mdw Exp $
*
* Generalized exponentiation
*
/*----- Revision history --------------------------------------------------*
*
* $Log: exp.h,v $
+ * Revision 1.3 2004/03/22 02:19:10 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.
*
# define EXP_WINSZ 4 /* Predefine if you need to */
#endif
-/* --- These are determined from the window size --- */
+/* --- These are determined from the window size --- *
+ *
+ * Given a %$k$%-bit exponent, I expect to do %$k/2$% multiplies if I use the
+ * simple way. If I use an n-bit sliding window, then I do %$2^n$%
+ * multiplies up front, but I only do %$(2^n - 1)/2^n k/n$% multiplies for
+ * the exponentiation. This is a win when
+ *
+ * %$k \ge \frac{n 2^{n+1}}{n - 2}$%
+ */
#define EXP_TABSZ (1 << EXP_WINSZ)
-#define EXP_THRESH (((MPW_BITS / EXP_WINSZ) << 2) + 1)
+#define EXP_THRESH \
+ ((EXP_WINSZ * (2 << EXP_WINSZ))/((EXP_WINSZ - 2) * MPW_BITS))
/* --- Required operations --- *
*
projects / u / mdw / catacomb / commitdiff