Efficient hyperelliptic arithmetic using balanced representation for divisors

Abstract

We discuss arithmetic in the Jacobian of a hyperelliptic curve C of genus g. The traditional approach is to fix a point P∞ ∈ C and represent divisor classes in the form E-d(P∞) where E is effective and 0 ≤ d ≤ g. We propose a different representation which is balanced at infinity. The resulting arithmetic is more efficient than previous approaches when there are 2 points at infinity. © 2008 Springer-Verlag Berlin Heidelberg.