Efficient Hyperelliptic Arithmetic Using Balanced Representation for Divisors

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.

• Type: Conference
• Year: 2008
• Where: ANTS
• Authors: Steven D. Galbraith, Michael Harrison, David J. Mireles Morales
• Keywords: Algorithms, ANTS 2008, Divisor Classes, Genus G, Hyperelliptic Curve