Halving in some genus 2 curves over binary fields

Abstract

We give a method to compute the halving of a divisor in the Jacobian variety of a genus 2 curve in characteristic 2. We present explicit halving formulae for each possible divisor class for some curves (those with h(x)=x), detailing all the process to obtain them. We improve the fastest known formulae for some divisor classes in the studied type of curves.