An improvement on the computation of 2-power torsion points on genus 2 hyperelliptic curves(Theory, Algorithmic Number Theory and Its Applications, <Special Issue> Joint Symposium of JSIAM Activity Groups 2007)

Abstract

Gaudry and Harley proposed a Schoof-like algorithm for genus 2 hyperelliptic curves which uses the 2-power torsion points on the Jacobians. Using actions of the 2 torsion subgroups on the 2-power torsion points, Gaudry and Schost improved the 2-power torsion point computation. This paper shows properties of the halved points of the 2-power torsion points and the actions of the 2 torsion subgroups. By using these properties, this paper improves the computation of the 2-power torsion points. Moreover, an implementation of the improved algorithm is shown in this paper. The implementation results show that the improvement is efficient.