Computing functions on Jacobians and their quotients

TL;DR

This paper presents efficient methods for computing functions on Jacobian varieties and their quotients, including a near-optimal algorithm for calculating (l,l) isogenies between genus two Jacobians.

Contribution

It introduces a novel, efficient approach to compute functions on Jacobians and develops a quasi-optimal algorithm for (l,l) isogenies between genus two Jacobians.

Findings

Developed an efficient method for functions on Jacobians.

Derived a quasi-optimal algorithm for (l,l) isogenies.

Enhanced computational techniques for genus two curves.

Abstract

We show how to efficiently compute functions on jacobian varieties and their quotients. We deduce a quasi-optimal algorithm to compute $(l,l)$ isogenies between jacobians of genus two curves.