Fast Jacobian arithmetic for hyperelliptic curves of genus 3

TL;DR

This paper develops efficient algorithms for Jacobian arithmetic on genus 3 hyperelliptic curves over fields with characteristic not 2, especially addressing cases without rational Weierstrass points using a balanced divisor approach.

Contribution

It introduces new explicit formulas for Jacobian computations on genus 3 hyperelliptic curves without assuming rational Weierstrass points.

Findings

Achieves faster Jacobian arithmetic in the general case

Provides explicit formulas applicable to a broader class of curves

Enhances computational efficiency for cryptographic applications

Abstract

We consider the problem of efficient computation in the Jacobian of a hyperelliptic curve of genus 3 defined over a field whose characteristic is not 2. For curves with a rational Weierstrass point, fast explicit formulas are well known and widely available. Here we address the general case, in which we do not assume the existence of a rational Weierstrass point, using a balanced divisor approach.