Counting points on hyperelliptic curves of genus 2 with real models

Abstract

A model of a hyperelliptic curve is called an imaginary or real model if it has one or two points at infinity, respectively. In this paper, we propose an algorithm to count points on hyperelliptic curves of genus 2 with real models defined over finite fields of large characteristics. We also estimate the complexity of our algorithm and prove that it has the same order as that of a previously known algorithm for imaginary models.