Overview of effective point counting algorithms for Jacobian of hyperelliptic curve over finite field
Various algorithms for finding of the order of Jacobian, their range of use and efficiency are considered.
A comparison of point counting methods for hyperelliptic curves over prime fields and fields of characteristic 2 // Cryptology ePrint Archive. 2004.
Haneda M., Kawazoe M., Takahashi T.
Suitable curves for genus-4 HCC over prime fields: point counting formulae for hyperelliptic ...
An efficient implementation of an exponential point-counting algorithm on Jacobians of genus 2 hyperelliptic curves
... constructions of DLP-based cryptosystems, as well as constructions of verifiable delay functions (VDF’s), since they can be viewed as large groups of unknown order. In this article, we present an overview of approaches to accelerate Gaudry-Schost point counting algorithm that is the fastest known algorithm for computing the order of Jacobians of hyperelliptic curves of genus 2. This algorithm consists of two stages: 1) computing the number of points (equivalently, the characteristic polynomial of ...