Paper 2008/265 Original: eprint.iacr.org/2008/265 ↗
Efficient Hyperelliptic Arithmetic using Balanced Representation for Divisors
Abstract
We discuss arithmetic in the Jacobian of a hyperelliptic curve $C$ of genus $g$. The traditional approach is to fix a point $P_\infty \in C$ and represent divisor classes in the form $E - d(P_\infty)$ where $E$ is effective and $0 \le d \le g$. We propose a different representation which is balanced at infinity. The resulting arithmetic is more efficient than previous approaches when there are 2 points at infinity. This is a corrected and extended version of the article presented in ANTS 2008. We include an appendix with explicit formulae to compute a very efficient `baby step' in genus 2 hyperelliptic curves given by an imaginary model.
Metadata
- Available format(s)
PDF- Category
- Foundations
- Publication info
- Preprint.
- History
- 2008-06-18: last updated
- 2008-06-18: published
- Short URL
- https://ia.cr/2008/265
- License
- https://creativecommons.org/licenses/by/4.0/
BibTeX
@misc{cryptoeprint:2008/265,
author = {Steven D. Galbraith and Michael Harrison and David J. Mireles Morales},
title = {Efficient Hyperelliptic Arithmetic using Balanced Representation for Divisors},
howpublished = {Cryptology {ePrint} Archive, Paper 2008/265},
year = {2008},
url = {https://eprint.iacr.org/2008/265}
}