CryptoDB
Efficient Hyperelliptic Arithmetic using Balanced Representation for Divisors
Authors: | |
---|---|
Download: | |
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. |
BibTeX
@misc{eprint-2008-17942, title={Efficient Hyperelliptic Arithmetic using Balanced Representation for Divisors}, booktitle={IACR Eprint archive}, keywords={foundations / hyperelliptic curves, real models, efficient arithmetic}, url={http://eprint.iacr.org/2008/265}, note={Extended and corrected version of the ANTS 2008 article. david.mireles@gmail.com 14041 received 11 Jun 2008}, author={Steven D. Galbraith and Michael Harrison and David J. Mireles Morales}, year=2008 }