Paper 2011/143 Original: eprint.iacr.org/2011/143 ↗
Computing $(\ell,\ell)$-isogenies in polynomial time on Jacobians of genus~$2$ curves
Abstract
In this paper, we compute $\ell$-isogenies between abelian varieties over a field of characteristic different from $2$ in polynomial time in $\ell$, when $\ell$ is an odd prime which is coprime to the characteristic. We use level~$n$ symmetric theta structure where $n=2$ or $n=4$. In a second part of this paper we explain how to convert between Mumford coordinates of Jacobians of genus~$2$ hyperelliptic curves to theta coordinates of level~$2$ or $4$. Combined with the preceding algorithm, this gives a method to compute $(\ell,\ell)$-isogenies in polynomial time on Jacobians of genus~$2$ curves.
Metadata
- Available format(s)
PDF- Category
- Public-key cryptography
- Publication info
- Preprint.
- History
- 2011-03-27: last updated
- 2011-03-27: published
- Short URL
- https://ia.cr/2011/143
- License
- https://creativecommons.org/licenses/by/4.0/
BibTeX
@misc{cryptoeprint:2011/143,
author = {Romain Cosset and Damien Robert},
title = {Computing $(\ell,\ell)$-isogenies in polynomial time on Jacobians of genus~$2$ curves},
howpublished = {Cryptology {ePrint} Archive, Paper 2011/143},
year = {2011},
url = {https://eprint.iacr.org/2011/143}
}