### Computing $(\ell,\ell)$-isogenies in polynomial time on Jacobians of genus~$2$ curves

Romain Cosset and Damien Robert

##### 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.

Available format(s)
Category
Public-key cryptography
Publication info
Published elsewhere. Unknown where it was published
Keywords
elliptic curve cryptosystem
Contact author(s)
damien robert @ inria fr
History
Short URL
https://ia.cr/2011/143

CC BY

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},
note = {\url{https://eprint.iacr.org/2011/143}},
url = {https://eprint.iacr.org/2011/143}
}

Note: In order to protect the privacy of readers, eprint.iacr.org does not use cookies or embedded third party content.