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

Romain Cosset; Damien Robert

Paper 2011/143

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.

Metadata

Available format(s): PDF
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: 2011-03-27: received
Short URL: https://ia.cr/2011/143
License: 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},
      url = {https://eprint.iacr.org/2011/143}
}