Paper 2012/167 Original: eprint.iacr.org/2012/167 ↗
Pairing-based methods for genus 2 jacobians with maximal endomorphism ring
Abstract
Using Galois cohomology, Schmoyer characterizes cryptographic non-trivial self-pairings of the \ell-Tate pairing in terms of the action of the Frobenius on the \ell-torsion of the Jacobian of a genus 2 curve. We apply similar techniques to study the non-degeneracy of the \ell-Tate pairing restrained to subgroups of the \ell-torsion which are maximal isotropic with respect to the Weil pairing. First, we deduce a criterion to verify whether the jacobian of a genus 2 curve has maximal endomorphism ring. Secondly, we derive a method to construct horizontal (\ell,\ell)-isogenies starting from a jacobian with maximal endomorphism ring.
Metadata
- Available format(s)
PDF- Publication info
- Preprint.
- History
- 2013-03-31: last updated
- 2012-03-30: published
- Short URL
- https://ia.cr/2012/167
- License
- https://creativecommons.org/licenses/by/4.0/
BibTeX
@misc{cryptoeprint:2012/167,
author = {Sorina Ionica},
title = {Pairing-based methods for genus 2 jacobians with maximal endomorphism ring},
howpublished = {Cryptology {ePrint} Archive, Paper 2012/167},
year = {2012},
url = {https://eprint.iacr.org/2012/167}
}