Pairing-based methods for genus 2 jacobians with maximal endomorphism ring

Sorina Ionica

Paper 2012/167

Pairing-based methods for genus 2 jacobians with maximal endomorphism ring

Sorina Ionica

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: Published elsewhere. submitted
Keywords: genus 2 endomorphism ring Tate pairing
Contact author(s): sorina ionica @ m4x org
History: 2013-03-31: last of 3 revisions; 2012-03-30: received; See all versions
Short URL: https://ia.cr/2012/167
License: CC BY

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}
}