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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.

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Publication info
Published elsewhere. submitted
Keywords
genus 2endomorphism ringTate pairing
Contact author(s)
sorina ionica @ m4x org
History
2013-03-31: last of 3 revisions
2012-03-30: received
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Short URL
https://ia.cr/2012/167
License
Creative Commons Attribution
CC BY
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