Zeta function and cryptographic exponent of supersingular curves of genus 2

Authors:
Gabriel Cardona;Enric Nart
Affiliations:
Dept. Ciències Matemàtiques i Informàtica, Universitat de les Illes Balears, Palma de Mallorca, Spain;Departament de Matemàtiques, Universitat Autònoma de Barcelona, Bellaterra, Barcelona, Spain
Venue:
Pairing'07 Proceedings of the First international conference on Pairing-Based Cryptography
Year:
2007

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Abstract

We compute in a direct (not algorithmic) way the zeta function of all supersingular curves of genus 2 over a finite field k, with many geometric automorphisms. We display these computations in an appendix where we select a family of representatives of all these curves up to k-isomorphism and we exhibit equations and the zeta function of all their k/k-twists. As an application we obtain a direct computation of the cryptographic exponent of the Jacobians of these curves.