English

Zeta function and cryptographic exponent of supersingular curves of genus 2

Number Theory 2007-05-23 v1

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 geometric isomorphism and we exhibit equations and the zeta function of all their twists. As an application we obtain a direct computation of the cryptographic exponent of the Jacobians of these curves.

Keywords

Cite

@article{arxiv.0704.1951,
  title  = {Zeta function and cryptographic exponent of supersingular curves of genus 2},
  author = {Gabriel Cardona and Enric Nart},
  journal= {arXiv preprint arXiv:0704.1951},
  year   = {2007}
}