Zeta function and cryptographic exponent of supersingular curves of genus 2

Details Zeta function and cryptographic exponent of supersingular curves of genus 2 Zeta function and cryptographic exponent of supersingular curves of genus 2

2007-04-16

arxiv.org/abs/0704.1951v1

Mathematics

Number Theory

Scientific paper

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.

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