Zeta function and cryptographic exponent of supersingular curves of genus 2

Gabriel Cardona; Enric Nart

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arXiv · 0704.1951

Zeta function and cryptographic exponent of supersingular curves of genus 2

Gabriel Cardona·Enric Nart

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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 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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BibTeX RIS

Gabriel Cardona, Enric Nart. 2007-04-16. Zeta function and cryptographic exponent of supersingular curves of genus 2. https://arxiv.org/abs/0704.1951

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