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 \({\overline{k}}\)-isomorphism and we exhibit equations and the zeta function of all their \({\overline{k}}/k\)-twists. As an application we obtain a direct computation of the cryptographic exponent of the Jacobians of these curves.
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Cardona, G., Nart, E. (2007). Zeta Function and Cryptographic Exponent of Supersingular Curves of Genus 2. In: Takagi, T., Okamoto, T., Okamoto, E., Okamoto, T. (eds) Pairing-Based Cryptography – Pairing 2007. Pairing 2007. Lecture Notes in Computer Science, vol 4575. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-73489-5_8
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DOI: https://doi.org/10.1007/978-3-540-73489-5_8
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