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}
}