Computing zeta functions in families of Ca,bcurves using deformation

Authors:
Wouter Castryck;Hendrik Hubrechts;Frederik Vercauteren
Affiliations:
Department of Electrical Engineering, University of Leuven, Leuven, Heverlee, Belgium;Department of Mathematics, University of Leuven, Leuven, Heverlee, Belgium;Department of Electrical Engineering, University of Leuven, Leuven, Heverlee, Belgium
Venue:
ANTS-VIII'08 Proceedings of the 8th international conference on Algorithmic number theory
Year:
2008

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Abstract

We apply deformation theory to compute zeta functions ina family of Ca,b curves over a finite field of small characteristic. Themethod combines Denef and Vercauteren's extension of Kedlaya's algorithmto Ca,b curves with Hubrechts' recent work on point counting onhyperelliptic curves using deformation. As a result, it is now possibleto generate Ca,b curves suitable for use in cryptography in a matter ofminutes.