Computing Zeta Functions of Hyperelliptic Curves over Finite Fields of Characteristic 2

Authors:
Frederik Vercauteren
Affiliations:
-
Venue:
CRYPTO '02 Proceedings of the 22nd Annual International Cryptology Conference on Advances in Cryptology
Year:
2002

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Abstract

We present an algorithm for computing the zeta function of an arbitrary hyperelliptic curve over a finite field Fq of characteristic 2, thereby extending the algorithm of Kedlaya for small odd characteristic. For a genus g hyperelliptic curve over F2n, the asymptotic running time of the algorithm is O(g5+驴n3+驴) and the space complexity is O(g3n3).