Computing zeta functions of hyperelliptic curves over finite fields of characteristic 2

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+εn3+ε) and the space complexity is O(g3n3).