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

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 n , the asymptotic running time of the algorithm is O(g ) and the space complexity is O(g )

An extension of Kedlaya's algorithm to Artin-Schreier curves in characteristic 2

In this paper we present an extension of Kedlaya's algorithm for computing the zeta function of an Artin-Schreier curve over a finite field F-q of characteristic 2. The algorithm has running time O(g(5+epsilon) log(3+epsilon) q) and needs O(g(3) log(3) q) storage space for a genus g curve. Our first implementation in MAGMA shows that one can now generate hyperelliptic curves suitable for cryptography in reasonable time. We also compare our algorithm with an algorithm by Lauder and Wan which has the same time and space complexity. Furthermore, the method introduced in this paper can be used for any hyperelliptic curve over a finite field of characteristic 2.status: publishe