Alan G.B. Lauder and Daqing Wan
October 2001, 22pp.
We present a low-degree polynomial-time algorithm for computing the zeta function of certain Artin-Schreier curves over finite fields. Our algorithm provides the first method of finding ``random'' hyperelliptic curves of arbitrary genus defined over large finite fields of characteristic 2 whose Jacobians have orders suitable for use in public key cryptosystems.