In this paper we determine the number of isomorphism classes of Picard curves, i.e., superelliptic curves y3 = f(x) of genus three, over finite fields of characteristic different f...
We present an algorithm to compute the zeta function of an arbitrary hyperelliptic curve over a finite field Fq of characteristic 2, thereby extending the algorithm of Kedlaya for ...
Abstract. The complex multiplication (CM) method for genus 2 is currently the most efficient way of generating genus 2 hyperelliptic curves defined over large prime fields and suit...
Pierrick Gaudry, T. Houtmann, D. Kohel, Christophe...
We provide a subexponential algorithm for solving the discrete logarithm problem in Jacobians of high-genus hyperelliptic curves over finite fields. Its expected running time for i...