Arithmetic on superelliptic curves

superelliptic curves, jacobians, cryptography, discrete logarithm problem In this paper we present an efficient, polynomial-time method to perform calculations in the divisor class group of a curve which has a single point on its normalization above infinity. In particular, we provide a unique representation of divisor classes and an algorithm for reducing a divisor on such a curve to its corresponding representative. Such curves include the case of elliptic, odd-degree hyperelliptic and superelliptic curves.