Two topics in hyperelliptic cryptography

Abstract

In this paper we address two important topics in hyperelliptic cryptography. The first is how to construct in a verifiably random manner hyperelliptic curves for use in cryptography in generas two and three. The second topic is how to perform divisor compression in the hyperelliptic case. Hence, in both cases we generalise concepts used in the more familiar elliptic curve case to the hyperelliptic context.