On the Performance of Hyperelliptic Cryptosystems

In this paper we discuss various aspects of cryptosystems based on hyperelliptic curves. In particular we cover the implementation of the group law on such curves and how to generate suitable curves for use in cryptography. This paper presents a practical comparison between the performance of elliptic curve based digital signature schemes and schemes based on hyperelliptic curves. We conclude that, at present, hyperelliptic curves offer no performance advantage over elliptic curves. Elliptic curve cryptosystems are now being deployed in the real world and there has been much work in recent years on their implementation. A natural generalization of such schemes was given by Koblitz [12], who described how the group law on a Jacobian of a hyperelliptic curve can be used to define a cryptographic system. Almost all of the standard discrete logarithm based protocols such as DSA and ElGamal have elliptic and hyperelliptic variants. This is because such protocols only require the presence ...

• Type: Conference
• Year: 1999
• Where: EUROCRYPT
• Authors: Nigel P. Smart
• Keywords: Cryptology, Curve Based Protocols, Elliptic Curve, EUROCRYPT 1999, Hyperelliptic Curves