Genus two hyperelliptic curve coprocessor

Abstract

Hyperelliptic curve cryptography with genus larger than one has not been seriously considered for cryptographic purposes because many existing implementations are significantly slower than elliptic curve versions with the same level of security. In this paper, the first ever complete hardware implementation of a hyperelliptic curve coprocessor is described. This coprocessor is designed for genus two curves over F2113. Additionally, a modification to the Extended Euclidean Algorithm is presented for the GCD calculation required by Cantor's algorithm. On average, this new method computes the GCD in one-fourth the time required by the Extended Euclidean Algorithm. © Springer-Verlag 2003.