The hyperelliptic curve cryptosystems (HECC) is one of the emerging cryptographic primitives of the last years. HECC offers the same security as established public-key cryptosystems with much shorter operand length. However, until recently the common belief was that HEC are out of scope for any practical application, because of the complex group operation. The thesis at hand is a step towards the practical use of HECC by narrowing the performance gap between elliptic curve (ECC) and HECC. We were able to reduce the complexity of the group operation for small genus hyperelliptic curves. Our theoretical comparison between ECC and HECC, as well as our software and hardware implementations show that the performance of both cryptographic primitives is in the same range. The implementations we investigated range from a general purpose processor to a variety of different embedded processors, and also include the prototype implementation of a HEC coprocessor on FPGAs.
