International Association for Cryptologic Research

International Association
for Cryptologic Research


Paper: High Performance Arithmetic for Hyperelliptic Curve Cryptosystems of Genus Two

Jan Pelzl
Thomas Wollinger
Christof Paar
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Abstract: Nowadays, there exists a manifold variety of cryptographic applications: from low level embedded crypto implementations up to high end cryptographic engines for servers. The latter require a flexible implementation of a variety of cryptographic primitives in order to be capable of communicating with several clients. On the other hand, on the client it only requires an implementation of one specific algorithm with fixed parameters such as a fixed field size or fixed curve parameters if using ECC/ HECC. In particular for embedded environments like PDAs or mobile communication devices, fixing these parameters can be crucial regarding speed and power consumption. In this contribution, we propose a highly efficient algorithm for a hyperelliptic curve cryptosystem of genus two, well suited for these constraint devices. In recent years, a lot of effort was made to speed up arithmetic on genus-2 HEC. This work is based on the work of Lange and presents a major improvement of HECC arithmetic for curves defined over fields of characteristic two. We optimized the group doubling operation for certain types of genus-2 curves and we were able to reduce the number of required multiplications to a total of 9 multiplications. The saving in multiplications is 47% for the cost of one additional squaring. Thus, the efficiency of the whole cryptosystem was drastically increased.
  title={High Performance Arithmetic for Hyperelliptic Curve Cryptosystems of Genus Two},
  booktitle={IACR Eprint archive},
  keywords={implementation / hyperelliptic curves, explicit formulae, hyperelliptic curves, explicit formulae, efficient implementation, genus two},
  note={ 12327 received 2 Oct 2003},
  author={Jan Pelzl and Thomas Wollinger and Christof Paar},