Hyperelliptic Curve Cryptosystems: Closing the Performance Gap to Elliptic Curves (Update)

For most of the time since they were proposed, it was widely believed that hyperelliptic curve cryptosystems (HECC) carry a substantial performance penalty compared to elliptic curve cryptosystems (ECC) and are, thus, not too attractive for practical applications. Only quite recently improvements have been made, mainly restricted to curves of genus 2. The work at hand advances the state-of-the-art considerably in several aspects. First, we generalize and improve the closed formulae for the group operation of genus 3 for HEC defined over fields of characteristic two. For certain curves we achieve over 50% complexity improvement compared to the best previously published results. Second, we introduce a new complexity metric for ECC and HECC defined over characteristic two fields which allow performance comparisons of practical relevance. It can be shown that the HECC performance is in the range of the performance of an ECC; for specific parameters HECC can even possess a lower complexity than an ECC at the same security level. Third, we describe the first implementation of a HEC cryptosystem on an embedded (ARM7) processor. Since HEC are particularly attractive for constrained environments, such a case study should be of relevance

Proceedings of the 5th International Workshop on Reconfigurable Communication-centric Systems on Chip 2010 - ReCoSoC\u2710 - May 17-19, 2010 Karlsruhe, Germany. (KIT Scientific Reports ; 7551)

ReCoSoC is intended to be a periodic annual meeting to expose and discuss gathered expertise as well as state of the art research around SoC related topics through plenary invited papers and posters. The workshop aims to provide a prospective view of tomorrow\u27s challenges in the multibillion transistor era, taking into account the emerging techniques and architectures exploring the synergy between flexible on-chip communication and system reconfigurability