Hyperelliptic Curve Cryptosystems: Closing the Performance Gap to Elliptic Curves

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-theart 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 complex...

• Type: Conference
• Year: 2003
• Where: CHES
• Authors: Jan Pelzl, Thomas J. Wollinger, Jorge Guajardo, Christof Paar
• Keywords: Characteristic Two, CHES 2003, Cryptography, Curve Cryptosystems, Hyperelliptic Curve Cryptosystems