In the work at hand we present for the first time explicit formulae for genus-4 HEC, resulting in a 60% speed-up compared to the best published results. In addition we implemented genus-4 HECC on a Pentium4 and an ARM microprocessor. Our implementations on the ARM show that for genus four HECC are only a factor of 1.66 slower than genus-2 curves considering group order ~2^{190}. For the same group order ECC and genus-3 HECC are about a factor of 2 faster than genus-4 curves on the ARM. The two most surprising results are: 1) for low cost security application, namely considering an underlying group of order 2^{128}, HECC with genus 4 outperform genus-2 curves by a factor of 1.46 and has similar performance to genus-3 curves on the ARM and 2) when compared to genus-2 and genus-3, genus-4 HECC are better suited to embedded microprocessors than to general purpose processors.
Category / Keywords: public-key cryptography / hyperelliptic curves, genus four, explicit formulae, efficient implementation, low cost security, embedded application, comparison HECC vs. ECC Date: received 20 May 2003 Contact author: pelzl at crypto rub de Available format(s): Postscript (PS) | Compressed Postscript (PS.GZ) | PDF | BibTeX Citation Version: 20030521:033303 (All versions of this report) Short URL: ia.cr/2003/097 Discussion forum: Show discussion | Start new discussion