Paper 2004/223

Inversion-Free Arithmetic on Genus 3 Hyperelliptic Curves

Xinxin Fan and Yumin Wang

Abstract

Hyperelliptic curve cryptosystem (HECC) is becoming more and more promising for network security applications because of the common effort of several academic and industrial organizations. With short operand size compared to other public key cryptosystems, HECC has showed excellent performance in embedded processors. Recently years, many effort has been made to investigate all kinds of explicit formulae for speeding up group operation of HECC. In this paper, explicit formulae without using inversion for genus 3 HECC are given. We introduce a further coordinate to collect the common denominator of the usual 6 coordinates. The proposed formulae can be used in smart card where inversion is much more expensive than multiplication.