Inversion-Free Arithmetic on Genus 3 Hyperelliptic Curves and Its Implementations

Recently, a lot of effort has been done to investigate all kinds of explicit formulae for speeding up group operation of hyperelliptic curve cryptosystem (HECC). In this paper, explicit formulae without using inversion for genus 3 HECC are given for the first time. When genus 3 HECC is defined over a prime field, our explicit formulae will cost respectively 122 9M S+ , 105 8M S+ and 110 11M S+ to perform a group addition, mixed addition and doubling. If we use special genus 3 hyperelliptic curves with ( ) 1h x = over a binary field, our explicit formulae will need only 119 9M S+ , 102 8M S+ and 42 15M S+ for a group addition, mixed addition and doubling, respectively. In the second part of our contribution, we implement inversion-free arithmetic on genus 3 hyperelliptic curves defined over one prime field and three binary fields on a Pentium-M processor and compare the speed of explicit formulae in affine and projective coordinate system. The proposed explicit formulae show excellent ...

• Type: Conference
• Year: 2005
• Where: ITCC
• Authors: Xinxin Fan, Thomas J. Wollinger, Yumin Wang
• Keywords: Explicit Formulae, HECC, Hyperelliptic Curves, Information Technology, ITCC 2005