Improvement of Inversion-Free Group Operations for Genus 3 Hyperelliptic Curve Cryptosystems


The efficient implementations of cryptographic algorithms is the key for applications. There are environments where inversions are extremely time and space critical, for example embedded processors. Although multiplications are optimized there, divisions are very slow. For elliptic curve case, one can turn to several inversion-free systems, like projective, Jacobian, Chudnovsky Jacobian, modified Jacobian and mixed coordinates. In this chapter, we propose for the first time inversion-free group operations for genus 3 HECC. In order to derive explicit formulae without using inversion for genus 3 HECC, we introduce a further coordinate to collect the common denominator of the usual 6 coordinates.

Chapter 7 in New Trends in Cryptographic Systems
Xinxin Fan
Xinxin Fan
Head of Cryptography

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