Evolution of hyperelliptic curve cryptosystems

Authors:
Kakali Chatterjee;Daya Gupta
Affiliations:
Research Scholar, Computer Engineering Deptt, Delhi Technological University, India;HOD, Computer Engineering Deptt, Delhi Technological University, India
Venue:
ICDCIT'10 Proceedings of the 6th international conference on Distributed Computing and Internet Technology
Year:
2010

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Abstract

Due to short operand size, Hyperelliptic Curve Cryptosystem (HECC) of genus 3 is well suited for all kinds of embedded processor architectures, where resources such as storage, time or power are constrained. In the implementation of HECC, a significant step is the selection of secure hyperelliptic curves on which the Jacobian is constructed and speed up the scalar multiplications in the Jacobians of hyperelliptic curves. In this paper, we have explored various possible attacks to the discrete logarithm in the Jacobian of a Hyperelliptic Curve (HEC) that are to be considered to establish a secure HEC, analysed addition and doubling of divisor which are the prime steps of scalar multiplication and then proposed certain improvements in the existing explicit formula that will result in a performance gain for HECC of genus 3.