Performance Study of genus 3 Hyperelliptic Curve Cryptosystem

Daya Gupta, Asok De and Kakali Chatterjee
Volume: 8, No: 1, Page: 145 ~ 158, Year: 2012
10.3745/JIPS.2012.8.1.145
Keywords: Hyperelliptic Curve Cryptosystem(HECC), Secure Hyperelliptic Curve, Hyperelliptic Curve Deffie-Hellman(HECDH), Hyperelliptic Curve Digital Signature Algorithm (HECDSA)
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Abstract
Hyperelliptic Curve Cryptosystem (HECC) is well suited for all kinds of embedded processor architectures, where resources such as storage, time, or power are constrained due to short operand sizes. We can construct genus 3 HECC on 54-bit finite fields in order to achieve the same security level as 160-bit ECC or 1024-bit RSA due to the algebraic structure of Hyperelliptic Curve. This paper explores various possible attacks to the discrete logarithm in the Jacobian of a Hyperelliptic Curve (HEC) and addition and doubling of the divisor using explicit formula to speed up the scalar multiplication. Our aim is to develop a cryptosystem that can sign and authenticate documents and encrypt / decrypt messages efficiently for constrained devices in wireless networks. The performance of our proposed cryptosystem is comparable with that of ECC and the security analysis shows that it can resist the major attacks in wireless networks.

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Cite this article
IEEE Style
Daya Gupta, Asok De and Kakali Chatterjee, "Performance Study of genus 3 Hyperelliptic Curve Cryptosystem," Journal of Information Processing Systems, vol. 8, no. 1, pp. 145~158, 2012. DOI: 10.3745/JIPS.2012.8.1.145.

ACM Style
Daya Gupta, Asok De and Kakali Chatterjee, "Performance Study of genus 3 Hyperelliptic Curve Cryptosystem," Journal of Information Processing Systems, 8, 1, (2012), 145~158. DOI: 10.3745/JIPS.2012.8.1.145.