IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences
Online ISSN : 1745-1337
Print ISSN : 0916-8508
Special Section on Discrete Mathematics and Its Applications
An Improvement of Scalar Multiplication by Skew Frobenius Map with Multi-Scalar Multiplication for KSS Curve
Md. Al-Amin KHANDAKERYasuyuki NOGAMI
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2017 Volume E100.A Issue 9 Pages 1838-1845

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Abstract

Scalar multiplication over higher degree rational point groups is often regarded as the bottleneck for faster pairing based cryptography. This paper has presented a skew Frobenius mapping technique in the sub-field isomorphic sextic twisted curve of Kachisa-Schaefer-Scott (KSS) pairing friendly curve of embedding degree 18 in the context of Ate based pairing. Utilizing the skew Frobenius map along with multi-scalar multiplication procedure, an efficient scalar multiplication method for KSS curve is proposed in the paper. In addition to the theoretic proposal, this paper has also presented a comparative simulation of the proposed approach with plain binary method, sliding window method and non-adjacent form (NAF) for scalar multiplication. The simulation shows that the proposed method is about 60 times faster than plain implementation of other compared methods.

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© 2017 The Institute of Electronics, Information and Communication Engineers
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