An Improvement of Scalar Multiplication by Skew Frobenius Map with Multi-Scalar Multiplication for KSS Curve

Md. Al-Amin KHANDAKER  Yasuyuki NOGAMI  

IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer Sciences   Vol.E100-A   No.9   pp.1838-1845
Publication Date: 2017/09/01
Online ISSN: 1745-1337
Type of Manuscript: Special Section PAPER (Special Section on Discrete Mathematics and Its Applications)
scalar multiplication,  skew Frobenius mapping,  KSS curve,  

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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.