An improvement of scalar multiplication by skew frobenius map with multi-scalar multiplication for KSS curve

Md Al Amin Khandaker, Yasuyuki Nogami

Research output: Contribution to journalArticle

1 Citation (Scopus)

Abstract

Scalar multiplication over higher degree rational point groups is often regarded as the bottleneck for faster pairing based cryp-tography. 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.

Original languageEnglish
Pages (from-to)1838-1845
Number of pages8
JournalIEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences
VolumeE100A
Issue number9
DOIs
Publication statusPublished - Sep 1 2017

Fingerprint

Point groups
Scalar multiplication
Frobenius
Skew
Curve
Pairing
Sliding Window
Subfield
Rational Points
Simulation
Isomorphic
Binary

Keywords

  • KSS curve
  • Scalar multiplication
  • Skew Frobenius mapping

ASJC Scopus subject areas

  • Signal Processing
  • Computer Graphics and Computer-Aided Design
  • Applied Mathematics
  • Electrical and Electronic Engineering

Cite this

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abstract = "Scalar multiplication over higher degree rational point groups is often regarded as the bottleneck for faster pairing based cryp-tography. 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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N2 - Scalar multiplication over higher degree rational point groups is often regarded as the bottleneck for faster pairing based cryp-tography. 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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