An improved twisted ate pairing over KSS curves with k=18

Authors:
Shan Chen;Kunpeng Wang;Dongdai Lin
Affiliations:
SKLOIS, Institute of Information Engineering, Chinese Academy of Sciences, Beijing, P.R. China,Graduate University of Chinese Academy of Sciences, Beijing, P.R. China;SKLOIS, Institute of Information Engineering, Chinese Academy of Sciences, Beijing, P.R. China;SKLOIS, Institute of Information Engineering, Chinese Academy of Sciences, Beijing, P.R. China
Venue:
Pairing'12 Proceedings of the 5th international conference on Pairing-Based Cryptography
Year:
2012

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Abstract

When implementing an efficient pairing calculation over KSS curves with embedding degree 18 and order r, the lower bound of the number of loop iterations of Miller's algorithm is $\frac{1}{6}\lfloor\log_2r\rfloor$. But the twisted Ate pairing requires $\frac{1}{2}\lfloor\log_2r\rfloor$ loop iterations, and thus is slower than the optimal Ate pairing which achieves the lower bound. This paper proposes an improved twisted Ate pairing and uses multi-pairing techniques to compute it. Therefore, the number of loop iterations in Miller's algorithm for the new pairing achieves the lower bound and it becomes faster than the original twisted Ate pairing by 30%.