New left-to-right radix-r signed-digit recoding algorithm for pairing-based cryptosystems

Authors:
Fanyu Kong;Jia Yu;Zhun Cai;Daxing Li
Affiliations:
Institute of Network Security, Shandong University, Jinan, China and Key Laboratory of Cryptographic Technology and Information Security, Ministry of Education, Jinan, China;College of Information Engineering, Qingdao University, Qingdao, China;Institute of Network Security, Shandong University, Jinan, China and Key Laboratory of Cryptographic Technology and Information Security, Ministry of Education, Jinan, China;Institute of Network Security, Shandong University, Jinan, China and Key Laboratory of Cryptographic Technology and Information Security, Ministry of Education, Jinan, China
Venue:
TAMC'07 Proceedings of the 4th international conference on Theory and applications of models of computation
Year:
2007

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Abstract

In pairing-based cryptosystems, radix-r signed-digit representations are used to speed up point multiplication over supersingular elliptic curves or hyper-elliptic curves in characteristic r. We propose a left-to-right radix-r signed-digit recoding algorithm, which can obtain a new signed-digit representation from left to right. It is proved that its average non-zero density is asymptotically 1/2- 2r+3/2r(r+1)2, which is reduced by 20%-50% compared with the previous left-to-right radix-r signed-digit representations. The proposed algorithm can be applied to efficient implementations of pairing-based cryptosystems over supersingular elliptic curves or hyper-elliptic curves.