Efficient Pairing Computation on Twisted Weierstrass Curves  

作　　者：WANG Bei OUYANG Yi HU Honggang 

机构地区：[1]School of Mathematical Sciences, University of Science and Technology of China [2]School of Information Science and Technology, University of Science and Technology of China

出　　处：《Chinese Journal of Electronics》2018年第4期739-745,共7页电子学报（英文版）

基　　金：supported by the National Key Basic Research Program of China(No.2013CB834202);the National Natural Science Foundation of China(No.11571328,No.61522210)

摘　　要：In this paper, we construct the twists of twisted Edwards curves in Weierstrass form. Then we define a new twisted Ate pairing on twisted Weierstrass curves named the Tx-Ate pairing. Following Miller's algorithm, we give a computation of the Tx-Ate pairing on high degree twisted Weierstrass curves, where the point operations are over Edwards form, and the computation of Miller function is over Weierstrass form. Although, in one doubling loop, our method to compute the Tx-Ate pairing is a litter slower than the previously fastest method.By twists, the Tx-Ate pairing can be calculated on more twisted Weierstrass curves with short loop length. The TxAte pairing is even competitive with optimal Ate pairing when they have the same short loop length.In this paper, we construct the twists of twisted Edwards curves in Weierstrass form. Then we define a new twisted Ate pairing on twisted Weierstrass curves named the Tx-Ate pairing. Following Miller＇s algorithm, we give a computation of the Tx-Ate pairing on high degree twisted Weierstrass curves, where the point operations are over Edwards form, and the computation of Miller function is over Weierstrass form. Although, in one doubling loop, our method to compute the Tx-Ate pairing is a litter slower than the previously fastest method.By twists, the Tx-Ate pairing can be calculated on more twisted Weierstrass curves with short loop length. The TxAte pairing is even competitive with optimal Ate pairing when they have the same short loop length.

关 键 词：Weierstrass curves Twisted Ate pairing Twisted Edwards curves Miller function 

分 类 号：TN918.4[电子电信—通信与信息系统]