Encapsulated scalar multiplications and line functions in the computation of Tate pairing

Authors:
Rongquan Feng;Hongfeng Wu
Affiliations:
LMAM, School of Math. Sciences, Peking University, Beijing, P.R. China;LMAM, School of Math. Sciences, Peking University, Beijing, P.R. 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

The efficient computation of the Tate pairing is a crucial factor to realize cryptographic applications practically. To compute the Tate pairing, two kinds of costs on the scalar multiplications and Miller's line functions of elliptic curves should be considered. In the present paper, encapsulated scalar multiplications and line functions are discussed. Some simplified formulas and improved algorithms to compute f3T, f4T, f2T±P, f6T, f3T±P and f4T±P etc., are presented from given points T and P on the elliptic curve.