Abstract
The efficient computation of the Tate pairing is crucial for various cryptographic applications. In the computation the Tate pairing, two types of costs should be considered: that of scalar multiplication and the evaluations of Miller's line functions for elliptic curves. In this paper we optimize the calculation of $$(f_{2j\pm 1}(Q),[2j\pm 1]P)$$(f2j±1(Q),[2j±1]P), $$(f_{3j}(Q),[3]P)$$(f3j(Q),[3]P), $$(f_{3j\pm 1}(Q),[3j\pm 1]P)$$(f3j±1(Q),[3j±1]P) given the points P and Q in an elliptic curve, to improve the efficiency of the Tate pairing, when using the representation of the scalar n in NAF, in signed ternary base, and in double-base chain. Finally we compare their computational costs. In the case of a double-base chain, a general comparison is not simple, so we consider a few examples.
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