New formulae for Tate pairing computation on Weierstrass curves

Abstract

This paper proposes a variation of Miller's algorithm for Tate pairing computation on Weierstrass curves. Unlike the original Miller's algorithm which consists of two major operations: the doubling operation and the addition operation, this new algorithm replaces the addition with a doubling-addition (DA) operation to take the advantage of the fast point doubling-addition formula. Explicit formulae are given for the new algorithm. We suggest to use the new formulae for Weierstrass curves with general parameters for Tate pairing to gain a better performance.