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.
