Efficient Implementation of Tate Pairing with Montgomery Ladder Method

The basic algorithm used in pairing computation was first described by Miller and this algorithm can be named double-and-add and line-and-tangle algorithm. We will describe, in detail sufficient, a variant of Miller´s which will replace double-and-add method with Montgomery ladder method. In order to achieve better efficiency, parallel method will be used. We observe that, in many practical settings, affine coordinate are faster than projective coordinate in Miller algorithm. Therefore, we mainly discuss situations in affine coordinate. In affine coordinate, the cost comparison of our algorithm with previously basic algorithms shows an efficiency improvement of around 30% in general elliptic curves.