用有效可计算自同态来计算Tate配对(英文)

A Note on Computing the Tate Pairing with Efficiently Computable Endomorphisms

研究用某些有效可计算的自同态来加速椭圆曲线上的Tate配对计算。针对两类嵌入指数k为偶数的椭圆曲线,用自同态对Miller算法做改进。针对k=2的情形分析了改进算法的效率,并给出一些特定条件和实例,表明改进算法比传统的Miller算法在计算Tate配对时计算速度明显加快。

The authors examine faster computation of Tate pairing on elliptic curves by using some efficiently computable endomorphism.Focused on two typical types of elliptic curves with even embedding degree k,Miller algorithm with some endomorphisms is modified.The authors analyze the efficiency for k = 2,and give the certain conditions and several examples,under which the proposed method is specifically faster than the traditional one.