Abstract: 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.

Key words: elliptic curve, Tate pairing, Miller algorithm, endomorphism

摘要： 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。

关键词: 椭圆曲线, Tate配对, Miller算法, 自同态