关键词: Weil 对, Tate 对, Miller 算法, 素数有限域, 离散对数

Abstract:

Weil pairing and Tate pairing are widely used in encryption, signature, password exchange and cryptosystem security analysis. It has been suggested that the computational efficiency of Tate pairing is better than that of Weil pairing, but this problem is still doubtful and needs to be further verified. The parameter selection algorithm of binary group structure proposed by Miller belongs to probabilistic algorithm, and the algorithm efficiency is not high. To solve the above problems, the analysis models of Tate pairing and Weil pairing on execution efficiency are established, and a new method is proposed to find the parameters of the distortion value by using the quadratic relation of the order of the elliptic curve. The research shows that when the distortion value is small, the computational efficiency of Tate pairing is better than that of Weil pairing, which is consistent with previous studies. However, when the distortion value is large, the computational efficiency of Weil pairing is better than that of Tate pairing, and the time complexity of the new method to find the distortion value parameter is less than that of Miller method O(M). Compared with Miller’s probabilistic

method, the new method is deterministic. The correctness of the analysis model is verified by analysis and example, and the new method greatly improves the efficiency and accuracy of parameter selection.

Key words: Weil pairing, Tate pairing, Miller algorithm, finite field of prime numbers, discrete logarithm