Abstract: The computation of Weil pairing of elliptic curves over finite fields is of great significance to the application of public-key cryptography. The research of Weil pairing focuses on theoretical research, but pays little attention to practical application, which leads to the need for new methods to support some theoretical research. For this reason, the Weil pairing calculation method is given, the point selection problem of Miller algorithm over finite field is pointed out by examples, and the difference between two different methods using Miller algorithm is analyzed. Through Miller algorithm, the limitation of MOV( Menezes-Okamoto-Vanstone) attack discrete logarithm is pointed out. The practical analysis shows that the Weil pairing of elliptic curves in finite fields are of small order and not very effective for large suborder.

Key words: Weil pairing')">

Weil pairing, Miller algorithm, menezes-okamoto-vanstone(MOV) algorithm, discrete logarithm