简单的说，Weil对可将椭圆曲线之挠群（torsion group）上的两个点，映射到一个特殊有限域之乘法子群上，借此可将椭圆曲线离散对数问题（ECDLP）投射到一般的离散对数问题（DLP）。

Weil对被用在数论以及代数几何上，以及椭圆曲线密码学的 ID-based cryptography 上。

对于更高维度的阿贝尔簇，相应的理论依然成立。

In mathematics, the Weil pairing is a pairing (bilinear form, though with multiplicative notation) on the points of order dividing n of an elliptic curve E, taking values in nth roots of unity. More generally there is a similar Weil pairing between points of order n of an abelian variety and its dual. It was introduced by André Weil (1940) for Jacobians of curves, who gave an abstract algebraic definition; the corresponding results for elliptic functions were known, and can be expressed simply by use of the Weierstrass sigma function.