Abelian varieties | Pairing-based cryptography | Elliptic curves

Weil pairing

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 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. (Wikipedia).

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Related pages

Abelian variety | Algebraic closure | Elliptic function | Tate pairing | Kummer theory | Root of unity | Function field of an algebraic variety | Dual abelian variety | André Weil | Pairing-based cryptography | Mathematics | Field (mathematics) | Jacobian variety | Algebraic geometry | Cyclic group | Pairing | Cartesian product | Number theory | Tate module | Bilinear form | Boneh–Franklin scheme | Divisor (algebraic geometry) | Elliptic curve