Editing Weil pairing (section)

{{Short description|Binary function non degenerative defined between the point of twist of an abelian variety}}
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 ''n''th [[root of unity|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]] ([[#{{harvid|Weil|1940}}|1940]]) for Jacobians of curves, who gave an abstract algebraic definition; the corresponding results for [[elliptic function]]s were known, and can be expressed simply by use of the [[Weierstrass sigma function]].