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.
Read more about Weil Pairing: Formulation, Generalisation To Abelian Varieties, Applications
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—Simone Weil (1909–1943)
“Through man, and woman, and sea, and star,
Saw the dance of nature forward far;
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Saw musical order, and pairing rhymes.”
—Ralph Waldo Emerson (1803–1882)