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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“Two prisoners whose cells adjoin communicate with each other by knocking on the wall. The wall is the thing which separates them but is also their means of communication. It is the same with us and God. Every separation is a link.”
—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)