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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.

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rdfs:label	Weil pairing (en) Accouplement de Weil (fr) 韦伊配对 (zh)
rdfs:comment	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. (en) 韋伊配對（英語：Weil pairing），簡單的說，Weil對可將橢圓曲線之撓群（torsion group）上的兩個點，映射到一個特殊有限域之乘法子群上，藉此可將橢圓曲線離散對數問題（ECDLP）投射到一般的離散對數問題（DLP）。 Weil對被用在數論以及代數幾何上，以及橢圓曲線密碼學的 ID-based cryptography 上。對於更高維度的，相應的理論依然成立。 (zh) En géométrie algébrique et en théorie des nombres, l'accouplement de Weil est une relation mathématique entre certains points d'une courbe elliptique, plus spécifiquement une application bilinéaire fonctorielle entre ses points de torsion. Cet accouplement est nommé en l'honneur du mathématicien français André Weil, qui en a systématisé l'étude. Il s'agit d'un outil important dans l'étude de ces courbes. (fr)
dcterms:subject	Abelian varieties Pairing-based cryptography Elliptic curves
Wikipage page ID	1131644 (xsd:integer)
Wikipage revision ID	1013187785 (xsd:integer)
Link from a Wikipage to another Wikipage	Cartesian product Root of unity Bilinear form Algebraic closure Jacobian variety Elliptic curve cryptography Mathematics Elliptic function Elliptic curve Homomorphic Signatures for Network Coding André Weil Function field of an algebraic variety Kummer theory Pairing Dual abelian variety Tate pairing Algebraic geometry Cyclic group Field (mathematics) Abelian varieties Number theory Abelian variety Abelian varieties Picard group Pairing-based cryptography Boneh–Franklin scheme Elliptic curves Weierstrass sigma function Divisors Pairing-based cryptography Tate module Primitive nth root of unity Autoduality of Jacobians Les Comptes rendus de l'Académie des sciences Identity based encryption Multiplicative notation Theta-divisor
Link from a Wikipage to an external page	http://www.isg.rhul.ac.uk/~sdg/pair-over-C.pdf
sameAs	Weil pairing Weil pairing Weil pairing Weil pairing Weil pairing Weil pairing
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has abstract	En géométrie algébrique et en théorie des nombres, l'accouplement de Weil est une relation mathématique entre certains points d'une courbe elliptique, plus spécifiquement une application bilinéaire fonctorielle entre ses points de torsion. Cet accouplement est nommé en l'honneur du mathématicien français André Weil, qui en a systématisé l'étude. Il s'agit d'un outil important dans l'étude de ces courbes. Il est possible de définir un accouplement de Weil pour les courbes définies sur le corps des complexes ou sur des corps finis ; dans ce dernier cas, l' permet de le calculer efficacement, ce qui est à la base de la cryptographie à base de couplages sur les courbes elliptiques. Une construction similaire s'étend aux variétés algébriques plus générales. (fr) 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. (en) 韋伊配對（英語：Weil pairing），簡單的說，Weil對可將橢圓曲線之撓群（torsion group）上的兩個點，映射到一個特殊有限域之乘法子群上，藉此可將橢圓曲線離散對數問題（ECDLP）投射到一般的離散對數問題（DLP）。 Weil對被用在數論以及代數幾何上，以及橢圓曲線密碼學的 ID-based cryptography 上。對於更高維度的，相應的理論依然成立。 (zh)
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page length (characters) of wiki page	5266 (xsd:nonNegativeInteger)
foaf:isPrimaryTopicOf	wikipedia-en:Weil_pairing
is Link from a Wikipage to another Wikipage of	List of algebraic geometry topics Decisional Diffie–Hellman assumption Level structure (algebraic geometry) Elliptic-curve cryptography Elliptic divisibility sequence Equations defining abelian varieties André Weil Computational hardness assumption Identity-based encryption Pairing Dual abelian variety Tate pairing Dan Boneh Abelian variety Homomorphic signatures for network coding Boneh–Franklin scheme List of things named after André Weil Pairing-based cryptography Theta characteristic
is known for of	André Weil
is foaf:primaryTopic of	wikipedia-en:Weil_pairing

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