Weil pairing (original) (raw)
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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| dbo: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) |
| dbo:wikiPageExternalLink | http://www.isg.rhul.ac.uk/~sdg/pair-over-C.pdf |
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| 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) |
| rdfs:label | Weil pairing (en) Accouplement de Weil (fr) 韦伊配对 (zh) |
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