, Volume 17, Issue 4, pp 235-261
Date: 12 Aug 2004

The Weil Pairing, and Its Efficient Calculation

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The Weil Pairing, first introduced by André Weil in 1940, plays an important role in the theoretical study of the arithmetic of elliptic curves and Abelian varieties. It has also recently become extremely useful in cryptologic constructions related to those objects. This paper gives the definition of the Weil Pairing, describes efficient algorithms to calculate it, gives two applications, and describes the motivation to considering it.