Journal of Cryptology

, Volume 17, Issue 4, pp 235–261

The Weil Pairing, and Its Efficient Calculation


DOI: 10.1007/s00145-004-0315-8

Cite this article as:
Miller, V. J Cryptology (2004) 17: 235. doi:10.1007/s00145-004-0315-8


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.

Elliptic curve Discrete logarithm Weil pairing 

Copyright information

© International Association for Cryptologic Research 2004

Authors and Affiliations

  1. 1.Center for Communications Research, Princeton, NJ 08540USA

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