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The Generalized Weil Pairing and the Discrete Logarithm Problem on Elliptic Curves

  • Theodoulos Garefalakis
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 2286)

Abstract

We review the construction of a generalization of the Weil pairing, which is non-degenerate and bilinear, and use it to construct a reduction from the discrete logarithm problem on elliptic curves to the discrete logarithm problem in finite fields, which is efficient for curves with trace of Frobenius congruent to 2modulo the order of the base point. The reduction is as simple to construct as that of Menezes, Okamoto, and Vanstone [16], and is provably equivalent to that of Frey and Rück [10].

Keywords

Elliptic Curve Elliptic Curf Prime Order Discrete Logarithm Elliptic Curve Cryptography 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2002

Authors and Affiliations

  • Theodoulos Garefalakis
    • 1
  1. 1.Department of Mathematics Royal HollowayUniversity of LondonEghamUK

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