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

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LATIN 2002: Theoretical Informatics (LATIN 2002)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 2286))

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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].

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Author information

Authors and Affiliations

  1. Department of Mathematics Royal Holloway, University of London, TW20 0EX, Egham, Surrey, UK

    Theodoulos Garefalakis

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  1. Theodoulos Garefalakis
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Editor information

Editors and Affiliations

  1. Compaq Cambridge Research Laboratory, One Cambridge Center, 02142-1612, Cambridge, MA, USA

    Sergio Rajsbaum

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Garefalakis, T. (2002). The Generalized Weil Pairing and the Discrete Logarithm Problem on Elliptic Curves. In: Rajsbaum, S. (eds) LATIN 2002: Theoretical Informatics. LATIN 2002. Lecture Notes in Computer Science, vol 2286. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45995-2_15

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  • DOI: https://doi.org/10.1007/3-540-45995-2_15

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-43400-9

  • Online ISBN: 978-3-540-45995-8

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