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

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

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 Frobeni...

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Bibliographische Detailangaben
1. Verfasser: Garefalakis, Theodoulos
Format: Buchkapitel
Sprache:eng
Schlagworte:
Applied sciences
Cryptography
Discrete Logarithm
Elliptic Curf
Elliptic Curve
Elliptic Curve Cryptography
Exact sciences and technology
Information, signal and communications theory
Prime Order
Signal and communications theory
Telecommunications and information theory
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Zusammenfassung: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].
ISSN:0302-9743
1611-3349
DOI:10.1007/3-540-45995-2_15