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 Frobenius congruent to 2mo dulo 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 Ruck [10].

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