The generalized weil pairing and the discrete logarithm problem on elliptic curves

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 2 modulo 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].