The Equivalence Between Elliptic Curve and Quadratic Function Field Discrete Logarithms in Characteristic 2

In this paper we show that solving the discrete logarithm problem for non-supersingular elliptic curves over finite fields of even characteristic is polynomial-time equivalent to solving a discrete logarithm type of problem in the infrastructure of a certain function field. We give an explicit correspondence between the two structures and show how to compute the equivalence.

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