A Guess and Determine Attack on the Elliptic Curve Discrete Logarithm Problem

Abstract

This paper is a continuation of our earlier work, in which we described a Las Vegas algorithm to solve the elliptic curve discrete logarithm problem. The Las Vegas algorithm reduces the elliptic curve discrete logarithm problem to finding a zero minor in a matrix. Using the intersection poset of a hyperplane arrangement, we develop an algorithm to find a zero minor in a rectangular matrix. Our methods are elementary. We discuss the complexity and success probability of our algorithm and provide implementation details. Finding a zero minor in a matrix is also of independent interest.