A Zero Minor Solves the Elliptic Curve Discrete Logarithm Problem

Abstract

The elliptic curve discrete logarithm problem is of fundamental importance in public-key cryptography. It has been in use for a long time. Moreover, it is an interesting challenge in computational mathematics. Its solution is supposed to provide interesting research directions. In this paper, we explore ways to solve the elliptic curve discrete logarithm problem. Our results are primarily computational. However, the methods we develop and directions we pursue can provide a potent attack on this problem. This work follows our earlier work, where we tried to solve this problem by finding a zero minor in a matrix over the same finite field on which the elliptic curve is defined. This paper is self-contained.