  The elliptic curve discrete logarithm problem is considered a secure
cryptographic primitive. The purpose of this paper is to propose a paradigm
shift in attacking the elliptic curve discrete logarithm problem. In this
paper, we will argue that initial minors are a viable way to solve this
problem. This paper will present necessary algorithms for this attack. We have
written a code to verify the conjecture of initial minors using Schur
complements. We were able to solve the problem for groups of order up to
$2^{50}$.
