A new method for solving the elliptic curve discrete logarithm problem
This addresses a fundamental problem in cryptography for securing digital communications, representing a paradigm shift rather than an incremental improvement.
The paper tackles the elliptic curve discrete logarithm problem by proposing a new attack method based on initial minors and Schur complements, achieving the ability to solve the problem for groups of order up to 2^50.
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 $2^{50}$.