A Guess and Determine Attack on the Elliptic Curve Discrete Logarithm Problem
Cryptography and Security
2026-07-10 v1 Distributed, Parallel, and Cluster Computing
Information Theory
Algebraic Geometry
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 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 of our algorithm, success probability and provide implementation details. We also provide simulation details. Finding a zero minor in a matrix is also of independent interest.
Cite
@article{arxiv.2607.09814,
title = {A Guess and Determine Attack on the Elliptic Curve Discrete Logarithm Problem},
author = {Ayan Mahalanobis},
journal= {arXiv preprint arXiv:2607.09814},
year = {2026}
}