Finding low-weight polynomial multiples using discrete logarithm

TL;DR

This paper introduces an improved algorithm for finding low-weight polynomial multiples in binary polynomials, leveraging discrete logarithms to enhance theoretical complexity and practical flexibility in cryptanalysis of stream ciphers.

Contribution

The paper presents a novel approach using discrete logarithms to improve the classical time-memory trade-off algorithm for low-weight polynomial multiples.

Findings

Improved theoretical complexity over classical methods

Enhanced practical flexibility in cryptanalysis tasks

Effective application to stream cipher cryptanalysis

Abstract

Finding low-weight multiples of a binary polynomial is a difficult problem arising in the context of stream ciphers cryptanalysis. The classical algorithm to solve this problem is based on a time memory trade-off. We will present an improvement to this approach using discrete logarithm rather than a direct representation of the involved polynomials. This gives an algorithm which improves the theoretical complexity, and is also very flexible in practice.