A Discrete Logarithm-based Approach to Compute Low-Weight Multiples of Binary Polynomials

TL;DR

This paper introduces a discrete logarithm-based method for efficiently computing low-weight multiples of binary polynomials, reducing memory usage while maintaining similar time complexity, aiding cryptanalysis of stream ciphers.

Contribution

It presents a novel discrete logarithm approach that improves memory efficiency over existing algorithms for finding low-weight polynomial multiples.

Findings

Lower memory complexity compared to generalized birthday algorithms

Comparable time complexity to existing methods

Potentially more practical for cryptanalysis applications

Abstract

Being able to compute efficiently a low-weight multiple of a given binary polynomial is often a key ingredient of correlation attacks to LFSR-based stream ciphers. The best known general purpose algorithm is based on the generalized birthday problem. We describe an alternative approach which is based on discrete logarithms and has much lower memory complexity requirements with a comparable time complexity.