A Modified KZ Reduction Algorithm

TL;DR

This paper introduces a modified KZ reduction algorithm that is faster and more numerically stable, especially for ill-conditioned matrices, improving upon recent methods in communications and cryptography.

Contribution

The paper presents a new version of the KZ reduction algorithm that enhances speed and numerical reliability over existing approaches.

Findings

Significantly faster reduction process.

Improved numerical stability for ill-conditioned matrices.

Enhanced performance in cryptography and communications applications.

Abstract

The Korkine-Zolotareff (KZ) reduction has been used in communications and cryptography. In this paper, we modify a very recent KZ reduction algorithm proposed by Zhang et al., resulting in a new algorithm, which can be much faster and more numerically reliable, especially when the basis matrix is ill conditioned.