Cracking the Liu key exchange protocol in its most secure state with Lorentzian spectra

TL;DR

This paper reveals a security vulnerability in Liu's key exchange protocol when using certain noise spectra, demonstrating how Lorentzian spectra can be exploited to crack the system and proposing filtering methods to enhance security.

Contribution

The paper introduces a method to crack Liu's protocol using Lorentzian spectra and suggests spectral filtering to mitigate this vulnerability.

Findings

Vulnerability exists when noise spectra can be whitened by linear filtering.

Lorentzian spectra can be exploited to break the protocol.

Filtering can improve the security of the key exchange.

Abstract

We have found a security risk in the Liu's cypher based on random signals and feedback, when it utilizes a large class of noises for communication in its most secure state, the steady state. For the vulnerability to exist, the noise must have a spectrum which can be transformed to white-like noise by linear filtering. For the cracking, we utilize the natural properties of power density spectra and autocorrelation functions. We introduce and demonstrate the method for Lorentzian spectra. Some of the implications of the results concern the transient operation during changing bits, where the modulation products of noise cannot be band-limited therefore the cypher is vulnerable. We propose the application of line filters to provide a proper spectral shape and to improve the security.