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

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.

💡 Research Summary

The paper revisits the security of Liu’s key‑exchange protocol, which relies on shared random signals and a feedback loop, and demonstrates a fundamental vulnerability that arises when the noise used in the protocol’s “steady‑state” (the purportedly most secure mode) possesses a spectrum that can be linear‑filtered into white‑like noise. The authors focus on Lorentzian spectra, whose power‑density function follows 1 /