Ultimate crack and lack of any security in the statistical key exchange protocol with random signals and feedback

Abstract: We deterministically crack the secure, statistical key exchange protocol based on feedback proposed by Pao-Lo Liu [ J. Lightwave Techology 27 (2009) pp. 5230-34]. The crack is ultimate and absolute because it works under idealized conditions, and produces much higher data visibility for the eavesdropper than the protocol provides for Alice and Bob. Even with the most idealistic driving noise spectrum stated by Liu, during the most secure phase of the protocol, far away from the transients, where the system is already in its most secure steady-state, the eavesdropper has 100% success rate in identifying the key bits, at the same time when Alice and Bob have less than 100% success rate while using the Liu protocol. No statistics is needed, Eve can extract the secure bit from two samples of the signal in the two direction. Thus the Liu-protocol offers no security against the attack described in this paper.