Improper Quantization Decision and Key Entropy Loss in Wireless Physical-Layer Security with False Channel Statistics Knowledge

Abstract

Wireless physical-layer security is recently proposed for several types of cutting-edge networks, such as 5G and 6G. In wireless physical-layer security, it is usually suggested in literature that eavesdroppers need to locate themselves near legitimate transmitters or receivers if they want to steal some secret key information. By means of scenario analysis, this paper shows that if the eavesdropper knows the channel statistics better than the legitimate stations, e.g., know the K-factor estimates of Rician fading channel, they can exploit these knowledges to derive some secret key information. We define a concept called “improper quantization decision loss <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$k$</tex> ” as the entropy loss in the generated key that can be obtained by the eavesdropper. We show step-by-step how the eavesdropper can obtain such information. We also propose mathematical expressions of <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$n$</tex> and derive some results based on empirical values of channel parameters available in literature. From our analytical result for an urban area case, the loss is as large as almost 4/5 of key information, thus requiring a privacy amplification process that yields about 1/5 of the original key length. With our new concept, the new upper and lower bounds of vulnerable key bits are derived.