Security Evaluation of Mutual Random Phase Injection Scheme for Secret Key Generation over Static Point-to-Point Communications

Physical layer secret key generation schemes, usually have two serious challenges in static point-to-point communications: 1) low key generation rate due to low entropy of channel state information and 2) security vulnerability at non-proximity regions due to spatial correlation. To solve the first challenge, local random generator-based schemes can be used. One of these schemes is mutual random phase injection, in which the channel probing signals with random phase are exchanged between the legitimate parties. In this paper, the security of the aforementioned scheme is reviewed in a static point-to-point link with a geometric secrecy approach. For this purpose, the vulnerability regions and secrecy regions are determined, and then a closed expression is provided for the key error probability. Moreover, based on the entropy analysis, the amount of eavesdropper’s equivocation about the key is calculated. The analytical results show that the eavesdropper’s equivocation is very low in static environments. In order to mitigate this weakness, we propose the idea of probing over multiple carrier frequencies instead of one frequency. The aim of this idea is to alter the equivalent channel phase, which leads to a significant increase in key entropy. As an example, the analytical results show that in static environments if single-bit quantization is utilized, the eavesdropper's equivocation about the key equals the number of different carrier frequencies which are used in the probing phase; so if channel probing is performed on a single frequency, the eavesdropper's equivocation will be only one bit, while, using the suggested idea, the eavesdropper's equivocation will be multifold. The simulation results show that if the probing process is performed on several frequencies, the vulnerability regions will decrease and the secrecy regions will increase. At the end of the paper, some suggestions are provided for further research in this field.