Physical layer multi-user key generation in wireless networks

Secret key generation by extracting the shared randomness in the wireless fading channel from physical layer is an interesting topic of practical value. Previous works have focused on the study of physical layer key generation with two nodes from the view point of key generation rate (KGR). Information theoretic limits and the KGRs in implementation have been derived. However, in real-world applications, the physical layer key generation problem involving multiple nodes is the common case, which lacks sufficient study so far. Multi-node case differs from two-node case in that there are two more important considerations: (1) the trade-off between KGR and probing efficiency at individual node pair; (2) channel probing schedule among multiple node pairs. This paper aims at minimizing the Overall Waiting Time of physical layer key generation with multiple users (shorten as OWT) through the optimization of probing rates at individual node pair and channel probing schedule. The theoretical lower bound of OWT is derived first, then a practical method (MUKEM) is proposed to compute reasonable probing rates and channel probing schedule for multiple node pairs to obtain a short OWT. Simulations are conducted to evaluate the effectiveness of our method. The results show that 70 % of OWT can be reduced by using our method comparing with one-by-one key generations; while it is only about 8 % longer than the lower bound of OWT.