Secrecy capacity scaling of large-scale cognitive networks

Increasingly, more spectrum bands are utilized for unlicensed use in wireless cognitive networks. It is important to study how information-theoretic secrecy capacity is affected in large-scale cognitive networks. We consider two scenarios: (1) non-colluding case, where eavesdroppers decode messages individually. In this case, we propose a new secure protocol model to analyze the transmission opportunities of secondary nodes. We show that the secrecy capacity of the primary network is not affected, while the secondary network can achieve the same performance as a standalone network in the order sense. Since our analysis is general as we only make a few relaxed assumptions on both networks, the conclusions hold when both networks are classic static networks, networks with i.i.d mobility, multicast networks etc. (2) colluding case where eavesdroppers can collude to decode a message. In that case, we show that the lower bound of per-node secrecy capacity of the primary network is Ω(1/√n φe-2/α-1(n)) when the eavesdropper density is φe(n)=Ω(log2n). Interestingly the existence of secondary nodes increases the secrecy capacity of the primary network.