On Secrecy Capacity Scaling in Wireless Networks

We study the achievable secure rate per source-destination pair in a random extended network. In our model, the legitimate and eavesdropper nodes are assumed to be placed according to Poisson point processes in a square region of area $n$. It is shown that, when the legitimate nodes have unit intensity, $\lambda=1$, and the eavesdroppers have an intensity of $\lambda_e=O((\log n)^{-2})$, almost all of the nodes achieve a perfectly secure rate of $\Omega(\frac{1}{\sqrt{n}})$. Therefore, under these assumptions, securing the transmissions of nodes does not entail a loss in the per-node throughput in terms of scaling. Our achievability argument is based on a novel multi-hop forwarding scheme where randomization is added in every hop to ensure maximal ambiguity at the eavesdropper(s).