On secrecy capacity scaling in wireless networks

We study a random extended network, where 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, ¿ = 1, and the eavesdroppers have an intensity of ¿
_e
= O((log n)
^-2
), almost all of the nodes achieve a perfectly secure rate of ¿ (1/¿n). The 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). Remarkable, under these assumptions, securing the transmissions of nodes does not entail a loss in the per-node throughput in terms of scaling.