Connectivity of wireless information-theoretic secure networks

Connectivity is one of the most fundamental properties of wireless multi-hop networks. This paper studies the connectivity of large wireless networks with secrecy constraint, i.e. a pair of nodes can communicate securely against eavesdropping. Specifically, we consider a network with a mixture of legitimate nodes and eavesdroppers that are distributed according to two independent Poisson point processes on a √n × √n square. Assuming that legitimate nodes can generate artificial noise, which is shown in the literature to be an effective way of suppressing eavesdropping, we provide sufficient conditions on the transmission power and the noise generation power required for a network with known intensity of eavesdroppers to be asymptotically almost surely connected with secrecy constraint as n → ∞, considering the cases of both non-colluding and colluding eavesdroppers.