Security-capacity trade-off in large wireless networks using keyless secrecy

We investigate the scalability of a class of algorithms that exploit the dynamics of wireless fading channels to achieve secret communication in a large wireless network of n randomly located nodes. We describe a construction in which nodes transmit artificial noise to suppress eavesdroppers whose locations are unknown and ensure secrecy of messages transported across the network. Under a model in which eavesdroppers operate independently and under appropriate conditions on the achievable per-node throughput Ψ(n), we show that the network can tolerate Ω((1⁄√n(n))^2c) eavesdroppers while ensuring that the aggregate rate at which eavesdroppers intercept packets goes to 0, where c is a constant such that 0 < c < 1. The result clearly establishes a trade-off between the achievable throughput and the allowable number of eavesdroppers. Under a collaborating eavesdropper model and a similar constraint on the eavesdropper throughput, we show that the network can tolerate a single eavesdropper with Ω((ln 1⁄√n(n))^1ε) antennas, ∀ε > 0. We also establish sufficient conditions on the number of eavesdroppers to achieve a non-zero throughput in our construction.