Cooperative jamming to improve the connectivity of the 1-D secrecy graph

Consider a one-dimensional wireless network with n nodes uniformly and independently distributed at random in the interval. In addition, m eavesdropper nodes are uniformly and independently distributed in. For a randomly selected source-destination pair, we consider the problem of securely delivering a message from the source to the destination and we present achievable results on the number of eavesdropper nodes that can be tolerated by the network. Our constructions make use of cooperative jamming, in which nodes located close to the eavesdroppers generate artificial noise. For the one-dimensional network case, our results provide an improvement to the connectivity properties of the recently-introduced secrecy graph which is disconnected for any positive number of eavesdroppers without cooperative jamming. We consider cases of both known and unknown eavesdropper locations. For known eavesdropper locations, we show that a message can be securely delivered from the source to the destination with probability one as the number of nodes n goes to infinity, for any number of independent eavesdroppers m(n) satisfying m(n) = o(√n / log n). For unknown eavesdropper locations, we present a construction which can tolerate m(n) = o(n/log n) under the assumption of independent eavesdroppers, but which is fragile in the face of collaborating eavesdroppers.