Network Information Theoretic Security With Omnipresent Eavesdropping

Shannon showed that to achieve perfect secrecy in point-to-point communication, the message rate cannot exceed the shared secret key rate giving rise to the simple one-time pad encryption scheme. In this paper, we extend this work from point-to-point to networks. We consider a connected network with pairwise communication between the nodes and assume that each node is provided with a certain amount of secret bits before communication commences. An eavesdropper with unlimited computing power has access to all communication and can hack a subset of the nodes not known to the rest of the nodes. We investigate the limits on information-theoretic secure communication with end-to-end encryption for this network. We establish a tradeoff between the secure channel rate (for a node pair) and the secure network rate (sum over all node pair rates) and show that information-theoretic secrecy can be achieved asymptotically if and only if the sum rate of any subset of unhacked channels does not exceed the shared unhacked-secret-bit rate of these channels. We also propose a practical scheme that achieves a good balance of network and channel rates with information-theoretic secrecy guarantee. This work has a wide range of potential applications for which strong secrecy is desired, such as cyber-physical systems, distributed-control systems, and ad-hoc networks.