Secure Capacity of Wireless Broadcast Networks

We give a constructive characterization for the capacity of wireless broadcast networks that are prone to Byzantine attacks. The adversary controls a single node in the network and can modify the packets flowing through the node. The central trade-off in such a scenario is that of security and throughput. We define secure capacity as the highest possible transmission rate from the source such that the destination can detect any modification in the information packets. Prior work in this direction mainly concentrate on nodes performing random network coding, where the capacity is shown to be bounded by C− z0, where C is the minimum cut between the source and the destination and z0 is the maximum number of packets the adversary can modify. We show that by carefully designing the transmission scheme, rates higher than C − z0 are achievable. In particular, we show that some nodes in the network carefully duplicating the packets results in increased capacity of the network. In order to efficiently search over all the possible transmission strategies, we formulate the problem of characterizing secure capacity as a linear optimization program. We give an explicit routing (and duplication) strategy that achieves the capacity given by the optimal solution of the optimization program, thus establishing the secure capacity of the given wireless broadcast network. We also show that there exist networks in which secure capacity with in-network monitoring can be arbitrarily larger than that without in-network monitoring.