On generalized active attacks by causal adversaries in networks

Active attacks are studied on noise-free graphical multicast networks. A malicious adversary may enter the network and arbitrarily corrupt transmissions. A very general model is adopted for the scope of attack: a collection of sets of edges is specified, and the adversary may control any one set of edges in this collection. The adversary is assumed to be omniscient but causal, such that the adversary is forced to decide on transmissions before knowing random choices by the honest nodes. Four main results are presented. First, a precise characterization of whether any positive rate can be achieved. Second, a simple erasure upper bound. Third, an achievable bound wherein random hashes are generated and distributed, so that nodes in the network can filter out adversarial corruption. Finally, an example network is presented that has capacity strictly between the general upper and lower bounds.