On Capacity Region of Wiretap Networks

In this paper we study the problem of secure communication over networks in which an unknown subset of nodes or links can be wiretapped. We first consider a general multi-terminal discrete memoryless network (DMN) described by its channel transition function from network inputs to network outputs, observed by network nodes and the eavesdropper. We prove that in such general networks with multiple sources and sinks, the capacity regions subject to strong and weak secrecy requirements are equal. We then focus on the special case of noiseless wiretap networks, i.e., wired networks of noiseless point-to-point directed channels, where an unknown subset of links, selected from a known collection of such subsets, can be wiretapped. We derive inner and outer bounds on the capacity regions of such networks in terms of the entropic region, for both zero probability of error and asymptotically zero probability of error.