What happens when a malicious adversary covertly controls part of a network? Large, distributed networks are more likely to be vulnerable to so-called Byzantine attacks; that is, when some nodes are seized by an adversary intent on disrupting the goals of the network. When such an adversary is present, but its location is unknown, how can we maintain reliable performance? We present an information theoretic framework to address this problem in the context of network coding and distributed source coding. Our approach is distinctive in that it relies on long-run statistics being observed by nodes in the network. The adversary can manipulate these statistics, but doing so may reveal its location, and it can subsequently be ignored by honest nodes.