We study the problem of secure message multicasting over graphs in the presence of a passive (node) adversary who tries to eavesdrop in the network. We show that use of feedback, facilitated through the existence of cycles or undirected edges, enables higher rates than possible in directed acyclic graphs of the same mincut. We demonstrate this using code constructions for canonical combination networks (CCNs). We also provide general outer bounds as well as schemes for passive node adversaries over CCNs.
This is joint work with Christina Fragouli, Vinod Prabhakaran and Suhas Diggavi, and was presented at ISIT 2013.