Using Feedback for Secrecy over Graphs

TL;DR

This paper explores how feedback mechanisms in network graphs, especially those with cycles or undirected edges, can enhance secure message multicasting rates against passive node adversaries, using code constructions and bounds.

Contribution

It introduces the use of feedback in graphs with cycles or undirected edges to improve secure multicasting rates, providing new code constructions and bounds for such networks.

Findings

Feedback enables higher secure rates in cyclic or undirected graphs.

Code constructions for canonical combination networks demonstrate these improvements.

Outer bounds and schemes for node adversaries are established.

Abstract

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 node adversaries over CCNs.