On the Equivalency of Reliability and Security Metrics for Wireline Networks

Abstract

In this paper, we consider a secure network coding problem in which some secret keys are shared among legitimate nodes, and there exists an eavesdropper which is able to hear a subset of links. We show the equivalency of secure network coding under and strong secrecy conditions. For linear network coding, we show a stronger result: equivalency of perfect secrecy and zero-error constraints to weak secrecy and $epsilon$-error constraints. This is a secure version of the result obtained by Langberg and Effros, on the equivalence of zero-error and $epsilon$-error regions in the network coding problem with co-located sources. Jalali and Ho exploit extractor functions to prove the and strong rate region equivalency for this network; however, to prove this equivalency, we develop some tools in random binning and prove the equivalency in a slightly more general setting.