# On the equivalency of reliability and security metrics for wireline networks

Document Type: Article

Authors

Electrical Engineering Department, Sharif University of Technology, Tehran, Iran

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 weak 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 weak 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.

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