on the equivalency of reliability and security metrics for wireline networks

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 zeroerror 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 zeroerror and $epsilon$error regions in the network coding problem with colocated 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.