@article { author = {Mojahedian, M.Mahdi. and Aref, M.Reza and Gohari, A.}, title = {On the equivalency of reliability and security metrics for wireline networks}, journal = {Scientia Iranica}, volume = {26}, number = {3}, pages = {1749-1761}, year = {2019}, publisher = {Sharif University of Technology}, issn = {1026-3098}, eissn = {2345-3605}, doi = {10.24200/sci.2018.5695.1428}, 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.}, keywords = {Wireline networks,perfect secrecy,strong secrecy,weak secrecy,epsilon-error decoding,zero-error decoding,random binning}, url = {https://scientiairanica.sharif.edu/article_20434.html}, eprint = {https://scientiairanica.sharif.edu/article_20434_34be6cd00a8cdc123d5322440da48f55.pdf} }