Weakly Secure MDS Codes for Simple Multiple Access Networks

Son Hoang Dau; Wentu Song; Chau Yuen

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arXiv · 1504.05662

Weakly Secure MDS Codes for Simple Multiple Access Networks

Son Hoang Dau·Wentu Song·Chau Yuen

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Abstract

We consider a simple multiple access network (SMAN), where $k$ sources of unit rates transmit their data to a common sink via $n$ relays. Each relay is connected to the sink and to certain sources. A coding scheme (for the relays) is weakly secure if a passive adversary who eavesdrops on less than $k$ relay-sink links cannot reconstruct the data from each source. We show that there exists a weakly secure maximum distance separable (MDS) coding scheme for the relays if and only if every subset of $\ell$ relays must be collectively connected to at least $\ell+1$ sources, for all $0 < \ell < k$. Moreover, we prove that this condition can be verified in polynomial time in $n$ and $k$. Finally, given a SMAN satisfying the aforementioned condition, we provide another polynomial time algorithm to trim the network until it has a sparsest set of source-relay links that still supports a weakly secure MDS coding scheme.

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Son Hoang Dau, Wentu Song, Chau Yuen. 2015-04-22. Weakly Secure MDS Codes for Simple Multiple Access Networks. https://arxiv.org/abs/1504.05662

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