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- W2102205282 abstract "Consider a communication network represented by a directed graph $mathcal{G}=(mathcal{V},mathcal{E})$, where $mathcal{V}$ is the set of nodes and $mathcal{E}$ is the set of point-to-point channels in the network. On the network a secure message $M$ is transmitted, and there may exist wiretappers who want to obtain information about the message. In secure network coding, we aim to find a network code which can protect the message against the wiretapper whose power is constrained. Cai and Yeung cite{cai2002secure} studied the model in which the wiretapper can access any one but not more than one set of channels, called a wiretap set, out of a collection $mathcal{A}$ of all possible wiretap sets. In order to protect the message, the message needs to be mixed with a random key $K$. They proved tight fundamental performance bounds when $mathcal{A}$ consists of all subsets of $mathcal{E}$ of a fixed size $r$. In this paper, we investigate the problem when $mathcal{A}$ consists of arbitrary subsets of $mathcal{E}$ and obtain the following results: 1) an upper bound on $H(M)$; 2) a lower bound on $H(K)$ in terms of $H(M)$. The upper bound on $H(M)$ is explicit, while the lower bound on $H(K)$ can be computed in polynomial time. The tightness of the lower bound for the point-to-point communication system is also proved." @default.
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- W2102205282 date "2011-07-01" @default.
- W2102205282 modified "2023-09-23" @default.
- W2102205282 title "Performance Bounds in Secure Network Coding" @default.
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- W2102205282 doi "https://doi.org/10.1109/isnetcod.2011.5978913" @default.
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