14,417 research outputs found
An Equivalence Between Secure Network and Index Coding
We extend the equivalence between network coding and index coding by Effros,
El Rouayheb, and Langberg to the secure communication setting in the presence
of an eavesdropper. Specifically, we show that the most general versions of
secure network-coding setup by Chan and Grant and the secure index-coding setup
by Dau, Skachek, and Chee, which also include the randomised encoding setting,
are equivalent
On the Capacity Region for Secure Index Coding
We study the index coding problem in the presence of an eavesdropper, where
the aim is to communicate without allowing the eavesdropper to learn any single
message aside from the messages it may already know as side information. We
establish an outer bound on the underlying secure capacity region of the index
coding problem, which includes polymatroidal and security constraints, as well
as the set of additional decoding constraints for legitimate receivers. We then
propose a secure variant of the composite coding scheme, which yields an inner
bound on the secure capacity region of the index coding problem. For the
achievability of secure composite coding, a secret key with vanishingly small
rate may be needed to ensure that each legitimate receiver who wants the same
message as the eavesdropper, knows at least two more messages than the
eavesdropper. For all securely feasible index coding problems with four or
fewer messages, our numerical results establish the secure index coding
capacity region
Perfectly Secure Index Coding
In this paper, we investigate the index coding problem in the presence of an
eavesdropper. Messages are to be sent from one transmitter to a number of
legitimate receivers who have side information about the messages, and share a
set of secret keys with the transmitter. We assume perfect secrecy, meaning
that the eavesdropper should not be able to retrieve any information about the
message set. We study the minimum key lengths for zero-error and perfectly
secure index coding problem. On one hand, this problem is a generalization of
the index coding problem (and thus a difficult one). On the other hand, it is a
generalization of the Shannon's cipher system. We show that a generalization of
Shannon's one-time pad strategy is optimal up to a multiplicative constant,
meaning that it obtains the entire boundary of the cone formed by looking at
the secure rate region from the origin. Finally, we consider relaxation of the
perfect secrecy and zero-error constraints to weak secrecy and asymptotically
vanishing probability of error, and provide a secure version of the result,
obtained by Langberg and Effros, on the equivalence of zero-error and
-error regions in the conventional index coding problem.Comment: 25 pages, 5 figures, submitted to the IEEE Transactions on
Information Theor
Universal Secure Multiplex Network Coding with Dependent and Non-Uniform Messages
We consider the random linear precoder at the source node as a secure network
coding. We prove that it is strongly secure in the sense of Harada and Yamamoto
and universal secure in the sense of Silva and Kschischang, while allowing
arbitrary small but nonzero mutual information to the eavesdropper. Our
security proof allows statistically dependent and non-uniform multiple secret
messages, while all previous constructions of weakly or strongly secure network
coding assumed independent and uniform messages, which are difficult to be
ensured in practice.Comment: 10 pages, 1 figure, IEEEtrans.cls. Online published in IEEE Trans.
Inform. Theor
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