Privacy in Index Coding: Improved Bounds and Coding Schemes

Karmoose, Mohammed; Song, Linqi; Cardone, Martina; Fragouli, Christina

doi:10.1109/isit.2018.8437802

Cited by 2 publications

References 11 publications

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On the Capacity Region for Secure Index Coding

Liu

Vellambi

Kim

et al. 2018

2018 IEEE Information Theory Workshop (ITW)

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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.

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On the Capacity Region for Secure Index Coding

Liu

Vellambi

Kim

et al. 2018

2018 IEEE Information Theory Workshop (ITW)

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Privacy in Index Coding: $k$ -Limited-Access Schemes

Karmoose

Song

Cardone

et al. 2020

IEEE Trans. Inform. Theory

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In the traditional index coding problem, a server employs coding to send messages to n clients within the same broadcast domain. Each client already has some messages as side information and requests a particular unknown message from the server. All clients learn the coding matrix so that they can decode and retrieve their requested data. Our starting observation is that, learning the coding matrix can pose privacy concerns: it may enable a client to infer information about the requests and side information of other clients. In this paper, we mitigate this privacy concern by allowing each client to have limited access to the coding matrix. In particular, we design coding matrices so that each client needs only to learn some of (and not all) the rows to decode her requested message. By means of two different privacy metrics, we first show that this approach indeed increases the level of privacy. Based on this, we propose the use of k-limited-access schemes: given an index coding scheme that employs T transmissions, we create a k-limited-access scheme with T k ≥ T transmissions, and with the property that each client needs at most k transmissions to decode her message. We derive upper and lower bounds on T k for all values of k, and develop deterministic designs for these schemes, which are universal, i.e., independent of the coding matrix. We show that our schemes are order-optimal when either k or n is large. Moreover, we propose heuristics that complement the universal schemes for the case when both n and k are small.

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Privacy in Index Coding: Improved Bounds and Coding Schemes

Cited by 2 publications

References 11 publications

On the Capacity Region for Secure Index Coding

On the Capacity Region for Secure Index Coding

Privacy in Index Coding: $k$ -Limited-Access Schemes

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