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In this paper, a joint source-channel coding approach is taken to the problem of securely computing a function of distributed sources over a multiple-access wiretap channel that is linear with respect to a finite field. It is shown that if the joint source distribution fulfills certain conditions and the function to be computed matches the linear structure of the channel, secrecy comes for free in the sense that the fundamental limit (i.e., the secrecy computation-capacity) is achieved without the need for stochastic encoding. Furthermore, the legitimate receiver does not need any advantage over the eavesdropper, which is in stark contrast to standard physical-layer security results.
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Secure Multi-Function Computation with Private Remote Sources
We consider a distributed function computation problem in which parties observing noisy versions of a remote source facilitate the computation of a function of their observations at a fusion center through public communication. The distributed function computation is subject to constraints, including not only reliability and storage but also privacy and secrecy. Specifically, 1) the remote source should remain private from an eavesdropper and the fusion center, measured in terms of the information leaked about the remote source; 2) the function computed should remain secret from the eavesdropper, measured in terms of the information leaked about the arguments of the function, to ensure secrecy regardless of the exact function used. We derive the exact rate regions for lossless and lossy single-function computation and illustrate the lossy single-function computation rate region for an information bottleneck example, in which the optimal auxiliary random variables are characterized for binary input symmetric output channels. We extend the approach to lossless and lossy asynchronous multiple-function computations with joint secrecy and privacy constraints, in which case inner and outer bounds for the rate regions differing only in the Markov chain conditions imposed are characterized.
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- Award ID(s):
- 1955401
- PAR ID:
- 10312109
- Date Published:
- Journal Name:
- Proceedings of IEEE International Symposium on Information Theory
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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- Free Publicly Accessible Full Text
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Accepted Manuscript1.0
- Conference Paper:
- https://doi.org/10.1109/ISIT45174.2021.9518019
