Private Remote Sources for Secure Multi-Function Computation

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, includin...

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Bibliographic Details
Published in:IEEE transactions on information theory Vol. 68; no. 10; pp. 6826 - 6841
Main Authors: Gunlu, Onur, Bloch, Matthieu, Schaefer, Rafael F.
Format: Journal Article
Language:English
Published: New York IEEE 01.10.2022
The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subjects:
Computation
Computational modeling
information bottleneck
Loss measurement
lossy function computation
Markov chains
Markov processes
Noise measurement
Privacy
private remote source
Random sequences
Random variables
rate-limited public communication
Remote observing
Secrecy aspects
Secure multiple function computation
ISSN:0018-9448, 1557-9654, 1557-9654
Online Access:Get full text
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Summary: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 secrecy and privacy. Specifically, 1) the function computed should remain secret from an eavesdropper observing the public communication and correlated observations, measured in terms of the information leaked about the arguments of the function, to ensure secrecy regardless of the exact function used; 2) the remote source should remain private from the eavesdropper and the fusion center, measured in terms of the information leaked about the remote source itself. 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 that differ only in the Markov chain conditions imposed are characterized.
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ISSN:0018-9448
1557-9654
1557-9654
DOI:10.1109/TIT.2022.3182416