Cryptology ePrint Archive: Report 2021/831

Private Remote Sources for Secure Multi-Function Computation

Onur Gunlu and Matthieu Bloch and Rafael F. Schaefer

Abstract: 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.

Category / Keywords: foundations / secure multiple function computation, private remote source, lossy function computation, information bottleneck, rate-limited public communication.

Date: received 17 Jun 2021, last revised 10 Sep 2021

Contact author: onur guenlue at uni-siegen de

Available format(s): PDF | BibTeX Citation

Version: 20210910:133549 (All versions of this report)

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