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, 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 This work has been supported in part by the German Research Foundation (DFG) under the Grant SCHA 1944/9-1 and in part by the National Science Foundation (NSF) under the Grant CCF 1955401. Parts of this work are accepted for presentation at the IEEE International Symposium on Information Theory 2021 [1]. O. Günlü and R. F. Schaefer are with the Chair of Communications Engineering and Security, University of Siegen, 57076 Siegen, Germany (email: {onur.guenlue, rafael.schaefer}@uni-siegen.de). M. Bloch is with the School of Electrical and Computer Engineering, Georgia Institute of Technology, Atlanta, GA 30332 (email: matthieu.bloch@ece.gatech.edu).