Distributed Function Computation with Confidentiality

TL;DR

This paper investigates the conditions under which distributed terminals can compute functions of correlated data while keeping a private function concealed from eavesdroppers, linking secure computability to information-theoretic entropy and communication rates.

Contribution

It establishes a necessary and sufficient condition for secure function computation in distributed settings and provides a single-letter formula for the communication rate in special cases.

Findings

Secure computability depends on conditional entropy and communication rate.

A class of functions is securely computable if entropy exceeds communication rate.

Single-letter formula derived for specific cases.

Abstract

A set of terminals observe correlated data and seek to compute functions of the data using interactive public communication. At the same time, it is required that the value of a private function of the data remains concealed from an eavesdropper observing this communication. In general, the private function and the functions computed by the nodes can be all different. We show that a class of functions are securely computable if and only if the conditional entropy of data given the value of private function is greater than the least rate of interactive communication required for a related multiterminal source-coding task. A single-letter formula is provided for this rate in special cases.