Distributed computing with privacy

A set of terminals that observe correlated data seek to compute functions of the data using interactive public communication. At the same time it is required that this communication, observed by an eavesdropper, does not reveal the value of a private function of the data. In general, the private function and the functions computed by the terminals 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 an appropriately chosen multiterminal source coding task. A single-letter formula is provided for this rate in special cases.