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