Private computations over the integers

The possibility of private distributed computations of n-argument functions defined over the integers is considered. A function f is t-private if there exists a protocol for computing f so that no coalition of ⩽t participants can infer any additional information from the execution of the protocol. It is shown that certain results for private computation over finite domains cannot be extended to infinite domains. The possibility of privately computing f is shown to be closely related to the communication complexity of f. A complete characterization of t-private Boolean functions over countable domains is given