Private Computations Over the Integers (Extended Abstract)

The subject of this work is the possibility of private distributed computations of nargument functions defined over the integers. A function f is t private if there exists a protocol for computing f , so that no coalition of 5 t participants can infer any additional information from the execution of the protocol. It is known that over finite domains, every function can be computed prieven n private. We prove that this result cannot be extended to infinite domains. The possibility of privately computing f is shown to be closely related to the communication complexity of f . Using this relation, we show, for example, that n argument addition is 191 private over the non-negative integers, but not even 1 private over all the integers. Finally, a complete characterization of tvately. Some functions, like a 1 ’ dition, are *e-mail: [email protected] . Department of Computer Science, Technion, Haifa 32000, Israel. Research supported in part by US-Israel BSF grant 88-00282. Part of this research was done while visiting the Computer Science Department in the University of Toronto. +e-mail: [email protected] . Department of Computer Science, Tufts University, Medford, MA 02155. Se-mail: [email protected] . Department of Computer Science, Technion, Haifa 32000, Israel. Research supported in part by US-Israel BSF grant 88-00282. private Boolean functions over countable domains is given. A Boolean function is l private if and only if its communication complexity is bounded. This characterization enables us to prove that every Boolean function falls into one of the following three categories: It is either n private, 191 private but not private, or not 1 private.