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Communication Complexity and Secure Function Evaluation

Abstract

A secure function evaluation protocol allows two parties to jointly compute a function f(x,y)f(x,y) of their inputs in a manner not leaking more information than necessary. A major result in this field is: ``any function ff that can be computed using polynomial resources can be computed securely using polynomial resources\u27\u27 (where `resources\u27 refers to communication and computation). This result follows by a general transformation from any circuit for ff to a secure protocol that evaluates ff. Although the resources used by protocols resulting from this transformation are polynomial in the circuit size, they are much higher (in general) than those required for an insecure computation of ff. For the design of efficient secure protocols we suggest two new methodologies, that differ with respect to their underlying computational models. In one methodology we utilize the communication complexity tree (or branching program) representation of ff. We start with an efficient (insecure) protocol for ff and transform it into a secure protocol. In other words, ``any function ff that can be computed using communication complexity cc can be can be computed securely using communication complexity that is polynomial in cc and a security parameter\u27\u27. The second methodology uses the circuit computing ff, enhanced with look-up tables as its underlying computational model. It is possible to simulate any RAM machine in this model with polylogarithmic blowup. Hence it is possible to start with a computation of ff on a RAM machine and transform it into a secure protocol. We show many applications of these new methodologies resulting in protocols efficient either in communication or in computation. In particular, we exemplify a protocol for the ``millionaires problem\u27\u27, where two participants want to compare their values but reveal no other information. Our protocol is more efficient than previously known ones in either communication or computation

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Cryptology ePrint Archive

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Last time updated on 25/08/2023

This paper was published in Cryptology ePrint Archive.

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