Communication Complexity and Secure Function Evaluation

TL;DR

This paper introduces two new methodologies for designing efficient secure protocols based on communication complexity trees and circuit models with look-up tables, enabling more efficient secure computations like the millionaires problem.

Contribution

It presents novel methodologies leveraging communication complexity and circuit models with look-up tables for constructing efficient secure protocols, improving on previous approaches.

Findings

Protocols with polynomial communication complexity in the original function's complexity.

Secure protocols with polylogarithmic overhead for RAM-based computations.

More efficient solution for the millionaires problem.

Abstract

We suggest two new methodologies for the design of efficient secure protocols, that differ with respect to their underlying computational models. In one methodology we utilize the communication complexity tree (or branching for f and transform it into a secure protocol. In other words, "any function f that can be computed using communication complexity c can be can be computed securely using communication complexity that is polynomial in c and a security parameter". The second methodology uses the circuit computing f, 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 f 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", 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.