Secure Multiparty Computation of Approximations

Approximation algorithms can sometimes provide effcient solutions when no efficient exact computation is known. In particular, approximations are often useful in a distributed setting where the inputs are held by different parties and are extremely large. Furthermore, for some applications, the parties want to cooperate to compute a function of their inputs without revealing more information than necessary.If f is an approximation to f, secure multiparty computation of f allows the parties to compute f without revealing unnecessary information. However, secure computation of f may not be as private as secure computation of f, because the output of f may itself reveal more information than the output of f. In this paper, we present definitions of secure multiparty approximate computations that retain the privacy of a secure computation of f. We present an efficient, sublinear-communication, private approximate computation for the Hamming distance and an efficient private approximation of the permanent.