Secure multiparty computation of approximations - (Extended abstract)

Approximation algorithms can sometimes provide efficient 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) over cap is an approximation to f, secure multiparty computation of (f) over cap allows the parties to compute (f) over cap without revealing unnecessary information. However, secure computation of (f) over cap 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.