Secure multiparty computation of approximations (extended abstract)

Approximation algorithms can sometimes provide effcient solutions when no effcient 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 f̂ is an approximation to f, secure multiparty computation of f̂ allows the parties to compute f̂ without revealing unnecessary information. However, secure computation of f̂ may not be as private as secure computation of f, because the output of f̂ 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 effcient, sublinear-communication, private approximate computation for the Hamming distance and an effcient private approximation of the permanent.