The author investigates the following problem: Suppose m people wish to compute the value of a function f(x ₁ , x ₂ , x ₃ , ..., x _m ), which is an integer-valued function of m integer variables xi of bounded range. Assume initially person Pi knows the value of xi and no other x's. Is it possible for them to compute the value of f, by communicating among themselves, without unduly giving away any information about the values of their own variables? The author gives a precise formulation of this general problem and describe three ways of solving it by use of one-way functions (i.e., functions which are easy to evaluate but hard to invert). These results have applications to secret voting, private querying of database, oblivious negotiation, playing mental poker, etc.. He also discusses the complexity question "How many bits need to be exchanged for the computation," and describes methods to prevent participants from cheating. Finally, he studies the question "What cannot be accomplished with one-way functions."