FAULT-TOLERANT COMPUTATION IN THE FULL INFORMATION MODEL

We initiate an investigation of general fault-tolerant distributed com putation in the full-information model. In the full information model no restrictions are made on the computational power of the faulty part ies or the information available to them. (Namely, the faulty players may be infinitely powerful and there are no private channels connectin g pairs of honest players). Previous work in this model has concentrat ed on the particular problem of simulating a single bounded-bias globa l coin ip (e.g., Ben-Or and Linial [Randomness and Computation, S. Mic ali, ed., JAI Press, Greenwich, CT, 1989, pp. 91-115] and Alon and Nao r [SIAM J. Comput., 22 (1993), pp. 403-417]). We widen the scope of in vestigation to the general question of how well arbitrary fault-tolera nt computations can be performed in this model. The results we obtain should be considered as first steps in this direction. We present effi cient two-party protocols for fault-tolerant computation of any bivari ate function. We prove that the advantage of a dishonest player in the se protocols is the minimum one possible (up to polylogarithmic factor s). We also present efficient m-party fault-tolerant protocols for sam pling a general distribution (m greater than or equal to 2). Such an a lgorithm seems an important building block towards the design of effic ient multiparty protocols for fault-tolerant computation of multivaria te functions.