Fault-tolerant computation in the full information model

We initiate an investigation of general fault-tolerant distributed computation in the full-information model. In the full information model no restrictions are made on the computational power of the faulty parties or the information available to them. (Namely, the faulty players may be infinitely powerful and there are no private channels connecting pairs of honest players). Previous work in this model has concentrated on the particular problem of simulating a single bounded-bias global coin flip (e.g., Ben-Or and Linial [Randomness and Computation, S. Micali, ed., JAI Press, Greenwich, CT, 1989, pp. 91-115] and Alon and Naor [SIAM J. Comput., 22 (1993), pp. 403-417]). We widen the scope of investigation to the general question of how well arbitrary fault-tolerant computations can be performed in this model. The results we obtain should be considered as first steps in this direction. We present efficient two-party protocols for fault-tolerant computation of any bivariate function. We prove that the advantage of a dishonest player in these protocols is the minimum one possible (up to polylogarithmic factors). We also present efficient m-party fault-tolerant protocols for sampling a general distribution (m ≥ 2). Such an algorithm seems an important building block towards the design of efficient multiparty protocols for fault-tolerant computation of multivariate functions.