Fault-tolerant computation in the full information model

Efficient two-party protocols for fault-tolerant computation of any two-argument function are presented. It is proved that the influence of a dishonest player in these protocols is the minimum one possible (up to polylogarithmic factors). Also presented are efficient m-party fault-tolerant protocols for sampling a general distribution (m⩾2). Efficient m-party protocols for computation of any m-argument function are given, and it is proved for these protocols that for most functions, the influence of any t dishonest players on the outcome of the protocol is the minimum one possible (up to polylogarithmic factors)