Completeness Theorems for Non-Cryptographic Fault-Tolerant Distributed Computation

Every function of n inputs can be efficiently computed by a complete network of n processors in such a way that: If no faults occur, no set of size t < n /2 of players gets any additional information (other than the function value), Even if Byzantine faults are allowed, no set of size t < n /3 can either disrupt the computation or get additional information. Furthermore, the above bounds on t are tight!