A Full Proof of the BGW Protocol for Perfectly Secure Multiparty Computation

In the setting of secure multiparty computation, a set of n parties with private inputs wish to jointly compute some functionality of their inputs. One of the most fundamental results of secure computation was presented by Ben-Or, Goldwasser, and Wigderson (BGW) in 1988. They demonstrated that any n-party functionality can be computed with perfect security, in the private channels model. When the adversary is semi-honest, this holds as long as t< n/ 2 parties are corrupted, and when the adversary is malicious, this holds as long as t< n/ 3 parties are corrupted. Unfortunately, a full proof of these results was never published. In this paper, we remedy this situation and provide a full proof of security of the BGW protocol. This includes a full description of the protocol for the malicious setting, including the construction of a new subprotocol for the perfect multiplication protocol that seems necessary for the case of n/ 4 ≤ t< n/ 3.