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 information-theoretically secure computation was presented by Ben-Or, Goldwasser and Wigderson (BGW) in 1988. They demonstrated that any $n$-party functionality can be computed with \emph{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 detailed proof of these results was never provided; in addition, a full specification of the protocol in the malicious setting has also never been published. In this paper, we remedy this situation and provide a full specification of the BGW protocol and a full proof of its security. We also derive corollaries for security in the presence of adaptive adversaries and under concurrent general composition (equivalently, universal composability).

This version corrects a small error in the proofs of Theorems 4.2 and 7.2.

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 information-theoretically secure computation was presented by Ben-Or, Goldwasser and Wigderson (BGW) in 1988. They demonstrated that any $n$-party functionality can be computed with \emph{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 detailed proof of these results was never provided; in addition, a full specification of the protocol in the malicious setting has also never been published. In this paper, we remedy this situation and provide a full specification of the BGW protocol and a full proof of its security. We also derive corollaries for security in the presence of adaptive adversaries and under concurrent general composition (equivalently, universal composability).

Final version of paper, accept to the Journal of Cryptology.

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 information-theoretically secure computation was presented by Ben-Or, Goldwasser and Wigderson (BGW) in 1988. They demonstrated that any $n$-party functionality can be computed with \emph{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 detailed proof of these results was never provided; in addition, a full specification of the protocol in the malicious setting has also never been published. In this paper, we remedy this situation and provide a full specification of the BGW protocol and a full proof of its security. We also derive corollaries for security in the presence of adaptive adversaries and under concurrent general composition (equivalently, universal composability).

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 information-theoretically secure computation was presented by Ben-Or, Goldwasser and Wigderson (BGW) in 1988. They demonstrated that any $n$-party functionality can be computed with \emph{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 detailed proof of these results was never given. In this paper, we remedy this situation and provide a full proof of security of the BGW protocol. We also derive corollaries for security in the presence of adaptive adversaries and under concurrent general composition (equivalently, universal composability). In addition, we give a full specification of the protocol for the malicious setting. This includes one new step for the perfect multiplication protocol in the case of $n/4\leq t<n/3$.

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 information-theoretically secure computation was presented by Ben-Or, Goldwasser and Wigderson (BGW) in 1988. They demonstrated that any $n$-party functionality can be computed with \emph{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 detailed proof of these results was never provided; in addition, a full specification of the protocol in the malicious setting has also never been published. In this paper, we remedy this situation and provide a full specification of the BGW protocol and a full proof of its security. We also derive corollaries for security in the presence of adaptive adversaries and under concurrent general composition (equivalently, universal composability).

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 information-theoretically secure computation was presented by Ben-Or, Goldwasser and Wigderson (BGW) in 1988. They demonstrated that any $n$-party functionality can be computed with \emph{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 detailed proof of these results was never provided; in addition, a full specification of the protocol in the malicious setting has also never been published. In this paper, we remedy this situation and provide a full specification of the BGW protocol and a full proof of its security. We also derive corollaries for security in the presence of adaptive adversaries and under concurrent general composition (equivalently, universal composability).