Completeness theorems for non-cryptographic fault-tolerant distributed computation
STOC '88 Proceedings of the twentieth annual ACM symposium on Theory of computing
An Optimal Probabilistic Protocol for Synchronous Byzantine Agreement
SIAM Journal on Computing
Simplified VSS and fast-track multiparty computations with applications to threshold cryptography
PODC '98 Proceedings of the seventeenth annual ACM symposium on Principles of distributed computing
Communications of the ACM
Parallel Reducibility for Information-Theoretically Secure Computation
CRYPTO '00 Proceedings of the 20th Annual International Cryptology Conference on Advances in Cryptology
Robustness for Free in Unconditional Multi-party Computation
CRYPTO '01 Proceedings of the 21st Annual International Cryptology Conference on Advances in Cryptology
Efficient Secure Multi-party Computation
ASIACRYPT '00 Proceedings of the 6th International Conference on the Theory and Application of Cryptology and Information Security: Advances in Cryptology
Universally Composable Security: A New Paradigm for Cryptographic Protocols
FOCS '01 Proceedings of the 42nd IEEE symposium on Foundations of Computer Science
Foundations of Cryptography: Volume 2, Basic Applications
Foundations of Cryptography: Volume 2, Basic Applications
Adaptive versus Non-Adaptive Security of Multi-Party Protocols
Journal of Cryptology
General secure multi-party computation from any linear secret-sharing scheme
EUROCRYPT'00 Proceedings of the 19th international conference on Theory and application of cryptographic techniques
Scalable and unconditionally secure multiparty computation
CRYPTO'07 Proceedings of the 27th annual international cryptology conference on Advances in cryptology
Perfectly-secure MPC with linear communication complexity
TCC'08 Proceedings of the 5th conference on Theory of cryptography
Information-Theoretically Secure Protocols and Security under Composition
SIAM Journal on Computing
Robust multiparty computation with linear communication complexity
CRYPTO'06 Proceedings of the 26th annual international conference on Advances in Cryptology
Efficient multi-party computation with dispute control
TCC'06 Proceedings of the Third conference on Theory of Cryptography
Universally composable synchronous computation
TCC'13 Proceedings of the 10th theory of cryptography conference on Theory of Cryptography
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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 perfect security, in the private channels model. The most technically challenging part of this result is a protocol for multiplying two shared values, with perfect security in the presence of up to t n/3 malicious adversaries. In this paper we provide a full specification of the BGW perfect multiplication protocol and prove its security. This includes one new step for the perfect multiplication protocol in the case of n/4 ≤ t n/3. As in the original BGW protocol, this protocol works whenever the parties hold univariate (Shamir) shares of the input values. In addition, we present a new multiplication protocol that utilizes bivariate secret sharing in order to achieve higher efficiency while maintaining a round complexity that is constant per multiplication. Both of our protocols are presented with full proofs of security.