Completeness theorems for non-cryptographic fault-tolerant distributed computation
STOC '88 Proceedings of the twentieth annual ACM symposium on Theory of computing
Multiparty unconditionally secure protocols
STOC '88 Proceedings of the twentieth annual ACM symposium on Theory of computing
PODC '97 Proceedings of the sixteenth annual ACM symposium on Principles of distributed computing
Communications of the ACM
The round complexity of verifiable secret sharing and secure multicast
STOC '01 Proceedings of the thirty-third annual ACM symposium on Theory of computing
Efficient Byzantine Agreement Secure Against General Adversaries
DISC '98 Proceedings of the 12th International Symposium on Distributed Computing
Trading Correctness for Privacy in Unconditional Multi-Party Computation (Extended Abstract)
CRYPTO '98 Proceedings of the 18th Annual International Cryptology Conference on Advances in Cryptology
General Adversaries in Unconditional Multi-party Computation
ASIACRYPT '99 Proceedings of the International Conference on the Theory and Applications of Cryptology and Information Security: Advances in Cryptology
Verifiable secret sharing and achieving simultaneity in the presence of faults
SFCS '85 Proceedings of the 26th Annual Symposium on Foundations of Computer Science
Towards optimal distributed consensus
SFCS '89 Proceedings of the 30th Annual Symposium on Foundations of Computer Science
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
INDOCRYPT '02 Proceedings of the Third International Conference on Cryptology: Progress in Cryptology
On Unconditionally Secure Distributed Oblivious Transfer
INDOCRYPT '02 Proceedings of the Third International Conference on Cryptology: Progress in Cryptology
Secure multi-party computation made simple
Discrete Applied Mathematics - Special issue: Coding and cryptography
Secure multi-party computation made simple
Discrete Applied Mathematics - Special issue: Coding and cryptography
Secure multi-party computation made simple
SCN'02 Proceedings of the 3rd international conference on Security in communication networks
Cryptography and Communications
On a relation between verifiable secret sharing schemes and a class of error-correcting codes
WCC'05 Proceedings of the 2005 international conference on Coding and Cryptography
Finding lower bounds on the complexity of secret sharing schemes by linear programming
LATIN'10 Proceedings of the 9th Latin American conference on Theoretical Informatics
Identifying cheaters without an honest majority
TCC'12 Proceedings of the 9th international conference on Theory of Cryptography
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We present a general treatment of all non-cryptographic (i.e., information-theoretically secure) linear verifiable-secret-sharing (VSS) and distributed-commitment (DC) schemes, based on an underlying secret sharing scheme, pairwise checks between players, complaints, and accusations of the dealer. VSS and DC are main building blocks for unconditional secure multi-party computation protocols. This general approach covers all known linear VSS and DC schemes. The main theorem states that the security of a scheme is equivalent to a pure linear-algebra condition on the linear mappings (e.g. described as matrices and vectors) describing the scheme. The security of all known schemes follows as corollaries whose proofs are pure linear-algebra arguments, in contrast to some hybrid arguments used in the literature. Our approach is demonstrated for the CDM DC scheme, which we generalize to be secure against mixed adversary settings (some curious and some dishonest players), and for the classical BGW VSS scheme, for which we show that some of the checks between players are superfluous, i.e., the scheme is not optimal. More generally, our approach, establishing the minimal conditions for security (and hence the common denominator of the known schemes), can lead to the design of more efficient VSS and DC schemes for general adversary structures.