Authentication theory/coding theory
Proceedings of CRYPTO 84 on Advances in cryptology
Principles and practice of information theory
Principles and practice of information theory
Completeness theorems for non-cryptographic fault-tolerant distributed computation
STOC '88 Proceedings of the twentieth annual ACM symposium on Theory of computing
Verifiable secret sharing and multiparty protocols with honest majority
STOC '89 Proceedings of the twenty-first annual ACM symposium on Theory of computing
PODC '97 Proceedings of the sixteenth annual ACM symposium on Principles of distributed 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
Cryptography: Theory and Practice
Cryptography: Theory and Practice
Efficient Multiparty Protocols Using Circuit Randomization
CRYPTO '91 Proceedings of the 11th Annual International Cryptology Conference on 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
Efficient multiparty computations secure against an adaptive adversary
EUROCRYPT'99 Proceedings of the 17th international conference on Theory and application of cryptographic techniques
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
Authentication theory and hypothesis testing
IEEE Transactions on Information Theory
Secure Computation from Random Error Correcting Codes
EUROCRYPT '07 Proceedings of the 26th annual international conference on Advances in Cryptology
Almost optimum t-cheater identifiable secret sharing schemes
EUROCRYPT'11 Proceedings of the 30th Annual international conference on Theory and applications of cryptographic techniques: advances in cryptology
Approximate quantum error-correcting codes and secret sharing schemes
EUROCRYPT'05 Proceedings of the 24th annual international conference on Theory and Applications of Cryptographic Techniques
On combining privacy with guaranteed output delivery in secure multiparty computation
CRYPTO'06 Proceedings of the 26th annual international conference on Advances in Cryptology
Unconditionally-Secure robust secret sharing with compact shares
EUROCRYPT'12 Proceedings of the 31st Annual international conference on Theory and Applications of Cryptographic Techniques
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Consider a scenario where an l-bit secret has been distributed among n players by an honest dealer using some secret sharing scheme. Then, if all players behave honestly, the secret can be reconstructed in one round with zero error probability, and by broadcasting nl bits. We ask the following question: how close to this ideal can we get if up to t players (but not the dealer) are corrupted by an adaptive, active adversary with unbounded computing power? - and where in addition we of course require that the adversary does not learn the secret ahead of reconstruction time. It is easy to see that t = ⌊(n - 1/2⌋ is the maximal value of t that can be tolerated, and furthermore, we show that the best we can hope for is a one-round reconstruction protocol where every honest player outputs the correct secret or "failure". For any such protocol with failure probability at most 2-Ω(k), we show a lower bound of Ω(nl + kn2) bits on the information communicated. We further show that this is tight up to a constant factor. The lower bound trivially applies as well to VSS schemes, where also the dealer may be corrupt. Using generic methods, the scheme establishing the upper bound can be turned into a VSS with efficient reconstruction. However, the distribution phase becomes very inefficient. Closing this gap, we present a new VSS protocol where the distribution complexity matches that of the previously best known VSS, but where the reconstruction phase meets our lower bound up to a constant factor. The reconstruction is a factor of n better than previous VSS protocols.We show an application of this to multi-party computation with pre-processing, improving the complexity of earlier similar protocols by a factor of n.