Strong (n,t,n) verifiable secret sharing scheme
Information Sciences: an International Journal
Efficient statistical asynchronous verifiable secret sharing with optimal resilience
ICITS'09 Proceedings of the 4th international conference on Information theoretic security
Secure multiparty computation with minimal interaction
CRYPTO'10 Proceedings of the 30th annual conference on Advances in cryptology
Secure message transmission in asynchronous networks
Journal of Parallel and Distributed Computing
Communication optimal multi-valued asynchronous byzantine agreement with optimal resilience
ICITS'11 Proceedings of the 5th international conference on Information theoretic security
AFRICACRYPT'10 Proceedings of the Third international conference on Cryptology in Africa
Computational verifiable secret sharing revisited
ASIACRYPT'11 Proceedings of the 17th international conference on The Theory and Application of Cryptology and Information Security
Verifiable secret sharing in a total of three rounds
Information Processing Letters
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The round complexity of interactive protocols is one of their most important complexity measures. In this work we prove that existing lower bounds for the round complexity of VSS can be circumvented by introducing a negligible probability of error in the reconstruction phase. Previous results show matching lower and upper bounds of three rounds for VSS, with n = 3t + 1, where the reconstruction of the secrets always succeeds, i.e. with probability 1. In contrast we show that with a negligible probability of error in the reconstruction phase: 1 There exists an efficient 2-round VSS protocol for n = 3t + 1. If we assume that the adversary is non-rushing then we can achieve a 1-round reconstruction phase. 1 There exists an efficient 1-round VSS for t = 1 and n 3. 1 We prove that our results are optimal both in resilience and number of sharing rounds by showing: 1 There does not exist a 2-round WSS (and hence VSS) for n ≤ 3t. 1 There does not exist a 1-round VSS protocol for t 驴 2 and n 驴 4.