Completeness theorems for non-cryptographic fault-tolerant distributed computation
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
Verifiable secret sharing and achieving simultaneity in the presence of faults
SFCS '85 Proceedings of the 26th Annual Symposium on Foundations of Computer Science
Improving the Round Complexity of VSS in Point-to-Point Networks
ICALP '08 Proceedings of the 35th international colloquium on Automata, Languages and Programming, Part II
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
Secure multi-party computation made simple
SCN'02 Proceedings of the 3rd international conference on Security in communication networks
Round-Optimal and efficient verifiable secret sharing
TCC'06 Proceedings of the Third conference on Theory of Cryptography
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The round complexity of verifiable secret sharing (VSS) schemes has been studied extensively for threshold adversaries. In particular, Fitzi et al. showed an efficient 3-round VSS for n ≥ 3t + 1 [4], where an infinitely powerful adversary can corrupt t (or less) parties out of n parties. This paper shows that for non-threshold adversaries: 1. Two round perfectly secure VSS is possible if and only if the underlying adversary structure satisfies the Q4 condition; 2. Three round perfectly secure VSS is possible if and only if the underlying adversary structure satisfies the Q3 condition. Further as a special case of our three round protocol, we can obtain a more efficient 3-round VSS than the VSS of Fitzi et al. for n = 3t + 1. More precisely, the communication complexity of the reconstruction phase is reduced from O(n3) to O(n2). We finally point out a flaw in the reconstruction phase of the VSS of Fitzi et al., and show how to fix it.