Verifiable secret sharing and multiparty protocols with honest majority
STOC '89 Proceedings of the twenty-first annual ACM symposium on Theory of computing
Journal of the ACM (JACM)
Perfectly secure message transmission
Journal of the ACM (JACM)
Fast asynchronous Byzantine agreement with optimal resilience
STOC '93 Proceedings of the twenty-fifth annual ACM symposium on Theory of 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
The round complexity of verifiable secret sharing and secure multicast
STOC '01 Proceedings of the thirty-third annual ACM symposium on Theory of computing
Asynchronous verifiable secret sharing and proactive cryptosystems
Proceedings of the 9th ACM conference on Computer and communications security
Non-Interactive and Information-Theoretic Secure Verifiable Secret Sharing
CRYPTO '91 Proceedings of the 11th Annual International Cryptology Conference on Advances in Cryptology
Proactive Secret Sharing Or: How to Cope With Perpetual Leakage
CRYPTO '95 Proceedings of the 15th Annual International Cryptology Conference on Advances in Cryptology
Practical and Provably-Secure Commitment Schemes from Collision-Free Hashing
CRYPTO '96 Proceedings of the 16th Annual International Cryptology Conference on Advances in Cryptology
On Unconditionally Secure Robust Distributed Key Distribution Centers
ASIACRYPT '02 Proceedings of the 8th International Conference on the Theory and Application of Cryptology and Information Security: Advances in Cryptology
APSS: proactive secret sharing in asynchronous systems
ACM Transactions on Information and System Security (TISSEC)
Secure Distributed Key Generation for Discrete-Log Based Cryptosystems
Journal of Cryptology
Statistically-hiding commitment from any one-way function
Proceedings of the thirty-ninth 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
A practical scheme for non-interactive verifiable secret sharing
SFCS '87 Proceedings of the 28th 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
Simple and efficient asynchronous byzantine agreement with optimal resilience
Proceedings of the 28th ACM symposium on Principles of distributed computing
Distributed Key Generation for the Internet
ICDCS '09 Proceedings of the 2009 29th IEEE International Conference on Distributed Computing Systems
The Round Complexity of Verifiable Secret Sharing Revisited
CRYPTO '09 Proceedings of the 29th Annual International Cryptology Conference on Advances in Cryptology
A threshold cryptosystem without a trusted party
EUROCRYPT'91 Proceedings of the 10th annual international conference on Theory and application of cryptographic techniques
MPSS: Mobile Proactive Secret Sharing
ACM Transactions on Information and System Security (TISSEC)
Efficient statistical asynchronous verifiable secret sharing with optimal resilience
ICITS'09 Proceedings of the 4th international conference on Information theoretic security
Round-Optimal and efficient verifiable secret sharing
TCC'06 Proceedings of the Third conference on Theory of Cryptography
Asynchronous computational VSS with reduced communication complexity
CT-RSA'13 Proceedings of the 13th international conference on Topics in Cryptology
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Verifiable secret sharing (VSS) is an important primitive in distributed cryptography that allows a dealer to share a secret among n parties in the presence of an adversary controlling at most t of them. In the computational setting, the feasibility of VSS schemes based on commitments was established over two decades ago. Interestingly, all known computational VSS schemes rely on the homomorphic nature of these commitments or achieve weaker guarantees. As homomorphism is not inherent to commitments or to the computational setting in general, a closer look at its utility to VSS is called for. In this work, we demonstrate that homomorphism of commitments is not a necessity for computational VSS in the synchronous or in the asynchronous communication model. We present new VSS schemes based only on the definitional properties of commitments that are almost as good as the existing VSS schemes based on homomorphic commitments. Importantly, they have significantly lower communication complexities than their (statistical or perfect) unconditional counterparts. Further, in the synchronous communication model, we observe that a crucial interactive complexity measure of round complexity has never been formally studied for computational VSS. Interestingly, for the optimal resiliency conditions, the least possible round complexity in the known computational VSS schemes is identical to that in the (statistical or perfect) unconditional setting: three rounds. Considering the strength of the computational setting, this equivalence is certainly surprising. In this work, we show that three rounds are actually not mandatory for computational VSS. We present the first two-round VSS scheme for n≥2t+1 and lower-bound the result tightly by proving the impossibility of one-round computational VSS for t≥2 or n≤3t. We also include a new two-round VSS scheme using homomorphic commitments that has the same communication complexity as the well-known three-round Feldman and Pedersen VSS schemes.