STOC '87 Proceedings of the nineteenth annual ACM symposium on Theory of computing
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
Optimal algorithms for Byzantine agreement
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
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
Asynchronous secure computation
STOC '93 Proceedings of the twenty-fifth annual ACM symposium on Theory of computing
Robust sharing of secrets when the dealer is honest or cheating
Journal of the ACM (JACM)
Asynchronous secure computations with optimal resilience (extended abstract)
PODC '94 Proceedings of the thirteenth annual ACM symposium on Principles of distributed computing
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 Multiparty Protocols Using Circuit Randomization
CRYPTO '91 Proceedings of the 11th Annual International Cryptology Conference on Advances in Cryptology
Efficient Secure Multi-party Computation
ASIACRYPT '00 Proceedings of the 6th International Conference on the Theory and Application of Cryptology and Information Security: Advances in Cryptology
An asynchronous [(n - 1)/3]-resilient consensus protocol
PODC '84 Proceedings of the third annual ACM symposium on Principles of distributed 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
Proceedings of the twenty-seventh ACM symposium on Principles of distributed computing
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
The Round Complexity of Verifiable Secret Sharing Revisited
CRYPTO '09 Proceedings of the 29th Annual International Cryptology Conference on Advances in Cryptology
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
Simple and efficient perfectly-secure asynchronous MPC
ASIACRYPT'07 Proceedings of the Advances in Crypotology 13th international conference on Theory and application of cryptology and information security
Perfectly-secure MPC with linear communication complexity
TCC'08 Proceedings of the 5th conference on Theory of cryptography
On expected constant-round protocols for byzantine agreement
CRYPTO'06 Proceedings of the 26th annual international conference on Advances in Cryptology
Efficient multi-party computation with dispute control
TCC'06 Proceedings of the Third conference on Theory of Cryptography
Round-Optimal and efficient verifiable secret sharing
TCC'06 Proceedings of the Third conference on Theory of Cryptography
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
Computational verifiable secret sharing revisited
ASIACRYPT'11 Proceedings of the 17th international conference on The Theory and Application of Cryptology and Information Security
Brief announcement: efficient optimally resilient statistical AVSS and its applications
PODC '12 Proceedings of the 2012 ACM symposium on Principles of distributed computing
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We present a new statistical asynchronous verifiable secret sharing (AVSS) protocol with optimal resilience; i.e. with n = 3t + 1, where n is the total number of participating parties and t is the maximum number of parties that can be under the control of a computationally unbounded active adversary At. Our protocol privately communicates O((ln3 + n4κ)κ) bits and A-casts O(n3 log(n)) bits to simultaneously share l ≥ 1 elements from a finite field F, where κ is the error parameter. There are only two known statistical AVSS protocols with n = 3t+1, reported in [11] and [26]. The AVSS protocol of [11] requires a private communication of O(n9κ4) bits and A-cast of O(n9κ2 log(n)) bits to share a single element from F. Thus our AVSS protocol shows a significant improvement in communication complexity over the AVSS of [11]. The AVSS protocol of [26] requires a private communication of O((ln3+n4)κ) bits and A-cast of O((ln3 +n4)κ) bits to share l ≥ 1 elements. However, the shared element(s) may be NULL ∉ F. Thus our AVSS is better than the AVSS of [26] due to two reasons: (a) The A-cast communication of our AVSS is independent of the number of secrets i.e. l; (b) Our AVSS makes sure that the shared value(s) always belong to F. Using our AVSS, we design a new primitive called Asynchronous Complete Secret Sharing (ACSS) which is an essential building block of asynchronous multiparty computation (AMPC). Using our ACSS scheme, we can design a statistical AMPC with optimal resilience; i.e., with n = 3t + 1, that privately communicates O(n5κ) bits per multiplication gate. This will significantly improve the only known statistical AMPC of [8] with n = 3t + 1, which privately communicates Ω(n11κ4) bits and A-cast Ω(n11κ2 log(n)) bits per multiplication gate.