Improving the round complexity of VSS in point-to-point networks

We revisit the following question: what is the optimal round complexity of verifiable secret sharing (VSS)? We focus here on the case of perfect VSS where the number of corrupted parties t satisfies t

[1]  Tal Rabin,et al.  Verifiable secret sharing and multiparty protocols with honest majority , 1989, STOC '89.

[2]  Adi Shamir,et al.  How to share a secret , 1979, CACM.

[3]  G. R. BLAKLEY.  Safeguarding cryptographic keys , 1979, 1979 International Workshop on Managing Requirements Knowledge (MARK).

[4]  K. Srinathan,et al.  Round-Optimal and Efficient Verifiable Secret Sharing , 2006, TCC.

[5]  Avi Wigderson,et al.  Completeness theorems for non-cryptographic fault-tolerant distributed computation , 1988, STOC '88.

[6]  C. Pandu Rangan,et al.  The Round Complexity of Verifiable Secret Sharing Revisited , 2009, CRYPTO.

[7]  Jonathan Katz,et al.  On expected constant-round protocols for Byzantine agreement , 2006, J. Comput. Syst. Sci..

[8]  Yehuda Lindell,et al.  Sequential composition of protocols without simultaneous termination , 2002, PODC '02.

[9]  Moti Yung,et al.  Perfectly secure message transmission , 1993, JACM.

[10]  Robert Parry,et al.  National Computer Conference: 4-7 May 1981 McCormick Place, Chicago, USA , 1981, Microprocess. Microsystems.

[11]  Matthias Fitzi,et al.  Efficient player-optimal protocols for strong and differential consensus , 2003, PODC '03.

[12]  Yuval Ishai,et al.  The round complexity of verifiable secret sharing and secure multicast , 2001, STOC '01.

[13]  Ueli Maurer,et al.  General Secure Multi-party Computation from any Linear Secret-Sharing Scheme , 2000, EUROCRYPT.

[14]  Chiu Yuen Koo.  Studies on Fault-tolerant Broadcast and Secure Computation , 2007 .

[15]  Silvio Micali,et al.  An Optimal Probabilistic Protocol for Synchronous Byzantine Agreement , 1997, SIAM J. Comput..

[16]  Aggelos Kiayias,et al.  Advances in Cryptology - EUROCRYPT 2004 , 2004 .

[17]  Jonathan Katz,et al.  Round-Efficient Secure Computation in Point-to-Point Networks , 2007, EUROCRYPT.

[18]  Nancy A. Lynch,et al.  A Lower Bound for the Time to Assure Interactive Consistency , 1982, Inf. Process. Lett..

[19]  Michael Wiener,et al.  Advances in Cryptology — CRYPTO’ 99 , 1999 .

[20]  Baruch Awerbuch,et al.  Verifiable secret sharing and achieving simultaneity in the presence of faults , 1985, 26th Annual Symposium on Foundations of Computer Science (sfcs 1985).

[21]  Silvio Micali,et al.  Collective Coin Tossing Without Assumptions nor Broadcasting , 1990, CRYPTO.