Unconditionally Secure Verifiable Secret Sharing Scheme

Abstract A (t, n) secret sharing scheme permits a secret to be divided into n shares in such a way that any t or more than t shares can reconstruct the secret, but fewer than t shares cannot reconstruct the secret. Verifiable secret sharing (VSS) has been proposed to allow each shareholder to verify the validity of his own share, but not other shareholders' shares. In this paper, we propose an efficient verifiable secret sharing scheme based on Shamir's (t, n) secret sharing scheme. Our proposed scheme can protect the secret and all shares unconditionally in the verification process. Our proposed solution can be used as an important cryptographic tool to design protocols for other related problems of secret sharing.

[1]  Douglas R. Stinson,et al.  Unconditionally Secure Proactive Secret Sharing Scheme with Combinatorial Structures , 1999, Selected Areas in Cryptography.

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

[3]  Xiao Zhu,et al.  Special Publicly Verifiable Secret Sharing Scheme for LEO Satellite Networks , 2011 .

[4]  Kun Peng,et al.  Efficient VSS free of computational assumption , 2011, J. Parallel Distributed Comput..

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

[6]  Torben P. Pedersen.  Non-Interactive and Information-Theoretic Secure Verifiable Secret Sharing , 1991, CRYPTO.

[7]  Douglas R. Stinson,et al.  On Unconditionally Secure Robust Distributed Key Distribution Centers , 2002, ASIACRYPT.

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

[9]  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).

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

[11]  Yang Yi,et al.  Publicly Verifiable Rational Secret Sharing , 2011 .

[12]  Paul Feldman,et al.  A practical scheme for non-interactive verifiable secret sharing , 1987, 28th Annual Symposium on Foundations of Computer Science (sfcs 1987).

[13]  C. Pandu Rangan,et al.  The Round Complexity of Verifiable Secret Sharing: The Statistical Case , 2010, ASIACRYPT.

[14]  Josh Benaloh,et al.  Secret Sharing Homomorphisms: Keeping Shares of A Secret Sharing , 1986, CRYPTO.

[15]  Jonathan Katz,et al.  Improving the round complexity of VSS in point-to-point networks , 2008, Inf. Comput..

[16]  Aniket Kate,et al.  Computational Verifiable Secret Sharing Revisited , 2011, ASIACRYPT.