Abstract
We consider perfect verifiable secret sharing (VSS) in a synchronous network of n processors (players) where a designated player called the dealer wishes to distribute a secret s among the players in a way that no t of them obtain any information, but any t + 1 players obtain full information about the secret. The round complexity of a VSS protocol is defined as the number of rounds performed in the sharing phase. Gennaro, Ishai, Kushilevitz and Rabin showed that three rounds are necessary and sufficient when n > 3t. Sufficiency, however, was only demonstrated by means of an inefficient (i.e., exponential-time) protocol, and the construction of an efficient three-round protocol was left as an open problem.
In this paper, we present an efficient three-round protocol for VSS. The solution is based on a three-round solution of so-called weak verifiable secret sharing (WSS), for which we also prove that three rounds is a lower bound. Furthermore, we also demonstrate that one round is sufficient for WSS when n > 4t, and that VSS can be achieved in 1 + ε amortized rounds (for any ε > 0 ) when n>3t.
The original version of this chapter was revised: The copyright line was incorrect. This has been corrected. The Erratum to this chapter is available at DOI: 10.1007/978-3-540-32732-5_32
Chapter PDF
Similar content being viewed by others
References
Ben-Or, M., Goldwasser, S., Wigderson, A.: Completeness theorems for noncryptographic fault-tolerant distributed computation. In: Proceedings of the 20th Annual ACM Symposium on Theory of Computing (STOC 1988), pp. 1–10 (1988)
Blakley, G.R.: Safeguarding cryptographic keys. In: 1979 National Computer Conference. AFIPS Conference proceedings, vol. 48, pp. 313–317. AFIPS Press (1979)
Chaum, D., Crépeau, C., Damgård, I.: Multiparty unconditionally secure protocols (extended abstract). In: Proceedings of the 20th Annual ACM Symposium on Theory of Computing (STOC 1988), pp. 11–19. ACM Press, New York (1988)
Chor, B., Goldwasser, S., Micali, S., Awerbuch, B.: Verifiable secret sharing and achieving simultaneity in the presence of faults. In: Proceedings of the 26thAnnual IEEE Symposium on Foundations of Computer Science (FOCS 1985), pp. 383–395 (1985)
Gennaro, R., Ishai, Y., Kushilevitz, E., Rabin, T.: The round complexity of verifiable secret sharing and secure multicast. In: Proceedings of the 33rd Annual ACM Symposium on Theory of Computing (STOC 2001), pp. 580–589 (2001)
Gennaro, R., Rabin, M.O., Rabin, T.: Simplified VSS and fast-track multiparty computations with applications to threshold cryptography. In: Proceedings of the 17th ACM Symposium on Principles of Distributed Computing (PODC 1998), pp. 101–111 (1998)
Goldreich, O.: Secure multi-party computation, final (incomplete) draft, version 1.4 (October 2002)
Rabin, T., Ben-Or, M.: Verifiable secret sharing and multiparty protocols with honest majority. In: Proceedings of the 21st Annual ACM Symposium on Theory of Computing (STOC 1989), pp. 73–85 (1989)
Shamir, A.: How to share a secret. Commun. ACM 22, 612–613 (1979)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2006 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Fitzi, M., Garay, J., Gollakota, S., Rangan, C.P., Srinathan, K. (2006). Round-Optimal and Efficient Verifiable Secret Sharing. In: Halevi, S., Rabin, T. (eds) Theory of Cryptography. TCC 2006. Lecture Notes in Computer Science, vol 3876. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11681878_17
Download citation
DOI: https://doi.org/10.1007/11681878_17
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-32731-8
Online ISBN: 978-3-540-32732-5
eBook Packages: Computer ScienceComputer Science (R0)