Abstract
We improve on the classical results in information-theoreti- cally secure multiparty computation among a set of n participants, by considering the special case of the computation of the addition function over binary inputs in the secure channels model with a simultaneous broadcast channel. This simple function is a useful building block for other applications. The classical results in multiparty computation show that in this model, every function can be computed with information-theoretic security if and only if less than n/2 participants are corrupt. In this article we show that, under certain conditions, this bound can be overcome.
More precisely, let t (p), t (r) and t (c) be the privacy, robustness and correctness thresholds; that is, the minimum number of participants that must be actively corrupted in order for privacy, robustness or correctness, respectively, to be compromised. We show a series of novel tradeoffs applicable to the multiparty computation of f(x 1, …,x n ) = x 1 + … + x n for x i ∈ {0,1}, culminating in the most general tradeoff: t (p) + t (r) = n + 1 and t (c) + t (r) = n + 1. These tradeoffs are applicable as long as t (r) < n/2, which implies that, at the cost of reducing robustness, privacy and correctness are achievable despite a dishonest majority (as an example, setting the robustness threshold to n/3 yields privacy and correctness thresholds of 2n/3 + 1).
We give applications to information-theoretically secure voting and anonymous message transmission, yielding protocols with the same tradeoffs.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Similar content being viewed by others
References
Yao, A.C.: Protocols for secure computations. In: Proceedings of the 23rd Annual Symposium on the Foundations of Computer Science (FOCS 1982), pp. 160–164. IEEE (1982)
Chaum, D., Crépeau, C., Damgård, I.: Multiparty unconditionally secure protocols. In: Simon, J. (ed.) Proceedings of the 20th annual ACM Symposium on Theory of Computing (STOC 1988), pp. 11–19. ACM (1988)
Ben-Or, M., Goldwasser, S., Wigderson, A.: Completeness theorems for non-cryptographic fault-tolerant distributed computation. In: Simon, J. (ed.) Proceedings of the 20th Annual ACM Symposium on Theory of Computing (STOC 1988), pp. 1–10. ACM (1988)
Rabin, T., Ben-Or, M.: Verifiable secret sharing and multiparty protocols with honest majority. In: Johnson, D.S. (ed.) Proceedings of the 21st Annual ACM Symposium on Theory of Computing (STOC 1989), pp. 73–85. ACM (1989)
Broadbent, A., Tapp, A.: Information-Theoretic Security Without an Honest Majority. In: Kurosawa, K. (ed.) ASIACRYPT 2007. LNCS, vol. 4833, pp. 410–426. Springer, Heidelberg (2007)
Broadbent, A., Tapp, A.: Information-theoretically secure voting without an honest majority. In: Proceedings of the IAVoSS Workshop On Trustworthy Elections, WOTE 2008 (2008), Cryptology ePrint Archive: Report 2008/266
Fitzi, M., Hirt, M., Holenstein, T., Wullschleger, J.: Two-Threshold Broadcast and Detectable Multi-party Computation. In: Biham, E. (ed.) EUROCRYPT 2003. LNCS, vol. 2656, pp. 51–67. Springer, Heidelberg (2003)
Fitzi, M., Hirt, M., Maurer, U.: Trading Correctness for Privacy in Unconditional Multi-party Computation. In: Krawczyk, H. (ed.) CRYPTO 1998. LNCS, vol. 1462, pp. 121–136. Springer, Heidelberg (1998)
Lucas, C., Raub, D., Maurer, U.: Hybrid-secure MPC: Trading information-theoretic robustness for computational privacy. In: Proceedings of the 29th Annual ACM SIGACT-SIGOPS Symposium on Principles of Distributed Computing (PODC 2010), pp. 219–228. ACM (2010)
Ishai, Y., Kushilevitz, E., Lindell, Y., Petrank, E.: On Combining Privacy with Guaranteed Output Delivery in Secure Multiparty Computation. In: Dwork, C. (ed.) CRYPTO 2006. LNCS, vol. 4117, pp. 483–500. Springer, Heidelberg (2006)
Fitzi, M., Gottesman, D., Hirt, M., Holenstein, T., Smith, A.: Detectable Byzantine agreement secure against faulty majorities. In: Proceedings of the 21st Annual Symposium on Principles of Distributed Computing (PODC 2002), pp. 118–126. ACM (2002)
Shamir, A.: How to share a secret. Communications of the ACM 22, 612–613 (1979)
Cramer, R., Damgård, I., Maurer, U.: General Secure Multi-party Computation from any Linear Secret-Sharing Scheme. In: Preneel, B. (ed.) EUROCRYPT 2000. LNCS, vol. 1807, pp. 316–334. Springer, Heidelberg (2000)
Cramer, R., Damgård, I., Dziembowski, S., Hirt, M., Rabin, T.: Efficient Multiparty Computations Secure against an Adaptive Adversary. In: Stern, J. (ed.) EUROCRYPT 1999. LNCS, vol. 1592, pp. 311–326. Springer, Heidelberg (1999)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2012 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Broadbent, A., Jeffery, S., Ranellucci, S., Tapp, A. (2012). Trading Robustness for Correctness and Privacy in Certain Multiparty Computations, beyond an Honest Majority. In: Smith, A. (eds) Information Theoretic Security. ICITS 2012. Lecture Notes in Computer Science, vol 7412. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-32284-6_2
Download citation
DOI: https://doi.org/10.1007/978-3-642-32284-6_2
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-32283-9
Online ISBN: 978-3-642-32284-6
eBook Packages: Computer ScienceComputer Science (R0)