Abstract
We describe an asynchronous algorithm to solve secure multiparty computation (MPC) over n players, when strictly less than a \({1}\over{8}\) fraction of the players are controlled by a static adversary. For any function f over a field that can be computed by a circuit with m gates, our algorithm requires each player to send a number of field elements and perform an amount of computation that is \(\tilde{O}(\frac{m}{n} + \sqrt n)\). This significantly improves over traditional algorithms, which require each player to both send a number of messages and perform computation that is Ω(nm).
Additionaly, we define the threshold counting problem and present a distributed algorithm to solve it in the asynchronous communication model. Our algorithm is load balanced, with computation, communication and latency complexity of O(logn), and may be of independent interest to other applications with a load balancing goal in mind.
Full version of this paper is available at http://cs.unm.edu/~movahedi/mpc.pdf .
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Ajtai, M., Komlós, J., Szemerédi, E.: An 0(n log n) sorting network. In: Proceedings of STOC 1983, pp. 1–9. ACM, New York (1983)
Aspnes, J., Herlihy, M., Shavit, N.: Counting networks and multi-processor coordination. In: Proceedings of STOC 1991, pp. 348–358. ACM (1991)
Attiya, H., Welch, J.: Distributed Computing: Fundamentals, Simulations and Advanced Topics, 2nd edn., p. 14. John Wiley Interscience (March 2004)
Beerliová-Trubíniová, Z., Hirt, M.: Efficient multi-party computation with dispute control. In: Halevi, S., Rabin, T. (eds.) TCC 2006. LNCS, vol. 3876, pp. 305–328. Springer, Heidelberg (2006)
Ben-Or, M., Canetti, R., Goldreich, O.: Asynchronous secure computation. In: Proceedings of STOC 1993 (1993)
Ben-Or, M., Goldwasser, S., Wigderson, A.: Completeness theorems for non-cryptographic fault-tolerant distributed computing. In: Proceedings of STOC 1988, pp. 1–10 (1988)
Bogetoft, P., et al.: Secure multiparty computation goes live. In: Dingledine, R., Golle, P. (eds.) FC 2009. LNCS, vol. 5628, pp. 325–343. Springer, Heidelberg (2009)
Boyle, E., Goldwasser, S., Tessaro, S.: Communication locality in secure multi-party computation: how to run sublinear algorithms in a distributed setting. In: Sahai, A. (ed.) TCC 2013. LNCS, vol. 7785, pp. 356–376. Springer, Heidelberg (2013)
Canetti, R., Rabin, T.: Fast asynchronous byzantine agreement with optimal resilience. In: Proceeding of STOC 1993, pp. 42–51 (1993)
Chaum, D., Crépeau, C., Damgård, I.: Multiparty unconditionally secure protocols. In: Proceedings of STOC 1988, pp. 11–19 (1988)
Chor, B., Dwork, C.: Randomization in Byzantine agreement. Advances in Computing Research 5, 443–498 (1989)
Damgård, I., Ishai, Y.: Scalable secure multiparty computation. In: Dwork, C. (ed.) CRYPTO 2006. LNCS, vol. 4117, pp. 501–520. Springer, Heidelberg (2006)
Damgård, I., Ishai, Y., Krøigaard, M., Nielsen, J.B., Smith, A.: Scalable multiparty computation with nearly optimal work and resilience. In: Wagner, D. (ed.) CRYPTO 2008. LNCS, vol. 5157, pp. 241–261. Springer, Heidelberg (2008)
Damgård, I., Nielsen, J.B.: Scalable and unconditionally secure multiparty computation. In: Menezes, A. (ed.) CRYPTO 2007. LNCS, vol. 4622, pp. 572–590. Springer, Heidelberg (2007)
Dani, V., King, V., Movahedi, M., Saia, J.: Breaking the o(nm) bit barrier: Secure multiparty computation with a static adversary. In: Proceedings of PODC 2012 (2012)
Dani, V., King, V., Movahedi, M., Saia, J.: Quorums quicken queries: Efficient asynchronous secure multiparty computation. Manuscript (2013)
Du, W., Atallah, M.: Secure multi-party computation problems and their applications: a review and open problems. In: Proceedings of the 2001 Workshop on New Security Paradigms, pp. 13–22. ACM (2001)
Frikken, K.: Secure multiparty computation. In: Algorithms and Theory of Computation Handbook, p. 14. Chapman & Hall/CRC (2010)
Goldreich, O.: Secure multi-party computation. Manuscript (1998)
Goldreich, O., Micali, S., Wigderson, A.: How to play any mental game. In: Proceedings of STOC 1987, pp. 218–229. ACM (1987)
Hirt, M., Maurer, U.: Robustness for free in unconditional multi-party computation. In: Kilian, J. (ed.) CRYPTO 2001. LNCS, vol. 2139, pp. 101–118. Springer, Heidelberg (2001)
Hirt, M., Nielsen, J.B.: Upper bounds on the communication complexity of optimally resilient cryptographic multiparty computation. In: Roy, B. (ed.) ASIACRYPT 2005. LNCS, vol. 3788, pp. 79–99. Springer, Heidelberg (2005)
King, V., Lonargan, S., Saia, J., Trehan, A.: Load balanced scalable byzantine agreement through quorum building, with full information. In: Aguilera, M.K., Yu, H., Vaidya, N.H., Srinivasan, V., Choudhury, R.R. (eds.) ICDCN 2011. LNCS, vol. 6522, pp. 203–214. Springer, Heidelberg (2011)
Klugerman, M., Plaxton, C.G.: Small-depth counting networks. In: Proceedings of STOC 1992, pp. 417–428 (1992)
Klugerman, M.R.: Small-depth counting networks and related topics (1994)
Rabin, T., Ben-Or, M.: Verifiable secret sharing and multiparty protocols with honest majority. In: Proceedings of STOC 1989, pp. 73–85. ACM (1989)
Yao, A.: Protocols for secure computations. In: Proceedings of FOCS 1982, pp. 160–164 (1982)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2014 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Dani, V., King, V., Movahedi, M., Saia, J. (2014). Quorums Quicken Queries: Efficient Asynchronous Secure Multiparty Computation. In: Chatterjee, M., Cao, Jn., Kothapalli, K., Rajsbaum, S. (eds) Distributed Computing and Networking. ICDCN 2014. Lecture Notes in Computer Science, vol 8314. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-45249-9_16
Download citation
DOI: https://doi.org/10.1007/978-3-642-45249-9_16
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-45248-2
Online ISBN: 978-3-642-45249-9
eBook Packages: Computer ScienceComputer Science (R0)