Abstract
Secure multi-party computation (MPC) allows a set of n players to securely compute an agreed function, even when up to t players are under the control of an adversary. Known perfectly secure MPC protocols require communication of at least Ω(n 3) field elements per multiplication, whereas cryptographic or unconditional security is possible with communication linear in the number of players. We present a perfectly secure MPC protocol communicating \(\mathcal{O}(n)\) field elements per multiplication. Our protocol provides perfect security against an active, adaptive adversary corrupting t < n/3 players, which is optimal. Thus our protocol improves the security of the most efficient information-theoretically secure protocol at no extra costs, respectively improves the efficiency of perfectly secure MPC protocols by a factor of Ω(n 2). To achieve this, we introduce a novel technique – constructing detectable protocols with the help of so-called hyper-invertible matrices, which we believe to be of independent interest. Hyper-invertible matrices allow (among other things) to perform efficient correctness checks of many instances in parallel, which was until now possible only if error-probability was allowed.
This work was partially supported by the Zurich Information Security Center. It represents the views of the authors.
Chapter PDF
Similar content being viewed by others
References
Beaver, D.: Efficient multiparty protocols using circuit randomization. In: Feigenbaum, J. (ed.) CRYPTO 1991. LNCS, vol. 576, pp. 420–432. Springer, Heidelberg (1992)
Beaver, D.: Secure multiparty protocols and zero-knowledge proof systems tolerating a faulty minority. Journal of Cryptology, 75–122 (1991)
Berman, P., Garay, J.A., Perry, K.J.: Bit optimal distributed consensus. In: Computer Science Research, Preliminary version has appeared in Proc. 21st STOC, pp. 313–322 (1992)
Ben-Or, M., Goldwasser, S., Wigderson, A.: Completeness theorems for non-cryptographic fault-tolerant distributed computation. In: Proc. 20th ACM Symposium on the Theory of Computing (STOC), pp. 1–10 (1988)
Beerliova-Trubiniova, 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)
Chaum, D., Crépeau, C., Damgård, I.: Multiparty unconditionally secure protocols (extended abstract). In: Proc. 20th ACM Symposium on the Theory of Computing (STOC), pp. 11–19 (1988)
Chaum, D., Damgård, I., van de Graaf, J.: Multiparty computations ensuring privacy of each party’s input and correctness of the result. In: Pomerance, C. (ed.) CRYPTO 1987. LNCS, vol. 293, pp. 87–119. Springer, Heidelberg (1988)
Coan, B.A., Welch, J.L.: Modular construction of a Byzantine agreement protocol with optimal message bit complexity. Information and Computation 97(1), 61–85 (1992); Preliminary version has appeared in Proc. 8th PODC (1989)
Damgård, I., Nielsen, J.B.: Robust multiparty computation with linear communication complexity. In: Menezes, A. (ed.) CRYPTO 2007. LNCS, vol. 4622, Springer, Heidelberg (2007)
Galil, Z., Haber, S., Yung, M.: Cryptographic computation: Secure fault-tolerant protocols and the public-key model. In: Pomerance, C. (ed.) CRYPTO 1987. LNCS, vol. 293, pp. 135–155. Springer, Heidelberg (1988)
Goldreich, O., Micali, S., Wigderson, A.: How to play any mental game — a completeness theorem for protocols with honest majority. In: Proc. 19th ACM Symposium on the Theory of Computing (STOC), pp. 218–229 (1987)
Hirt, M., Maurer, U., Przydatek, B.: Efficient secure multi-party computation. In: Okamoto, T. (ed.) ASIACRYPT 2000. LNCS, vol. 1976, pp. 143–161. Springer, Heidelberg (2000)
Hirt, M., Nielsen, J.B.: Robust multiparty computation with linear communication complexity. In: Dwork, C. (ed.) CRYPTO 2006. LNCS, vol. 4117, pp. 463–482. Springer, Heidelberg (2006)
Rabin, T., Ben-Or, M.: Verifiable secret sharing and multiparty protocols with honest majority. In: Proc. 21st ACM Symposium on the Theory of Computing (STOC), pp. 73–85 (1989)
Shamir, A.: How to share a secret. Communications of the ACM 22, 612–613 (1979)
Yao, A.C.: Protocols for secure computations. In: Proc. 23rd IEEE Symposium on the Foundations of Computer Science (FOCS), pp. 160–164. IEEE, Los Alamitos (1982)
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 2008 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Beerliová-Trubíniová, Z., Hirt, M. (2008). Perfectly-Secure MPC with Linear Communication Complexity. In: Canetti, R. (eds) Theory of Cryptography. TCC 2008. Lecture Notes in Computer Science, vol 4948. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-78524-8_13
Download citation
DOI: https://doi.org/10.1007/978-3-540-78524-8_13
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-78523-1
Online ISBN: 978-3-540-78524-8
eBook Packages: Computer ScienceComputer Science (R0)