Abstract
In the setting of secure multiparty computation, a set of n parties with private inputs wish to jointly compute some functionality of their inputs. One of the most fundamental results of information-theoretically secure computation was presented by Ben-Or, Goldwasser and Wigderson (BGW) in 1988. They demonstrated that any n-party functionality can be computed with perfect security, in the private channels model. The most technically challenging part of this result is a protocol for multiplying two shared values, with perfect security in the presence of up to t < n/3 malicious adversaries.
In this paper we provide a full specification of the BGW perfect multiplication protocol and prove its security. This includes one new step for the perfect multiplication protocol in the case of n/4 ≤ t < n/3. As in the original BGW protocol, this protocol works whenever the parties hold univariate (Shamir) shares of the input values. In addition, we present a new multiplication protocol that utilizes bivariate secret sharing in order to achieve higher efficiency while maintaining a round complexity that is constant per multiplication. Both of our protocols are presented with full proofs of security.
Keywords
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
Download to read the full chapter text
Chapter PDF
References
Asharov, G., Lindell, Y., Rabin, T.: A Full Proof of the Perfectly-Secure BGW Protocol and Improvements. Cryptology ePrint Archive, 2011/136 (2011)
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)
Beerliová-Trubíniová, Z., Hirt, M.: Perfectly-Secure MPC with Linear Communication Complexity. In: Canetti, R. (ed.) TCC 2008. LNCS, vol. 4948, pp. 213–230. Springer, Heidelberg (2008)
Ben-Or, M., Goldwasser, S., Wigderson, A.: Completeness Theorems for Non-Cryptographic Fault-Tolerant Distributed Computation. In: 20th STOC, pp. 1–10 (1988)
Canetti, R.: Security and Composition of Multiparty Cryptographic Protocols. Journal of Cryptology 13(1), 143–202 (2000)
Canetti, R.: Universally Composable Security: A New Paradigm for Cryptographic Protocols. In: 42nd FOCS, pp. 136–145 (2001)
Canetti, R., Damgård, I., Dziembowski, S., Ishai, Y., Malkin, T.: Adaptive versus Non-Adaptive Security of Multi-Party Protocols. Journal of Cryptology 17(3), 153–207 (2004)
Cramer, R., Damgård, I., Maurer, U.M.: 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)
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)
Dodis, Y., Micali, S.: Parallel Reducibility for Information-Theoretically Secure Computation. In: Bellare, M. (ed.) CRYPTO 2000. LNCS, vol. 1880, pp. 74–92. Springer, Heidelberg (2000)
Goldreich, O.: Foundations of Cryptography: Volume 2 – Basic Applications. Cambridge University Press, Cambridge (2004)
Feldman, P.: Optimal Algorithms for Byzantine Agreement. PhD thesis, Massachusetts Institute of Technology (1988)
Feldman, P., Micali, S.: An Optimal Probabilistic Protocol for Synchronous Byzantine Agreement. SIAM - Journal on Computing 26(4), 873–933 (1997)
Gennaro, R., Rabin, M.O., Rabin, T.: Simplified VSS and Fact-Track Multiparty Computations with Applications to Threshold Cryptography. In: 17th PODC, pp. 101–111 (1998)
Hirt, M., Maurer, U.M., Przydatek, B.: Efficient Secure Multi-party Computation. In: Okamoto, T. (ed.) ASIACRYPT 2000. LNCS, vol. 1976, pp. 143–161. Springer, Heidelberg (2000)
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.: Robust Multiparty Computation with Linear Communication Complexity. In: Dwork, C. (ed.) CRYPTO 2006. LNCS, vol. 4117, pp. 463–482. Springer, Heidelberg (2006)
Kushilevitz, E., Lindell, Y., Rabin, T.: Information-Theoretically Secure Protocols and Security Under Composition. SIAM Journal on Computing 39(5), 2090–2112 (2010)
Shamir, A.: How to Share a Secret. Communications of the ACM 22(11), 612–613 (1979)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2011 International Association for Cryptologic Research
About this paper
Cite this paper
Asharov, G., Lindell, Y., Rabin, T. (2011). Perfectly-Secure Multiplication for Any t < n/3. In: Rogaway, P. (eds) Advances in Cryptology – CRYPTO 2011. CRYPTO 2011. Lecture Notes in Computer Science, vol 6841. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-22792-9_14
Download citation
DOI: https://doi.org/10.1007/978-3-642-22792-9_14
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-22791-2
Online ISBN: 978-3-642-22792-9
eBook Packages: Computer ScienceComputer Science (R0)