Abstract
Most previous work on unconditionally secure multiparty computation has focused on computing over a finite field (or ring). Multiparty computation over other algebraic structures has not received much attention, but is an interesting topic whose study may provide new and improved tools for certain applications. At CRYPTO 2007, Desmedt et al introduced a construction for a passive-secure multiparty multiplication protocol for black-box groups, reducing it to a certain graph coloring problem, leaving as an open problem to achieve security against active attacks.
We present the first n-party protocol for unconditionally secure multiparty computation over a black-box group which is secure under an active attack model, tolerating any adversary structure Δ satisfying the Q 3 property (in which no union of three subsets from Δ covers the whole player set), which is known to be necessary for achieving security in the active setting. Our protocol uses Maurer’s Verifiable Secret Sharing (VSS) but preserves the essential simplicity of the graph-based approach of Desmedt et al, which avoids each shareholder having to rerun the full VSS protocol after each local computation. A corollary of our result is a new active-secure protocol for general multiparty computation of an arbitrary Boolean circuit.
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
Barrington, D.A.: Bounded-Width Polynomial-Size Branching Programs Recognize Exactly Those Languages in NC 1. In: STOC 1986, pp. 1–5 (1986)
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: STOC 1988, pp. 1–10 (1988)
Chaum, D., Crépeau, C., Damgård, I.: Multiparty unconditionally secure protocols. In: STOC 1988, pp. 11–19 (1988)
Cramer, R., Fehr, S., Ishai, Y., Kushilevitz, E.: Efficient Multi-Party Computation Over Rings. In: Biham, E. (ed.) EUROCRYPT 2003. LNCS, vol. 2656, pp. 596–613. Springer, Heidelberg (2003)
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)
Damgård, I., Ishai, Y., Krøigaard, M.: Perfectly Secure Multiparty Computation and the Computational Overhead of Cryptography. In: Gilbert, H. (ed.) EUROCRYPT 2010. LNCS, vol. 6110, pp. 445–465. Springer, Heidelberg (2010)
Desmedt, Y., Pieprzyk, J., Steinfeld, R., Sun, X., Tartary, C., Wang, H., Yao, A.C.-C.: Graph coloring applied to secure computation in non-abelian groups. J. Cryptology (to appear, 2011)
Desmedt, Y., Pieprzyk, J., Steinfeld, R., Wang, H.: On Secure Multi-party Computation in Black-Box Groups. In: Menezes, A. (ed.) CRYPTO 2007. LNCS, vol. 4622, pp. 591–612. Springer, Heidelberg (2007)
Fitzi, M., Hirt, M., Maurer, U.M.: Trading Correctness for Privacy in Unconditional Multi-party Computation. In: Krawczyk, H. (ed.) CRYPTO 1998. LNCS, vol. 1462, pp. 121–136. Springer, Heidelberg (1998)
Fitzi, M., Hirt, M., Maurer, U.M.: General Adversaries in Unconditional Multi-party Computation. In: Lam, K.-Y., Okamoto, E., Xing, C. (eds.) ASIACRYPT 1999. LNCS, vol. 1716, pp. 232–246. Springer, Heidelberg (1999)
Fitzi, M., Maurer, U.: Efficient Byzantine Agreement Secure against General Adversaries. In: Kutten, S. (ed.) DISC 1998. LNCS, vol. 1499, pp. 134–148. Springer, Heidelberg (1998)
Goldreich, O.: Foundations of Cryptography: vol. II - Basic Applications. Cambridge University Press (2004)
Goldreich, O., Micali, S., Wigderson, A.: How to Play Any Mental Game. In: STOC 1987, pp. 218–229 (1987)
Hirt, M., Maurer, U.: Complete Characterization of Adversaries Tolerable in Secure Multi-Party Computation. In: PODC 1997, pp. 25–34 (1997)
Hirt, M., Maurer, U.: Player simulation and general adversary structures in perfect multiparty computation. J. Cryptology 13(1), 31–60 (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., Maurer, U., Przydatek, B.: Efficient Secure Multi-party Computation. In: Okamoto, T. (ed.) ASIACRYPT 2000. LNCS, vol. 1976, pp. 143–161. Springer, Heidelberg (2000)
Maurer, U.: Secure multi-party computation made simple. Discrete Applied Mathematics 154, 370–381 (2006)
Prabhu, B.S., Srinathan, K., Pandu Rangan, C.: Trading Players for Efficiency in Unconditional Multiparty Computation. In: Cimato, S., Galdi, C., Persiano, G. (eds.) SCN 2002. LNCS, vol. 2576, pp. 342–353. Springer, Heidelberg (2003)
Sun, X., Yao, A.C.-C., Tartary, C.: Graph Design for Secure Multiparty Computation over Non-Abelian Groups. In: Pieprzyk, J. (ed.) ASIACRYPT 2008. LNCS, vol. 5350, pp. 37–53. Springer, Heidelberg (2008)
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
Desmedt, Y., Pieprzyk, J., Steinfeld, R. (2012). Active Security in Multiparty Computation over Black-Box Groups. In: Visconti, I., De Prisco, R. (eds) Security and Cryptography for Networks. SCN 2012. Lecture Notes in Computer Science, vol 7485. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-32928-9_28
Download citation
DOI: https://doi.org/10.1007/978-3-642-32928-9_28
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-32927-2
Online ISBN: 978-3-642-32928-9
eBook Packages: Computer ScienceComputer Science (R0)