Abstract
At STOC ’87, Goldreich et al. presented two protocols for secure multi-party computation (MPC) among n parties: The first protocol provides passive security against t < n corrupted parties. The second protocol provides even active security, but only against t < n/2 corrupted parties. Although these protocols provide security against the provably highest possible number of corruptions, each of them has its limitation: The first protocol is rendered completely insecure in presence of a single active corruption, and the second protocol is rendered completely insecure in presence of ⌈n/2 ⌉ passive corruptions.
At Crypto 2006, Ishai et al. combined these two protocols into a single protocol which provides passive security against t < n corruptions and active security against t < n/2 corruptions. This protocol unifies the security guarantees of the passive world and the active world (“best of both worlds”). However, the corruption threshold t < n can be tolerated only when all corruptions are passive. With a single active corruption, the threshold is reduced to t < n/2.
As our main result, we introduce a dynamic tradeoff between active and passive corruptions: We present a protocol which provides security against t < n passive corruptions, against t < n/2 active corruptions, and everything in between. In particular, our protocol provides full security against k active corruptions, as long as less than n − k parties are corrupted in total, for any unknown k.
The main technical contribution is a new secret sharing scheme that, in the reconstruction phase, releases secrecy gradually. This allows to construct non-robust MPC protocols which, in case of an abort, still provide some level of secrecy. Furthermore, using similar techniques, we also construct protocols for reactive MPC with hybrid security, i.e., different thresholds for secrecy, correctness, robustness, and fairness. Intuitively, the more corrupted parties, the less security is guaranteed.
Chapter PDF
Similar content being viewed by others
References
Beaver, D.: Secure multiparty protocols and zero-knowledge proof systems tolerating a faulty minority. Journal of Cryptology 4(2), 75–122 (1991)
Ben-Or, M., Goldwasser, S., Wigderson, A.: Completeness theorems for non-cryptographic fault-tolerant distributed computation. In: STOC 1988, pp. 1–10. ACM (1988)
Blum, M.: How to exchange (secret) keys (extended abstract). In: STOC 1983, pp. 440–447. ACM (1983)
Chaum, D., Crépeau, C., Damgård, I.: Multiparty unconditionally secure protocols. In: STOC 1988, pp. 11–19. ACM (1988)
Chaum, D.: The spymasters double-agent problem: Multiparty computations secure unconditionally from minorities and cryptograhically from majorities. In: Brassard, G. (ed.) CRYPTO 1989. LNCS, vol. 435, pp. 591–602. Springer, Heidelberg (1990)
Dolev, D., Dwork, C., Waarts, O., Yung, M.: Perfectly secure message transmission. Journal of the ACM 40(1), 17–47 (1993)
Dolev, D., Strong, H.R.: Polynomial algorithms for multiple processor agreement. In: STOC 1982, pp. 401–407. ACM (1982)
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.M.: Trading correctness for privacy in unconditional multi-party computation (extended abstract). In: Krawczyk, H. (ed.) CRYPTO 1998. LNCS, vol. 1462, pp. 121–136. Springer, Heidelberg (1998)
Fitzi, M., Holenstein, T., Wullschleger, J.: Multi-party computation with hybrid security. In: Cachin, C., Camenisch, J.L. (eds.) EUROCRYPT 2004. LNCS, vol. 3027, pp. 419–438. Springer, Heidelberg (2004)
Goldreich, O., Micali, S., Wigderson, A.: How to play any mental game or a completeness theorem for protocols with honest majority. In: STOC 1987, pp. 218–229. ACM (1987)
Goldreich, O.: Foundations of Cryptography. Basic Applications, vol. 2. Cambridge University Press (2004)
Hirt, M., Lucas, C., Maurer, U., Raub, D.: Graceful degradation in multi-party computation (extended abstract). In: Fehr, S. (ed.) ICITS 2011. LNCS, vol. 6673, pp. 163–180. Springer, Heidelberg (2011)
Hirt, M., Lucas, C., Maurer, U., Raub, D.: Passive corruption in statistical multi-party computation. In: Smith, A. (ed.) ICITS 2012. LNCS, vol. 7412, pp. 129–146. Springer, Heidelberg (2012)
Hirt, M., Maurer, U., Zikas, V.: MPC vs. SFE: Unconditional and computational security. In: Pieprzyk, J. (ed.) ASIACRYPT 2008. LNCS, vol. 5350, pp. 1–18. Springer, Heidelberg (2008)
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)
Katz, J.: On achieving the “best of both worlds” in secure multiparty computation. In: STOC 2007, pp. 11–20. ACM (2007)
Lucas, C., Raub, D., Maurer, U.: Hybrid-secure MPC: Trading information-theoretic robustness for computational privacy. In: PODC 2010, pp. 219–228. ACM (2010)
Pedersen, T.P.: Non-interactive and information-theoretic secure verifiable secret sharing. In: Feigenbaum, J. (ed.) CRYPTO 1991. LNCS, vol. 576, pp. 129–140. Springer, Heidelberg (1992)
Rabin, T., Ben-Or, M.: Verifiable secret sharing and multiparty protocols with honest majority. In: STOC 1989, pp. 73–85. ACM (1989)
Shamir, A.: How to share a secret. Communications of the ACM 22(11), 612–613 (1979)
Yao, A.C.: Protocols for secure computations (extended abstract). In: FOCS 1982, pp. 160–164. IEEE (1982)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2013 International Association for Cryptologic Research
About this paper
Cite this paper
Hirt, M., Maurer, U., Lucas, C. (2013). A Dynamic Tradeoff between Active and Passive Corruptions in Secure Multi-Party Computation. In: Canetti, R., Garay, J.A. (eds) Advances in Cryptology – CRYPTO 2013. CRYPTO 2013. Lecture Notes in Computer Science, vol 8043. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-40084-1_12
Download citation
DOI: https://doi.org/10.1007/978-3-642-40084-1_12
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-40083-4
Online ISBN: 978-3-642-40084-1
eBook Packages: Computer ScienceComputer Science (R0)