Abstract
Adaptively secure multiparty computation is an essential and fundamental notion in cryptography. In this work we focus on the basic question of constructing a multiparty computation protocol secure against a malicious, adaptive adversary in the stand-alone setting without assuming an honest majority, in the plain model. It has been believed that this question can be resolved by composing known protocols from the literature. We show that in fact, this belief is fundamentally mistaken. In particular, we show:
-
Round inefficiency is unavoidable when using black-box simulation: There does not exist any \(o(\frac{n}{\log {n}})\) round protocol that adaptively securely realizes a (natural) n-party functionality with a black-box simulator. Note that most previously known protocols in the adaptive security setting relied on black-box simulators.
-
A constant round protocol using non-black-box simulation: We construct a constant round adaptively secure multiparty computation protocol in a setting without honest majority that makes crucial use of non-black box techniques.
Taken together, these results give the first resolution to the question of adaptively secure multiparty computation protocols with a malicious dishonest majority in the plain model, open since the first formal treatment of adaptive security for multiparty computation in 1996.
Chapter PDF
References
Yao, A.C.: How to generate and exchange secrets. In: Proc. 27th FOCS, pp. 162–167 (1986)
Goldreich, O., Micali, S., Wigderson, A.: How to play any mental game or a completeness theorem for protocols with honest majority. In: STOC, pp. 218–229 (1987)
Canetti, R., Feige, U., Goldreich, O., Naor, M.: Adaptively secure multi-party computation. In: STOC, pp. 639–648 (1996)
Beaver, D.: Adaptive zero knowledge and computational equivocation (extended abstract). In: STOC, pp. 629–638 (1996)
Lindell, Y., Zarosim, H.: Adaptive zero-knowledge proofs and adaptively secure oblivious transfer. J. Cryptology 24(4), 761–799 (2011)
Beaver, D.: Equivocable Oblivious Transfer. In: Maurer, U.M. (ed.) EUROCRYPT 1996. LNCS, vol. 1070, pp. 119–130. Springer, Heidelberg (1996)
Beaver, D.: Adaptively Secure Oblivious Transfer. In: Ohta, K., Pei, D. (eds.) ASIACRYPT 1998. LNCS, vol. 1514, pp. 300–314. Springer, Heidelberg (1998)
Katz, J., Ostrovsky, R.: Round-Optimal Secure Two-Party Computation. In: Franklin, M. (ed.) CRYPTO 2004. LNCS, vol. 3152, pp. 335–354. Springer, Heidelberg (2004)
Canetti, R., Lindell, Y., Ostrovsky, R., Sahai, A.: Universally composable two-party and multi-party secure computation. In: STOC, pp. 494–503 (2002)
Choi, S.G., Dachman-Soled, D., Malkin, T., Wee, H.: Improved Non-committing Encryption with Applications to Adaptively Secure Protocols. In: Matsui, M. (ed.) ASIACRYPT 2009. LNCS, vol. 5912, pp. 287–302. Springer, Heidelberg (2009)
Choi, S.G., Dachman-Soled, D., Malkin, T., Wee, H.: Simple, Black-Box Constructions of Adaptively Secure Protocols. In: Reingold, O. (ed.) TCC 2009. LNCS, vol. 5444, pp. 387–402. Springer, Heidelberg (2009)
Pass, R., Wee, H.: Black-Box Constructions of Two-Party Protocols from One-Way Functions. In: Reingold, O. (ed.) TCC 2009. LNCS, vol. 5444, pp. 403–418. Springer, Heidelberg (2009)
Canetti, R.: Security and composition of multi-party cryptographic protocols. Cryptology ePrint Archive, Report 1998/018 (1998), http://eprint.iacr.org/
De Santis, A., Persiano, G.: Zero-knowledge proofs of knowledge without interaction. In: Proceedings of the 33rd Annual Symposium on Foundations of Computer Science, SFCS 1992, pp. 427–436. IEEE Computer Society, Washington, DC (1992)
Beaver, D., Haber, S.: Cryptographic Protocols Provably Secure against Dynamic Adversaries. In: Rueppel, R.A. (ed.) EUROCRYPT 1992. LNCS, vol. 658, pp. 307–323. Springer, Heidelberg (1993)
Barak, B.: How to go beyond the black-box simulation barrier. In: Proc. 42nd FOCS, pp. 106–115 (2001)
Pass, R., Rosen, A.: Bounded-concurrent secure two-party computation in a constant number of rounds. In: FOCS, pp. 404–413 (2003)
Pass, R., Rosen, A.: New and improved constructions of nonmalleable cryptographic protocols. SIAM J. Comput. 38(2), 702–752 (2008)
Barak, B., Sahai, A.: How to play almost any mental game over the net - concurrent composition via super-polynomial simulation. In: FOCS, pp. 543–552 (2005)
Ishai, Y., Prabhakaran, M., Sahai, A.: Founding Cryptography on Oblivious Transfer – Efficiently. In: Wagner, D. (ed.) CRYPTO 2008. LNCS, vol. 5157, pp. 572–591. Springer, Heidelberg (2008)
Katz, J., Ostrovsky, R., Smith, A.: Round Efficiency of Multi-Party Computation with a Dishonest Majority. In: Biham, E. (ed.) EUROCRYPT 2003. LNCS, vol. 2656, pp. 578–595. Springer, Heidelberg (2003)
Pass, R.: Bounded-concurrent secure multi-party computation with a dishonest majority. In: Proc. 36th STOC, pp. 232–241 (2004)
Feige, U., Shamir, A.: Zero Knowledge Proofs of Knowledge in Two Rounds. In: Brassard, G. (ed.) CRYPTO 1989. LNCS, vol. 435, pp. 526–544. Springer, Heidelberg (1990)
Barak, B., Goldreich, O.: Universal arguments and their applications. SIAM J. Comput. 38(5), 1661–1694 (2008)
Naor, M.: Bit commitment using pseudorandomness. Journal of Cryptology 4(2), 151–158 (1991); Preliminary version In: Brassard, G. (ed.) CRYPTO 1989. LNCS, vol. 435, pp. 128–136. Springer, Heidelberg (1990)
Canetti, R.: Universally composable security: A new paradigm for cryptographic protocols (2000), http://eprint.iacr.org/
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2012 International Association for Cryptologic Research 2012
About this paper
Cite this paper
Garg, S., Sahai, A. (2012). Adaptively Secure Multi-Party Computation with Dishonest Majority. In: Safavi-Naini, R., Canetti, R. (eds) Advances in Cryptology – CRYPTO 2012. CRYPTO 2012. Lecture Notes in Computer Science, vol 7417. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-32009-5_8
Download citation
DOI: https://doi.org/10.1007/978-3-642-32009-5_8
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-32008-8
Online ISBN: 978-3-642-32009-5
eBook Packages: Computer ScienceComputer Science (R0)