Adaptively Secure Multi-Party Computation with Dishonest Majority

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.

[1]  Tal Malkin,et al.  Improved Non-committing Encryption with Applications to Adaptively Secure Protocols , 2009, ASIACRYPT.

[2]  Silvio Micali,et al.  How to play ANY mental game , 1987, STOC.

[3]  Moni Naor,et al.  Adaptively secure multi-party computation , 1996, STOC '96.

[4]  Alfredo De Santis,et al.  Zero-knowledge proofs of knowledge without interaction , 1992, Proceedings., 33rd Annual Symposium on Foundations of Computer Science.

[5]  Vipul Goyal,et al.  Constant round non-malleable protocols using one way functions , 2011, STOC '11.

[6]  Yehuda Lindell,et al.  Adaptive Zero-Knowledge Proofs and Adaptively Secure Oblivious Transfer , 2009, Journal of Cryptology.

[7]  Moni Naor,et al.  Bit Commitment Using Pseudo-Randomness , 1989, CRYPTO.

[8]  Rafael Pass,et al.  Constant-round non-malleable commitments from any one-way function , 2011, STOC '11.

[9]  Rafael Pass,et al.  New and Improved Constructions of Nonmalleable Cryptographic Protocols , 2008, SIAM J. Comput..

[10]  Manuel Blum,et al.  How to Prove a Theorem So No One Else Can Claim It , 2010 .

[11]  Adi Shamir,et al.  Zero Knowledge Proofs of Knowledge in Two Rounds , 1989, CRYPTO.

[12]  Donald Beaver,et al.  Adaptively Secure Oblivious Transfer , 1998, ASIACRYPT.

[13]  Donald Beaver,et al.  Cryptographic Protocols Provably Secure Against Dynamic Adversaries , 1992, EUROCRYPT.

[14]  Rafael Pass,et al.  Bounded-concurrent secure multi-party computation with a dishonest majority , 2004, STOC '04.

[15]  Hoeteck Wee,et al.  Black-Box Constructions of Two-Party Protocols from One-Way Functions , 2009, TCC.

[16]  Oded Goldreich,et al.  Universal arguments and their applications , 2002, Proceedings 17th IEEE Annual Conference on Computational Complexity.

[17]  Moni Naor,et al.  Bit commitment using pseudorandomness , 1989, Journal of Cryptology.

[18]  Joe Kilian,et al.  Founding crytpography on oblivious transfer , 1988, STOC '88.

[19]  Rafail Ostrovsky,et al.  Round-Optimal Secure Two-Party Computation , 2004, CRYPTO.

[20]  Ran Canetti,et al.  Security and Composition of Multiparty Cryptographic Protocols , 2000, Journal of Cryptology.

[21]  Donald Beaver,et al.  Equivocable Oblivious Transfer , 1996, EUROCRYPT.

[22]  Moni Naor,et al.  Non-Malleable Cryptography (Extended Abstract) , 1991, STOC 1991.

[23]  Amit Sahai,et al.  How to play almost any mental game over the net - concurrent composition via super-polynomial simulation , 2005, 46th Annual IEEE Symposium on Foundations of Computer Science (FOCS'05).

[24]  Daniel Wichs,et al.  Somewhat Non-Committing Encryption and Efficient Adaptively Secure Oblivious Transfer , 2009, IACR Cryptol. ePrint Arch..

[25]  Rafail Ostrovsky,et al.  Round Efficiency of Multi-party Computation with a Dishonest Majority , 2003, EUROCRYPT.

[26]  Yuval Ishai,et al.  Founding Cryptography on Oblivious Transfer - Efficiently , 2008, CRYPTO.

[27]  Boaz Barak,et al.  How to go beyond the black-box simulation barrier , 2001, Proceedings 2001 IEEE International Conference on Cluster Computing.

[28]  Amit Sahai,et al.  Concurrent zero knowledge with logarithmic round-complexity , 2002, The 43rd Annual IEEE Symposium on Foundations of Computer Science, 2002. Proceedings..

[29]  Tal Malkin,et al.  Simple, Black-Box Constructions of Adaptively Secure Protocols , 2009, TCC.

[30]  A. Yao,et al.  Fair exchange with a semi-trusted third party (extended abstract) , 1997, CCS '97.

[31]  Donald Beaver,et al.  Adaptive zero knowledge and computational equivocation (extended abstract) , 1996, STOC '96.

[32]  Alon Rosen,et al.  A Note on Constant-Round Zero-Knowledge Proofs for NP , 2004, TCC.

[33]  Yehuda Lindell,et al.  Universally composable two-party and multi-party secure computation , 2002, STOC '02.

[34]  Rafael Pass,et al.  Bounded-concurrent secure two-party computation in a constant number of rounds , 2003, 44th Annual IEEE Symposium on Foundations of Computer Science, 2003. Proceedings..

[35]  Ran Canetti,et al.  Universally composable security: a new paradigm for cryptographic protocols , 2001, Proceedings 2001 IEEE International Conference on Cluster Computing.

[36]  Yehuda Lindell,et al.  Strict Polynomial-Time in Simulation and Extraction , 2004, SIAM J. Comput..