Constant-Round MPC with Fairness and Guarantee of Output Delivery

We study the round complexity of multiparty computation with fairness and guaranteed output delivery, assuming existence of an honest majority. We demonstrate a new lower bound and a matching upper bound. Our lower bound rules out any two-round fair protocols in the standalone model, even when the parties are given access to a common reference string (CRS). The lower bound follows by a reduction to the impossibility result of virtual black box obfuscation of arbitrary circuits.

[1]  Adi Shamir,et al.  How to share a secret , 1979, CACM.

[2]  Andrew Chi-Chih Yao,et al.  How to Generate and Exchange Secrets (Extended Abstract) , 1986, FOCS.

[3]  Richard Cleve,et al.  Limits on the security of coin flips when half the processors are faulty , 1986, STOC '86.

[4]  Avi Wigderson,et al.  Completeness Theorems for Non-Cryptographic Fault-Tolerant Distributed Computation (Extended Abstract) , 1988, STOC.

[5]  Avi Wigderson,et al.  Completeness theorems for non-cryptographic fault-tolerant distributed computation , 1988, STOC '88.

[6]  Silvio Micali,et al.  The Round Complexity of Secure Protocols (Extended Abstract) , 1990, STOC 1990.

[7]  Silvio Micali,et al.  The round complexity of secure protocols , 1990, STOC '90.

[8]  Amit Sahai,et al.  On the (im)possibility of obfuscating programs , 2001, JACM.

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

[10]  Rafail Ostrovsky,et al.  Robust Non-interactive Zero Knowledge , 2001, CRYPTO.

[11]  Yuval Ishai,et al.  On 2-Round Secure Multiparty Computation , 2002, CRYPTO.

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

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

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

[15]  Yuval Ishai,et al.  Constant-Round Multiparty Computation Using a Black-Box Pseudorandom Generator , 2005, CRYPTO.

[16]  Oded Regev,et al.  On lattices, learning with errors, random linear codes, and cryptography , 2009, JACM.

[17]  Chris Peikert,et al.  Public-key cryptosystems from the worst-case shortest vector problem: extended abstract , 2009, STOC '09.

[18]  Anat Paskin-Cherniavsky,et al.  Secure Multiparty Computation with Minimal Interaction , 2010, CRYPTO.

[19]  Vinod Vaikuntanathan,et al.  Multiparty Computation with Low Communication, Computation and Interaction via Threshold FHE , 2012, EUROCRYPT.

[20]  Vinod Vaikuntanathan,et al.  On-the-fly multiparty computation on the cloud via multikey fully homomorphic encryption , 2012, STOC '12.

[21]  Brent Waters,et al.  Homomorphic Encryption from Learning with Errors: Conceptually-Simpler, Asymptotically-Faster, Attribute-Based , 2013, CRYPTO.

[22]  Brent Waters,et al.  Witness encryption and its applications , 2013, STOC '13.

[23]  Mihir Bellare,et al.  Adaptive Witness Encryption and Asymmetric Password-Based Cryptography , 2015, Public Key Cryptography.

[24]  S. Rajsbaum.  Foundations of Cryptography , 2014 .

[25]  Craig Gentry,et al.  Two-Round Secure MPC from Indistinguishability Obfuscation , 2014, TCC.

[26]  Yehuda Lindell,et al.  Fairness Versus Guaranteed Output Delivery in Secure Multiparty Computation , 2014, Journal of Cryptology.