Optimally Resilient and Adaptively Secure Multi-Party Computation with Low Communication Locality

Secure multi-party computation (MPC) has been thoroughly studied over the past decades. The vast majority of works assume a full communication pattern: every party exchanges messages with all the network participants over a complete network of point-to-point channels. This can be problematic in modern large scale networks, where the number of parties can be of the order of millions, as for example when computing on large distributed data. Motivated by the above observation, Boyle, Goldwasser, and Tessaro [TCC 2013] recently put forward the notion of communication locality, namely, the total number of point-to-point channels that each party uses in the protocol, as a quality metric of MPC protocols. They proved that assuming a public-key infrastructure (PKI) and a common reference string (CRS), an MPC protocol can be constructed for computing any n-party function, with communication localityO(log c n) and round complexityO(log c 0

[1]  Oded Goldreich.  Basing Non-Interactive Zero-Knowledge on (Enhanced) Trapdoor Permutations: The State of the Art , 2011, Studies in Complexity and Cryptography.

[2]  Jonathan Katz,et al.  Composability and On-Line Deniability of Authentication , 2009, TCC.

[3]  Manuel Blum,et al.  Non-Interactive Zero-Knowledge and Its Applications (Extended Abstract) , 1988, STOC 1988.

[4]  Craig Gentry,et al.  (Leveled) fully homomorphic encryption without bootstrapping , 2012, ITCS '12.

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

[6]  Ran Canetti,et al.  Security and composition of cryptographic protocols: a tutorial (part I) , 2006, SIGA.

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

[8]  Adi Shamir,et al.  Multiple non-interactive zero knowledge proofs based on a single random string , 1990, Proceedings [1990] 31st Annual Symposium on Foundations of Computer Science.

[9]  Rafail Ostrovsky,et al.  Almost-Everywhere Secure Computation , 2008, EUROCRYPT.

[10]  Dan Bogdanov,et al.  Sharemind: A Framework for Fast Privacy-Preserving Computations , 2008, ESORICS.

[11]  Jonathan Katz,et al.  On expected constant-round protocols for Byzantine agreement , 2006, J. Comput. Syst. Sci..

[12]  Jared Saia,et al.  Brief announcement: breaking the O(nm) bit barrier, secure multiparty computation with a static adversary , 2012, PODC '12.

[13]  Marcel Keller,et al.  An architecture for practical actively secure MPC with dishonest majority , 2013, IACR Cryptol. ePrint Arch..

[14]  Rafail Ostrovsky,et al.  Sequential Aggregate Signatures and Multisignatures Without Random Oracles , 2006, EUROCRYPT.

[15]  Yehuda Lindell,et al.  The IPS Compiler: Optimizations, Variants and Concrete Efficiency , 2011, CRYPTO.

[16]  Shafi Goldwasser,et al.  Communication Locality in Secure Multi-party Computation - How to Run Sublinear Algorithms in a Distributed Setting , 2013, TCC.

[17]  Ivan Damgård,et al.  Semi-Homomorphic Encryption and Multiparty Computation , 2011, IACR Cryptol. ePrint Arch..

[18]  Ivan Damgård,et al.  Multiparty Computation from Somewhat Homomorphic Encryption , 2012, IACR Cryptol. ePrint Arch..

[19]  Eli Upfal.  Tolerating linear number of faults in networks of bounded degree , 1992, PODC '92.

[20]  Silvio Micali,et al.  Accountable-subgroup multisignatures: extended abstract , 2001, CCS '01.

[21]  Leslie Lamport,et al.  The Byzantine Generals Problem , 1982, TOPL.

[22]  Vinod Vaikuntanathan,et al.  Efficient Fully Homomorphic Encryption from (Standard) LWE , 2011, 2011 IEEE 52nd Annual Symposium on Foundations of Computer Science.

[23]  W. Hoeffding.  Probability Inequalities for sums of Bounded Random Variables , 1963 .

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

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

[26]  Ivan Damgård,et al.  Improved Non-committing Encryption Schemes Based on a General Complexity Assumption , 2000, CRYPTO.

[27]  David Chaum,et al.  Multiparty Unconditionally Secure Protocols (Extended Abstract) , 1988, STOC.

[28]  Rafail Ostrovsky,et al.  Edge Fault Tolerance on Sparse Networks , 2012, ICALP.

[29]  Ran Canetti,et al.  Security and composition of cryptographic protocols: a tutorial (part I) , 2006, SIGA.

[30]  Marcel Keller,et al.  Practical Covertly Secure MPC for Dishonest Majority - Or: Breaking the SPDZ Limits , 2013, ESORICS.

[31]  Rafail Ostrovsky,et al.  Improved Fault Tolerance and Secure Computation on Sparse Networks , 2010, ICALP.

[32]  Marcel Keller,et al.  Implementing AES via an Actively/Covertly Secure Dishonest-Majority MPC Protocol , 2012, SCN.

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

[34]  Erik Vee,et al.  Towards Secure and Scalable Computation in Peer-to-Peer Networks , 2006, 2006 47th Annual IEEE Symposium on Foundations of Computer Science (FOCS'06).

[35]  Leslie Lamport,et al.  Reaching Agreement in the Presence of Faults , 1980, JACM.

[36]  Russell Impagliazzo,et al.  One-way functions are essential for complexity based cryptography , 1989, 30th Annual Symposium on Foundations of Computer Science.

[37]  Yehuda Lindell,et al.  On the composition of authenticated byzantine agreement , 2002, STOC '02.

[38]  Eli Upfal,et al.  Fault Tolerance in Networks of Bounded Degree (Preliminary Version) , 1986, STOC 1986.

[39]  Jonathan Katz,et al.  On Expected Constant-Round Protocols for Byzantine Agreement , 2006, CRYPTO.

[40]  Jared Saia,et al.  Breaking the O(n2) bit barrier: scalable byzantine agreement with an adaptive adversary , 2010, PODC.

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

[42]  Erik Vee,et al.  Scalable leader election , 2006, SODA '06.