Parallel Oblivious Array Access for Secure Multiparty Computation and Privacy-Preserving Minimum Spanning Trees

Abstract In this paper, we describe efficient protocols to perform in parallel many reads and writes in private arrays according to private indices. The protocol is implemented on top of the Arithmetic Black Box (ABB) and can be freely composed to build larger privacypreserving applications. For a large class of secure multiparty computation (SMC) protocols, our technique has better practical and asymptotic performance than any previous ORAM technique that has been adapted for use in SMC. Our ORAM technique opens up a large class of parallel algorithms for adoption to run on SMC platforms. In this paper, we demonstrate how the minimum spanning tree (MST) finding algorithm by Awerbuch and Shiloach can be executed without revealing any details about the underlying graph (beside its size). The data accesses of this algorithm heavily depend on the location and weight of edges (which are private) and our ORAM technique is instrumental in their execution. Our implementation is the first-ever realization of a privacypreserving MST algorithm with sublinear round complexity.

[1]  Rafail Ostrovsky,et al.  On the (in)security of hash-based oblivious RAM and a new balancing scheme , 2012, SODA.

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

[3]  Tomas Toft.  Secure data structures based on multi-party computation , 2011, PODC '11.

[4]  David Sands,et al.  Differential Privacy , 2015, POPL.

[5]  2013 ACM SIGSAC Conference on Computer and Communications Security, CCS'13, Berlin, Germany, November 4-8, 2013 , 2013, Conference on Computer and Communications Security.

[6]  Marina Blanton,et al.  Data-oblivious graph algorithms for secure computation and outsourcing , 2013, ASIA CCS '13.

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

[8]  Wolfgang Middelmann,et al.  An Efficient Parallel Algorithm for Graph-Based Image Segmentation , 2009, CAIP.

[9]  Joseph JáJá,et al.  An Introduction to Parallel Algorithms , 1992 .

[10]  Elaine Shi,et al.  Automating Efficient RAM-Model Secure Computation , 2014, 2014 IEEE Symposium on Security and Privacy.

[11]  Jonathan Katz,et al.  Secure two-party computation in sublinear (amortized) time , 2012, CCS.

[12]  Craig Gentry,et al.  Private Database Access with HE-over-ORAM Architecture , 2015, ACNS.

[13]  Peeter Laud,et al.  Privacy-preserving String-Matching With PRAM Algorithms Report in MTAT , 2014 .

[14]  Vitaly Shmatikov,et al.  Privacy-Preserving Graph Algorithms in the Semi-honest Model , 2005, ASIACRYPT.

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

[16]  Jaroslav Nesetril,et al.  Otakar Boruvka on minimum spanning tree problem Translation of both the 1926 papers, comments, history , 2001, Discret. Math..

[17]  Payman Mohassel,et al.  How to Hide Circuits in MPC: An Efficient Framework for Private Function Evaluation , 2013, IACR Cryptol. ePrint Arch..

[18]  Elaine Shi,et al.  Oblivious RAM with O((logN)3) Worst-Case Cost , 2011, ASIACRYPT.

[19]  Michael Zohner,et al.  ABY - A Framework for Efficient Mixed-Protocol Secure Two-Party Computation , 2015, NDSS.

[20]  Tal Rabin,et al.  Simplified VSS and fast-track multiparty computations with applications to threshold cryptography , 1998, PODC '98.

[21]  Dan Bogdanov,et al.  High-performance secure multi-party computation for data mining applications , 2012, International Journal of Information Security.

[22]  Kai-Min Chung,et al.  Oblivious Parallel RAM , 2014, IACR Cryptol. ePrint Arch..

[23]  Mathieu Van Vyve,et al.  Securely Solving Simple Combinatorial Graph Problems , 2013, Financial Cryptography.

[24]  Ahmad-Reza Sadeghi,et al.  TASTY: tool for automating secure two-party computations , 2010, CCS '10.

[25]  S. Sitharama Iyengar,et al.  Introduction to parallel algorithms , 1998, Wiley series on parallel and distributed computing.

[26]  Marina Blanton,et al.  Private and oblivious set and multiset operations , 2012, ASIACCS '12.

[27]  Katsumi Takahashi,et al.  Practically Efficient Multi-party Sorting Protocols from Comparison Sort Algorithms , 2012, ICISC.

[28]  Xenofontas A. Dimitropoulos,et al.  SEPIA: Privacy-Preserving Aggregation of Multi-Domain Network Events and Statistics , 2010, USENIX Security Symposium.

[29]  Benny Pinkas,et al.  FairplayMP: a system for secure multi-party computation , 2008, CCS.

[30]  Jonathan Katz,et al.  Private Set Intersection: Are Garbled Circuits Better than Custom Protocols? , 2012, NDSS.

[31]  I. Damglurd.  Unconditionally secure constant-rounds multi-party computation for equality, comparison, bits and exponentiation , 2006 .

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

[33]  Lior Malka,et al.  VMCrypt: modular software architecture for scalable secure computation , 2011, CCS '11.

[34]  Jan Willemson,et al.  Composable Oblivious Extended Permutations , 2014, FPS.

[35]  Octavian Catrina,et al.  Improved Primitives for Secure Multiparty Integer Computation , 2010, SCN.

[36]  Harold Joseph Highland,et al.  Random bits & bytes , 1994, Computers & security.

[37]  Jan Willemson,et al.  Round-Efficient Oblivious Database Manipulation , 2011, ISC.

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

[39]  Abraham Waksman,et al.  A Permutation Network , 1968, JACM.

[40]  Ivan Damgård,et al.  Multiparty Computation from Threshold Homomorphic Encryption , 2000, EUROCRYPT.

[41]  Tomas Toft,et al.  Secure Equality and Greater-Than Tests with Sublinear Online Complexity , 2013, ICALP.

[42]  Rafail Ostrovsky,et al.  Software protection and simulation on oblivious RAMs , 1996, JACM.

[43]  Baruch Awerbuch,et al.  New Connectivity and MSF Algorithms for Shuffle-Exchange Network and PRAM , 1987, IEEE Transactions on Computers.

[44]  David Evans,et al.  Circuit Structures for Improving Efficiency of Security and Privacy Tools , 2013, 2013 IEEE Symposium on Security and Privacy.

[45]  Marcel Keller,et al.  Efficient, Oblivious Data Structures for MPC , 2014, IACR Cryptol. ePrint Arch..

[46]  John Launchbury,et al.  Efficient lookup-table protocol in secure multiparty computation , 2012, ICFP.

[47]  Vladimir Kolesnikov,et al.  A Practical Universal Circuit Construction and Secure Evaluation of Private Functions , 2008, Financial Cryptography.

[48]  Abhi Shelat,et al.  SCORAM: Oblivious RAM for Secure Computation , 2014, IACR Cryptol. ePrint Arch..

[49]  Craig Gentry,et al.  Optimizing ORAM and Using It Efficiently for Secure Computation , 2013, Privacy Enhancing Technologies.

[50]  Ling Ren,et al.  Path ORAM , 2012, J. ACM.

[51]  Ying Xu,et al.  Clustering gene expression data using a graph-theoretic approach: an application of minimum spanning trees , 2002, Bioinform..

[52]  Ivan Damgård,et al.  Perfectly Secure Oblivious RAM Without Random Oracles , 2011, IACR Cryptol. ePrint Arch..

[53]  Ivan Damgård,et al.  Universally Composable Efficient Multiparty Computation from Threshold Homomorphic Encryption , 2003, CRYPTO.

[54]  Ivan Damgård,et al.  Asynchronous Multiparty Computation: Theory and Implementation , 2008, IACR Cryptol. ePrint Arch..

[55]  Andrew Chi-Chih Yao,et al.  Protocols for Secure Computations (Extended Abstract) , 1982, FOCS.

[56]  Kazuo Ohta,et al.  Multiparty Computation for Interval, Equality, and Comparison Without Bit-Decomposition Protocol , 2007, Public Key Cryptography.

[57]  Yihua Zhang,et al.  Secure Computation on Floating Point Numbers , 2013, NDSS.