Jump to ContentJump to Main Navigation
Show Summary Details

Proceedings on Privacy Enhancing Technologies

2 Issues per year

Open Access
See all formats and pricing

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

Peeter Laud
  • Cybernetica AS
  • :
Published Online: 2015-06-22 | DOI: https://doi.org/10.1515/popets-2015-0011


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.

Keywords: Secure Multiparty Computation; Oblivious Arrays; Minimum Spanning Tree


  • [1] M. Aliasgari, M. Blanton, Y. Zhang, and A. Steele. Secure computation on floating point numbers. In 20th Annual Network and Distributed System Security Symposium, NDSS 2013, San Diego, California, USA, February 24-27, 2013. The Internet Society, 2013.

  • [2] A. Aly, E. Cuvelier, S. Mawet, O. Pereira, and M. V. Vyve. Securely solving simple combinatorial graph problems. In A.-R. Sadeghi, editor, Financial Cryptography, volume 7859 of Lecture Notes in Computer Science, pages 239–257. Springer, 2013.

  • [3] B. Awerbuch and Y. Shiloach. New connectivity and MSF algorithms for shuffle-exchange network and PRAM. IEEE Trans. Computers, 36(10):1258–1263, 1987.

  • [4] A. Ben-David, N. Nisan, and B. Pinkas. FairplayMP: a system for secure multi-party computation. In CCS ’08: Proceedings of the 15th ACM conference on Computer and communications security, pages 257–266, New York, NY, USA, 2008. ACM.

  • [5] M. Blanton and E. Aguiar. Private and oblivious set and multiset operations. In H. Y. Youm and Y. Won, editors, 7th ACM Symposium on Information, Compuer and Communications Security, ASIACCS ’12, Seoul, Korea, May 2-4, 2012, pages 40–41. ACM, 2012.

  • [6] M. Blanton, A. Steele, and M. Aliasgari. Data-oblivious graph algorithms for secure computation and outsourcing. In K. Chen, Q. Xie, W. Qiu, N. Li, and W. Tzeng, editors, 8th ACM Symposium on Information, Computer and Communications Security, ASIA CCS ’13, Hangzhou, China - May 08 - 10, 2013, pages 207–218. ACM, 2013.

  • [7] D. Bogdanov, S. Laur, and J. Willemson. Sharemind: A framework for fast privacy-preserving computations. In S. Jajodia and J. López, editors, ESORICS, volume 5283 of Lecture Notes in Computer Science, pages 192–206. Springer, 2008.

  • [8] D. Bogdanov, M. Niitsoo, T. Toft, and J. Willemson. High-performance secure multi-party computation for data mining applications. Int. J. Inf. Sec., 11(6):403–418, 2012.

  • [9] E. Boyle, K.-M. Chung, and R. Pass. Oblivious parallel ram. Cryptology ePrint Archive, Report 2014/594, 2014. http://eprint.iacr.org/.

  • [10] J. Brickell and V. Shmatikov. Privacy-preserving graph algorithms in the semi-honest model. In B. K. Roy, editor, ASIACRYPT, volume 3788 of Lecture Notes in Computer Science, pages 236–252. Springer, 2005.

  • [11] M. Burkhart, M. Strasser, D. Many, and X. Dimitropoulos. SEPIA: Privacy-preserving aggregation of multi-domain network events and statistics. In USENIX Security Symposium, pages 223–239, Washington, DC, USA, 2010.

  • [12] R. Canetti. Universally composable security: A new paradigm for cryptographic protocols. In FOCS, pages 136–145. IEEE Computer Society, 2001.

  • [13] O. Catrina and S. de Hoogh. Improved primitives for secure multiparty integer computation. In J. Garay and R. De Prisco, editors, Security and Cryptography for Networks, volume 6280 of LNCS, pages 182–199. Springer, 2010.

  • [14] O. Catrina and A. Saxena. Secure computation with fixedpoint numbers. In R. Sion, editor, Financial Cryptography and Data Security, volume 6052 of LNCS, pages 35–50. Springer, 2010.

  • [15] T. H. Cormen, C. E. Leiserson, R. L. Rivest, and C. Stein. Introduction to Algorithms, chapter 23.2 The algorithms of Kruskal and Prim, pages 567–574. MIT Press and McGraw-Hill, 2nd edition, 2001.

  • [16] R. Cramer, I. Damgård, and J. B. Nielsen. Multiparty computation from threshold homomorphic encryption. In B. Pfitzmann, editor, EUROCRYPT, volume 2045 of Lecture Notes in Computer Science, pages 280–299. Springer, 2001.

  • [17] I. Damgård, M. Fitzi, E. Kiltz, J. B. Nielsen, and T. Toft. Unconditionally secure constant-rounds multi-party computation for equality, comparison, bits and exponentiation. In S. Halevi and T. Rabin, editors, TCC, volume 3876 of Lecture Notes in Computer Science, pages 285–304. Springer, 2006.

  • [18] I. Damgård, M. Geisler, M. Krøigaard, and J. B. Nielsen. Asynchronous Multiparty Computation: Theory and Implementation. In S. Jarecki and G. Tsudik, editors, Public Key Cryptography, volume 5443 of Lecture Notes in Computer Science, pages 160–179. Springer, 2009.

  • [19] I. Damgård, M. Keller, E. Larraia, V. Pastro, P. Scholl, and N. P. Smart. Practical Covertly Secure MPC for Dishonest Majority - Or: Breaking the SPDZ Limits. In J. Crampton, S. Jajodia, and K. Mayes, editors, ESORICS, volume 8134 of Lecture Notes in Computer Science, pages 1–18. Springer, 2013.

  • [20] I. Damgård, S. Meldgaard, and J. B. Nielsen. Perfectly secure oblivious ram without random oracles. In Y. Ishai, editor, TCC, volume 6597 of Lecture Notes in Computer Science, pages 144–163. Springer, 2011.

  • [21] I. Damgård and J. B. Nielsen. Universally composable efficient multiparty computation from threshold homomorphic encryption. In D. Boneh, editor, CRYPTO, volume 2729 of Lecture Notes in Computer Science, pages 247–264. Springer, 2003.

  • [22] D. Demmler, T. Schneider, and M. Zohner. ABY - A frame-work for efficient mixed-protocol secure two-party computation. In 22nd Annual Network and Distributed System Security Symposium, NDSS 2015, San Diego, California, USA, February 8-11, 2014. The Internet Society, 2015.

  • [23] H. Ebadi, D. Sands, and G. Schneider. Differential privacy: Now it’s getting personal. In S. K. Rajamani and D. Walker, editors, Proceedings of the 42nd Annual ACM SIGPLANSIGACT Symposium on Principles of Programming Languages, POPL 2015, Mumbai, India, January 15-17, 2015, pages 69–81. ACM, 2015.

  • [24] R. Gennaro, M. O. Rabin, and T. Rabin. Simplified vss and fact-track multiparty computations with applications to threshold cryptography. In PODC, pages 101–111, 1998.

  • [25] C. Gentry, K. A. Goldman, S. Halevi, C. S. Jutla, M. Raykova, and D. Wichs. Optimizing oram and using it efficiently for secure computation. In E. D. Cristofaro and M. Wright, editors, Privacy Enhancing Technologies, volume 7981 of Lecture Notes in Computer Science, pages 1–18. Springer, 2013.

  • [26] C. Gentry, S. Halevi, C. Jutla, and M. Raykova. Private Database Access With HE-over-ORAM Architecture. Cryptology ePrint Archive, Report 2014/345, 2014. http://eprint.iacr.org/.

  • [27] O. Goldreich, S. Micali, and A. Wigderson. How to Play any Mental Game or A Completeness Theorem for Protocols with Honest Majority. In STOC, pages 218–229. ACM, 1987.

  • [28] O. Goldreich and R. Ostrovsky. Software Protection and Simulation on Oblivious RAMs. J. ACM, 43(3):431–473, 1996.

  • [29] S. D. Gordon, J. Katz, V. Kolesnikov, F. Krell, T. Malkin, M. Raykova, and Y. Vahlis. Secure Two-Party Computation in Sublinear (Amortized) Time. In T. Yu, G. Danezis, and V. D. Gligor, editors, the ACM Conference on Computer and Communications Security, CCS’12, Raleigh, NC, USA, October 16-18, 2012, pages 513–524. ACM, 2012.

  • [30] K. Hamada, R. Kikuchi, D. Ikarashi, K. Chida, and K. Takahashi. Practically efficient multi-party sorting protocols from comparison sort algorithms. In T. Kwon, M.-K. Lee, and D. Kwon, editors, ICISC, volume 7839 of Lecture Notes in Computer Science, pages 202–216. Springer, 2012.

  • [31] W. Henecka, S. Kögl, A.-R. Sadeghi, T. Schneider, and I. Wehrenberg. TASTY: tool for automating secure two-party computations. In CCS ’10: Proceedings of the 17th ACM conference on Computer and communications security, pages 451–462, New York, NY, USA, 2010. ACM.

  • [32] Y. Huang, D. Evans, and J. Katz. Private Set Intersection: Are Garbled Circuits Better than Custom Protocols? In 19th Annual Network and Distributed System Security Symposium, NDSS 2012, San Diego, California, USA, February 5-8, 2012. The Internet Society, 2012.

  • [33] J. JáJá. An Introduction to Parallel Algorithms. Addison-Wesley, 1992.

  • [34] M. Keller and P. Scholl. Efficient, Oblivious Data Structures for MPC. In P. Sarkar and T. Iwata, editors, Advances in Cryptology - ASIACRYPT 2014 - 20th International Conference on the Theory and Application of Cryptology and Information Security, Kaoshiung, Taiwan, R.O.C., December 7-11, 2014, Proceedings, Part II, volume 8874 of Lecture Notes in Computer Science, pages 506–525. Springer, 2014.

  • [35] M. Keller, P. Scholl, and N. P. Smart. An architecture for practical actively secure mpc with dishonest majority. In Sadeghi et al. [47], pages 549–560.

  • [36] V. Kolesnikov and T. Schneider. A practical universal circuit construction and secure evaluation of private functions. In G. Tsudik, editor, Financial Cryptography, volume 5143 of Lecture Notes in Computer Science, pages 83–97. Springer, 2008.

  • [37] E. Kushilevitz, S. Lu, and R. Ostrovsky. On the (in)security of hash-based oblivious RAM and a new balancing scheme. In Y. Rabani, editor, Proceedings of the Twenty-Third Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2012, Kyoto, Japan, January 17-19, 2012, pages 143–156. SIAM, 2012.

  • [38] P. Laud and J. Willemson. Composable oblivious extended permutations. In F. Cuppens, J. García-Alfaro, A. N. Z. Heywood, and P. W. L. Fong, editors, Foundations and Practice of Security - 7th International Symposium, FPS 2014, Montreal, QC, Canada, November 3-5, 2014. Revised Selected Papers, volume 8930 of Lecture Notes in Computer Science, pages 294–310. Springer, 2014.

  • [39] J. Launchbury, I. S. Diatchki, T. DuBuisson, and A. Adams-Moran. Efficient lookup-table protocol in secure multiparty computation. In P. Thiemann and R. B. Findler, editors, ICFP, pages 189–200. ACM, 2012.

  • [40] S. Laur, J. Willemson, and B. Zhang. Round-Efficient Oblivious Database Manipulation. In Proceedings of the 14th International Conference on Information Security. ISC’11, pages 262–277, 2011.

  • [41] H. Lipmaa and T. Toft. Secure equality and greater-than tests with sublinear online complexity. In F. V. Fomin, R. Freivalds, M. Z. Kwiatkowska, and D. Peleg, editors, ICALP (2), volume 7966 of Lecture Notes in Computer Science, pages 645–656. Springer, 2013.

  • [42] C. Liu, Y. Huang, E. Shi, J. Katz, and M. W. Hicks. Automating efficient ram-model secure computation. In 2014 IEEE Symposium on Security and Privacy, SP 2014, Berkeley, CA, USA, May 18-21, 2014, pages 623–638. IEEE Computer Society, 2014.

  • [43] L. Malka. Vmcrypt: modular software architecture for scalable secure computation. In Y. Chen, G. Danezis, and V. Shmatikov, editors, Proceedings of the 18th ACM Conference on Computer and Communications Security, CCS 2011, Chicago, Illinois, USA, October 17-21, 2011, pages 715–724. ACM, 2011.

  • [44] P. Mohassel and S. S. Sadeghian. How to Hide Circuits in MPC: an Efficient Framework for Private Function Evaluation. In T. Johansson and P. Q. Nguyen, editors, EUROCRYPT, volume 7881 of Lecture Notes in Computer Science, pages 557–574. Springer, 2013.

  • [45] J. Nešetřil, E. Milkovà, and H. Nešetřilovà. Otakar Borůvka on minimum spanning tree problem; Translation of both the 1926 papers, comments, history. Discrete Mathematics, 233(1-3):3–36, 2001.

  • [46] T. Nishide and K. Ohta. Multiparty computation for interval, equality, and comparison without bit-decomposition protocol. In T. Okamoto and X. Wang, editors, Public Key Cryptography, volume 4450 of Lecture Notes in Computer Science, pages 343–360. Springer, 2007.

  • [47] A. Sadeghi, V. D. Gligor, and M. Yung, editors. 2013 ACM SIGSAC Conference on Computer and Communications Security, CCS’13, Berlin, Germany, November 4-8, 2013. ACM, 2013.

  • [48] A. Shamir. How to share a secret. Commun. ACM, 22(11):612–613, 1979.

  • [49] E. Shi, T. H. Chan, E. Stefanov, and M. Li. Oblivious RAM with O((logN)3) worst-case cost. In D. H. Lee and X. Wang, editors, Advances in Cryptology - ASIACRYPT 2011 - 17th International Conference on the Theory and Application of Cryptology and Information Security, Seoul, South Korea, December 4-8, 2011. Proceedings, volume 7073 of Lecture Notes in Computer Science, pages 197–214. Springer, 2011.

  • [50] S. Siim. Privacy-Preserving String Matching with PRAM Algorithms. Cryptography Seminar report, University of Tartu, 12 2014. https://courses.cs.ut.ee/MTAT.07.022/2014_fall/uploads/Main/sander-report-f14.pdf.

  • [51] E. Stefanov, M. van Dijk, E. Shi, C. W. Fletcher, L. Ren, X. Yu, and S. Devadas. Path ORAM: an extremely simple oblivious RAM protocol. In Sadeghi et al. [47], pages 299–310.

  • [52] T. Toft. Secure data structures based on multi-party computation. In C. Gavoille and P. Fraigniaud, editors, Proceedings of the 30th Annual ACM Symposium on Principles of Distributed Computing, PODC 2011, San Jose, CA, USA, June 6-8, 2011, pages 291–292. ACM, 2011. Full version in Cryptology ePrint archive, http://eprint.iacr.org/2011/081.

  • [53] A. Waksman. A permutation network. J. ACM, 15(1):159–163, 1968.

  • [54] X. S. Wang, Y. Huang, T. H. Chan, A. Shelat, and E. Shi. SCORAM: Oblivious RAM for Secure Computation. In G. Ahn, M. Yung, and N. Li, editors, Proceedings of the 2014 ACM SIGSAC Conference on Computer and Communications Security, Scottsdale, AZ, USA, November 3-7, 2014, pages 191–202. ACM, 2014.

  • [55] J. Wassenberg, W. Middelmann, and P. Sanders. An efficient parallel algorithm for graph-based image segmentation. In X. Jiang and N. Petkov, editors, Computer Analysis of Images and Patterns, 13th International Conference, CAIP 2009, Münster, Germany, September 2-4, 2009. Proceedings, volume 5702 of Lecture Notes in Computer Science, pages 1003–1010. Springer, 2009.

  • [56] Y. Xu, V. Olman, and D. Xu. Clustering gene expression data using a graph-theoretic approach: an application of minimum spanning trees. Bioinformatics, 18(4):536–545, 2002.

  • [57] A. C.-C. Yao. Protocols for secure computations (extended abstract). In FOCS, pages 160–164. IEEE, 1982.

  • [58] S. Zahur and D. Evans. Circuit structures for improving efficiency of security and privacy tools. In 2013 IEEE Symposium on Security and Privacy, SP 2013, Berkeley, CA, USA, May 19-22, 2013, pages 493–507. IEEE Computer Society, 2013.

Received: 2015-02-15

Revised: 2015-05-09

Accepted: 2015-05-15

Published Online: 2015-06-22

Published in Print: 2015-06-01

Citation Information: Proceedings on Privacy Enhancing Technologies. Volume 2015, Issue 2, Pages 188–205, ISSN (Online) 2299-0984, DOI: https://doi.org/10.1515/popets-2015-0011, June 2015

© Peeter Laud. This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License. (CC BY-NC-ND 3.0)

Comments (0)

Please log in or register to comment.