Practically Efficient Multi-party Sorting Protocols from Comparison Sort Algorithms

  • Koki Hamada
  • Ryo Kikuchi
  • Dai Ikarashi
  • Koji Chida
  • Katsumi Takahashi
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7839)


Sorting is one of the most important primitives in various systems, for example, database systems, since it is often the dominant operation in the running time of an entire system. Therefore, there is a long list of work on improving its efficiency. It is also true in the context of secure multi-party computation (MPC), and several MPC sorting protocols have been proposed. However, all existing MPC sorting protocols are based on less efficient sorting algorithms, and the resultant protocols are also inefficient. This is because only a method for converting data-oblivious algorithms to corresponding MPC protocols is known, despite the fact that most efficient sorting algorithms such as quicksort and merge sort are not data-oblivious. We propose a simple and general approach of converting non-data-oblivious comparison sort algorithms, which include the above algorithms, into corresponding MPC protocols. We then construct an MPC sorting protocol from the well known efficient sorting algorithm, quicksort, with our approach. The resultant protocol is practically efficient since it significantly improved the running time compared to existing protocols in experiments.


Multi-party protocol sorting comparison sort secret sharing unconditional security 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Ajtai, M., Komlós, J., Szemerédi, E.: An O(n log n) sorting network. In: STOC, pp. 1–9. ACM (1983)Google Scholar
  2. 2.
    Batcher, K.E.: Sorting networks and their applications. In: AFIPS Spring Joint Computing Conference, pp. 307–314 (1968)Google Scholar
  3. 3.
    Ben-David, A., Nisan, N., Pinkas, B.: Fairplaymp: a system for secure multi-party computation. In: Ning, P., Syverson, P.F., Jha, S. (eds.) ACM Conference on Computer and Communications Security, pp. 257–266. ACM (2008)Google Scholar
  4. 4.
    Ben-Or, M., Goldwasser, S., Wigderson, A.: Completeness theorems for non-cryptographic fault-tolerant distributed computation (extended abstract). In: [29], pp. 1–10Google Scholar
  5. 5.
    Blum, M., Floyd, R.W., Pratt, V.R., Rivest, R.L., Tarjan, R.E.: Time bounds for selection. J. Comput. Syst. Sci. 7(4), 448–461 (1973)CrossRefzbMATHMathSciNetGoogle Scholar
  6. 6.
    Bogdanov, D., Laur, S., Willemson, J.: Sharemind: A framework for fast privacy-preserving computations. In: Jajodia, S., Lopez, J. (eds.) ESORICS 2008. LNCS, vol. 5283, pp. 192–206. Springer, Heidelberg (2008)CrossRefGoogle Scholar
  7. 7.
    Burkhart, M., Strasser, M., Many, D., Dimitropoulos, X.A.: Sepia: Privacy-preserving aggregation of multi-domain network events and statistics. In: USENIX Security Symposium, pp. 223–240. USENIX Association (2010)Google Scholar
  8. 8.
    Chaum, D., Crépeau, C., Damgård, I.: Multiparty unconditionally secure protocols (extended abstract). In: [29], pp. 11–19Google Scholar
  9. 9.
    Cormen, T.H., Leiserson, C.E., Rivest, R.L., Stein, C.: Introduction to Algorithms, 2nd edn. MIT Press, Cambridge (2001)zbMATHGoogle Scholar
  10. 10.
    Damgård, I., Fitzi, M., Kiltz, E., Nielsen, J.B., Toft, T.: Unconditionally secure constant-rounds multi-party computation for equality, comparison, bits and exponentiation. In: Halevi, S., Rabin, T. (eds.) TCC 2006. LNCS, vol. 3876, pp. 285–304. Springer, Heidelberg (2006)CrossRefGoogle Scholar
  11. 11.
    Damgård, I., Ishai, Y.: Constant-round multiparty computation using a black-box pseudorandom generator. In: Shoup, V. (ed.) CRYPTO 2005. LNCS, vol. 3621, pp. 378–394. Springer, Heidelberg (2005)CrossRefGoogle Scholar
  12. 12.
    Damgård, I., Meldgaard, S., Nielsen, J.B.: Perfectly secure oblivious RAM without random oracles. In: Ishai, Y. (ed.) TCC 2011. LNCS, vol. 6597, pp. 144–163. Springer, Heidelberg (2011)CrossRefGoogle Scholar
  13. 13.
    Geisler, M.: Cryptographic Protocols: Theory and Implementation. PhD thesis, University of Aarhus (2010)Google Scholar
  14. 14.
    Goldreich, O.: The Foundations of Cryptography. Basic Applications, vol. 2. Cambridge University Press (2004)Google Scholar
  15. 15.
    Goldreich, O., Micali, S., Wigderson, A.: How to play any mental game or a completeness theorem for protocols with honest majority. In: STOC, pp. 218–229. ACM (1987)Google Scholar
  16. 16.
    Goodrich, M.T.: Randomized shellsort: A simple oblivious sorting algorithm. In: SODA, pp. 1262–1277 (2010)Google Scholar
  17. 17.
    Henecka, W., Kögl, S., Sadeghi, A.R., Schneider, T., Wehrenberg, I.: Tasty: tool for automating secure two-party computations. In: Al-Shaer, E., Keromytis, A.D., Shmatikov, V. (eds.) ACM Conference on Computer and Communications Security, pp. 451–462. ACM (2010)Google Scholar
  18. 18.
    Hoare, C.A.R.: Algorithm 65: find. Commun. ACM 4(7), 321–322 (1961)CrossRefGoogle Scholar
  19. 19.
    Huang, Y., Evans, D., Katz, J.: Private set intersection: Are garbled circuits better than custom protocols? In: NDSS (2012)Google Scholar
  20. 20.
    Jónsson, K.V., Kreitz, G., Uddin, M.: Secure multi-party sorting and applications. IACR Cryptology ePrint Archive 2011, 122 (2011)Google Scholar
  21. 21.
    Knuth, D.E.: Art of Computer Programming, 2nd edn. Sorting and Searching, vol. 3, ch. 5. Addison-Wesley Professional (1998)Google Scholar
  22. 22.
    Laur, S., Willemson, J., Zhang, B.: Round-efficient oblivious database manipulation. In: Lai, X., Zhou, J., Li, H. (eds.) ISC 2011. LNCS, vol. 7001, pp. 262–277. Springer, Heidelberg (2011)CrossRefGoogle Scholar
  23. 23.
    Malkhi, D., Nisan, N., Pinkas, B., Sella, Y.: Fairplay - secure two-party computation system. In: USENIX Security Symposium, pp. 287–302 (2004)Google Scholar
  24. 24.
    Ning, C., Xu, Q.: Multiparty computation for modulo reduction without bit-decomposition and a generalization to bit-decomposition. In: Abe, M. (ed.) ASIACRYPT 2010. LNCS, vol. 6477, pp. 483–500. Springer, Heidelberg (2010)CrossRefGoogle Scholar
  25. 25.
    Nishide, T., Ohta, K.: Multiparty computation for interval, equality, and comparison without bit-decomposition protocol. In: Okamoto, T., Wang, X. (eds.) PKC 2007. LNCS, vol. 4450, pp. 343–360. Springer, Heidelberg (2007)CrossRefGoogle Scholar
  26. 26.
    Obana, S., Araki, T.: Almost optimum secret sharing schemes secure against cheating for arbitrary secret distribution. In: Lai, X., Chen, K. (eds.) ASIACRYPT 2006. LNCS, vol. 4284, pp. 364–379. Springer, Heidelberg (2006)CrossRefGoogle Scholar
  27. 27.
    Ogata, W., Kurosawa, K.: Optimum secret sharing scheme secure against cheating. In: Maurer, U.M. (ed.) EUROCRYPT 1996. LNCS, vol. 1070, pp. 200–211. Springer, Heidelberg (1996)CrossRefGoogle Scholar
  28. 28.
    Shamir, A.: How to share a secret. Commun. ACM 22(11), 612–613 (1979)CrossRefzbMATHMathSciNetGoogle Scholar
  29. 29.
    Simon, J. (ed.): Proceedings of the 20th Annual ACM Symposium on Theory of Computing, STOC, Chicago, Illinois, USA, May 2-4. ACM (1988)Google Scholar
  30. 30.
    Skiena, S.S.: The Algorithm Design Manual, 2nd edn. Springer Publishing Company, Incorporated (2008)Google Scholar
  31. 31.
    Wang, G., Luo, T., Goodrich, M.T., Du, W., Zhu, Z.: Bureaucratic protocols for secure two-party sorting, selection, and permuting. In: ASIACCS, pp. 226–237 (2010)Google Scholar
  32. 32.
    Zhang, B.: Generic constant-round oblivious sorting algorithm for MPC. In: Boyen, X., Chen, X. (eds.) ProvSec 2011. LNCS, vol. 6980, pp. 240–256. Springer, Heidelberg (2011)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  • Koki Hamada
    • 1
  • Ryo Kikuchi
    • 1
  • Dai Ikarashi
    • 1
  • Koji Chida
    • 1
  • Katsumi Takahashi
    • 1
  1. 1.NTT Secure Platform LaboratoriesNTT CorporationMusashino-shiJapan

Personalised recommendations