Abstract
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.
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References
Ajtai, M., Komlós, J., Szemerédi, E.: An O(n log n) sorting network. In: STOC, pp. 1–9. ACM (1983)
Batcher, K.E.: Sorting networks and their applications. In: AFIPS Spring Joint Computing Conference, pp. 307–314 (1968)
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)
Ben-Or, M., Goldwasser, S., Wigderson, A.: Completeness theorems for non-cryptographic fault-tolerant distributed computation (extended abstract). In: [29], pp. 1–10
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)
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)
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)
Chaum, D., Crépeau, C., Damgård, I.: Multiparty unconditionally secure protocols (extended abstract). In: [29], pp. 11–19
Cormen, T.H., Leiserson, C.E., Rivest, R.L., Stein, C.: Introduction to Algorithms, 2nd edn. MIT Press, Cambridge (2001)
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)
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)
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)
Geisler, M.: Cryptographic Protocols: Theory and Implementation. PhD thesis, University of Aarhus (2010)
Goldreich, O.: The Foundations of Cryptography. Basic Applications, vol. 2. Cambridge University Press (2004)
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)
Goodrich, M.T.: Randomized shellsort: A simple oblivious sorting algorithm. In: SODA, pp. 1262–1277 (2010)
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)
Hoare, C.A.R.: Algorithm 65: find. Commun. ACM 4(7), 321–322 (1961)
Huang, Y., Evans, D., Katz, J.: Private set intersection: Are garbled circuits better than custom protocols? In: NDSS (2012)
Jónsson, K.V., Kreitz, G., Uddin, M.: Secure multi-party sorting and applications. IACR Cryptology ePrint Archive 2011, 122 (2011)
Knuth, D.E.: Art of Computer Programming, 2nd edn. Sorting and Searching, vol. 3, ch. 5. Addison-Wesley Professional (1998)
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)
Malkhi, D., Nisan, N., Pinkas, B., Sella, Y.: Fairplay - secure two-party computation system. In: USENIX Security Symposium, pp. 287–302 (2004)
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)
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)
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)
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)
Shamir, A.: How to share a secret. Commun. ACM 22(11), 612–613 (1979)
Simon, J. (ed.): Proceedings of the 20th Annual ACM Symposium on Theory of Computing, STOC, Chicago, Illinois, USA, May 2-4. ACM (1988)
Skiena, S.S.: The Algorithm Design Manual, 2nd edn. Springer Publishing Company, Incorporated (2008)
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)
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)
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Hamada, K., Kikuchi, R., Ikarashi, D., Chida, K., Takahashi, K. (2013). Practically Efficient Multi-party Sorting Protocols from Comparison Sort Algorithms. In: Kwon, T., Lee, MK., Kwon, D. (eds) Information Security and Cryptology – ICISC 2012. ICISC 2012. Lecture Notes in Computer Science, vol 7839. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-37682-5_15
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DOI: https://doi.org/10.1007/978-3-642-37682-5_15
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