Accelerating the Secure Distributed Computation of the Mean by a Chebyshev Expansion

  • Peter Lory
  • Manuel Liedel
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7372)


Lindell and Pinkas (2002) have proposed the idea of using the techniques of secure multi-party computations to generate efficient algorithms for privacy preserving data-mining. In this context Kiltz, Leander, and Malone-Lee (2005) have presented a protocol for the secure distributed computation of the mean and related statistics in a two-party setting. Their protocol achieves constant round complexity. As a novel suggestion we use a Chebyshev expansion to accelerate this protocol. This approach considerably reduces the overhead of the protocol in terms of both computation and communication. The proposed technique can be applied to other protocols in the field of privacy preserving data-mining as well.


Privacy preserving data mining secure two-party computations oblivious polynomial evaluation Chebyshev expansion 


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  1. 1.
    Algesheimer, J., Camenisch, J., Shoup, V.: Efficient Computation Modulo a Shared Secret with Application to the Generation of Shared Safe-Prime Products. In: Yung, M. (ed.) CRYPTO 2002. LNCS, vol. 2442, pp. 417–432. Springer, Heidelberg (2002)CrossRefGoogle Scholar
  2. 2.
    Bulirsch, R., Stoer, J.: Darstellung von Funktionen in Rechenautomaten. In: Sauer, R., Szabó, I. (eds.) Mathematische Hilfsmittel des Ingenieurs. Grundlehren der mathematischen Wissenschaften, vol. 141, pp. 352–446. Springer, Berlin (1968)Google Scholar
  3. 3.
    Chang, Y.-C., Lu, C.-J.: Oblivious Polynomial Evaluation and Oblivious Neural Learning. In: Boyd, C. (ed.) ASIACRYPT 2001. LNCS, vol. 2248, pp. 369–384. Springer, Heidelberg (2001)CrossRefGoogle Scholar
  4. 4.
    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
  5. 5.
    The GNU Multiple Precision Arithmetic Library, Edition 5.0.3 (2012),
  6. 6.
    Kiltz, E., Leander, G., Malone-Lee, J.: Secure Computation of the Mean and Related Statistics. In: Kilian, J. (ed.) TCC 2005. LNCS, vol. 3378, pp. 283–302. Springer, Heidelberg (2005)CrossRefGoogle Scholar
  7. 7.
    Lindell, Y., Pinkas, B.: Privacy preserving data mining. Journal of Cryptology 15, 177–206 (2002)MathSciNetzbMATHCrossRefGoogle Scholar
  8. 8.
    Mason, J.C., Handscomb, D.C.: Chebyshev Polynomials. Chapman & Hall/CRC, Boca Raton (2003)zbMATHGoogle Scholar
  9. 9.
    Naor, M., Pinkas, B.: Oblivious transfer and polynomial evaluation. In: Vitter, J.S., Larmore, L., Leighton, T. (eds.) Proceedings of the 31st ACM Symposium on Theory of Computing (STOC 1999), pp. 245–254. ACM Press (1999)Google Scholar
  10. 10.
    Naor, M., Pinkas, B.: Efficient oblivious transfer protocols. In: Proceedings of the 12th Annual ACM–SIAM Symposium on Discrete Algorithms (SODA 2001), pp. 448–457. Society for Industrial and Applied Mathematics (2001)Google Scholar
  11. 11.
    Naor, M., Pinkas, B.: Computationally secure oblivious transfer. Journal of Cryptology 18, 1–35 (2005)MathSciNetzbMATHCrossRefGoogle Scholar
  12. 12.
    Naor, M., Pinkas, B.: Oblivious polynomial evaluation. SIAM Journal on Computing 35(5), 1254–1281 (2006)MathSciNetzbMATHCrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Peter Lory
    • 1
  • Manuel Liedel
    • 1
  1. 1.University of RegensburgRegensburgGermany

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