Quadratic Error Minimization in a Distributed Environment with Privacy Preserving

  • Gérald Gavin
  • Julien Velcin
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6549)


In this paper, we address the issue of privacy preserving data-mining. Specifically, we consider a scenario where each member j of T parties has its own private database. The party j builds a private classifier h j for predicting a binary class variable y. The aim of this paper consists in aggregating these classifiers h j in order to improve the individual predictions. Precisely, the parties wish to compute an efficient linear combinations over their classifier in a secure manner.


Encryption Scheme Generalization Error Privacy Preserve Quadratic Error Gradient Descent Algorithm 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Bartlett, P.L.: For valid generalization the size of the weights is more important than the size of the network. In: NIPS, pp. 134–140 (1996)Google Scholar
  2. 2.
    Boneh, D., Goh, E.-J., Nissim, K.: Evaluating 2-dnf formulas on ciphertexts. In: Kilian, J. (ed.) TCC 2005. LNCS, vol. 3378, pp. 325–341. Springer, Heidelberg (2005)CrossRefGoogle Scholar
  3. 3.
    Canetti, R.: Universally composable security: A new paradigm for cryptographic protocols. In: FOCS, pp. 136–145 (2001)Google Scholar
  4. 4.
    Cesa-Bianchi, N., Lugosi, G., Stoltz, G.: Minimizing regret with label efficient prediction. IEEE Transactions on Information Theory 51(6), 2152–2162 (2005)MathSciNetCrossRefzbMATHGoogle Scholar
  5. 5.
    Chen, T., Zhong, S.: Privacy-preserving backpropagation neural network learning. Trans. Neur. Netw. 20(10), 1554–1564 (2009)CrossRefGoogle Scholar
  6. 6.
    Cramer, R., Damgård, I., Nielsen, J.B.: Multiparty computation from threshold homomorphic encryption. In: Pfitzmann, B. (ed.) EUROCRYPT 2001. LNCS, vol. 2045, pp. 280–299. Springer, Heidelberg (2001)CrossRefGoogle Scholar
  7. 7.
    Damgård, I., Jurik, M.: A generalisation, a simplification and some applications of paillier’s probabilistic public-key system. In: Kim, K.-c. (ed.) PKC 2001. LNCS, vol. 1992, pp. 119–136. Springer, Heidelberg (2001)CrossRefGoogle Scholar
  8. 8.
    Elgamal, T.: A public key cryptosystem and a signature sheme based on discrete logarithms. IEEE Transactions on Information Theory 31, 469–472 (1985)MathSciNetCrossRefzbMATHGoogle Scholar
  9. 9.
    Fouque, P., Stern, J.: Fully distributed threshold rsa under standard assumptions. In: IACR Cryptology ePrint Archive: Report 2001/2008 (February 2001)Google Scholar
  10. 10.
    Gambs, S., Kégl, B., Aïmeur, E.: Privacy-preserving boosting. Data Min. Knowl. Discov. 14(1), 131–170 (2007)MathSciNetCrossRefGoogle Scholar
  11. 11.
    Garay, J.A., Schoenmakers, B., Villegas, J.: Practical and secure solutions for integer comparison. In: Okamoto, T., Wang, X. (eds.) PKC 2007. LNCS, vol. 4450, pp. 330–342. Springer, Heidelberg (2007)CrossRefGoogle Scholar
  12. 12.
    Goldwasser, S., Micali, S., Rackoff, C.: The knowledge complexity of interactive proof-systems (extended abstract). In: STOC, pp. 291–304 (1985)Google Scholar
  13. 13.
    Han, S., Ng, W.K., Wan, L., Lee, V.C.S.: Privacy-preserving gradient-descent methods. IEEE Trans. Knowl. Data Eng. 22(6), 884–899 (2010)CrossRefGoogle Scholar
  14. 14.
    Guajardo, J., Mennink, B., Schoenmakers, B.: Modulo reduction for paillier encryptions and application to secure statistical analysis. In: Sion, R. (ed.) FC 2010. LNCS, vol. 6052, pp. 375–382. Springer, Heidelberg (2010)CrossRefGoogle Scholar
  15. 15.
    Lindell, Y., Pinkas, B.: Privacy preserving data mining. In: Bellare, M. (ed.) CRYPTO 2000. LNCS, vol. 1880, pp. 36–54. Springer, Heidelberg (2000)CrossRefGoogle Scholar
  16. 16.
    Goldreich, O., Michali, S., Wigderson, A.: How to play any mental game or a completeness theorem for protocols with honest majority. In: STOC, pp. 218–229 (1987)Google Scholar
  17. 17.
    Paillier, P.: Public-key cryptosystems based on composite degree residuosity classes. In: Stern, J. (ed.) EUROCRYPT 1999. LNCS, vol. 1592, pp. 223–238. Springer, Heidelberg (1999)CrossRefGoogle Scholar
  18. 18.
    Ross Quinlan, J.: C4.5: Programs for Machine Learning. Morgan Kaufmann, San Francisco (1993)Google Scholar
  19. 19.
    Schapire, R.E.: Theoretical views of boosting. In: Fischer, P., Simon, H.U. (eds.) EuroCOLT 1999. LNCS (LNAI), vol. 1572, pp. 1–10. Springer, Heidelberg (1999)CrossRefGoogle Scholar
  20. 20.
    Schapire, R.E., Freund, Y., Barlett, P., Lee, W.S.: Boosting the margin: A new explanation for the effectiveness of voting methods. In: ICML, pp. 322–330 (1997)Google Scholar
  21. 21.
    Schoenmakers, B., Tuyls, P.: Efficient binary conversion for paillier encrypted values. In: Vaudenay, S. (ed.) EUROCRYPT 2006. LNCS, vol. 4004, pp. 522–537. Springer, Heidelberg (2006)CrossRefGoogle Scholar
  22. 22.
    Vaidya, J., Clifton, C., Kantarcioglu, M., Scott Patterson, A.: Privacy-preserving decision trees over vertically partitioned data. TKDD 2(3) (2008)Google Scholar
  23. 23.
    Vapnik, V.: Principles of risk minimization for learning theory. In: NIPS, pp. 831–838 (1991)Google Scholar
  24. 24.
    Yu, H., Vaidya, J., Jiang, X.: Privacy-preserving svm classification on vertically partitioned data. In: Ng, W.-K., Kitsuregawa, M., Li, J., Chang, K. (eds.) PAKDD 2006. LNCS (LNAI), vol. 3918, pp. 647–656. Springer, Heidelberg (2006)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  • Gérald Gavin
    • 1
  • Julien Velcin
    • 1
  1. 1.Laboratory ERICUniversity of LyonFrance

Personalised recommendations