Generalized Universal Circuits for Secure Evaluation of Private Functions with Application to Data Classification

  • Ahmad-Reza Sadeghi
  • Thomas Schneider
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5461)


Secure Evaluation of Private Functions (PF-SFE) allows two parties to compute a private function which is known by one party only on private data of both. It is known that PF-SFE can be reduced to Secure Function Evaluation (SFE) of a Universal Circuit (UC). Previous UC constructions only simulated circuits with gates of d = 2 inputs while gates with d > 2 inputs were decomposed into many gates with 2 inputs which is inefficient for large d as the size of UC heavily depends on the number of gates.

We present generalized UC constructions to efficiently simulate any circuit with gates of d ≥ 2 inputs having efficient circuit representation. Our constructions are non-trivial generalizations of previously known UC constructions.

As application we show how to securely evaluate private functions such as neural networks (NN) which are increasingly used in commercial applications. Our provably secure PF-SFE protocol needs only one round in the semi-honest model (or even no online communication at all using non-interactive oblivious transfer) and evaluates a generalized UC that entirely hides the structure of the private NN. This enables applications like privacy-preserving data classification based on private NNs without trusted third party while simultaneously protecting user’s data and NN owner’s intellectual property.


universal circuits secure evaluation of private functions neural networks private data classification privacy 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Aiello, W., Ishai, Y., Reingold, O.: Priced oblivious transfer: How to sell digital goods. In: Pfitzmann, B. (ed.) EUROCRYPT 2001. LNCS, vol. 2045, pp. 119–135. Springer, Heidelberg (2001)CrossRefGoogle Scholar
  2. 2.
    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
  3. 3.
    Drewes, R.: An artifical neural network spam classifier (August 2002),
  4. 4.
    Gorman, R.P., Sejnowski, T.J.: Analysis of hidden units in a layered network trained to classify sonar targets. Neural Networks 1(1), 75–89 (1988)CrossRefGoogle Scholar
  5. 5.
    Goyal, V., Mohassel, P., Smith, A.: Efficient two party and multi party computation against covert adversaries. In: Smart, N.P. (ed.) EUROCRYPT 2008. LNCS, vol. 4965, pp. 289–306. Springer, Heidelberg (2008)CrossRefGoogle Scholar
  6. 6.
    Gunupudi, V., Tate, S.R.: Generalized non-interactive oblivious transfer using count-limited objects with applications to secure mobile agents. In: Tsudik, G. (ed.) FC 2008. LNCS, vol. 5143, pp. 98–112. Springer, Heidelberg (2008)CrossRefGoogle Scholar
  7. 7.
    Hornik, K., Stinchcombe, M., White, H.: Multilayer feedforward networks are universal approximators. Neural Networks 2(5), 359–366 (1989)CrossRefGoogle Scholar
  8. 8.
    Ishai, Y., Kilian, J., Nissim, K., Petrank, E.: Extending Oblivious Transfers Efficiently. In: Boneh, D. (ed.) CRYPTO 2003. LNCS, vol. 2729, pp. 145–161. Springer, Heidelberg (2003)CrossRefGoogle Scholar
  9. 9.
    Kolesnikov, V., Schneider, T.: Improved garbled circuit: Free XOR gates and applications. In: Aceto, L., Damgård, I., Goldberg, L.A., Halldórsson, M.M., Ingólfsdóttir, A., Walukiewicz, I. (eds.) ICALP 2008, Part II. LNCS, vol. 5126, pp. 486–498. Springer, Heidelberg (2008)CrossRefGoogle Scholar
  10. 10.
    Kolesnikov, V., Schneider, T.: A practical universal circuit construction and secure evaluation of private functions. In: Tsudik, G. (ed.) FC 2008. LNCS, vol. 5143, pp. 83–97. Springer, Heidelberg (2008), CrossRefGoogle Scholar
  11. 11.
    Lindell, Y., Pinkas, B., Smart, N.: Implementing two-party computation efficiently with security against malicious adversaries. In: Ostrovsky, R., De Prisco, R., Visconti, I. (eds.) SCN 2008. LNCS, vol. 5229, pp. 2–20. Springer, Heidelberg (2008)CrossRefGoogle Scholar
  12. 12.
    Lindell, Y., Pinkas, B.: A proof of Yao’s protocol for secure two-party computation. Cryptology ePrint Archive, Report 2004/175 (2004)Google Scholar
  13. 13.
    Lindell, Y., Pinkas, B.: An efficient protocol for secure two-party computation in the presence of malicious adversaries. In: Naor, M. (ed.) EUROCRYPT 2007. LNCS, vol. 4515, pp. 52–78. Springer, Heidelberg (2007)CrossRefGoogle Scholar
  14. 14.
    Malkhi, D., Nisan, N., Pinkas, B., Sella, Y.: Fairplay — a secure two-party computation system. In: USENIX (2004),
  15. 15.
    Orlandi, C., Piva, A., Barni, M.: Oblivious neural network computing via homomorphic encryption. European Journal of Information Systems (EURASIP) 2007(1), 1–10 (2007)Google Scholar
  16. 16.
    Pinkas, B.: Cryptographic techniques for privacy-preserving data mining. SIGKDD Explor. Newsl. 4(2), 12–19 (2002)MathSciNetCrossRefGoogle Scholar
  17. 17.
    Piva, A., Caini, M., Bianchi, T., Orlandi, C., Barni, M.: Enhancing privacy in remote data classification. In: New Approaches for Security, Privacy and Trust in Complex Environments (SEC 2008) (2008)Google Scholar
  18. 18.
    Plagianakos, V.P., Vrahatis, M.N.: Parallel evolutionary training algorithms for hardware-friendly neural networks. Natural Computing 1(2-3), 307–322 (2002)MathSciNetCrossRefzbMATHGoogle Scholar
  19. 19.
    Rabin, M.O.: How to exchange secrets with oblivious transfer. Technical report, Harward University, Available at Cryptology ePrint Archive, Report 2005/187 (1981)Google Scholar
  20. 20.
    Sander, T., Young, A., Yung, M.: Non-interactive cryptocomputing for NC 1. In: Proc. 40th IEEE Symp. on Foundations of Comp. Science, FOCS 1999, New York, pp. 554–566. IEEE, Los Alamitos (1999)Google Scholar
  21. 21.
    Sato, K., Hikawa, H.: Implementation of multilayer neural network with threshold neurons and its analysis. Artificial Life and Robotics 3(3), 170–175 (1999)CrossRefGoogle Scholar
  22. 22.
    Schneider, T.: Practical secure function evaluation. Master’s thesis, University of Erlangen-Nuremberg (2008),
  23. 23.
    StatSoft, Inc. STATISTICA Automated Neural Networks (2008),
  24. 24.
    Tebelskis, J.: Speech Recognition using Neural Networks. PhD thesis, School of Computer Science, Pittsburgh (1995)Google Scholar
  25. 25.
    Valiant, L.G.: Universal circuits (preliminary report). In: STOC 1976, pp. 196–203. ACM Press, New York (1976)Google Scholar
  26. 26.
    Waksman, A.: A permutation network. J. ACM 15(1), 159–163 (1968)MathSciNetCrossRefzbMATHGoogle Scholar
  27. 27.
    Yao, A.C.: How to generate and exchange secrets. In: FOCS 1986, Toronto, pp. 162–167. IEEE, Los Alamitos (1986)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2009

Authors and Affiliations

  • Ahmad-Reza Sadeghi
    • 1
  • Thomas Schneider
    • 1
  1. 1.Horst Görtz Institute for IT-SecurityRuhr-University BochumGermany

Personalised recommendations