A Practical Universal Circuit Construction and Secure Evaluation of Private Functions

  • Vladimir Kolesnikov
  • Thomas Schneider
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5143)


We consider general secure function evaluation (SFE) of private functions (PF-SFE). Recall, privacy of functions is often most efficiently achieved by general SFE [18,19,10] of a Universal Circuit (UC).

Our main contribution is a new simple and efficient UC construction. Our circuit UC k , universal for circuits of k gates, has size ~1.5 k log2 k and depth ~k logk. It is up to 50% smaller than the best UC (of Valiant [16], of size ~19klogk) for circuits of size up to ≈ 5000 gates.

Our improvement results in corresponding performance improvement of SFE of (small) private functions. Since, due to cost, only small circuits (i.e. < 5000 gates) are practical for PF-SFE, our construction appears to be the best fit for many practical PF-SFE.

We implement PF-SFE based on our UC and Fairplay SFE system [11].


SFE of private functions universal circuit privacy 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Blake, I.F., Kolesnikov, V.: Conditional encrypted mapping and comparing encrypted numbers. In: Di Crescenzo, G., Rubin, A. (eds.) FC 2006. LNCS, vol. 4107, pp. 206–220. Springer, Heidelberg (2006)CrossRefGoogle Scholar
  2. 2.
    Cachin, C., Camenisch, J., Kilian, J., Müller, J.: One-round secure computation and secure autonomous mobile agents. In: Welzl, E., Montanari, U., Rolim, J.D.P. (eds.) ICALP 2000. LNCS, vol. 1853, pp. 512–523. Springer, Heidelberg (2000)CrossRefGoogle Scholar
  3. 3.
    Di Crescenzo, G.: Private Selective Payment Protocols. In: Frankel, Y. (ed.) FC 2000. LNCS, vol. 1962. Springer, Heidelberg (2001)CrossRefGoogle Scholar
  4. 4.
    Even, S., Goldreich, O., Lempel, A.: A randomized protocol for signing contracts. Commun. ACM 28(6), 637–647 (1985)CrossRefMathSciNetGoogle Scholar
  5. 5.
    Fischlin, M.: A cost-effective pay-per-multiplication comparison method for millionaires. In: Naccache, D. (ed.) CT-RSA 2001. LNCS, vol. 2020, pp. 457–471. Springer, Heidelberg (2001)CrossRefGoogle Scholar
  6. 6.
    Frikken, K., Atallah, M., Zhang, C.: Privacy-preserving credit checking. In: EC 2005: Proceedings of the 6th ACM conference on Electronic commerce, pp. 147–154. ACM Press, New York (2005)CrossRefGoogle Scholar
  7. 7.
    Kantarcioglu, M., Clifton, C.: Privacy-preserving distributed mining of association rules on horizontally partitioned data. In: ACM SIGMOD Workshop on Research Issues on Data Mining and Knowledge Discovery (DMKD 2002) (2002)Google Scholar
  8. 8.
    Kolesnikov, V., Schneider, T.: FairplayPF,
  9. 9.
    Lindell, Y., Pinkas, B.: Privacy preserving data mining. In: Bellare, M. (ed.) CRYPTO 2000. LNCS, vol. 1880, pp. 20–24. Springer, Heidelberg (2000)CrossRefGoogle Scholar
  10. 10.
    Lindell, Y., Pinkas, B.: A proof of Yao’s protocol for secure two-party computation. Cryptology ePrint Archive, Report 2004/175 (2004)Google Scholar
  11. 11.
    Malkhi, D., Nisan, N., Pinkas, B., Sella, Y.: Fairplay — a secure two-party computation system. In: USENIX (2004)Google Scholar
  12. 12.
    Naor, M., Pinkas, B., Sumner, R.: Privacy preserving auctions and mechanism design. In: 1st ACM Conf. on Electronic Commerce (1999)Google Scholar
  13. 13.
    Ostrovsky, R., Skeith III, W.E.: Private Searching on Streaming Data. In: Shoup, V. (ed.) CRYPTO 2005. LNCS, vol. 3621, pp. 223–240. Springer, Heidelberg (2005)Google Scholar
  14. 14.
    Pinkas, B.: Cryptographic techniques for privacy-preserving data mining. SIGKDD Explor. Newsl. 4(2), 12–19 (2002)CrossRefGoogle Scholar
  15. 15.
    Sander, T., Young, A., Yung, M.: Non-interactive cryptocomputing for NC 1. In: Proc. 40th IEEE Symp. on Foundations of Comp. Science, New York, pp. 554–566. IEEE, Los Alamitos (1999)Google Scholar
  16. 16.
    Valiant, L.G.: Universal circuits (preliminary report). In: Proc. 8th ACM Symp. on Theory of Computing, pp. 196–203. ACM Press, New York (1976)Google Scholar
  17. 17.
    Waksman, A.: A permutation network. J. ACM 15(1), 159–163 (1968)CrossRefGoogle Scholar
  18. 18.
    Yao, A.C.: Protocols for secure computations. In: Proc. 23rd IEEE Symp. on Foundations of Comp. Science, Chicago, pp. 160–164. IEEE, Los Alamitos (1982)Google Scholar
  19. 19.
    Yao, A.C.: How to generate and exchange secrets. In: Proc. 27th IEEE Symp. on Foundations of Comp. Science, Toronto, pp. 162–167. IEEE, Los Alamitos (1986)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2008

Authors and Affiliations

  • Vladimir Kolesnikov
    • 1
  • Thomas Schneider
    • 2
  1. 1.Bell Laboratories USA
  2. 2.Dept. of Comp. Sci.University of Erlangen-NurembergGermany

Personalised recommendations