Private Computations in Networks: Topology versus Randomness

  • Andreas Jakoby
  • Maciej Liśkiewicz
  • Rüdiger Reischuk
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 2607)


In a distributed network, computing a function privately requires that no participant gains any additional knowledge other than the value of the function.We study this problem for incomplete networks and establish a tradeoff between connectivity properties of the network and the amount of randomness needed. First, a general lower bound on the number of random bits is shown. Next, for every k ≥2 we design a quite efficient (with respect to randomness) protocol for symmetric functions that works in arbitrary k-connected networks. Finally, for directed cycles that compute threshold functions privately almost matching lower and upper bounds for the necessary amount of randmoness are proven.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    J. Bar-Ilan, D. Beaver, Non-Cryptographic Fault-Tolerant Computing in Constant Number of Rounds of Interaction, Proc. 8. PODC, 1989, 201–209.Google Scholar
  2. 2.
    M. Bläser, A. Jakoby, M. Liśkiewicz, and B. Siebert, Private Computation-kconnected versus 1-connected Networks, Proc. 22. CRYPTO, 2002, 194–209.Google Scholar
  3. 3.
    C. Blundo, A. De Santis, G. Persiano, U. Vaccaro, On the Number of Random Bits in Totally Private Computation, Proc. 22. ICALP, 1995, 171–182.Google Scholar
  4. 4.
    M. Ben-Or, S. Goldwasser, A. Wigderson, Completeness Theorem for Non cryptographic Fault-tolerant Distributed Computing, Proc. 20. STOC, 1988, 1–10.Google Scholar
  5. 5.
    D. Chaum, C. Crépeau, I. Damgård, Multiparty unconditionally secure protocols, Proc. 20. STOC, 1988, 11–19.Google Scholar
  6. 6.
    B. Chor, M. Geréb-Graus, E. Kushilevitz, Private Computations Over the Integers, SIAM J. Computing 24, 1995, 376–386.zbMATHCrossRefGoogle Scholar
  7. 7.
    B. Chor, E. Kushilevitz, A Communication-Privacy Tradeo. for Modular Addition, Information Processing Letters 45, 1993, 205–210.zbMATHCrossRefMathSciNetGoogle Scholar
  8. 8.
    R. Canetti, R. Ostrovsky, Secure Computation with Honest-Looking Parties: What if nobody is truly honest?, Proc. 31. STOC, 1999, 35–44.Google Scholar
  9. 9.
    Y. Egawa, R. Glas, S. C. Locke, Cycles and paths through specified vertices in kconnected graphs, Journal of Combinatorial Theory Series B 52, 1991, 20–29.zbMATHCrossRefMathSciNetGoogle Scholar
  10. 10.
    M. Franklin, M. Yung, Secure hypergraphs: privacy from partial broadcast (Extended Abstract), Proc. 27. STOC, 1995, 36–44.Google Scholar
  11. 11.
    A. Gál, A. Rosén, A Theorem on Sensitivity and Applications in Private Computation, Proc. 31. STOC, 1999, 348–357.Google Scholar
  12. 12.
    O. Goldreich, S. Micali, A. Wigderson, How to Play any Mental Game or a Completeness Theorem for Protocols with Honest Majority, 28. FOCS, 1987, 218–229.Google Scholar
  13. 13.
    E. Kushilevitz, R. Ostrovsky, A. Rosén, Characterizing Linear Size Circuits in Terms of Privacy, Proc. 28. STOC, 1996, 541–550.Google Scholar
  14. 14.
    E. Kushilevitz, Y. Mansour, Randomness in Private Computations, SIAM J. Discrete Math 10, 1997, 647–661.zbMATHCrossRefMathSciNetGoogle Scholar
  15. 15.
    E. Kushilevitz, A. Rosén, A Randomness-Rounds Tradeo. in Private Computation, SIAM J. Discrete Math 11, 1998, 61–80.zbMATHCrossRefMathSciNetGoogle Scholar
  16. 16.
    E. Kushilevitz, Privacy and Communication Complexity, SIAM J. Discrete Math 5, 1992, 273–284.zbMATHCrossRefMathSciNetGoogle Scholar
  17. 17.
    A. C. Yao, Protocols for Secure Computations, Proc. 23. FOCS, 1982, 160–164.Google Scholar
  18. 18.
    A. C. Yao, How to generate and exchange secrets, Proc. 27. FOCS, 1986, 162–167.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2003

Authors and Affiliations

  • Andreas Jakoby
    • 1
  • Maciej Liśkiewicz
    • 1
  • Rüdiger Reischuk
    • 1
  1. 1.Institut für Theoretische InformatikUniversität zu LübeckGermany

Personalised recommendations