Collusion-Preserving Computation

  • Joël Alwen
  • Jonathan Katz
  • Ueli Maurer
  • Vassilis Zikas
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7417)


In collusion-free protocols, subliminal communication is impossible and parties are thus unable to communicate any information “beyond what the protocol allows.” Collusion-free protocols are interesting for several reasons, but have specifically attracted attention because they can be used to reduce trust in game-theoretic mechanisms. Collusion-free protocols are impossible to achieve (in general) when all parties are connected by point-to-point channels, but exist under certain physical assumptions (Lepinksi et al., STOC 2005) or when parties are connected in specific network topologies (Alwen et al., Crypto 2008).

We provide a “clean-slate” definition of the stronger notion of collusion preservation. Our goals in revisiting the definition are:
  • To give a definition with respect to arbitrary communication resources (including as special cases the communication models from prior work). We can then, in particular, better understand what types of resources enable collusion-preserving protocols.

  • To construct protocols that allow no additional subliminal communication when parties can communicate via other means. (This property is not implied by collusion-freeness.)

  • To support composition, so protocols can be designed in a modular fashion using sub-protocols run among subsets of the parties.

In addition to proposing the definition, we explore implications of our model and show a general feasibility result for collusion-preserving computation of arbitrary functionalities. We formalize a model for concurrently playing multiple extensive-form, mediated games while preserving many important equilibrium notions.


  1. 1.
    Abraham, I., Dolev, D., Gonen, R., Halpern, J.: Distributed computing meets game theory: robust mechanisms for rational secret sharing and multiparty computation. In: 25th ACM PODC, pp. 53–62. ACM Press (2006)Google Scholar
  2. 2.
    Abraham, I., Dolev, D., Halpern, J.Y.: Lower Bounds on Implementing Robust and Resilient Mediators. In: Canetti, R. (ed.) TCC 2008. LNCS, vol. 4948, pp. 302–319. Springer, Heidelberg (2008)CrossRefGoogle Scholar
  3. 3.
    Alwen, J., Katz, J., Lindell, Y., Persiano, G., Shelat, A., Visconti, I.: Collusion-Free Multiparty Computation in the Mediated Model. In: Halevi, S. (ed.) CRYPTO 2009. LNCS, vol. 5677, pp. 524–540. Springer, Heidelberg (2009)CrossRefGoogle Scholar
  4. 4.
    Alwen, J., Katz, J., Maurer, U., Zikas, V.: Collusion preserving computation. Cryptology ePrint Archive, Report 2011/443 (2011),
  5. 5.
    Alwen, J., Shelat, A., Visconti, I.: Collusion-Free Protocols in the Mediated Model. In: Wagner, D. (ed.) CRYPTO 2008. LNCS, vol. 5157, pp. 497–514. Springer, Heidelberg (2008)CrossRefGoogle Scholar
  6. 6.
    Aumann, R.: Subjectivity and Correlation in Randomized Strategies. Journal of Math. Econ. 1, 67–96 (1974)Google Scholar
  7. 7.
    Aumann, R.J.: Acceptable points in general cooperative n-person games. In: Topics in Mathematical Economics and Game Theory Essays in Honor of Robert J Aumann, vol. 23, pp. 287–324 (1959)Google Scholar
  8. 8.
    Barany, I.: Fair distribution protocols, or how the players replace fortune. Mathematics of Operations Research 17, 327–340 (1992)Google Scholar
  9. 9.
    Canetti, R.: Universally composable security: A new paradigm for cryptographic protocols. In: 42nd FOCS, pp. 136–145. IEEE (2001), Full version at
  10. 10.
    Canetti, R., Dodis, Y., Pass, R., Walfish, S.: Universally Composable Security with Global Setup. In: Vadhan, S.P. (ed.) TCC 2007. LNCS, vol. 4392, pp. 61–85. Springer, Heidelberg (2007)CrossRefGoogle Scholar
  11. 11.
    Canetti, R., Lindell, Y., Ostrovsky, R., Sahai, A.: Universally composable two-party and multi-party secure computation. In: STOC, pp. 494–503 (2002)Google Scholar
  12. 12.
    Canetti, R., Vald, M.: Universally composable security with local adversaries. Cryptology ePrint Archive, Report 2012/117 (2012),
  13. 13.
    Crawford, V., Sobel, J.: Strategic information transmission. Econometrica 50, 1431–1451 (1982)Google Scholar
  14. 14.
    Dodis, Y., Katz, J., Smith, A., Walfish, S.: Composability and On-Line Deniability of Authentication. In: Reingold, O. (ed.) TCC 2009. LNCS, vol. 5444, pp. 146–162. Springer, Heidelberg (2009)CrossRefGoogle Scholar
  15. 15.
    Forges, F.: Universal mechanisms. Econometrica 58, 1342–1364 (1990)Google Scholar
  16. 16.
    Goldreich, O.: Foundations of Cryptography. Basic Applications, vol. 2. Cambridge University Press, Cambridge (2004)Google Scholar
  17. 17.
    Goldreich, O., Micali, S., Wigderson, A.: How to play any mental game, or a completeness theorem for protocols with honest majority. In: 19th ACM STOC, pp. 218–229. ACM Press (1987)Google Scholar
  18. 18.
    Izmalkov, S., Lepinski, M., Micali, S.: Rational Secure Computation and Ideal Mechanism Design. In: FOCS 2005: Proceedings of the 46th Annual IEEE Symposium on Foundations of Computer Science, pp. 585–595. IEEE Computer Society, Washington, DC (2005)Google Scholar
  19. 19.
    Izmalkov, S., Lepinski, M., Micali, S.: Verifiably Secure Devices. In: Canetti, R. (ed.) TCC 2008. LNCS, vol. 4948, pp. 273–301. Springer, Heidelberg (2008)CrossRefGoogle Scholar
  20. 20.
    Izmalkov, S., Lepinski, M., Micali, S.: Perfect implementation. Games and Economic Behavior 71(1), 121–140 (2011),
  21. 21.
    Izmalkov, S., Micali, S., Lepinski, M.: Rational secure computation and ideal mechanism design. In: 46th FOCS, pp. 585–595. IEEE (2005), Full version available at
  22. 22.
    Lepinksi, M., Micali, S., Shelat, A.: Collusion-Free Protocols. In: STOC 2005: Proceedings of the Thirty-Seventh Annual ACM Symposium on Theory of Computing, pp. 543–552. ACM, New York (2005)Google Scholar
  23. 23.
    Lepinski, M., Micali, S., Peikert, C., Shelat, A.: Completely fair SFE and coalitionsafe cheap talk. In: 23rd ACM PODC, pp. 1–10. ACM Press (2004)Google Scholar
  24. 24.
    Lepinski, M., Micali, S., Shelat, A.: Collusion-free protocols. In: 37th ACM STOC, pp. 543–552. ACM Press (2005)Google Scholar
  25. 25.
    Lepinski, M., Micali, S., Shelat, A.: Fair-Zero Knowledge. In: Kilian, J. (ed.) TCC 2005. LNCS, vol. 3378, pp. 245–263. Springer, Heidelberg (2005)CrossRefGoogle Scholar
  26. 26.
    Maurer, U., Renner, R.: Abstract cryptography. In: Innovations in Computer Science. Tsinghua University Press (2011)Google Scholar
  27. 27.
    Nisan, N., Roughgarden, T., Tardos, E., Vazirani, V.V.: Algorithmic Game Theory. Cambridge University Press, New York (2007)Google Scholar
  28. 28.
    Simmons, G.J.: The prisoners’ problem and the subliminal channel. In: Crypto 1983, pp. 51–67. Plenum Press (1984)Google Scholar
  29. 29.
    Simmons, G.J.: Cryptanalysis and protocol failures. Communications of the ACM 37(11), 56–65 (1994)Google Scholar
  30. 30.
    Simmons, G.J.: The History of Subliminal Channels. In: Anderson, R. (ed.) IH 1996. LNCS, vol. 1174, pp. 237–256. Springer, Heidelberg (1996)Google Scholar

Copyright information

© International Association for Cryptologic Research 2012 2012

Authors and Affiliations

  • Joël Alwen
    • 1
  • Jonathan Katz
    • 2
  • Ueli Maurer
    • 1
  • Vassilis Zikas
    • 2
  1. 1.ETH ZürichZürichSwitzerland
  2. 2.University of MarylandCollege ParkUSA

Personalised recommendations