Privacy-Enhancing Auctions Using Rational Cryptography

  • Peter Bro Miltersen
  • Jesper Buus Nielsen
  • Nikos Triandopoulos
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5677)


We consider enhancing with privacy concerns a large class of auctions, which include sealed-bid single-item auctions but also general multi-item multi-winner auctions, our assumption being that bidders primarily care about monetary payoff and secondarily worry about exposing information about their type to other players and learning information about other players’ types, that is, bidders are greedy then paranoid. To treat privacy explicitly within the game theoretic context, we put forward a novel hybrid utility model that considers both monetary and privacy components in players’ payoffs.

We show how to use rational cryptography to approximately implement any given ex interim individually strictly rational equilibrium of such an auction without a trusted mediator through a cryptographic protocol that uses only point-to-point authenticated channels between the players. By “ex interim individually strictly rational” we mean that, given its type and before making its move, each player has a strictly positive expected utility. By “approximately implement” we mean that, under cryptographic assumptions, running the protocol is a computational Nash equilibrium with a payoff profile negligibly close to the original equilibrium.


  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: PODC 2006, pp. 53–62. ACM, New York (2006)Google Scholar
  2. 2.
    Bogetoft, P., Damgård, I., Jakobsen, T., Nielsen, K., Pagter, J., Toft, T.: A practical implementation of secure auctions based on multiparty integer computation. In: Di Crescenzo, G., Rubin, A. (eds.) FC 2006. LNCS, vol. 4107, pp. 142–147. Springer, Heidelberg (2006)CrossRefGoogle Scholar
  3. 3.
    Bradford, P.G., Park, S., Rothkopf, M.H., Park, H.: Protocol completion incentive problems in cryptographic Vickrey auctions. Electronic Commerce Research 8(1-2), 57–77 (2008)CrossRefMATHGoogle Scholar
  4. 4.
    Dodis, Y., Halevi, S., Rabin, T.: A cryptographic solution to a game theoretic problem. In: Bellare, M. (ed.) CRYPTO 2000. LNCS, vol. 1880, pp. 112–130. Springer, Heidelberg (2000)CrossRefGoogle Scholar
  5. 5.
    Escamocher, G., Miltersen, P.B., Santillan-Rodriguez, R.: Existence and computation of equilibria of first-price auctions with integral valuations and bids. In: AAMAS 2009 (2009)Google Scholar
  6. 6.
    Gordon, S.D., Hazay, C., Katz, J., Lindell, Y.: Complete fairness in secure two-party computation. In: STOC 2008, pp. 413–422. ACM, New York (2008)Google Scholar
  7. 7.
    Gordon, S.D., Katz, J.: Rational secret sharing, revisited. In: De Prisco, R., Yung, M. (eds.) SCN 2006. LNCS, vol. 4116, pp. 229–241. Springer, Heidelberg (2006)CrossRefGoogle Scholar
  8. 8.
    Halpern, J., Pass, R.: Game theory with costly computation (manuscript) (2008)Google Scholar
  9. 9.
    Halpern, J., Teague, V.: Rational secret sharing and multiparty computation: extended abstract. In: STOC 2004, pp. 623–632. ACM, New York (2004)Google Scholar
  10. 10.
    Izmalkov, S., Lepinski, M., Micali, S.: Rational secure computation and ideal mechanism design. In: FOCS 2005, pp. 585–594. IEEE, Los Alamitos (2005)Google Scholar
  11. 11.
    Kol, G., Naor, M.: Cryptography and game theory: Designing protocols for exchanging information. In: Canetti, R. (ed.) TCC 2008. LNCS, vol. 4948, pp. 320–339. Springer, Heidelberg (2008)CrossRefGoogle Scholar
  12. 12.
    Kol, G., Naor, M.: Games for exchanging information. In: STOC 2008, pp. 423–432. ACM, New York (2008)Google Scholar
  13. 13.
    Lepinksi, M., Micali, S., shelat, a.: Collusion-free protocols. In: STOC 2005, pp. 543–552. ACM, New York (2005)Google Scholar
  14. 14.
    Lepinski, M., Micali, S., Peikert, C., shelat, a.: Completely fair SFE and coalition-safe cheap talk. In: PODC 2004, pp. 1–10. ACM, New York (2004)Google Scholar
  15. 15.
    Lindell, A.Y.: Legally-enforceable fairness in secure two-party computation. In: Malkin, T.G. (ed.) CT-RSA 2008. LNCS, vol. 4964, pp. 121–137. Springer, Heidelberg (2008)CrossRefGoogle Scholar
  16. 16.
    Lysyanskaya, A., Triandopoulos, N.: Rationality and adversarial behavior in multi-party computation. In: Dwork, C. (ed.) CRYPTO 2006. LNCS, vol. 4117, pp. 180–197. Springer, Heidelberg (2006)CrossRefGoogle Scholar
  17. 17.
    Micali, S., shelat, a.: Purely rational secret sharing (extended abstract). In: TCC 2009. LNCS, vol. 5444, pp. 54–71. Springer, Heidelberg (2009)Google Scholar
  18. 18.
    Naor, M., Pinkas, B., Sumner, R.: Privacy preserving auctions and mechanism design. In: 1st International Conference on Electronic Commerce, pp. 129–139. ACM, New York (1999)Google Scholar
  19. 19.
    Nisan, N., Roughgarden, T., Tardos, E., Vazirani, V.V.: Algorithmic Game Theory. Cambridge University Press, Cambridge (2007)CrossRefMATHGoogle Scholar
  20. 20.
    Ong, S.J., Parkes, D., Rosen, A., Vadhan, S.: Fairness with an honest minority and a rational majority. In: TCC 2009. LNCS, vol. 5444, pp. 36–53. Springer, Heidelberg (2009)Google Scholar
  21. 21.
    Parkes, D.C., Rabin, M.O., Shieber, S.M., Thorpe, C.A.: Practical secrecy-preserving, verifiably correct and trustworthy auctions. In: 8th International Conference on Electronic Commerce, pp. 70–81. ACM, New York (2006)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2009

Authors and Affiliations

  • Peter Bro Miltersen
    • 1
  • Jesper Buus Nielsen
    • 1
  • Nikos Triandopoulos
    • 2
  1. 1.Dept. of Computer ScienceAarhus UniversityDenmark
  2. 2.Dept. of Computer ScienceBoston UniversityUSA

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