Advertisement

21 - Bringing Down the Complexity: Fast Composable Protocols for Card Games Without Secret State

  • Bernardo DavidEmail author
  • Rafael Dowsley
  • Mario Larangeira
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10946)

Abstract

While many cryptographic protocols for card games have been proposed, all of them focus on card games where players have some state that must be kept secret from each other, e.g closed cards and bluffs in Poker. This scenario poses many interesting technical challenges, which are addressed with cryptographic tools that introduce significant computational and communication overheads (e.g. zero-knowledge proofs). In this paper, we consider the case of games that do not require any secret state to be maintained (e.g. Blackjack and Baccarat). Basically, in these games, cards are chosen at random and then publicly advertised, allowing for players to publicly announce their actions (before or after cards are known). We show that protocols for such games can be built from very lightweight primitives such as digital signatures and canonical random oracle commitments, yielding constructions that far outperform all known card game protocols in terms of communication, computational and round complexities. Moreover, in constructing highly efficient protocols, we introduce a new technique based on verifiable random functions for extending coin tossing, which is at the core of our constructions. Besides ensuring that the games are played correctly, our protocols support financial rewards and penalties enforcement, guaranteeing that winners receive their rewards and that cheaters get financially penalized. In order to do so, we build on blockchain-based techniques that leverage the power of stateful smart contracts to ensure fair protocol execution.

References

  1. 1.
    Andrychowicz, M., Dziembowski, S., Malinowski, D., Mazurek, Ł.: Fair two-party computations via bitcoin deposits. In: Böhme, R., Brenner, M., Moore, T., Smith, M. (eds.) FC 2014. LNCS, vol. 8438, pp. 105–121. Springer, Heidelberg (2014).  https://doi.org/10.1007/978-3-662-44774-1_8CrossRefGoogle Scholar
  2. 2.
    Andrychowicz, M., Dziembowski, S., Malinowski, D., Mazurek, L.: Secure multiparty computations on bitcoin. In: 2014 IEEE Symposium on Security and Privacy, pp. 443–458. IEEE Computer Society Press, May 2014Google Scholar
  3. 3.
    Barnett, A., Smart, N.P.: Mental poker revisited. In: Paterson, K.G. (ed.) Cryptography and Coding 2003. LNCS, vol. 2898, pp. 370–383. Springer, Heidelberg (2003).  https://doi.org/10.1007/978-3-540-40974-8_29CrossRefGoogle Scholar
  4. 4.
    Bentov, I., Kumaresan, R., Miller, A.: Instantaneous decentralized poker. In: Takagi, T., Peyrin, T. (eds.) ASIACRYPT 2017. LNCS, vol. 10625, pp. 410–440. Springer, Cham (2017).  https://doi.org/10.1007/978-3-319-70697-9_15CrossRefGoogle Scholar
  5. 5.
    Buterin, V.: White paper (2013). https://github.com/ethereum/wiki/wiki/White-Paper. Accessed 12 May 2017
  6. 6.
    Canetti, R.: Universally composable security: a new paradigm for cryptographic protocols. In: 42nd FOCS, pp. 136–145. IEEE Computer Society Press, October 2001Google Scholar
  7. 7.
    Canetti, R., Fischlin, M.: Universally composable commitments. In: Kilian, J. (ed.) CRYPTO 2001. LNCS, vol. 2139, pp. 19–40. Springer, Heidelberg (2001).  https://doi.org/10.1007/3-540-44647-8_2CrossRefGoogle Scholar
  8. 8.
    Castellà-Roca, J., Sebé, F., Domingo-Ferrer, J.: Dropout-tolerant TTP-free mental poker. In: Katsikas, S., López, J., Pernul, G. (eds.) TrustBus 2005. LNCS, vol. 3592, pp. 30–40. Springer, Heidelberg (2005).  https://doi.org/10.1007/11537878_4CrossRefGoogle Scholar
  9. 9.
    Chase, M., Lysyanskaya, A.: Simulatable VRFs with applications to multi-theorem NIZK. In: Menezes, A. (ed.) CRYPTO 2007. LNCS, vol. 4622, pp. 303–322. Springer, Heidelberg (2007).  https://doi.org/10.1007/978-3-540-74143-5_17CrossRefGoogle Scholar
  10. 10.
    Crépeau, C.: A secure poker protocol that minimizes the effect of player coalitions. In: Williams, H.C. (ed.) CRYPTO 1985. LNCS, vol. 218, pp. 73–86. Springer, Heidelberg (1986).  https://doi.org/10.1007/3-540-39799-X_8CrossRefGoogle Scholar
  11. 11.
    Crépeau, C.: A zero-knowledge poker protocol that achieves confidentiality of the players’ strategy or how to achieve an electronic poker face. In: Odlyzko, A.M. (ed.) CRYPTO 1986. LNCS, vol. 263, pp. 239–247. Springer, Heidelberg (1987).  https://doi.org/10.1007/3-540-47721-7_18CrossRefGoogle Scholar
  12. 12.
    David, B., Dowsley, R., Larangeira, M.: Kaleidoscope: an efficient poker protocol with payment distribution and penalty enforcement. Cryptology ePrint Archive, Report 2017/899 (2017). http://eprint.iacr.org/2017/899
  13. 13.
    David, B., Dowsley, R., Larangeira, M.: 21 - bringing down the complexity: fast composable protocols for card games without secret state. Cryptology ePrint Archive, Report 2018/303 (2018). https://eprint.iacr.org/2018/303
  14. 14.
    David, B., Dowsley, R., Larangeira, M.: ROYALE: a framework for universally composable card games with financial rewards and penalties enforcement. Cryptology ePrint Archive, Report 2018/157 (2018). https://eprint.iacr.org/2018/157
  15. 15.
    David, B., Gaži, P., Kiayias, A., Russell, A.: Ouroboros praos: an adaptively-secure, semi-synchronous proof-of-stake protocol. Cryptology ePrint Archive, Report 2017/573 (2017). https://eprint.iacr.org/2017/573. (to appear in Eurocrypt 2018)
  16. 16.
    Jarecki, S., Kiayias, A., Krawczyk, H.: Round-optimal password-protected secret sharing and T-PAKE in the password-only model. In: Sarkar, P., Iwata, T. (eds.) ASIACRYPT 2014. LNCS, vol. 8874, pp. 233–253. Springer, Heidelberg (2014).  https://doi.org/10.1007/978-3-662-45608-8_13CrossRefzbMATHGoogle Scholar
  17. 17.
    Kumaresan, R., Moran, T., Bentov, I.: How to use bitcoin to play decentralized poker. In: Ray, I., Li, N., Kruegel, C. (eds.) ACM CCS 2015, pp. 195–206. ACM Press, New York (2015)Google Scholar
  18. 18.
    Schindelhauer, C.: A toolbox for mental card games. Technical report, University of Lübeck (1998)Google Scholar
  19. 19.
    Sebe, F., Domingo-Ferrer, J., Castella-Roca, J.: On the security of a repaired mental poker protocol. In: Third International Conference on Information Technology: New Generations, pp. 664–668 (2006)Google Scholar
  20. 20.
    Shamir, A., Rivest, R.L., Adleman, L.M.: Mental poker. In: Klarner, D.A. (ed.) The Mathematical Gardner, pp. 37–43. Springer, Boston (1981).  https://doi.org/10.1007/978-1-4684-6686-7_5CrossRefGoogle Scholar
  21. 21.
    Wei, T.: Secure and practical constant round mental poker. Inf. Sci. 273, 352–386 (2014)CrossRefGoogle Scholar
  22. 22.
    Wei, T., Wang, L.-C.: A fast mental poker protocol. J. Math. Cryptol. 6(1), 39–68 (2012)MathSciNetCrossRefGoogle Scholar
  23. 23.
    Zhao, W., Varadharajan, V.: Efficient TTP-free mental poker protocols. In: International Conference on Information Technology: Coding and Computing (ITCC 2005) - Volume II, vol. 1, pp. 745–750, April 2005Google Scholar
  24. 24.
    Zhao, W., Varadharajan, V., Mu, Y.: A secure mental poker protocol over the internet. In: Proceedings of the Australasian Information Security Workshop Conference on ACSW Frontiers 2003 - Volume 21, ACSW Frontiers 2003, pp. 105–109, Darlinghurst, Australia. Australian Computer Society Inc. (2003)Google Scholar

Copyright information

© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  • Bernardo David
    • 1
    • 3
    Email author
  • Rafael Dowsley
    • 2
    • 3
  • Mario Larangeira
    • 1
    • 3
  1. 1.Tokyo Institute of TechnologyTokyoJapan
  2. 2.Aarhus UniversityAarhusDenmark
  3. 3.IOHKHong KongChina

Personalised recommendations