Secure Computation of Any Boolean Function Based on Any Deck of Cards

  • Kazumasa ShinagawaEmail author
  • Takaaki Mizuki
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 11458)


It is established that secure computation can be achieved by using a deck of physical cards. Almost all existing card-based protocols are based on a specific deck of cards. In this study, we design card-based protocols that are executable using any deck of cards (e.g., playing cards, UNO, and trading cards). Specifically, we construct a card-based protocol for any Boolean function based on any deck of cards. As corollaries of our result, a standard deck of playing cards (having 52 cards) enables secure computation of any 22-variable Boolean function, and UNO (having 112 cards) enables secure computation of any 53-variable Boolean function.


Secure computation Card-based protocols Playing cards 



This work was supported in part by JSPS KAKENHI Grant Numbers 17J01169 and 17K00001.


  1. 1.
    Crépeau, C., Kilian, J.: Discreet solitary games. In: Stinson, D.R. (ed.) CRYPTO 1993. LNCS, vol. 773, pp. 319–330. Springer, Heidelberg (1994). Scholar
  2. 2.
    Boer, B.: More efficient match-making and satisfiability the five card trick. In: Quisquater, J.-J., Vandewalle, J. (eds.) EUROCRYPT 1989. LNCS, vol. 434, pp. 208–217. Springer, Heidelberg (1990). Scholar
  3. 3.
    Koch, A., Walzer, S., Härtel, K.: Card-based cryptographic protocols using a minimal number of cards. In: Iwata, T., Cheon, J.H. (eds.) ASIACRYPT 2015. LNCS, vol. 9452, pp. 783–807. Springer, Heidelberg (2015). Scholar
  4. 4.
    Mizuki, T.: Efficient and secure multiparty computations using a standard deck of playing cards. In: Foresti, S., Persiano, G. (eds.) CANS 2016. LNCS, vol. 10052, pp. 484–499. Springer, Cham (2016). Scholar
  5. 5.
    Mizuki, T., Sone, H.: Six-card secure AND and four-card secure XOR. In: Deng, X., Hopcroft, J.E., Xue, J. (eds.) FAW 2009. LNCS, vol. 5598, pp. 358–369. Springer, Heidelberg (2009). Scholar
  6. 6.
    Niemi, V., Renvall, A.: Solitaire zero-knowledge. Fundam. Inform. 38(1–2), 181–188 (1999)MathSciNetzbMATHGoogle Scholar
  7. 7.
    Nishida, T., Hayashi, Y., Mizuki, T., Sone, H.: Card-based protocols for any boolean function. In: Jain, R., Jain, S., Stephan, F. (eds.) TAMC 2015. LNCS, vol. 9076, pp. 110–121. Springer, Cham (2015). Scholar
  8. 8.
    Ueda, I., Nishimura, A., Hayashi, Y., Mizuki, T., Sone, H.: How to implement a random bisection cut. In: Martín-Vide, C., Mizuki, T., Vega-Rodríguez, M.A. (eds.) TPNC 2016. LNCS, vol. 10071, pp. 58–69. Springer, Cham (2016). Scholar

Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Tokyo Institute of TechnologyMeguroJapan
  2. 2.Institute of Advanced Industrial Science and Technology (AIST)KōtōJapan
  3. 3.Tohoku UniversitySendaiJapan

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