Four Cards Are Sufficient for a Card-Based Three-Input Voting Protocol Utilizing Private Permutations

  • Takeshi Nakai
  • Satoshi Shirouchi
  • Mitsugu IwamotoEmail author
  • Kazuo Ohta
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10681)


The card-based cryptographic protocol is a variant of multi-party computation that enables us to compute a certain function securely by using playing cards. In existing card-based cryptographic protocols, a special operation of cards called a shuffle is used to achieve the information-theoretic security. Recently, card-based cryptographic protocols have been reconsidered from the viewpoint of multi-party computations. In this direction, a new model of card-based cryptographic protocol including a new assumption called Private Permutations (PP, for short) is introduced and succeeds in constructing efficient protocols for the millionaires’ protocol. In this paper, we construct efficient card-based cryptographic OR and XOR protocols based on the existing AND protocol. Furthermore, by unifying AND and OR protocols, it is shown that a majority voting protocol with three inputs is efficiently obtained. Our construction requires only four cards thanks to PPs, whereas the previous work requires eight cards.


Card-based cryptographic protocols Multi-party computation Logic gates Majority voting Private permutation 



The authors are grateful to the anonymous reviewers for their helpful comments. They also would like to thank Prof. Takaaki Mizuki for drawing the authors’ attention to [2]. This work was partially supported by JSPS KAKENHI Grant Numbers JP15H02710 and JP17H01752.


  1. 1.
    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). CrossRefGoogle Scholar
  2. 2.
    Marcedone, A., Wen, W., Shi, E.: Secure Dating with Four or Fewer Cards. IACR ePrint Archive, 1031 (2015),
  3. 3.
    Nakai, T., Tokushige, Y., Misawa, Y., Iwamoto, M., Ohta, K.: Efficient card-based cryptographic protocols for millionaires’ problem utilizing private permutations. In: Foresti, S., Persiano, G. (eds.) CANS 2016. LNCS, vol. 10052, pp. 500–517. Springer, Cham (2016). CrossRefGoogle Scholar
  4. 4.
    Yao, A.: Protocols for secure computations. In: IEEE Symposium on FOCS, vol. 23, pp. 160–164. IEEE (1982)Google 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). CrossRefGoogle Scholar
  6. 6.
    Mizuki, T., Kumamoto, M., Sone, H.: The five-card trick can be done with four cards. In: Wang, X., Sako, K. (eds.) ASIACRYPT 2012. LNCS, vol. 7658, pp. 598–606. Springer, Heidelberg (2012). CrossRefGoogle Scholar
  7. 7.
    Mizuki, T., Asiedu, I.K., Sone, H.: Voting with a logarithmic number of cards. In: Mauri, G., Dennunzio, A., Manzoni, L., Porreca, A.E. (eds.) UCNC 2013. LNCS, vol. 7956, pp. 162–173. Springer, Heidelberg (2013). CrossRefGoogle Scholar
  8. 8.
    Nishida, T., Mizuki, T., Sone, H.: Securely computing the three-input majority function with eight cards. In: Dediu, A.-H., Martín-Vide, C., Truthe, B., Vega-Rodríguez, M.A. (eds.) TPNC 2013. LNCS, vol. 8273, pp. 193–204. Springer, Heidelberg (2013). CrossRefGoogle Scholar
  9. 9.
    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). CrossRefGoogle Scholar
  10. 10.
    Mizuki, T., Shizuya, H.: Practical card-based cryptography. In: Ferro, A., Luccio, F., Widmayer, P. (eds.) FUN 2014. LNCS, vol. 8496, pp. 313–324. Springer, Cham (2014).
  11. 11.
    Shinagawa, K., Nuida, K., Nishide, T., Hanaoka, G., Okamoto, E.: Commited AND protocol using three cards with more handy shuffle. In: ISITA 2016, pp. 736–738 (2016)Google Scholar

Copyright information

© Springer International Publishing AG 2017

Authors and Affiliations

  • Takeshi Nakai
    • 1
  • Satoshi Shirouchi
    • 1
  • Mitsugu Iwamoto
    • 1
    Email author
  • Kazuo Ohta
    • 1
  1. 1.Department of InformaticsThe University of Electro-CommunicationsChofuJapan

Personalised recommendations