Card-Based Cryptography with Invisible Ink

  • Kazumasa ShinagawaEmail author
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 11436)


It is known that secure computation can be done by using a deck of physical cards; card-based cryptography makes people understand the correctness and security of secure computation, even for people who are not familiar with mathematics. In this paper, we propose a new type of cards, layered polygon cards, based on the use of invisible ink. A deck of cards with invisible ink naturally hides the contents of cards and allows to open some pieces of contents, which we referred to it as partial opening. Based on them, we construct novel protocols for various interesting functions such as carry of addition, equality, and greater-than.



This work was supported in part by JSPS KAKENHI Grant Number 17J01169.


  1. 1.
    Abe, Y., Hayashi, Y., Mizuki, T., Sone, H.: Five-card AND protocol in committed format using only practical shuffles. In: Proceedings of the 5th ACM on ASIA Public-Key Cryptography Workshop, APKC@AsiaCCS, Incheon, Republic of Korea, 4 June 2018, pp. 3–8. ACM (2018)Google Scholar
  2. 2.
    Cheung, E., Hawthorne, C., Lee, P.: CS 758 project: secure computation with playing cards (2013).
  3. 3.
    Crépeau, C., Kilian, J.: Discreet solitary games. In: Stinson, D.R. (ed.) CRYPTO 1993. LNCS, vol. 773, pp. 319–330. Springer, Heidelberg (1994). Scholar
  4. 4.
    den 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
  5. 5.
    Kastner, J., et al.: The minimum number of cards in practical card-based protocols. In: Takagi, T., Peyrin, T. (eds.) ASIACRYPT 2017, Part III. LNCS, vol. 10626, pp. 126–155. Springer, Cham (2017). Scholar
  6. 6.
    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, Part I. LNCS, vol. 9452, pp. 783–807. Springer, Heidelberg (2015). Scholar
  7. 7.
    Marcedone, A., Wen, Z., Shi, E.: Secure dating with four or fewer cards. Cryptology ePrint Archive, Report 2015/1031 (2015).
  8. 8.
    Mizuki, T.: Applications of card-based cryptography to education. IEICE Tech. Rep. 116(289), 13–17 (2016)Google Scholar
  9. 9.
    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). Scholar
  10. 10.
    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
  11. 11.
    Mizuki, T., Uchiike, F., Sone, H.: Securely computing XOR with 10 cards. Australas. J. Comb. 36, 279–293 (2006)MathSciNetzbMATHGoogle Scholar
  12. 12.
    Niemi, V., Renvall, A.: Secure multiparty computations without computers. Theor. Comput. Sci. 191(1–2), 173–183 (1998)MathSciNetCrossRefGoogle Scholar
  13. 13.
    Shinagawa, K., Mizuki, T.: Card-based protocols using triangle cards. In: 9th International Conference on Fun with Algorithms, FUN 2018, La Maddalena, Italy, 13–15 June 2018. LIPIcs, vol. 100, pp. 31:1–31:13 (2018)Google Scholar
  14. 14.
    Shinagawa, K., et al.: Card-based protocols using regular polygon cards. IEICE Trans. 100–A(9), 1900–1909 (2017)CrossRefGoogle Scholar
  15. 15.
    Stiglic, A.: Computations with a deck of cards. Theor. Comput. Sci. 259(1–2), 671–678 (2001)MathSciNetCrossRefGoogle Scholar

Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Tokyo Institute of TechnologyMeguro-kuJapan
  2. 2.National Institute of Advanced Industrial Science and TechnologyKoto-kuJapan

Personalised recommendations