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Card-Based Protocol Against Actively Revealing Card Attack

  • Ken Takashima
  • Daiki MiyaharaEmail author
  • Takaaki Mizuki
  • Hideaki Sone
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 11934)

Abstract

In 1989, den Boer presented the first card-based protocol, called the “five-card trick” that securely computes the AND function using a deck of physical cards via a series of actions such as shuffling and turning over cards. This protocol enables a couple to confirm their mutual love without revealing their individual feelings. During such a secure computation protocol, it is important to keep any information about the inputs secret. Almost all existing card-based protocols are secure under the assumption that all players participating in a protocol are semi-honest or covert, i.e., they do not deviate from the protocol if there is a chance that they will be caught when cheating. In this paper, we consider a more malicious attack in which a player as an active adversary can reveal cards illegally without any hesitation. Against such an actively revealing card attack, we define the t-secureness, meaning that no information about the inputs leaks even if at most t cards are revealed illegally. Subsequently, we design a 1-secure AND protocol. Thus, our contribution is the construction of the first formal framework to handle actively revealing card attacks and their countermeasures.

Keywords

Cryptography Card-based protocols Active Security Secure multiparty computations 

Notes

Acknowledgments

This work was supported by JSPS KAKENHI Grant Numbers JP17K00001 and JP19J21153. We would like to thank the anonymous reviewers for their fruitful comments.

References

  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).  https://doi.org/10.1007/3-540-46885-4_23CrossRefGoogle Scholar
  2. 2.
    Ishikawa, R., Chida, E., Mizuki, T.: Efficient card-based protocols for generating a hidden random permutation without fixed points. In: Calude, C.S., Dinneen, M.J. (eds.) UCNC 2015. LNCS, vol. 9252, pp. 215–226. Springer, Cham (2015).  https://doi.org/10.1007/978-3-319-21819-9_16CrossRefGoogle Scholar
  3. 3.
    Koch, A., Walzer, S.: Foundations for actively secure card-based cryptography. Cryptology ePrint Archive, Report 2017/423 (2017). https://eprint.iacr.org/2017/423
  4. 4.
    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).  https://doi.org/10.1007/978-3-662-48797-6_32CrossRefGoogle Scholar
  5. 5.
    Mizuki, T., Komano, Y.: Analysis of information leakage due to operative errors in card-based protocols. In: Iliopoulos, C., Leong, H.W., Sung, W.-K. (eds.) IWOCA 2018. LNCS, vol. 10979, pp. 250–262. Springer, Cham (2018).  https://doi.org/10.1007/978-3-319-94667-2_21CrossRefGoogle 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).  https://doi.org/10.1007/978-3-642-34961-4_36CrossRefGoogle Scholar
  7. 7.
    Mizuki, T., Shizuya, H.: A formalization of card-based cryptographic protocolsvia abstract machine. Int. J. Inf. Secur. 13(1), 15–23 (2014).  https://doi.org/10.1007/s10207-013-0219-4CrossRefGoogle Scholar
  8. 8.
    Mizuki, T., Shizuya, H.: Practical card-based cryptography. In: Ferro, A., Luccio, F., Widmayer, P. (eds.) Fun with Algorithms. Lecture Notes in Computer Science, vol. 8496, pp. 313–324. Springer, Cham (2014).  https://doi.org/10.1007/978-3-319-07890-8_27CrossRefGoogle Scholar
  9. 9.
    Mizuki, T., Shizuya, H.: Computational model of card-based cryptographic protocols and its applications. IEICE Trans. Fundam. Electron. Commun. Comput. Sci. 100(1), 3–11 (2017).  https://doi.org/10.1587/transfun.E100.A.3CrossRefGoogle 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).  https://doi.org/10.1007/978-3-642-02270-8_36CrossRefGoogle Scholar
  11. 11.
    Niemi, V., Renvall, A.: Secure multiparty computations without computers. Theor. Comput. Sci. 191(1–2), 173–183 (1998).  https://doi.org/10.1016/S0304-3975(97)00107-2MathSciNetCrossRefzbMATHGoogle Scholar
  12. 12.
    Shamir, A.: How to share a secret. In: Ashenhurst, R.L. (ed.) Communications of the ACM, vol. 22, pp. 612–613. ACM, New York (1979).  https://doi.org/10.1145/359168.359176MathSciNetCrossRefGoogle Scholar
  13. 13.
    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).  https://doi.org/10.1007/978-3-319-49001-4_5CrossRefGoogle Scholar

Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Graduate School of Information SciencesTohoku UniversityAoba-ku, SendaiJapan
  2. 2.National Institute of Advanced Industrial Science and TechnologyKoto-ku TokyoJapan
  3. 3.Cyberscience CenterTohoku UniversityAoba-ku, SendaiJapan

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