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Multi-party Computation Based on Physical Coins

  • Yuichi Komano
  • Takaaki Mizuki
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 11324)

Abstract

In the history of cryptography, many cryptographic protocols rely on random coin tosses to discuss their provable security. Although flipping coins is indispensable in this manner, the coins themselves have never been in the spotlight. Therefore, we would like to make physical coins go up to the stage of cryptography, as a deck of physical playing cards has been used to perform a secure multi-party computation. Such a card-based protocol is helpful both to perform a secure computation without any black-box computers and to understand the principles of secure protocols. In this paper, we propose a new framework of secure multi-party computation using physical coins, named a coin-based protocol. Whereas a face-down card can conceal the information about its face side, one side of a coin leaks the information of its other side. Hence, more careful design is required for a secure coin-based protocol than the card-based one. We introduce a computational model of the coin-based protocol and explicitly give protocols for NOT, AND, and copy computations. We also discuss how to implement the protocols in practice.

Keywords

Multi-party computation Card-based protocol Physical coin 

Notes

Acknowledgments

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

References

  1. 1.
    den Boer, B.: More efficient match-making and satisfiability: the five card trick. In: Quisquater, J.J., Vandewalle, J. (eds.) Advances in Cryptology – EUROCRYPT ’89. Lecture Notes in Computer Science, vol. 434, pp. 208–217. Springer, Berlin Heidelberg (1990)CrossRefGoogle Scholar
  2. 2.
    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
  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).  https://doi.org/10.1007/978-3-662-48797-6_32CrossRefGoogle Scholar
  4. 4.
    Mizuki, T.: Card-based protocols for securely computing the conjunction of multiple variables. Theor. Comput. Sci. 622, 34–44 (2016)MathSciNetCrossRefGoogle Scholar
  5. 5.
    Mizuki, T., Shizuya, H.: Computational model of card-based cryptographic protocols and its applications. IEICE Trans. Fundam. Electron. Commun. Comput. Sci. E100.A(1), 3–11 (2017)CrossRefGoogle Scholar
  6. 6.
    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
  7. 7.
    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
  8. 8.
    Marcedone, A., Wen, Z., Shi, E.: Secure dating with four or fewer cards. Cryptology ePrint Archive, Report 2015/1031 (2015)Google Scholar
  9. 9.
    Goldwasser, S.: Multi-party computations: past and present. In: Burns, J.E., Attiya, H. (eds.) Proceedings of the Sixteenth Annual ACM Symposium on Principles of Distributed Computing, pp. 1–6. ACM (1997)Google Scholar
  10. 10.
    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

Copyright information

© Springer Nature Switzerland AG 2018

Authors and Affiliations

  1. 1.Toshiba CorporationSaiwai-ku, KawasakiJapan
  2. 2.Tohoku UniversityAoba-ku, SendaiJapan

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