Analysis of Information Leakage Due to Operative Errors in Card-Based Protocols

  • Takaaki MizukiEmail author
  • Yuichi Komano
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10979)


Card-based protocols provide secure multi-party computation using a deck of physical cards, via a series of operations such as shuffling and turning over cards, which are supposed to be executed by humans. Although almost all existing protocols have been designed to be perfectly secure, operative errors by humans would cause information leakage. In this paper, we propose a technique for analyzing information leakage due to operative errors in card-based protocols. To be specific, we introduce a concept, which we call a “probability trace,” and propose a new diagram for displaying how much information leaks, by enhancing the KWH diagram proposed by Koch, Walzer, and Härtel. By applying our diagram to a card-based protocol with an operative error, we can precisely reveal the leakage of players’ inputs from the protocol output. We also discuss an application of the diagram to human-error-free implementations of the existing six-card AND protocol.



This work was supported by JSPS KAKENHI Grant Number JP17K00001.


  1. 1.
    Marcedone, A., Wen, Z., Shi, E.: Secure dating with four or fewer cards. Cryptology ePrint Archive, Report 2015/1031 (2015)Google Scholar
  2. 2.
    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
  3. 3.
    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
  4. 4.
    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
  5. 5.
    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
  6. 6.
    Mizuki, T., Shizuya, H.: A formalization of card-based cryptographic protocols via abstract machine. Int. J. Inf. Secur. 13(1), 15–23 (2014)CrossRefGoogle Scholar
  7. 7.
    Kastner, J., Koch, A., Walzer, S., Miyahara, D., Hayashi, Y., Mizuki, T., Sone, H.: 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
  8. 8.
    Mizuki, T.: Card-based protocols for securely computing the conjunction of multiple variables. Theor. Comput. Sci. 622, 34–44 (2016)MathSciNetCrossRefGoogle Scholar

Copyright information

© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Tohoku UniversitySendaiJapan
  2. 2.Toshiba CorporationKawasakiJapan

Personalised recommendations