Secure Grouping Protocol Using a Deck of Cards

  • Yuji HashimotoEmail author
  • Kazumasa Shinagawa
  • Koji Nuida
  • Masaki Inamura
  • Goichiro Hanaoka
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10681)


We consider a problem, which we call secure grouping, of dividing a number of parties into some subsets (groups) in the following manner: Each party has to know the other members of his/her group, while he/she may not know anything about how the remaining parties are divided (except for certain public predetermined constraints, such as the number of parties in each group). In this paper, we construct an information-theoretically secure protocol using a deck of physical cards to solve the problem, which is jointly executable by the parties themselves without a trusted third party. Despite the non-triviality and the potential usefulness of the secure grouping, our proposed protocol is fairly simple to describe and execute. Our protocol is based on algebraic properties of conjugate permutations. A key ingredient of our protocol is our new techniques to apply multiplication and inverse operations to hidden permutations (i.e., those encoded by using face-down cards), which would be of independent interest and would have various potential applications.



We thank the members of Shin-Akarui-Angou-Benkyou-Kai for their helpful comments. In particular we would like to thank Shuichi Katsumata for his helpful comments. A part of this work is supported by JST CREST grant number JPMJCR1688.


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Copyright information

© Springer International Publishing AG 2017

Authors and Affiliations

  • Yuji Hashimoto
    • 1
    • 2
    Email author
  • Kazumasa Shinagawa
    • 2
    • 3
  • Koji Nuida
    • 2
  • Masaki Inamura
    • 1
  • Goichiro Hanaoka
    • 2
  1. 1.Tokyo Denki UniversitySaitamaJapan
  2. 2.National Institute of Advanced Industrial Science and TechnologyTokyoJapan
  3. 3.Tokyo Institute of TechnologyTokyoJapan

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