Card-based Protocols Using Triangle Cards

Authors Kazumasa Shinagawa, Takaaki Mizuki

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Author Details

Kazumasa Shinagawa
  • Tokyo Institute of Technology, Tokyo, Japan, Institute of Advanced Industrial Science and Technology (AIST), Tokyo, Japan
Takaaki Mizuki
  • Tohoku University, Sendai, Japan

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Kazumasa Shinagawa and Takaaki Mizuki. Card-based Protocols Using Triangle Cards. In 9th International Conference on Fun with Algorithms (FUN 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 100, pp. 31:1-31:13, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)


Suppose that three boys and three girls attend a party. Each boy and girl have a crush on exactly one of the three girls and three boys, respectively. The following dilemma arises: On one hand, each person thinks that if there is a mutual affection between a girl and boy, the couple should go on a date the next day. On the other hand, everyone wants to avoid the possible embarrassing situation in which their heart is broken "publicly." In this paper, we solve the dilemma using novel cards called triangle cards. The number of cards required is only six, which is minimal in the case where each player commits their input at the beginning of the protocol. We also construct multiplication and addition protocols based on triangle cards. Combining these protocols, we can securely compute any function f: {0,1,2}^n --> {0,1,2}.

Subject Classification

ACM Subject Classification
  • Theory of computation → Cryptographic protocols
  • Cryptography without computer
  • Secure computation
  • Card-based protocols
  • Triangle cards
  • Three-valued computation
  • Secure matching problem


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