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Card-Based ZKP Protocols for Takuzu and Juosan

Authors Daiki Miyahara , Léo Robert , Pascal Lafourcade , So Takeshige, Takaaki Mizuki , Kazumasa Shinagawa , Atsuki Nagao , Hideaki Sone

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Subject Classification

ACM Subject Classification
  • Security and privacy → Information-theoretic techniques
Keywords
  • Zero-knowledge proof
  • Card-based cryptography
  • Takuzu
  • Juosan

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Abstract

Takuzu and Juosan are logical Nikoli games in the spirit of Sudoku. In Takuzu, a grid must be filled with 0’s and 1’s under specific constraints. In Juosan, the grid must be filled with vertical and horizontal dashes with specific constraints. We give physical algorithms using cards to realize zero-knowledge proofs for those games. The goal is to allow a player to show that he/she has the solution without revealing it. Previous work on Takuzu showed a protocol with multiple instances needed. We propose two improvements: only one instance needed and a soundness proof. We also propose a similar proof for Juosan game.

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Daiki Miyahara, Léo Robert, Pascal Lafourcade, So Takeshige, Takaaki Mizuki, Kazumasa Shinagawa, Atsuki Nagao, and Hideaki Sone. Card-Based ZKP Protocols for Takuzu and Juosan. In 10th International Conference on Fun with Algorithms (FUN 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 157, pp. 20:1-20:21, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020) https://doi.org/10.4230/LIPIcs.FUN.2021.20

Author Details

Daiki Miyahara
  • Graduate School of Information Sciences, Tohoku University, Sendai, Japan
  • National Institute of Advanced Industrial Science and Technology (AIST), Tokyo, Japan
Léo Robert
  • University Clermont Auvergne, LIMOS, CNRS UMR (6158), Aubière, France
Pascal Lafourcade
  • University Clermont Auvergne, LIMOS, CNRS UMR (6158), Aubière, France
So Takeshige
  • School of Engineering, Tohoku University, Sendai, Japan
Takaaki Mizuki
  • Cyberscience Center, Tohoku University, Sendai, Japan
Kazumasa Shinagawa
  • Graduate School of Informatics and Engineering, The University of Electro-Communications, Tokyo, Japan
  • National Institute of Advanced Industrial Science and Technology (AIST), Tokyo, Japan
Atsuki Nagao
  • Department of Information Science, Ochanomizu University, Tokyo, Japan
Hideaki Sone
  • Cyberscience Center, Tohoku University, Sendai, Japan

Funding

  • Miyahara, Daiki: This work was supported by JSPS KAKENHI Grant Number JP19J21153.
  • Robert, Léo: This work was partially supported by the French project ANR-18-CE39-0019 (MobiS5).
  • Lafourcade, Pascal: This work was partially supported by the project ANR-18-CE39-0019 (MobiS5).
  • Mizuki, Takaaki: This work was supported by JSPS KAKENHI Grant Number JP17K00001.
  • Shinagawa, Kazumasa: This work was supported by JSPS KAKENHI Grant Number JP17J01169.

Acknowledgements

We thank the anonymous referees, whose comments have helped us to improve the presentation of the paper. In particular, Protocol 1 for Takuzu presented in Section 3.2.1 is based on the fruitful comments given by one referee.

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