Card-Based Zero-Knowledge Proof for Sudoku

Authors Tatsuya Sasaki, Takaaki Mizuki, Hideaki Sone

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Author Details

Tatsuya Sasaki
  • Graduate School of Information Sciences, Tohoku University, 6--3--09 Aramaki-Aza-Aoba, Aoba, Sendai 980--8579, Japan
Takaaki Mizuki
  • Cyberscience Center, Tohoku University, 6--3 Aramaki-Aza-Aoba, Aoba, Sendai 980--8578, Japan
Hideaki Sone
  • Cyberscience Center, Tohoku University, 6--3 Aramaki-Aza-Aoba, Aoba, Sendai 980--8578, Japan

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Tatsuya Sasaki, Takaaki Mizuki, and Hideaki Sone. Card-Based Zero-Knowledge Proof for Sudoku. In 9th International Conference on Fun with Algorithms (FUN 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 100, pp. 29:1-29:10, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)


In 2009, Gradwohl, Naor, Pinkas, and Rothblum proposed physical zero-knowledge proof protocols for Sudoku. That is, for a puzzle instance of Sudoku, their excellent protocols allow a prover to convince a verifier that there is a solution to the Sudoku puzzle and that he/she knows it, without revealing any information about the solution. The possible drawback is that the existing protocols have a soundness error with a non-zero probability or need special cards (such as scratch-off cards). Thus, in this study, we propose new protocols to perform zero-knowledge proof for Sudoku that use a normal deck of playing cards and have no soundness error. Our protocols can be easily implemented by humans with a reasonable number of playing cards.

Subject Classification

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


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