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DOI: 10.4230/LIPIcs.FUN.2021.20

Card-Based ZKP Protocols for Takuzu and Juosan

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

Published in: LIPIcs, Volume 157, 10th International Conference on Fun with Algorithms (FUN 2021) (2020)

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)

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@InProceedings{miyahara_et_al:LIPIcs.FUN.2021.20,
  author =	{Miyahara, Daiki and Robert, L\'{e}o and Lafourcade, Pascal and Takeshige, So and Mizuki, Takaaki and Shinagawa, Kazumasa and Nagao, Atsuki and Sone, Hideaki},
  title =	{{Card-Based ZKP Protocols for Takuzu and Juosan}},
  booktitle =	{10th International Conference on Fun with Algorithms (FUN 2021)},
  pages =	{20:1--20:21},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-145-0},
  ISSN =	{1868-8969},
  year =	{2020},
  volume =	{157},
  editor =	{Farach-Colton, Martin and Prencipe, Giuseppe and Uehara, Ryuhei},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FUN.2021.20},
  URN =		{urn:nbn:de:0030-drops-127817},
  doi =		{10.4230/LIPIcs.FUN.2021.20},
  annote =	{Keywords: Zero-knowledge proof, Card-based cryptography, Takuzu, Juosan}
}

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Card-Based ZKP Protocols for Takuzu and Juosan

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