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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}
}

Document

DOI: 10.4230/LIPIcs.FUN.2018.29

Card-Based Zero-Knowledge Proof for Sudoku

Authors: Tatsuya Sasaki, Takaaki Mizuki, and Hideaki Sone

Published in: LIPIcs, Volume 100, 9th International Conference on Fun with Algorithms (FUN 2018)

Abstract

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.

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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)

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@InProceedings{sasaki_et_al:LIPIcs.FUN.2018.29,
  author =	{Sasaki, Tatsuya and Mizuki, Takaaki and Sone, Hideaki},
  title =	{{Card-Based Zero-Knowledge Proof for Sudoku}},
  booktitle =	{9th International Conference on Fun with Algorithms (FUN 2018)},
  pages =	{29:1--29:10},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-067-5},
  ISSN =	{1868-8969},
  year =	{2018},
  volume =	{100},
  editor =	{Ito, Hiro and Leonardi, Stefano and Pagli, Linda and Prencipe, Giuseppe},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FUN.2018.29},
  URN =		{urn:nbn:de:0030-drops-88207},
  doi =		{10.4230/LIPIcs.FUN.2018.29},
  annote =	{Keywords: Zero-knowledge proof, Card-based cryptography, Sudoku}
}

Document

DOI: 10.4230/LIPIcs.FUN.2018.31

Card-based Protocols Using Triangle Cards

Authors: Kazumasa Shinagawa and Takaaki Mizuki

Published in: LIPIcs, Volume 100, 9th International Conference on Fun with Algorithms (FUN 2018)

Abstract

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}.

Cite as

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)

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@InProceedings{shinagawa_et_al:LIPIcs.FUN.2018.31,
  author =	{Shinagawa, Kazumasa and Mizuki, Takaaki},
  title =	{{Card-based Protocols Using Triangle Cards}},
  booktitle =	{9th International Conference on Fun with Algorithms (FUN 2018)},
  pages =	{31:1--31:13},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-067-5},
  ISSN =	{1868-8969},
  year =	{2018},
  volume =	{100},
  editor =	{Ito, Hiro and Leonardi, Stefano and Pagli, Linda and Prencipe, Giuseppe},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FUN.2018.31},
  URN =		{urn:nbn:de:0030-drops-88228},
  doi =		{10.4230/LIPIcs.FUN.2018.31},
  annote =	{Keywords: Cryptography without computer, Secure computation, Card-based protocols, Triangle cards, Three-valued computation, Secure matching problem}
}

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Documents authored by Mizuki, Takaaki

Card-Based ZKP Protocols for Takuzu and Juosan

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Card-Based Zero-Knowledge Proof for Sudoku

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Card-based Protocols Using Triangle Cards

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