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Card-Based ZKP Protocol for Nurimisaki

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Stabilization, Safety, and Security of Distributed Systems (SSS 2022)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 13751))

Abstract

Proving to someone else the knowledge of a secret without revealing any of its information is an interesting feature in cryptography. The best solution to solve this problem is a Zero-Knowledge Proof (ZKP) protocol.

Nurimisaki is a Nikoli puzzle. The goal of this game is to draw a kind of abstract painting (“Nuri”) that represents the sea with some capes (“Misaki”) of an island (represented by white cells). For this, the player has to fulfill cells of a grid in black (representing the sea) in order to draw some capes while respecting some simple rules. One of the specificity of the rules of this game is that the cells called “Misaki” can only have one white neighbour and all white cells need to be connected. In 2020, this puzzle has been proven to be NP-complete.

Using a deck of cards, we propose a physical ZKP protocol to prove that a player knows a solution of a Nurimisaki grid without revealing any information about the solution.

We thank the anonymous referees, whose comments have helped us to improve the presentation of the paper. This work was supported in part by JSPS KAKENHI Grant Numbers JP18H05289 and JP21K11881. This study was partially supported by the French ANR project ANR-18-CE39-0019 (MobiS5).

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Notes

  1. 1.

    Note that we described the protocol for Misaki cell not at the border of the grid. If a Misaki cell is at a border (but not a corner) then the 4-neighbours becomes the 3-neighbours and the protocol is the same (there will be only three piles instead of four). For Misaki cells at a corner, P and V consider the 2-neighbours (thus only two piles).

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Author information

Authors and Affiliations

  1. Université Clermont-Auvergne, CNRS, Mines de Saint-Étienne, Saint-Étienne, France

    Léo Robert & Pascal Lafourcade

  2. LIMOS, 63000, Clermont-Ferrand, France

    Léo Robert & Pascal Lafourcade

  3. The University of Electro-Communications, Tokyo, Japan

    Daiki Miyahara

  4. National Institute of Advanced Industrial Science and Technology, Tokyo, Japan

    Daiki Miyahara & Takaaki Mizuki

  5. Cyberscience Center, Tohoku University, Sendai, Japan

    Takaaki Mizuki

Authors
  1. Léo Robert
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  2. Daiki Miyahara
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  3. Pascal Lafourcade
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  4. Takaaki Mizuki
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Corresponding author

Correspondence to Léo Robert .

Editor information

Editors and Affiliations

  1. University of Picardie Jules Verne, Amiens, France

    Stéphane Devismes

  2. Sorbonne University, Paris, France

    Franck Petit

  3. Grenoble Alpes University, Saint-Martin-d'Hères, France

    Karine Altisen

  4. Sapienza University of Rome, Rome, Italy

    Giuseppe Antonio Di Luna

  5. IMDEA Networks Institute, Madrid, Spain

    Antonio Fernandez Anta

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Robert, L., Miyahara, D., Lafourcade, P., Mizuki, T. (2022). Card-Based ZKP Protocol for Nurimisaki. In: Devismes, S., Petit, F., Altisen, K., Di Luna, G.A., Fernandez Anta, A. (eds) Stabilization, Safety, and Security of Distributed Systems. SSS 2022. Lecture Notes in Computer Science, vol 13751. Springer, Cham. https://doi.org/10.1007/978-3-031-21017-4_19

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  • DOI: https://doi.org/10.1007/978-3-031-21017-4_19

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