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Interactive Physical ZKP for Connectivity: Applications to Nurikabe and Hitori

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Connecting with Computability (CiE 2021)

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Abstract

During the last years, many Physical Zero-knowledge Proof (ZKP) protocols for Nikoli’s puzzles have been designed. In this paper, we propose two ZKP protocols for the two Nikoli’s puzzles called Nurikabe and Hitori. These two puzzles have some similarities, since in their rules at least one condition requires that some cells are connected to each other, horizontally or vertically. The novelty in this paper is to propose two techniques that allow us to prove such connectivity without leaking any information about a solution.

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Notes

  1. 1.

    Nikoli is a game publisher famously known for its Sudoku puzzle.

  2. 2.

    For a numbered cell where 1 is written, V simply reveals the commitment on it and its four neighbours to confirm that the island is surrounded by the sea.

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Acknowledgements

This work was supported in part by JSPS KAKENHI Grant Numbers JP19J21153 and JP21K11881. This study was partially supported by the French ANR project ANR-18-CE39-0019 (MobiS5), by the research program “Investissements d\(^{\prime }\)Avenir” through the IDEX-ISITE initiative 16-IDEX-0001 (CAP 20-25), by the IMobS3 Laboratory of Excellence (ANR-10-LABX-16-01), by the French ANR project DECRYPT (ANR-18-CE39-0007) and SEVERITAS (ANR-20-CE39-0009).

Author information

Authors and Affiliations

  1. LIMOS, University Clermont Auvergne, CNRS UMR 6158, Aubière, France

    Léo Robert & Pascal Lafourcade

  2. Graduate School of Information Sciences, Tohoku University, Sendai, Japan

    Daiki Miyahara

  3. Cyberscience Center, Tohoku University, Sendai, Japan

    Takaaki Mizuki

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

    Daiki Miyahara & 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 Lille, Lille, France

    Liesbeth De Mol

  2. Vakgroep Wiskunde, Ghent University, Ghent, Belgium

    Andreas Weiermann

  3. University of Göttingen, Göttingen, Germany

    Florin Manea

  4. Ghent University, Ghent, Belgium

    David Fernández-Duque

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Robert, L., Miyahara, D., Lafourcade, P., Mizuki, T. (2021). Interactive Physical ZKP for Connectivity: Applications to Nurikabe and Hitori. In: De Mol, L., Weiermann, A., Manea, F., Fernández-Duque, D. (eds) Connecting with Computability. CiE 2021. Lecture Notes in Computer Science(), vol 12813. Springer, Cham. https://doi.org/10.1007/978-3-030-80049-9_37

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  • DOI: https://doi.org/10.1007/978-3-030-80049-9_37

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