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Physical Zero-Knowledge Proof for Makaro

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Stabilization, Safety, and Security of Distributed Systems (SSS 2018)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 11201))

Abstract

Makaro is a logic game similar to Sudoku. In Makaro, a grid has to be filled with numbers such that: given areas contain all the numbers up to the number of cells in the area, no adjacent numbers are equal and some cells provide restrictions on the largest adjacent number. We propose a proven secure physical algorithm, only relying on cards, to realize a zero-knowledge proof of knowledge for Makaro. It allows a player to show that he knows a solution without revealing it.

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Notes

  1. 1.

    Moreover, if \(\mathcal {P}\) is NP-complete, then the ZKP should be run in a polynomial time [11]. Otherwise it might be easier to find a solution than proving that a solution is a correct solution, making the proof pointless.

  2. 2.

    This implies the standard soundness property, which ensures that if there exists no solution of the puzzle, then the prover is not able to convince the verifier regardless of the prover’s behavior.

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Acknowledgments

This work was supported in part by JSPS KAKENHI Grant Numbers 17J01169 and 17K00001. It was conducted with the support of the FEDER program of 2014-2020, the region council of Auvergne-Rhône-Alpes, the Indo-French Centre for the Promotion of Advanced Research (IFCPAR) and the Center Franco-Indien Pour La Promotion De La Recherche Avancée (CEFIPRA) through the project DST/CNRS 2015-03 under DST-INRIA-CNRS Targeted Programme.

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Authors and Affiliations

  1. University of Rennes 1, IRISA, Rennes, France

    Xavier Bultel

  2. Université de Lorraine, CNRS, Inria, LORIA, 54000, Nancy, France

    Jannik Dreier

  3. Université Grenoble Alpes, IMAG-LJK, CNRS UMR 5224, 700 avenue centrale, 38058, Grenoble, France

    Jean-Guillaume Dumas

  4. University Clermont Auvergne, LIMOS, CNRS UMR 6158, Campus des Cézeaux, Aubière, France

    Pascal Lafourcade

  5. Tohoku University, Sendai, Japan

    Daiki Miyahara, Takaaki Mizuki, Tatsuya Sasaki & Hideaki Sone

  6. National Institute of Advanced Industrial Science and Technology, Kōtō, Japan

    Daiki Miyahara & Kazumasa Shinagawa

  7. Ochanomizu University, Bunkyō, Japan

    Atsuki Nagao

  8. Tokyo Institute of Technology, Meguro, Japan

    Kazumasa Shinagawa

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  1. Xavier Bultel
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  2. Jannik Dreier
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Corresponding author

Correspondence to Kazumasa Shinagawa .

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  1. Nagoya Institute of Technology, Nagoya, Japan

    Taisuke Izumi

  2. Telecom ParisTech, Paris, France

    Petr Kuznetsov

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Bultel, X. et al. (2018). Physical Zero-Knowledge Proof for Makaro. In: Izumi, T., Kuznetsov, P. (eds) Stabilization, Safety, and Security of Distributed Systems. SSS 2018. Lecture Notes in Computer Science(), vol 11201. Springer, Cham. https://doi.org/10.1007/978-3-030-03232-6_8

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  • DOI: https://doi.org/10.1007/978-3-030-03232-6_8

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