Physical Zero-Knowledge Proof for Makaro

  • Xavier Bultel
  • Jannik Dreier
  • Jean-Guillaume Dumas
  • Pascal Lafourcade
  • Daiki Miyahara
  • Takaaki Mizuki
  • Atsuki Nagao
  • Tatsuya Sasaki
  • Kazumasa ShinagawaEmail author
  • Hideaki Sone
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 11201)


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.


Zero-knowledge proofs Card-based secure two-party protocols Puzzle Makaro Privacy 



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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Copyright information

© Springer Nature Switzerland AG 2018

Authors and Affiliations

  • Xavier Bultel
    • 1
  • Jannik Dreier
    • 2
  • Jean-Guillaume Dumas
    • 3
  • Pascal Lafourcade
    • 4
  • Daiki Miyahara
    • 5
    • 6
  • Takaaki Mizuki
    • 5
  • Atsuki Nagao
    • 7
  • Tatsuya Sasaki
    • 5
  • Kazumasa Shinagawa
    • 6
    • 8
    Email author
  • Hideaki Sone
    • 5
  1. 1.University of Rennes 1, IRISARennesFrance
  2. 2.Université de Lorraine, CNRS, Inria, LORIANancyFrance
  3. 3.Université Grenoble Alpes, IMAG-LJK, CNRS UMR 5224GrenobleFrance
  4. 4.University Clermont Auvergne, LIMOS, CNRS UMR 6158AubièreFrance
  5. 5.Tohoku UniversitySendaiJapan
  6. 6.National Institute of Advanced Industrial Science and TechnologyKōtōJapan
  7. 7.Ochanomizu UniversityBunkyōJapan
  8. 8.Tokyo Institute of TechnologyMeguroJapan

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