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When Locality Implies Globality: Card-Based ZKP Protocol for Shakashaka Puzzle

Authors Daiki Miyahara , Léo Robert , Pascal Lafourcade , Shohei Kaneko

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LIPIcs.FUN.2026.33.pdf
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Subject Classification

ACM Subject Classification
  • Theory of computation → Cryptographic protocols
Keywords
  • Card-based cryptography
  • ShakaShaka
  • Nikoli
  • ZKP

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Abstract

Shakashaka is an NP-complete Nikoli puzzle that requires to draw white rectangles by filling a grid with black triangles. Verifying that there are only rectangles drawn in the solution was an open problem for card-based ZKP protocols designers.
In this paper, we construct a card-based ZKP protocol to show that a prover can prove to a verifier that he knows a solution of this puzzle without revealing any information. For doing this we prove a local property on all possible 2 × 2 subgrids drawn according to the rules of the game and such configurations are possible valid shapes for rectangles. This local property implies a global property on the shape of the constructed areas. Thanks to this local result for all 2 × 2 subgrids, we are able to establish that the only possible shape in the global grid are rectangles. We also verify other classical rules of Shakashaka.

Cite As Get BibTex

Daiki Miyahara, Léo Robert, Pascal Lafourcade, and Shohei Kaneko. When Locality Implies Globality: Card-Based ZKP Protocol for Shakashaka Puzzle. In 13th International Conference on Fun with Algorithms (FUN 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 366, pp. 33:1-33:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026) https://doi.org/10.4230/LIPIcs.FUN.2026.33

Author Details

Daiki Miyahara
  • The University of Electro-Communications, Tokyo, Japan
  • National Institute of Advanced Industrial Science and Technology, Tokyo, Japan
Léo Robert
  • MIS, Université de Picardie Jules Verne, Amiens, France
Pascal Lafourcade
  • Université Clermont Auvergne, CNRS UMR 6158, LIMOS, Clermont-Ferrand, France
Shohei Kaneko
  • The University of Electro-Communications, Tokyo, Japan

Funding

This work was supported in part by PHC Sakura (53290WD), by ANR Project PRIVA-SIQ (ANR-23-CE39-0008), by JSPS KAKENHI Grant Numbers JP23H00479 and JP26K21164, by JSPS Bilateral Joint Research Projects JPJSBP120253206, and by Institute of Mathematics for Industry, Joint Usage/Research Center in Kyushu University, 2023a020, 2024a035, and 2025a036.

Acknowledgements

We thank the anonymous referees, whose comments have helped us to improve the presentation of the paper. We also thank Alexander Koch for helpful discussions in the early stages of this work.

References

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