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DOI: 10.4230/LIPIcs.FUN.2026.33

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

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

Published in: LIPIcs, Volume 366, 13th International Conference on Fun with Algorithms (FUN 2026)

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.

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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)

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@InProceedings{miyahara_et_al:LIPIcs.FUN.2026.33,
  author =	{Miyahara, Daiki and Robert, L\'{e}o and Lafourcade, Pascal and Kaneko, Shohei},
  title =	{{When Locality Implies Globality: Card-Based ZKP Protocol for Shakashaka Puzzle}},
  booktitle =	{13th International Conference on Fun with Algorithms (FUN 2026)},
  pages =	{33:1--33:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-417-8},
  ISSN =	{1868-8969},
  year =	{2026},
  volume =	{366},
  editor =	{Iacono, John},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FUN.2026.33},
  URN =		{urn:nbn:de:0030-drops-257525},
  doi =		{10.4230/LIPIcs.FUN.2026.33},
  annote =	{Keywords: Card-based cryptography, ShakaShaka, Nikoli, ZKP}
}

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

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