License: Creative Commons Attribution 4.0 International license (CC BY 4.0)
When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.FUN.2022.24
URN: urn:nbn:de:0030-drops-159947
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2022/15994/
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Ruangwises, Suthee ; Itoh, Toshiya

How to Physically Verify a Rectangle in a Grid: A Physical ZKP for Shikaku

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LIPIcs-FUN-2022-24.pdf (0.6 MB)

Abstract

Shikaku is a pencil puzzle consisting of a rectangular grid, with some cells containing a number. The player has to partition the grid into rectangles such that each rectangle contains exactly one number equal to the area of that rectangle. In this paper, we propose two physical zero-knowledge proof protocols for Shikaku using a deck of playing cards, which allow a prover to physically show that he/she knows a solution of the puzzle without revealing it. Most importantly, in our second protocol we develop a general technique to physically verify a rectangle-shaped area with a certain size in a rectangular grid, which can be used to verify other problems with similar constraints.

BibTeX - Entry

@InProceedings{ruangwises_et_al:LIPIcs.FUN.2022.24,
  author =	{Ruangwises, Suthee and Itoh, Toshiya},
  title =	{{How to Physically Verify a Rectangle in a Grid: A Physical ZKP for Shikaku}},
  booktitle =	{11th International Conference on Fun with Algorithms (FUN 2022)},
  pages =	{24:1--24:12},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-232-7},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{226},
  editor =	{Fraigniaud, Pierre and Uno, Yushi},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/opus/volltexte/2022/15994},
  URN =		{urn:nbn:de:0030-drops-159947},
  doi =		{10.4230/LIPIcs.FUN.2022.24},
  annote =	{Keywords: Zero-knowledge proof, Card-based cryptography, Shikaku, Puzzles, Games}
}

Keywords: Zero-knowledge proof, Card-based cryptography, Shikaku, Puzzles, Games
Collection: 11th International Conference on Fun with Algorithms (FUN 2022)
Issue Date: 2022
Date of publication: 23.05.2022

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