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

Authors Suthee Ruangwises , Toshiya Itoh

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Author Details

Suthee Ruangwises
  • Department of Mathematical and Computing Science, Tokyo Institute of Technology, Japan
Toshiya Itoh
  • Department of Mathematical and Computing Science, Tokyo Institute of Technology, Japan

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Suthee Ruangwises and Toshiya Itoh. How to Physically Verify a Rectangle in a Grid: A Physical ZKP for Shikaku. In 11th International Conference on Fun with Algorithms (FUN 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 226, pp. 24:1-24:12, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022) https://doi.org/10.4230/LIPIcs.FUN.2022.24

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.

Subject Classification

ACM Subject Classification
  • Security and privacy → Information-theoretic techniques
  • Theory of computation → Cryptographic protocols
Keywords
  • Zero-knowledge proof
  • Card-based cryptography
  • Shikaku
  • Puzzles
  • Games

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References

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