eng
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
Leibniz International Proceedings in Informatics
1868-8969
2022-05-23
24:1
24:12
10.4230/LIPIcs.FUN.2022.24
article
How to Physically Verify a Rectangle in a Grid: A Physical ZKP for Shikaku
Ruangwises, Suthee
1
https://orcid.org/0000-0002-2820-1301
Itoh, Toshiya
1
https://orcid.org/0000-0002-1149-7046
Department of Mathematical and Computing Science, Tokyo Institute of Technology, Japan
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.
https://drops.dagstuhl.de/storage/00lipics/lipics-vol226-fun2022/LIPIcs.FUN.2022.24/LIPIcs.FUN.2022.24.pdf
Zero-knowledge proof
Card-based cryptography
Shikaku
Puzzles
Games