Physical zero-knowledge proof and NP-completeness proof of Suguru puzzle

Suguru is a paper and pencil puzzle invented by Naoki Inaba. The goal of the game is to fill a grid with numbers between 1 and 5 while respecting three simple constraints. We first prove the NP-completeness of Suguru puzzle. For this we design gadgets to encode the PLANAR-CIRCUIT-SAT in a Suguru gri...

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Bibliographic Details
Published in:Information and computation Vol. 285; p. 104858
Main Authors: Robert, Léo, Miyahara, Daiki, Lafourcade, Pascal, Libralesso, Luc, Mizuki, Takaaki
Format: Journal Article
Language:English
Published: Elsevier Inc 01.05.2022
Elsevier
Subjects:
Completeness
Computer Science
Cryptography and Security
Extractability
Physical zero-knowledge proof
Security
Suguru
Zero-knowledge
Suguru
Zero-knowledge
Physical zero-knowledge proof
Extractability
Security
Completeness
ISSN:0890-5401, 1090-2651
Online Access:Get full text
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Summary:Suguru is a paper and pencil puzzle invented by Naoki Inaba. The goal of the game is to fill a grid with numbers between 1 and 5 while respecting three simple constraints. We first prove the NP-completeness of Suguru puzzle. For this we design gadgets to encode the PLANAR-CIRCUIT-SAT in a Suguru grid. We then design a physical Zero-Knowledge Proof (ZKP) protocol for Suguru. This ZKP protocol allows a prover to prove that he knows a solution of a Suguru grid to a verifier without leaking any information on the solution. To construct such a physical ZKP protocol, we only rely on a few physical cards and adapted encoding. For a Suguru grid with n cells, we only use 5n+5 cards. Moreover, we prove the three classical security properties of a ZKP: completeness, extractability, and zero-knowledge.
ISSN:0890-5401
1090-2651
DOI:10.1016/j.ic.2021.104858