Physical Zero-Knowledge Proof for Suguru Puzzle

Léo Robert (1) , Daiki Miyahara (2) , Pascal Lafourcade (1) , Takaaki Mizuki (2)

1 LIMOS - Laboratoire d'Informatique, de Modélisation et d'Optimisation des Systèmes
2 Tohoku University [Sendai]

Suguru is a paper and pencil puzzle invented by Naoki Inaba. The goal of the game is to fulfil a grid with numbers between 1 and 5 and to respect three simple constraints. In this paper we design a physical Zero-Knowledge Proof (ZKP) protocol for Suguru. A ZKP protocol allows a prover (P) to prove that he knows a solution of a Suguru grid to a verifier (V) without leaking any information on the solution. For constructing such a physical ZKP protocol, we only rely on a small number of physical cards and an adapted encoding. For a grid of Suguru 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.

Mots clés: Physical zero-knowledge proof; Suguru; Security; Completeness; Extractability; Zero-knowledge proof

Domaines: Cryptographie et sécurité [cs.CR]

Léo Robert, Daiki Miyahara, Pascal Lafourcade, Takaaki Mizuki. Physical Zero-Knowledge Proof for Suguru Puzzle. 22nd International Symposium on Stabilization, Safety, and Security of Distributed Systems SSS 2020, Nov 2020, Austin, United States. ⟨hal-03017693⟩