Card-Based Zero-Knowledge Proof for Dosun-Fuwari

Abstract

Dosun-Fuwari is one of Nikoli’s pencil puzzles. It is known that the generalized Dosun-Fuwari puzzle is NP-complete. Due to the inherent difficulty of the puzzle, solvers may often question whether a solution exists. Such questions highlight the need for a method that can verify the existence of a solution without revealing it, thereby preserving the puzzle’s challenge. In this paper, we propose a physical zero-knowledge proof protocol for the Dosun-Fuwari puzzle, which can be executed using 4mn + 2n cards. Here, m × n is the size of the instance of the puzzle.