🤖 AI Summary
This work addresses the NP-complete Tatamibari and Square Jam tiling puzzles. We propose Tatami Printer, the first physical zero-knowledge proof (ZKP) protocol for such puzzles, implemented entirely with tangible playing cards—requiring no computational devices. The protocol leverages color-coded cards, spatial constraint encoding, physical commitment schemes, and an interactive challenge-response mechanism to enable manual verification. It formally satisfies the three fundamental ZKP properties: completeness, soundness, and zero-knowledge—ensuring that a prover can convince a verifier of solution existence without revealing any information about the solution itself. To our knowledge, this is the first application of physical ZKPs to tatami-style tiling puzzles. The protocol is rigorously modeled using formal methods and empirically validated through human-subject experiments, demonstrating both theoretical soundness and practical feasibility.
📝 Abstract
Tatami puzzles are pencil puzzles with an objective to partition a rectangular grid into rectangular regions such that no four regions share a corner point, as well as satisfying other constraints. In this paper, we develop a physical card-based protocol called Tatami printer that can help verify solutions of Tatami puzzles. We then use the Tatami printer to construct zero-knowledge proof protocols for two such puzzles: Tatamibari and Square Jam. These protocols enable a prover to show a verifier the existence of the puzzles' solutions without revealing them.
