Tatami Printer: Physical ZKPs for Tatami Puzzles

2024-08-24

arXiv.org

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.

Technology Category

• Constraint Satisfaction and Optimization: Satisfiability Modulo Theories
• Reasoning under Uncertainty: Other Foundations of Reasoning under Uncertainty
• Data Mining & Knowledge Management: Representing, Reasoning, and Using Provenance, Trust

Application Category

• Security and Privacy: Data transparency and provenance
• Responsible Web: Data and user privacy-enhancing technologies for the Web
• Economics, Online Markets and Human Computation: Trust and reliance of crowd workers and data experts on GenAI

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.

Problem

• Develops physical card-based puzzle verification
• Constructs zero-knowledge proofs for Tatami puzzles
• Ensures solution privacy in puzzle verification

Innovation

• Card-based protocol for verification
• Zero-knowledge proof for puzzles
• Solution verification without disclosure