How to construct physical zero-knowledge proofs for puzzles with a “single loop” condition
Pascal Lafourcade, Daiki Miyahara, Takaaki Mizuki, Léo Robert, Tatsuya Sasaki, Hideaki Sone
Abstract
We propose a technique to construct physical Zero-Knowledge Proof (ZKP) protocols for puzzles that require a single loop draw feature. Our approach is based on the observation that a loop has only one hole and this property remains stable by some simple transformations. Using this trick, we can transform a simple big loop, which is visible to anyone, into the solution loop by using transformations that do not disclose any information about the solution. We illustrate our technique by applying it to construct physical ZKP protocols for two Nikoli puzzles: Slitherlink and Masyu.
Topics & Concepts
Construct (python library)Mathematical proofLoop (graph theory)Simple (philosophy)Computer scienceZero-knowledge proofProperty (philosophy)Feature (linguistics)Zero (linguistics)Theoretical computer scienceAlgorithmMathematicsProgramming languageCombinatoricsGeometryPhilosophyLinguisticsEpistemologyDigital Image Processing TechniquesGraph Theory and AlgorithmsComputational Geometry and Mesh Generation