NP-Completeness and Physical Zero-Knowledge Proof of Hotaru Beam
🤖 AI Summary
This study investigates the computational complexity of the Hotaru Beam logic puzzle and constructs a zero-knowledge proof protocol for it. By means of a polynomial-time reduction, the paper establishes for the first time that Hotaru Beam is NP-complete. Building upon this result, the authors design the first physical zero-knowledge proof protocol—employing simple tangible objects such as playing cards—that enables a prover to convince a verifier of possessing a valid solution without revealing any information about the solution itself. The protocol operates entirely without computational devices, offering both strong security guarantees and practical usability, thereby presenting a novel paradigm for applying physical zero-knowledge proofs to logic puzzles.
Application Category
📝 Abstract
Hotaru Beam is a logic puzzle which objective is to connect circles placed on a grid by drawing only lines with specified starting points and numbers of bends. A zero-knowledge proof is a communication protocol that allows one player to persuade the other that they are in possession of a certain piece of information without actually revealing it. We show that Hotaru Beam is NP-complete and present a physical zero-knowledge proof (i.e. implementable using physical items) for proving that one knows a solution to the puzzle.
Problem
Research questions and friction points this paper is trying to address.
NP-Completeness
Zero-Knowledge Proof
Hotaru Beam
Logic Puzzle
Physical Protocol
Innovation
Methods, ideas, or system contributions that make the work stand out.
NP-completeness
Hotaru Beam
physical zero-knowledge proof
logic puzzle
computational complexity
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