NP-Completeness and Physical Zero-Knowledge Proof of Hotaru Beam

TL;DR

This paper proves Hotaru Beam is NP-complete and introduces a physical zero-knowledge proof protocol for demonstrating knowledge of a solution without revealing it.

Contribution

It establishes the NP-completeness of Hotaru Beam and presents the first physical zero-knowledge proof for this puzzle.

Findings

Hotaru Beam is NP-complete.

A physical zero-knowledge proof protocol is developed.

The protocol allows solution verification without disclosure.

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.