NP-Completeness and Physical Zero-Knowledge Proof of Hotaru Beam
Computational Complexity
2026-03-03 v1 Cryptography and Security
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.
Cite
@article{arxiv.2603.01393,
title = {NP-Completeness and Physical Zero-Knowledge Proof of Hotaru Beam},
author = {Taisei Otsuji and Peter Fulla and Takuro Fukunaga},
journal= {arXiv preprint arXiv:2603.01393},
year = {2026}
}
Comments
A preliminary version of this paper was presented at the 30th International Conference on Computing and Combinatorics (COCOON)