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.

翻译：萤火虫光束是一种逻辑谜题，其目标是通过仅绘制具有指定起点和弯折次数的线条来连接网格上的圆圈。零知识证明是一种通信协议，允许一方使另一方确信其拥有某个信息，而无需实际透露该信息。我们证明萤火虫光束是NP完全的，并提出了一种物理零知识证明（即可使用物理物品实现），用于证明某人知晓该谜题的解法。