Ball sort puzzle is a popular logic puzzle consisting of several bins containing balls of multiple colors. Each bin works like a stack; a ball has to follow the last-in first-out order. The player has to sort the balls by color such that each bin contains only balls of a single color. In this paper, we propose a physical zero-knowledge proof protocol for the ball sort puzzle using a deck of playing cards, which enables a prover to physically show that he/she knows a solution with $t$ moves of the ball sort puzzle without revealing it. Our protocol is the first zero-knowledge proof protocol for an interactive puzzle involving moving objects.

翻译：球排序谜题是一种流行的逻辑谜题，由多个装有不同颜色球的容器组成。每个容器的工作原理类似于栈，球需遵循后进先出（LIFO）顺序。玩家需按颜色对球进行排序，使得每个容器内仅包含单一颜色的球。本文提出了一种基于扑克牌的物理零知识证明协议，用于解决球排序谜题：证明者可通过该协议物理地展示其知道一个能在$t$步内完成谜题的解，而无需泄露该解的具体内容。本协议是首个针对涉及物体移动的交互式谜题的零知识证明协议。