Five Cells is a logic puzzle consisting of a rectangular grid, with some cells containg a number. The player has to partition the grid into pentominoes such that the number in each cell must be equal to the number of edges of that cell that are borders of pentominoes. In this paper, we propose two physical zero-knowledge proof protocols for Five Cells using a deck of playing cards, which allow a prover to physically show that he/she knows a solution of the puzzle without revealing it. In the optimization of our first protocol, we also develop a technique to reduce the number of required cards from quadratic to linear in the number of cells, which can be used in other zero-knowledge proof protocols related to graph coloring as well.

翻译：五格谜题是一种逻辑谜题，由矩形网格组成，部分格子包含数字。玩家需要将网格划分为五格骨牌，使得每个格子中的数字等于该格子作为五格骨牌边界的边数。本文提出了两种基于扑克牌的五格谜题物理零知识证明协议，允许证明者在不泄露解法的情况下物理展示其知晓谜题解答。在首个协议的优化中，我们还开发了一种技巧，将所需卡牌数量从网格单元数的二次方降至线性，该技巧还可用于其他与图着色相关的零知识证明协议。