Five Cells is a pencil puzzle consisting of a rectangular grid, with some cells containg a number. The player has to partition the grid into blocks, each consisting of five cells, such that the number in each cell must be equal to the number of edges of that cell that are borders of blocks. In this paper, we propose a physical zero-knowledge proof protocol for Shikaku using a deck of playing cards, which allows a prover to physically show that he/she knows a solution of the puzzle without revealing it. More importantly, in the optimization we develop a technique to verify a graph coloring that no two adjacent vertices have the same color without revealing any information about the coloring. This technique reduces the number of required cards in our protocol from quadratic to linear in the number of cells, and can also be used in other protocols related to graph coloring.

翻译：五格谜题是一种由矩形网格构成的铅笔谜题，其中部分单元格包含数字。玩家需要将网格划分为多个由五个单元格组成的区块，使得每个单元格内的数字等于该单元格作为区块边界的边数。本文针对Shikaku谜题提出了一种基于扑克牌的物理零知识证明协议，证明者可物理地展示其知晓谜题的解而不泄露任何信息。更重要的是，在优化过程中我们发展了一种技术，能够在不泄露着色信息的前提下验证图着色中任意相邻顶点颜色不同。该技术将协议所需卡牌数量从单元格数的二次方降低至线性，并可推广至其他与图着色相关的协议。