Two Standard Decks of Playing Cards are Sufficient for a ZKP for Sudoku

Abstract

Sudoku is a logic puzzle with an objective to fill a number between 1 and 9 in each empty cell of a 9×9 grid such that every number appears exactly once in each row, each column, and each 3×3 block. In 2020, Sasaki et al. proposed a physical zero-knowledge proof (ZKP) protocol for Sudoku using 90 cards, which allows a prover to physically show that he/she knows a solution without revealing it. However, their protocol requires nine identical copies of some cards, which cannot be found in a standard deck of playing cards. Therefore, nine decks of cards are actually required in order to perform that protocol. In this paper, we propose a new ZKP protocol for Sudoku that can be performed using only two standard decks of playing cards. In general, we develop the first ZKP protocol for an n × n Sudoku that can be performed using a deck of all different cards.