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

TL;DR

This paper introduces a more practical zero-knowledge proof protocol for Sudoku using only two standard decks of playing cards, improving on previous methods that required multiple non-standard cards or decks.

Contribution

The authors present a novel ZKP protocol for Sudoku that operates with only two standard decks, making it more feasible and adaptable than prior protocols requiring special or multiple decks.

Findings

Protocol works with only two standard decks of cards.

First ZKP protocol for generalized n x n Sudoku with all different cards.

Reduces complexity and improves practicality of Sudoku ZKP protocols.

Abstract

Sudoku is a famous logic puzzle where the player has to fill a number between 1 and 9 into each empty cell of a $9 \times 9$ grid such that every number appears exactly once in each row, each column, and each $3 \times 3$ block. In 2020, Sasaki et al. developed a physical card-based protocol of zero-knowledge proof (ZKP) for Sudoku, which enables a prover to convince a verifier that he/she knows a solution of the puzzle without revealing it. Their protocol uses 90 cards, but requires nine identical copies of some cards, which cannot be found in a standard deck of playing cards (consisting of 52 different cards and two jokers). Hence, nine identical standard decks are required to perform that protocol, making the protocol not very practical. In this paper, we propose a new ZKP protocol for Sudoku that can be performed using only two standard decks of playing cards, regardless of whether the two decks are identical or different. In general, we also develop the first ZKP protocol for a generalized $n \times n$ Sudoku that can be performed using a deck of all different cards.