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

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Computing and Combinatorics (COCOON 2021)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 13025))

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Abstract

Sudoku is a logic puzzle with an objective 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. 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 (with 52 different cards and two jokers). Therefore, nine identical decks 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 \(n \times n\) Sudoku that can be performed using a deck of all different cards.

A full version of this paper is available at https://arxiv.org/abs/2106.13646.

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Notes

  1. 1.

    The number of shuffles can be reduced to 108 after optimization. See the full version.

  2. 2.

    The number of shuffles can be reduced to 322 after optimization. See the full version.

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Authors and Affiliations

  1. Department of Mathematical and Computing Science, Tokyo Institute of Technology, Tokyo, Japan

    Suthee Ruangwises

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  1. Suthee Ruangwises
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Editors and Affiliations

  1. National Cheng Kung University, Tainan, Taiwan

    Chi-Yeh Chen

  2. National Tsing Hua University, Hsinchu, Taiwan

    Wing-Kai Hon

  3. National Taipei University of Business, Taoyuan, Taiwan

    Ling-Ju Hung

  4. National Taitung University, Taitung, Taiwan

    Chia-Wei Lee

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Ruangwises, S. (2021). Two Standard Decks of Playing Cards Are Sufficient for a ZKP for Sudoku. In: Chen, CY., Hon, WK., Hung, LJ., Lee, CW. (eds) Computing and Combinatorics. COCOON 2021. Lecture Notes in Computer Science(), vol 13025. Springer, Cham. https://doi.org/10.1007/978-3-030-89543-3_52

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  • DOI: https://doi.org/10.1007/978-3-030-89543-3_52

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  • Print ISBN: 978-3-030-89542-6

  • Online ISBN: 978-3-030-89543-3

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