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A Physical Zero-Knowledge Proof for Sumplete, a Puzzle Generated by ChatGPT

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Computing and Combinatorics (COCOON 2023)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 14422))

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Abstract

In March 2023, ChatGPT generated a new puzzle, Sumplete. Sumplete consists of an \(n \times n\) grid, each whose cell has an integer. In addition, each row and column of the grid has an integer, which we call a target value. The goal of Sumplete is to make the sum of integers in each row and column equal to the target value by deleting some integers of the cells. In this paper, we prove that Sumplete is NP-complete and propose a physical zero-knowledge proof for Sumplete. To show the NP-completeness, we give a polynomial reduction from the subset sum problem to Sumplete. In our physical zero-knowledge proof protocol, we use a card protocol that realizes the addition of negative and positive integers using cyclic permutation on a sequence of cards. To keep the solution secret, we use a technique named decoy technique.

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Notes

  1. 1.

    This name was also named by ChatGPT [19].

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Acknowledgments

This work was supported by JSPS KAKENHI Grant Numbers JP22KJ1362 and JP23KJ0968.

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Authors and Affiliations

  1. The University of Electro-Communications, 1-5-1 Chofugaoka, Chofu, Tokyo, 182-8585, Japan

    Kyosuke Hatsugai, Kyoichi Asano & Yoshiki Abe

  2. National Institute of Advanced Industrial Science and Technology, 2-3-26 Aomi, Koto-ku, Tokyo, 135-0064, Japan

    Yoshiki Abe

Authors
  1. Kyosuke Hatsugai
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  2. Kyoichi Asano
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  3. Yoshiki Abe
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Correspondence to Kyosuke Hatsugai .

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Editors and Affiliations

  1. University of Texas at Dallas, Richardson, TX, USA

    Weili Wu

  2. University of Delaware, Newark, DE, USA

    Guangmo Tong

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Hatsugai, K., Asano, K., Abe, Y. (2024). A Physical Zero-Knowledge Proof for Sumplete, a Puzzle Generated by ChatGPT. In: Wu, W., Tong, G. (eds) Computing and Combinatorics. COCOON 2023. Lecture Notes in Computer Science, vol 14422. Springer, Cham. https://doi.org/10.1007/978-3-031-49190-0_29

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  • DOI: https://doi.org/10.1007/978-3-031-49190-0_29

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  • Print ISBN: 978-3-031-49189-4

  • Online ISBN: 978-3-031-49190-0

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