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Physically Verifying the First Nonzero Term in a Sequence: Physical ZKPs for ABC End View and Goishi Hiroi

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Frontiers of Algorithmics (IJTCS-FAW 2023)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 13933))

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Abstract

In this paper, we develop a physical protocol to verify the first nonzero term of a sequence using a deck of cards. This protocol enables a prover to show a verifier the value of the first nonzero term in a given sequence without revealing which term it is. Our protocol uses \(\varTheta (1)\) shuffles, making it simpler and more practical than a similar protocol recently developed by Fukusawa and Manabe in 2022, which uses \(\varTheta (n)\) shuffles, where n is the length of the sequence. We also apply our protocol to construct zero-knowledge proof protocols for two famous logic puzzles: ABC End View and Goishi Hiroi. These zero-knowledge proof protocols allow a prover to physically show that he/she know solutions of the puzzles without revealing them.

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Acknowledgement

The author would like to thank Daiki Miyahara and Kyosuke Hatsugai for a valuable discussion on this research.

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Authors and Affiliations

  1. Department of Informatics, The University of Electro-Communications, Tokyo, Japan

    Suthee Ruangwises

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  1. Suthee Ruangwises
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Correspondence to Suthee Ruangwises .

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Editors and Affiliations

  1. City University of Hong Kong, Hong Kong SAR, China

    Minming Li

  2. Chinese Academy of Sciences, Beijing, China

    Xiaoming Sun

  3. University of Macau, Macau, China

    Xiaowei Wu

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Ruangwises, S. (2023). Physically Verifying the First Nonzero Term in a Sequence: Physical ZKPs for ABC End View and Goishi Hiroi. In: Li, M., Sun, X., Wu, X. (eds) Frontiers of Algorithmics. IJTCS-FAW 2023. Lecture Notes in Computer Science, vol 13933. Springer, Cham. https://doi.org/10.1007/978-3-031-39344-0_13

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  • DOI: https://doi.org/10.1007/978-3-031-39344-0_13

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  • Online ISBN: 978-3-031-39344-0

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