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Card-Based Cryptographic Protocols with the Minimum Number of Cards Using Private Operations

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Foundations and Practice of Security (FPS 2018)

Part of the book series: Lecture Notes in Computer Science ((LNSC,volume 11358))

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Abstract

This paper proposes new card-based cryptographic protocols with the minimum number of cards using private operations under the semi-honest model. Though various card-based cryptographic protocols were shown, the minimum number of cards used in the protocol has not been achieved yet for many problems. Operations executed by a player where the other players cannot see are called private operations. Private operations have been introduced in some protocols to solve a particular problem or to input private values. However, the effectiveness of introducing private operations to the calculation of general logic functions has not been considered. This paper introduces three new private operations: private random bisection cuts, private reverse cuts, and private reveals. With these three new operations, we show that all of logical and, logical xor, and copy protocols are achieved with the minimum number of cards by simple three round protocols. This paper, then shows a protocol to calculate any logical functions using these private operations.

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Authors and Affiliations

  1. Kogakuin University, Shinjuku, Tokyo, 163-8677, Japan

    Hibiki Ono & Yoshifumi Manabe

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  1. Hibiki Ono
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  2. Yoshifumi Manabe
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Correspondence to Yoshifumi Manabe .

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Editors and Affiliations

  1. Dalhousie University, Halifax, NS, Canada

    Nur Zincir-Heywood

  2. École des Mines de Nancy, Nancy, France

    Guillaume Bonfante

  3. Concordia University, Montreal, QC, Canada

    Mourad Debbabi

  4. Telecom SudParis, Evry, France

    Joaquin Garcia-Alfaro

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Ono, H., Manabe, Y. (2019). Card-Based Cryptographic Protocols with the Minimum Number of Cards Using Private Operations. In: Zincir-Heywood, N., Bonfante, G., Debbabi, M., Garcia-Alfaro, J. (eds) Foundations and Practice of Security. FPS 2018. Lecture Notes in Computer Science(), vol 11358. Springer, Cham. https://doi.org/10.1007/978-3-030-18419-3_13

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  • DOI: https://doi.org/10.1007/978-3-030-18419-3_13

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-18418-6

  • Online ISBN: 978-3-030-18419-3

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