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International Computing and Combinatorics Conference

COCOON 2021: Computing and Combinatorics pp 668–679Cite as

A Card-Minimal Three-Input AND Protocol Using Two Shuffles

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

Abstract

Card-based cryptography typically uses a physical deck comprising black and red cards to perform secure computations, where a one-bit value is encoded using a pair of cards with different colors such that the order of black to red represents 0 and red to black represents 1. One of the most fundamental classes of card-based protocols is the class of “card-minimal” n-input AND protocols, which require 2n face-down cards as input to securely evaluate the AND value after applying a number of shuffles; here, the 2n cards are minimally required to describe an n-bit input. The best n-input AND protocols currently known use two shuffles for \(n=2\), five shuffles for \(n=3\), and \(n+1\) shuffles for \(n>3\). These upper bounds on the numbers of shuffles have not been improved for several years. In this work, we present a better upper bound for the \(n=3\) case by designing a new card-minimal three-input AND protocol using only two shuffles. Therefore, our proposed protocol reduces the number of required shuffles from five to two; we believe that this is a significant improvement.

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Acknowledgements

We thank the anonymous referees, whose comments have helped us improve the presentation of the paper. We would like to thank Hideaki Sone for his cooperation in preparing a Japanese draft version at an earlier stage of this work. This work was supported in part by JSPS KAKENHI Grant Numbers JP19J21153 and JP21K11881.

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Authors and Affiliations

  1. Tohoku University, Sendai, Japan

    Raimu Isuzugawa, Kodai Toyoda, Yu Sasaki & Takaaki Mizuki

  2. National Institute of Advanced Industrial Science and Technology, Tokyo, Japan

    Daiki Miyahara & Takaaki Mizuki

  3. The University of Electro-Communications, Tokyo, Japan

    Daiki Miyahara

Authors
  1. Raimu Isuzugawa
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  2. Kodai Toyoda
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  3. Yu Sasaki
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  4. Daiki Miyahara
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  5. Takaaki Mizuki
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Correspondence to Raimu Isuzugawa .

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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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Isuzugawa, R., Toyoda, K., Sasaki, Y., Miyahara, D., Mizuki, T. (2021). A Card-Minimal Three-Input AND Protocol Using Two Shuffles. 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_55

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  • DOI: https://doi.org/10.1007/978-3-030-89543-3_55

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