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Five-Card Secure Computations Using Unequal Division Shuffle

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Theory and Practice of Natural Computing (TPNC 2015)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 9477))

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Abstract

Card-based cryptographic protocols can perform secure computation of Boolean functions. Cheung et al. recently presented an elegant protocol that securely produces a hidden AND value using five cards; however, it fails with a probability of 1/2. The protocol uses an unconventional shuffle operation called unequal division shuffle; after a sequence of five cards is divided into a two-card portion and a three-card portion, these two portions are randomly switched. In this paper, we first show that the protocol proposed by Cheung et al. securely produces not only a hidden AND value but also a hidden OR value (with a probability of 1/2). We then modify their protocol such that, even when it fails, we can still evaluate the AND value. Furthermore, we present two five-card copy protocols using unequal division shuffle. Because the most efficient copy protocol currently known requires six cards, our new protocols improve upon the existing results.

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Acknowledgments

This work was supported by JSPS KAKENHI Grant Numbers 25289068 and 26330001.

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Authors and Affiliations

  1. Sone-Mizuki Laboratory, Graduate School of Information Sciences, Tohoku University, 6-3 Aramaki-Aza-Aoba, Aoba, Sendai, 980-8578, Japan

    Akihiro Nishimura & Takuya Nishida

  2. Faculty of Engineering, Tohoku Gakuin University, 1-13-1 Chuo, Tagajo, Miyagi, 985-8537, Japan

    Yu-ichi Hayashi

  3. Cyberscience Center, Tohoku University, 6-3 Aramaki-Aza-Aoba, Aoba, Sendai, 980-8578, Japan

    Takaaki Mizuki & Hideaki Sone

Authors
  1. Akihiro Nishimura
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  2. Takuya Nishida
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  3. Yu-ichi Hayashi
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  4. Takaaki Mizuki
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  5. Hideaki Sone
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Corresponding author

Correspondence to Akihiro Nishimura .

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Editors and Affiliations

  1. Research Group on Mathematical Linguistics, Universitat Rovira i Virgili, Tarragona, Spain

    Adrian-Horia Dediu

  2. European Centre for Soft Computing, Asturias, Spain

    Luis Magdalena

  3. Research Group on Mathematical Linguistics, Universitat Rovira i Virgili, Tarragona, Spain

    Carlos Martín-Vide

A How to Perform Unequal Division Shuffle

A How to Perform Unequal Division Shuffle

Here, we discuss how to implement unequal division shuffle. We consider the card cases shown in Fig. 1. Each case can store a deck of cards and has two sliding covers, an upper cover and a lower cover. We assume that the weight of a deck of cards is negligible compared to the case. To apply unequal division shuffle, we stow each portion in such a case and shuffle these two cases. Then, the cases are stacked one on top of the other. Removing the two middle sliding covers results in the desired sequence.

Fig. 1.
figure 1

Card cases suited for unequal division shuffle

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Nishimura, A., Nishida, T., Hayashi, Yi., Mizuki, T., Sone, H. (2015). Five-Card Secure Computations Using Unequal Division Shuffle. In: Dediu, AH., Magdalena, L., Martín-Vide, C. (eds) Theory and Practice of Natural Computing. TPNC 2015. Lecture Notes in Computer Science(), vol 9477. Springer, Cham. https://doi.org/10.1007/978-3-319-26841-5_9

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  • DOI: https://doi.org/10.1007/978-3-319-26841-5_9

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-26840-8

  • Online ISBN: 978-3-319-26841-5

  • eBook Packages: Computer ScienceComputer Science (R0)

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