Soft Computing

, Volume 22, Issue 2, pp 361–371 | Cite as

Card-based protocols using unequal division shuffles

  • Akihiro Nishimura
  • Takuya Nishida
  • Yu-ichi Hayashi
  • Takaaki Mizuki
  • Hideaki Sone


Card-based cryptographic protocols can perform secure computation of Boolean functions. In 2013, Cheung et al. presented a 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 an 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 so that nobody knows which is which. 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 in the clear. Furthermore, we present two five-card copy protocols (which can duplicate a hidden value) using unequal division shuffle. Because the most efficient copy protocol currently known requires six cards, our new protocols improve upon the existing results. We also design a general copy protocol that produces multiple copies using an unequal division shuffle. Furthermore, we show feasible implementations of unequal division shuffles by the use of card cases.


Cryptography Card-based protocols Card games Cryptography without computers Real-life hands-on cryptography Secure multi-party computations 



We thank the anonymous referees, whose comments have helped us to improve the presentation of the paper. This work was supported by JSPS KAKENHI Grant Nos. 25289068, 26330001, and 17K00001.

Compliance with ethical standards

Conflict of interest

The authors declare that they have no conflict of interest.

Ethical approval

This article does not contain any studies with human participants or animals performed by any of the authors.


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Copyright information

© Springer-Verlag GmbH Germany 2017

Authors and Affiliations

  • Akihiro Nishimura
    • 1
  • Takuya Nishida
    • 1
  • Yu-ichi Hayashi
    • 2
  • Takaaki Mizuki
    • 3
  • Hideaki Sone
    • 3
  1. 1.Sone-Mizuki Laboratory, Graduate School of Information SciencesTohoku UniversitySendaiJapan
  2. 2.Graduate School of Information SciencesNara Institute of Science and TechnologyNaraJapan
  3. 3.Cyberscience CenterTohoku UniversitySendaiJapan

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