Paper 2017/425

Card-Based Protocols Using Unequal Division Shuffles

Akihiro Nishimura, Takuya Nishida, Yu-ichi Hayashi, Takaaki Mizuki, and 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.

Available format(s)
Cryptographic protocols
Publication info
Published elsewhere. Soft Computing
Card-based protocols
Contact author(s)
tm-paper+card5cop @ g-mail tohoku-university jp
2017-09-26: last of 2 revisions
2017-05-22: received
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Creative Commons Attribution


      author = {Akihiro Nishimura and Takuya Nishida and Yu-ichi Hayashi and Takaaki Mizuki and Hideaki Sone},
      title = {Card-Based Protocols Using Unequal Division Shuffles},
      howpublished = {Cryptology ePrint Archive, Paper 2017/425},
      year = {2017},
      doi = {10.1007/s00500-017-2858-2},
      note = {\url{}},
      url = {}
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