Card-based protocols using unequal division shuffles

Akihiro Nishimura, Takuya Nishida, Yu ichi Hayashi, Takaaki Mizuki, Hideaki Sone

Research output: Contribution to journalArticlepeer-review

21 Citations (Scopus)


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.

Original languageEnglish
Pages (from-to)361-371
Number of pages11
JournalSoft Computing
Issue number2
Publication statusPublished - 2018 Jan 1


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


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