A formalization of card-based cryptographic protocols via abstract machine

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66 Citations (Scopus)


Consider a face-down card lying on the table such that we do not know whether its suit color is black or red. Then, how do we make identical copies of the card while keeping its color secret? A partial solution has been devised: using a number of additional black and red cards, Niemi and Renvall proposed an excellent protocol which can copy a face-down card while allowing only a small probability of revealing its color. In contrast, this paper shows the nonexistence of a perfect solution, namely, the impossibility of copying a face-down card with perfect secrecy. To prove such an impossibility result, we construct a rigorous mathematical model of card-based cryptographic protocols; giving this general computational model is the main result of this paper.

Original languageEnglish
Pages (from-to)15-23
Number of pages9
JournalInternational Journal of Information Security
Issue number1
Publication statusPublished - 2014 Feb


  • Card games
  • Card-based protocols
  • Cryptography without computers
  • Recreational cryptography
  • Secure computations


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