International Journal of Information Security

, Volume 13, Issue 1, pp 15–23 | Cite as

A formalization of card-based cryptographic protocols via abstract machine

Regular Contribution
First Online:

Abstract

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.

Keywords

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

Acknowledgments

This work was supported by JSPS KAKENHI Grant Number 23700007.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  1. 1.Cyberscience CenterTohoku UniversitySendai Japan
  2. 2.Center for Information Technology in EducationTohoku UniversitySendai Japan

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