Three Steps

  • Hans van Ditmarsch
  • Fernando Soler–Toscano
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6814)


Given is a deal of ten cards over three players, such that two players each get four cards and the remaining player (the ‘eavesdropper’) two cards. We show that there does not exist a protocol of two steps for the four-card players to inform each other safely of their hands of cards, and we then present a protocol of three steps that achieves that goal. We verify the properties of that protocol by combinatorial and, mainly, logical (model checking) means. No such three-step protocol for cards was known. The method can be generalized. This will advance the characterization of card deals for which such exchanges of secrets are possible.


Model Check Common Knowledge Epistemic Logic Public Announcement Actual Hand 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  • Hans van Ditmarsch
    • 1
  • Fernando Soler–Toscano
    • 1
  1. 1.University of SevillaSpain

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