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A secure additive protocol for card players

 

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Author: Cordón Franco, Andrés
Ditmarsch, Hans P. van
Fernández Duque, David
Joosten, Joost J.
Soler Toscano, Fernando
Department: Universidad de Sevilla. Departamento de Filosofía y Lógica y Filosofía de la Ciencia
Universidad de Sevilla. Departamento de Ciencias de la Computación e Inteligencia Artificial
Date: 2012
Published in: The Australasian Journal of Combinatorics, 54, 163-175.
Document type: Article
Abstract: Consider three players Alice, Bob and Cath who hold a, b and c cards, respectively, from a deck of d=a+b+c cards. The cards are all different and players only know their own cards. Suppose Alice and Bob wish to communicate their cards to each other without Cath learning whether Alice or Bob holds a specific card. Considering the cards as consecutive natural numbers 0, 1,..., we investigate general conditions for when Alice or Bob can safely announce the sum of the cards they hold modulo an appropriately chosen integer. We demonstrate that this holds whenever a, b > 2 and c=1. Because Cath holds a single card, this also implies that Alice and Bob will learn the card deal from the other player’s announcement.
Cite: Cordón Franco, A., Ditmarsch, H.P.v., Fernández Duque, D., Joosten, J.J. y Soler Toscano, F. (2012). A secure additive protocol for card players. The Australasian Journal of Combinatorics, 54, 163-175.
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URI: http://hdl.handle.net/11441/64194

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