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A geometric protocol for cryptography with cards

(2013) DESIGNS CODES AND CRYPTOGRAPHY. 74(1). p.113-125
Author
Organization
Abstract
In the generalized Russian cards problem, the three players Alice, Bob and Cath draw and cards, respectively, from a deck of cards. Players only know their own cards and what the deck of cards is. Alice and Bob are then required to communicate their hand of cards to each other by way of public messages. For a natural number , the communication is said to be -safe if Cath does not learn whether or not Alice holds any given set of at most cards that are not Cath's, a notion originally introduced as weak -security by Swanson and Stinson. An elegant solution by Atkinson views the cards as points in a finite projective plane. We propose a general solution in the spirit of Atkinson's, although based on finite vector spaces rather than projective planes, and call it the 'geometric protocol'. Given arbitrary , this protocol gives an informative and -safe solution to the generalized Russian cards problem for infinitely many values of with . This improves on the collection of parameters for which solutions are known. In particular, it is the first solution which guarantees -safety when Cath has more than one card.
Keywords
Information-based cryptography, Secure communication, Secret-exchange protocols

Citation

Please use this url to cite or link to this publication:

MLA
Cordón-Franco, Andrés et al. “A Geometric Protocol for Cryptography with Cards.” DESIGNS CODES AND CRYPTOGRAPHY 74.1 (2013): 113–125. Print.
APA
Cordón-Franco, A., van Ditmarsch, H., Fernández-Duque, D., & Soler-Toscano, F. (2013). A geometric protocol for cryptography with cards. DESIGNS CODES AND CRYPTOGRAPHY, 74(1), 113–125.
Chicago author-date
Cordón-Franco, Andrés, Hans van Ditmarsch, David Fernández-Duque, and Fernando Soler-Toscano. 2013. “A Geometric Protocol for Cryptography with Cards.” Designs Codes and Cryptography 74 (1): 113–125.
Chicago author-date (all authors)
Cordón-Franco, Andrés, Hans van Ditmarsch, David Fernández-Duque, and Fernando Soler-Toscano. 2013. “A Geometric Protocol for Cryptography with Cards.” Designs Codes and Cryptography 74 (1): 113–125.
Vancouver
1.
Cordón-Franco A, van Ditmarsch H, Fernández-Duque D, Soler-Toscano F. A geometric protocol for cryptography with cards. DESIGNS CODES AND CRYPTOGRAPHY. 2013;74(1):113–25.
IEEE
[1]
A. Cordón-Franco, H. van Ditmarsch, D. Fernández-Duque, and F. Soler-Toscano, “A geometric protocol for cryptography with cards,” DESIGNS CODES AND CRYPTOGRAPHY, vol. 74, no. 1, pp. 113–125, 2013.
@article{8566411,
  abstract     = {In the generalized Russian cards problem, the three players Alice, Bob and Cath draw and cards, respectively, from a deck of cards. Players only know their own cards and what the deck of cards is. Alice and Bob are then required to communicate their hand of cards to each other by way of public messages. For a natural number , the communication is said to be -safe if Cath does not learn whether or not Alice holds any given set of at most cards that are not Cath's, a notion originally introduced as weak -security by Swanson and Stinson. An elegant solution by Atkinson views the cards as points in a finite projective plane. We propose a general solution in the spirit of Atkinson's, although based on finite vector spaces rather than projective planes, and call it the 'geometric protocol'. Given arbitrary , this protocol gives an informative and -safe solution to the generalized Russian cards problem for infinitely many values of with . This improves on the collection of parameters for which solutions are known. In particular, it is the first solution which guarantees -safety when Cath has more than one card.},
  author       = {Cordón-Franco, Andrés and van Ditmarsch, Hans and Fernández-Duque, David and Soler-Toscano, Fernando},
  issn         = {0925-1022},
  journal      = {DESIGNS CODES AND CRYPTOGRAPHY},
  keywords     = {Information-based cryptography,Secure communication,Secret-exchange protocols},
  language     = {eng},
  number       = {1},
  pages        = {113--125},
  title        = {A geometric protocol for cryptography with cards},
  url          = {http://dx.doi.org/10.1007/s10623-013-9855-y},
  volume       = {74},
  year         = {2013},
}

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