Abstract
Given an interpreted system, we investigate ways for two agents to communicate secrets by public announcements. For card deals, the problem to keep all of your cards a secret (i) can be distinguished from the problem to keep some of your cards a secret (ii). For (i): we characterize a novel class of protocols consisting of two announcements, for the case where two agents both hold n cards and the third agent a single card; the communicating agents announce the sum of their cards modulo 2n + 1. For (ii): we show that the problem to keep at least one of your cards a secret is equivalent to the problem to keep your local state (hand of cards) a secret; we provide a large class of card deals for which exchange of secrets is possible; and we give an example for which there is no protocol of less than three announcements.
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References
Albert, M., Aldred, R., Atkinson, M., van Ditmarsch, H., Handley, C.: Safe communication for card players by combinatorial designs for two-step protocols. Australasian Journal of Combinatorics 33, 33–46 (2005)
van Ditmarsch, H.: The Russian cards problem. Studia Logica 75, 31–62 (2003)
Erdös, P., Heilbronn, H.: On the addition of residue classes modulo p. Acta Arithmetica 9, 149–159 (1964)
Fagin, R., Halpern, J., Moses, Y., Vardi, M.: Reasoning about Knowledge. MIT Press, Cambridge (1995)
Fischer, M., Wright, R.: Multiparty secret key exchange using a random deal of cards. In: Feigenbaum, J. (ed.) CRYPTO 1991. LNCS, vol. 576, pp. 141–155. Springer, Heidelberg (1992)
Fischer, M., Wright, R.: Bounds on secret key exchange using a random deal of cards. Journal of Cryptology 9(2), 71–99 (1996)
Kirkman, T.: On a problem in combinations. Camb. and Dublin Math. J. 2, 191–204 (1847)
Makarychev, K., Makarychev, Y.: The importance of being formal. Mathematical Intelligencer 23(1), 41–42 (2001)
da Silva, J.D., Hamidourne, Y.: Cyclic spaces for Grassmann derivatives and additive theory. Bull. London Math. Soc. 26, 140–146 (1994)
Stinson, D.: Combinatorial Designs – Constructions and Analysis. Springer, Heidelberg (2004)
Wang, Y.: Epistemic modelling and protocol dynamics. Ph.D. thesis, University of Amsterdam, ILLC Dissertation Series DS-2010-06 (2010)
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Albert, M., Cordón-Franco, A., van Ditmarsch, H., Fernández-Duque, D., Joosten, J.J., Soler-Toscano, F. (2011). Secure Communication of Local States in Interpreted Systems. In: Abraham, A., Corchado, J.M., González, S.R., De Paz Santana, J.F. (eds) International Symposium on Distributed Computing and Artificial Intelligence. Advances in Intelligent and Soft Computing, vol 91. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-19934-9_15
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DOI: https://doi.org/10.1007/978-3-642-19934-9_15
Publisher Name: Springer, Berlin, Heidelberg
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