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ACM Transactions on Information and System Security (TISSEC)
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New Results and New Trends in Computer Science
A Combinatorial Approach to Anonymous Membership Broadcast
COCOON '02 Proceedings of the 8th Annual International Conference on Computing and Combinatorics
CRYPTO '88 Proceedings of the 8th Annual International Cryptology Conference on Advances in Cryptology
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Proceedings of the 5th International Workshop on Security Protocols
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A membership broadcast scheme is a method by which a dealer broadcasts a secret identity among a set of users, in such a way that only a single user is sure that he is the intended recipient. Anonymous membership broadcast schemes have several applications, such as anonymous delegation, cheating prevention, etc. In a w-anonymous membership broadcast scheme any coalition of at most w users, which does not include the user chosen by the dealer, has no information about the identity of the chosen user. Wang and Pieprzyk proposed a combinatorial approach to 1-anonymous membership broadcast schemes. In particular, they proposed a 1-anonymous membership broadcast scheme offering a logarithmic complexity for both communication and storage. However, their result is non-constructive. In this paper, we consider w-anonymous membership broadcast schemes. First, we propose a formal model to describe such schemes and show lower bounds on the communication and randomness complexities of the schemes. Afterwards, we show that w-anonymous membership broadcast schemes can be constructed starting from (w + 1)-wise independent families of permutations. The communication and storage complexities of our schemes are logarithmic in the number of users.