Abstract
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.
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De Santis, A., Masucci, B. Anonymous Membership Broadcast Schemes. Designs, Codes and Cryptography 32, 135–151 (2004). https://doi.org/10.1023/B:DESI.0000029218.71926.b0
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DOI: https://doi.org/10.1023/B:DESI.0000029218.71926.b0