# American Institute of Mathematical Sciences

February  2007, 1(1): 29-44. doi: 10.3934/amc.2007.1.29

## New constructions of anonymous membership broadcasting schemes

 1 Department of Mathematics and Computer Science, Eindhoven University of Technology, P.O. Box 513, 5600 MB Eindhoven, Netherlands 2 Centre for Advanced Computing – Algorithms and Cryptography, Department of Computing, Macquarie University, Sydney, Australia, Australia 3 School of Physical and Mathematical Sciences, Nanyang Technological University, Singapore

Received  March 2006 Revised  October 2006 Published  January 2007

An anonymous membership broadcast scheme is a method in which a sender broadcasts the secret identity of one out of a set of $n$ receivers, in such a way that only the right receiver knows that he is the intended receiver, while the others can not determine any information about this identity (except that they know that they are not the intended ones). In a $w$-anonymous membership broadcast scheme no coalition of up to $w$ receivers, not containing the selected receiver, is able to determine any information about the identity of the selected receiver. We present two new constructions of $w$-anonymous membership broadcast schemes. The first construction is based on error-correcting codes and we show that there exist schemes that allow a flexible choice of $w$ while keeping the plexities for broadcast communication, user storage and required randomness polynomial in log $n$. The second construction is based on the concept of collision-free arrays, which is introduced in this paper. The construction results in more flexible schemes, allowing trade-offs between different complexities.
Citation: Henk van Tilborg, Josef Pieprzyk, Ron Steinfeld, Huaxiong Wang. New constructions of anonymous membership broadcasting schemes. Advances in Mathematics of Communications, 2007, 1 (1) : 29-44. doi: 10.3934/amc.2007.1.29
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