The Algebraic Structure of a Broadcast Encryption Scheme

• In this paper we consider the subset difference scheme for broadcast encryption and count the number of required broadcast transmissions when using this scheme. The subset difference scheme organizes receivers in a tree structure and we note that isomorphic trees yield the same number of required broadcast transmissions. Based on the isomorphism the trees can be partitioned into classes. We suggest to use the vast amount of tools available from the theory of groups to analyze the subset difference scheme and therefore we formulate the mappings between isomorphic trees using concepts from group theory. Finally we identify some research issues for further study of the performance of the subset difference scheme using group theory.

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