Effects of User Adjacency in the Subset Difference Scheme for Broadcast Encryption

• We consider the broadcast encryption problem where one sender wishes to transmit messages securely to a selected set of receivers using a broadcast channel, as is the case in digital television for example. Specifically, we study the subset difference scheme for broadcast encryption and the number of broadcast transmissions required when using this scheme. The effects of adjacency in the user set are considered and we introduce the notion of transitions in the user set as a means to quantify the adjacency. We present upper and lower bounds for the number of transmissions based on the number of transitions between privileged and nonprivileged users in the user set. For cases where the privileged users are gathered in a few groups we derive the maximum number of transmissions.

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