Tree Structures in Broadcast Encryption

Abstract: The need for broadcast encryption arises when a sender wishes to securely distribute messages to varying subsets of receivers, using a broadcast channel, for instance in a pay-TV scenario. This is done by selecting subsets of users and giving all users in the same subset a common decryption key. The subsets will in general be overlapping so that each user belongs to many subsets and has several different decryption keys. When the sender wants to send a message to some users, the message is encrypted using keys that those users have. In this thesis we describe some broadcast encryption schemes that have been proposed in the literature. We focus on stateless schemes which do not require receivers to update their decryption keys after the initial keys have been received; particularly we concentrate on the Subset Difference (SD) scheme.We consider the effects that the logical placement of the receivers in the tree structure used by the SD scheme has on the number of required transmissions for each message. Bounds for the number of required transmissions are derived based on the adjacency of receivers in the tree structure. The tree structure itself is also studied, also resulting in bounds on the number of required transmissions based on the placement of the users in the tree structure.By allowing a slight discrepancy between the set of receivers that the sender intends to send to and the set of receivers that actually can decrypt the message, we can reduce the cost in number of transmissions per message. We use the concept of distortion to quantify the discrepancy and develop three simple algorithms to illustrate how the cost and distortion are related.