Punctured interval broadcast encryption scheme with free riders

In Broadcast Encryption (BE) schemes, the problem is to encrypt a content for a group of dynamically changing privileged (subscriber) subset within a receiver population. A popular approach is to carefully distribute a group of keys to several, carefully designed subsets of the receivers beforehand, and later use a precise subset of keys so that only intended users have those keys, thus decrypt the content. This approach is known as the subset cover framework. In the subset cover framework, one concern is the number of copies that must be encrypted, which affects the bandwidth requirement. This problem can be relaxed by allowing a limited number of free riders   so that, by sacrificing some coverage accuracy, the transmission cost is reduced. Several BE schemes are proposed since 90s, and one of the most efficient schemes so far is the punctured interval BE scheme (Cheon et al., 2008). In this paper, we attack the problem of how to assign a given number of free riders effectively in the punctured interval BE scheme. We give the optimal free rider assignment algorithm which runs in poly(n)poly(n) time, where n is the number of all users in the system, and we provide a heuristic which performs slightly worse than the optimal algorithm in terms of transmission cost reduction but is much faster, i.e., linear in terms of n. We also propose a hybrid approach which employs the core ideas of both optimal and heuristic methods in order to achieve a trade-off between speed and accuracy.