Abstract. We study two closely related primitives: Broadcast Encryption and Key Predistribution Schemes (KPS). Broadcast Encryption allows a broadcaster to broadcast an encrypted message so that only a designated group of users can decrypt it. KPS allows a designated group of users to establish a common key non-interactively. We discover a generic method to construct efficient broadcast encryption schemes and KPSs naturally from Pseudo-Random Sequence Generators (PRSG) by observing that there are general “patterns” to do so. The two currently best PRSG-based broadcast encryption schemes such as the “Subset Difference” (SD) scheme by Naor Naor and Lotspiech and its refinement, the “Layered SD” (LSD) scheme by Halevy and Shamir, are indeed two special cases of our method. We demonstrate the power of this generic method by giving: (1) A solution to the most challenging variant of KPS: the one which supports arbitrary number of users to form a group yet secure against any coll...