Broadcast Encryption Scheme π ?

We propose a new broadcast encryption scheme π based on the idea of ‘one key per each punctured interval’. Let N and r be the numbers of total users and revoked users, respectively. In our scheme with p-punctured c-intervals, the transmission overhead is asymptotically r p+1 as r grows. We also introduce two variants of our scheme to improve the efficiency for small r. Our scheme is very flexible with two parameters p and c. We may take p as large as possible if a user device allows a large key storage, and set c as small as possible if the storage size and the computing power is limited. Our scheme also possesses another remarkable feature that any number of new users can join at any time without key refreshment, which is not possible in other known practical schemes.