The group key management is for a group manager to maintain a consistent group key for a dynamic group of members through a broadcast channel. In this paper we propose a group key management scheme based on a meta proxy re-encryption (PRE) scheme. In particular, we propose an RSA-based PRE scheme with special properties. It is the first RSA-based PRE scheme for group key management and has the desired properties of uni-directionality and multi-hop.In our group key management scheme, each group member holds just one secret auxiliary key and log N public auxiliary keys. The size of rekey messages for each group key update remains O(log N ). Additionally, our scheme has some distinct features. Firstly, the size of the key update history is a constant O(N ) no matter how many times of group key updates occur. Secondly, the computation time of computing the newest group key from the key update history is always O(log N ) no matter how many group key updates are missed. This feature provides a practical solution for group key update when members go offline from time to time. Finally, the proposed scheme is immune to the collusion attack of other members.

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Pay-TV has become a popular subscribed-based service in recent years. To prevent unauthorized access from non-paid users over a broadcast channel, the TV server usually encrypts TV programs into ciphertexts such that only the legal members can decrypt them. The way of maintaining the common decryption key of a TV program to a dynamic subscription group of members is called the group key management.In this paper, we propose a secure and efficient tree-based group key management scheme that is very suitable for Pay-TV systems. In addition to possessing the advantages of the former tree-based scheme, such as O(log N ) communication cost for each group key update and O(log N ) secret keys for each member, our scheme has two distinct features, where N is the total number of members. (1) Each member only needs to decrypt one ciphertext or compute one hash value to get the group key from the rekey messages for each member leaving/joining. (2) To handle the key update for reconnected members who have missed the group key updates in his off-line period of time, the server only needs to store O(N ) public tokens on the bulletin and each off-line member only needs O(log N ) decryptions for getting the newest group key, which are independent of the number of group key updates. In Pay-TV systems, these features not only minimize the delay time for each group key update, but also let the system more practical even if the key update frequency is very high, such as, the Pay-Per-View TV service. Finally, we have a discussion of applying our GKM scheme to a multi-program service.