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Abstract. Ciphertext Policy Attribute Based Encryption (CP-ABE) enforces an expressive data access policy, which consists of a number of attributes connected by logical gates. Only those decryptors whose attributes satisfy the data access policy can decrypt the ciphertext. CP-ABE is very appealing since the ciphertext and data access policies are integrated together in a natural and effective way. However, all existing CP-ABE schemes incur very large ciphertext size, which increases linearly with respect to the number of attributes in the access policy. Large ciphertext prevents CP-ABE from being adopted in the communication constrained environments. In this paper, we proposed a new construction of CP-ABE, named Constant-size CP-ABE (denoted as CCP-ABE) that significantly reduces the ciphertext to a constant size for an AND gate access policy with any given number of attributes. Each ciphertext in CCP-ABE requires only 2 elements on a bilinear group. Based on CCP-ABE, we further proposed an Attribute Based Broadcast Encryption (ABBE) scheme. Compared to existing Broadcast Encryption (BE) schemes, ABBE is more flexible because a broadcasted message can be encrypted by an expressive access policy, either with or without explicit specifying the receivers. Moreover, ABBE significantly reduces the storage and communication overhead to the order of O(log N ), where N is the system size. Also, we proved, using information theoretical approaches, ABBE attains minimal bound on storage overhead for each user to construct all possible subgroups in the communication system.

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Many IP multicast-based applications, such as multimedia conferencing, multiplayer games, require controlling the group memberships of senders and receivers. One common solution is to encrypt the data with a session key shared with all authorized senders/receivers. To efficiently update the session key in the event of member removal, many rooted-tree based group key distribution schemes have been proposed. However, most of the existing rooted-tree based schemes are not optimal. In other words, given the O(log N ) storage overhead, the communication overhead is not minimized. On the other hand, although Flat Table scheme [1] achieves optimality [2], it is rather dismissed due to the vulnerability to collusion attacks.In this paper, we propose a key distribution scheme -EGK that attains the same optimality as Flat Table without collusion vulnerability. Additionally, EGK provides constant message size and requires O(log N ) storage overhead at the group controller, which makes EGK suitable for applications containing a large number of multicasting group members. Moreover, adding members in EGK requires just one multicasting message. EGK is the first work with such features and out-performs all existing schemes.