Ciphertext Policy Attribute-Based Encryption (CP-ABE) enforces expressive data access policies and each policy consists of a number of attributes. Most existing CP-ABE schemes incur a very large ciphertext size, which increases linearly with respect to the number of attributes in the access policy. Recently, Herranz proposed a construction of CP-ABE with constant ciphertext. However, Herranz do not consider the recipients’ anonymity and the access policies are exposed to potential malicious attackers. On the other hand, existing privacy preserving schemes protect the anonymity but require bulky, linearly increasing ciphertext size. In this paper, we proposed a new construction of CP-ABE, named Privacy Preserving Constant CP-ABE (denoted as PP-CP-ABE) that significantly reduces the ciphertext to a constant size with any given number of attributes. Furthermore, PP-CP-ABE leverages a hidden policy construction such that the recipients’ privacy is preserved efficiently. As far as we know, PP-CP-ABE is the first construction with such properties. Furthermore, we developed a Privacy Preserving Attribute-Based Broadcast Encryption (PP-AB-BE) scheme. Compared to existing Broadcast Encryption (BE) schemes, PP-AB-BE is more flexible because a broadcasted message can be encrypted by an expressive hidden access policy, either with or without explicit specifying the receivers. Moreover, PP-AB-BE significantly reduces the storage and communication overhead to the order of ${\mbi {O}}(\log {\mbi {N}})$ , where ${\mbi {N}}$ is the system size. Also, we proved, using information theoretical approaches, PP-AB-BE attains minimal bound on storage overhead for each user to cover all possible subgroups in the communication system.

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