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. Herranz et al. [101] proposed a construction of CP-ABE with constant ciphertext. However, [101] does not consider the recipients’ anonymity and the access policies are exposed to potential malicious attackers. On the other hand, existing privacy preserving schemes [127, 165] protect the anonymity but blackrequire bulky, linearly-increasing ciphertext size.