Nowadays, encryption is used in order to determine the access policy and data security. In PBE [1] encryption, the publisher sends a message to a subset of users with access to the broadcasted data, so that only the desired users can decrypt the data and other users cannot access the data even with colliding their key and information. In ABE [2] encryption, a set of attributes is used as the main index to generate the private key. This encryption system can well provide the appropriate access control in environments such as Cloud Control. In this paper, we attempt to explain the strengths and weaknesses of the two ABE and PBE methods, and examine the pioneer methods for their implementation.