Attribute Based Encryption(ABE), in which a user with his credentials wants to encrypt the sensitive data, it is necessary that he/she establishes an access structure control policy on who can decrypt this data. According to the proposed idea ABE scheme , several techniques have been proposed to improve and implement the advantage and disadvantage of this idea to many other useful, flexible and secure schemes in the real systems. There are three types of ABE called Ciphertext-Policy ABE(CP-ABE), Key-Policy(KE-ABE) and Dual-Policy ABE (DP-ABE) was proposed in recent years. Following the development of promising result of Cihpertext-Policy Attribute based encryption(CP-ABE), in which every secret key is associated with a set of attributes, and every cihpertext is associated with an access structure on attributes. Decryption is enabled if and only if the user's attribute set satisfies the access structure embedded in the ciphertext. Apart from the proposed properties of CP-ABE, we propose the first scheme with a new construction of CP-ABE that significantly reduces the ciphertext with a very short constant size for any number of AND gate access policy on any number of attributes. Our first scheme is proven(Chosen Plaintext Attack) CPA and (Chosen Ciphertext Attack) CCA-secure under the Decisional Diffie Hellman assumption. In addition , we present the construction our CCA scheme with public key encryption non-interactive opening(PKENO)scheme and using CHK technique to achieve efficient CCA secure under the Decisional Bilinear-Diffie-Hellman assumption(DBDH). Our second scheme based Dual-Policy Attribute Based Encryption(DP-ABE), proposed in 2009, a combination of two variants CP-ABE and KP-ABE, where an encrytor can associate the date simultaneously with both a set of objective attributes and a subjective access policies. Or , a user is given a private key assigned simultaneously for both a set of objective attributes and a subjective access policy. A major problem of the above DP-ABE scheme, is the ciphertext size linear to the number of attributes while LSSS access structure can be assumed. We propose two novel DP-ABEs construcion, which achieves constant size of cihpertext, regardless of number of attributes in a logical AND data access policy with wildcards. We present two constructions: once scheme under the q-Bilinear Diffie Hellman Exponent(q-BDHE) and once scheme under the DBDH.