The paper presents a new methodology for realizing Ciphertext-Policy Attribute-Based Encryption (CP-ABE) under concrete and noninteractive cryptographic assumptions in the standard model. The authors introduce a framework that allows any encryptor to specify access control using any access formula over the attributes in the system. The most efficient system scales linearly with the complexity of the access formula in terms of ciphertext size, encryption, and decryption time. The paper includes three constructions within this framework, with the first being proven selectively secure under a decisional Parallel Bilinear Diffie-Hellman Exponent (PBDHE) assumption. The other two constructions provide performance trade-offs to achieve provable security under weaker assumptions, such as the decisional Bilinear-Diffie-Hellman Exponent and decisional Bilinear Diffie-Hellman assumptions. The main contribution is a method for directly realizing provably secure CP-ABE systems, where the ciphertext distributes shares of a secret encryption exponent across different attributes according to an access control Linear Secret Sharing Scheme (LSSS) matrix. The paper also discusses related work and provides background on access structures, LSSS, and bilinear maps.The paper presents a new methodology for realizing Ciphertext-Policy Attribute-Based Encryption (CP-ABE) under concrete and noninteractive cryptographic assumptions in the standard model. The authors introduce a framework that allows any encryptor to specify access control using any access formula over the attributes in the system. The most efficient system scales linearly with the complexity of the access formula in terms of ciphertext size, encryption, and decryption time. The paper includes three constructions within this framework, with the first being proven selectively secure under a decisional Parallel Bilinear Diffie-Hellman Exponent (PBDHE) assumption. The other two constructions provide performance trade-offs to achieve provable security under weaker assumptions, such as the decisional Bilinear-Diffie-Hellman Exponent and decisional Bilinear Diffie-Hellman assumptions. The main contribution is a method for directly realizing provably secure CP-ABE systems, where the ciphertext distributes shares of a secret encryption exponent across different attributes according to an access control Linear Secret Sharing Scheme (LSSS) matrix. The paper also discusses related work and provides background on access structures, LSSS, and bilinear maps.