Designing lightweight security protocols for cloud-based Internet-of-Things (IoT) applications for battery-limited mobile devices, such as smart phones and laptops, is a topic of recent focus. Ciphertext-policy attribute-based encryption (CP-ABE) is a viable solution, particularly for cloud deployment, as an encryptor can "write" the access policy so that only authorized users can decrypt and have access to the data. However, most existing CP-ABE schemes are based on the costly bilinear maps, and require long decryption keys, ciphertexts and incur significant computation costs in the encryption and decryption (e.g. costs is at least linear to the number of attributes involved in the access policy). These design drawbacks prevent the deployment of CP-ABE schemes on battery-limited mobile devices. In this paper, we propose a new RSA-based CP-ABE scheme with constant size secret keys and ciphertexts (CSKC) and has O(1) time complexity for each decryption and encryption. Our scheme is then shown to be secure against a chosen-ciphertext adversary, as well as been an efficient solution with the expressive AND gate access structures (in comparison to other related existing schemes). Thus, the proposed scheme is suitable for deployment on battery-limited mobile devices.