Lightweight devices, such as a smartcard associated with a top-box decoder in pay-TV or a SIM card coupled with a powerful (but not totally trusted) smartphone, play an important role in modern applications. The essential requirements for a cryptographic scheme to be truly implemented in lightweight devices is that it should have compact secret key size and support fast decryption. Attribute-based Broadcast Encryption (ABBE) combines the functionalities of both Broadcast encryption and Attribute-based Encryption (ABE) in an efficient way, ABBE is therefore a promising cryptographic scheme to be used in practical applications such as mobile pay-TV, satellite transmission, or IoT. Designing an ABBE scheme which can be truly implemented in lightweight devices is still an open question. In this paper, we solve it by proposing an efficient constant-size private key ciphertext-policy ABBE scheme for DNF form supporting fast decryption and achieving standard security levels of an attribute-based broadcast encryption scheme. We concretely show that our scheme can be truly implemented in a prototype for a smartphone based cloud storage use case. In particular, we show how to alleviate some parts of our scheme so as to obtain a very practical system, and we give some concrete benchmarks.