I just read "Certificateless Public Key Encryption Scheme with Hybrid Problems and Its Application to Internet of Things"

I am not sure why they are working in a Z_pq. Also:
1. They omit some of the checks on the integrity of the public key that the other scheme by Al-Riyani and Paterson.
2. They move an exponentiation inside a pairing, to turn it into a scalar multiplication

Which makes things more efficient.

However it had a dependency on the RSA problem as well as Diffie-Hellman