Nowadays, users prefer to encrypt their sensitive data before outsourcing it to the cloud. although, performing the encryption assures the data privacy, but it jeopardizes the search functionality. Public key encryption with keyword search (PEKS) is a potential solution for addressing this problem. However, most PEKS schemes are either inefficient, or susceptible to some type of attack(s) (i.e. inside keyword guessing attack, outside keyword guessing attack,..etc.). Therefore, we propose a sustainable certificateless authenticated encryption system with keyword search scheme. To the best of our knowledge, the proposed scheme considers the multi-trapdoor indistinguishability in the certificateless primitive. Moreover, a thorough security analysis shows that our scheme also guarantees the security against both online and offline keyword guessing attacks. Finally, based on the performance analysis results, we find that the suggested scheme is efficient and outperforms the other schemes.