Data privacy is one of the main concerns for clients who rely on cloud storage services. Standard encryption techniques can offer confidentiality; however, they prevent search capabilities over the encrypted data, thereby significantly degrading the utilization of cloud storage services. Public key Encryption with Keyword Search (PEKS) schemes offer encrypted search functionality to mitigate the impacts of privacy versus data utilization dilemma. PEKS schemes allow any client to encrypt their data under a public key such that the cloud, using the corresponding trapdoor, can later test whether the encrypted records contain certain keywords. Despite this great functionality, the existing PEKS schemes rely on extremely costly operations at the server-side, which often introduce unacceptable cryptographic delays in practical applications. Moreover, while data outsourcing applications usually demand long-term security, existing PEKS schemes do not offer post-quantum security.In this paper, we propose (to the best of our knowledge) the first post-quantum secure PEKS scheme that is also significantly more computationally efficient than the existing (non-post-quantum) PEKS schemes. By harnessing the recently developed tools in lattice-based cryptography, the proposed scheme significantly outperforms the existing PEKS schemes in terms of computational overhead. For instance, the test (search) operation per item at the cloud side is approximately 36$$\times $$ faster than that of the most prominent pairing-based scheme in the literature (for 192-bit security). The proposed PEKS scheme also offers faster encryptions at the client side, which is suitable for mobile devices.