Outsourcing data to cloud services is a good solution for users with limited computing resources. Privacy and confidentiality of data is jeopardized when data is transferred and shared in the cloud. The development of searchable cryptography offers the possibility to solve these problems. Symmetric searchable encryption (SSE) is popular among researchers because it is efficient and secure. SSE often requires the data sender and data receiver to use the same key to generate key ciphertext and trapdoor, which will obviously cause the problem of key management. Searchable encryption based on public key can simplify the key management problem. A public key encryption scheme with keyword search (PEKS) allows multiple senders to encrypt keywords under the receiver’s public key. It is vulnerable to keyword guessing attacks (KGA) due to the small size of the keywords. The proposal of public key authenticated encryption with keyword search (PAEKS) is mainly to resist inside keyword guessing attacks. The previous security models do not involve the indistinguishability of the same keywords (w0××=w1), which brings the user’s search pattern easy to leak. The essential reason is that the trapdoor generation algorithm is deterministic. At the same time, most of the existing schemes use bilinear pair design, which greatly reduces the efficiency of the scheme. To address these problems, the paper introduces an improved PAEKS model. We design a lightweight public key authentication encryption scheme based on the Diffie-Hellman protocol. Then, we prove the ciphertext indistinguishability security and trapdoor indistinguishability security of the scheme in the improved security model. Finally, the paper demonstrates its comparable security and computational efficiency by comparing it with previous PAEKS schemes. Meanwhile, we conduct an experimental evaluation based on the cryptographic library. Experimental results show that the computational overhead of our scheme compared with the ciphertext generation algorithm, trapdoor generation algorithm and test algorithm of other schemes Our scheme reduces 274, 158 and 60 times, respectively.