The cloud-assisted Internet of Things (CIoT) is booming, which utilizes powerful data processing capabilities of the cloud platform to solve massive Internet of Things (IoT) data. However, the CIoT faces new security challenges, such as the confidentiality of the outsourced data. Data encryption is a fundamental technique that can guarantee the confidentiality of outsourced data, but it limits target encrypted data retrieval from cloud platform. Public key encryption with keyword search (PEKS) provides a promising solution to address this problem. In PEKS, a cloud server can be authorized to search the keyword in encrypted documents and retrieve associated encrypted documents for the receiver. However, most existing PEKS schemes merely focus on keyword search function while ignoring the associated documents encryption/decryption function. Thus, in practice, a PEKS scheme must cooperate with another separated public key encryption (PKE) scheme to fulfill a completely secure data sharing scheme. To address this problem, in this paper, we propose a secure data sharing scheme with designated server that combines PKE scheme with PEKS scheme, which provides both keyword search and documents encryption/decryption functions. Furthermore, only the designated server can search the keyword via encrypted documents for enhanced security in our work. Moreover, our scheme also satisfies the public verifiability of search results, which includes both keywords and documents ciphertexts’ correctness and integrity. As to the security, our scheme provides stronger indistinguishability security of document and keyword in the proposed security model.