Internet of Things (IoT) and cloud computing are adopted widely in daily life and industrial production. Sensors of IoT equipment gather personal, sensitive and important data, which is stored in a cloud server. The cloud helps users to save cost and collaborate. However, the privacy of data is also at risk. Public-key encryption with keyword search (PEKS) is convenient for users to use the data without leaking privacy. In this article, we give a scheme of PEKS for a multi-user to realize the multi-keyword search at once and extend it to show a rank based on keywords match. The receiver can finish the search by himself or herself. With private cloud and server cloud, most users' computing can be outsourced. Moreover, the PEKS can be transferred to a multi-user model in which the private cloud is used to manage receivers and outsource. The store cloud and the private cloud both obtain nothing with the keyword information. Then our IoT devices can easily run these protocols. As we do not use any pairing operations, the scheme is under more general assumptions that means the devices do not need to take on the heavy task of calculating pairing.
Keywords: PEKS; multi-keyword; multi-user; public key encryption with keyword search.