With the popularization of cloud computing, many business and individuals prefer to outsource their data to cloud in encrypted form to protect data confidentiality. However, how to search over encrypted data becomes a concern for users. To address this issue, searchable encryption is a novel cryptographic primitive that enables user to search queries over encrypted data stored on an untrusted server while guaranteeing the privacy of the data. Public key encryption with keyword search (PEKS) has received a lot of attention as an important branch. In this paper, we focus on the development of PEKS in cloud by providing a comprehensive research survey. From a technological viewpoint, the existing PEKS schemes can be classified into several variants: PEKS based on public key infrastructure, PEKS based on identity-based encryption, PEKS based on attribute-based encryption, PEKS based on predicate encryption, PEKS based on certificateless encryption, and PEKS supporting proxy re-encryption. Moreover, we propose some potential applications and valuable future research directions in PEKS.
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