Public key encryption with conjunctive keyword search on lattice

Outsourcing data in cloud storage is gaining popularity recently. For protecting data privacy, the data should be encrypted, and it is thus critical to provide search services for encrypted outsourced data. However, it becomes a problem about how to retrieve encrypted data while protecting data privacy at the same time. Therefore, public key encryption with keyword search (PEKS) is proposed. Nevertheless, the majority of the existing PEKS schemes are based on bilinear mappings and do not provide quantum security. Although some lattice-based PEKS schemes have been proposed, they cannot support conjunctive keyword search. In this paper, we first propose a public key encryption with conjunctive keyword search (PECK) using lattices. Our PECK scheme provides efficient search over encrypted data containing multiple keywords for a single data user. To support multiple data users, a multi-user PECK scheme is also presented. The two schemes are proved secure against indistinguishable chosen keyword attacks (IND-CKA) based on learning with errors (LWE) problem in the random oracle model. Finally, we provide performance evaluation of our proposed scheme by theoretical analysis and experimental simulation.