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Attribute-based encryption with keyword search (ABEKS) is a novel cryptographic paradigm that can be used to implement fine-grained access control and retrieve ciphertexts without disclosing the sensitive information. It is a perfect combination of attribute-based encryption (ABE) and public key encryption with keyword search (PEKS). Nevertheless, most of the existing ABEKS schemes have limited search capabilities and only support single or simple conjunctive keyword search. Due to the weak search capability and inaccurate search results, it is difficult to apply these schemes to practical applications. In this paper, an efficient expressive ABEKS (EABEKS) scheme supporting unbounded keyword universe over prime-order groups is designed, which supplies the expressive keyword search function supporting the logical connectives of "AND" and "OR". The proposed scheme not only leads to low computation and communication costs, but also supports unbounded keyword universe. In the standard model, the scheme is proven to be secure under the chosen keyword attack and the chosen plaintext attack. The comparison analysis and experimental results show that it has better performance than the existing EABEKS schemes in the storage, computation and communication costs.