With the advent of the big data era, the size and complexity of data continue to increase, which makes the requirement for data privacy and security increasingly urgent. However, traditional encryption methods cannot meet the demand for efficient searching in large-scale datasets. To solve this problem and enable users to search within encryped data and without decrypting the entire dataset, trapdoor functions and other cryptograhic techniques are introduced in searchable encryption. However, searchable encryption still cannot meet the needs in the real world. Therefore, researchers have introduced the concept of attribute-based encryption into searchable encryption, resulting in attribute-based searchable encryption (ABSE). This approach aims to achieve efficient search by attributes in encrypted datasets. ABSE has a wide range of applications in the fields of privacy protection, data sharing, and cloud computing. In this paper, we describe the trends in development, focusing on enhancing security, improving computational efficiency, and increasing flexibility. We also present the related schemes. In addition, several common application areas are introduced and the relevant schemes proposed by researchers are summarized. Moreover, the challenges and future directions of ABSE are discussed in this paper.

To ensure secure and flexible data sharing in cloud storage, attribute-based encryption (ABE) is introduced to meet the requirements of fine-grained access control and secure one-to-many data sharing. However, the computational burden imposed by attribute encryption renders it unsuitable for resource-constrained environments such as the Internet of Things (IoT) and edge computing. Furthermore, the issue of accountability for illegal keys is crucial, as authorized users may actively disclose or sell authorization keys for personal gain, and keys may also passively leak due to management negligence or hacking incidents. Additionally, since all authorization keys are generated by the attribute authorization center, there is a potential risk of unauthorized key forgery. In response to these challenges, this paper proposes an efficient and accountable leakage-resistant scheme based on attribute encryption. The scheme adopts more secure online/offline encryption mechanisms and cloud server-assisted decryption to alleviate the computational burden on resource-constrained devices. For illegal keys, the scheme supports accountability for both users and the authorization center, allowing the revocation of decryption privileges for malicious users. In the case of passively leaked keys, timely key updates and revocation of decryption capabilities for leaked keys are implemented. Finally, the paper provides selective security and accountability proofs for the scheme under standard models. Efficiency analysis and experimental results demonstrate that the proposed scheme enhances encryption/decryption efficiency, and the storage overhead for accountability is also extremely low.