## 1 Introduction  
With the increasing popularity of blockchain technology, blockchain has been widely used in data access and sharing in weak-trusted or no-trusted networks. However, privacy data protection on the blockchain has become a challenge due to the characteristics of \"non-tampering\" and \"open and transparent\". In recent years, many scholars have put forward some new solutions for privacy protection and data sharing on the blockchain [1, 2, 3, 4, 5, 6], among which attribute-based encryption algorithm has been widely used in various schemes on the blockchain, such as in data traceability [1], cloud storage [7], medical data sharing [8, 9], power systems [10] and Internet of Things [11] due to its advantages of \"one-to-many\" encryption, fine-grained access control and so on. The attribute-based encryption (ABE) originated from the fuzzy identity-based encryption [12] proposed by [PERSON] and [PERSON] in 2005 and then developed into ABE. In key policy attribute-based encryption [13] (KP-ABE), the ciphertext is associated with the attribute and the key with the access policy. However, in ciphertext policy attribute-based encryption (CP-ABE), the key is associated with the attribute and the ciphertext with the access policy. The CP-ABE allows the data owner to freely formulate the access control policy and is more suitable for the distributed storage environment and uncertain deciphering [14]. In recent years, the main research on the ABE mainly focused on computation efficiency [15; 16], access policy and attribute hiding [17], and identity management [18; 19]. In 2007, [PERSON] et al. [20] proposed a system for the CP-ABE algorithm which allows policies to be expressed as any monotonic tree access structure and is resistant to collusion attacks in which an attacker might obtain multiple private keys. In addition, the \"one-to-many\" encryption and fine-grained access control could be achieved this way. However, it is proved secure under the generic group heuristic. In 2011, [PERSON] [21] proved the security of the CP-ABE under the standard model and put forward a CP-ABE adopting the linear secret sharing scheme, which improved the efficiency significantly. In 2012, [PERSON] [22] et al. proposed the first unbounded inner product ABE scheme, which lifted the restrictions on the predicate terms and size attributes of the previous ABE scheme. In 2013, [PERSON] [23] proposed an ABE scheme based on the polynomial logic circuit. This scheme was designed to resist collusion attacks effectively, and its public parameter and ciphertext size increased linearly with the circuit depth. This scheme made it possible to transform from Boolean formula-based to circuit-based, which had better security by nature. In 2014, [PERSON] [24] proposed an Online-Offline ABE scheme to address the computational bottleneck of encryption and key generation. This scheme was inspired by the ABE scheme put forward by [PERSON] et al. [25], and developed new techniques for ABE that split the computation for encryption into two phases, thus reducing the computation consumption in the online stage. Recently, the blockchain-enhanced CP-ABE scheme using elliptic curve cryptography (ECC) has become a popular research area due to its potential to provide secure data access and sharing without involving a third party. In 2020, [PERSON] [26] presented a privacy-preserving, recoverable, and revocable edge data-sharing scheme based on blockchain technology to achieve attribute revocation in ciphertext-policy attribute-based encryption (CP-ABE), which can protect user's privacy and resist many attacks. [PERSON] [27] proposed a new trustworthy, secure ciphertext policy and attribute hiding access control scheme based on blockchain to achieve trustworthy access while guaranteeing the privacy of policy and attribute.