# Unified Ciphertext-Policy Weighted Attribute-Based Encryption for Sharing Data in Cloud Computing
## 2 Related Work  
As a popular cryptographic primitive used in cloud computing, ABE has two categories. One is ciphertext-policy ABE (CP-ABE) [24], and the other is key-policy ABE (KP-ABE) [25]. The major difference between CP-ABE and KP-ABE is the relationship of the ciphertext and secret key with the access policy and attributes. Specifically, for the former, a ciphertext is associated with an access policy that is expressed by threshold gates and attributes. A consumer's secret key has attributes  
Figure 1: Two data providers have data \(M_{1}\) and \(M_{2}\) to share separately. \(\Gamma_{1}\) and \(\Gamma_{2}\) are the weighted access policies of \(M_{1}\) and \(M_{2}\). embedded. For the latter, a ciphertext is associated with attributes, and an access policy is embedded into a consumer's secret key. CP-ABE enables data providers to construct its access policy freely; in other words, the providers describe who can get the shared data flexibly. Therefore, CP-ABE is more suitable for data sharing in the cloud. In order to increase the efficiency and enlarge the use scope of ABE for data sharing, many researchers have made great efforts. [PERSON] et al. [PERSON] et al. (2017) introduced the concept of weight into CP-ABE and proposed a ciphertext-policy weighted attribute-based encryption scheme. In this scheme, the authority transforms the attribute set into the weight attribute separation set, then the data provider encrypts the data with linear secret sharing methods [PERSON] et al. (2016). Although the size of the ciphertext and private key increases, the scheme achieves fine-grained access control and reflects the significance of attributes. Therefore, the scheme is more suitable for the practical applications. However, the scheme only supports the linear secret sharing scheme (LSSS) [PERSON] et al. (2017) access structure. On the basis of [PERSON] et al. [PERSON] et al. (2017), [PERSON] et al. [PERSON] et al. (2017) proposed another ciphertext-policy weighted attribute-based encryption scheme that supports threshold access structure [PERSON] et al. (2017). This structure can consist of a threshold and many attributes. Therefore, this scheme is more expressive and is more appropriate for the cloud computing environment. Meanwhile, the scheme is proven secure under the selective-weighted attribute model. Nevertheless, the scheme only supports the threshold access structure, which only contains one threshold gate in one structure, and this still limits the expression. [PERSON] et al. [PERSON] et al. (2018) proposed a multi-authority-based weighted attribute encryption scheme, which introduced the concept of weight into multi-authority-based attribute encryption [PERSON] et al. (2017). In this scheme, a central authority assigns a unique user identifier (UID) to each consumer. The UID is the global identity of a consumer in the system, and it is used to generate the attribute secret keys issued by multiple authorities. The attribute authorities assign different weights to attributes depending on their importance; whereas, the scheme only supports the threshold access structure. [PERSON] et al. [PERSON] et al. (2017) proposed an improved ciphertext-policy weighted attribute-based encryption (CP-WABE) to improve the efficiency over the traditional CP-ABE scheme. In this scheme, every attribute has its own weight according to its importance. The data provider encrypts its data under a weighted access policy. The data consumer can decrypt the ciphertext only if his/her attributes satisfy the weighted access policy. The scheme supports the tree access structure, so it can encrypt data under a more complex access policy. The scheme is proven to be secure under the decision \(\ell\)-Expanded bilinear Diffie-Hellmann exponent (\(\ell\)-Expanded BDHE) assumption [PERSON] et al. (2018). [PERSON] et al. [PERSON] et al. (2018) proposed a secure and efficient data collaboration scheme, which is called blowfish hybridized weighted attribute-based encryption.