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Big data has emerged as a new paradigm that gives exceptional value to the large volume of data, which indeed helps the industry, business, engineering, and science to grow (Grover, Chiang, Liang, & Zhang, 2018). On the other hand, storing and managing big data locally is a challenging task for the organizations because the organization should set up the infrastructure. Infrastructure setup in an organization is an expensive and time-consuming process. The cost effective and timely solution is outsourcing the big data into the cloud because the cloud computing offers a diversity of resources such as storage, compute, network, platform and software as services in a pay-per-use model (Hashem et al., 2015). It also supports the scalability, dynamic provisioning and de-provisioning. However, the privacy and security challenges in the cloud restrict the organizations to adopt the cloud (Takabi, Joshi, & Ahn, 2010; Gupta, Agrawal, & Yamaguchi, 2016). The foremost important issues are data privacy and access control.
Privacy can be preserved through public key encryption, but it fails to support access control. Later, Identity Based Encryption (IBE) schemes evolved to provide the access control along with encryption. However, the problem with IBE is the user's details should know before the encryption. To overcome this problem, Attribute-Based Encryption (ABE) was introduced by Sahai, and Waters (2005). Later, the variants of ABE Key Policy Attribute-Based Encryption (KP-ABE) (Goyal, Pandey, Sahai, & Waters, 2006) and the CP-ABE (Bethencourt, Sahai, & Waters, 2007) were introduced. Comparatively the CP-ABE is the best approach than KP-ABE because it allows the data owners to set control over their data.
In CP-ABE, the encrypted data is outsourced to the cloud and shared with the users based on the access policy defined. The access policy consists of attributes, which describes what attributes the user should hold. The user decryption key is generated by the authority according to her/his attributes. Later, various efforts have been taken to enhance the basic CP-ABE scheme (Deng et al., 2014; Jiang, Susilo, Mu, & Guo, 2018; Kumar, Kumar, & Alphonse, 2017; Zhang et al., 2017; Premkamal, Pasupuleti, & Alphonse, 2018; Li, Zhang, Chen, & Xiang, 2019a; Liu, Jiang, Wang, & Yiu, 2018; Premkamal, Pasupuleti, & Alphonse, 2019b). While the CP-ABE perfectly addresses the unauthorized access, the previous CP-ABE schemes do not directly deploy for practical big data applications in the cloud due to the higher computation overhead because of long ciphertext, which is proportionate to the attributes in the access policy and long secret key, which is proportionate to the number of user attributes.
To address this issue, the constant size ciphertext schemes (Attrapadung et al., 2012; Doshi & Jinwala, 2014; Teng, Yang, Xiang, Zhang, & Wang, 2017; Susilo, Yang, Guo, & Huang, 2018) were presented to reduce the computation cost, but these schemes limit the data access from resource constraint devices because of the large size secret key and decryption computation overhead. Correspondingly, the constant size secret key schemes (Guo, Mu, Susilo, Wong, & Varadharajan, 2014; Li et al., 2017) were presented to improve the data accessibility in the resource constraint devices, but it suffered from large ciphertext size which inturn increases the computation cost of encryption. To achieve both, Emura, Miyaji, Nomura, Omote, & Soshi, (2010) and Odelu et al., (2017) proposed the CSC-S schemes. However, the existing CSC-S schemes suffered with the following issues such as (1) Key escrow: The authority generates the secret key for the users to decrypt the data based on their attributes. The curious authority can decrypt the data with the generated user secret key, which indeed reduces the security. (2) Efficiency: Inefficiency in encryption and decryption computation for large universal attribute set.