### Related Works
#### 1.2.1 Multi-Authority ABE Schemes  
Multi-authority ABE was first discussed in the work [13], where only one CA, also known as the central authority, and numerous AAs, also known as attribute authorities, controlled key management. The CA and AAs were responsible for issuing keys for identity and keys for attributes, respectively. The use of the global identifier GID prevented user collusion problems. However, the CA was capable of decrypting any ciphertext. [PERSON] and [PERSON] [14] improved their scheme (CC-MA-ABE) by removing the CA and introducing an anonymous key distribution mechanism with the help of pseudo-random functions. Both schemes in [13; 14] had the limitation that they supported an AND policy architecture only. [PERSON] et al. [15] presented the MACP-ABE scheme, a fully secure scheme in  
Figure 1: Cloud-based healthcare data sharing.  
the standard model where multiple central and attribute authorities collaborate to work together. The central authorities are responsible for issuing keys related to the user's identity, and the attribute authorities control the issuance of the attribute-related keys. [PERSON] and [PERSON] (1976) designed a decentralized CP-ABE and demonstrated security under the random oracle model. The linear secret sharing scheme, also known as LSSS, was used for specifying the access policy. At setup and key generation, no coordination between authorities was necessary, nor was there a central authority. [PERSON] et al. (2017) proposed a scheme where the user's community can be divided into public and personal domains (PUD and PSD, respectively) depending upon their role in the system. Their scheme was based on scheme ([PERSON] et al., 2017) and policy was specified using a conjunctive normal form (CNF) structure. [PERSON] et al. (2018) suggested a scheme for patient health record sharing in a multi-authority (two authorities) setting. They introduced social domains and professional domains for different authorized users. Several pieces were proposed to cater to different issues regarding MA-ABE. [PERSON] et al. (2019) addressed the revocation function in a multi-authority setting. However, their method had heavy communication overhead and key update computation overhead. The authors of (2019) proposed cipher policy ABE schemes for supporting multi-authority scenarios and handling user revocation features. To improve efficiency, the decryption process was outsourced. AA became a bottleneck in the scheme, as it had to calculate update keys for each unevoked user. The scheme presented in ([PERSON] et al., 2019) improved the CP-ABE scheme for secure PHR sharing ([PERSON] et al., 2019) for the multi-authority scenario. The authors also defined public and private domains for their PHR-sharing scheme. [PERSON] et al. (2019) introduced an access control scheme for cloud storage supporting decryption outsourcing. The scheme was also a multi-authority scheme and was evidenced to be adaptive and secure. In order to eliminate key escrow and minimize computation and communication costs, [PERSON] et al. (2019) provided an MA-ABE scheme that resisted key escrow and had a ciphertext of constant size. Furthermore, in the MA-KPABE scheme presented in ([PERSON] et al., 2019), verifiability of partial decryption ciphertext (PDC) and delegation features were added. [PERSON] et al. (2019) presented two decentralized CP-ABE techniques for the standard model. The CAs and AAs operated independently of one another. The first technique was constructed using a group of composite orders. The second technique produced ciphertexts of constant size in the groups of prime order. The first technique worked for any monotonic structure, while the second worked for AND-gate policies.