# A Secure Key Aggregate Searchable Encryption with Multi Delegation in Cloud Data Sharing Service
## 2 Related Works
### Literature Reviews  
In 2016, [PERSON] et al. [9] proposed the notion of KAE scheme that can reduce the number of distributed data encryption keys for data sharing system environments. The KAE allows documents or data sets encrypted with different keys to be decrypted with a single aggregate key. In 2018, [PERSON] et al. [15] proposed a scheme for sharing encrypted data with other users through public cloud storage. Their approach involves an authentication process, and they argue that the authentication process can solve the key leak problem of data sharing. However, [PERSON] et al. [16] proved that [PERSON] et al.'s scheme does not have security against impersonation and forging authentication key attacks. They demonstrated that the proposed [PERSON] et al.'s scheme could allow anyone to forge an authentication key and access an arbitrary set of files stored in the cloud. Therefore, they proposed a new KASE scheme to solve the problems of [PERSON] et al.  
However, since there was no search function for keywords in documents at [9; 15; 16], [PERSON] et al. [10] proposed a KASE scheme that enables group keyword search in the existing KAE. The scheme of [10], which first proposed the KASE method, provides the searchable group data sharing function, i.e., all users can selectively share selected groups of users and selected groups of files, the latter can perform keyword searches against the former. Unfortunately, [PERSON] et al. [17] proved that [PERSON] et al.'s scheme is insecure against insider attack. They demonstrated that the adversary can guess the valid user's key with the insider attacker. Furthermore, [PERSON] et al.'s scheme [10] did not support searching over multi-owner data using a single key of constant size.  
To address this problem, [PERSON] et al. [18] proposed the scheme for searching over multi-owner's data using a single trapdoor. Their scheme allows verification of search results using an aggregate key. They also offered advance planning in multi-owner settings.  
[PERSON] et al. [17] proposed a KASE scheme of data-centric framework in an Industrial Internet of Things (IIoT) environment.Sensors in IIoT do not support the computational power of pairing operations as their hardware resources are very limited. Therefore, [PERSON] et al. proposed a KASE scheme that does not use the pairing operation in the encryption phase.  
[PERSON] et al. [19] also proposed a KASE scheme for multi-owner data. [PERSON] et al.'s scheme is a practical way to generate keyword ciphertext without the use of expensive pairing operations given resource-constrained environments. They also discussed scenarios for federated clouds and proposed methods for delegating search authority when data are stored in federated clouds.  
[PERSON] et al. [20] proposed a scheme to validate keyword search results using a single aggregation key. The KASE method of [PERSON] et al. also provides user authentication. In their scheme, the cloud server can verify the legitimacy of a sub-user by verifying that the authorized user's identity set includes the sub-user's identity. However, [PERSON] et al.'s protocol is insecure against user impersonation attacks.  
In addition to delegating the searchable authority to the user, it is also necessary to consider the case where the delegated user must delegate the authority to another user for time-sensitive tasks, processing and creation of various information, and managing a large amount of data. However, there are many KASE schemes dealing with data sharing between DOs and DUs, but none dealing with cases where DU delegates to other DUs without help of the TTP. Furthermore, no KASE scheme works out the problem of user authentication and fine-grained multi-delegation at the same time. Authentication is one of the basic security services absolutely necessary to provide secure services in various network environments [21; 22; 23; 24; 25; 26; 27; 28].