# Secure and Efficient Deduplication for Cloud Storage with Dynamic Ownership Management
## 6 Discussion
### Security Analysis  
Certainly, the security analysis is explained with respect to the data privacy, data integrity, backward secrecy, and forward secrecy described in Section 4.2. * **Data privacy. ** In our protocol, the CS can access \(M\), but \(M\) has blind encryption applied to plaintext \(m\). Hash functions used in blind encryption have structural safety thatcannot recover input values from hash values due to preimage resistance. Therefore, the CS cannot recover \(m\) from \(M\). The proposed protocol can ensure safety and solve key exchange problems with a relatively simple hash operation. The data delivered to cloud storage in the proposed protocol are a value encrypted with the message-locked encryption (MLE) key by the CS. Since these data are encrypted with the same key, if they are a request for the same plaintext, they will have the same ciphertext. Therefore, cloud storage may perform deduplication on the same encrypted data. * **Data integrity. ** In our protocol, when a client uploads data, the CS verifies if the received hash value matches the one that it computes directly. The cloud storage also checks if the hash value received from the CS matches the one it calculates independently. In essence, during the upload process, data integrity is inherently confirmed, preventing the storage of corrupted data. * **Forward secrecy. ** In our protocol, when a client deletes their ownership, they are no longer included in the ownership group for that session, and they cannot access the original data. The ownership group is updated immediately when a client's ownership changes, and the refreshed group key is also modified. Therefore, following a request for ownership deletion, whether data have been deleted or retained, the client cannot access data stored in the cloud storage. * **Backward secrecy. ** In our protocol, a client can only access data stored in the cloud if they have uploaded the data and acquired ownership. Even if a client owns the data, they do not automatically become a part of the ownership group for that session. In the proposed protocol, when a client uploads data, the ownership group is immediately updated, and the refreshed group key is changed. Therefore, even if a client uploads data, they cannot gain access to information about data previously stored by the ownership group. Through these measures, the proposed protocol addresses the aspects of data privacy, data integrity, backward secrecy, and forward secrecy, providing a comprehensive security framework for the system. Table 2 provides a comparison between our proposed approach and five closely related proposals from Section 2. It aims to highlight how our protocol offers enhanced security and the ability to update ownership in the context of SeDaSC. The table demonstrates the key differences and advantages of our proposal compared to existing proposals. Ref. [4] proposed the concept of convergent encryption (CE), which allows for secure data deduplication by encrypting data using the hash value of the message. However, it had the drawback of not providing a mechanism for verifying data integrity. Ref. [9] proposed a method within the framework of MLE called hash and CE with tag check (HCE2). HCE2 overcomes the limitations of CE by employing cryptographic hash functions to create tags that verify data integrity. Both of these data deduplication techniques offer privacy features but do not consider methodologies for scenarios where ownership changes. Ref. [5] proposed the SeDaSC protocol for authenticated client groups, using a CS to enhance client computational efficiency. However, it lacked data privacy as data sent to the CS were not encrypted. Moreover, it assumed the trustworthiness of the CS performing data deduplication, making it difficult to ensure data integrity since it had access to plaintext data. Ref. [7] proposed a solution to address the privacy issue in SeDaSC by using CE to provide data privacy. However, as it relies on CE, it does not guarantee data integrity.