# Secure and Efficient Deduplication for Cloud Storage with Dynamic Ownership Management
## 6 Discussion
### Performance Analysis  
Table 3 provides a comparative analysis of the proposed protocol concerning client computational complexity and the presence of server-aided features, particularly the server computational complexity required for the dynamic ownership update. It is important to note that our proposed protocol is a type of server-side deduplication. In Section 2.1, we compare our protocol with other server-side deduplication protocols. The computational complexity of the client refers to the amount of computational resources required when uploading or downloading data. The server computational complexity refers to the amount of computational resources required when cloud storage updates dynamic ownership. Notably, refs. [11; 12] and the data download of [15] did not provide explicit mathematical formulations in the paper. \begin{table}
\begin{tabular}{c c c c c} \hline \hline  & **Data** & **Data** & **Forward** & **Backward** \\  & **Privacy** & **Integrity** & **Secrecy** & **Secrecy** \\ \hline
[4] & O & X & X & X \\
[9] & O & O & X & X \\
[5] & X & X & 0 & 0 \\
[7] & O & X & X & X \\
[6] & O & O & O & O \\ \hline
**Ours** & O & O & O & O \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Comparison of security requirements. \begin{table}
\begin{tabular}{c c c c c} \hline \hline  & **Client Computational Complexity** & & & **Server Computational Complexity** \\ \cline{2-5}  & **Initial Upload** & **Subsequent Upload** & **Download** & **Dynamic Ownership Update** \\ \hline
[4] & \(1H+1\)SE & \(1H+1\)SE & \(15\)D & X & X \\ \hline
[8] & \(2H+2\)SE + \(2M+3E\) & \(2H+2\)SE + \(2M+3E\) & \(25\)D & O & X \\ \hline
[10] & \(2H+4B*\)SE + \(B*\)DS & \(2H+4B*\)SE + \(B*\)DS & \(2B*\)SE + \(B*\)SD & X & X \\ \hline
[11] & - & - & - & O & X \\ \hline
[6] & \(2H+1\)SE + \(1\bigoplus\) & \(2H+1\)SE + \(1\bigoplus\) & \(2H+2\)SD + \(1\bigoplus\) & X & \(1H+3\)SE + \(1\bigoplus\) \\ \hline
[12] & - & - & - & X & X \\ \hline
[13] & \(1H+5M+\) & \(1H+5M+\) & \(1H+1\)SD + \(3M\) & O & X \\  & \((5+2B)*E+1\)DDH & \((5+2B)*E+1\)DDH & \(1H+1\)SD & O & X \\ \hline
[14] & \(3H+1\)SE + \(1M+1E\) & \(3H+1\)SE + \(1M+1E\) & \(1H+1\)SD & O & X \\  & \(+1\)DS & \(+1\)DS & & \(1H+1\)SD & O & X \\ \hline
[7] & \(1H+1\)SE & \(1H+1\)SE & \(1H+1\)SE & \(1\)SD & O & X \\ \hline
[15] & \(1H+1\)DS + \(1\)PRE-Dn & \(1H+1\)DS + \(1\)PRE-Dn & - & X & \(1\)PRE-ReEn \\  & \(+1\)PRE-En + \(1\)SE & \(+1\)PRE-En & - & X & \(1\)PRE-ReEn \\ \hline Ours & \(2H+2\bigoplus\) & \(2H+2\bigoplus\) & \(1\bigoplus\) & O & \(1\)SE + \(4\bigoplus\) \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Comparison of computational complexity. * Client computational complexity: 1. **Upload. ** Among the existing server-side deduplication protocols, [4,7] stand out in terms of minimal client computational requirements for data uploads, as depicted in Table 3. These protocols involve a single \(H\) and a single SE during both initial and subsequent uploads. In contrast, our protocol necessitates two operations of \(H\) and two operations of \(\bigoplus\). SE algorithms are typically resource-intensive and computationally complex, used for encrypting data. On the other hand, operations like transforming an input into a fixed-size hash value using \(H\) and relatively simpler bit-wise operations like \(\bigoplus\) are generally performed faster and more efficiently. However, actual performance may vary based on factors such as the algorithm used, implementation methods, and hardware configurations, among others. 2. **Download. ** Even for data download, our protocol outperforms [4,7] since they require a single SD while our protocol requires only a single \(\bigoplus\). Table 3 reveals that our approach excels in minimizing computational complexity when uploading and downloading data, offering an efficient solution for clients. * Server computational complexity, on the other hand, pertains to the computational resources required by the cloud storage server when re-encrypting data and distributing group keys during ownership changes.