## 6 Discussions  
Our newly introduced protocol is a lightweight privacy-preserving protocol allowing secure validations between the cloud's three main players, namely: the CC, CSP, and the TPA; with the aim to detect, on the fly, dishonest activities of the TPA as well as auditing the CSP's procedures. We start by presenting the methods that we compare LAPP to, namely SPS, PPA, PPPAS, and SEPPPA (Table 3). Figure 4: Time complexity (input files). Figure 3: Accuracy (number of malicious attempts). \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Security Models** & \multicolumn{2}{c}{**Security Requirements**} & **Threats** & \multicolumn{1}{c}{**Advantages**} \\ \hline \multirow{6}{*}{SPS} & \(\bullet\) & Third-party auditing & & & \\  & \(\bullet\) & Supports data dynamics & & & \\  & \(\bullet\) & Support privacy-preserving public auditing & & & \\  & \(\bullet\) & Use of private channels to relay & \(\bullet\) & Communication overhead & \(\bullet\) & Practical for cloud system on a large scale. \\  & \(\bullet\) & Use of private channels to relay & \(\bullet\) & Communication overhead & \(\bullet\) & Considers the vulnerability of dynamic data \\  & \(\bullet\) & KeyGen, SigGen, GenProof, and & & & \\  & VerifyProof features & & & \\ \hline \multirow{6}{*}{PPA} & \(\bullet\) & Third-party auditing & & & \\  & \(\bullet\) & Support data dynamics & \(\bullet\) & TPA is used as an intermediary & \(\bullet\) & Practical for cloud system on a large scale. \\  & \(\bullet\) & Double block transportation & & to send encrypted data & \\  & \(\bullet\) & Supports privacy-preserving public auditing & \(\bullet\) & Hidden server failure. & \(\bullet\) & TPA doesn’t need a local copy of Data \\  & \(\bullet\) & KeyGen, SigGen, GenProof, and & & & \\  & VerifyProof features & & & \\ \hline \multirow{6}{*}{PPPAS} & \(\bullet\) & Third party auditing. & & & \\  & \(\bullet\) & Supports batch auditing. & \(\bullet\) & TPA is somehow trusted & \(\bullet\) & Identification of invalid Response. \\  & \(\bullet\) & KeyGen, SigGen, GenProof, and & & & \(\bullet\) & Supports for dynamic data \\  & \(\bullet\) & VerifyProof features & & & \\ \hline \multirow{6}{*}{SEPPPA} & \(\bullet\) & Third party auditing. & & & \\  & \(\bullet\) & Supports batch auditing. & \(\bullet\) & TPA does not need a local copy of data. \\  & \(\bullet\) & Supports privacy preserving public auditing. & \(\bullet\) & TPA is somehow trusted & \(\bullet\) & To date, a pioneer in privacy-preserving schemes for cloud \\  & \(\bullet\) & KeyGen, SigGen, GenProof, and & & & \\  & VerifyProof features & & & \\ \hline \multirow{6}{*}{LAPP} & \(\bullet\) & Third-party auditing & & & \\  & \(\bullet\) & Determining malicious TPA activity & & & \\  & \(\bullet\) & Supports data dynamics & & & \\  & \(\bullet\) & Support privacy-preserving & \(\bullet\) & TPA is somehow trusted & \\  & \(\bullet\) & Testing process & & & \\  & \(\bullet\) & Substantiation process & & & \\  & \(\bullet\) & Validation process & & & \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Comparison of LAPP and competing approaches. In our first experiment, we measured the computation time of auditing in seconds versus the number of challenged blocks, increasing the number of blocks by 500 for each measurement. The results presented a better response for LAPP by 28% compared to PPA and 44.45% compared to SPS. In our second simulation, we measured the accuracy in percentage compared to the number of malicious attempts, and our results showed a steady accuracy for LAPP, whereas it started degrading considerably for the other methods. In our last simulation, we measured the time complexity in seconds versus the size of input files in KB by increasing the size of the input files by 4 KB each time. Our results showed a constant proportional increase in time to run LAPP after increasing the number of input files, while the other methods showed a logarithmic or quadratic increase.