## 3 Reputation Model
### Determination of Reputation by Security Service and Global Reputation  
The aim in this stage is to determine the reputation of an application based on the number of reviews recorded in Google Play, as well as their respective polarities while taking into account the security service that each review releases. We obtain the probability that an application has a good or a bad reputation, by subsequently relying on a probabilistic model defined as in Equation (3) [25]. \[E(p\mid\alpha,\beta)=\frac{\alpha}{\alpha+\beta},\text{ with }0\leq p\leq 1; \;\alpha,\beta>0, \tag{3}\]  
where  
* \(\alpha=\sum N_{p}os=\alpha_{C}+\alpha_{I}+\alpha_{A}+\alpha_{D}\) (total number of positive polarity); \begin{table}
\begin{tabular}{c c c} \hline \hline
**Reviews** & **Positive Polarity (\%)** & **Negative Polarity (\%)** \\ \hline C1 & 0.22 & 0.78 \\ C2 & 0.16 & 0.84 \\ C3 & 0.27 & 0.73 \\ C4 & 0.31 & 0.69 \\ C5 & 0.32 & 0.68 \\ C6 & 0.51 & 0.49 \\ C7 & 0.36 & 0.64 \\ C8 & 0.33 & 0.67 \\ C9 & 0.22 & 0.78 \\ C10 & 0.64 & 0.36 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Polarity of reviews related to the security of the Instagram application. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline  & **Sentiment** & **Confidentiality** & **Integrity** & **Authentication** & **Availability** \\  & **Related** & **Words** & **Words** & **Related** & **Words** \\ \hline C1 & _Negative_ & 2 & 0 & 0 & 1 \\ C2 & _Negative_ & 0 & 1 & 0 & 2 \\ C3 & _Negative_ & 0 & 1 & 0 & 1 \\ C4 & _Negative_ & 0 & 0 & 0 & 1 \\ C5 & _Negative_ & 0 & 0 & 1 & 1 \\ C6 & _Positive_ & 0 & 1 & 0 & 1 \\ C7 & _Negative_ & 1 & 1 & 0 & 1 \\ C8 & _Negative_ & 0 & 0 & 1 & 2 \\ C9 & _Negative_ & 1 & 1 & 0 & 2 \\ C10 & _Positive_ & 0 & 1 & 0 & 2 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Distribution of security-related keywords. \(\beta=\sum N_{p}os=\beta_{C}+\beta_{I}+\beta_{A}+\beta_{D}\) (total number of negative polarity)  
and  
* \(\alpha_{C}\) (resp.) \(\beta_{C}\) is the positive (resp. negative) polarity value for the service confidentiality;
* \(\alpha_{I}\) (resp.) \(\beta_{I}\) is the positive (resp. negative) polarity value for the service integrity;
* \(\alpha_{A}\) (resp.) \(\beta_{A}\) is the positive (resp. negative) polarity value for the service authentication;
* \(\alpha_{D}\) (resp.) \(\beta_{D}\) is the positive (resp. negative) polarity value for the service availability. Such that  
\[\sum(\alpha_{i},\beta_{i})=1. \tag{4}\]  
Table 3 summarizes different polarity values for each review in the Instagram application. These values are obtained as follows: the value obtained after implementing the Python script on a given review, the polarities obtained, namely positive and negative (Table 3) are represented here while respecting the distribution of word numbers linked to the various security services mentioned above (Table 2). Thus to obtain the values \(\alpha_{i}\) and \(\beta_{i}\) for a given review, we recover the number of words of the review distributed by security service, then we bring out the exact value of polarity obtained in Table 3 for each security service having a positive number (i.e., \(\alpha_{i}\), \(\beta_{i}>0\)). The final polarity value is therefore obtained as a function of the total number of words in the review highlighting the security aspect and the number of words distributed by security service (Table 3). We can therefore determine the reputation likelihood by security service by exploiting the formula of the probabilistic model \(E(p\mid\alpha,\beta)\) for each service. We have:  
* Confidentiality: \(E_{C}=\alpha_{c}/(\alpha_{c}+\beta_{c})=0.6\). * Integrity: \(E_{I}=\alpha_{I}/(\alpha_{I}+\beta_{I})=0.7\). * Authentication: \(E_{A}=\alpha_{A}/(\alpha_{A}+\beta_{A})=0.2\). * Availability: \(E_{D}=\alpha_{D}/(\alpha_{D}+\beta_{D})=0.4\).