## 5 Simulation Results
### Analyzing the Impact of the Developed Method  
The proposed solution was implemented at the University of Bucharest, Romania. The study presented in this paper was conducted on 74 users divided into two groups of 37 people. The first group in the sample was authenticated only with the username and password from the Moodle account. The second group in the sample was authenticated using the proposed two-factor authentication scheme. The number of password reset requests for both schemes is shown in Figure 4.  
Thus, it is noticed that when using the implemented authentication, the number of users who forgot their password decreased with the use of the new solution, having a visible and favorable decreasing trend compared to the solution related to the login with the user and password. On the first day, the number of users who forgot their password using the proposed solution was higher than those who used the username and password authentication. Considering that it is a new solution, this situation is understandable since users have not used it before; they need a little time to get used to the new method. Gradually, the number of those who forgot their password decreased, highlighting the solution's ease of implementation and increased user convenience. Upon analyzing the results presented in the chart above, it has been observed that on the first day of usage, employing the simple login method with the username and password, five users reported suspicions of unauthorized access to their accounts, while with the implemented solution, seven users had similar suspicions, as depicted in Figure 5. Similarly, on the seventh day of usage, employing the aforementioned simple login method, nine users reported suspicions of unauthorized access to their accounts, whereas five users reported similar suspicions with the implemented solution. This trend was observed to hold for intervals of 14, 21, and 31 days, with only minor variations in the number of users. Consequently, it has been noted that the employment of the implemented authentication method led to a marginal increase in the number of users suspecting unauthorized access to their accounts, followed by a substantial decrease compared to the simple username and password authentication solution. Notably, on the first day of usage, a higher number of users employing the proposed solution reported forgetting their passwords compared to those using the username and password authentication method. This observation is explicable, as the proposed solution was novel, and the users were not accustomed to using it. With continued use of the solution, the number of users suspecting unauthorized access to their accounts decreased, underscoring the confidence in the employed solution. Next, the number of suspicions of missing content was measured and is plotted in Figure 6.  
From the analysis of the results obtained from the above chart, the following are identified: On the first day using the simple login with a user and password, four users suspected missing documents or deleted or modified courses, and with the implemented solution, two users suspected missing documents or deleted or modified courses (Figure 6). On the seventh day, using the simple login with a user and password, nine users suspected missing documents or deleted or modified courses, and with the implemented solution, five users suspected missing documents or deleted or modified courses. The same happened on days 14, 21, and 31; only the number of users varied. Thus, it was observed that when using the implemented authentication, the number of users who suspected missing documents or deleted was increased, and the number of users who  
Figure 4: Comparison between Moodle account and the proposed solution regarding resetting the account password. deleted or modified courses had a slight increase, after which it decreased with the use of the new solution, having a visible and favorable decreasing trend compared to the related solution login with the user and password.