## 3 Password Generation Selection Model
### Password Generation Selection Model
The OMECDN model counts and classifies the passwords generated by OMEN into 41 intervals, and then calculates the efficiency of the OMECDN model (\(Efficiency_{\text{OMECDN}}\)) for each interval. The efficient calculation method is shown in Equation (8). \[Efficiency_{\text{OMECDN}}=\frac{Hit_{\text{GAN-D}(X)}\geq-1.3}{MaxTry_{\text{ GAN-D}(X)}\geq-1.3}*100\% \tag{8}\]

Furthermore, the calculation method of the efficiency of the OMEN model (\(Efficiency_{\text{OMEN}}\)) is shown in Equation (9). \[Efficiency_{\text{OMEN}}=\frac{Hit}{MaxTry}*100\% \tag{9}\]

In Equation (8), \(Hit_{\text{GAN-D}(X)}\geq-1.3\) represents the number of passwords in the test set generated by the OMECDN model, and \(MaxTry_{\text{GAN-D}(X)}\geq-1.3\) represents the number of passwords in the final password set of the OMECDN model. In Equation (9), \(Hit\) is the number of hit passwords in the test set for the generated password set for the OMEN model, and \(MaxTry\) is the total number of passwords generated for the OMEN model. The statistical results of the password score distribution are shown in Figures 8-11. Figure 7: The hit rate amounts of the three hit models for four datasets. the same training set and test set. The red line represents the efficiency of the OMECDN model in different intervals when the same number of passwords are generated under the same training set and test set. To better visualize the effects in the figures, we enlarged the columns for the data of the frequency of hitting passwords. To facilitate readers to better understand these figures, we take Figure 8 as an example for analysis. The abscissa represents the interval (it can be simply understood as these discrete intervals corresponding to or correlating with the probability of the N-gram character sequence in the Markov model). The side ordinate represents the password frequency, the red bar corresponds to the password frequency of the OMECDN model in the current interval, the blue bar corresponds to the number of missed passwords in the current interval, and the sum of the heights of the red and blue bars is the current experiment. The total number of password sets is \(10^{5}\) (for better visualization, we enlarged the height of the red column accordingly, which does not affect the conclusion, and this is enlarged by two times in Figure 8). After understanding the bar graph to indicate the distribution of password scores, we continue to analyze the line graph. The ordinate on the right represents the efficiency of the password guessing model. The calculation method was introduced above. The green line corresponds to the OMEN model (as a reference). When the red line is above the green line, it means that the OMECDN model is more efficient than the OMEN model. It can be seen in Figure 9 that, on the right side of the interval \"\(-1.1\)\", the efficiency of the OMECDN model is almost better than that of the OMEN model. From the password score distribution diagram, the PassGAN neural network discriminator has a certain rule for the password output score distribution, and the hit password score distribution is concentrated around \(-1.0\) and \(0.3\). When it is greater than or equal to the threshold constant \(-1.3\), the OMECDN model is more efficient. Some intervals are higher than the overall efficiency of the OMEN model, and thus the overall efficiency of the OMECDN model is higher than the overall efficiency of the OMEN model. This proves that an appropriate threshold constant was selected, and the performance of the OMECDN model is better than that of the OMEN model. In a real-world scenario, the threshold can be chosen flexibly to ensure the highest possible cracking efficiency. This also proves the validity and feasibility of the password generation selection model. ## 6 Conclusions

The use of password-generation technology to generate large-scale password sets, to detect the defects of existing user password-protection mechanisms, and to evaluate the efficiency of password-guessing algorithms is important for studying password security.