# Strength Analysis of Real-Life Passwords Using Markov Models
## 5 Results
### Data Collections Characteristics  
Before we present our main results, we present some summary statistics about our datasets, regarding the characteristics of the passwords they contain. We are interested in passwords characteristics like the average length, uniqueness, the percentage of passwords that were only numerical, only lower-case letters, only upper-case letters, mixed-case letters, alphanumerical, and that contain at least one special character. Table 2 shows a summary of the distributions of passwords and the average password length in each dataset. As we can observe, the most common passwords in every dataset are alphanumeric passwords. Table 3 shows the percentages of passwords that appear 1-5 or more times in every dataset. As we can observe from the table, out of all 12 dataset only three (_10_million_passwords_, _passwords_, and _scribd_) do not contain a 100% unique passwords. The high percentage of uniqueness of the datasets goes in hand with our experiment, since it allows us to train our models over a wide variety of passwords. Table 4 shows the average password length in our datasets. The table shows that the average password length (weighted by the size of the datasets) is 8.38 characters, which is in line with findings in [17; 31; 32]. \begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**Dataset**} & \multirow{2}{*}{**Size**} & \multicolumn{4}{c}{**Password Length**} \\ \cline{3-5}  & & \multicolumn{2}{c}{**Mean**} & \multicolumn{2}{c}{**Standard Deviation**} \\ \hline rockyou & 14,344,390 & 8.75 & 2.898 \\
10\_million\_passwords & 10,000,000 & 7.59 & 2.15 \\ passwords & 2,151,220 & 8.37 & 1.995 \\ uniqpass\_preview & 1,999,984 & 9.92 & 3.51 \\ phpbb & 184,389 & 7.54 & 1.75 \\ scribd & 106,358 & 7.51 & 2.6 \\ tuscl & 38,820 & 7.37 & 1.75 \\ myspace & 37,139 & 8.23 & 2.6 \\ singles\_org & 12,233 & 6.74 & 1.19 \\
10k\_most\_common & 10,000 & 6.30 & 1.3 \\ hotmail & 8930 & 8.79 & 2.89 \\ faithwriters & 8347 & 7.71 & 1.86 \\
**Simple average** & & **7.9** \\
**Weighted average** & & **8.38** \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Password length. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multicolumn{1}{c}{**Dataset**} & \multirow{2}{*}{**Digits Only**} & \multirow{2}{*}{**Lowercase Only**} & \multicolumn{2}{c}{**Uppercase Only**} & \multicolumn{2}{c}{**Mixedcase**} & \multicolumn{2}{c}{**Alphanumeric**} & \multicolumn{2}{c}{**A special Character *} \\ \hline
1. rockyou & 16.36\% & 26.06\% & 1.61\% & 1.12\% & 47.51\% & 6.82\% \\
2. 10 million passwords & 20.36\% & 38.25\% & 1.09\% & 2.52\% & 35.90\% & 1.10\% \\
3. passwords & 23.22\% & 23.85\% & 0.75\% & 1.56\% & 47.08\% & 3.02\% \\
4. uniqpass preview & 6.70\% & 28.96\% & 0.00\% & 0.00\% & 48.86\% & 15.48\% \\
5. phpbb & 11.24\% & 41.25\% & 0.93\% & 2.69\% & 41.19\% & 2.13\% \\
6. scribd & 0.27\% & 81.71\% & 0.18\% & 7.57\% & 2.94\% & 7.32\% \\
7. tuscl & 8.70\% & 42.36\% & 0.94\% & 2.38\% & 43.17\% & 1.72\% \\
8. myspace & 0.72\% & 6.75\% & 0.29\% & 0.18\% & 80.43\% & 10.66\% \\
9. singles\_org & 8.37\% & 55.11\% & 2.26\% & 4.37\% & 29.00\% & 0.24\% \\
10. 10k most common & 5.54\% & 83.10\% & 0.00\% & 0.00\% & 11.20\% & 0.16\% \\
11. hotmail & 18.52\% & 41.59\% & 2.21\% & 1.05\% & 29.50\% & 6.93\% \\
12. faithwriters & 6.27\% & 50.15\% & 1.32\% & 3.83\% & 37.14\% & 0.53\% \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Passwords information.