## 3 Proposed LAO-3D Block Cipher
### Encryption Algorithm
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline  & \multicolumn{4}{c}{**Data Category**} \\  & **Statistical Test** & **LDK** & **HDK** & **LDP** & **HDP** \\ \hline \multicolumn{5}{c}{**Range of Acceptable Rejection: [0, 20]**} \\ \hline
1. & Runs & 990/1000 & 986/1000 & 992/1000 & 992/1000 \\
2. & Frequency & 987/1000 & 988/1000 & 992/1000 & 991/1000 \\
3. & Spectral DFT & 988/1000 & 984/1000 & 986/1000 & 984/1000 \\
4. & Block Frequency & 994/1000 & 991/1000 & 986/1000 & 990/1000 \\
5. & Binary Matrix Rank & 990/1000 & 989/1000 & 993/1000 & 990/1000 \\
6. & Approximate Entropy & 987/1000 & 992/1000 & 987/1000 & 989/1000 \\
7. & Longest Runs of Ones & 995/1000 & 989/1000 & 987/1000 & 989/1000 \\
8. & Serial & 992/1000 & 989/1000 & 986/1000 & 991/1000 \\
9. & Cumulative Sums & 985/1000 & 987/1000 & 993/1000 & 986/1000 \\
10. & Non-Overlapping Templates & 990/1000 & 990/1000 & 990/1000 & 989/1000 \\
11. & Maurer’s Universal & 989/1000 & 992/1000 & & * \\
12. & Linear Complexity & * & * & * & * \\
13. & Overlapping Templates & * & * & * & * \\ \hline \hline \multicolumn{5}{c}{**Range of Acceptable Rejection: Not Available**} \\ \hline
14. & Random Excursion & * & * & * & * \\
15. & Random Excursion Variant & * & * & * & * \\ \hline \hline \end{tabular}

* no effective trail from the encryption round onward.

\end{table} 
Table 12: Randomness Analysis Results (CBC, PCC, RPRK, SKA, and SPA). \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline  & \multicolumn{4}{c}{**Data Category**} \\  & **Statistical Test** & **CBC** & **PCC** & **RPRK** & **SKA** & **SPA** \\ \hline \multicolumn{5}{c}{**Range of Acceptable Rejection: [0, 20]**} \\ \hline
1. & Runs & 992/1000 & 987/1000 & 990/1000 & 990/1000 & 988/1000 \\
2. & Frequency & 989/1000 & 992/1000 & 993/1000 & 984/1000 & 989/1000 \\
3. & Spectral DFT & 991/1000 & 996/1000 & 988/1000 & 990/1000 & 985/1000 \\
4. & Block Frequency & 986/1000 & 986/1000 & 993/1000 & 994/1000 & 996/1000 \\
5. & Binary Matrix Rank & 987/1000 & 985/1000 & 992/1000 & 995/1000 & 989/1000 \\
6. & Approximate Entropy & 994/1000 & 995/1000 & 989/1000 & 988/1000 \\
7. & Longest Runs of Ones & 989/1000 & 991/1000 & 994/1000 & 997/1000 & 985/1000 \\
8. & Serial & 992/1000 & 992/1000 & 990/1000 & 991/1000 & 990/1000 \\
9. & Cumulative Sums & 991/1000 & 992/1000 & 989/1000 & 989/1000 & 991/1000 \\
10. & Non-Overlapping Templates & 990/1000 & 990/1000 & 990/1000 & 990/1000 & 990/1000 \\
11. & Maurer’s Universal & 992/1000 & 989/1000 & 988/1000 & 983/1000 & 986/1000 \\
12. & Linear Complexity & 986/1000 & 986/1000 & 992/1000 & 989/1000 & 991/1000 \\
13. & Overlapping Template & 983/1000 & 987/1000 & 992/1000 & 995/1000 & 987/1000 \\ \hline \multicolumn{5}{c}{**Range of Acceptable Rejection: [0, 14]**} \\ \hline
14. & Random Excursion & 577/584 & 609/617 & 590/595 & 613/622 & 627/633 \\
15. & Random Excursion Variant & 578/584 & 611/617 & 590/595 & 616/622 & 627/633 \\ \hline \hline \end{tabular}

* no effective trail from the encryption round onward.

\end{table} 
Table 13: Randomness Analysis Results (LDK, HDK, LDP, and HDP). differential trails with the optimal probability for six rounds of LAO-3D that are depicted in Figure 17.