## 3 Proposed LAO-3D Block Cipher
### Encryption Algorithm
\begin{table}
\begin{tabular}{c c c c c c} \hline  & & & \multicolumn{3}{c}{**Data Category**} \\  & **Statistical Test** & **LDK** & **HDK** & **LDP** & **HDP** \\ \hline
1. & Runs & 0.291091 & 0.177628 & 0.239266 & 0.496351 \\
2. & Frequency & 0.114712 & 0.566688 & 0.773405 & 0.639202 \\
3. & Spectral DFT & 0.274341 & 0.914025 & 0.684890 & 0.943242 \\
4. & Block Frequency & 0.500279 & 0.769527 & 0.361938 & 0.118812 \\
5. & Binary Matrix & 0.370262 & 0.711601 & 0.001953 & 0.118120 \\  & Rank & & & & \\
6. & Approximate & 0.889118 & 0.316052 & 0.072066 & 0.009535 \\
7. & Longest Runs of & & & & \\
7. & Ones & 0.757790 & 0.301194 & 0.749884 & 0.821937 \\
8. & Serial & 0.226422 & 0.576050 & 0.262395 & 0.804706 \\
9. & Cumulative Sums & 0.141130 & 0.181735 & 0.660295 & 0.418857 \\
10. & Non-Overlapping & & & & \\
11. & Tampelates & & & & \\
12. & Tampelates & & & & \\
13. & Tampelates & & & & \\
14. & Tampelates & & & & \\
15. & Tampelates & & & & \\ \hline \end{tabular}
\end{table} 
Table 15: The \(p\)-values of the Uniformity Test (LDK, HDK, LDP, and HDP). \begin{table}
\begin{tabular}{c c c c c c} \hline  & & & \multicolumn{3}{c}{**Data Category**} \\  & **Statistical Test** & **CBC** & **PCC** & **RPRK** & **SKA** & **SPA** \\ \hline
1. & Runs & 0.870856 & 0.691081 & 0.061260 & 0.069430 & 0.402962 \\
2. & Frequency & 0.336111 & 0.530120 & 0.626709 & 0.641284 & 0.731886 \\
3. & Spectral DFT & 0.771469 & 0.765632 & 0.651693 & 0.225998 & 0.277082 \\
4. & Block Frequency & 0.092041 & 0.711601 & 0.116746 & 0.552383 & 0.719747 \\
5. & Binary Matrix Rank & 0.377007 & 0.122325 & 0.682823 & 0.944274 & 0.264901 \\
6. & Approximate Entropy & 0.431754 & 0.331408 & 0.881662 & 0.128874 & 0.739918 \\
7. & Longest Runs of Ones & 0.070737 & 0.302657 & 0.591409 & 0.771469 & 0.334538 \\
8. & Serial & 0.366038 & 0.391685 & 0.089581 & 0.624739 & 0.560316 \\
9. & Cumulative Sums & 0.741256 & 0.712763 & 0.082836 & 0.687575 & 0.379922 \\
10. & Non-Overlapping Templates & 0.540168 & 0.477106 & 0.538421 & 0.501121 & 0.500920 \\
11. & Maurer’s Universal & 0.814724 & 0.164425 & 0.245490 & 0.277082 & 0.689019 \\
12. & Linear Complexity & 0.120207 & 0.471146 & 0.668321 & 0.298282 & 0.463512 \\
13. & Overlapping Templates & 0.102526 & 0.199045 & 0.554420 & 0.743915 & 0.228367 \\
14. & Random Excursion & 0.533205 & 0.399313 & 0.592636 & 0.556975 & 0.585012 \\
15. & Random Excursion Variant & 0.474550 & 0.414868 & 0.472390 & 0.577133 & 0.547103 \\ \hline \end{tabular}
\end{table} 
Table 14: The \(p\)-values of the Uniformity Test (CBC, PCC, RPRK, SKA, and SPA). The highest probability of difference propagation found in the sixth round is \(2^{-64}\), which is lower than \(2^{-63}\). Differential cryptanalysis results of lightweight block ciphers are shown in Figure 17. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Round** & **Input Difference of S-box** & **Output Difference of S-box** & **Probability** & **Probability of Differential Trails** \\ \hline
1 & 0000000000000001 & 00000000000003 & \(2^{-2}\) & \(2^{-2}\) \\
2 & 0000000000000088 & 0000000000000039 & \(2^{-6}\) & \(2^{-8}\) \\
3 & 000000040000C008 & 00000000050003 & \(2^{-7}\) & \(2^{-15}\) \\
4 & 0001200000090088 & 0003500000040099 & \(2^{-12}\) & \(2^{-27}\) \\
5 & 500008020000E008 & 10003035000002009 & \(2^{-17}\) & \(2^{-44}\) \\
6 & 0000890100229108 & 000034030034303 & \(2^{-20}\) & \(2^{-64}\) \\ \hline \hline \end{tabular}
\end{table} 
Table 16: Differential Trails with Optimal Probability. Figure 17: The 6-round Differential Characteristics of LAO-3D. shown in Table 17. An effective differential distinguisher with more than five rounds for the algorithm was impossible to be constructed; the 20-round LAO-3D is sufficient to resist differential cryptanalysis. To apply linear cryptanalysis on an \(n\)-bit block cipher, there should be a predictable linear propagation overall but a few rounds with a significant amplitude greater than \(2^{-\frac{n}{2}}\).