## 3 Proposed LAO-3D Block Cipher
### Encryption Algorithm
The result of a decent cryptographic algorithm must be close to 0.5 or 50% of the total ciphertext bit modification. In this experiment, a random plaintext and five random keys were included to examine the LAO-3D block cipher. The scatter charts of the experimental results are shown in Figure 16. \begin{table}
\begin{tabular}{c c} \hline \hline
**Algorithm** & **Average Avalanche Effect** \\ \hline LAO-3D & 50.05\% \\ LED & 52.83\% \\ LRBC & 58.00\% \\ PRINCE & 51.18\% \\ PRINT & 49.08\% \\ QTL & 52.56\% \\ SIMECK & 53.00\% \\ TEA & 49.12\% \\ \hline \hline \end{tabular}
\end{table} 
Table 8: Avalanche Effect on Plaintext Modifications. Figure 16: Scatter Charts of the Key Sensitivity Results. Table 9 summarizes the key sensitivity experimental results presented in the scatter charts. On average, the proposed LAO-3D block cipher obtained 32-bit differences with an approximate 50% bit error rate. The results suggest that LAO-3D has a non-linear relationship between the key and ciphertext that represents a high key sensitivity on the ciphertext. Similar observations were made on the key alteration while retaining a constant plaintext performed against other algorithms [10], presented in Table 10. The 50% key sensitivity result denotes that the entire key bits have an impact on every ciphertext bit. Based on the findings, the LAO-3D block cipher showed some improvements over the existing works on the avalanche effect of the key sensitivity. ### Randomness Test

The randomness of the proposed LAO-3D block cipher was tested using 15 statistical tests of the NIST Special Publication 800-22 [31]. The NIST accommodates an open-source randomness test application called NIST Statistical Suite. The randomness test application is aimed at varieties of non-random characteristics from the generated ciphertext. Eight tests inclusive of random excursion (8 \(p\)-values), random excursion variant (18 \(p\)-values), cumulative sums (2 \(p\)-values), binary matrix rank (1 \(p\)-value), longest runs of ones (1 \(p\)-value), frequency (1 \(p\)-value), spectral DFT (1 \(p\)-value), and runs (1 \(p\)-value) are classified as the non-parameterized tests. Seven other tests, i.e., non-overlapping (148 \(p\)-values), serial (2 \(p\)-values), linear complexity (1 \(p\)-value), maurer's universal (1 \(p\)-value), approximate entropy (1 \(p\)-value), overlapping templates (1 \(p\)-value), and block frequency (1 \(p\)-value) are labeled as parameterized tests that require parameter inputs. A significant level, \(\alpha\), must be set within 0.1% (0.001) to 1% (0.01) before assessing the randomness test. Moreover, the sample size should at least be the inverse of the significant level (\(1\div 0.01=100\) samples). For the test results, the ciphertext is regarded as random if the \(p\)-value \(\geq\alpha\). Conversely, if the \(p\)-value \(<\alpha\), the ciphertext is determined as not random. \begin{table}
\begin{tabular}{c c} \hline \hline
**Algorithm** & **Average Avalanche Effect** \\ \hline LAO-3D & 50.00\% \\ LED & 50.37\% \\ LRBC & 55.75\% \\ PRINCE & 49.06\% \\ PRINT & 46.42\% \\ QTL & 50.31\% \\ SIMECK & 51.25\% \\ TEA & 47.12\% \\ \hline \hline \end{tabular}
\end{table} 
Table 10: Avalanche Effect on Key Modifications. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Input** & **Average Different Bits** & **Average Bit Error Rate** \\ \hline Key 1 & 32.000122 & 0.500002 \\ Key 2 & 32.028317 & 0.500442 \\ Key 3 & 32.007694 & 0.500120 \\ Key 4 & 31.948364 & 0.499193 \\ Key 5 & 32.013795 & 0.500216 \\ \hline Average & 50.00\% & 50.00\% \\ \hline \hline \end{tabular}
\end{table} 
Table 9: Key Sensitivity Results. Equation (9) defines the proportion of test samples that will determine the randomness of an algorithm. \[p_{\alpha}= (1-\alpha)-3\sqrt{\frac{\alpha(1-\alpha)}{s}} \tag{9}\]

where \(s\) symbolizes the size of the test sample (1000 ciphertexts) and \(\alpha\) indicates the significance level (0.01) that is used in this paper. If the total rejection exceeds the computed proportion \(p_{\alpha}\), the sample is regarded as not random.