## 3 Proposed LAO-3D Block Cipher
### Encryption Algorithm
A total of 1000 random plaintexts and five random keys were examined on the algorithm. Figure 14 displays the scatter charts of the analysis results. The values in the charts are plotted according to the computed correlation coefficient based on the key and plaintext inputs. A summary of the results presented in the scatter charts is shown in Table 6. According to the experimental results, the LAO-3D block cipher offers performance advantages (98.2% of the correlation coefficients, in the range \(0<R\leq 0.3\) and \(-0.3\leq R<0\)), indicating a weak linear relationship. The results generated by all five keys show that the adoption of the 3D cipher design on the LAO-3D block cipher provided high correlation coefficient characteristics. ### Bit Error Test

The bit error computes the differences in the ciphertext affected by the plaintext modifications. The number of changed ciphertext bits after modification of a plaintext bit is defined as the bit error. For the bit error test, the optimum result is 0.5 or 50% plaintext \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Result** & **Key 1** & **Key 2** & **Key 3** & **Key 4** & **Key 5** & **Average** \\ \hline \(R=0\) & 0 & 0 & 0 & 0 & 0 & 0\% \\ \(0<R\leq 0.3\) and \(-0.3\leq R<0\) & 979 & 977 & 990 & 982 & 982 & 98.2\% \\ \(0.3<R<0.7\) and \(-0.7<R<-0.3\) & 21 & 23 & 10 & 18 & 18 & 1.8\% \\ \(0.7\leq R<1\) and \(-1<R\leq-0.7\) & 0 & 0 & 0 & 0 & 0 & 0\% \\ \(R=-1\) and \(R=1\) & 0 & 0 & 0 & 0 & 0 & 0\% \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Correlation Coefficient Results. Figure 14: Scatter Charts of the Correlation Coefficient Results. bit alterations [29]. The formulation of the bit error rate, \(BER\), is defined in the following equation. \[BER=\frac{\text{Number of ciphertext bit difference}}{\text{Total number of ciphertext bit}} \tag{8}\]

The purpose of the bit error test is to measure the relationship between plaintext and ciphertext. A random key and five random plaintexts were used to examine the LAO-3D block cipher. As seen in Figure 15, the experimental results are presented in the scatter charts. The data plots in each chart display the bit error values that represent the changes of ciphertext upon plaintext modifications. An overall summarization of the bit error results presented in the scatter charts is shown in Table 7. After modifying the plaintext bits, the \(BER\) of the LAO-3D block cipher is more likely to be close to 0.5. The results generated by all five plaintexts prove that the LAO-3D block cipher achieved optimum bit error test results. By carefully examining the data, it is found that the LAO-3D block cipher obtains an average 50% bit error rate, which verifies that the ciphertext is entirely modified with a single alteration in the plaintext bit. Table 8 presents the comparison of the avalanche effect \begin{table}
\begin{tabular}{c c c} \hline \hline
**Input** & **Average Different Bits** & **Average Bit Error Rate** \\ \hline Plaintext 1 & 31.703125 & 0.495361 \\ Plaintext 2 & 32.203125 & 0.503174 \\ Plaintext 3 & 32.046875 & 0.500732 \\ Plaintext 4 & 32.046875 & 0.500732 \\ Plaintext 5 & 32.156250 & 0.502441 \\ \hline Average & 50.05\% & 50.05\% \\ \hline \hline \end{tabular}
\end{table} 
Table 7: Bit Error Results. Figure 15: Scatter Charts of Bit Error Rate Results. on the modification of the plaintext against existing block ciphers [10]. The results achieved by the proposed LAO-3D surpass the earlier works in terms of non-linearity between the plaintext and its corresponding ciphertext. ### Key Sensitivity Test

The key sensitivity test examines the affected ciphertext upon key alteration [30]. An algorithm has a high-security level against the key sensitivity attack if changing a small portion of the key will cause major modifications on the ciphertext bits. During the observation of key sensitiveness, the key bit is manipulated by changing one bit from its first to the last bit position. The bit error rate equation is applied to compute the experimental results.