## 3 Proposed LAO-3D Block Cipher
### Encryption Algorithm
Nine data categories of block cipher were implemented to generate the keys and plaintexts. Every data category generated unique 1000 samples where each sample consisted of 2081 to 15,744 ciphertexts that equaled 133,184 to 1,007,616 bits of data with a size range of 127 to 960 MB. The block and key lengths determine the total number of blocks for each sample [32]. The blocks were derived by appending the ciphertexts to establish large bit sequences. Table 11 listed each of the data categories that generate multiple lengths of derived ciphertext bits based on the input data. All 15 statistical tests can be applied to evaluate CBC, PCC, RPRK, SPA, and SKA data categories [33]. Due to insufficient data lengths, only 11 tests could be used to examine HDK and LDK, and 10 tests for HDP and LDP. The experimental results demonstrate that the LAO-3D block cipher passed all data categories and statistical tests as shown in Tables 12 and 13. In addition, the \(p\)-values produced by the block cipher from the NIST Statistical Suite are uniformly distributed since the values are larger than 0.0001, as shown in Tables 14 and 15. The 100% passing rate achieved in the randomness and uniformity test results verified the randomness characteristics of the cipher output. Combinations of substitution and permutation components in LAO-3D have optimized the confusion and diffusion properties of the algorithm that contribute to the randomization of the ciphertext. \begin{table}
\begin{tabular}{c c c c c} \hline \hline  & **Data Category** & **Key** & **Plaintext** & **Derived Blocks** & **Derived Bits** \\ \hline
1. & Strict Key Avalanche (SKA) & 123 128-bit keys & One all-zero 64-bit plaintext & 15,744 & 1,007,616 \\
2. & Strict Plaintext Avalanche (SPA) & One all-zero 128-bit key & 245 64-bit plaintexts & 15,680 & 1,003,520 \\
3. & Plaintext/Ciphertext & One 128-bit key & 15,625 64-bit plaintexts & 15,625 & 1,000,000 \\
4. & Ciphertext Block Chaining Mode (CBCM) & One 128-bit key & One all-zero 64-bit plaintext & 15,625 & 1,000,000 \\
5. & Random Plaintext/Random Key (RPRK) & One 128-bit key & 15,625 64-bit plaintexts & 15,625 & 1,000,000 \\
6. & Low-Density Key (LDK) & 3241 128-bit keys & 8257 64-bit plaintexts & 8257 & 528,448 \\
7. & High-Density Key (HDK) & 3241 128-bit keys & 8257 64-bit plaintexts & 8257 & 528,448 \\
8. & Low-Density Plaintext (LDP) & 2081 128-bit keys & 2081 64-bit plaintexts & 2081 & 133,184 \\
9. & High-Density Plaintext (HDP) & 2081 128-bit keys & 2081 64-bit plaintexts & 2081 & 133,184 \\ \hline \hline \end{tabular}
\end{table} 
Table 11: Input of Data Categories. ### Differential and Linear Cryptanalysis

A cryptanalysis attack is an experimental method used to distinguish a cryptosystem from a random function [34]. To ensure that the confidentiality of the proposed LAO-3D output is robust, it is necessary to examine the security strength of the algorithm against a variety of attack types. Differential cryptanalysis (DC) and linear cryptanalysis (LC) are methods used to attack cryptographic algorithms, thereby, it is important to consider a secure cipher to withstand these attacks. To apply differential cryptanalysis on an \(n\)-bit block cipher, a predictable difference has to be propagated in all (except for a few) rounds with probabilities greater than \(2^{1-n}\). For the LAO-3D block cipher to be immune to differential cryptanalysis, there should be no difference propagation with a probability higher than \(2^{-63}\). Table 16 represents the