# Design of a Lightweight Cryptographic Scheme for Resource-Constrained Internet of Things Devices
## 3 Block Cipher SLA
### Permutation Layer
The differential potential (item \(\mathcal{DP}\) in Table 2) is identical to 0.25 over the best known for a Sbox_Nibble with four input variables, which is 0.0625. These findings demonstrate that Sbox_Nibble has the best defense against differential attacks. The robustness of our S-box design compared to the Mini AES S-box is shown in \[\text{K}^{i}=k_{63}k_{62}\cdots k_{0} \tag{6}\]2 For a \(4\times 4\) S-box, the Mini AES does not provide effective defense against linear attacks. In addition, it does not exhibit the best defense against differential attacks. The algebraic degree of the Mini AES S-box is two. This number is too low for immunity against high order differential attacks. Consequently, algebraic attacks can be efficiently executed if a multivariate algebraic equations system is solved. The S-box Mini AES's absolute indicator reaches the upper bound of 16 and its sum\(-\)of\(-\)squares indicator is close to 4096, hence its inability to achieve a great diffusion. Table 2 provides an overview of the findings for these criteria. The range of values accepted by the Walsh transform of the Sbox_Nibble are 8, 4, 0, \(-\)4, and \(-\)8. The range of values accepted by the linear profile are 64, 16, and 0; the range of values accepted by the differential profile are 1, 024, 512, and 0; finally, the autocorrelation has three levels: 8, 0, and \(-\)8. The results of the linear characteristic and the differential characteristic SLA scheme are shown in Tables 3 and 4. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Criteria** & **Lower Bound** & **Upper Bound** & **Our S-Box** & **Mini AES S-Box** & **Ref.** \\ \hline \(\mathcal{D}\)\(\epsilon\mathcal{G}\) & 0 (constant functions) & **n** & 3 & 2 & \\ \(\mathcal{NL}\) & 0 (affine functions) & **2\({}^{n-1}\)**-2\({}^{n-1}\)**(\(\geq\)**2m and n even**) & 4 & 2 & \\ \(\mathcal{CL}\) & 0 & **n** & 1 & 1 & \\ \(\mathcal{SD}\)\(\mathcal{B}\)\(\mathcal{D}\)**Balanced** & - & - & Balanced & Balanced & \\ \(\mathcal{AL}\) & 0 & [32] [\(\frac{n}{2}\)] & 2 & 2 & [40] \\ MAXAC & 0 (bent functions) & **2\({}^{n}\)**(affine functions) & 8 & 16 & \\ \(\sigma\) & **2\({}^{2n}\)** (bent functions) & **2\({}^{2n}\)**(affine functions) & 640 & 1408 & \\ \(\mathcal{LD}\) & 0 (if it has linear & 2\({}^{n-2}\) & 2 & 0 \\ structures) & **2\({}^{n-2}\)** & 2 & 0 & \\ \(\mathcal{PC}\) & 0 & **n** & 1 & 1 & \\ \(\mathcal{LP}\) & 0.0625 (\({}^{2-n}\)) & 1 & 0.25 & 0.5 & \\ \(\mathcal{DP}\) & 0.0625 (\({}^{2-m}\)) & 1 & 0.25 & 0.5 & \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Comparison with Respect to Cryptographic Criteria of Sbox_Nibble Layer for our design Approach and Mini AES. The results of the minimal number of active S-boxes in the linear and differential characteristics are shown in Tables 5 and 6. The comparison of the linear and differential attack of SLA with the other algorithms is shown in Table 7. The results show that 16 rounds of SLA are secure enough against differential and linear attacks. By changing just one bit in the input plaintext/key bits, the output seen in Tables 8 and 9 is produced. Each time a bit in the key is changed when using the SLA scheme; over half of the ciphertext bits are also changed. \begin{table}
\begin{tabular}{c c} \hline \hline
**Rounds** & **Min. No. of Active S-Boxes** \\ \hline First & 1 \\ Second & 3 \\ Third & 9 \\ Fourth & 20 \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Minimal Number of Active S-boxes in the Differential Characteristics. \begin{table}
\begin{tabular}{c c} \hline \hline
**Rounds** & **Input to S-Box** & **Output of S-Box** \\ \hline First & 0000 0000 0008 0000 & 0000 0000 0003 0000 \\ Second & 0000 000 5000 5000 & 0000 0000 0000 000 0000 \\ Third & 0360 0060 0300 0360 & 04b0 000 0400 04b0 \\ Fourth & 2024 2004 0040 204c & 5051 5001 0010 5012 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Minimal Number of Active S-boxes from the Linear Characteristics.