## 4 Discussion  
Table 8 compares our obtained S-box with the existing \(8\times 8\) cryptographically strong S-boxes available in literature, as discussed in the previous section. Only S-boxes that satisfy our prerequisite requirements are selected for comparison. The S-boxes were then arranged based on the optimal cryptographic properties exhibits by each S-box, starting with the highest NL, lowest DU, highest AD and, lastly, lowest LA. From there, we rank the S-boxes based on these four properties. Also included in Table 8 are the number of terms exhibited by an S-box and lastly the generic design method of each proposal. In total, there are 39 S-boxes listed in Table 8 where we classify 16 ranks. The first rank is occupied by the AES S-box which was constructed using multiplicative inversion in \(\mathbb{F}_{28}\). There are 13 others S-box construction that are similar to AES's S-box construction; thus, they exhibit the same cryptographic properties as AES, which consists of (112, 4, 7, 16) for its (NL, DU, AD, LA), respectively. So far, this multiplicative inverse technique over finite field \(\mathbb{F}_{28}\) leads to the best-known cryptographic properties for an \(8\times 8\) S-box. Ranked second is the S-box construction proposed by [PERSON] et al. [91]. Their S-box construction exhibits cryptographic properties of (112, 4, 5, 16) for (NL, DU, AD, LA), \begin{table}
\begin{tabular}{c c c c c c c c c c c c c c c c} \hline \hline  & 0 & 1 & 2 & 3 & 4 & 5 & 6 & 7 & 8 & 9 & A & B & C & D & E & F \\ \hline
0 & 8B & C3 & 6E & 5E & 9B & E9 & 03 & 68 & BE & BD & 12 & 27 & 2C & F4 & BB & 41 \\
1 & 31 & A3 & 8A & 86 & C8 & 38 & 94 & 3C & 08 & 32 & 3E & B5 & 56 & ED & 14 & 47 \\
2 & 37 & 1B & 7B & DE & 35 & 99 & 1F & A0 & 81 & 65 & BD & SB & DC & E3 & 79 & 9C \\
3 & 64 & E5 & 90 & 06 & D5 & 3A & AE & B4 & DF & 71 & 6D & 16 & A9 & 6C & 25 & BA \\
4 & CF & 90 & 30 & D3 & EC & A5 & D6 & 0B & 05 & C1 & 6F & OE & TF & 04 & 91 & 62 \\
5 & B9 & E1 & 61 & C9 & DE & C6 & 43 & E2 & B8 & 52 & OB & 87 & 4E & 17 & EF & CC \\
6 & 60 & 2D & 3F & 78 & 2E & 24 & 45 & CB & D1 & C4 & FC & 1C & 22 & FE & 4D & 6B \\
7 & B6 & CE & 07 & 6A & 66 & 58 & F9 & CF & 70 & 76 & F5 & 98 & 74 & D0 & FD & 82 \\
8 & 3B & FB & B3 & 9A & EE & 75 & F2 & 77 & 76 & 34 & 63 & EF & 29 & 10 & 36 & 44 \\
9 & 4A & 89 & BC & D8 & 18 & 2F & DA & FA & 19 & AB & EB & TA & 13 & 72 & 50 & D2 \\ A & 9F & 4F & 96 & F3 & 7C & CA & 7D & C0 & 09 & D7 & B1 & C5 & 57 & 73 & 48 & 04 \\ B & A6 & 5A & 11 & A7 & 93 & 97 & 1A & 00 & 26 & OA & C7 & 69 & F0 & 30 & 39 & 8E \\ C & 00 & 20 & 2A & 49 & 9C & AC & E6 & 40 & 59 & 23 & 92 & A8 & 33 & 49 & 02 & F1 & AA \\ D & 15 & 8F & SF & IE & SO & 53 & 4B & 42 & F6 & TF & 28 & 01 & 9E & 54 & CD & AF \\ E & 5C & 2A & 55 & F7 & 8C & 28 & OC & E8 & B8 & 5D & 4C & E0 & 84 & 21 & FF & A1 \\ F & B7 & A2 & B2 & BF & F9 & DD & 54 & 83 & 1D & EA & C2 & 85 & 51 & AD & 46 & D9 \\ \hline \hline \end{tabular}
\begin{tabular}{c c c c c c c c c c c c c c} \hline \hline  & NL = 108 & & & & & & & & & & & & & & & & & \\ (Fp/OFp) = (1/0) & & & & & & & & & & & & & & & & & & & \\ \end{tabular}
\end{table} 
Table 7: Optimal S-box using Proposed Technique. respectively. Their S-box proposal is constructed in \(\mathbb{F}_{2^{9}}\) using Quadratic APN functions which are heuristically converted into an \(8\times 8\) S-box as the final result. There are also some authors that proposed several S-boxes such as [PERSON] et al. [80], [PERSON] et al. [43], [PERSON] et al. [70] and [PERSON] et al. in [12; 77; 93]. The S-box constructions proposed by [PERSON] et al. [80] are ranked third, fourth and fifth and classified as mathematical functions-generated methods, as multiplicative inverse, addition and multiplication are only used in the algorithm. Ranked third and fifth are the S-boxes proposed by [PERSON] et al. [70] that use the reversed genetic algorithm on the initial S-box that was generated beforehand using multiplicative inverse. Thus, we classify this algorithm as a combination method that lies between the mathematical function approach and heuristic approach.