## 4 Discussion
The third ranked S-box has the same nonlinearity as AES (i.e., NL = 112); however, the value for differential uniformity is slightly higher which is DU = 6. By the same S-box construction, [PERSON] et al. [70] also produced S-boxes that are ranked seventh, ninth and tenth in Table 8.  
We classify the S-box construction of [PERSON] et al. [43] as random generation. This is because the S-box is constructed by randomly swapping two elements in an initial function. This step is repeated until their desired criteria are achieved. Their best proposed S-box is ranked eleventh with cryptographic properties of (104, 8, 7, 24), while the other one is ranked thirteenth. Our proposed S-box construction is ranked sixth. The final S-box that we obtained exhibits cryptographic properties of (108, 4, 7, 20). The S-box also produces a complex algebraic expression of 255 terms. The best S-box by [PERSON] et al. [93] shares the same rank of sixth, while the other two proposed S-boxes are ranked eighth and ninth with cryptographic properties of (108, 6, 4, 20) and (106, 6, 7, 22) for (NL, DU, AD, LA), respectively. However, their S-box, which can be constructed using simple algebraic expression (i.e., only three terms involved), might be vulnerable to an interpolation attack [6]. There are other S-boxes proposed by [PERSON] et al. in [12; 77] using the combination method. Ranked seventh, [PERSON] et al. [77] used an algorithm called _Bee Waggle Dance_ on the multiplicative inverse function. This construction produced an S-box with cryptographic properties of (108, 6, 7, 20). Ranked tenth is the construction of [PERSON] et al. [12], who used an algorithm called the _Redundancy Removal Algorithm_ on the non-permutation power function that exhibits cryptographic properties of (104, 6, 7, 24). [PERSON] et al. [11] first introduced the original version of the _Redundancy Removal Algorithm_, which is ranked twelfth and has cryptographic properties of (102, 8, 7, 26). Empirically, our proposed construction, which is an inspired and enhanced version of the _Redundancy Removal Algorithm_, managed to obtain cryptographically strong S-boxes that compare well with and even outperform the originally proposed constructions [11; 12]. From our observation, all the S-boxes listed in Table 8 are designed and constructed either through mathematical functions or through combination methods between mathematical functions and heuristic methods. So far, the best S-box that we found using random generation is the S-box proposed by [PERSON] et al. [43], which is ranked eleventh. Nevertheless, this S-box exhibits DU = 8; thus, it fails to fulfill our cryptographically strong criteria. In fact, the S-boxes ranked from eleventh to sixteenth all fail to fulfill our prerequisite requirement for cryptographically strong S-boxes. The S-boxes are included in Table 8 for a comparative analysis. The research results that are included in the comparative analysis are obtained by applying the security measurement using a mini-workstation with properties of Intel (R) Core (TM) i7-6600U CPU @ 2.60 GHz, 16 GB of RAM, 64-bit Operating System and pre-installed with MATLAB R2022a. All simulations were performed in MATLAB programming language, and no external embedded devices were involved. Since MATLAB is a high-level programming language, we did not conduct a computational complexity analysis of our S-box construction.