## 3 The S-Box Generation Algorithm Design and Performance Analysis
### Performance Analysis Results of Proposed S-Boxes  
In order to be able to use the generated S-boxes in the encryption process, performance tests are required. S-box structures with strong cryptographic properties play a major role in encryption. By using the developed S-box generation algorithm, three different S-boxes have been proposed to be used in image encryption processes and the performance tests of these S-boxes have been carried  
Performance tests have been applied to show the cryptographic performance values of the produced S-boxes. Nonlinearity [21] is one of the most important features in the S-box value evaluation criteria. The min. and max. nonlinearity values of produced S-boxes are found as follows: min. value of 104, max. value of 110 for S-box1; min. value of 104, max. value of 108 for S-box2; min. value of 106, max. value of 108 for S-box3. The min., avg. and max. nonlinearity values of the S-boxes suggested in Table 4 are given. It shows the best values after the Advanced Encryption Standard (AES) algorithm application for the max., min. and avg. nonlinearity values of proposed S-box1, 2 and 3 respectively. The strict avalanche criterion (SAC) is a another important performance measure method that calculates the probability of change in output bits based on the change in input bits. This method was developed by [PERSON] and [PERSON] [22]. The optimum value for the calculated coefficient is 0.5. This method calculates the probability of a change in half of the output bits when a single change occurs from the input bits. Table 4 shows that the SAC values of the proposed S-boxes are very close to the ideal value of 0.5. The bit independence criteria (BIC) is a performance criterion recommended by [PERSON] and [PERSON] [22] and is evaluated in two different ways. In these tests, it is tested whether the vector set generated with the plaintext inverse bit is independent of all the avalanche variable sets. BIC-SAC and BIC-nonlinearity values of S-boxes are calculated in BIC performance evaluation. BIC-SAC and BIC-nonlinearity values of the S-boxes suggested in Table 4 are shown. Suggested S-boxes have been found to have good values. Differential approximation probability (DP) [23] is a differential cryptanalysis evaluation criterion that examines the the exclusive or XOR distribution balance between the input and output bits of an S-box. Each output XOR value must have equal probability when compared to input values. The close XOR distribution between the input and output bits and the low DP value suggests that the S-box is more resistant to differential cryptanalysis. As shown in Table 4, the AES S-box has the lowest DP value. Compared to all the S-boxes given in Table 4, it is seen that the proposed S-boxes have the lowest DP values. As a result, as shown in Table 4, the proposed S-boxes have good nonlinearity and DP values after AES S-box construction compared to the S-boxes presented in the literature. SAC, BIC-SAC and BIC-nonlinearity values of proposed S-boxes were found to be close to optimum values. When examining the S-box studies in the literature, it is seen that the S-box produced by the AES algorithm has the best values. The studies in the literature are trying to realize S-box production with low load processing and high cryptographic properties by using different methods.  
\begin{table}
\begin{tabular}{r r r r r r r r r r r r r r r} \hline
37 & 61 & 12 & 130 & 208 & 4