# Enhancing Visual Data Security: A Novel FSM-Based Image Encryption and Decryption Methodology
## 4 Results and Discussion
### Comparison of Results  
Table 5 presents a comparative analysis of the correlation coefficients for the encrypted Lenna image using various encryption methods. The correlation coefficients are measured across three orientations: horizontal, vertical, and diagonal. These coefficients, which range from \(-\)1 to 1, quantify the degree of linear relationship between pixel values in specified directions. Values close to 0 indicate a lack of linear correlation, reflecting effective encryption in disrupting the predictable patterns of the original image. The encryption methods are diverse, encompassing approaches based on finite state machines, elliptic curve cryptography (ECC), chaotic and hyperchaotic maps, generalized Arnold maps, spatiotemporal chaos processes, particle swarm optimization algorithms, and spatial bit-level permutations. The correlation coefficients for these methods exhibit a wide range of effectiveness in obscuring linear relationships within the encrypted image. The Finite State Machine-based proposed method shows coefficients close to zero (\(-\)0.0066, \(-\)0.0106, \(-\)0.0014), indicating a high degree of encryption effectiveness. In contrast, the spatiotemporal chaos process-based method shows a significantly high correlation coefficient in the diagonal orientation (0.4466), suggesting a lesser degree of effectiveness in disrupting patterns in this particular direction. The ECC-based method and the methods utilizing chaotic maps, hyper-chaos, and generalized Arnold maps generally demonstrate low correlation coefficients, implying effective encryption. However, the spatial bit-level permutation method exhibits a notably high negative correlation coefficient in the horizontal orientation (\(-\)0.0574) and a high positive coefficient in the diagonal orientation (0.0578), indicating varying degrees of pattern disruption. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Encrypt Lenna Image** & **Horizontal** & **Vertical** & **Diagonal** \\ \hline Finite State Machine based proposed method & \(-\)0.0066 & \(-\)0.0106 & \(-\)0.0014 \\ Elliptic curve cryptography-based method using & \(-\)0.0022 & \(-\)0.0123 & \(-\)0.0067 \\ primitive polynomial [41] & & & \\ Chaotic and hyperchaotic-based methods using & 0.0484 & 0.0119 & 0.0141 \\ enhanced S-box pixel permutator [42] & 0.0059 & 0.0105 & 0.0142 \\ Hyper-chaos-based method [43] & 0.0173 & \(-\)0.0027 & \(-\)0.0177 \\ Hyper-chaotic system with only one round diffusion & 0.0117 & \(-\)0.0369 & \(-\)0.0422 \\ process-based method [40] & 0.0143 & 0.0280 & 0.4466 \\ Spatiotemporal chaos process-based method [45] & 0.0053 & \(-\)0.0089 & 0.0126 \\ Particle swarm optimization algorithm and cellular & & & \\ automata-based method [46] & & & \\ Spatial bit-level permutation and high-dimension-based & & & \\ method [47] & \(-\)0.0574 & \(-\)0.0035 & 0.0578 \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Correlation coefficient comparison of the encrypted Lenna image. The proposed method employs a finite state machine architecture, which is not typically utilized in the context of image encryption. This approach allows for dynamic adjustment of encryption behaviors based on the state transitions, providing unique adaptability in the encryption process that can enhance security against attacks that exploit static characteristics of encryption algorithms. The proposed FSM-based method achieves a horizontal correlation coefficient of \(-0.0066\), which is significantly lower compared to methods such as the Chaotic and hyperchaotic-based method (0.0484) and the Spatiotemporal chaos process-based method (0.0143). This suggests that the FSM-based method is particularly effective in disrupting horizontal pixel patterns and enhancing security against horizontal analysis techniques. The FSM method's diagonal correlation coefficient of \(-0.0014\) is notably lower than many other methods, such as the Hyper-chaos-based method (0.0142), the Particle swarm optimization algorithm, and the cellular automata-based method (0.0126).