## 4 Results and Analysis
### Evaluation of Hybrid Encryption Algorithm Strength
#### 4.1.5 Linear Cryptanalysis  
Linear cryptanalysis is a critical technique for evaluating the strength of encryption algorithms. It systematically identifies potential linear relationships between plaintext, ciphertext, and the key. This method assumes that by refining the algorithm design, the security can be enhanced, making it more resistant to attacks aimed at decrypting the encrypted data [57]. By guaranteeing that the relationship between plaintext, ciphertext, and key is complicated and non-linear, this technique is a measure of how well an algorithm gives confusion and diffusion features [58]. In this experiment, the linear cryptanalysis was performed through the study of bit correlation and distribution of correlation coefficients, which were visualized through various plots so that a clear analytical conclusion could be drawn. The correlation coefficients of bit pairs have been plotted on a scatter plot in Figure 13, providing linear relationships that exist between the bits of the encrypted messages. Most of the points in the scatter plot presented in Figure 13 coalesce around a coefficient of correlation close to zero, showing that most bit pairs lacked significant linear relationships. This dense clustering in the middle is, in fact, a positive sign of the encryption algorithm producing bit sequences close to random, giving no predictable relationship to work with. An encryption system would ideally pass with a minimum degree of correlation, as any form of predictability could present an exposure of the key or plaintext. However, scatter  
Figure 12: Density plot of plaintext and respective ciphertext differences in byte value, highlighting the range of diffusion among them. plots extend the correlation coefficients, ranging from approximately \(-0.8\) to \(0.8\). The scatter plot shows that although most bit pairings appear uncorrelated, some pairs exhibit positive or negative correlation. In the plots, a few of the clusters plotted are positive, with correlation coefficients greater than \(0.4\). These clusters indicate certain linear relationships within particular bit pairs. Changes in one bit are predictably mirrored by changes in the other. Positive correlations here might indicate a structural weakness in the encryption algorithm, which may arise from low diffusion or linear transformations that do not adequately obscure plaintext relationships. Similar clusters of datasets have also shown very strong correlations below \(-0.4\). In these cases, the alteration in one bit would be expected to bring about an alteration in the opposite direction in the other bit. Negative correlations are just as significant as positive correlations, given that they will put together a systematic relationship. It could be true for linear cryptanalysis purposes. The presence of both positive and negative correlations suggests that the encryption algorithm may have deterministic behaviors that linear cryptanalysis techniques could leverage [59]. The presence of linear approximation in the algorithm could also be observed through the distribution of correlation coefficients between the bit pairs, as shown in Figure 14.  
The histogram in Figure 14 is centered around a correlation coefficient of zero, indicating minimal correlation among most bit pairs. This reflects the encryption algorithm's randomness, a key trait for security. Correlation coefficients range from \(-0.8\) to \(0.8\), with most values between \(-0.2\) and \(0.2\). A value close to zero implies that there are no significant linear correlations that would not support linear cryptanalysis. The density falls off smoothly away from zero. However, a couple of outliers are worth considering for possible enhancement.