## 4 Results and Analysis
### Evaluation of Hybrid Encryption Algorithm Strength
#### 4.1.4 Differential Cryptanalysis  
Differential cryptanalysis is a method for assessing the strength and security of cryptographic algorithms by analyzing the effect of plaintext differences on the corresponding ciphertext output differences [57]. The technique aims to identify patterns or correlations with byte differences that may exist within the entire encryption operation. These patterns could potentially reveal the internal workings of the cipher or even the secret key itself. The difference value in the plaintexts was compared to the difference value in the ciphertexts for the differential analysis, as shown in Figure 11.  
Figure 10: Byte distribution in plaintext (**left**) and ciphertext (**right**) for 31 different messages where byte distribution in ciphertext shows an avalanche effect. The histogram illustration on the left of Figure 11 depicts the frequency distribution of differences within the plaintext value range of 0 to 80. Important observations include a noticeable peak at the 0 mark. This indicates that several plaintext pairs are either identical or have no difference at all. Byte differences near values 20 and 30 also appear frequently. There is a deep dip in the frequency distribution within the range of byte value differences from 40 to 60. Once again, there are few or almost no occurrences within this range. Another slight clustering of differences appears around the 60-80 range. The peak at 0 suggests that a significant number of plaintext pairs are identical, which may imply a high occurrence of repetitive data. Furthermore, clusters around 20 and 30 indicate regions where certain differences are more prevalent, possibly revealing weaknesses or patterns in the plaintext structure. This histogram implies that certain types of differences between plaintext pairs are more common than others. The histogram on the right of Figure 11 displays the frequency distribution of the corresponding ciphertext byte values' differences across a much wider range from 0 to 250. Among the various observations, one can note that there is a pronounced peak at 0, showing that while plaintexts may be different, some pairs of ciphertexts remained identical. The distribution appears to be much more dispersed than that of the plaintext difference, showing several peaks along the range. The observed byte difference value frequently appears at intervals of around 50, 100, 150, and 250. The wider and varied distribution indicates a higher level of diffusion in the ciphertext for plaintext differences in byte values. More evidence can further be substantiated through the analysis by creating a density plot of the byte values' difference for plaintext and ciphertext, as demonstrated in Figure 12.  
The density plot presented in Figure 12 indicates that it achieves a peak near a zero difference score. It suggests that many plaintext pairs differ slightly or not at all from one another. Similar pairs are either almost identical or differ slightly, as indicated by the peak close to zero. This may be the result of repeated data or particular test circumstances. There is a smaller peak at a difference value of 20, indicating that there is another prevalent difference amongst the pairs of plaintext. The secondary peak around the difference value of 20 indicates another prevailing difference, which may be due to a certain structural or patterned nature in plaintext. The distribution of plaintext differences is relatively narrow, mainly concentrated between \(-20\) and \(100\), with very few instances toward longer differences. Such observations suggest that, in general, differences among plaintext pairs  
Figure 11: Histogram of the difference value of plaintext (**left**) and the respective ciphertext (**right**) for 31 different messages; varied distribution indicates a higher level of diffusion in the ciphertext. are minor and occur around particular values, letting certain patterns or characteristics emerge from the plaintext data.