## 4 Results and Analysis
### Evaluation of Hybrid Encryption Algorithm Strength
#### 4.1.2 Pattern Analysis of Encryption Algorithm  
Pattern analysis of byte occurrences in assessing the strength of encryption provides an indication of how uniformly or evenly the distribution of 0s and 1s appears, describing levels of randomness [50]. The analysis of patterns in cryptography evaluates the frequency and occurrence of byte values or bit sequences within the encoded data. It checks for possible correlations and dependencies between bits to ensure that there are no predictable patterns [51]. An ideal encryption algorithm should yield ciphertext without perceivable \begin{table}
\begin{tabular}{c c} \hline \hline
**Description** & **Value** \\ \hline Count (No. of Messages) & 31 \\ Mean & 0.989152 \\ Standard Deviation & 0.001774 \\ Minimum Entropy & 0.985688 \\
25 th Percentile & 0.987888 \\ Median & 0.989167 \\
75 th Percentile & 0.989937 \\ Maximum Entropy & 0.991961 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Summary of statistics of entropy values. Figure 7: Entropy values of 31 different encrypted message. differences. It should make both a single bit and a complete byte equally probable to be true or false, irrespective of the plaintext. For instance, an output \"10101010100\" reveals a definite weakness due to the alternating pattern of 1s and 0s. In contrast, \"1101010001\" appears random and patternless, indicating a secure encryption. The analysis confirms that a change in one bit does not affect any other bits, maintaining independence between them [51]. Moreover, it identifies vulnerabilities for the cryptographic attacks, catching malignant patterns that expose the weak links or faults in the algorithm. In addition, it evaluates the quality of the PRNGs carried out in the encryption process [51]. The heatmap in Figure 8 renders the pattern of occurrences of bytes at the varied position across a blend of 31 encrypted messages. It provides valuable insight into the behavior and characteristics of the cipher algorithm used. The axes and color gradations on the heatmap reveal patterns of how the algorithm addresses and deals with longer and shorter messages, giving clues about the underlying work of the cryptographic facilities. The most important feature of the heatmap is the emergence of regions of high-frequency byte clusters, highlighted in red. The clusters are mostly prominent in the ranges of byte positions 48 to 64 and 96 to 128. Active, medium-length messages indicate activity in those areas, thereby affirming that those positions play a crucial role in the encryption process. Moreover, the presence of these clusters across all message lengths shows that there might be some periodic or structural elements in the encryption algorithm affecting these positions, probably in relation to the rounds in the encryption process or in particular stages that induce higher levels of data transformations [52]. On the other hand, only the longest messages use byte positions after 200, thereby showing low-frequency occurrences represented by the blue regions. This indicates that those positions are less frequently used, with shorter messages seldom reaching these byte ranges. The low-frequency distribution also suggests that even in longer messages, these positions might be used sparingly or in a more randomized manner, reflecting the padding or additional data added to complete encryption blocks [53]. Additionally, the visible patterns and high-frequency clusters, as shown in Figure 8, suggest some level of predictability in how the encryption algorithm processes data. This means certain keys having similar characteristics are preferred for several generations, which creates predictable patterns. These predictable patterns can also arise through fixed initialization  
Figure 8: Pattern of byte occurrences of encrypted messages at the varied byte position across a blend of 31 encrypted messages of different lengths. vectors, repetitive key scheduling, or inherent deterministic features in the algorithm.