## 7 Experimental Results and Analysis
### Safety Discussion  
#### 7.3.1 Information Entropy Experiment  
Information entropy is a mathematical concept used to measure the degree of information chaos. In information theory, information entropy measures uncertainty, the expected value of the information available for all possibilities. If a random variable has more possible values, its entropy will be more significant, and vice versa. The more orderly a system is, the lower the information entropy; conversely, the more chaotic a system is, the higher the information entropy. Therefore, information entropy can be used to measure the degree of orderliness of a system. In cryptography, information entropy can be used to assess the strength and security of a password. The strength of a password depends on its information entropy, i.e., the randomness and unpredictability of the password. If a password's information entropy is high, it will be tough to crack that password, as the cracker will need to traverse all possible combinations of passwords to find the correct one. Security in cryptography depends on the information entropy of a password, which, in turn, depends on the randomness and unpredictability of the password. The higher the information entropy of a password, the more secure it is, and the more difficult it is to break through guessing or cracking methods. Calculating the information entropy of a ciphertext effectively reflects the degree of confusion of the ciphertext; the higher the degree of confusion, the better the encryption effect. The formula to calculate information  
Figure 16: Results of “avalanche effect” test with different encryption factors.  
entropy is shown above, where \(p(x)\) represents the probability of event \(X\) occurring and \(log_{2}10\) is the logarithm with a base of 2.  
\[H(X)=-\sum p(x)\log_{2}p(x) \tag{5}\]  
Using the likelihood of each character, we calculated the information entropy for the present chunked chaotic exchange algorithm, as well as the DES, AES, and RC4 algorithms.  
In addition, we conducted experiments to change one bit of plaintext and tested the information entropy of the resulting ciphertext. The experimental results show that the average information entropy of the present chunking disorder algorithm remains primarily in the range of 4.5-4.9, which is essentially higher than the average information entropy of the DES algorithm and is closer to that of the AES and RC4 algorithms. These results indicate that the present chunking disorder algorithm has better encryption effectiveness, more confusion in the ciphertext, and more robust security. Figure 18 illustrates change in the average information entropy of a ciphertext under one plaintext.  
By changing one bit of the key, we can test the information entropy of the plaintext. Due to the random nature of the chunked jumbled algorithm-sharing code generation, we can perform relevant tests by varying the key length.  
The experimental results demonstrate that the average information entropy of the present chunking disorder algorithm remains primarily in the range of 4.5-4.9, which is better than that of the DES algorithm and, to some extent, closer to that of the AES and RC4 algorithms. These results indicate that the present chunking disorder algorithm has better encryption effectiveness, more confusion in the ciphertext, and more robust security. Figure 19 illustrates change in the average information entropy of the ciphertext under one key.  
Figure 17: “Avalanche effect” compared to AES and RC4 algorithm regarding the secret key test results.