## 4 Experiments and Analysis of Results
### Security
#### 4.4.3 Uncertainty  
To prevent attackers from retrieving accurate information from the marked encrypted image, it is imperative that the digital attributes of the image align closely with those of a randomly generated noise image. This has been empirically examined from three distinct perspectives: pixel distribution, correlation, and information entropy. We embed randomly generated identifying information and secret data into the Man image using our algorithm based on a \((3,3)\) threshold. Figure 11 demonstrates the pixel distribution in the correlation image, indicating that the pixel values are uniformly distributed in both the encrypted image and the marked encrypted images. \begin{table}
\begin{tabular}{c c c} \hline
**Other Existing Distributed Locks** & **Disadvantages** & **Redisson Distributed Lock Advantages** \\ \hline ZooKeeper distributed lock [33] & Relies on external storage media, increasing system development costs & Built-in complete persistence support \\ Memcached distributed lock [34] & Slower response speed & Fast response speed and low latency \\ Hazelcast distributed lock [35] & Lacks flexibility & Suitable for a wider range of \\ Apache Curator distributed lock [36] & Complex deployment & Simele and easy to use \\ Etcd distributed lock [37] & Lacks fault tolerance & High fault tolerance, supports \\ \hline \end{tabular}
\end{table} 
Table 8: Comparison results between Redisson distributed lock and other distributed locks. \begin{table}
\begin{tabular}{c c c} \hline
**Timestamps** & **Behavior of Thread B after Attempting to Lock** & **Remaining Time for the Lock to Expire** \\ \hline t = 5.00 s & Failed locking attempt, message subscription for listening & 25.04 s \\ t = 10.00 s & Listening & 29.97 s \\ t = 15.00 s & Listening & 24.98 s \\ t = 25.00 s & Listening & 25.04 s \\ t = 30.00 s & Listening & 19.94 s \\ t = 50.00 s & Successful locking, system occupation & 30.00s \\ t = 55.00 s & Occupying the system & 25.83 s \\ t = 65.00 s & Occupying the system & 26.00 s \\ \hline \end{tabular}
\end{table} 
Table 9: Results of concurrent user access under Redisson distributed lock. Next, we leverage the security of the pixel correlation analysis algorithm. We randomly select 26,000 pairs of adjacent pixels in the original image and the marked encrypted image with embedded secret data, analyzing the correlation coefficients in three directions: horizontal, vertical, and diagonal. The formula below represents the correlation coefficient \(r_{xy}\). \[ \begin{split}& r_{xy}=\frac{\text{cov}(x,y)}{\sqrt{D(x)}\sqrt{D(y)}} \\ & D(x)=\frac{1}{N-1}\sum\limits_{i=1}^{N}\left(x_{i}-E(x)\right)^{ 2}\\ & D(y)=\frac{1}{N-1}\sum\limits_{i=1}^{N}\left(y_{i}-E(y)\right)^{ 2}\\ &\text{cov}(x,y)=\frac{1}{N-1}\sum\limits_{i=1}^{N}\left(x_{i}-E(x )\right)(y_{i}-E(y))\\ & E(x)=\frac{1}{N}\sum\limits_{i=1}^{N}x_{i},E(y)=\frac{1}{N}\sum \limits_{i=1}^{N}y_{i}\end{split}  \tag{22}\]  
where \(x\) and \(y\) represent the values of the paired neighboring pixels in the test image. Table 10 presents the correlation coefficient test results for the Man image. These results reveal that the correlation coefficients of the original image demonstrate strong correlations in various directions, with an average value of 0.9540, nearing 1. In contrast, the correlation coefficients of the marked encrypted images approach 0 in different directions, indicating a significant reduction in correlation. Figure 12 displays the scatter plot of the correlation coefficients for both the original and the marked encrypted images. It is observed that most samples from the original image cluster around the line \(y=x\), indicating a strong correlation. Meanwhile, the scatter plots for the marked encrypted images show a uniform distribution, aligning with the mathematical statistical characteristics of random grayscale images.