## 2 Related Works
### Data Obfuscation-Based Security Methods  
Compared to encryption techniques, data obfuscation methods focus on directly perturbing the data itself to achieve privacy protection. DP [38] is one of the most representative methods in this category. The basic principle of DP is to introduce random noise into data queries or statistical results, making it impossible for an attacker to infer specific information about an individual data point [39; 40; 41]. Mathematically, DP is defined as follows: for any two adjacent datasets \(D\) and \(D^{\prime}\), if an algorithm \(\mathcal{A}\) satisfies  
\[P[\mathcal{A}(D)\in S]\leq e^{\epsilon}P[\mathcal{A}(D^{\prime})\in S] \tag{3}\]  
where \(S\) is any subset of the output space and \(\epsilon\) is the privacy budget, \(\mathcal{A}\) is said to satisfy \(\epsilon\)-differential privacy. A smaller \(\epsilon\) means better privacy protection, but it also results in a larger amount of noise being introduced, which can affect the data's usability. Specifically, the Laplace mechanism is commonly used to add noise \(\eta\) to the query results \(f(D)\) to achieve differential privacy, where the noise \(\eta\) follows the distribution  
\[\eta\sim\text{Lap}\left(0,\frac{\Delta f}{\epsilon}\right) \tag{4}\]  
where \(\Delta f\) is the global sensitivity of the function \(f\), which measures the maximum impact of a single data point's change on the output. While this method performs well in privacy protection, the introduction of random noise can severely affect the accuracy of the data. For instance, in financial prediction tasks, random perturbation of key features may obscure important market trends, leading to reduced prediction accuracy. FL [42] is a distributed machine learning method that focuses on local data processing. Models are trained locally at each participant, and their gradient information is aggregated to protect privacy. The training process can be represented as  
\[\theta_{t}^{k+1}=\theta_{t}^{k}-\eta\
abla L(\theta_{t}^{k};D_{k}) \tag{5}\]  
where \(\theta_{t}^{k}\) represents the model parameters at the \(k\)-th node at round \(t\), \(\eta\) is the learning rate, \(L\) is the loss function, and \(D_{k}\) is the dataset of the \(k\)-th node. The advantage of FL is that data do not need to be centralized, which reduces the risk of data leakage. However, in complex data scenarios (such as multi-modal data or highly non-independent and identically distributed data), the performance of FL may be limited by the effectiveness of model aggregation, and communication overhead remains a major bottleneck in real-world deployments.  
The limitations of the aforementioned methods are addressed by the proposed data obfuscation strategy, which combines probability density and information entropy for targeted data protection. In traditional methods, while FHE offers high security, its computational overhead makes it unsuitable for real-time scenarios. DP, although superior in performance, significantly impacts data usability. Federated learning shows distinct advantages in distributed scenarios but still faces technical challenges in model aggregation and complex environments. By combining feature extraction based on probability density with dynamic control through information entropy, the proposed approach achieves a significant improvement in both data security and task performance. This new solution offers an innovative way to protect sensitive data in healthcare, finance, and other domains where privacy is critical.