## 1 Introduction  
The importance of data security has become increasingly prominent in the modern information society. With the widespread adoption of artificial intelligence technologies and big data applications, the dependence on data analysis across various industries has significantly increased [1, 2]. However, this trend is accompanied by potential risks of data privacy breaches. Once sensitive data in fields such as healthcare, finance, and education are exposed, irreversible social and economic consequences may ensue [3, 4, 5]. Therefore, ensuring the effective use of processing data while ensuring privacy protection has become a focal issue in both academia and industry during data-driven decision-making processes. Traditional privacy-preserving techniques primarily include methods such as differential privacy (DP), homomorphic encryption (HE), and federated learning (FL). Thesetechniques each have advantages in data protection. For example, DP mitigates the risk of data leakage by adding random noise to obscure individual information [6]; HE allows data to be processed in an encrypted state, ensuring privacy during computation [7]; and FL avoids direct centralization of data by employing distributed training [8]. However, these methods still present significant limitations in practical applications. HE has a high computational complexity, making it difficult to meet real-time requirements. Although FL avoids data sharing, challenges such as communication overhead and inconsistencies among participating parties persist. Furthermore, these methods generally focus on data encryption or noise addition and lack dedicated designs for abstracting data features and efficiently utilizing nonsensitive information, which may hinder achieving optimal results in certain scenarios. Existing privacy-preserving methods mainly concentrate on data concealment and security, with relatively less exploration on how to balance privacy and utility [9; 10; 11]. Although DP is widely used, the design of noise mechanisms often fails to meet the specific needs of different scenarios; [PERSON] et al. [12] proposed a method to address these challenges and enhance privacy protection by applying DP with stochastic gradient descent to train surrogate models that protect original data. A differential evolution operator was used to generate personalized new samples for multiple clients based on promising auxiliary samples, preventing the exposure of newly generated data. Additionally, a similarity-based aggregation algorithm was integrated to effectively build a global surrogate model. Experimental results showed that their method demonstrated significant optimization performance on a set of synthetic problems in a joint setup while maintaining data privacy. Methods like HE and secure multi-party computation, while enhancing privacy protection, face issues related to high computational cost and system complexity. [PERSON] et al. [13] proposed a blockchain-based transaction privacy protection method using lightweight HE, focusing on securing transaction data and safeguarding user privacy while enhancing transaction efficiency. The experimental results demonstrated that the method achieved strong privacy and security protection. The data leakage probability was as low as 2.8%, successfully preventing replay attacks and forged transaction attacks. [PERSON] et al. [14] sought to protect gradients in FL systems while maintaining practical performance by analyzing the impact of security parameters, such as polynomial modulus and coefficient modulus, on homomorphic operations. Based on the evaluation results, they provided a method for selecting the optimal multiplication depth while satisfying operational requirements. An adaptive segmented encryption method tailored for CKKS was introduced to circumvent its encryption length limitations, enhancing the processing capabilities of encrypted neural network models.