An Efficient and Privacy-Preserving Evaluation for Kernel Functions

Kernel function,which serve as a common mathematical tool in machine learning for addressing nonlinear problems, employed in algorithms such as Support Vector Machines (SVM) and Principal Component Analysis (PCA) to map sample inputs from a lower-dimensional space to a higherdimensional feature space, thus transforming originally linearly inseparable problems into linearly separable ones. Various types of kernel functions exist, including linear, polynomial, and Gaussian radial basis kernels, each with distinct expressions K(x, t) designed to quantify the similarity between different sample vectors $\mathbf{x}$ and $\mathbf{t}$. However, since these sample vectors may belong to sensitive data from different entities, direct computation in plaintext may lead to privacy leakage. In this paper, we propose a general secure kernel function computation scheme based on two non-colluding servers model. Specifically, we design secure twoparty computation protocols for linear, polynomial, and Gaussian kernel functions by data slicing and homomorphic encryption methods. Furthermore, we also provide practical implementations, which allow both parties to compute kernel function offline. Finally, experiments demonstrate that the proposed scheme effectively protects privacy during kernel function calculations while offering advantages of lower computational complexity and user-friendliness for data owners.