Homomorphic encryption (HE) is pivotal for secure computation on encrypted data, crucial in privacy-preserving data analysis. However, efficiently processing high-dimensional data in HE, especially for machine learning and statistical (ML/STAT) algorithms, poses a challenge. In this paper, we present an effective acceleration method using the kernel method for HE schemes, enhancing time performance in ML/STAT algorithms within encrypted domains. This technique, independent of underlying HE mechanisms and complementing existing optimizations, notably reduces costly HE multiplications, offering near constant time complexity relative to data dimension. Aimed at accessibility, this method is tailored for data scientists and developers with limited cryptography background, facilitating advanced data analysis in secure environments.

翻译：同态加密（HE）对于加密数据的安全计算至关重要，在隐私保护数据分析中具有关键作用。然而，在HE中高效处理高维数据，尤其是针对机器学习与统计（ML/STAT）算法，仍面临挑战。本文提出一种利用核方法对HE方案进行有效加速的方法，以提升加密域内ML/STAT算法的时间性能。该技术独立于底层HE机制，并与现有优化方法互补，显著减少了昂贵的HE乘法运算，实现了相对于数据维度近乎恒定的时间复杂度。为提升可及性，本方法专为密码学背景有限的数据科学家和开发者设计，以促进安全环境下的高级数据分析。