Principal Component Analysis over the Boolean Circuit Within TFHE Scheme

In today’s information-driven world, the need to protect personal data while maintaining efficient data processing capabilities is crucial. Homomorphic Encryption (HE) has emerged as a potential solution, allowing secure processing of encrypted information without compromising privacy. However, current HE schemes suffer from slow processing speeds, especially when dealing with high-dimensional data. This paper focuses on leveraging the PCA technique within the Fast Fully Homomorphic Encryption over the Torus (TFHE) scheme to optimize the speed of subsequent algorithms. TFHE offers the advantage of enabling the homomorphic implementation of any circuit but suffers from extensive execution time. We present tailored PCA algorithms for TFHE, utilizing the power method and eigen-shift techniques to extract eigenvalues and eigenvectors. These techniques provide efficient solutions for performing PCA computations within the TFHE framework. By designing a dedicated PCA circuit using TFHE’s fundamental homomorphic gates, we achieve efficient evaluation times for PCA. The performance analysis shows execution times of 3.42 h for a 16-bit dataset and 12.22 h for a 32-bit dataset, with potential for further improvement.