Paper 2023/1544 Original: eprint.iacr.org/2023/1544 ↗

Arithmetic PCA for Encrypted Data

Abstract

Reducing the size of large dimensional data is a critical task in machine learning (ML) that often involves using principal component analysis (PCA). In privacy-preserving ML, data confidentiality is of utmost importance, and reducing data size is a crucial way to cut overall costs. This work focuses on minimizing the number of normalization processes in the PCA algorithm, which is a costly procedure in encrypted PCA. By modifying Krasulina's algorithm, non-polynomial operations were eliminated, except for a single delayed normalization at the end. Our PCA algorithm demonstrated similar performance to conventional PCA algorithms in face recognition applications. We also implemented it using the CKKS (Cheon-Kim-Kim-Song) homomorphic encryption scheme and obtained the first 6 principal components of a 128$\times$128 real matrix in 7.85 minutes using 8 threads.