Evaluation of Homomorphic Encryption for Privacy in Principal Component Analysis

Principal Component Analysis (PCA) is a versatile Unsupervised Learning (UL) technique for reducing the dimensionality of datasets. As a result, PCA is widely used in consumer and research applications as a preprocessing tool for identifying important features prior to further analysis. In instances where on-site personnel or developers do not have the expertise to apply UL techniques, third party processors are frequently retained. However, the release of client or proprietary data poses a substantial security risk. This risk increases the regulatory and contractual burden on analysts when interacting with sensitive or classified information. Homomorphic Encryption (HE) cryptosystems are a novel family of encryption algorithms that permit approximate addition and multiplication on encrypted data. When applied to UL models, such as PCA, experts may apply their expertise while maintaining data privacy. In order to evaluate the potential application of Homomorphic Encryption, we implemented Principal Component Analysis using the Microsoft SEAL HE libraries. The resulting implementation was applied to the MNIST Handwritten dataset for feature reduction and image reconstruction. Based on our results, HE considerably increased the time required to process the dataset. However, the HE algorithm is still viable for non-real-time applications as it had an average pixel error of near-zero for all image reconstructions.