Activate Me!: Designing Efficient Activation Functions for Privacy-Preserving Machine Learning with Fully Homomorphic Encryption

The growing adoption of machine learning in sensitive areas such as healthcare and defense introduces significant privacy and security challenges. These domains demand robust data protection, as models depend on large volumes of sensitive information for both training and inference. Fully Homomorphic Encryption (FHE) presents a compelling solution by enabling computations directly on encrypted data, maintaining confidentiality across the entire machine learning workflow. However, FHE inherently supports only linear operations, making it difficult to implement non-linear activation functions, essential components of modern neural networks. This work focuses on designing, implementing, and evaluating activation functions tailored for FHE-based machine learning. We investigate two commonly used functions: the Square function and Rectified Linear Unit (ReLU), using LeNet-5 and ResNet-20 architectures with the CKKS scheme from the OpenFHE library. For ReLU, we assess two methods: a conventional low-degree polynomial approximation and a novel scheme-switching technique that securely evaluates ReLU under FHE constraints. Our findings show that the Square function performs well in shallow networks like LeNet-5, achieving 99.4% accuracy with 128 seconds per image. In contrast, deeper models like ResNet-20 benefit more from ReLU. The polynomial approximation yields 83.8% accuracy with 1,145 seconds per image, while our scheme-switching method improves accuracy to 89.8%, albeit with a longer inference time of 1,697 seconds. These results underscore a critical trade-off in FHE-based ML: faster activation functions often reduce accuracy, whereas those preserving accuracy demand greater computational resources.