The rising demand for cloud-based machine learning services has intensified concerns about data privacy, particularly in sensitive fields like healthcare and finance. Homomorphic Encryption (HE) enables computations on encrypted data, offering a promising solution for Privacy-Preserving Machine Learning (PPML). However, the non-linear nature of activation functions, such as Sigmoid and Tanh, presents challenges for efficient encrypted inference in Artificial Neural Networks (ANNs). This paper proposes an innovative approach that utilizes ANN-based estimators to approximate these activation functions, balancing accuracy and computational efficiency. Our estimators are trained on plaintext data and deployed during encrypted inference, achieving competitive performance compared to traditional polynomial and piecewise linear approximations. Experimental results demonstrate that the proposed ANN estimators provide superior accuracy and Mean Squared Error (MSE) while maintaining feasible computation times. This approach advances the practicality of secure, efficient machine learning on encrypted data, paving the way for broader adoption of PPML solutions in cloud environments.

This paper presents a novel approach to estimating Sigmoid and Tanh activation functions using Artificial Neural Networks (ANN) optimized for homomorphic encryption. The proposed method is compared against second-degree polynomial and Piecewise Linear approximations, demonstrating a minor loss in accuracy while maintaining computational efficiency. Our results suggest that the ANN-based estimator is a viable alternative for secure machine learning models requiring privacypreserving computation.