Enhancing Cloud Security through Efficient Polynomial Approximations for Homomorphic Evaluation of Neural Network Activation Functions

Current security cloud practices can successfully protect stored data and data in transit, but they do not keep the same protection during data processing. The data value extraction requires decryption, creating critical exposure points. As a result, privacy-preserving techniques are emerging as a crucial consideration in cloud computing. The homomorphic processing of machine learning models in the cloud represents a central challenge. The activation function is fundamental in constructing a privacy-preserving Neural Network (NN) with Homomorphic Encryption (HE). Standard activation functions require operations not supported by HE, so it is necessary to find cryptographically compatible replacement functions to operate over encrypted data. Multiple approaches address the limitation of function compatibility with polynomial approximation. These functions should exhibit a trade-off between complexity and accuracy, limiting the efficiency of conventional approximation techniques. The current literature on polynomial approximation of NN activation functions still lacks a thorough review. In this paper, we comprehensively review the standard activation functions of modern NN models and current polynomial approximation approaches. We highlight fundamental features to consider in the activation function and the approximation technique to operate over encrypted data.