t-BMPNet: Trainable Bitwise Multilayer Perceptron Neural Network over Fully Homomorphic Encryption Scheme

Homomorphic encryption (HE) is notable for enabling computation on encrypted data as well as guaranteeing high-level security based on the hardness of the lattice problem. In this sense, the advantage of HE has facilitated research that can perform data analysis in an encrypted state as a purpose of achieving security and privacy for both clients and the cloud. However, much of the literature is centered around building a network that only provides an encrypted prediction result rather than constructing a system that can learn from the encrypted data to provide more accurate answers for the clients. Moreover, their research uses simple polynomial approximations to design an activation function causing a possibly significant error in prediction results. Conversely, our approach is more fundamental; we present t-BMPNet which is a neural network over fully homomorphic encryption scheme that is built upon primitive gates and fundamental bitwise homomorphic operations. Thus, our model can tackle the nonlinearity problem of approximating the activation function in a more sophisticated way. Moreover, we show that our t-BMPNet can perform training—backpropagation and feedforward algorithms—in the encrypted domain, unlike other literature. Last, we apply our approach to a small dataset to demonstrate the feasibility of our model.