Homomorphic Encryption (HE) allows for training and deployment of neural networks on encrypted data. Furthermore, HE allows for encryption of neural network model parameters such as weights. Thus, HE provides robustness against both black-box and white-box attacks. In the emerging cloud-based AI environments with edge computing nodes, HE enables privacy-preserving training and deployment of neural networks without leakage of classified or sensitive data. There are many practical technological issues that need to be resolved before HE can be used for realistic use-cases. Chief among them is the fact that HE doesn't work well with non-linear activation units such as ReLU used in most neural networks. Furthermore, HE encryption works by adding noise which is substantially amplified by successive multiplications performed in deep neural networks; this would render HE decryption impossible if it is not handled appropriately. Finally, HE encrypted deep neural networks cannot be directly deployed on edge computing nodes which have very limited computing and memory resources. We propose a novel neural network training and deployment architecture that addresses all these issues and provides a suitable technological solution for practical real-world use-cases.