Device authentication, encryption, and key distribution are of vital importance to any Internet-of-Things (IoT) systems, such as the new smart city infrastructures. This is due to the concern that attackers could easily exploit the lack of strong security in IoT devices to gain unauthorized access to the system or to hijack IoT devices to perform denial-of-service attacks on other networks. With the rise of fog and edge computing in IoT systems, increasing numbers of IoT devices have been equipped with computing capabilities to perform data analysis with deep learning technologies. Deep learning on edge devices can be deployed in numerous applications, such as local cardiac arrhythmia detection on a smart sensing patch, but it is rarely applied to device authentication and wireless communication encryption. In this paper, we propose a novel lightweight IoT device authentication, encryption, and key distribution approach using neural cryptosystems and binary latent space. The neural cryptosystems adopt three types of end-to-end encryption schemes: symmetric, public-key, and without keys. A series of experiments were conducted to test the performance and security strength of the proposed neural cryptosystems. The experimental results demonstrate the potential of this novel approach as a promising security and privacy solution for the next-generation of IoT systems.