Fog computing is a new paradigm that extends cloud computing and services to the edge of the network. Although it has several distinct characteristics, however, the conventional fog computing model does not support some of the imperative features such as D2D communications, which can be useful for several critical IoT applications and services. Besides, fog computing faces numerous new security and privacy challenges apart from those inherited from cloud computing, however, security issues in fog computing have not been addressed properly. In this article, first we introduce a new privacy-preserving security architecture for fog computing model with the cooperative D2D communication support, which can be useful for various IoT applications. Subsequently, based on the underlying foundation of our proposed security architecture we design three lightweight anonymous authentication protocols (LAAPs) to support three distinct circumstances in D2D-Aided fog computing. In this regard, we utilize the lightweight cryptographic primitives like one-way function and EXCLUSIVE-OR operations, which will cause limited computational overhead for the resource limited edge devices
