## 1 Introduction  
The edge-fog-cloud (three-tier) computing environment is a distributed computing architecture that combines the capabilities of cloud computing, fog computing, and edge computing to provide a comprehensive and flexible framework for processing, storing, and managing data and services. This environment takes advantage of the strengths of each computing paradigm to address a wide range of applications. Cloud computing provides a scalable infrastructure for storing and processing data and running applications. Cloud resources offer extensive computational power and storage capacity, making them suitable for tasks requiring significant resources and complex data analysis [1]. Fog computing extends the cloud capabilities to the network edge, closer to the data source and end-users. Fog nodes, which include routers, switches, and gateways, process and filter data locally, reducing latency and supporting real-time applications. Fog computing is beneficial for scenarios where low-latency interactions and immediate responses are critical [2]. Edge computing brings computation closer to the data source, often directly on the devices themselves. This minimizes the need for data transmission to distant data centers, reducing latency and bandwidth usage. Edge computing is ideal for applications demanding rapid data processing and quick decision making, such as autonomous vehicles and robotics [3]. Security in an edge-fog-cloud computing environment refers to the set of measures, practices, and technologies to protect data, resources, applications, and communication within the context of these distributed computing paradigms. One of the key aspects of security in an edge-fog-cloud computing environment is authentication, establishing robust authentication processes to confirm entities' identity and determine their access rights based on authorization policies [4]. User authentication involves verifying an identity asserted by or on behalf of a system entity [5; 6]. In the edge-fog-cloud environment, authentication is critical in ensuring secure communication, protecting sensitive data, and mitigating the risks associated with unauthorized access or malicious activities [7]. This environment encompasses a wide range of entities, including cloud servers, fog nodes, edge devices, and users, each with unique characteristics and requirements. The distributed nature of the edge-fog-cloud environment poses challenges to authentication. Due to the mobility of edge users and the low-latency requirements, authentication protocols must be fast to adhere to this requirement. The convergence of fog, cloud, and edge computing significantly benefits data processing, storage, and decision making. However, a robust and high-speed communication infrastructure is required for this convergence to be effective. The 5G network, with its ultra-fast data transfer rates, low latency, and high capacity, provides the necessary capabilities to meet the demanding communication requirements of fog, cloud, and edge computing environments [8]. One of the key advantages of 5G network connectivity is its ability to support massive machine-type communications (mMTC) and ultra-reliable and low-latency communications (URLLC). mMTC enables the efficient handling of a large number of IoT devices, sensors, and actuators, which is a main characteristic of edge and fog computing environments [9]. These devices can generate vast amounts of data to be transmitted and processed in real time. Furthermore, the 5G network's mMTC capabilities ensure reliable and efficient communication between these devices and fog/cloud resources. Fog computing brings security and authentication challenges that must be carefully addressed [10]. Security and authentication challenges in fog computing arise due to the distributed and heterogeneous nature of the environment, where a variety of devices, communication protocols, and data processing locations are involved.