In this work, we present a secure authentication protocol for edge computing using the Software-Defined Networking platform and wireless network virtualization. The main contribution of the presented protocol lies in: (1) designing and implementing a practical solution to the security problem of rogue Fog nodes, and (2) providing the cloud service provider with exclusive control over the security configuration and specification of its leased virtual networks independent of the security mechanisms implemented by the underlying infrastructure provider. The cloud provider dynamically enforces its security policies on the communication at the network edge, therefore circumventing any possible security vulnerabilities in the underlying physical wireless infrastructure. The authentication protocol manages the trusted communication among the mobile client, the infrastructure provider, and the cloud service provider, yet confines the Public-Key Infrastructure (PKI) deployment to solely the infrastructure and cloud providers. This enhances the scalability of the system and reduces the complexity of its security management and configuration. A system testbed is simulated using the Mininet emulator and the Amazon EC2 Cloud.