The exponentially increasing number of ubiquitous wireless devices connected to the Internet in Internet of Things (IoT) networks highlights the need for a new paradigm of data flow management in such large-scale networks under software defined wireless networking (SDWN). The limited power and computation capability available at IoT devices as well as the centralized management and decision-making approach in SDWN introduce a whole new set of security threats to the networks. In particular, the authentication mechanism between the controllers and the forwarding devices in SDWNs is a key challenge from both secrecy and integrity aspects. Conventional authentication protocols based on public key infrastructure (PKI) are no longer sufficient for these networks considering the large-scale and heterogeneity nature of the networks as well as their deployment cost, and security vulnerabilities due to key distribution and storage. We propose a novel security protocol based on physical unclonable functions (PUFs) known as hardware security primitives to enhance the authentication security in SDWNs. In this approach, digital PUFs are developed using the inherent randomness of the nanomaterials of Resistive Random Access Memory (ReRAM) that are embedded in most IoT devices to enable a secure authentication and access control in these networks. These PUFs are developed based on a novel approach of multi-states, in which the natural drifts due to the physical variations in the environment are predicted to reduce the potential errors in challenge-response pairs of PUFs being tested in different situations. We also proposed a PUF-based PKI protocol to secure the controller in SDWNs. The performance of the developed ReRAM-based PUFs are evaluated in the experimental results.