<p>Wireless sensor networks (WSNs) communication systems represent a flexible, reliable, and efficient paradigm that enables bidirectional real-time data exchange, as well as mutual identity authentication between the User and the Sensor Node. However, due to the open nature of these networks, communications among entities may be intercepted or manipulated by attackers through public channels at any time. As WSNs often lack fundamental security mechanisms, they are vulnerable to various potential threats. In response to these challenges, we propose a three-party authentication and key agreement scheme for WSNs based on physical unclonable functions (PUFs) and the lightweight Chebyshev chaotic map cryptographic operation. This approach ensures the preservation of privacy and resilience against machine learning-based modeling attacks, as well as other existing security risks. Furthermore, by incorporating hash functions and XOR operations into the framework design, the pseudonyms of Users and the parameters used for identity authentication are dynamically generated and updated, achieving one-time usage. The correctness and security of the proposed scheme are validated through both formal and informal analysis methods. Additionally, a simulation of practical deployment scenarios is conducted to evaluate its computational and communication overhead in comparison with competing schemes. The detailed comparative results demonstrate that the proposed scheme outperforms existing approaches in terms of efficiency and security.</p>