The inherent complexity and the critical nature of data privacy in IoT networks necessitate rigorous validation of privacy mechanisms to preempt vulnerabilities and ensure compliance with security standards. This research article extends the concept of the SDN-enabled Consumer-Centric Content Delivery Network (CCDN) model for the IoT by introducing a rigorous mathematical framework to formalize the dialogues integral to user privacy and data integrity. With the help of a comprehensive mathematical formulation, the research captures the dynamics of credential exchange and user interactions within the CCDN architecture. To ensure the robustness of the proposed model, this research employs formal verification techniques to validate the correctness and security properties of the mathematical formulation. Furthermore, the research conducts an extensive simulative analysis to evaluate the performance of the CCDN architecture under various operational conditions. This analysis encompasses aggregate analysis, amortized analysis, and scalability analysis, focusing on critical performance metrics such as latency, packet loss ratio, and throughput. The results demonstrate that the implemented CCDN model maintains user privacy and personalization for content delivery in scalable IoT environments. This work lays the groundwork for future research in secure and efficient content delivery systems, addressing the growing demands of IoT applications while ensuring user-centric privacy and data protection.