This paper introduces a novel methodology to enhance privacy in Cooperative Intelligent Transport Systems (C-ITS) by improving unlinkability in vehicle-to-everything (V2X) communication. Focusing on the Cooperative Awareness Basic Service, we employ a Hidden Markov Model (HMM) to model the unlinkability of Cooperative Awareness Messages (CAMs) exchanged between vehicles and roadside units (RSUs) under the surveillance of a Global Passive Adversary (GPA). Implementing a joint obfuscation approach maximizes unlinkability by transforming the CAMs’ original data within a distortion threshold, preserving data utility while confounding the GPA's ability to reliably link messages to specific vehicles. The experimental evaluation confirms the superiority of our method when compared with multivariate independent noise models, including Gaussian and Laplace. Our approach also incorporates an authentication protocol, ensuring the secure and collaborative execution of the obfuscation algorithm by the vehicles involved.