This thesis addresses the inherent security challenges associated with Vehicle-to-Everything (V2X) communication systems, which facilitate real-time data exchange between vehicles, infrastructure, pedestrians, and networks. V2X technology is of great significance in enhancing road safety, optimising traffic management and minimising environmental impact. However, its open and dynamic nature renders it susceptible to a range of security threats. The aim of this study is to implement cryptographic solutions to guarantee the security of these communications, particularly through the utilisation of Public Key Infrastructure (PKI) and the Elliptic Curve Digital Signature Algorithm (ECDSA). It is imperative that these techniques be employed to ensure the integrity and authenticity of transmitted messages.