© The Author(s) 2022.The Internet of vehicles technology has developed rapidly in recent years and has become increasingly important. The social Internet of vehicles provides better resources and services for the development of the Internet of vehicles and provides better experience for users. However, there are still many security problems in social vehicle networking environments. Once the vehicle is networked, the biggest problem is data security according to the three levels of data collection, intelligent analysis, and decision control of the Internet of vehicles. Recently, Wu et al. proposed a lightweight vehicle social network security authentication protocol based on fog nodes. They claimed that their security authentication protocol could resist various attacks. However, we found that their authentication protocols are vulnerable to internal attacks, smart card theft attacks, and lack perfect forward security. In this study, we propose a new protocol to overcome these limitations. Finally, security and performance analyses show that our protocol perfectly overcomes these limitations and exhibits excellent performance and efficiency.