Notation and their definition.

Fifth-generation (5G)-enabled vehicular fog computing technologies have always been at the forefront of innovation because they support smart transport like the sharing of traffic data and cooperative processing in the urban fabric. Nevertheless, the most important factors limiting progress are concerns over message protection and safety. To cope with these challenges, several scholars have proposed certificateless authentication schemes with pseudonyms and traceability. These schemes avoid complicated management of certificate and escrow of key in the public key infrastructure-based approaches in the identity-based approaches, respectively. Nevertheless, problems such as high communication costs, security holes, and computational complexity still exist. Therefore, this paper proposes an efficient certificateless authentication called the ECA-VFog scheme for fog computing with 5G-assisted vehicular systems. The proposed ECA-VFog scheme applied efficient operations based on elliptic curve cryptography that is supported by a fog server through a 5G-base station. This work conducts a safety analysis of the security designs to analysis the viability and value of the proposed ECA-VFog scheme. In the performance ovulation section, the computation costs for signing and verification process are 2.3539 ms and 1.5752 ms, respectively. While, the communication costs and energy consumption overhead of the ECA-VFog are 124 bytes and 25.610432 mJ, respectively. Moreover, comparing the ECA-VFog scheme to other existing schemes, the performance estimation reveals that it is more cost-effective with regard to computation cost, communication cost, and energy consumption.支持第五代移动通信（5G）的车载雾计算技术始终处于创新前沿，因其可支撑智能交通应用，例如城市场景下的交通数据共享与协同处理。然而，制约其发展的核心因素在于消息保护与安全性方面的顾虑。为应对这些挑战，诸多学者提出了具备假名与可追溯性的无证书认证（certificateless authentication）方案。此类方案分别规避了基于公钥基础设施方案中的复杂证书管理问题，以及基于身份认证方案中的密钥托管问题。然而，此类方案仍存在通信开销过高、存在安全漏洞以及计算复杂度高等问题。为此，本文针对5G辅助车载系统下的雾计算场景，提出了一种高效无证书认证方案——ECA-VFog方案。所提出的ECA-VFog方案依托5G基站与雾服务器的支撑，采用基于椭圆曲线密码学（elliptic curve cryptography）的高效运算流程。本研究对该安全设计开展安全性分析，以验证所提ECA-VFog方案的可行性与应用价值。在性能评估章节中，签名与验证流程的计算开销分别为2.3539毫秒与1.5752毫秒；与此同时，ECA-VFog方案的通信开销与能耗开销分别为124字节与25.610432毫焦。此外，通过与现有其他方案的对比，性能评估结果表明，ECA-VFog方案在计算开销、通信开销与能耗方面均具备更优的性价比。