## 1 Introduction  
The Internet of Vehicles (IoVs) represents an emerging application scenario for Internet of Things (IoIs) technology. At the heart of this technological evolution are vehicular ad hoc networks (VANETs), which facilitate communication between vehicles and between vehicles and infrastructures, thus constituting a key subset of the IoVs. VANETs have emerged as one of the most exciting research fields within intelligent transport systems, thereby providing safety and convenience information for drivers [1]. These networks can communicate the complex and dynamic data generated by vehicles, humans, and the environment in real time, such as traffic conditions, traffic accidents, road construction, and congestion. However, VANETs are especially vulnerable to a variety of security threats, including malicious attacks and the distribution of unreliable information, which can have severe consequences, such as traffic accidents. Additionally, the distinct characteristics of VANETs introduce significant challenges in terms of security management, privacy, and reliability in their design [2; 3]. So, creating an efficient anonymous authentication system with low computational cost [4] in a vehicular ad hoc network (VANET) represents a considerable challenge [5]. Specifically, in the realm of vehicular ad hoc networks (VANETs), the development of an efficient anonymous authentication system that maintains low computational costs poses significant challenges due to several intrinsic characteristics of these networks:  
1. High Vehicle Mobility: The highly dynamic nature of VANETs, which are characterized by vehicles moving at high speeds, results in frequent changes in network nodes. This demands an authentication system that is capable of rapidly adapting to changes in network topology without compromising on security or performance. 2. Resource Limitations in Vehicles: Despite being equipped with advanced technologies, modern vehicles still face limitations in terms of processing power and storage capacity. An efficient authentication system must operate within these resource constraints, thereby ensuring light computational loads. 3. Anonymity and Privacy Needs: Given the sensitive nature of vehicular data, such as location and movement patterns, ensuring user anonymity and privacy is paramount. Achieving this without significantly increasing the computational burden adds complexity to system design. 4. Diversity and Scalability: VANETs support a wide array of applications, from road safety to infotainment services, each with its unique security requirements. The authentication system must be versatile enough to cater to these diverse needs and scalable to handle the increasing number of connected vehicles. 5. Resistance to Attacks and Frauds: Authentication systems in VANETs must be robust against various security threats, including impersonation attacks, Sybil attacks, and data manipulation. Designing a system that can effectively counter these threats without imposing excessive computational demands is a significant challenge. For these reasons, developing an efficient and low-cost computational anonymous authentication system for VANETs is not only crucial for ensuring security and privacy within these networks, but also poses substantial technical challenges. Our research aims to address these challenges through an innovative approach that balances security, efficiency, and practicality. On the other hand, the incorporation of blockchain technology in VANETs presents a paradigm shift from traditional centralized systems to a more resilient, transparent, and decentralized framework. The blockchain, known for its immutable and secure ledger, is leveraged to enhance the tracking and verification of vehicular movements and interactions. This technology has shown promise in mitigating the inherent vulnerabilities of VANETs, thereby providing a robust platform for secure vehicular communication.