## 2 Related Work  
To overcome pseudonym-linking attacks, especially semantic attacks, the mix zone has been proved as a widely acknowledged and the most effective technology [20; 30; 31; 32; 33; 34; 35; 36]. The mix zone allows a group of vehicles to enter an area within a close time frame, change pseudonyms, and exit through different exits to achieve anonymity. [PERSON] et al. [30] first introduced a mix zone in the VANET named CMIX (Cryptographic MIX), where beacons are encrypted. The pseudonym-changing process is concealed, preventing continuous vehicle tracking by eavesdroppers. In addition, some studies proposed maintaining silence within the mix zone [31; 32]. However, this can lead to reduced awareness of the vehicle's surroundings, giving rise to other issues such as the inability to promptly prevent collisions [33]. Conversely, while encryption might lead to increased computational overhead, the inherent low latency of VANETs ensures the timely delivery of beacons. To enhance the privacy protection of CMIX, other encryption-based mix-zone schemes focus on supplementary techniques like game theory [34] and statistical approaches [35; 36]. Research on mix-zone deployment locations and methods aims to strike a balance between maximizing privacy protection and minimizing the impact on network performance and resource utilization. Instead of junctions, some studies have concentrated on repositioning mix zones to areas where vehicles come to a full stop. For instance, [PERSON] et al. [37] recommended establishing mix zones at social locations like shopping mall parking lots, while [38] proposed sites like gas stations and toll booths. However, this approach limits the opportunities for encountering a mix zone, which subsequently diminishes privacy due to the scarcity of suitable locations. Another alternative line of study suggests using dynamic mix zones since the VANET is decentralized and self-organized. A cluster of vehicles initiates a dynamic mix zone, enabling them to change or swap pseudonyms based on their awareness of the surrounding traffic through encrypted V2V transmissions [39]. This occurs, for instance, when vehicles share a similar direction and velocity [40] or possess simultaneous intent [41]. However, establishing the optimal timing to trigger dynamic mix zones in scenarios with low vehicle density remains a challenging task. The methods mentioned above either overlook low-vehicle-density scenarios or exhibit inadequate performance in such situations. Recently, some approaches based on generating fake beacons have been proposed to address privacy concerns in low-vehicle-density scenarios. The usage of fake states is widespread in Mobile Ad Hoc Networks (MANETs) [42], where user mobility is uncertain, making it challenging to discern real location information through semantic analysis. In terms of the VANET, RSUs can generate fake beacons as dummy nodes to artificially increase the number of vehicles and maintain the anonymity. However, in Vehicular Ad Hoc Networks (VANETs), vehicles are constrained to move along roads, and due to the dense interconnections between frequently broadcasted beacons, attackers can more easily reveal complete vehicle trajectories through semantic analysis. Therefore, introducing fake beacons in VANETs presents greater challenges. In the context of low vehicle density, [PERSON] et al. [26] enhanced the CMIX approach by introducing chaff beacons whenever a vehicle enters a junction to fill up exits. The quantity of chaff vehicles is regulated based on the current number of vehicles within the CMIX zone. Additionally, ref. [43] redesigned the authentication process of employing Cuckoo Filters to differentiate between genuine beacons and chaff beacons. [PERSON] and [PERSON] [27] suggested using relaying vehicles to cooperatively disseminate decoy traffic without the requirement from vehicles to provide their intended trajectory path to the RSUs. [PERSON] et al.