## 1 Introduction
This makes it challenging for attackers to associate a vehicle's trace inside and outside the mix zone, as well as the new pseudonym, with the vehicle's real ID or previous pseudonyms based solely on beacons [23]. However, most research assumes a high-vehicle-density scenario where vehicles have enough neighbors to maintain anonymity. Yet the efficacy of the mix zone is compromised when there are insufficient vehicles, allowing attackers to employ beacon-based semantic attacks and disclose vehicle trajectories despite the full anonymity of beacons [24]. A vehicle may not be able to travel to a high-density area where privacy protection remains a priority for an extended period. Therefore, changing pseudonyms in low-density areas is a critical issue that must be addressed to ensure privacy. Several studies [25; 26; 27] have addressed the problem of low vehicle density by implementing fake beacons generated by the RSU, commonly referred to as chaff or decoy beacons. The purpose of these beacons is to mimic real vehicles and artificially augment the vehicle density. The inclusion of supplementary fake beacons poses a challenge for adversaries attempting to accurately link inbound and outbound traces within the mix zone. While these approaches effectively mitigate the susceptibility to pseudonym-linking attacks in scenarios characterized by low vehicle density, they also introduce new challenges. It is crucial to generate accurate fake beacon trajectories for the pseudonym-changing scheme. These trajectories should mimic genuine vehicle behavior in terms of location and speed, but originate from different exits to confuse attackers. However, generating such trajectories can be challenging due to the requirement for timely updates on the vehicle's behavior to accurately predict its trajectory. Inaccurate predictions may potentially expose vehicle trajectories to attackers through semantic analysis. On the other hand, most fake-beacon-based pseudonym-changing schemes involve generating multiple fake trajectories to effectively deceive attackers [22; 24; 26]. However, generating fake trajectories to mimic real vehicles requires the fake beacons to be processed by RSUs similarly to genuine ones. While this approach reduces the risk of vehicle privacy leakage, it also introduces excessive network overhead to the VANET, threatening the environment awareness functionality of the VANETs [28; 29]. Inspired by the capability of neural network models to assist in vehicle trajectory prediction, which can be further applied to the protection of vehicle privacy, we propose the Communication-Efficient Pseudonym-Changing Scheme Within the Restricted Online Knowledge Scheme (CPCROK) to protect vehicle privacy in low-density VANETs and effectively address the shortcomings of the aforementioned pseudonym-changing scheme. CPCROK outperforms the state-of-the-art safeguards (the plain mix zone, other fake beacon schemes) in reducing the attacker's success rate while minimizing transmission overhead. The contributions of this work are summarized as follows:  
1. We propose CPCROK to protect vehicle privacy in VANET scenarios with minimal additional network overhead, even in low-vehicle-density and limited real-time vehicle information scenarios. CPCROK achieves this through a modular design, consisting of three modules: the IKF-CGTGM, an improved Kalman filter method to capture non-linear vehicle movements, providing real-time coarse-grained trajectory knowledge for the next phase; the RNN-FGTGM, a lightweight RNN model to capture intricate vehicle motion patterns and adjust predicted trajectories based on previous IKF results; and the FBG module, an iterator to generate a single, highly convincing fake trajectory outside the mix zone to deceive attackers. CPCROK minimizes the need to generate a large number of fake beacons by introducing an accurate hierarchical vehicle trajectory prediction approach and reducing the reliance on real-time vehicle state information. 2.