## 1 Introduction  
The integration of wireless technology into modern vehicles has greatly enhanced the exchange of crucial information such as location, speed, and direction, offering drivers real-time traffic updates and reducing the risk of accidents [1]. However, the wireless channel used for this exchange can also be vulnerable to malicious attacks, such as the interception and alteration of transmitted data [2, 3]. Public-key cryptography (PKC) has been widely used to secure these communications and protect privacy. However, PKC-based key management faces power-consumption and computational-complexity challenges [4]. Symmetric-key cryptography is a more effective alternative in that respect. However, establishing a symmetric shared key using cryptographic operations still depends on PKC-based approaches such as Diffie-Hellman key exchange [5]. In this context, the study of secret key generation through the physical-layer security mechanism has gained increasing attention, especially since [PERSON] proposed the idea in 1993 [6]. The unique properties of wireless channels, such as their time-varying, short-term reciprocity, and space-time uniqueness within the coherence interval \(T_{c}\), provide a natural source for generating secret keys [7]. The key-generation process involves channel probing, measurement quantization, information reconciliation, and privacy amplification, resulting in the establishment of a secure shared key between the sender and receiver [8]. The secret key capacity is a crucial aspect of this field of study. Theoretical upper limits of secret key capacity have been established through the works of [PERSON] and [PERSON] et al. [9] in source-type and channel-type models with wiretappers. Subsequently, research on the secret key capacity under more complex system models has been developed. The channel-phase response is a valuable resource for secure key extraction, as it is highly sensitive to the distance between terminals [10]. This makes it effective in highly dynamic vehicular networks, generating high-entropy cryptographic keys. However, it is important to consider the shadowing effect from surrounding terminals (i.e., vehicles and infrastructures) that can lead to unpredictable channel-fading variations in urban and rural areas. Additionally, the key-extraction performance is adversely affected by the decrease in signal-to-noise ratio (SNR) values. This limitation results in reduced PHY-layer key-extraction performance for non-line-of-sight (NLoS) communication scenarios and long-range applications. Recently, the reconfigurable intelligent surface (RIS) field has emerged as a technology that can improve communication quality by adjusting reflection coefficients such as phase, amplitude, frequency, or polarization [11]. The RIS has been employed in various applications, such as satellite communications [12], physical-layer security [13], and internet-of-things (IoT) networks [14], demonstrating its versatility and the potential for diverse use cases. RISs comprise many passive reflecting units that can be placed at adaptable locations and independently alter the incident signal, therefore improving signal transmission [15]. In recent years, some researchers have applied RISs to the physical-layer security of wireless communications to improve the secrecy data rate under the wiretap channel, a concept referred to as keyless information theory security [16]. However, the application of RISs to phase-based key-extraction mechanisms has not yet been explored. The effective extraction of keys with the aid of the RIS and the use of channel-phase responses to generate shared keys remains an open issue in the field of physical-layer security technology. Given the ability of RISs to configure the wireless channel in real time through passive reflection, they have the potential to improve secret key capacity significantly.