Intelligent transportation systems increasingly depend on wireless communication for broadcasting traffic messages and facilitating real-time vehicular communication. In this context, message authentication is crucial for establishing secure and reliable communication. However, security solutions must consider the dynamic nature of vehicular communication links, which fluctuate between line-of-sight (LoS) and non-line-of-sight (NLoS) due to obstructions. This paper proposes a lightweight cross-layer authentication scheme that employs public-key infrastructure (PKI)-based authentication for initial legitimacy detection/handshaking while using key-based physical-layer re-authentication for message verification. This approach reduces signature generation and signaling overheads associated with each transmission, thereby enhancing network scalability. However, the receiver operating characteristic (ROC; Pd: detection vs. PFA: false alarm probabilities) of the latter decreases with lower signal-to-noise ratio (SNR). To address this, we investigate the use of reconfigurable intelligent surfaces (RISs) to strengthen the SNR directed toward the designated vehicle in shadowed areas (i.e., NLoS scenarios), thereby improving the ROC. Theoretical analysis and practical implementation are conducted using a 1-bit RIS consisting of 64 x 64 reflective meta-surfaces. Experimental results show a significant improvement in Pd, increasing from 0.82 to 0.96 at SNR = -6 dB for an orthogonal frequency-division multiplexing (OFDM) system with 128 subcarriers. We also conducted informal and formal security analyses using Burrows-Abadi-Needham (BAN) logic to prove the scheme's ability to resist passive and active attacks.