Vehicular ad hoc networks (VANETs), which are the backbone of intelligent transportation systems (ITSs), facilitate critical data exchanges between vehicles. This necessitates secure transmission, which requires guarantees of message availability, integrity, source authenticity, and user privacy. Moreover, the traceability of network participants is essential as it deters malicious actors and allows lawful authorities to identify message senders for accountability. This introduces a challenge: balancing privacy with traceability. Conditional privacy-preserving authentication (CPPA) schemes are designed to mitigate this conflict. CPPA schemes utilize cryptographic protocols, including certificate-based schemes, group signatures, identity-based schemes, and certificateless schemes. Due to the critical time constraints in VANETs, efficient batch verification techniques are crucial. Combining certificateless schemes with batch verification leads to certificateless aggregate signature (CLAS) schemes. In this paper, cryptanalysis of Xiong’s CLAS scheme revealed its vulnerabilities to partial key replacement and identity replacement attacks, alongside mathematical errors in the batch verification process. Our proposed CLAS scheme remedies these issues by incorporating an identity authentication module that leverages chameleon hashing within elliptic curve cryptography (CHAM-CLAS). The signature and verification modules are also redesigned to address the identified vulnerabilities in Xiong’s scheme. Additionally, we implemented the small exponents test within the batch verification module to achieve Type III security. While this enhances security, it introduces a slight performance trade-off. Our scheme has been subjected to formal security and performance analyses to ensure robustness.