Vehicle ad hoc networks (VANETs) enable efficient communication for enhanced safety and convenience. However, due to their open network environment, VANETs are highly vulnerable to attacks, including eavesdropping and vehicle impersonation. Therefore, authentication and data confidentiality are the basic security requirements, achieved through vehicle authentication and establishing secure channels using a shared secret key \(({\textbf{sk}})\) . The Password-Authenticated Key Exchange (PAKE) protocol generates a high-entropy \({\textbf{sk}}\) using a simple password. However, the traditional PAKE scheme stores passwords on a single server, significantly increasing vulnerability to offline dictionary attacks. To mitigate this, the threshold PAKE scheme distributes the password among multiple servers, avoiding a single point of failure. In this paper, we present a novel threshold PAKE protocol that enables a vehicle to authenticate with the authentication server while keeping the password secret. In particular, we integrate a threshold public key encryption scheme and an asymmetric key consensus (AKC) mechanism for password authentication and key exchange. The password is encrypted using the public key of distributed decryption servers, and a threshold number of these servers collaboratively decrypt and verify it. After verification, the vehicle and authentication server establish a \({\textbf{sk}}\) using an AKC mechanism. Our scheme is proven secure against chosen ciphertext attacks, based on the decision module learning with error assumption, resists offline dictionary attacks, provides password and key secrecy, and mutual authentication. Additionally, it achieves transparency by ensuring vehicles communicate only with the authentication server. Performance analysis shows our protocol achieves enhanced efficiency with minimal communication rounds, reduced computational costs, and faster execution compared to existing solutions.
