Vehicle Ad Hoc Networks (VANETs) play a pivotal role in intelligent transportation systems, offering dynamic communication between vehicles, road side units, and the internet. Given the open-access nature of VANETs and the associated threats, such as impersonation and privacy violations, ensuring the security of these communications is of utmost importance. This paper presents the Identity-based Cluster Authentication and Key Exchange (ID-CAKE) scheme, a new approach to address security challenges in VANETs. The ID-CAKE scheme integrates the Cluster Consensus Identity-based Identification (CCIBI) with Zero-Knowledge (ZK) proof and the Identity-based Multi-receiver Key Exchange Mechanism (ID-mKEM) signature scheme. This integration provides robust authorization via CCIBI, while the ID-mKEM signature ensures message integrity, and guarantees both non-repudiation and unforgeability through mKEM for message broadcasting. The scheme employs a novel three-party ZK proof for batch verification using mKEM, which significantly reduces computational burdens. Our scheme also ensures anonymity and unlinkability by introducing pseudo-identities to all users in the cluster. The rigorous security proof provided confirms the resilience of the ID-CAKE scheme against potential attacks, adhering to the different scenarios, against the hardness of the elliptic curve computational diffie-hellman under the random oracle model. The ID-CAKE scheme establishes a robust security framework for VANETs, and its introduction highlights potential pathways for future exploration in the realm of VANET security.