Vehicular ad hoc networks (VANETs) establish wireless connections among all vehicles, enabling seamless mobile communication. However, existing conditional privacy protection VANETs authentication schemes fail to address the issue of potential key-exposure and do not provide accelerated vehicle authentication. In this paper, we propose a reputation incentive committee-based secure conditional dual authentication scheme for VANETs called RIC-SDA. Our proposed scheme incorporates dual authentication of the consensus committee and vehicle-to-vehicle (V2V) communication. It enables the rapid provision of dynamic vehicle epoch-key from consensus committee authentication for V2V authentication through our designed reputation incentive mechanism. To mitigate the potential key-exposure problem, we introduce a novel concept of secure vehicle epoch communication, which means V2V authentication is valid for only one epoch blockchain unit time. The proposed scheme achieves lightweight computation and incurs minimal communication overheads, with the signature size being just 137 bytes. The RIC-SDA scheme supports fast batch verification. We prove that our proposed scheme is unforgeable security under random oracle and demonstrate its feasibility by implementing it in a test network based on Ethereum Sepolia. The results demonstrate that our RIC-SDA solution outperforms the existing state-of-the-art authentication VANET schemes regarding efficiency and communication costs.