Ubiquitous connection to modern vehicles is mandatory to support diverse intelligent functions, including autonomous driving, telediagnosis, infotainment services, and others. Since the deployment of the cellular access points is still scarce in rural areas, the low earth orbit (LEO) constellation-based communication is believed to provide a realistic alternative. However, due to the long propagation delay and limited satellite on-board processing ability, the design of security protocols in LEO constellations remain challenging. Aiming at these challenges, we propose a secure user access and inter-satellite handover mechanism, which achieves the control- and user-plane key separation. Specifically, our proposed scheme exploits an identity-based encryption scheme with proxy re-encryption to achieve the key establishments with high efficiency, and it also achieves the highly efficient secure batch handover with the assistance of a stack. Detailed analysis is performed to demonstrate the security properties of our proposed scheme, in terms of confidentiality, authentication, and forward/backward key separation. Furthermore, simulation results illustrate that our proposed scheme achieves high computational complexity and communication overheads in comparison with a traditional scheme.