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Recently, Lu et al. proposed an efficient conditional privacy preservation protocol, named ECPP, based on group signature scheme for generating anonymous certificates from roadside units (RSUs). However, ECPP does not provide unlinkability and traceability when multiple RSUs are compromised. In this paper, we make up for the limitations and propose a robust and efficient anonymous authentication protocol without loss of efficiency as compared with ECPP. Furthermore, in the proposed protocol, RSUs can issue multiple anonymous certificates to an OBU to alleviate system overheads for mutual authentication between OBUs and RSUs. In order to achieve these goals, we consider a universal re-encryption scheme and identity-based key establishment scheme as our building blocks. Several simulations are conducted to verify the efficiency and effectiveness of the proposed protocol by comparing with those of the existing ECPP.