  In [3], the authors proposed a highly efficient secure and privacy-preserving
scheme for secure vehicular communications. The proposed scheme consists of
four protocols: system setup, protocol for STP and STK distribution, protocol
for common string synchronization, and protocol for vehicular communications.
Here we define the security models for the protocol for STP and STK
distribution, and the protocol for vehicular communications,respectively. We
then prove that these two protocols are secure in our models.
