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For telematics applications, entity authentication between vehicles and roadside units (RSUs) with vehicle anonymity plays an important role on providing security and privacy. In 2009, Yim, Choi, and Kim proposed an anonymous authentication protocol in Vehicular Ad-hoc Networks (VANETs) for communications between vehicles and RSUs. The Yim-Choi-Kim scheme employs a traceable ring signature with t-times anonymity as a building block. The t-times anonymity is for the privacy requirement of movement tracking avoidance, however, it has a weakness in the strong unlinkability property. This paper improves the weakness of the Yim-Choi-Kim scheme.