Many wearable devices identify themselves in a pervasive way. But at the same time, people want to remain anonymous. Modeling anonymity and unlinkability in identification protocols is a delicate issue. In this paper, we revisit the privacy model from Asiacrypt 2007. We show how to achieve forward-privacy (in the V07 sense) using an IND-CCA secure cryptosystem with the PKC protocol. We review the impossibility result of strong privacy and the model extension from CANS~2012 to reach strong privacy (in the OV12 sense) using the PKC protocol with plaintext awareness. We also discuss on the simplified model from ESORICS 2011 and achieve strong-privacy (in the HPVP11 sense) using IND-CCA security only. Finally, we apply these results to add privacy protection in distance bounding protocols.