Recently, the spectrum scarcity is becoming a big issue because there are exponential growth of broadcasting and communication systems in the spectrum demand. Cognitive radio is a technology that is envisaged to solve the problems in wireless networks resulting from the limited available spectrum and the inefficiency in the spectrum usage by exploiting the existing wireless spectrum opportunistically. Kuroda et al. proposed a radio-independent authentication protocol for cognitive radio networks. This paper first shows the privacy weaknesses in the authentication protocol by Kuroda et al. and proposes a privacy aware authentication protocol to solve the weaknesses.