In this paper, we propose a new remote biometric based authentication scheme, which is designed for distributed systems with a central database for the storage of the biometric data. For our scheme, we consider the recently introduced security notions of Identity and Transaction privacy and present a different storage mechanism for biometrics resulting in a reduced database storage cost. Besides, the components of the system do not need to store any biometric template in cleartext or in encrypted form, which affects the social acceptance of the system positively. Finally, we compare our results with existing schemes satisfying the current security notions and achieve improved computational complexity.