A biometric representation of a fingerprint from which the original biometric cannot be recovered (privacy) and which can be canceled and reissued. For example, based on an individual's token, the representation can be scrambled uniquely to the individual. From the scrambled biometric representation it is not feasible to reconstruct the biometric and if the representation is compromised, a new one is easily issued. In another aspect, if a biometric can be represented by some other one-dimensional structure, a distance or similarity measure is defined to compare biometrics. Verification decisions can be made based on the distance between or similarity of biometrics.