Analytical template protection performance and maximum key size given a Gaussian-modeled biometric source

Template protection techniques are used within biometric systems in order to protect the stored biometric template against privacy and security threats. A great portion of template protection techniques are based on extracting a key from or binding a key to a biometric sample. The achieved protection depends on the size of the key and its closeness to being random. In the literature it can be observed that there is a large variation on the reported key lengths at similar classification performance of the same template protection system, even when based on the same biometric modality and database. In this work we determine the analytical relationship between the system performance and the theoretical maximum key size given a biometric source modeled by parallel Gaussian channels. We consider the case where the source capacity is evenly distributed across all channels and the channels are independent. We also determine the effect of the parameters such as the source capacity, the number of enrolment and verification samples, and the operating point selection on the maximum key size. We show that a trade-off exists between the privacy protection of the biometric system and its convenience for its users.