Maximum Key Size and Classification Performance of Fuzzy Commitment for Gaussian Modeled Biometric Sources

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 the binary vector derived from the biometric sample. The size of the key plays an important role, as the achieved privacy and security mainly depend on the entropy of the key. 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 classification performance of the fuzzy commitment scheme and the theoretical maximum key size given as input a Gaussian biometric source. We show the effect of the system parameters such as the biometric source capacity, the number of feature components, the number of enrolment and verification samples, and the target performance on the maximum key size. Furthermore, we provide an analysis of the effect of feature interdependencies on the estimated maximum key size and classification performance. Both the theoretical analysis, as well as an experimental evaluation using the MCYT fingerprint database showed that feature interdependencies have a large impact on performance and key size estimates. This property can explain the large deviation in reported key sizes in literature.