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.

Template protection techniques are used within biometric systems in order to safeguard the privacy of the system's subjects. This protection also includes unlinkability, i.e., preventing cross-matching between two or more reference templates from the same subject across different applications. In the literature, the template protection techniques based on fuzzy commitment, also known as the code-offset construction, have recently been investigated. Recent work presented the decodability attack vulnerability facilitating cross-matching based on the protected templates and its theoretical analysis. First, we extend the theoretical analysis and include the comparison between the system and cross-matching performance. We validate the presented analysis using real biometric data from the MCYT fingerprint database. Second, we show that applying a random bit-permutation process secures the fuzzy commitment scheme from cross-matching based on the decodability attack.

In recent years, the protection of biometric data has gained increased interest from the scientific community. Methods such as the fuzzy commitment scheme, helper-data system, fuzzy extractors, fuzzy vault, and cancelable biometrics have been proposed for protecting biometric data. Most of these methods use cryptographic primitives or error-correcting codes (ECCs) and use a binary representation of the real-valued biometric data. Hence, the difference between two biometric samples is given by the Hamming distance (HD) or bit errors between the binary vectors obtained from the enrollment and verification phases, respectively. If the HD is smaller (larger) than the decision threshold, then the subject is accepted (rejected) as genuine. Because of the use of ECCs, this decision threshold is limited to the maximum error-correcting capacity of the code, consequently limiting the false rejection rate (FRR) and false acceptance rate tradeoff. A method to improve the FRR consists of using multiple biometric samples in either the enrollment or verification phase. The noise is suppressed, hence reducing the number of bit errors and decreasing the HD. In practice, the number of samples is empirically chosen without fully considering its fundamental impact. In this paper, we present a Gaussian analytical framework for estimating the performance of a binary biometric system given the number of samples being used in the enrollment and the verification phase. The error-detection tradeoff curve that combines the false acceptance and false rejection rates is estimated to assess the system performance. The analytic expressions are validated using the Face Recognition Grand Challenge v2 and Fingerprint Verification Competition 2000 biometric databases.