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We present a theoretical framework for the analysis of privacy and security trade-offs in secure biometric authentication systems. We use this framework to conduct a comparative information-theoretic analysis of two biometric systems that are based on linear error correction codes, namely fuzzy commitment and secure sketches. We derive upper bounds for the probability of false rejection <formula formulatype="inline"><tex Notation="TeX">$(P_{FR})$</tex></formula> and false acceptance <formula formulatype="inline"><tex Notation="TeX">$(P_{FA})$</tex> </formula> for these systems. We use mutual information to quantify the information leaked about a user's biometric identity, in the scenario where one or multiple biometric enrollments of the user are fully or partially compromised. We also quantify the probability of successful attack <formula formulatype="inline"> <tex Notation="TeX">$(P_{SA})$</tex></formula> based on the compromised information. Our analysis reveals that fuzzy commitment and secure sketch systems have identical <formula formulatype="inline"><tex Notation="TeX">$P_{FR}$</tex> </formula>, <formula formulatype="inline"><tex Notation="TeX">$P_{FA}$</tex> </formula>, <formula formulatype="inline"><tex Notation="TeX">$P_{SA}$</tex> </formula>, and information leakage, but secure sketch systems have lower storage requirements. We analyze both single-factor (keyless) and two-factor (key-based) variants of secure biometrics, and consider the most general scenarios in which a single user may provide noisy biometric enrollments at several access control devices, some of which may be subsequently compromised by an attacker. Our analysis highlights the revocability and reusability properties of key-based systems and exposes a subtle design trade-off between reducing information leakage from compromised systems and preventing successful attacks on systems whose data have not been compromised.

A Theoretical Analysis of Authentication, Privacy, and Reusability Across Secure Biometric Systems