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We present a theoretical framework for the analysis of privacy and securitytradeoffs in secure biometric authentication systems. We use this framework toconduct a comparative information-theoretic analysis of two biometric systemsthat are based on linear error correction codes, namely fuzzy commitment andsecure sketches. We derive upper bounds for the probability of false rejection($P_{FR}$) and false acceptance ($P_{FA}$) for these systems. We use mutualinformation to quantify the information leaked about a user's biometricidentity, in the scenario where one or multiple biometric enrollments of theuser are fully or partially compromised. We also quantify the probability ofsuccessful attack ($P_{SA}$) based on the compromised information. Our analysisreveals that fuzzy commitment and secure sketch systems have identical $P_{FR},P_{FA}, P_{SA}$ and information leakage, but secure sketch systems have lowerstorage requirements. We analyze both single-factor (keyless) and two-factor(key-based) variants of secure biometrics, and consider the most generalscenarios in which a single user may provide noisy biometric enrollments atseveral access control devices, some of which may be subsequently compromisedby an attacker. Our analysis highlights the revocability and reusabilityproperties of key-based systems and exposes a subtle design tradeoff betweenreducing information leakage from compromised systems and preventing successfulattacks on systems whose data have not been compromised.

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