Binary Biometrics: An Analytic Framework to Estimate the Bit Error Probability under Gaussian Assumption

Abstract

In recent years the protection of biometric data has gained increased interest from the scientific community. Methods such as the helper data system, fuzzy extractors, fuzzy vault and cancellable biometrics have been proposed for protecting biometric data. Most of these methods use cryptographic primitives and require a binary representation from the real-valued biometric data. Hence, the similarity of biometric samples is measured in terms of the Hamming distance between the binary vector obtained at the enrolment and verification phase. The number of errors depends on the expected error probability P <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">e</sub> of each bit between two biometric samples of the same subject. In this paper we introduce a framework for analytically estimating P <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">e</sub> under the assumption that the within-and between-class distribution can be modeled by a Gaussian distribution. We present the analytic expression of P <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">e</sub> as a function of the number of samples used at the enrolment (N <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">e</sub> ) and verification (N <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">v</sub> ) phases. The analytic expressions are validated using the FRGC v2 and FVC2000 biometric databases.