An information theoretic approach for formulating probability of random correspondence of biometrics

Distinctiveness of users in biometric authentication can be limited when multiple samples of a user´s biometric information differ due to intra-class variability in the acquisition, thus resulting in random correspondence between users. Most of the currently known methods based on error correcting codes, fuzzy vault have been proposed for protecting biometric data against the intra-class variability. These methods require a binary representation from the real-valued biometric data to measure the security by a discrete model. In this work, we analytically formulate probability of random correspondence (PRC) for biometrics by developing a discrete noisy source model using statistics of real-valued features that helps us to propose error exponent of biometrics. The quantized template of real-valued features represented by Ns bits inherently has t error bits occurring due to the intra-class variability and modeled by a binary symmetric noise channel. The values of t, error probability of binary symmetric channel and information rate R for the discrete noisy source are combined in the framework of error exponents to develop analytic expression for PRC of biometrics. We illustrate our approach with simulations, using available data and approximations, to validate the analytic expression of PRC for palmprint and iris biometrics.