A fresh look into the biometric authentication Perspective from Shannon´s secrecy system and a special wiretap channel

In this paper, we first look at the biometric authentication scheme as an extension of Shannon´s secrecy system with an error-prone key, and derive the necessary condition for the perfect secrecy. Furthermore, we show that the Juels-Wattenberg scheme is optimal by fulfilling such a condition once the biometric key and its error pattern satisfy certain statistical distributions; otherwise, it is possible to improve its performance by coding on basis of the biometric. We further confirm this proposition by reformulating the Juels-Wattenberg scheme with a smart encoder to a specific model of wiretap channel with side information, where the side information is the enrolled biometric template and assumed to be known at the encoder. The idea of the smart encoder is inspired by the fact that the authorities are collecting the biometric information from people since years, and this knowledge could in turn be used to better design the biometric systems for people´s good. From an information theoretic perspective, we explore the secrecy capacity of this specific wiretap channel and demonstrate that the knowledge of the enrolled biometric template at the smart encoder does provide an advantage so as to enhance the performance of the biometric authentication scheme.