Fundamental Limits-Achieving Polar Code Designs for Biometric Identification and Authentication

In this work, we present polar code designs that offer a provably optimal solution for biometric identification and authentication systems under noisy enrollment for certain sources and observation channels. We consider a discrete memoryless biometric source and discrete symmetric memoryless observation channels. It is shown that the proposed polar code designs achieve the fundamental limits with privacy and secrecy constraints. Depending on how the secret keys are extracted and whether the privacy leakage rate should be close to zero, we consider four related setups, which are (i) the generated secret key system, (ii) the chosen secret key system, (iii) the generated secret key system with zero leakage, and (iv) the chosen secret key system with zero leakage. For the first two setups, (i) and (ii), the privacy level is characterized by the privacy leakage rate. For the last two setups (iii) and (iv), private keys are additionally employed to achieve close to zero privacy leakage rate. In setups (i) and (iii), it is assumed that the secret keys are generated, i.e., extracted from biometric information. While in setups (ii) and (iv), secret keys provided to the system are chosen uniformly at random from some trustful source. This work provides the first examples of fundamental limits-achieving code designs for identification and authentication. Moreover, since the code designs are based on polar codes and many existing works study low-complexity and short block-length polar coding, the proposed code designs in this work provide the code design structure and a framework for the application of biometric identification and authentication.