Biometric identification systems are principally related to the information security as well as data protection and encryption. The paper proposes a method to integrate biometrics data encryption and authentication into error correction techniques. The normal methods of biometric templates matching are replaced by a more powerful and high quality identification approach based on Grobner bases computations. In the normal biometric systems, where the data are always noisy, an approximate matching is expected;however, our cryptographic method gives particularly exact matching.