Block Coding Schemes Designed for Biometric Authentication

We address the biometric authentication setup where the outcomes of biometric observations received at the verification stage are compared with the sample data formed at the enrollment stage. The result of comparison is either the acceptance or the rejection of the identity claim. The acceptance decision corresponds to the case when the analyzed values belong to the same person. A possible solution to the problem, called the direct authentication, is implemented when the outcomes of biometric observations at the enrollment stage are stored in the database, and they are available to the verifier. The possible incorrect verifier’s decisions are caused by the fact that these observations are noisy. The probabilities of errors are called the false rejection and the false acceptance rates. The features of the direct authentication are as follows: 1) data compression is not included at the enrollment stage; 2) the scheme does not require an additional external randomness; 3) if the stored data become available to an attacker, then he knows the outcomes of biometric observations of the person and can pass through the verification stage with the acceptance decision by presenting these data to the verifier. The considered below coding approaches to the problem require an external randomness and relax the constraint that the database has to be protected against reading. These approaches include the additive and the permutation coding schemes. Both the direct authentication and an additive coding scheme are illustrated using a proposed mathematical model for the DNA measurements. We present the model and describe a data compression method that can be used to approach a uniform probability distribution over the obtained data for their further use in the additive scheme and other purposes. The processing of the DNA data also serves as an example of possible processing data generated by an arbitrary memoryless source. The additive block coding scheme can be viewed as a variant of stream ciphering scheme where the data, to be hidden, are added to a key. The subtraction of the noisy version of the data creates a corrupted version of the key. If the key is a codeword of a code having certain error–correcting property, then the fact, whether the key can be reconstructed or not, 15