In this paper, we study fundamental trade-offs in privacy-preserving biometric identification systems with noisy enrollment. The proposed identification systems include helper data, secret keys, and private keys. Helper data are stored in a public database and used for identification. Secret keys are either stored in a secure database or provided to the user, and can be used in a next step, e.g. for authentication. Private keys are provided by users, and are also used for identification. In this paper, we impose a noisy enrollment channel and an arbitrarily small privacy and secrecy leakage rate. We characterize the optimal trade-off among the identification, secret key, private key, and helper data rates. Depending on how secret keys are produced, we study two cases of the proposed privacy-preserving identification systems, where the secret keys are generated and chosen respectively. By introducing private keys, it is shown that the identification system achieves close to zero privacy leakage rate in both generated and chosen secret key settings. The results also show that the identification rate and the secret key rate can be enlarged by increasing the private key rate. This work provides a framework for analyzing privacy-preserving identification systems and an insight on the design of optimal systems.

We study hypothesis testing problems with fixed compression mappings and with user-dependent compression mappings to decide whether or not an observation sequence is related to one of the users in a database, which contains compressed versions of previously enrolled users' data. We first provide the optimal characterization of the exponent of the probability of the second type of error for the fixed compression mappings scenario when the number of users in the database grows exponentially. We then establish operational equivalence relations between the Wyner-Ahlswede-Körner network, the single-user hypothesis testing problem, the multi-user hypothesis testing problem with user-dependent compression mappings and the identification systems with user-dependent compression mappings. These equivalence relations imply the strong converse and exponentially strong converse for the multi-user hypothesis testing and the identification systems both with user-dependent compression mappings. Finally they also show how an identification scheme can be turned into a multi-user hypothesis testing scheme with an explicit transfer of rate and error probability conditions and vice versa.

High-dimensional identification systems consisting of two groups of users in the presence of statistical uncertainties are considered in this work. The task is to design enrollment mappings to compress users' information and an identification mapping that combines the stored information in the database and an observation to estimate the underlying user index. The compression-identification trade-off regions are established for the compound, extended compound, general and mixture settings. It is shown that several settings admit the same compression-identification trade-offs. We then study a connection between the Wyner-Ahlswede-Körner network and the identification setting. It indicates that a strong converse for the WAK network is equivalent to a strong converse for the identification setting. Finally, we present strong converse arguments for the discrete identification setting that are extensible to the Gaussian scenario.

We study a two-stage identification problem with pre-processing to enable efficient data retrieval and reconstruction. In the enrollment phase, users' data are stored into the database in two layers. In the identification phase an observer obtains an observation, which originates from an unknown user in the enrolled database through a memoryless channel. The observation is sent for processing in two stages. In the first stage, the observation is pre-processed, and the result is then used in combination with the stored first layer information in the database to output a list of compatible users to the second stage. Then the second step uses the information of users contained in the list from both layers and the original observation sequence to return the exact user identity and a corresponding reconstruction sequence. The rate-distortion regions are characterized for both discrete and Gaussian scenarios. Specifically, for a fixed list size and distortion level, the compression-identification trade-off in the Gaussian scenario results in three different operating cases characterized by three auxiliary functions. While the choice of the auxiliary random variable for the first layer information is essentially unchanged when the identification rate is varied, the second one is selected based on the dominant function within those three. Due to the presence of a mixture of discrete and continuous random variables, the proof for the Gaussian case is highly non-trivial, which makes a careful measure theoretic analysis necessary. In addition, we study a connection of the previous setting to a two observer identification and a related problem with a lower bound for the list size, where the latter is motivated from privacy concerns.

In this paper we revisit the connections of the distributed hypothesis testing against independence (HT) problem with the Wyner-Ahlswede-Korner (WAK) problem and thë identification systems (ID). We show that the strong converse for the WAK problem is equivalent to the strong converse for the HT problem via constructive and nonconstructive transformations of codes. As another consequence of the transformation we provide a new exponentially strong converse equivalence statement. Applying the same idea, we prove a new result that the -identification capacity of the ID problem is equal to the maximum ε-exponent of type II of error in the HT problem when both side compression is allowed.

In this work we consider a two-stage identification problem with pre-processing where the users' data and observation are Gaussian distributed. In the first stage the processing unit returns a list of compatible users using the information from the first storage layer and the pre-processed observation. Then, the refined search is performed in the second stage where the processing unit returns the exact user's identity and a corresponding reconstruction sequence. We provide a complete rate-distortion trade-off for the Gaussian setting.

We study the high-dimensional identification systems under the presence of statistical uncertainties. The task is to design mappings for enrollment and identification purposes. The identification mapping compresses users' information then stores the index in the corresponding position in a database. The identification mapping combines the information in the database and the observation which originates randomly from an enrolled user to produce an estimate of the underlying user index. We study two scenarios. Users' data are generated from the same unknown distribution while the observation channel is also subjected to uncertainty. Each user's data are generated iid from the distribution corresponding to its own state, while the observation channel is known. We provide an achievable compression-identification trade-off for the first and second settings considering both discrete and continuous cases. In the discrete scenario, the described regions are also the correspondingly complete characterizations.

We study a hypothesis testing problem to decide whether or not an observ!ation sequence is related to one of users in a database which contains compressed versions of users' data. Our main interest lies on the characterization of the exponent of the probability of the second kind of error when the number of users in the database grows exponentially. We show a lower bound on the error exponent and identify special cases where the bound is tight. Next, we study the ε-achievable error exponent and show a sub-region where the lower bound is tight.

We study a two-stage identification problem with pre-processing to enable efficient data retrieval and reconstruction. The first stage outputs a list of compatible users to the second stage which uses it to return the exact user identity with a corresponding reconstruction sequence. The rate-distortion region is characterized. A connection to a two observer identification problem is also studied.