In this study, we investigate fundamental trade-off among identification, secrecy, template, and privacy-leakage rates in biometric identification system. Ignatenko and Willems (2015) studied this system assuming that the channel in the enrollment process of the system is noiseless and they did not consider the template rate. In the enrollment process, however, it is highly considered that noise occurs when bio-data is scanned. In this paper, we impose a noisy channel in the enrollment process and characterize the capacity region of the rate tuples. The capacity region is proved by a novel technique via two auxiliary random variables, which has never been seen in previous studies. As special cases, the obtained result shows that the characterization reduces to the one given by Ignatenko and Willems (2015) where the enrollment channel is noiseless and there is no constraint on the template rate, and it also coincides with the result derived by Günlü and Kramer (2018) where there is only one individual.

We propose a biometric identification system where the chosen- and generated-secret keys are used simultaneously, and investigate its fundamental limits from information theoretic perspectives. The system consists of two phases: enrollment and identification phases. In the enrollment phase, for each user, the encoder uses a secret key, which is chosen independently, and the biometric identifier to generate another secret key and a helper data. In the identification phase, observing the biometric sequence of the identified user, the decoder estimates index, chosen- and generated-secret keys of the identified user based on the helper data stored in the system database. In this study, the capacity region of such system is characterized. In the problem settings, we allow chosen- and generated-secret keys to be correlated. As a result, by permitting the correlation of the two secret keys, the sum rate of the identification, chosen- and generated-secret key rates can achieve a larger value compared to the case where the keys do not correlate. Moreover, the minimum amount of the storage rate changes in accordance with both the identification and chosen-secret key rates, but that of the privacy-leakage rate depends only on the identification rate.

The biometrical identification system, introduced by Willems et al., is a system to identify individuals based on their measurable physical characteristics. Willems et al. characterized the identification capacity of a discrete memoryless biometrical identification system from information theoretic perspectives. Recently, Mori et al. have extended this scenario to list-decoding whose list size is an exponential function of the data length. However, as the data length increases, how the maximum identification error probability (IEP) behaves for a given rate has not yet been characterized for list-decoding. In this letter, we investigate the reliability function of the system under fixed-size list-decoding, which is the optimal exponential behavior of the maximum IEP. We then use Arimoto's argument to analyze a lower bound on the maximum IEP with list-decoding when the rate exceeds the capacity, which leads to the strong converse theorem. All results are derived under the condition that an unknown individual need not be uniformly distributed and the identification process is done without the knowledge of the prior distribution.