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arXiv:2202.10018 · IEEE International Symposium on Information Theory (ISIT)

Secret Key-based Authentication With Passive Eavesdropper for Scalar Gaussian Sources

Vamoua Yachongka, Hideki Yagi, Yasutada Oohama

Published Jun 26, 2022• 8 citations
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Abstract

We analyze the fundamental trade-off of secret key-based authentication systems in the presence of an eavesdropper for correlated Gaussian sources. A complete characterization of the trade-off among secret-key, storage, and privacy-leakage rates of both generated and chosen secret models is provided. One of the main contributions is revealing that unlike the known results for discrete sources, there is no need for the second auxiliary random variable in characterizing the capacity regions for the Gaussian cases. In addition, it is shown that the strong secrecy for secrecy-leakage of the systems can be achieved by an information-spectrum approach, and the parametric expressions (computable forms) of the capacity regions are also derived.

DOI
10.1109/isit50566.2022.9834725

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We analyze the fundamental trade-off of secret key-based authentication systems in the presence of an eavesdropper for correlated Gaussian sources. A complete characterization of the trade-off among secret-key, storage, and privacy-leakage rates of both generated and chosen secret models is provided. One of the main contributions is revealing that unlike the known results for discrete sources, there is no need for the second auxiliary random variable in characterizing the capacity regions for the Gaussian cases. In addition, it is shown that the strong secrecy for secrecy-leakage of the systems can be achieved by an information-spectrum approach, and the parametric expressions (computable forms) of the capacity regions are also derived.
In the present paper, we investigate the fundamental trade-off of identification, secrecy, storage, and privacy-leakage rates in biometric identification systems for hidden or remote Gaussian sources. We introduce a technique for deriving the capacity region of these rates by converting the system to one where the data flow is in one-way direction. Also, we provide numerical calculations of three different examples for the generated-secret model. The numerical results imply that it seems hard to achieve both high secrecy and small privacy-leakage rates simultaneously. In addition, as special cases, the characterization coincides with several known results in previous studies.
Secret-key agreement using physical identifiers is a promising security protocol for the authentication of users and devices with small chips, owing to its lightweight security. In the previous studies, the fundamental limits of such a protocol were analyzed, and the results showed that two auxiliary random variables were involved in the capacity region expressions. However, with two auxiliary random variables, it is difficult to directly apply the expressions to derive the computable forms of the capacity regions for certain information sources such as binary and Gaussian sources, which hold importance in practical applications. In this paper, we explore the structure of authentication channels and reveal that for the classes of degraded and less noisy authentication channels, a single auxiliary random variable is sufficient to express the capacity regions. As specific examples, we use the expressions with one auxiliary random variable to derive the computable forms for binary and Gaussian sources. Numerical calculations for the Gaussian case show the trade-off between secret-key and privacy-leakage rates under a given storage rate, which illustrates how the noise in the enrollment phase affects the capacity region.
Secret-key agreement based on biometric or physical identifiers is a promising security protocol for authenticating users or devices with small chips and has been extensively studied recently. Kittichokechai and Caire (2015) investigated the optimal trade-off in a secret-key agreement model with physical identifiers, where the structure of the authentication channels is similar to the wiretap channels, from information theoretic approaches. Later, the model was extended by Günlü et al. (2018) introducing noise in the enrollment phase and cost-constrained actions at the decoder. The results of these studies show that two auxiliary random variables are involved in the expressions of the optimal rate regions of secret-key, storage, and privacy-leakage rates. However, with these two auxiliary random variables, the complexity of computing the rate region may be prohibitively high. Due to this problem, we are interested in exploring classes of authentication channels that need only one auxiliary random variable in the capacity region expression for discrete source settings. The result shows for the class of degraded and less noisy authentication channels, a single auxiliary random variable is sufficient to express the capacity region of the model. As an example, we also derive the capacity region of secret-key, storage, and privacy-leakage rates for binary sources. Furthermore, the capacity region for scalar Gaussian sources is derived under Gaussian authentication channels.
This paper studies the Gaussian wiretap channel with correlated sources available not only at the transmitter and legitimate receiver, but also the eavesdropper. In particular, we are interested in the open problem of finding the optimal auxiliary random variable, which provides a closed-form solution to the secret-message and secret-key capacity region. To do that, we first take a deterministic approach and give a precise characterization of its secrecy capacity region. Then we translate the insights gained to the Gaussian case. As a result, we provide a sub-optimal solution by employing a specified Gaussian choice of the auxiliary random variable. This suggested choice is a compromise of keeping most source information subject to the constraint imposed by the channel capability of conducting source coding. Nevertheless, it is shown to be able to approach the secrecy capacity region within half a bit as the signal-noise-ratio of the main channel is no less than 1.
In the present paper, we investigate the fundamental trade-off of identification, secret-key, storage, and privacy-leakage rates in biometric identification systems for remote or hidden Gaussian sources. We use a technique of converting the system to one where the data flow is in one-way direction to derive the capacity region of these rates. Also, we provide numerical calculations of three different examples for the system. The numerical results imply that it seems hard to achieve both high secret-key and small privacy-leakage rates simultaneously.