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Privacy, Secrecy, and Storage with Noisy Identifiers.

Onur Günlü, Gerhard G. Kramer

Published Jan 25, 2016• 4 citations
OpenAlex

Abstract

The key-leakage-storage capacity regions for a hidden identifier's noisy measurements at two terminals of a secrecy system are derived. The capacity regions of binary sources with multiple measurements are obtained by applying Mrs. Gerber's lemma twice in different directions to a Markov chain to show gains in privacy-leakage as compared to assuming a noise-free identifier at the encoder.

Related papers

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Onur Günlü, Gerhard G. Kramer

The key-leakage-storage region is derived for a generalization of a classic two-terminal key agreement model. The additions to the model are that the encoder observes a hidden, or noisy, version of the identifier, and that the encoder and decoder can perform multiple measurements. To illustrate the behavior of the region, the theory is applied to binary identifiers and noise modeled via binary symmetric channels. In particular, the key-leakage-storage region is simplified by applying Mrs. Gerber's lemma twice in different directions to a Markov chain. The growth in the region as the number of measurements increases is quantified. The amount by which the privacy-leakage rate reduces for a hidden identifier as compared to a noise-free (visible) identifier at the encoder is also given. If the encoder incorrectly models the source as visible, it is shown that substantial secrecy leakage may occur and the reliability of the reconstructed key might decrease.

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Multiple measurements of a physical or biometric identifier are used at the decoder of a secrecy system to improve the secret-key vs. privacy-leakage capacity region of the single-measurement case. The capacity regions of doubly symmetric binary sources with multiple measurements are derived by applying Mrs. Gerber's lemma to mixtures of binary channels.

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Key Agreement Using Physical Identifiers for Degraded and Less Noisy Authentication Channels

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arXiv:2205.05068•IEEE Information Theory Workshop (ITW)•Nov 1, 2022•3 citations
The key-leakage-storage capacity regions for a hidden identifier's noisy measurements at two terminals of a secrecy system are derived. The capacity regions of binary sources with multiple measurements are obtained by applying Mrs. Gerber's lemma twice in different directions to a Markov chain to show gains in privacy-leakage as compared to assuming a noise-free identifier at the encoder.
The key-leakage-storage region is derived for a generalization of a classic two-terminal key agreement model. The additions to the model are that the encoder observes a hidden, or noisy, version of the identifier, and that the encoder and decoder can perform multiple measurements. To illustrate the behavior of the region, the theory is applied to binary identifiers and noise modeled via binary symmetric channels. In particular, the key-leakage-storage region is simplified by applying Mrs. Gerber's lemma twice in different directions to a Markov chain. The growth in the region as the number of measurements increases is quantified. The amount by which the privacy-leakage rate reduces for a hidden identifier as compared to a noise-free (visible) identifier at the encoder is also given. If the encoder incorrectly models the source as visible, it is shown that substantial secrecy leakage may occur and the reliability of the reconstructed key might decrease.
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.
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.
The problem of secure source coding with multiple terminals is extended by considering a remote source whose noisy measurements are the correlated random variables used for secure source reconstruction. The main additions to the problem include 1) all terminals noncausally observe a noisy measurement of the remote source; 2) a private key is available to all legitimate terminals; 3) the public communication link between the encoder and decoder is rate-limited; and 4) the secrecy leakage to the eavesdropper is measured with respect to the encoder input, whereas the privacy leakage is measured with respect to the remote source. Exact rate regions are characterized for a lossy source coding problem with a private key, remote source, and decoder side information under security, privacy, communication, and distortion constraints. By replacing the distortion constraint with a reliability constraint, we obtain the exact rate region also for the lossless case. Furthermore, the lossy rate region for scalar discrete-time Gaussian sources and measurement channels is established.