🤖 AI Summary
This work addresses the high computational complexity of characterizing the information-theoretic capacity region for biometric- or PUF-based key agreement protocols, where multiple auxiliary random variables are conventionally required. Focusing on degraded and less-noisy authentication channels, we establish—for the first time—a rigorous proof that a single auxiliary random variable suffices to fully characterize the joint capacity region of secret key rate, storage rate, and privacy leakage rate, thereby significantly simplifying the characterization and reducing computational overhead. Leveraging information-theoretic analysis, random coding constructions, and modeling of discrete and Gaussian sources, we derive closed-form expressions for the exact capacity regions under binary discrete and scalar Gaussian source models. The results provide computationally tractable and practically relevant information-theoretic performance bounds for secure authentication in resource-constrained devices.
📝 Abstract
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.
