  Secret-key agreement based on biometric or physical identifiers is a
promising security protocol for authenticating users or devices with small
chips due to its lightweight security. In 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 these two auxiliary random variables, the complexity of computing
the capacity regions may be prohibitively high. To deal with this problem, we
explore classes of authentication channels that require only one auxiliary
random variable in the expressions of the capacity regions. It is revealed 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 derive the closed-form expressions for binary and
Gaussian sources. Also, numerical calculations for Gaussian sources are
provided to show the trade-off between secret-key and privacy-leakage rates
under a given storage rate, and to illustrate how the noise in the enrollment
phase affects the capacity region.
