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Secret-key agreement based on biometric or physical identifiers is apromising security protocol for authenticating users or devices with smallchips due to its lightweight security. In previous studies, the fundamentallimits of such a protocol were analyzed, and the results showed that twoauxiliary random variables were involved in the capacity region expressions.However, with these two auxiliary random variables, the complexity of computingthe capacity regions may be prohibitively high. To deal with this problem, weexplore classes of authentication channels that require only one auxiliaryrandom variable in the expressions of the capacity regions. It is revealed thatfor the classes of degraded and less noisy authentication channels, a singleauxiliary random variable is sufficient to express the capacity regions. Asspecific examples, we derive the closed-form expressions for binary andGaussian sources. Also, numerical calculations for Gaussian sources areprovided to show the trade-off between secret-key and privacy-leakage ratesunder a given storage rate, and to illustrate how the noise in the enrollmentphase affects the capacity region.

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