This study investigates secret-key generation for device authentication using physical identifiers, such as responses from physical unclonable functions (PUFs). The system includes two legitimate terminals (encoder and decoder) and an eavesdropper (Eve), each with access to different measurements of the identifier. From the device identifier, the encoder generates a secret key, which is securely stored in a private database, along with helper data that is saved in a public database accessible by the decoder for key reconstruction. Eve, who also has access to the public database, may use both her own measurements and the helper data to attempt to estimate the secret key and identifier. Our setup focuses on authentication scenarios where channel statistics are uncertain, with the involved parties employing multiple antennas to enhance signal reception. Our contributions include deriving inner and outer bounds on the optimal trade-off among secret-key, storage, and privacy-leakage rates for general discrete sources, and showing that these bounds are tight for Gaussian sources.