  We study the fundamental limits of biometric identification systems with
chosen secret from an information theoretic perspective. Ignatenko and Willems
(2015) characterized the capacity region of identification, secrecy, and
privacy-leakage rates of the system provided that the enrollment channel is
noiseless. In the enrollment process, however, it is highly considered that
noise occurs when bio-data is scanned. Recently, Yachongka and Yagi (2019)
characterized the capacity region of the system with generated secret
considering noisy enrollment and template constraint. In this paper, we are
interested in characterizing the capacity region of identification, secrecy,
template, and privacy-leakage rates of the system with chosen secret under the
same settings as Yachongka and Yagi (2019). As special cases, the obtained
result shows that the characterization reduces to the one given by Ignatenko
and Willems (2015) where the enrollment channel is noiseless and there is no
constraint on the template rate, and it also coincides with the result derived
by G\"unl\"u and Kramer (2018) where there is only one individual.
