  This paper investigates the secret key authentication capacity region.
Specifically, the focus is on a model where a source must transmit information
over an adversary controlled channel where the adversary, prior to the source's
transmission, decides whether or not to replace the destination's observation
with an arbitrary one of their choosing (done in hopes of having the
destination accept a false message). To combat the adversary, the source and
destination share a secret key which they may use to guarantee authenticated
communications. The secret key authentication capacity region here is then
defined as the region of jointly achievable message rate, authentication rate,
and key consumption rate (i.e., how many bits of secret key are needed).
  This is the second of a two part study, with the studies separated by how the
authentication rate is measured. Here, the authentication rate is measured by
the minimum of the maximum probability of false acceptance where the
minimization is over all highly probable subsets of observations at the
adversary. That is, consider the maximum probability of false authentication as
a function of the adversary's observation, and the adversary's observation as a
random variable. The authentication rate is then measured as the smallest
number for which the probability that the maximum probability of false
authentication is greater than said number is arbitrary small. This is termed
typical authentication, since it only needs to consider adversarial
observations which are typical with the transmission. Under this measure of
authentication matching inner and outer bounds are determined.
