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This paper investigates the secret key authentication capacity region.Specifically, the focus is on a model where a source must transmit informationover an adversary controlled channel where the adversary, prior to the source'stransmission, decides whether or not to replace the destination's observationwith an arbitrary one of their choosing (done in hopes of having thedestination accept a false message). To combat the adversary, the source anddestination share a secret key which they may use to guarantee authenticatedcommunications. The secret key authentication capacity region here is thendefined 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 theauthentication rate is measured. Here, the authentication rate is measured bythe minimum of the maximum probability of false acceptance where theminimization is over all highly probable subsets of observations at theadversary. That is, consider the maximum probability of false authentication asa function of the adversary's observation, and the adversary's observation as arandom variable. The authentication rate is then measured as the smallestnumber for which the probability that the maximum probability of falseauthentication is greater than said number is arbitrary small. This is termedtypical authentication, since it only needs to consider adversarialobservations which are typical with the transmission. Under this measure ofauthentication matching inner and outer bounds are determined.

Secret key authentication capacity region, Part II: typical authentication rate