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

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.

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