  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 first of a two part study, with the parts differing in how the
authentication rate is measured. In this first study the authenticated rate is
measured by the traditional metric of the maximum expected probability of false
authentication. For this metric, we provide an inner bound which improves on
those existing in the literature. This is achieved by adopting and merging
different classical techniques in novel ways. Within these classical
techniques, one technique derives authentication capability directly from the
noisy communications channel, and the other technique derives its'
authentication capability directly from obscuring the source.
