  In this work, message authentication over noisy channels is studied. The
model developed in this paper is the authentication theory counterpart of
Wyner's wiretap channel model. Two types of opponent attacks, namely
impersonation attacks and substitution attacks, are investigated for both
single message and multiple message authentication scenarios. For each
scenario, information theoretic lower and upper bounds on the opponent's
success probability are derived. Remarkably, in both scenarios, lower and upper
bounds are shown to match, and hence the fundamental limit of message
authentication over noisy channels is fully characterized. The opponent's
success probability is further shown to be smaller than that derived in the
classic authentication model in which the channel is assumed to be noiseless.
These results rely on a proposed novel authentication scheme in which key
information is used to provide simultaneous protection again both types of
attacks.
