On Message Authentication Channel Capacity Over a Wiretap Channel

In this paper, a novel message authentication model using the same key over wiretap channel is proposed to achieve
information-theoretic security
. Specifically, in the proposed model, there is a discrete memoryless channel
$W_{1}\!: \! \mathscr {X}\!\!\rightarrow \!\!{ \mathscr {Y}}$
between transmitter Alice and receiver Bob, while an attacker Oscar is connected with Alice via discrete memoryless channel
$W_{2}\!:\! \mathscr {X}\!\rightarrow \! { \mathscr {Z}}$
. Alice encodes message
$M$
to codeword
$(\!S,X^{n}\!)$
, using an encoding function with secret key
$K$
. Then,
$S$
is sent to Bob over a one-way noiseless channel (fully controlled by Oscar), and
$X^{n}$
is sent over the wiretap channel, say
${X}\!\rightarrow \!{(Y,Z)}$
. Building on this model, a new message authentication scheme is proposed. The scheme incorporates a secure channel coding, which uses random coding techniques to detect man-in-the-middle (MITM) attacks. The authentication channel capacity is studied in a specific channel model when
$W_{2}$
is not less noisy than
$W_{1}$
. We theoretically demonstrate that the authentication channel capacity is much larger than the secrecy capacity, since Bob does not need to recover information transmitted over the noisy channel.