Message Authentication Code over a wiretap channel

Message Authentication Code (MAC) is a keyed function f
_K
such that when Alice, who shares the secret K with Bob, sends f
_K
(M) to the latter, Bob will be assured of the integrity and authenticity of M. Traditionally, it is assumed that the channel is noiseless. Unfortunately, Maurer showed that in this case an attacker can succeed with probability equation after authenticating ∓ messages, where H(K) is the entropy of K. In this paper, we consider the setting where the channel is noisy. Specifically, Alice and Bob are connected by a discrete memoryless channel (DMC) W
₁
and a noiseless but insecure channel. In addition, there is a DMC W
₂
between Alice and attacker Oscar. We regard the noisy channel as an expensive resource and define the authentication rate ρ
_auth
as the ratio of message length to the number n of channel W
₁
uses. The security of this model depends on the channel coding for f
_K
(M). A natural coding scheme is to use the secrecy capacity achieving code of Csiszár and Körner. Intuitively, this is also the optimal strategy. However, we propose a coding scheme that achieves a higher ρ
_auth
. Our crucial point is that under a secrecy capacity code, Bob can fully recover f
_K
(M) while in our model this is not necessary as we only need to detect the existence of the modification. How to detect the malicious modification without recovering f
_K
(M) is the main contribution of this work. We achieve this through random coding techniques.