Message Authentication Code over a Wiretap Channel

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Message Authentication Code (MAC) is a keyed function fₖ such that when Alice, who shares the secret K with Bob, sends fₖ(M) to the latter, Bob will be assured of the integrity and authenticity of M. Traditionally, it is assumed that the channel is noiseless. However, Maurer showed that in this case an attacker can succeed with probability 2⁻ʰ⁽ᵏ⁾/ℓ⁺¹ after authenticating ℓ messages. In this paper, we consider the setting where the channel is noisy. Specifically, Alice and Bob are connected by a discrete memoryless channel (DMC) W₁ and a noiseless but insecure channel. In addition, an attacker Oscar is connected with Alice through DMC W₂ and with Bob through a noiseless channel. In this setting, we study the framework that sends M over the noiseless channel and the traditional MAC fₖ(M) over channel (W₁, W₂). We regard the noisy channel as an expensive resource and define the authentication rate ρauth as the ratio of message length to the number n of channel W₁ uses. The security of this framework depends on the channel coding scheme for fₖ(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 ρauth. Our crucial point for this is that in the secrecy capacity setting, Bob needs to recover fₖ(M) while in our coding scheme this is not necessary. How to detect the attack without recovering fₖ(M) is the main contribution of this work. We achieve this through random coding techniques.