Multiple Access Channels with Adversarial Users

We study authenticated communication over two-user multiple access channels (MAC) where one of the users is possibly adversarial. When both users behave non-adversarially, we want their messages to be decoded reliably. However, we also want to ensure that an adversarial user cannot cause an undetected error on the other (honest) user's message. We show that the following three-phase scheme is rate-optimal: a standard MAC code is first used to achieve unauthenticated communication; this is followed by two authentication phases where each user authenticates their message treating the other user as a possible adversary. We show that the authentication phases can be very short since this form of authentication itself, when possible, can be achieved for message sets whose size grow doubly exponentially in blocklength. This leads to our result that the authenticated communication capacity region of a discrete memoryless MAC is either zero or the (unauthenticated) MAC capacity region itself. This also, arguably, explains the similar nature of authenticated communication capacity of a discrete memoryless point-to-point adversarial channel recently found by Kosut and Kliewer (ITW, 2018). We also obtain analogous results for additive Gaussian noise channels.