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IEEE International Symposium on Information Theory (ISIT)

Multiple Access Channels with Adversarial Users

Neha Sangwan, Mayank Bakshi, Bikash Kumar Dey, Vinod M. Prabhakaran

Published Jul 1, 2019• 13 citations
Publisher

Abstract

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.

DOI
10.1109/isit.2019.8849729

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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.
We study communication over a Multiple Access Channel (MAC) where users can possibly be adversarial. The receiver is unaware of the identity of the adversarial users (if any). When all users are non-adversarial, we want their messages to be decoded reliably. When a user behaves adversarially, we require that the honest users’ messages be decoded reliably. An adversarial user can mount an attack by sending any input into the channel rather than following the protocol. It turns out that the 2-user MAC capacity region follows from the point-to-point Arbitrarily Varying Channel (AVC) capacity. For the 3-user MAC in which at most one user may be malicious, we characterize the capacity region for deterministic codes and randomized codes (where each user shares an independent random secret key with the receiver). These results are then generalized for thekkk-user MAC where the adversary may control all users in one out of a collection of given subsets.
We consider a scenario in which K transmitters attempt to communicate covert messages reliably to a legitimate receiver over a discrete memoryless multiple-access channel (MAC) while simultaneously escaping detection from an adversary who observes their communication through another discrete memoryless MAC. We assume that each transmitter may use a secret key that is shared only between itself and the legitimate receiver. We show that each of the K transmitters can transmit on the order of √n reliable and covert bits per n channel uses, exceeding which, the warden will be able to detect the communication. We identify the optimal pre-constants of the scaling, which leads to a complete characterization of the covert capacity region of the K-user binary-input MAC. We show that, asymptotically, all sum-rate constraints are inactive unlike the traditional MAC capacity region. We also characterize the channel conditions that have to be satisfied for the transmitters to operate without a secret key.
We consider a scenario in which two legitimate transmitters attempt to communicate with a legitimate receiver over a discrete memoryless Multiple-Access Channel (MAC), while escaping detection from an adversary who observes their communication through another discrete memoryless MAC. If the MAC to the legitimate receiver is “better” than the one to the adversary, in a sense that we make precise, then the legitimate users can reliably communicate on the order of √n bits per n channel uses with arbitrarily Low Probability of Detection (LPD) without using a secret key. We also identify the pre-constants of the scaling, which leads to a characterization of the covert capacity region.
In this paper, we present results on the authentication capacity region for the two-user arbitrarily-varying multipleaccess channel. We first consider a standard definition of authentication, in which the receiver may discard both messages if an adversary is detected. For this setting, we show that an extension of the arbitrarily-varying channel condition overwritability characterizes the authentication capacity region. We then define γ-correcting authentication, where we require that at least a γ fraction of the users' messages be correctable, even in the presence of an adversary. We give necessary conditions for the γ-correcting authentication capacity region to have nonempty interior, and show that positive rate pairs are achievable over a particular channel that satisfies these conditions.
We introduce the problem of determining the identity of a byzantine user (internal adversary) in a communication system. We consider a two-user discrete memoryless multiple access channel where either user may deviate from the prescribed behaviour. Owing to the noisy nature of the channel, it may be overly restrictive to attempt to detect all deviations. In our formulation, we only require detecting deviations which impede the decoding of the non-deviating user's message. When neither user deviates, correct decoding is required. When one user deviates, the decoder must either output a pair of messages of which the message of the non-deviating user is correct or identify the deviating user. The users and the receiver do not share any randomness. The results include a characterization of the set of channels where communication is feasible, and an inner and outer bound on the capacity region.
Keyless authentication is considered in an adversarial point-to-point channel. Namely, a legitimate transmitter and receiver aim to communicate over a noisy channel that may or may not also contain an active adversary, capable of transmitting an arbitrary signal into the channel. If the adversary is not present, then the receiver must successfully decode the message with high probability; if it is present, then the receiver must either decode the message or detect the adversary's presence. Thus, whenever the receiver decodes, it can be certain that the decoded message is authentic. The exact authentication capacity is characterized for discrete-memoryless adversary channels, where the adversary is assumed to know the code but not the message. The authentication capacity is shown to be either zero or equal to the no-adversary capacity, depending on whether the channel satisfies a condition termed overwritability.