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arXiv:2502.12047

Quantum Byzantine Multiple Access Channels

Minglai Cai, Christian Deppe

Published Feb 17, 2025• 0 citations
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Abstract

In communication theory, attacks like eavesdropping or jamming are typically assumed to occur at the channel level, while communication parties are expected to follow established protocols. But what happens if one of the parties turns malicious? In this work, we investigate a compelling scenario: a multiple-access channel with two transmitters and one receiver, where one transmitter deviates from the protocol and acts dishonestly. To address this challenge, we introduce the Byzantine multiple-access classical-quantum channel and derive an achievable communication rate for this adversarial setting.

DOI
10.48550/arxiv.2502.12047

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In communication theory, attacks like eavesdropping or jamming are typically assumed to occur at the channel level, while communication parties are expected to follow established protocols. But what happens if one of the parties turns malicious? In this work, we investigate a compelling scenario: a multiple-access channel with two transmitters and one receiver, where one transmitter deviates from the protocol and acts dishonestly. To address this challenge, we introduce the Byzantine multiple-access classical-quantum channel and derive an achievable communication rate for this adversarial setting.
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 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.
We study covert classical communication over a quantum multiple-access channel (MAC) with a helper. Specifically, we consider three transmitters, where one transmitter helps the other two transmitters communicate covertly with a receiver. We demonstrate the feasibility of achieving a positive covert rate over this channel and establish an achievable rate region. Our result recovers as a special case known results for classical communication over classical MACs with a degraded message set, classical communication over quantum MACs, and classical communication over MACs with a helper. To the best of our knowledge, our result is the first to achieve covert communication with positive rates over both classical and quantum MACs.
We investigate the security of generalized quantum multiple-access channels. We provide the formula for the achievable rate region of secure communication in the scenario of two senders and a single receiver. We explicitly specify a protocol for secure communication in this scenario, which employs superdense coding. The protocol is based on the distribution of a tripartite GHZ state. It allows for both symmetric and asymmetric key distribution whereby one of the senders can have twice the capacity of the other sender. We prove the security of the protocol against general quantum attacks, analyze different strategies of the eavesdropper and compute the key rate for a range of noisy quantum channels.
In this paper, we study the information-theoretic limits of oblivious transfer via noisy channels. We also investigate oblivious transfer over a noisy multiple-access channel with two non-colluding senders and a single receiver. The channel is modeled through correlations among the parties, who may be honest-but-curious or, in the case of the receiver, potentially malicious. We first revisit the information-theoretic limits of two-party oblivious transfer and then extend these results to the multiple-access setting. For honest-but-curious participants, we introduce a multiparty protocol that reduces a general multiple access channel to a suitable correlation model. In scenarios with a malicious receiver, we characterize an achievable oblivious transfer rate region.
We study quantum-state oblivious transfer over the quantum erasure channel under information-theoretic security guarantees. Specifically, Alice holds two quantum systems, Bob wishes to recover one of them, and the parties have access to independent channel uses and authenticated public classical communication, with no initial shared entanglement. We consider both honest-but-curious and malicious behavior. We establish finite-blocklength converse and achievability bounds, which match in the honest-but-curious setting. The malicious setting construction combines interactive hashing with tests of whether Bob received selected channel outputs, and distributes each input across several qubits so that erasures conceal an entire input from a dishonest receiver, even when the inputs are entangled with an external reference. We also derive fixed-error asymptotic expansions and show that both malicious and honest-but-curious settings have the same capacity.