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IEEE Information Theory Workshop (ITW)

Capacity Region for Covert Secret Key Generation over Multiple Access Channels

Yingxin Zhang, Lin Zhou, Qiaosheng Eric Zhang

Published Sep 29, 2025• 1 citation
Publisher

Abstract

We study covert secret key generation over a binary-input two-user multiple access channel with one-way public discussion and derive bounds on the capacity region. Specifically, in this problem, there are three legitimate parties: Alice, Bob and Charlie. The goal is to allow Charlie to generate a secret key with Alice and another secret key with Bob, reliably, secretly and covertly. Reliability ensures that the key generated by Alice and Charlie is the same and the key generated by Bob and Charlie is the same. Secrecy ensures that the secret keys generated are only known to specific legitimate parties. Covertness ensures that the key generation process is undetectable by a warden Willie. As a corollary of our result, we establish bounds on the capacity region of wiretap secret key generation without the covertness constraint and discuss the impact of covertness. Our results generalize the point-to-point result of Tahmasbi and Bloch (TIFS 2020) to the setting of multiterminal communication.

DOI
10.1109/itw62417.2025.11240257

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We study covert secret key generation over a binary-input two-user multiple access channel with one-way public discussion and derive bounds on the capacity region. Specifically, in this problem, there are three legitimate parties: Alice, Bob and Charlie. The goal is to allow Charlie to generate a secret key with Alice and another secret key with Bob, reliably, secretly and covertly. Reliability ensures that the key generated by Alice and Charlie is the same and the key generated by Bob and Charlie is the same. Secrecy ensures that the secret keys generated are only known to specific legitimate parties. Covertness ensures that the key generation process is undetectable by a warden Willie. As a corollary of our result, we establish bounds on the capacity region of wiretap secret key generation without the covertness constraint and discuss the impact of covertness. Our results generalize the point-to-point result of Tahmasbi and Bloch (TIFS 2020) to the setting of multiterminal communication.
We study covert secret key generation over a binary-input two-user multiple access channel with one-way public discussion and derive bounds on the capacity region. Specifically, in this problem, there are three legitimate parties: Alice, Bob and Charlie. The goal is to allow Charlie to generate a secret key with Alice and another secret key with Bob, reliably, secretly and covertly. Reliability ensures that the key generated by Alice and Charlie is the same and the key generated by Bob and Charlie is the same. Secrecy ensures that the secret keys generated are only known to specific legitimate parties. Covertness ensures that the key generation process is undetectable by a warden Willie. As a corollary of our result, we establish bounds on the capacity region of wiretap secret key generation without the covertness constraint and discuss the impact of covertness. Our results generalize the point-to-point result of Tahmasbi and Bloch (TIFS 2020) to the setting of multiterminal communication.
We study covert secret key generation over a two-user multiple access channel with one-way public discussion and derive bounds on the capacity region. Specifically, in this problem, there are three legitimate parties: Alice, Bob and Charlie. The goal is to allow Charlie to generate a secret key with Alice and another secret key with Bob, reliably, secretly and covertly. Reliability ensures that the key generated by Alice and Charlie is the same and the key generated by Bob and Charlie is the same. Secrecy ensures that the secret keys generated are only known to specific legitimate parties. Covertness ensures that the key generation process is undetectable by a warden Willie. As a corollary of our result, we establish bounds on the capacity region of wiretap secret key generation without the covertness constraint and discuss the impact of covertness. Our results generalize the point-to-point result of Tahmasbi and Bloch (TIFS 2020) to the setting of multiterminal communication.
In this paper, the problem of simultaneously generating multiple keys over a cascade of a noiseless channel and a wiretap channel is considered. The problem consists of three legitimate parties (i.e., Alice, Bob, and Carol) and an eavesdropper (Eve), where Alice and Bob wish to agree with Carol on independent secret keys, both of which should be kept secret from Eve. Alice and Bob are connected via a noiseless channel, and Bob is connected with Carol via a wiretap channel, while there is no direct connection between Alice and Carol. To Alice and Carol, Bob acts as a relay. Under this model, a full characterization of the secret-key capacity region is provided for the case in which Eve has no side information. This result shows that there exists a tradeoff between the individual secret-key rates. Then, this result is generalized to the case in which Eve has side information, and the corresponding secret-key capacity region is fully characterized.
In this paper, the problem of simultaneously generating multiple keys in a model where the key generating parties have restricted access to public discussions is considered. The model consists of four terminals, i.e., Alice, Bob, Carol and Eve. Alice and Bob are connected via a noiseless channel while Bob connects with Carol and Eve via a wiretap channel. There is no direct link connecting Alice with Carol or Eve, and hence Carol and Eve cannot directly access the discussion between Alice and Bob. Alice wishes to share a secret key with Carol while Bob wishes to share another independent secret key with Carol. Under this model, inner and outer bounds on the secret-key capacity region are provided. It is shown that the two bounds match when a certain Markov chain relationship holds.
Shannon theoretic secret key generation by several parties is considered for models in which a secure noisy channel with multiple input and output terminals and a public noiseless channel of unlimited capacity are available for accomplishing this goal. The secret key is generated for a setAof terminals of the noisy channel, with the remaining terminals (if any) cooperating in this task through their public communication. Single-letter lower and upper bounds for secrecy capacities are obtained when secrecy is required from an eavesdropper that observes only the public communication and perhaps also a set of terminals disjoint fromA. These bounds coincide in special cases, but not in general. We also consider models in which different sets of terminals share multiple keys, one for the terminals in each set with secrecy required from the eavesdropper as well as from the terminals not in this set. Partial results include showing links among the associated secrecy capacity region for multiple keys, the transmission capacity region of the multiple access channel defined by the secure noisy channel, and achievable rates for a single secret key for all the terminals.
Shannon theoretic secret key generation by several parties is considered for models in which a secure noisy channel with multiple input and output terminals and a public noiseless channel of unlimited capacity are available for accomplishing this goal. The secret key is generated for a set A of terminals of the noisy channel, with the remaining terminals (if any) cooperating in this task through their public communication. Single-letter lower and upper bounds for secrecy capacities are obtained when secrecy is required from an eavesdropper that observes only the public communication and perhaps also a set of terminals disjoint from A. These bounds coincide in special cases, and the lower bounds are not tight in general. We also consider models in which different sets of terminals share multiple keys, one for terminals in each set with secrecy required from the eavesdropper as well as the remaining terminals in the other sets. Partial results include showing links among the associated secrecy capacity region for multiple keys, the transmission capacity region of the multiple access channel defined by the secure noisy channel, and achievable rates for a single secret key for all the terminals.