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arXiv:1712.05099

The Sound and the Fury: Hiding Communications in Noisy Wireless Networks with Interference Uncertainty

Zhihong Liu, Jiajia Liu, Yong Zeng, Li Yang, Jianfeng Ma

Published Dec 14, 2017• 5 citations
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Abstract

Covert communication can prevent the adversary from knowing that a wireless transmission has occurred. In the additive white Gaussian noise channels, a square root law is obtained and the result shows that Alice can reliably and covertly transmit $\mathcal{O}(\sqrt{n})$ bits to Bob in $n$ channel uses. If additional "friendly" node near the adversary can inject artificial noise to aid Alice in hiding her transmission attempt, covert throughput can be improved, i.e., Alice can covertly transmit $\mathcal{O}(\min\{n,λ^{α/2}\sqrt{n}\})$ bits to Bob over $n$ uses of the channel ($λ$ is the density of friendly nodes and $α$ is the path loss exponent of wireless channels). In this paper, we consider the covert communication in a noisy wireless network, where Bob and the adversary Willie not only experience the background noise, but also the aggregated interference from other transmitters. Our results show that uncertainty in interference experienced by Willie is beneficial to Alice. When the distance between Alice and Willie $d_{a,w}=ω(n^{δ/4})$ ($δ=2/α$ is stability exponent), Alice can reliably and covertly transmit $\mathcal{O}(\log_2\sqrt{n})$ bits to Bob in $n$ channel uses. Although the covert throughput is lower than the square root law and the friendly jamming scheme, the spatial throughput is higher. From the network perspective, the communications are hidden in "the sound and the fury" of noisy wireless networks, and what Willie sees is merely a "shadow" wireless network. He knows for certain that some nodes are transmitting, but he cannot catch anyone red-handed.

DOI
10.48550/arxiv.1712.05099

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Covert communication can prevent the adversary from knowing that a wireless transmission has occurred. In the additive white Gaussian noise channels, a square root law is obtained and the result shows that Alice can reliably and covertly transmit O(n)\mathcal{O}(\sqrt{n})O(n​) bits to Bob in nnn channel uses. If additional "friendly" node near the adversary can inject artificial noise to aid Alice in hiding her transmission attempt, covert throughput can be improved, i.e., Alice can covertly transmit O(min⁡{n,λα/2n})\mathcal{O}(\min\{n,λ^{α/2}\sqrt{n}\})O(min{n,λα/2n​}) bits to Bob over nnn uses of the channel (λλλ is the density of friendly nodes and ααα is the path loss exponent of wireless channels). In this paper, we consider the covert communication in a noisy wireless network, where Bob and the adversary Willie not only experience the background noise, but also the aggregated interference from other transmitters. Our results show that uncertainty in interference experienced by Willie is beneficial to Alice. When the distance between Alice and Willie da,w=ω(nδ/4)d_{a,w}=ω(n^{δ/4})da,w​=ω(nδ/4) (δ=2/αδ=2/αδ=2/α is stability exponent), Alice can reliably and covertly transmit O(log⁡2n)\mathcal{O}(\log_2\sqrt{n})O(log2​n​) bits to Bob in nnn channel uses. Although the covert throughput is lower than the square root law and the friendly jamming scheme, the spatial throughput is higher. From the network perspective, the communications are hidden in "the sound and the fury" of noisy wireless networks, and what Willie sees is merely a "shadow" wireless network. He knows for certain that some nodes are transmitting, but he cannot catch anyone red-handed.
Covert communication can prevent an adversary from knowing that a wireless transmission has occurred. In additive white Gaussian noise (AWGN) channels, a square root law is found that Alice can reliably and covertly transmit O(n)\mathcal{O}(\sqrt{n})O(n​) bits to Bob in nnn channel uses. In this paper, we consider covert communications in noisy wireless networks, where the receivers not only experience the background noise, but also the aggregate interference from other transmitters. Our results show that uncertainty in interference experienced by the adversary Willie is beneficial to Alice. In AWGN channels, when the distance between Alice and Willie da,w=ω(n1/(2α))d_{a,w}=ω(n^{1/(2α)})da,w​=ω(n1/(2α)) (ααα is the path loss exponent), Alice can reliably and covertly transmit O(log⁡2n)\mathcal{O}(\log_2\sqrt{n})O(log2​n​) bits to Bob in nnn channel uses. Although the covert throughput is lower than the square root law, the spatial throughput is higher. In THz (Terahertz) Band networks,covert communication is more difficult because Willie can simply place a receiver in the narrow beam between Alice and Bob to detect or block their LOS (Line-of-Sight) communications. We then present a covert communication scheme that utilizes the reflection or diffuse scattering from a rough surface to prevent being detected by Willie. From the network perspective, the communications are hidden in the interference of noisy wireless networks, and what Willie sees is merely a "shadow" wireless network.
Covert communication conceals the transmission of the message from an attentive adversary. Recent work on the limits of covert communication in additive white Gaussian noise channels has demonstrated that a covert transmitter (Alice) can reliably transmit a maximum of O(√n) bits to a covert receiver (Bob) without being detected by an adversary (Warden Willie) in n channel uses. This paper focuses on the scenario where other “friendly” nodes distributed according to a two-dimensional Poisson point process with density m are present. We propose a strategy where the friendly node closest to the adversary, without close coordination with Alice, produces artificial noise. We show that this method allows Alice to reliably and covertly send O(min{n, mγ/2√n}) bits to Bob in n channel uses, where γ is the path-loss exponent. We also consider a setting where there are Nw collaborating adversaries uniformly and randomly located in the environment and show that in n channel uses, Alice can reliably and covertly send O(min{n, (mγ/2√n/Nwγ)}) bits to Bob when γ>2, and O(min{n, (m√n/Nw2log2Nw)}) when γ=2. Conversely, we demonstrate that no higher covert throughput is possible for γ>2.
Wireless channels are increasingly being used to transmit highly sensitive information in the Internet of Things. However, traditional cryptography methods cannot solve all security problems in IoT systems. Covert wireless communication can prevent an adversary from knowing the existence of a user's transmission; thus, it can provide stronger security protection for IoT devices. In this article, we consider the covert communication in a noisy wireless network, and find that the uncertainty of the aggregated interference experienced by the adversary is beneficial to the potential transmitters. From the network perspective, wireless communications can be hidden in the interference of the noisy wireless network, which the adversary observes as a "shadow" network to a certain extent. Furthermore, we discuss some new results on the effect of active eavesdropper. Square root law becomes invalid, and even jammer-assisted schemes have little effect on the covertness in the presence of active eavesdropper. Finally, we provide a vision for future research.
Covert communication can prevent the opponent from knowing that a wireless communication has occurred. If only the additive white Gaussian noise (AWGN) channels and ambient noise are taken into consideration, a square root law was obtained and the result shows that the privacy rate approaches zero asymptotically. In this paper, we consider the covert communication in large-scale wireless networks, where the transmitters form a stationary Poisson point process, and Alice wishes to communicate covertly to Bob without being detected by warden Dave. In this scenario, Bob and Dave not only experience the ambient noise, but also the aggregate interference simultaneously. Although the interference sources are not in collusion with Alice, and Bob's noise increases as well, our results show that, the measurement uncertainty of Dave will increase along with the increase of interference, and interference can indeed improve the performance of covert communication.
Covert wireless communication can prevent an adversary from knowing the existence of user's transmission, thus provide stronger security protection. In AWGN channels, a square root law was obtained and the result shows that Alice can reliably and covertly transmit O(n)\mathcal{O}(\sqrt{n})O(n​) bits to Bob in n channel uses in the presence of a passive eavesdropper (Willie). However, existing work presupposes that Willie is static and only samples the channels at a fixed place. If Willie can dynamically adjust the testing distance between him and Alice according to his sampling values, his detection probability of error can be reduced significantly via a trend test. We found that, if Alice has no prior knowledge about Willie, she cannot hide her transmission behavior in the presence of an active Willie, and the square root law does not hold in this situation. We then proposed a novel countermeasure to deal with the active Willie. Through randomized transmission scheduling, Willie cannot detect Alice's transmission attempts if Alice can set her transmission probability below a threshold. Additionally, we systematically evaluated the security properties of covert communications in a dense wireless network, and proposed a density-based routing scheme to deal with multi-hop covert communication in a wireless network. As the network grows denser, Willie's uncertainty increases, and finally resulting in a "shadow" network to Willie.
Covert communication, also known as low probability of detection (LPD) communication, prevents the adversary from knowing that a communication is taking place. Recent work has demonstrated that, in a three-party scenario with a transmitter (Alice), intended recipient (Bob), and adversary (Warden Willie), the maximum number of bits that can be transmitted reliably from Alice to Bob without detection by Willie, when additive white Gaussian noise (AWGN) channels exist between all parties, is on the order of the square root of the number of channel uses. In this paper, we begin consideration of network scenarios by studying the case where there are additional “friendly” nodes present in the environment that can produce artificial noise to aid in hiding the communication. We establish achievability results by considering constructions where the system node closest to the warden produces artificial noise and demonstrate a significant improvement in the throughput achieved covertly, without requiring close coordination between Alice and the noise-generating node. Conversely, under mild restrictions on the communication strategy, we demonstrate no higher covert throughput is possible. Extensions to the consideration of the achievable covert throughput when multiple wardens randomly located in the environment collaborate to attempt detection of the transmitter are also considered.