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arXiv:1909.12752

Hiding Communications in AWGN Channels and THz Band with Interference Uncertainty

Zhihong Liu, Jiajia Liu, Yong Zeng, Jianfeng Ma

Published Sep 26, 2019• 0 citations
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Abstract

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 $\mathcal{O}(\sqrt{n})$ bits to Bob in $n$ 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 $d_{a,w}=ω(n^{1/(2α)})$ ($α$ is the path loss 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, 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.

DOI
10.48550/arxiv.1909.12752

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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 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 transmission has occurred between two users. In this article, we consider covert wireless communications in an Internet-of-Things (IoT) network with dense deployment, where an IoT device experiences not only the background noise but also the aggregates interference from other Tx devices. Our results show that in a dense IoT network with lower frequency AWGN channels, when the distance between Alice and the adversary Willie da,w= ω(n1/(2α)), Alice can reliably and covertly transmit O(log2√n) bits to Bob in n channel uses. In an IoT network with terahertz (THz) band, covert communication is more difficult because Willie can simply place a receiver in the narrow beam between Alice and Bob in order to detect or block their line-of-sight communications. We demonstrated that covert communication is still possible in this occasion by utilizing the reflection or diffuse scattering from a rough surface. From the physical-layer security perspective, covert communication can enhance the security of IoT network from the bottom layer.
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.
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.
Recent work has established that when transmitter Alice wishes to communicate reliably to recipient Bob without detection by warden Willie, with additive white Gaussian noise (AWGN) channels between all parties, communication is limited to O(n)\mathcal{O}(\sqrt{n})O(n​) bits in nnn channel uses. However, this assumes Willie has an accurate statistical characterization of the channel. When Willie has uncertainty about such and his receiver is limited to a threshold test on the received power, Alice can transmit covertly with a power that does not decrease with nnn, thus conveying O(n)\mathcal{O}(n)O(n) bits covertly and reliably in nnn uses of an AWGN channel. Here, we consider covert communication of O(n)\mathcal{O}(n)O(n) bits in nnn channel uses while generalizing the environment and removing any restrictions on Willie's receiver. We assume an uninformed "jammer" is present to help Alice, and we consider AWGN and block fading channels. In some scenarios, Willie's optimal detector is a threshold test on the received power. When the channel between the jammer and Willie has multiple fading blocks per codeword, a threshold test on the received power is not optimal. However, we establish that Alice can remain covert with a transmit power that does not decrease with nnn even when Willie employs an optimal detector.