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arXiv:1610.00384 · Allerton Conference on Communication, Control, and Computing

Covert single-hop communication in a wireless network with distributed artificial noise generation

Ramin Soltani, Boulat A. Bash, Dennis Goeckel, Saikat Guha, Don Towsley

Published Sep 1, 2014• 39 citations
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Abstract

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.

DOI
10.1109/allerton.2014.7028575

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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.
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.
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) bits in n channel uses. However, this assumes that 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 n, thus conveying O(n) bits covertly and reliably in n uses of an AWGN channel. Here, we consider covert communication of O(n) bits in n channel uses while generalizing the environment and removing any restrictions on Willie's receiver. We assume that 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 n even when Willie employs an optimal detector.
Covert communication has recently been recognized as a highly promising security technology that enables a transmitter Alice to reliably and covertly communicate with a receiver Bob without being detected by a malicious warden. Available works on covert communication mainly focus on scenarios with only one warden, while the fundamental limits of covert communication in more practical multi-warden scenarios remain largely unknown. This paper therefore investigates the fundamental limits of covert communication over an additive white Gaussian noise (AWGN) channel in the presence of multiple wardens. We first consider a scenario with two wardens and derive the maximum number of bits Alice can transmit to Bob over n channel uses while ensuring a negligible detection probability at wardens. We then generalize this result to the multi-warden case and find that the minimal power of wardens has impacts on the scaling law of the performance limits of covert communication over AWGN channels.
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.
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) bits in n channel uses. However, this result is predicated on Willie having an accurate statistical characterization of the background noise. When Willie has uncertainty about his noise characteristics and his receiver is limited to a power detector, O(n) bits can be covertly delivered. Here, we establish covert communication of O(n) bits in n channel uses while: (i) generalizing the environment; and (ii) removing any restrictions on Willie's receiver. We consider the case where an additional node, called the "jammer", is present to help Alice and Bob communicate covertly. This jammer is termed "uninformed", as it does not know the content or timing of Alice's transmission. We consider both AWGN channels and a scenario with a block faded jammer with a single fade per codeword. In these scenarios, we are able to establish the optimality of the power detector for Willie, from which the achievability of reliable and covert communication at a positive rate follows.
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.