We analyze the problem of stealth communication and low probability of detection from the perspective of channel resolvability. We show that stealth communication over discrete memoryless channels and additive white Gaussian noise channels is possible without secret key as soon as the legitimate receiver's channel is “better” than the warden's channel, which generalizes previously known results to a much larger class of channels. The underlying technical problem that we solve is how to develop concentration inequalities for “low weight” sequences; the crux of our approach is to define modified “typical sets” that are amenable to concentration inequalities.
We analyze the problem of stealth communication and low probability of detection from the perspective of channel resolvability. We show that stealth communication over discrete memoryless channels and additive white Gaussian noise channels is possible without secret key as soon as the legitimate receiver's channel is “better” than the warden's channel, which generalizes previously known results to a much larger class of channels. The underlying technical problem that we solve is how to develop concentration inequalities for “low weight” sequences; the crux of our approach is to define modified “typical sets” that are amenable to concentration inequalities.
We consider the situation in which a transmitter attempts to communicate reliably over a discrete memoryless channel, while simultaneously ensuring covertness (low probability of detection) with respect to a warden, who observes the signals through another discrete memoryless channel. We develop a coding scheme based on the principle of channel resolvability, which generalizes and extends prior work in several directions. First, it shows that irrespective of the quality of the channels, it is possible to communicate on the order of √n reliable and covert bits over n channel uses if the transmitter and the receiver share on the order of √n key bits. This improves upon earlier results requiring on the order of √n log n key bits. Second, it proves that if the receiver's channel is better than the warden's channel in a sense that we make precise, it is possible to communicate on the order of √n reliable and covert bits over n channel uses without a secret key. This generalizes earlier results established for binary symmetric channels. We also identify the fundamental limits of covert and secret communications in terms of the optimal asymptotic scaling of the message size and key size, and we extend the analysis to Gaussian channels. The main technical problem that we address is how to develop concentration inequalities for low-weight sequences. The crux of our approach is to define suitably modified typical sets that are amenable to concentration inequalities.
Physical-layer security aims to exploit the randomness inherent in communication channels in order to guarantee confidentiality even against computationally unlimited attackers. In this thesis, we focus on covert communication, also known as “communication with low probability of detection”. This is a scenario where a transmitter and receiver try to prevent an eavesdropper from making a good guess on whether a communication is ongoing or not. We assume that the receiver and the eavesdropper share the same channel and therefore see the same outputs. In this scenario, the transmitter shares a key with the legitimate receiver to provide the necessary advantage to detect the communication and reliably decode the message. Asymptotically, the amount of information that can be sent reliably and covertly scales like the square root of the number of channel uses; this is known as the square root law of covert communication.We study the corresponding scaling constant of the square root law for general memoryless channels including non-Gaussian additive noise, as well as Gaussian channels with memory. In the latter case, we show that the scaling constant is the same as over the memoryless Gaussian channel. For continuous memoryless channels, under mild integrability conditions, we show that the scaling constant is upper bounded by a simple expression which only involves the variance of the logarithm of the probability density function of the noise. Moreover, we show that under some additional assumptions, this upper bound is tight. Furthermore, we provide upper bounds on the length of the secret key required to achieve covertness.The second objective of this work is to investigate the limits of covert communication over continuous memoryless channels in the finite blocklength regime. We provide bounds for the first and second-order asymptotics for covert communication over an AWGN channel under a maximal error probability criterion and for the first-order asymptotics under an average error probability criterion.
We consider the problem of covert communication over a state-dependent channel, where the transmitter has non-causal knowledge of the channel states. Here, “covert” means that the probability that a warden on the channel can detect the communication must be small. In contrast with traditional models without noncausal channel-state information at the transmitter, we show that covert communication can be possible with positive rate. We derive closed-form formulas for the maximum achievable covert communication rate (“covert capacity”) in this setting for discrete memoryless channels as well as additive white Gaussian noise channels. We also derive lower bounds on the rate of the secret key that is needed for the transmitter and the receiver to achieve the covert capacity.
We consider a scenario in which two legitimate transmitters attempt to communicate with a legitimate receiver over a discrete memoryless Multiple-Access Channel (MAC), while escaping detection from an adversary who observes their communication through another discrete memoryless MAC. If the MAC to the legitimate receiver is “better” than the one to the adversary, in a sense that we make precise, then the legitimate users can reliably communicate on the order of √n bits per n channel uses with arbitrarily Low Probability of Detection (LPD) without using a secret key. We also identify the pre-constants of the scaling, which leads to a characterization of the covert capacity region.
This paper considers the problem of communication over a discrete memoryless channel (DMC) or an additive white Gaussian noise (AWGN) channel subject to the constraint that the probability that an adversary who observes the channel outputs can detect the communication is low. In particular, the relative entropy between the output distributions when a codeword is transmitted and when no input is provided to the channel must be sufficiently small. For a DMC whose output distribution induced by the “off” input symbol is not a mixture of the output distributions induced by other input symbols, it is shown that the maximum amount of information that can be transmitted under this criterion scales like the square root of the blocklength. The same is true for the AWGN channel. Exact expressions for the scaling constant are also derived.
To conceal the behavior of communications, we may adopt covert or stealthy communications under different scenarios and demands. However, when legitimate users have worse channels than the eavesdropper, the legitimate users may need additional keys to attain the concealment. Normal secret key generation (SKG) schemes may raise Willie's attention due to the public discussion breaking the concealment. Therefore, in this work, we investigate how to conceal the SKG itself, especially according to the stealth constraint. We prove that if the virtual channel between the common random source observed by the legitimate Alice and Bob, namely, X and Y, respectively, is more capable than that between Bob and Willie (the warden), namely, Y and Z, respectively, the same stealthy SK rate as in the case without stealth constraint can be achieved. Furthermore, if (X, Y, Z) form a Markov chain, then the key capacity of the SKG with the stealth constraint can be achieved for free.