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We investigate the fundamental limit of quantum-secure covert communication over the lossy thermal noise bosonic channel, the quantum-mechanical model underlying many practical channels. We assume that the adversary has unlimited quantum information processing capabilities as well as access to all transmitted photons that do not reach the legitimate receiver. Given existence of noise that is uncontrolled by the adversary, the square root law (SRL) governs covert communication: up to c√n covert bits can be transmitted reliably in n channel uses. Attempting to surpass this limit results in detection with unity probability as n → ∞. Here we present the expression for c, characterizing the SRL for the bosonic channel. We also prove that discrete-valued coherent state quadrature phase shift keying (QPSK) constellation achieves the optimal c, which is the same as that achieved by a circularly-symmetric complex-valued Gaussian prior on coherent state amplitude. Finally, while binary phase shift keying (BPSK) achieves the Holevo capacity for non-covert bosonic channels in the low received signal-to-noise ratio regime, we show that it is strictly sub-optimal for covert communication. [ABSTRACT FROM AUTHOR]

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 $\mathcal {O}(\sqrt {n})$ 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 $\mathcal {O}(\min \{{n,m^{\gamma /2}\sqrt {n}}\})$ bits to Bob in $n$ channel uses, where $\gamma $ is the path-loss exponent. We also consider a setting where there are $N_{\mathrm {w}}$ collaborating adversaries uniformly and randomly located in the environment and show that in $n$ channel uses, Alice can reliably and covertly send $\mathcal {O}(\min \{n,({m^{\gamma /2} \sqrt {n}}/{N_{\mathrm {w}}^{\gamma }})\})$ bits to Bob when $\gamma >2$ , and $\mathcal {O}(\min \{n,({m \sqrt {n}}/{N_{\mathrm {w}}^{2}\log ^{2} {N_{\mathrm {w}}}})\})$ when $\gamma = 2$. Conversely, we demonstrate that no higher covert throughput is possible for $\gamma >2$. [ABSTRACT FROM AUTHOR]

In covert communication, Alice tries to communicate with Bob without being detected by a warden Willie. When the distance between Alice and Bob becomes large compared with the distance between Alice and Willie(s), the performance of covert communication will be degraded. In this case, multi-hop message transmission via intermediate relays can help to improve the performance. Hence, in this paper, multi-hop covert communication over a moderate size network and in the presence of multiple collaborating Willies is considered. The relays can transmit covertly using either a single key for all relays or different independent keys at the relays. For each case, we develop efficient algorithms to find optimal paths with maximum throughput and minimum end-to-end delay between Alice and Bob. As expected, employing multiple hops significantly improves the ability to communicate covertly versus the case of a single-hop transmission. Furthermore, at the expense of more shared key bits, analytical results and numerical simulations demonstrate that the multi-hop covert communication with different independent keys at the relays has better performance than the multi-hop covert communication with a single key. [ABSTRACT FROM AUTHOR]

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 \mathcal O(\sqrt 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 \mathcal O(n) bits covertly and reliably in n uses of an AWGN channel. Here, we consider covert communication of \mathcal 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. [ABSTRACT FROM PUBLISHER]

The recent square root law (SRL) for covert communication demonstrates that Alice can reliably transmit \mathcal O(\sqrt n) bits to Bob in n uses of an additive white Gaussian noise (AWGN) channel while keeping ineffective any detector employed by the adversary; conversely, exceeding this limit either results in detection by the adversary with high probability or non-zero decoding error probability at Bob. This SRL is under the assumption that the adversary knows when Alice transmits (if she transmits); however, in many operational scenarios, he does not know this. Hence, here, we study the impact of the adversary’s ignorance of the time of the communication attempt. We employ a slotted AWGN channel model with T(n) slots each containing n symbol periods, where Alice may use a single slot out of T(n) . Provided that Alice’s slot selection is secret, the adversary needs to monitor all T(n) bits to Bob (but no more) while keeping the adversary’s detector ineffective. To achieve this gain over SRL, Bob does not have to know the time of transmission provided T(n)<2^c\mathrm{ Tn} , c\mathrm{ T}=\mathcal {O}(1) . [ABSTRACT FROM PUBLISHER]

If the warden Willie attempting to detect the transmission knows the statistics of his receiver noise, Alice can transmit no more than\mathcalO(\sqrtn) covert bits reliably to Bob in n channel uses of an AWGN channel. However, if Willie does not know his noise statistics exactly, Alice can covertly transmit \mathcal{O}(n) bits. In this letter, Willie lacks knowledge of his channel statistics but observes T(n)$ length-$n$ codeword slots, where some number may be used by Alice to attempt covert transmission. We show that Willie can often limit Alice to the same performance scaling as when he knows his channel statistics. [ABSTRACT FROM PUBLISHER]

Widely deployed encryption-based security prevents unauthorized decoding, but does not ensure undetectability of communication. However, covert, or low probability of detection/intercept communication is crucial in many scenarios ranging from covert military operations and the organization of social unrest, to privacy protection for users of wireless networks. In addition, encrypted data or even just the transmission of a signal can arouse suspicion, and even the most theoretically robust encryption can often be defeated by a determined adversary using non-computational methods such as side-channel analysis. Various covert communication techniques have been developed to address these concerns, including steganography for finite-alphabet noiseless applications and spread-spectrum systems for wireless communications. After reviewing these covert communication systems, this article discusses new results on the fundamental limits of their capabilities, and provides a vision for the future of such systems as well. [ABSTRACT FROM AUTHOR]

We present a square root limit on the amount of information transmitted reliably and with low probability of detection (LPD) over additive white Gaussian noise (AWGN) channels. Specifically, if the transmitter has AWGN channels to an intended receiver and a warden, both with non-zero noise power, we prove that o(\sqrtn) bits can be sent from the transmitter to the receiver in n channel uses while lower-bounding α+β≥1-ε for any ε>0, where α and β respectively denote the warden's probabilities of a false alarm when the sender is not transmitting and a missed detection when the sender is transmitting. Moreover, in most practical scenarios, a lower bound on the noise power on the channel between the transmitter and the warden is known and \mathcalO(\sqrtn) bits can be sent in n LPD channel uses. Conversely, attempting to transmit more than \mathcalO(\sqrtn) bits either results in detection by the warden with probability one or a non-zero probability of decoding error at the receiver as n→∞. [ABSTRACT FROM AUTHOR]

Computational encryption, information-theoretic secrecy and quantum cryptography offer progressively stronger security against unauthorized decoding of messages contained in communication transmissions. However, these approaches do not ensure stealth-that the mere presence of message-bearing transmissions be undetectable. We characterize the ultimate limit of how much data can be reliably and covertly communicated over the lossy thermal-noise bosonic channel (which models various practical communication channels). We show that whenever there is some channel noise that cannot in principle be controlled by an otherwise arbitrarily powerful adversary-for example, thermal noise from blackbody radiation-the number of reliably transmissible covert bits is at most proportional to the square root of the number of orthogonal modes (the time-bandwidth product) available in the transmission interval. We demonstrate this in a proof-of-principle experiment. Our result paves the way to realizing communications that are kept covert from an all-powerful quantum adversary. [ABSTRACT FROM AUTHOR]

In the diffraction-limited near-field propagation regime, free-space optical quantum key distribution (QKD) systems can employ multiple spatial modes to improve their key rate. This improvement can be effected by means of high-dimensional QKD or by spatial-mode multiplexing of independent QKD channels, with the latter, in general, offering higher key rates. Here, we theoretically analyze spatial-mode-multiplexed, decoy-state BB84 whose transmitter mode set is either a collection of phase-tilted, flat-top focused beams (FBs) or the Laguerre-Gaussian (LG) modes. Although for vacuum propagation the FBs suffer a QKD rate penalty relative to the LG modes, their potential ease of implementation make them an attractive alternative. Moreover, in the presence of turbulence, the FB modes may outperform the LG modes.