arXiv subjects

Dennis Goeckel

Publications and source records attributed to Dennis Goeckel.

36 records · Page 2Linked to original sources

arXiv2017

Covert Communications on Renewal Packet Channels

Security and privacy are major concerns in modern communication networks. In recent years, the information theory of covert communications, where the very presence of the communication is undetectable to a watchful and determined adversary, has been of great interest. This emerging body of work has focused on additive white Gaussian noise (AWGN), discrete memoryless channels (DMCs), and optical channels. In contrast, our recent work introduced the information-theoretic limits for covert communications over packet channels whose packet timings are governed by a Poisson point process. However, actual network packet arrival times do not generally conform to the Poisson process assumption, and thus here we consider the extension of our work to timing channels characterized by more general renewal processes of rate $λ$. We consider two scenarios. In the first scenario, the source of the packets on the channel cannot be authenticated by Willie, and therefore Alice can insert packets into the channel. We show that if the total number of transmitted packets by Jack is $N$, Alice can covertly insert $\mathcal{O}\left(\sqrt{N}\right)$ packets and, if she transmits more, she will be detected by Willie. In the second scenario, packets are authenticated by Willie but we assume that Alice and Bob share a secret key; hence, Alice alters the timings of the packets according to a pre-shared codebook with Bob to send information to him over a $G/M/1$ queue with service rate $μ>λ$. We show that Alice can covertly and reliably transmit $\mathcal{O}(N)$ bits to Bob when the total number of packets sent from Jack to Steve is $N$.

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arXiv2017

Covert Single-hop Communication in a Wireless Network with Distributed Artificial Noise Generation

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.

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arXiv2017

Covert Communications on Poisson Packet Channels

Consider a channel where authorized transmitter Jack sends packets to authorized receiver Steve according to a Poisson process with rate $λ$ packets per second for a time period $T$. Suppose that covert transmitter Alice wishes to communicate information to covert receiver Bob on the same channel without being detected by a watchful adversary Willie. We consider two scenarios. In the first scenario, we assume that warden Willie cannot look at packet contents but rather can only observe packet timings, and Alice must send information by inserting her own packets into the channel. We show that the number of packets that Alice can covertly transmit to Bob is on the order of the square root of the number of packets that Jack transmits to Steve; conversely, if Alice transmits more than that, she will be detected by Willie with high probability. In the second scenario, we assume that Willie can look at packet contents but that Alice can communicate across an $M/M/1$ queue to Bob by altering the timings of the packets going from Jack to Steve. First, Alice builds a codebook, with each codeword consisting of a sequence of packet timings to be employed for conveying the information associated with that codeword. However, to successfully employ this codebook, Alice must always have a packet to send at the appropriate time. Hence, leveraging our result from the first scenario, we propose a construction where Alice covertly slows down the packet stream so as to buffer packets to use during a succeeding codeword transmission phase. Using this approach, Alice can covertly and reliably transmit $\mathcal{O}(λT)$ covert bits to Bob in time period $T$ over an $M/M/1$ queue with service rate $μ> λ$.

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arXiv2017

Covert Communication in the Presence of an Uninformed Jammer

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 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 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.

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arXiv2017

Energy-Efficient Secrecy in Wireless Networks Based on Random Jamming

This paper considers secure energy-efficient routing in the presence of multiple passive eavesdroppers. Previous work in this area has considered secure routing assuming probabilistic or exact knowledge of the location and channel-state-information (CSI) of each eavesdropper. In wireless networks, however, the locations and CSIs of passive eavesdroppers are not known, making it challenging to guarantee secrecy for any routing algorithm. We develop an efficient (in terms of energy consumption and computational complexity) routing algorithm that does not rely on any information about the locations and CSIs of the eavesdroppers. Our algorithm guarantees secrecy even in disadvantaged wireless environments, where multiple eavesdroppers try to eavesdrop each message, are equipped with directional antennas, or can get arbitrarily close to the transmitter. The key is to employ additive random jamming to exploit inherent non-idealities of the eavesdropper's receiver, which makes the eavesdroppers incapable of recording the messages. We have simulated our proposed algorithm and compared it with existing secrecy routing algorithms in both single-hop and multi-hop networks. Our results indicate that when the uncertainty in the locations of eavesdroppers is high and/or in disadvantaged wireless environments, our algorithm outperforms existing algorithms in terms of energy consumption and secrecy.

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arXiv2017

Optimal Dynamic Routing for the Wireless Relay Channel

Consider a communication network with a source, a relay and a destination. Each time interval, the source may dynamically choose between a few possible coding schemes, based on the channel state, traffic pattern and its own queue status. For example, the source may choose between a direct route to the destination and a relay-assisted scheme. Clearly, due to the difference in the performance achieved, as well as the resources each scheme uses, a sender might wish to choose the most appropriate one based on its status. In this work, we formulate the problem as a Semi-Markov Decision Process. This formulation allows us to find an optimal policy, expressed as a function of the number of packets in the source queue and other parameters. In particular, we show a general solution which covers various configurations, including different packet size distributions and varying channels. Furthermore, for the case of exponential transmission times, we analytically prove the optimal policy has a threshold structure, that is, there is a unique value of a single parameter which determines which scheme (or route) is optimal. Results are also validated with simulations for several interesting models.

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arXiv2017

An SMDP Approach to Optimal PHY Configuration in Wireless Networks

In this work, we study the optimal configuration of the physical layer in wireless networks by means of Semi-Markov Decision Process (SMDP) modeling. In particular, assume the physical layer is characterized by a set of potential operating points, with each point corresponding to a rate and reliability pair; for example, these pairs might be obtained through a now-standard diversity-vs-multiplexing tradeoff characterization. Given the current network state (e.g., buffer occupancies), a Decision Maker (DM) needs to dynamically decide which operating point to use. The SMDP problem formulation allows us to choose from these pairs an optimal selection, which is expressed by a decision rule as a function of the number of awaiting packets in the source's finite queue, channel state, size of the packet to be transmitted. We derive a general solution which covers various model configurations, including packet size distributions and varying channels. For the specific case of exponential transmission time, we analytically prove the optimal policy has a threshold structure. Numerical results validate this finding, as well as depict muti-threshold policies for time varying channels such as the Gilber-Elliott channel.

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arXiv2016

Covert Communication Gains from Adversary's Ignorance of Transmission Time

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 $T(n)$ slots for possible transmission. We show that this allows Alice to reliably transmit $\mathcal{O}(\min\{\sqrt{n\log T(n)},n\})$ 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 $T(n)<2^{c_{\rm T}n}$, $c_{\rm T}=\mathcal{O}(1)$.

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arXiv2016

Energy-Efficient Routing in Wireless Networks in the Presence of Jamming

The effectiveness and simple implementation of physical layer jammers make them an essential threat for wireless networks. In a multihop wireless network, where jammers can interfere with the transmission of user messages at intermediate nodes along the path, one can employ jamming oblivious routing and then employ physical-layer techniques (e.g. spread spectrum) to suppress jamming. However, whereas these approaches can provide significant gains, the residual jamming can still severely limit system performance. This motivates the consideration of routing approaches that account for the differences in the jamming environment between different paths. First, we take a straightforward approach where an equal outage probability is allocated to each link along a path and develop a minimum energy routing solution. Next, we demonstrate the shortcomings of this approach and then consider the joint problem of outage allocation and routing by employing an approximation to the link outage probability. This yields an efficient and effective routing algorithm that only requires knowledge of the measured jamming at each node. Numerical results demonstrate that the amount of energy saved by the proposed methods with respect to a standard minimum energy routing algorithm, especially for parameters appropriate for terrestrial wireless networks, is substantial.

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arXiv2015

Hiding Information in Noise: Fundamental Limits of Covert Wireless Communication

Widely-deployed encryption-based security prevents unauthorized decoding, but does not ensure undetectability of communication. However, covert, or low probability of detection/intercept (LPD/LPI) 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 were 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, as well as provides a vision for the future of such systems.

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arXiv2014

Jamming Based on an Ephemeral Key to Obtain Everlasting Security in Wireless Environments

Secure communication over a wiretap channel is considered in the disadvantaged wireless environment, where the eavesdropper channel is (possibly much) better than the main channel. We present a method to exploit inherent vulnerabilities of the eavesdropper's receiver to obtain everlasting secrecy. Based on an ephemeral cryptographic key pre-shared between the transmitter Alice and the intended recipient Bob, a random jamming signal is added to each symbol. Bob can subtract the jamming signal before recording the signal, while the eavesdropper Eve is forced to perform these non-commutative operations in the opposite order. Thus, information-theoretic secrecy can be obtained, hence achieving the goal of converting the vulnerable "cheap" cryptographic secret key bits into "valuable" information-theoretic (i.e. everlasting) secure bits. We evaluate the achievable secrecy rates for different settings, and show that, even when the eavesdropper has perfect access to the output of the transmitter (albeit through an imperfect analog-to-digital converter), the method can still achieve a positive secrecy rate. Next we consider a wideband system, where Alice and Bob perform frequency hopping in addition to adding the random jamming to the signal, and we show the utility of such an approach even in the face of substantial eavesdropper hardware capabilities.

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arXiv2014

Covert Optical Communication

Encryption prevents unauthorized decoding, but does not ensure stealth---a security demand that a mere presence of a message be undetectable. We characterize the ultimate limit of covert communication that is secure against the most powerful physically-permissible adversary. We show that, although it is impossible over a pure-loss channel, covert communication is attainable in the presence of any excess noise, such as a $300$K thermal blackbody. In this case, $\mathcal{O}(\sqrt{n})$ bits can be transmitted reliably and covertly in $n$ optical modes using standard optical communication equipment. The all-powerful adversary may intercept all transmitted photons not received by the intended receiver, and employ arbitrary quantum memory and measurements. Conversely, we show that this square root scaling cannot be outperformed. We corroborate our theory in a proof-of-concept experiment. We believe that our findings will enable practical realizations of covert communication and sensing, both for point-to-point and networked scenarios.

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arXiv2014

Quantum-noise limited communication with low probability of detection

We demonstrate the achievability of a square root limit on the amount of information transmitted reliably and with low probability of detection (LPD) over the single-mode lossy bosonic channel if either the eavesdropper's measurements or the channel itself is subject to the slightest amount of excess noise. Specifically, Alice can transmit $\mathcal{O}(\sqrt{n})$ bits to Bob over $n$ channel uses such that Bob's average codeword error probability is upper-bounded by an arbitrarily small $δ>0$ while a passive eavesdropper, Warden Willie, who is assumed to be able to collect all the transmitted photons that do not reach Bob, has an average probability of detection error that is lower-bounded by $1/2-ε$ for an arbitrarily small $ε>0$. We analyze the thermal noise and pure loss channels. The square root law holds for the thermal noise channel even if Willie employs a quantum-optimal measurement, while Bob is equipped with a standard coherent detection receiver. We also show that LPD communication is not possible on the pure loss channel. However, this result assumes Willie to possess an ideal receiver that is not subject to excess noise. If Willie is restricted to a practical receiver with a non-zero dark current, the square root law is achievable on the pure loss channel.

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arXiv2013

Everlasting Secrecy by Exploiting Non-Idealities of the Eavesdropper's Receiver

Secure communication over a memoryless wiretap channel in the presence of a passive eavesdropper is considered. Traditional information-theoretic security methods require an advantage for the main channel over the eavesdropper channel to achieve a positive secrecy rate, which in general cannot be guaranteed in wireless systems. Here, we exploit the non-linear conversion operation in the eavesdropper's receiver to obtain the desired advantage - even when the eavesdropper has perfect access to the transmitted signal at the input to their receiver. The basic idea is to employ an ephemeral cryptographic key to force the eavesdropper to conduct two operations, at least one of which is non-linear, in a different order than the desired recipient. Since non-linear operations are not necessarily commutative, the desired advantage can be obtained and information-theoretic secrecy achieved even if the eavesdropper is given the cryptographic key immediately upon transmission completion. In essence, the lack of knowledge of the key during the short transmission time inhibits the recording of the signal in such a way that the secret information can never be extracted from it. The achievable secrecy rates for different countermeasures that the eavesdropper might employ are evaluated. It is shown that even in the case of an eavesdropper with uniformly better conditions (channel and receiver quality) than the intended recipient, a positive secure rate can be achieved.

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arXiv2013

Efficient Wireless Security Through Jamming, Coding and Routing

There is a rich recent literature on how to assist secure communication between a single transmitter and receiver at the physical layer of wireless networks through techniques such as cooperative jamming. In this paper, we consider how these single-hop physical layer security techniques can be extended to multi-hop wireless networks and show how to augment physical layer security techniques with higher layer network mechanisms such as coding and routing. Specifically, we consider the secure minimum energy routing problem, in which the objective is to compute a minimum energy path between two network nodes subject to constraints on the end-to-end communication secrecy and goodput over the path. This problem is formulated as a constrained optimization of transmission power and link selection, which is proved to be NP-hard. Nevertheless, we show that efficient algorithms exist to compute both exact and approximate solutions for the problem. In particular, we develop an exact solution of pseudo-polynomial complexity, as well as an epsilon-optimal approximation of polynomial complexity. Simulation results are also provided to show the utility of our algorithms and quantify their energy savings compared to a combination of (standard) security-agnostic minimum energy routing and physical layer security. In the simulated scenarios, we observe that, by jointly optimizing link selection at the network layer and cooperative jamming at the physical layer, our algorithms reduce the network energy consumption by half.

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arXiv2013

Limits of Reliable Communication with Low Probability of Detection on AWGN Channels

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 $o(\sqrt{n})$ bits can be sent from the transmitter to the receiver in $n$ channel uses while lower-bounding $α+β\geq1-ε$ 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 $O(\sqrt{n})$ bits can be sent in $n$ LPD channel uses. Conversely, attempting to transmit more than $O(\sqrt{n})$ bits either results in detection by the warden with probability one or a non-zero probability of decoding error at the receiver as $n\rightarrow\infty$.

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arXiv2013

Asymptotic Optimality of Equal Power Allocation for Linear Estimation of WSS Random Processes

This letter establishes the asymptotic optimality of equal power allocation for measurements of a continuous wide-sense stationary (WSS) random process with a square-integrable autocorrelation function when linear estimation is used on equally-spaced measurements with periodicity meeting the Nyquist criterion and with the variance of the noise on any sample inversely proportional to the power expended by the user to obtain that measurement.

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arXiv2011

Broadcast Analysis for Large Cooperative Wireless Networks

The capability of nodes to broadcast their message to the entire wireless network when nodes employ cooperation is considered. We employ an asymptotic analysis using an extended random network setting and show that the broadcast performance strongly depends on the path loss exponent of the medium. In particular, as the size of the random network grows, the probability of broadcast in a one-dimensional network goes to zero for path loss exponents larger than one, and goes to a nonzero value for path loss exponents less than one. In two-dimensional networks, the same behavior is observed for path loss exponents above and below two, respectively.

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