Reliable, Deniable, and Hidable Communication over Multipath Networks

We consider the scenario wherein Alice wants to (potentially) communicate to the intended receiver Bob over a network consisting of multiple parallel links in the presence of a passive eavesdropper Willie, who observes an unknown subset of links. A primary goal of our communication protocol is to make the communication "deniable", {\it i.e.}, Willie should not be able to {\it reliably} estimate whether or not Alice is transmitting any {\it covert} information to Bob. Moreover, if Alice is indeed actively communicating, her covert messages should be information-theoretically "hidable" in the sense that Willie's observations should not {\it leak any information} about Alice's (potential) message to Bob -- our notion of hidability is slightly stronger than the notion of information-theoretic strong secrecy well-studied in the literature, and may be of independent interest. It can be shown that deniability does not imply either hidability or (weak or strong) information-theoretic secrecy; nor does any form of information-theoretic secrecy imply deniability. We present matching inner and outer bounds on the capacity for deniable and hidable communication over {\it multipath networks}.Comment: 26 pages, 4 figures; Extended version of the paper submitted for ISIT 201

Anonymity Mixes as (Partial) Assembly Queues: Modeling and Analysis

Anonymity platforms route the traffic over a network of special routers that are known as mixes and implement various traffic disruption techniques to hide the communicating users' identities. Batch mixes in particular anonymize communicating peers by allowing message exchange to take place only after a sufficient number of messages (a batch) accumulate, thus introducing delay. We introduce a queueing model for batch mix and study its delay properties. Our analysis shows that delay of a batch mix grows quickly as the batch size gets close to the number of senders connected to the mix. We then propose a randomized batch mixing strategy and show that it achieves much better delay scaling in terms of the batch size. However, randomization is shown to reduce the anonymity preserving capabilities of the mix. We also observe that queueing models are particularly useful to study anonymity metrics that are more practically relevant such as the time-to-deanonymize metric.Comment: IEEE Information Theory Workshop, 201

Stealthy Communication over Adversarially Jammed Multipath Networks

We consider the problem of stealthy communication over a multipath network in the presence of an active adversary. The multipath network consists of multiple parallel noiseless links, and the adversary is able to eavesdrop and jam a subset of links. We consider two types of jamming---erasure jamming and overwrite jamming. We require the communication to be both stealthy and reliable, i.e., the adversary should be unable to detect whether or not meaningful communication is taking place, while the legitimate receiver should reconstruct any potential messages from the transmitter with high probability simultaneously. We provide inner bounds on the stealthy capacities under both adversarial erasure and adversarial overwrite jamming.Comment: To appear in the IEEE Transactions on Communication

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 $T(n)<2^{c_{\rm T}n}$, $c_{\rm T}=\mathcal{O}(1)$.Comment: v2: updated references/discussion of steganography, no change in results; v3: significant update, includes new theorem 1.2; v4 and v5: fixed minor technical issue

Covert Wireless Communication with Artificial Noise Generation

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 (AWGN) channels has demonstrated that a covert transmitter (Alice) can reliably transmit a maximum of $\mathcal{O}\left(\sqrt{n}\right)$ 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 in the environment. 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. Moreover, 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 $\mathcal{O}\left(\min\left\{n,\frac{m^{\gamma/2} \sqrt{n}}{N_{\mathrm{w}}^{\gamma}}\right\}\right)$ bits to Bob when $\gamma >2$, and $\mathcal{O}\left(\min\left\{n,\frac{m \sqrt{n}}{N_{\mathrm{w}}^{2}\log^2 {N_{\mathrm{w}}}}\right\}\right)$ when $\gamma = 2$. Conversely, we demonstrate that no higher covert throughput is possible for $\gamma>2$