Secure Degrees Of Freedom Research Articles

A Full-Duplex Bob in the MIMO Gaussian Wiretap Channel: Scheme and Performance

This letter considers secrecy communication from an information-theoretic perspective, and studies the secrecy capacity of a multi-input multi-output (MIMO) Gaussian wiretap channel with a source (Alice), an eavesdropper (Eve) and a Full-Duplex (FD) legitimate receiver (Bob). Bob can allocate part of his antennas to transmit jamming signals to impair Eve’s channel. Our goal is to identify the secrecy capacity behavior in the high signal-to-noise ratio (SNR) regimes, i.e., the maximal achievable secure degrees of freedom (S.D.o.F). Such S.D.o.F maximization is generally difficult to solve since it requires to face a nonlinear fractional problem. To deal with this issue, we first propose a cooperative secrecy transmission scheme, and prove its optimality in the sense of achieving the maximal S.D.o.F.. By studying this proposed transmission scheme, we obtain the maximal achievable S.D.o.F. in closed form for any given antenna allocation at Bob. Based on this closed-form result, we further analytically derive the optimal antenna allocation at Bob. To the best of our knowledge, this is the first time that the benefit brought by using the FD jamming Bob has been quantified.

The Gaussian Diamond-Wiretap Channel with Conferencing Relays

In this letter, we consider the Gaussian diamond-wiretap channel with conferencing links between relays for the following three cases: 1) both conferencing links are confidential; 2) both conferencing links are public; and 3) one conferencing link is confidential, the other link is public, and the legitimate parties do not know which link is confidential or public. For all the cases, we establish the exact secure degrees of freedom (d.o.f.). Our results show that if at least one of conferencing links is confidential, the secure d.o.f. improves upon the case of no conferencing. In these cases of fully and partially confidential conferencing, it is shown to be sufficient to use the conferencing links only for transmitting noise symbols. On the other hand, if conferencing information is fully revealed to the eavesdropper, it is shown that there is no gain in secure d.o.f. due to conferencing, even if the conferencing information is also known to the legitimate destination.

Cooperative Secrecy Beamforming in Wiretap Interference Channels

This paper exploits co-channel interference (CCI) to secure the multi-antenna wiretap IFC consisting of two source-destination-eavesdropper triples, where each source-destination link is wiretapped by an external eavesdropper. To this end, we first propose a cooperative secrecy beamforming scheme, which is proved to be sufficient and necessary to achieve the secure degrees of freedom (S.D.o.F.) pair (1,1). By investigating the feasibility of the proposed beamforming scheme, we obtain the sufficient and necessary condition and also the beamforming vectors in closed-form to achieve the S.D.o.F pair (1,1). To the best of our knowledge, this is the first time that the benefit brought by CCI has been quantified.

Secure Degrees of Freedom in Cooperative MIMO Cognitive Radio Systems

We study the achievable secure degrees of freedom (DoF) in a cooperative MIMO cognitive radio system consisting of one primary source-destination pair, one or two secondary source-destination pairs, and one eavesdropper who is interested only in primary user's data. The cognitive radio users help to secure primary user's transmission against the eavesdropper and in return, the primary user allows the secondary users to access its licensed spectrum. All users are equipped with multiple antennas. We investigate the secure DoF using the interference alignment concept coupled with a zero inter-user interference constraint. We propose a beamforming design based only on the channel state information (CSI) between the primary and secondary user pairs which the legitimate users exchange among each other; no information data are exchanged and no eavesdropper CSI is needed. In the case of a single secondary user pair, we show that if all users have $M$ antennas, secure DoF $d_p$ and DoF $d_s$ of primary and secondary users, respectively, are achievable if they satisfy $2d_p\leq M$ and $d_s \leq M-2d_p$ . In the case of two secondary user pairs, secure DoF $d_p$ and DoFs $d_{s_1},d_{s_2}$ of primary user and two secondary users, respectively, are achievable if they satisfy $2d_p , $d_p+d_i\le M$ , $d_{s_1}+d_{s_2}\le M$ , $i\in\{s_1,s_2\}$ , or $2d_p=M$ , $d_p+d_i\le M$ , $d_{s_1}+d_{s_2} , $i\in\{s_1, s_2\}$ . Simulation examples corroborating the theoretical results are presented.

Broadcasting Into the Uncertainty: Authentication and Confidentiality by Physical-Layer Processing

The wireless medium offers many opportunities for broadcast communications. However, it also opens the possibility for attackers to eavesdrop the broadcast data or to pretend to be another node or device. These two attacks define the protection goals, namely, confidentiality and authenticity. Traditionally, both are solved by cryptographic approaches exploiting knowledge available in the surrounding infrastructure. The novel communication paradigms for the Internet of Things or cyber–physical systems do not scale with the standard cryptographic approach. Instead it is possible to exploit properties of the underlying physical channel to provide countermeasures against eavesdropping and impersonation attacks. Thereby, the random fading channel induces uncertainty which is detrimental but at the same time also helpful. In this paper, we review and describe a generalized model for physical-layer-based confidential data transmission and wireless authentication. A key role is played by the channel uncertainty and available design dimensions such as time, frequency, and space. We show that wireless authentication and secret-key generation can work in multicarrier and multiple-antenna systems and explain how even outdated channel state information can help to increase the available secure degrees of freedom. This survey focuses on the system design of wireless physical-layer confidentiality and authenticity under channel uncertainty. The insights could lead to a design of practical systems which are preparing the ground for confidentiality and authenticity already on the physical layer of the communication protocol stack.

On Secrecy Capacity of Helper-Assisted Wiretap Channel with an Out-of-Band Link

We consider a physical layer security problem where there is a source, an external helper, a legitimate receiver, and an eavesdropper, each equipped with one antenna. We assume that an additional out-of-band link from the source to the helper is available to improve the transmission security rate. A two-stage cooperative scheme is proposed. The proposed scheme consists of an information sharing stage and a cooperative transmission stage. Specifically, in the information sharing stage the source informs the helper of the signal to be transmitted, while in the cooperative transmission stage the source and the helper cooperate to transmit the signal to the legitimate receiver. Under this framework, we determine the optimal weights associated with this scheme and examine the secrecy capacity of the helper-assisted wiretap channel. The optimal weight design problem is generally nonconvex. To deal with this issue, an algorithm involving a one-dimensional search is developed. On the other hand, an analytical lower bound on the secrecy capacity is derived. Based on this lower bound, we further analyze the sufficient and necessary condition to ensure a positive secrecy capacity and derive the maximal achievable secure degrees of freedom, which are shown to be exactly the same as those of the multi-input single-output (MISO) wiretap channel.

Secure Degrees of Freedom of Wireless X Networks Using Artificial Noise Alignment

The problem of transmitting confidential messages in $M \times K$ wireless X networks is considered, in which each transmitter intends to send one confidential message to every receiver. In particular, the secure degrees of freedom (SDOF) of the considered network are studied based on an artificial noise alignment (ANA) approach, which integrates interference alignment and artificial noise transmission. At first, an SDOF upper bound is derived for the $M \times K$ X network with confidential messages (XNCM) to be $\frac{K(M-1)}{K+M-2}$. By proposing an ANA approach, it is shown that the SDOF upper bound is tight when $K=2$ for the considered XNCM with time/frequency varying channels. For $K \geq 3$, it is shown that SDOF of $\frac{K(M-1)}{K+M-1}$ can be achieved, even when an external eavesdropper is present. The key idea of the proposed scheme is to inject artificial noise into the network, which can be aligned in the interference space at receivers for confidentiality. Moreover, for the network with no channel state information at transmitters, a blind ANA scheme is proposed to achieve SDOF of $\frac{K(M-1)}{K+M-1}$ for $K,M \geq 2$, with reconfigurable antennas at receivers. The proposed method provides a linear approach to secrecy coding and interference alignment.

Secure MIMO Communications Under Quantized Channel Feedback in the Presence of Jamming

We consider the problem of secure communications in a MIMO setting in the presence of an adversarial jammer equipped with $n_j$ transmit antennas and an eavesdropper equipped with $n_e$ receive antennas. A multiantenna transmitter, equipped with $n_t$ antennas, desires to secretly communicate a message to a multiantenna receiver equipped with $n_r$ antennas. We propose a transmission method based on artificial noise and linear precoding and a two-stage receiver method employing beamforming. Under this strategy, we first characterize the achievable secrecy rates of communication and prove that the achievable secure degrees-of-freedom (SDoF) is given by $d_s = n_r - n_j$ in the perfect channel state information (CSI) case. Second, we consider quantized CSI feedback using Grassmannian quantization of a function of the direct channel matrix and derive sufficient conditions for the quantization bit rate scaling as a function of transmit power for maintaining the achievable SDoF $d_s$ with perfect CSI and for having asymptotically zero secrecy rate loss due to quantization. Numerical simulations are also provided to support the theory.

Multiuser Diversity for Secrecy Communications Using Opportunistic Jammer Selection: Secure DoF and Jammer Scaling Law

In this paper, we propose opportunistic jammer selection in a wireless security system for increasing the secure degrees of freedom (DoF) between a transmitter and a legitimate receiver (say, Alice and Bob). There is a jammer group consisting of S jammers among which Bob selects K jammers. The selected jammers transmit independent and identically distributed Gaussian signals to hinder the eavesdropper (Eve). Since the channels of Bob and Eve are independent, we can select the jammers whose jamming channels are aligned at Bob, but not at Eve. As a result, Eve cannot obtain any DoF unless it has more than KNj receive antennas, where Nj is the number of each jammer's transmit antenna, and hence KNj can be regarded as defensible dimensions against Eve. For the jamming signal alignment at Bob, we propose two opportunistic jammer selection schemes and find the scaling law of the required number of jammers for target secure DoF by a geometrical interpretation of the received signals.

Artificial-Noise Alignment for Secure Multicast using Multiple Antennas

We propose an artificial-noise alignment scheme for multicasting a common-confidential message to a group of legitimate receivers. Our scheme transmits a superposition of information and noise symbols. At each legitimate receiver, the noise symbols are aligned in such a way that the information symbols can be decoded with high probability. In contrast, the noise symbols completely mask the information symbols at the eavesdroppers. Our proposed scheme does not use the knowledge of the eavesdropper's channel gains at the transmitter for alignment, yet it achieves the best-known lower bound on the secure degrees of freedom. The knowledge of the eavesdropper's channel gains is still necessary when selecting the rate of the wiretap code. Our scheme is also a natural generalization of the approach of transmitting artificial noise in the null-space of the legitimate receiver's channel, previously proposed in the literature.

Interference Alignment for Secrecy

This paper studies the frequency/time selective <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">K</i> -user Gaussian interference channel with secrecy constraints. Two distinct models, namely the interference channel with confidential messages and the interference channel with an external eavesdropper, are analyzed. The key difference between the two models is the lack of channel state information (CSI) of the external eavesdropper. Using interference alignment along with secrecy precoding, it is shown that each user can achieve non-zero secure degrees of freedom (DoF) for both cases. More precisely, the proposed coding scheme achieves [( <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">K</i> -2)/(2 <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">K</i> -2)] secure DoF with probability one per user in the confidential messages model. For the external eavesdropper scenario, on the other hand, it is shown that each user can achieve [( <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">K</i> -2)/(2 <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">K</i> )] secure DoF in the ergodic setting. Remarkably, these results establish the positive impact of interference on the secrecy capacity region of wireless networks.

Interference Alignment for the Multiantenna Compound Wiretap Channel

We study a wiretap channel model where the sender has M transmit antennas and there are two groups consisting of J1 and J2 receivers respectively. Each receiver has a single antenna. We consider two scenarios. First we consider the compound wiretap model - group 1 constitutes the set of legitimate receivers, all interested in a common message, whereas group 2 is the set of eavesdroppers. We establish new lower and upper bounds on the secure degrees of freedom (d.o.f.). Our lower bound is based on the recently proposed real interference alignment scheme. The upper bound provides the first known example which illustrates that the pairwise upper bound used in earlier works is not tight. The second scenario we study is the compound private broadcast channel. Each group is interested in a message that must be protected from the other group. Upper and lower bounds on the d.o.f. are developed by extending the results on the compound wiretap channel.

On the Secure Degrees of Freedom of Relaying With Half-Duplex Feedback

Secure communication protocols over a single-relay system in the presence of a multiple-antenna eavesdropper are investigated. When there is no direct link between the source and the destination, an amplify-and-forward (AF) protocol that allows both the destination and the source to jam the eavesdropper is shown to achieve secrecy rates that grow linearly with the transmit power in dB, even if all the legitimate nodes have strictly fewer antennas than the eavesdropper. The number of achievable secure degrees of freedom is quantified and shown to match an upper bound when the number of antennas at the destination is sufficiently large. However, in the presence of a direct link between source and destination, this scaling rule no longer applies. The bottleneck of the AF scheme in the presence of a direct source-destination link is identified, motivating the use of another AF scheme and a novel compress-and-forward protocol that can achieve a positive number of secure degrees of freedom using an insecure feedback link.

Secure Communications With Insecure Feedback: Breaking the High-SNR Ceiling

A multiple-antenna Gaussian wiretap channel in which the number of antennas at the source is not greater than that at the eavesdropper is considered. Without feedback, the secrecy capacity over such a channel generally converges to a constant at high signal-to-noise ratio (SNR). A half-duplex secure protocol allowing the destination to actively transfer random keys in the form of known interference is proposed. It is shown that using multiple antennas at the destination is instrumental in achieving a secrecy rate that grows linearly with logSNR. The pre-log factor of the secrecy rate, i.e., the number of secure degrees of freedom, is characterized, revealing an interesting interplay between the numbers of antennas at the three communication nodes. The relationship of the achievable secure degrees of freedom to those obtained in the case without feedback is finally discussed.