This work investigates providing information theoretically secure communication in a scenario where the eavesdropper is more powerful as compared to models considered to date. Specifically, we consider the setting where the eavesdropper, based on signals it received in the past, modifies its channel state in order to benefit its reception of the legitimate parties' messages. Natural to this setting is that the legitimate parties do not have any knowledge of the eavesdropper's channel state. In this setting, we study the Gaussian two-way wiretap channel, namely two legitimate nodes connected by a bi-directional link in the presence of an eavesdropper that receives the superposition of signals from both nodes. We show that a positive secrecy rate in the sense of strong secrecy is achievable even under these assumptions. The secrecy rate obtained scales with transmit power. The achievable strategy involves cooperative jamming pointing out to its robustness to the adaptive nature of the eavesdropper channel.
This work investigates providing information theoretically secure communication in a scenario where the eavesdropper is more powerful as compared to models considered to date. Specifically, we consider the setting where the eavesdropper, based on signals it received in the past, modifies its channel state in order to benefit its reception of the legitimate parties' messages. Natural to this setting is that the legitimate parties do not have any knowledge of the eavesdropper's channel state. In this setting, we study the Gaussian two-way wiretap channel, namely two legitimate nodes connected by a bi-directional link in the presence of an eavesdropper that receives the superposition of signals from both nodes. We show that a positive secrecy rate in the sense of strong secrecy is achievable even under these assumptions. The secrecy rate obtained scales with transmit power. The achievable strategy involves cooperative jamming pointing out to its robustness to the adaptive nature of the eavesdropper channel.
We investigate the fundamental communication limits when messages are sent via a Gaussian two-way channel, which must at the same time be kept secret from an external eavesdropper. In this two-way wiretap channel that models two legitimate transceivers and an eavesdropping receiver, there are two techniques to provide confidentiality for the messages: one entails the legitimate nodes to jam the eavesdropper, i.e., cooperative jamming, while the other entails generating keys from the feedback signals received by the two legitimate nodes and using them to encrypt the messages. Previous work has shown that both methods can be used concurrently to improve the secrecy rates of a channel with a degradedness condition. In this work, we consider the general case, and derive a new outer bound for the secrecy capacity region of this channel. A case is identified where the loss in secrecy rate, due to ignoring the backward (feedback) link at each legitimate transmitter from the other, is bounded by a constant which only depends on the channel gains. This is the case when the power of the two legitimate nodes increases proportionally. In all other cases, we show that ignoring feedback signals causes unbounded loss in the secrecy rate. The loss is measured as the gap between the achievable rate when the feedback signals are taken into account, and the upper bound when the feedback is not used, and hence is not affected by the choice of the achievable scheme. This result therefore establishes that, for the Gaussian two-way channel with an external eavesdropper, the encoders need to be designed with memory. This is in contrast to the result for this channel in the absence of an eavesdropper.
Cooperative jamming approach has been commonly used in the field of physical layer security to achieve a good secrecy rate of wireless networks. In this approach, the Gaussian noise signal sent by a friendly jammer can disrupt the reception of the eavesdropper, however, it may also interfere with the legitimate receiver. In this paper, we propose a novel approach, namely, information jamming, to go beyond the secrecy rate achieved by the traditional cooperative jamming approach in a multiple-input single-output (MISO) wiretap channel. We propose that a multi-antenna friendly jammer transmits the source message rather than Gaussian noise signal for simultaneously enhancing the signal strength at the legitimate receiver and canceling the received signal at the eavesdropper. In particular, we aim to maximize the achievable secrecy rate by optimizing the information jammer's beamforming vector. Though the optimization problem is non-convex, we successfully solve it optimally via a two-stage based numerical approach. To gain more useful analytical results, we also propose two suboptimal jamming schemes with low computation, by targeting at improving the legitimate reception and avoiding the eavesdropping, respectively. Finally, numerical results show that the proposed information jamming approach significantly helps go beyond the secrecy rate of the existing cooperative jamming approach, especially when the transmit power of the jammer is large enough.
A usual concern against physical layer security is that the legitimate parties would need to have (partial) channel state information (CSI) of the eavesdropper in order to design transmission schemes that provide secrecy. In this work, to overcome this concern, we consider the model where the eavesdropper's CSI is completely unknown at the legitimate transmitter(s) and the receiver. A static channel setting, and multiple antennas are considered for all parties, and it is assumed that the eavesdropper has perfect self-CSI. In this setting, assuming that the legitimate parties can employ a larger number of antennas than the eavesdropper, we provide a positive secure communication rate in the sense of strong secrecy. The achievable (guaranteed) secrecy rate we derive for the MIMO wiretap channel matches its converse in terms of secure degrees of freedom. As a side result of our approach, we also derive the secure degrees of freedom region for the MIMO MAC-wiretap channel where the transmitters and the intended receiver have the same number of antennas.
In this paper, a class of information theoretic secrecy problems is addressed where the eavesdropper channel state is completely unknown to the legitimate parties. In particular, a Gaussian MIMO wiretap channel is considered, where the eavesdropper channel state can vary from one channel use to the next, and the overall channel state sequence is known only to the eavesdropper. When the eavesdropper has fewer antennas than the transmitter and its intended receiver, a positive secrecy rate in the sense of strong secrecy is proved to be achievable and shown to match with the converse in secure degrees of freedom. This yields the conclusion that secure communication is possible regardless of the location or channel states of the eavesdropper. Additionally, it is observed that, the present setting renders the secrecy capacity problems for some multiterminal wiretap-type channels more tractable as compared to the case with full or partial knowledge of eavesdropper channel states. To demonstrate this observation, secure degrees of freedom regions are derived for the Gaussian MIMO multiple access (MAC) wiretap channel and the two-user Gaussian MIMO broadcast (BC) wiretap channel, where the transmitter(s) and intended receiver(s) have the same number of antennas.
Most practical communication links are bidirectional. In these models, since the source node also receives signals, its encoder has the option of computing its output based on the signals it received in the past. On the other hand, from a practical point of view, it would also be desirable to identify the cases where such an encoder design may not improve communication rates. This question is particularly interesting for the case where the transmitted messages and the feedback signals are subject to eavesdropping. In this paper, we investigate the question of how much impact the feedback has on the secrecy capacity by studying two fundamental models. First, we consider the Gaussian two-way wiretap channel and derive an outer bound for its secrecy capacity region. We show that the secrecy rate loss can be unbounded when feedback signals are not utilized except for a special case we identify, and thus conclude that utilizing feedback can be highly beneficial in general. Second, we consider a half-duplex Gaussian two-way relay channel where the relay node is also an eavesdropper, and find that the impact of feedback is less pronounced compared to the previous scenario. Specifically, the loss in secrecy rate, when ignoring the feedback, is quantified to be less than 0.5 bit per channel use when the relay power goes to infinity. This achievable rate region is obtained with simple time sharing along with cooperative jamming, which, with its simplicity and near optimum performance, is a viable alternative to an encoder that utilizes feedback signals.
The study of the physical layer has offered a new perspective to the problem of communication security. This led to the development of a vast set of ideas and techniques rooted in information theory which can be employed in practice to provide unbreakable security. The information-theoretic approach relies mainly on the physical nature of the communication medium. In a wireless medium, the unique features of the wireless communication channel, such as its fading and broadcast nature, can be exploited to achieve higher secure information rates. In this dissertation, we study the secure transmission problem in wireless channels from an information-theoretic perspective. We first consider the fading multiple access wiretap channel. We give two new achievable schemes that use the time-varying (fading) nature of the channel to align the interference from different users at the eavesdropper perfectly in a one-dimensional space while creating a higher-dimensional space for the interfering signals at the legitimate receiver hence allowing for better chance of recovery. While we achieve this alignment through signal scaling at the transmitters in our first scheme (scaling based alignment), we let nature provide this alignment through the ergodicity of the channel coefficients in the second scheme (ergodic secret alignment). For each scheme, we show that the achievable secrecy rates scale logarithmically with the signal-to-noise ratio (SNR). Next, we study the security gains that can be achieved in a wireless network by employing cooperation among the nodes which is possible due to the broadcast nature of the wireless channel. We investigate the role of passive (also known as deaf) cooperation in improving the achievable secrecy rates in a Gaussian multiple relay network with an external eavesdropper. We distinguish between two modes of deaf cooperation, namely, cooperative jamming (CJ) and noise forwarding (NF). We derive the conditions in which each mode of deaf cooperation achieves secrecy rates that are higher than the secrecy capacity of the original Gaussian wiretap channel. As a result, we show that a deaf helper cannot be a useful cooperative jammer and noise forwarder at the same time. We derive the optimal power control policy for each mode. We consider the deaf helper selection problem where a fixed-size set of deaf helpers (possibly operating in different modes) are to be selected from the set of available relays so that the achievable secrecy rate is maximized. We propose a simple and efficient suboptimal strategy for selection which is shown to be optimal when only one helper is selected. Furthermore, we study the role of a multi-antenna deaf helper. Unlike the single antenna case, we show that, in general, it is useful to split the helper's power between cooperative jamming and noise forwarding. Hence, we propose a deaf cooperation strategy for this model and derive its optimal power control policy. We also show, for specific class of relay-eavesdropper channels, that a simple cooperative jamming strategy yields a secrecy rate that approaches the secrecy capacity as the helper's power is increased. Finally, we consider the role of active cooperation for secrecy in the multiple relay networks. We propose several relaying strategies for secure communication and derive the achievable secrecy rate for each strategy. In our strategies the relays decode the source signal and then forward it to the destination either in a single-hop or a multi-hop fashion. Each relay scales its transmitted signal in a way that ensures that signal components from different relays are canceled out at the eavesdropper.