Secrecy Capacity Region Research Articles

Strong Secrecy in Bidirectional Broadcast Channels With Confidential Messages

To increase the spectral efficiency of future wireless networks, it is important to wisely integrate multiple services at the physical layer. Here the efficient integration of confidential services in the three-node bidirectional relay channel is studied. A relay node establishes a bidirectional communication between two other nodes using a decode-and-forward protocol, which is also known as two-way relaying. In the broadcast phase, the relay transmits not only the two bidirectional messages it received in the previous multiple access phase, but also an additional confidential message to one node while keeping the other node completely ignorant of it. The concept of strong information theoretic secrecy is used to ensure that the nonlegitimate node cannot decode the confidential message no matter what its computational resources are. Moreover, this implies that the average decoding error at the nonlegitimate node goes exponentially fast to one for any decoding strategy it may use. This results in the study of the bidirectional broadcast channel with confidential messages for which the strong secrecy capacity region is established. Furthermore, it is shown that the efficient integration of confidential messages with strong secrecy extends to such scenarios, where the relay further transmits an additional common message to both nodes.

A Class of Three-Receiver Broadcast Channels with Degraded Message Sets and Side Information

We study a class of three-receiver discrete memoryless broadcast channel (DM-BC) with three degraded message sets and side information. We derive achievable rate region for this three-receive DM-BC with side information noncausally available at the transmitter. When the receivers follow a degradedness order, we determine the perfect secrecy capacity region of this class of three-receiver DM-BC with three degraded message sets and side information noncausally available at both the transmitter and the receiver. The achievable secrecy region of this paper subsumes Steinberg’s rate region for two-receiver degraded BC with the side information and the secrecy capacity region for one-receiver two-eavesdropper DM-BC with no side information as its special cases.

Secrecy Generation for Multiaccess Channel Models

Shannon theoretic secret key generation by several parties is considered for models in which a secure noisy channel with multiple input and output terminals and a public noiseless channel of unlimited capacity are available for accomplishing this goal. The secret key is generated for a set A of terminals of the noisy channel, with the remaining terminals (if any) cooperating in this task through their public communication. Single-letter lower and upper bounds for secrecy capacities are obtained when secrecy is required from an eavesdropper that observes only the public communication and perhaps also a set of terminals disjoint from A. These bounds coincide in special cases, but not in general. We also consider models in which different sets of terminals share multiple keys, one for the terminals in each set with secrecy required from the eavesdropper as well as from the terminals not in this set. Partial results include showing links among the associated secrecy capacity region for multiple keys, the transmission capacity region of the multiple access channel defined by the secure noisy channel, and achievable rates for a single secret key for all the terminals.

Degraded Compound Multi-Receiver Wiretap Channels

We study the degraded compound multi-receiver wiretap channel (DCMRWC). DCMRWC consists of two groups of users and a group of eavesdroppers, where, if we pick an arbitrary user from each group of users and an arbitrary eavesdropper, they satisfy a certain Markov chain. We study two different communication scenarios for this channel. In the first scenario, the transmitter wants to send a confidential message to users in the first (stronger) group and a different confidential message to users in the second (weaker) group, where both messages need to be kept confidential from the eavesdroppers. For this scenario, we assume that there is only one eavesdropper. We obtain the secrecy capacity region for the discrete memoryless channel model, the parallel channel model, and the Gaussian parallel channel model. For the Gaussian multiple-input multiple-output (MIMO) channel model, we obtain the secrecy capacity region when there is only one user in the second group. In the second scenario we study, the transmitter sends a confidential message to users in the first group which needs to be kept confidential from the second group of users and the eavesdroppers. Moreover, the transmitter sends a different confidential message to users in the second group which needs to be kept confidential only from the eavesdroppers. For this scenario, we do not put any restriction on the number of eavesdroppers. As in the first scenario, we obtain the secrecy capacity region for the discrete memoryless channel model, the parallel channel model, and the Gaussian parallel channel model. For the Gaussian MIMO channel model, we establish the secrecy capacity region when there is only one user in the second group.

Physical Layer Integration of Private, Common, and Confidential Messages in Bidirectional Relay Networks

In order to increase spectral efficiency, it is becoming more and more important that next generation wireless networks wisely integrate multiple services such as transmissions of private, common, and confidential messages at the physical layer. This is referred to as physical layer service integration, and in this paper is being studied for bidirectional relay networks. Here, a relay node establishes a bidirectional communication between two other nodes using a decode-and-forward protocol. This is also known as two-way relaying. In the broadcast phase, the relay efficiently integrates additional common and confidential services at the physical layer, which then requires the study of the bidirectional broadcast channel (BBC) with common and confidential messages. The entire secrecy capacity regions for discrete memoryless and MIMO Gaussian channels are established. These results further unify previous partial results such as the BBC with common messages or the classical broadcast channel with common and confidential messages, where the relay node provides only some of the services.

Privacy in Bidirectional Relay Networks

In this work, the bidirectional broadcast channel (BBC) with confidential messages is studied. The problem is motivated by the concept of bidirectional relaying in a three-node network, where a half-duplex relay node establishes a bidirectional communication between two other nodes using a decode-and-forward protocol and thereby transmits additional confidential information to one of them in the broadcast phase. The corresponding confidential message is transmitted at a certain secrecy level which characterizes the amount of information that can be kept secret from the non-legitimate node. The capacity-equivocation and secrecy capacity regions of the BBC with confidential messages are established where the latter characterizes the communication scenario with perfect secrecy, which means that the confidential information is completely hidden from the non-legitimate node. Thereby, it is shown that the optimal processing exploits ideas and concepts of the BBC with common messages and of the classical broadcast channel with confidential messages.

Three-Receiver Broadcast Channels With Common and Confidential Messages

This paper establishes inner bounds on the secrecy capacity regions for the general three-receiver broadcast channel with one common and one confidential message sets. We consider two setups. The first is when the confidential message is to be sent to two receivers and kept secret from the third receiver. Achievability is established using indirect decoding, Wyner wiretap channel coding, and the new idea of generating secrecy from a publicly available superposition codebook. The inner bound is shown to be tight for a class of reversely degraded broadcast channels and when both legitimate receivers are less noisy than the third receiver. The second setup investigated in this paper is when the confidential message is to be sent to one receiver and kept secret from the other two receivers. Achievability in this case follows from Wyner wiretap channel coding and indirect decoding. This inner bound is also shown to be tight for several special cases.

Security Embedding Codes

This paper considers the problem of simultaneously communicating two messages, a high-security message and a low-security message, to a legitimate receiver, referred to as the security embedding problem. An information-theoretic formulation of the problem is presented. A coding scheme that combines rate splitting, superposition coding, nested binning, and channel prefixing is considered and is shown to achieve the secrecy capacity region of the channel in several scenarios. Specifying these results to both scalar and independent parallel Gaussian channels (under an average individual per-subchannel power constraint), it is shown that the high-security message can be embedded into the low-security message at full rate (as if the low-security message does not exist) without incurring any loss on the overall rate of communication (as if both messages are low-security messages). Extensions to the wiretap channel II setting of Ozarow and Wyner are also considered, where it is shown that "perfect" security embedding can be achieved by an encoder that uses a two-level coset code.

Secure Communications Over Wireless Broadcast Networks: Stability and Utility Maximization

A wireless broadcast network model with secrecy constraints is investigated, in which a source node broadcasts K confidential message flows to K user nodes, with each message intended to be decoded accurately by one user and to be kept secret from all other users (who are thus considered to be eavesdroppers with regard to all other messages but their own). The source maintains a queue for each message flow if it is not served immediately. The channel from the source to the K users is modeled as a fading broadcast channel, and the channel state information is assumed to be known to the source and the corresponding receivers. Two eavesdropping models are considered. For a collaborative eavesdropping model, in which the eavesdroppers exchange their outputs, the secrecy capacity region is obtained, within which each rate vector is achieved by using a time-division scheme and a source power control policy over channel states. A throughput optimal queue-length-based rate scheduling algorithm is further derived that stabilizes all arrival rate vectors contained in the secrecy capacity region. Moreover, the network utility function is maximized via joint design of rate control, rate scheduling, power control, and secure coding. More precisely, a source controls the message arrival rate according to its message queue, the rate scheduling selects a transmission rate based the queue length vector, and the rate vector is achieved by power control and secure coding. These components work jointly to solve the network utility maximization problem. For a noncollaborative eavesdropping model, in which eavesdroppers do not exchange their outputs, an achievable secrecy rate region is derived based on a time-division scheme, and the queue-length-based rate scheduling algorithm and the corresponding power control policy are obtained that stabilize all arrival rate vectors in this region. The network utility maximizing rate control vector is also obtained.

Cooperative Encoding for Secrecy in Interference Channels

This paper investigates the fundamental performance limits of the two-user interference channel in the presence of an external eavesdropper. In this setting, we construct an inner bound, to the secrecy capacity region, based on the idea of cooperative encoding in which the two users cooperatively design their randomized codebooks and jointly optimize their channel prefixing distributions. Our achievability scheme also utilizes message-splitting in order to allow for partial decoding of the interference at the nonintended receiver. Outer bounds are then derived and used to establish the optimality of the proposed scheme in certain cases. In the Gaussian case, the previously proposed cooperative jamming and noise-forwarding techniques are shown to be special cases of our proposed approach. Overall, our results provide structural insights on how the interference can be exploited to increase the secrecy capacity of wireless networks.

Fading Cognitive Multiple-Access Channels With Confidential Messages

The fading cognitive multiple-access channel with confidential messages (CMAC-CM) is investigated, in which two users (users 1 and 2) wish to transmit a common message to a destination and user 1 also has a confidential message intended for the destination. The two users transmit to the destination via a multiple access channel, and user 2 also receives noisy channel outputs. Such channel outputs potentially help user 2 to learn user 1's confidential information (although they are not exploited by user 2 for channel transmission). Hence, user 1 views user 2 as an eavesdropper and wishes to keep its confidential message as secret as possible from user 2. A parallel CMAC-CM with independent subchannels is first studied. The secrecy capacity region of the parallel CMAC-CM is established, which yields the secrecy capacity regions of the parallel CMAC-CM with degraded subchannels and the parallel Gaussian CMAC-CM. These results are then applied to study the fading CMAC-CM, in which both the user-to-user channel and the user-to-destination channel are corrupted by multiplicative fading gain coefficients in addition to additive white Gaussian noise. The channel state information (CSI) is assumed to be known at both the users and the destination. With the CSI, users can dynamically change their transmission powers with the channel realization to achieve the optimal performance. The closed-form power allocation function that achieves every boundary point of the secrecy capacity region is derived.

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.

The Secrecy Capacity Region of the Gaussian MIMO Multi-Receiver Wiretap Channel

In this paper, we consider the Gaussian multiple-input multiple-output (MIMO) multi-receiver wiretap channel in which a transmitter wants to have confidential communication with an arbitrary number of users in the presence of an external eavesdropper. We derive the secrecy capacity region of this channel for the most general case. We first show that even for the single-input single-output (SISO) case, existing converse techniques for the Gaussian scalar broadcast channel cannot be extended to this secrecy context, to emphasize the need for a new proof technique. Our new proof technique makes use of the relationships between the minimum-mean-square-error and the mutual information, and equivalently, the relationships between the Fisher information and the differential entropy. Using the intuition gained from the converse proof of the SISO channel, we first prove the secrecy capacity region of the degraded MIMO channel, in which all receivers have the same number of antennas, and the noise covariance matrices can be arranged according to a positive semi-definite order. We then generalize this result to the aligned case, in which all receivers have the same number of antennas; however, there is no order among the noise covariance matrices. We accomplish this task by using the channel enhancement technique. Finally, we find the secrecy capacity region of the general MIMO channel by using some limiting arguments on the secrecy capacity region of the aligned MIMO channel. We show that the capacity achieving coding scheme is a variant of dirty-paper coding with Gaussian signals.

Multiple-Input Multiple-Output Gaussian Broadcast Channels With Common and Confidential Messages

This paper considers the problem of the multiple-input multiple-output (MIMO) Gaussian broadcast channel with two receivers (receivers 1 and 2) and two messages: a common message intended for both receivers and a confidential message intended only for receiver 1 but needing to be kept asymptotically perfectly secure from receiver 2. A matrix characterization of the secrecy capacity region is established via a channel enhancement argument. The enhanced channel is constructed by first splitting receiver 1 into two virtual receivers and then enhancing only the virtual receiver that decodes the confidential message. The secrecy capacity region of the enhanced channel is characterized using an extremal entropy inequality previously established for characterizing the capacity region of a degraded compound MIMO Gaussian broadcast channel.

A Vector Generalization of Costa's Entropy-Power Inequality With Applications

This paper considers an entropy-power inequality (EPI) of Costa and presents a natural vector generalization with a real positive semidefinite matrix parameter. The new inequality is proved using a perturbation approach via a fundamental relationship between the derivative of mutual information and the minimum mean-square error (MMSE) estimate in linear vector Gaussian channels. As an application, a new extremal entropy inequality is derived from the generalized Costa EPI and then used to establish the secrecy capacity regions of the degraded vector Gaussian broadcast channel with layered confidential messages.

Secrecy Capacity of a Class of Broadcast Channels with an Eavesdropper

We study the security of communication between a single transmitter and many receivers in the presence of an eavesdropper for several special classes of broadcast channels. As the first model, we consider the degraded multireceiver wiretap channel where the legitimate receivers exhibit a degradedness order while the eavesdropper is more noisy with respect to all legitimate receivers. We establish the secrecy capacity region of this channel model. Secondly, we consider the parallel multireceiver wiretap channel with a less noisiness order in each subchannel, where this order is not necessarily the same for all subchannels, and hence the overall channel does not exhibit a less noisiness order. We establish the common message secrecy capacity and sum secrecy capacity of this channel. Thirdly, we study a class of parallel multireceiver wiretap channels with two subchannels, two users and an eavesdropper. For channels in this class, in the first (resp., second) subchannel, the second (resp., first) receiver is degraded with respect to the first (resp., second) receiver, while the eavesdropper is degraded with respect to both legitimate receivers in both subchannels. We determine the secrecy capacity region of this channel, and discuss its extensions to arbitrary numbers of users and subchannels. Finally, we focus on a variant of this previous channel model where the transmitter can use only one of the subchannels at any time. We characterize the secrecy capacity region of this channel as well.

Physical layer security in broadcast networks

AbstractThis paper reviews the information theoretic characterization of security in broadcast channels, in which a transmitter has both public and confidential messages intended for multiple receivers. All messages must be successfully received by their intended receivers, and the confidential messages must be kept as secret as possible from non‐intended recipients. Various scenarios are considered in the context of two‐user broadcast channels, for which known results on the secrecy capacity region are reviewed and corresponding coding schemes for achieving rates in these regions are described. Copyright © 2009 John Wiley &amp; Sons, Ltd.

Secrecy Capacity Region of a Multiple-Antenna Gaussian Broadcast Channel With Confidential Messages

Wireless communication is particularly susceptible to eavesdropping due to its broadcast nature. Security and privacy systems have become critical for wireless providers and enterprise networks. This paper considers the problem of secret communication over the Gaussian broadcast channel, where a multiple-antenna transmitter wishes to send independent confidential messages to two users with information-theoretic secrecy. That is, each user would like to obtain its own confidential message in a reliable and safe manner. This communication model is referred to as the multiple-antenna Gaussian broadcast channel with confidential messages (MGBC-CM). Under this communication scenario, a secret dirty-paper coding scheme and the corresponding achievable secrecy rate region are first developed based on Gaussian codebooks. Next, a computable Sato-type outer bound on the secrecy capacity region is provided for the MGBC-CM. Furthermore, the Sato-type outer bound proves to be consistent with the boundary of the secret dirty-paper coding achievable rate region, and hence, the secrecy capacity region of the MGBC-CM is established. Finally, two numerical examples demonstrate that both users can achieve positive rates simultaneously under the information-theoretic secrecy requirement.

Secure Communication Over Fading Channels

The fading broadcast channel with confidential messages (BCC) is investigated, where a source node has common information for two receivers (receivers 1 and 2), and has confidential information intended only for receiver 1. The confidential information needs to be kept as secret as possible from receiver 2. The broadcast channel from the source node to receivers 1 and 2 is corrupted by multiplicative fading gain coefficients in addition to additive Gaussian noise terms. The channel state information (CSI) is assumed to be known at both the transmitter and the receivers. The parallel BCC with independent subchannels is first studied, which serves as an information-theoretic model for the fading BCC. The secrecy capacity region of the parallel BCC is established, which gives the secrecy capacity region of the parallel BCC with degraded subchannels. The secrecy capacity region is then established for the parallel Gaussian BCC, and the optimal source power allocations that achieve the boundary of the secrecy capacity region are derived. In particular, the secrecy capacity region is established for the basic Gaussian BCC. The secrecy capacity results are then applied to study the fading BCC. The ergodic performance is first studied. The ergodic secrecy capacity region and the optimal power allocations that achieve the boundary of this region are derived. The outage performance is then studied, where a long-term power constraint is assumed. The power allocation is derived that minimizes the outage probability where either the target rate of the common message or the target rate of the confidential message is not achieved. The power allocation is also derived that minimizes the outage probability where the target rate of the confidential message is not achieved subject to the constraint that the target rate of the common message must be achieved for all channel states.

Multiple-Access Channels With Confidential Messages

A discrete memoryless multiple-access channel (MAC) with confidential messages is studied, where two users attempt to transmit common information to a destination and each user also has private (confidential) information intended for the destination. This channel generalizes the classical MAC model in that each user also receives channel outputs, and hence may obtain the confidential information sent by the other user from the channel output it receives. However, each user views the other user as a wiretapper or eavesdropper, and wishes to keep its confidential information as secret as possible from the other user. The level of secrecy of the confidential information is measured by the equivocation rate, i.e., the entropy rate of the confidential information conditioned on channel outputs at the wiretapper (the other user). The performance measure is the rate-equivocation tuple that includes the common rate, two private rates, and two equivocation rates as components. The set that includes all achievable rate-equivocation tuples is referred to as the capacity-equivocation region. The case of perfect secrecy is particularly of interest, in which each user's confidential information is perfectly hidden from the other user. The set that includes all achievable rates with perfect secrecy is referred to as the secrecy capacity region. For the MAC with two confidential messages, in which both users have confidential messages for the destination, inner bounds on the capacity-equivocation region, and secrecy capacity region are obtained. It is demonstrated that there is a tradeoff between the two equivocation rates (secrecy levels) achieved for the two confidential messages. For the MAC with one confidential message, in which only one user (user 1) has private (confidential) information for the destination, inner and outer bounds on the capacity-equivocation region are derived. These bounds match partially, and hence the capacity-equivocation region is partially characterized. Furthermore, the outer bound provides a tight converse for the case of perfect secrecy, and hence establishes the secrecy capacity region. A class of degraded MACs with one confidential message is further studied, and the capacity-equivocation region and the secrecy capacity region are established. These results are further explored via two example channels: the binary and Gaussian MACs. For both channels, the capacity-equivocation regions and the secrecy capacity regions are obtained.