786 research outputs found
Secrecy Capacity of a Class of Broadcast Channels with an Eavesdropper
We study the security of communication between a single transmitter and
multiple receivers in a broadcast channel in the presence of an eavesdropper.
We consider several special classes of channels. As the first model, we
consider the degraded multi-receiver 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 multi-receiver
wiretap channel with a less noisiness order in each sub-channel, where this
order is not necessarily the same for all sub-channels. We establish the common
message secrecy capacity and sum secrecy capacity of this channel. Thirdly, we
study a special class of degraded parallel multi-receiver wiretap channels and
provide a stronger result. In particular, we study the case with two
sub-channels two users and one eavesdropper, where there is a degradedness
order in each sub-channel such that in the first (resp. second) sub-channel 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 sub-channels. We determine the secrecy capacity
region of this channel. Finally, we focus on a variant of this previous channel
model where the transmitter can use only one of the sub-channels at any time.
We characterize the secrecy capacity region of this channel as well.Comment: Submitted to EURASIP Journal on Wireless Communications and
Networking (Special Issue on Wireless Physical Layer Security
Information-theoretic Secrecy in Multi-user Channels
Inherent openness of the wireless medium imposes stronger challenges on the security of wireless communications. Information-theoretic security addresses these challenges at the physical layer by using tools from wireless communication theory, signal processing and information theory. In information-theoretic security, physical layer communication is intelligently designed to exploit the characteristics of the wireless medium, such as fading, interference, cooperation, and multi-dimensional signaling, in order to provide or improve security. In this dissertation, we study the security of several fundamental wireless network configurations from an information-theoretic perspective.
First, we study the Gaussian multiple-input multiple-output (MIMO)
wiretap channel. In this channel, the transmitter sends a common
message to both the legitimate user and the eavesdropper. In addition
to the common message, a private message is sent only to the legitimate user, which needs to be kept hidden as much as possible from the eavesdropper. We obtain the entire capacity-equivocation region for this channel model. In particular, we show the sufficiency of jointly Gaussian auxiliary random variables and channel input to evaluate the existing single-letter description of the capacity-equivocation region due to Csiszar-Korner.
Next, we study the secure broadcasting problem, where a
transmitter wants to have secure communication with multiple
legitimate users in the presence of an external eavesdropper. We study
several special cases of the secure broadcasting problem. First, we consider the degraded multi-receiver wiretap channel, and establish its secrecy capacity region. Second, we consider the parallel less noisy multi-receiver wiretap channel, and obtain its common message secrecy capacity and sum secrecy capacity. Third, we consider the parallel degraded multi-receiver wiretap channel for the two-user and two-sub-channel case, and obtain its entire secrecy capacity region. Finally, we consider a parallel channel model with two sub-channels, where the transmitter can use only one of the subchannels at any time, and characterize its secrecy capacity region.
Then, we study the two-user Gaussian MIMO broadcast channel with common and confidential messages. In this channel model, the transmitter sends a common message to both users, and a confidential message to each user which needs to be kept perfectly secret from the other user. We obtain the entire capacity region of this channel. We also explore the connections between this channel model and its non-confidential counterpart, i.e., the Gaussian MIMO broadcast channel with common and private message.
Next, we consider the Gaussian MIMO multi-receiver wiretap channel and obtain its secrecy capacity region for the most general case. We first show that even for the single-input single-output (SISO) case, existing converse techniques fall short of proving the secrecy capacity region, to emphasize the need for a new proof technique, which we develop by using the relationships between the
Fisher information and the differential entropy. Using this new proof technique, we obtain the secrecy capacity region of the degraded MIMO channel. We then establish the secrecy capacity region of the general MIMO channel by using the channel enhancement
technique in conjunction with the capacity result we obtained for the degraded MIMO channel. For the general MIMO channel, we show that dirty-paper coding (DPC) combined with stochastic encoding attains the entire secrecy capacity region.
Then, we study the multi-receiver wiretap channel for a more general scenario, where, in addition to confidential messages, the transmitter sends public messages to the legitimate users, on which there are no secrecy constraints. First, we consider the degraded discrete memoryless channel, and obtain inner and outer bounds for the capacity region. These inner and outer bounds match for certain cases, providing the capacity region. Second, we obtain an inner bound for the general discrete memoryless channel by using Marton's inner bound. Third, we consider the degraded Gaussian MIMO
channel, and show that jointly Gaussian auxiliary random variables and channel input are sufficient to exhaust the inner and outer bounds. Finally, we provide an inner bound for the capacity region of the general Gaussian MIMO channel.
Next, we focus on the multiple access wiretap (MAC-WT) channel
whose capacity region is unknown. We consider a special class of MAC-WT channels which we call the weak eavesdropper class, where
each user's link to the legitimate receiver is stronger than its link to the
eavesdropper. For this class of channels, we develop an outer bound for the secrecy capacity region, which partially matches the achievable
region in an n-letter form. We evaluate a looser version of our
outer bound for the Gaussian case, and show that our outer bound is within 0.5 bits/channel use of the achievable rates along the individual secrecy rates for all weak eavesdropper Gaussian MAC-WT.
Then, we investigate the effects of user cooperation on the secrecy of
broadcast channels by considering the cooperative relay broadcast
channel (CRBC). We propose an achievable scheme that combines
Marton's coding scheme for broadcast channels and Cover and El
Gamal's compress-and-forward (CAF) scheme for relay channels. For the Gaussian CRBC, we show that both users can have positive
secrecy rates, which is not possible for scalar Gaussian broadcast
channels without cooperation.
We further investigate the effects of user cooperation on secrecy
by considering the multiple access channel with generalized feedback (MAC-GF), which can be viewed as the MAC-dual of the CRBC.
We propose a CAF-based achievable secrecy rate region for the MAC-GF. Specializing our results to a Gaussian MAC-GF, we present numerical results which demonstrate that cooperation can improve secrecy for the MAC-GF.
Next, we study the two-user one-eavesdropper discrete memoryless
compound wiretap channel, and provide the best known lower bound for the secrecy capacity of this compound channel. We evaluate this achievable secrecy rate for the Gaussian MIMO case by using DPC. We show that this achievable secrecy rate achieves at least half of the secrecy capacity of this Gaussian MIMO compound wiretap channel,
and also attains the secrecy capacity when the eavesdropper is degraded with respect to one of the two users.
Then, we study the degraded compound multi-receiver wiretap channel (DCMRWC), which, in addition to a group of eavesdroppers, has two groups of users, namely the stronger group and the weaker group. We study two different communication scenarios for this channel. In the first scenario, there is only one eavesdropper, and
the transmitter sends a confidential message to each group of
legitimate users while keeping both messages secret from the eavesdropper. In the second scenario, we study the DCMRWC with layered messages without any restriction on the number of eavesdroppers. For both scenarios, we obtain the secrecy capacity region for the discrete memoryless channel, the parallel channel, and the Gaussian parallel channel. For the Gaussian MIMO channel, we obtain the secrecy capacity region when there is only one user in the second group.
Next, we study the two-user fading broadcast channel and obtain its ergodic secrecy capacity region. We show that, thanks to fading,
both users can have simultaneous secure communication with the transmitter, although this is not possible in the scalar non-fading Gaussian broadcast channel where only one user can have secure communication. This simultaneous secrecy of both users is achieved by an opportunistic communication scheme, in which, at each time instant, the transmitter communicates with the user having a better channel gain.
Then, we study the secure lossy transmission of a vector Gaussian source to a legitimate user in the presence of an eavesdropper, where
both the legitimate user and the eavesdropper have vector Gaussian
side information. We obtain an outer bound for the rate, equivocation and distortion region. Moreover, we obtain the maximum equivocation at the eavesdropper when there is no constraint on the transmission rate. By using this maximum equivocation result, we show two facts. First, for this problem, in general, Wyner-Ziv scheme is suboptimal, although, it is optimal in the absence of an eavesdropper. And, second, even when there is no transmission rate constraint, an uncoded transmission scheme is suboptimal; the presence of an eavesdropper necessitates the use of a coded scheme to attain the maximum equivocation.
Finally, we revisit the secure lossy source coding problem. In all works on this problem, either the equivocation of the source at the eavesdropper or the equivocation of the legitimate user's reconstruction of the source at the eavesdropper is used to measure secrecy. We first propose the relative equivocation of the source at the eavesdropper with respect to the legitimate user as a new secrecy measure. We argue that this new secrecy measure is the one that corresponds to the natural generalization of the equivocation in a wiretap channel to the context of secure lossy source coding. Under this new secrecy measure, we provide a single-letter description of the rate, relative equivocation and distortion region, as well as its specializations to degraded and reversely degraded cases. We
investigate the relationships between the optimal scheme that attains this region and the Wyner-Ziv scheme
Secrecy Capacity Region of Some Classes of Wiretap Broadcast Channels
This work investigates the secrecy capacity of the Wiretap Broadcast Channel
(WBC) with an external eavesdropper where a source wishes to communicate two
private messages over a Broadcast Channel (BC) while keeping them secret from
the eavesdropper. We derive a non-trivial outer bound on the secrecy capacity
region of this channel which, in absence of security constraints, reduces to
the best known outer bound to the capacity of the standard BC. An inner bound
is also derived which follows the behavior of both the best known inner bound
for the BC and the Wiretap Channel. These bounds are shown to be tight for the
deterministic BC with a general eavesdropper, the semi-deterministic BC with a
more-noisy eavesdropper and the Wiretap BC where users exhibit a less-noisiness
order between them. Finally, by rewriting our outer bound to encompass the
characteristics of parallel channels, we also derive the secrecy capacity
region of the product of two inversely less-noisy BCs with a more-noisy
eavesdropper. We illustrate our results by studying the impact of security
constraints on the capacity of the WBC with binary erasure (BEC) and binary
symmetric (BSC) components.Comment: 19 pages, 8 figures, To appear in IEEE Trans. on Information Theor
Cooperation with an Untrusted Relay: A Secrecy Perspective
We consider the communication scenario where a source-destination pair wishes
to keep the information secret from a relay node despite wanting to enlist its
help. For this scenario, an interesting question is whether the relay node
should be deployed at all. That is, whether cooperation with an untrusted relay
node can ever be beneficial. We first provide an achievable secrecy rate for
the general untrusted relay channel, and proceed to investigate this question
for two types of relay networks with orthogonal components. For the first
model, there is an orthogonal link from the source to the relay. For the second
model, there is an orthogonal link from the relay to the destination. For the
first model, we find the equivocation capacity region and show that answer is
negative. In contrast, for the second model, we find that the answer is
positive. Specifically, we show by means of the achievable secrecy rate based
on compress-and-forward, that, by asking the untrusted relay node to relay
information, we can achieve a higher secrecy rate than just treating the relay
as an eavesdropper. For a special class of the second model, where the relay is
not interfering itself, we derive an upper bound for the secrecy rate using an
argument whose net effect is to separate the eavesdropper from the relay. The
merit of the new upper bound is demonstrated on two channels that belong to
this special class. The Gaussian case of the second model mentioned above
benefits from this approach in that the new upper bound improves the previously
known bounds. For the Cover-Kim deterministic relay channel, the new upper
bound finds the secrecy capacity when the source-destination link is not worse
than the source-relay link, by matching with the achievable rate we present.Comment: IEEE Transactions on Information Theory, submitted October 2008,
revised October 2009. This is the revised versio
Interference Alignment for the Multi-Antenna Compound Wiretap Channel
We study a wiretap channel model where the sender has transmit antennas
and there are two groups consisting of and 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. Our lower bound is based on the recently proposed
\emph{real interference alignment} scheme. The upper bound provides the first
known example which illustrates that the \emph{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 degrees of freedom are developed by extending the
results on the compound wiretap channel.Comment: Minor edits. Submitted to IEEE Trans. Inf. Theor
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