1,356 research outputs found
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
On SDoF of Multi-Receiver Wiretap Channel With Alternating CSIT
We study the problem of secure transmission over a Gaussian multi-input
single-output (MISO) two receiver channel with an external eavesdropper, under
the assumption that the state of the channel which is available to each
receiver is conveyed either perfectly () or with delay () to the
transmitter. Denoting by , , and the channel state information
at the transmitter (CSIT) of user 1, user 2, and eavesdropper, respectively,
the overall CSIT can then alternate between eight possible states, i.e.,
. We denote by the
fraction of time during which the state occurs. Under these
assumptions, we first consider the Gaussian MISO wiretap channel and
characterize the secure degrees of freedom (SDoF). Next, we consider the
general multi-receiver setup and characterize the SDoF region of fixed hybrid
states , , and . We then focus our attention on the symmetric
case in which . For this case, we establish bounds
on SDoF region. The analysis reveals that alternating CSIT allows synergistic
gains in terms of SDoF; and shows that, by opposition to encoding separately
over different states, joint encoding across the states enables strictly better
secure rates. Furthermore, we specialize our results for the two receivers
channel with an external eavesdropper to the two-user broadcast channel. We
show that, the synergistic gains in terms of SDoF by alternating CSIT is not
restricted to multi-receiver wiretap channels; and, can also be harnessed under
broadcast setting.Comment: To Appear in IEEE Transactions on Information Forensics and Securit
Principles of Physical Layer Security in Multiuser Wireless Networks: A Survey
This paper provides a comprehensive review of the domain of physical layer
security in multiuser wireless networks. The essential premise of
physical-layer security is to enable the exchange of confidential messages over
a wireless medium in the presence of unauthorized eavesdroppers without relying
on higher-layer encryption. This can be achieved primarily in two ways: without
the need for a secret key by intelligently designing transmit coding
strategies, or by exploiting the wireless communication medium to develop
secret keys over public channels. The survey begins with an overview of the
foundations dating back to the pioneering work of Shannon and Wyner on
information-theoretic security. We then describe the evolution of secure
transmission strategies from point-to-point channels to multiple-antenna
systems, followed by generalizations to multiuser broadcast, multiple-access,
interference, and relay networks. Secret-key generation and establishment
protocols based on physical layer mechanisms are subsequently covered.
Approaches for secrecy based on channel coding design are then examined, along
with a description of inter-disciplinary approaches based on game theory and
stochastic geometry. The associated problem of physical-layer message
authentication is also introduced briefly. The survey concludes with
observations on potential research directions in this area.Comment: 23 pages, 10 figures, 303 refs. arXiv admin note: text overlap with
arXiv:1303.1609 by other authors. IEEE Communications Surveys and Tutorials,
201
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
Improved Rate-Equivocation Regions for Secure Cooperative Communication
A simple four node network in which cooperation improves the
information-theoretic secrecy is studied. The channel consists of two senders,
a receiver, and an eavesdropper. One or both senders transmit confidential
messages to the receiver, while the eavesdropper tries to decode the
transmitted message. The main result is the derivation of a newly achievable
rate-equivocation region that is shown to be larger than a rate-equivocation
region derived by Lai and El Gamal for the relay-eavesdropper channel. When the
rate of the helping interferer is zero, the new rate-equivocation region
reduces to the capacity-equivocation region over the wire-tap channel, hence,
the new achievability scheme can be seen as a generalization of a coding scheme
proposed by Csiszar and Korner. This result can naturally be combined with a
rate-equivocation region given by Tang et al. (for the interference assisted
secret communication), yielding an even larger achievable rate-equivocation
region.Comment: 18 pages, 5 figure
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