380 research outputs found
Percolation and Connectivity in the Intrinsically Secure Communications Graph
The ability to exchange secret information is critical to many commercial,
governmental, and military networks. The intrinsically secure communications
graph (iS-graph) is a random graph which describes the connections that can be
securely established over a large-scale network, by exploiting the physical
properties of the wireless medium. This paper aims to characterize the global
properties of the iS-graph in terms of: (i) percolation on the infinite plane,
and (ii) full connectivity on a finite region. First, for the Poisson iS-graph
defined on the infinite plane, the existence of a phase transition is proven,
whereby an unbounded component of connected nodes suddenly arises as the
density of legitimate nodes is increased. This shows that long-range secure
communication is still possible in the presence of eavesdroppers. Second, full
connectivity on a finite region of the Poisson iS-graph is considered. The
exact asymptotic behavior of full connectivity in the limit of a large density
of legitimate nodes is characterized. Then, simple, explicit expressions are
derived in order to closely approximate the probability of full connectivity
for a finite density of legitimate nodes. The results help clarify how the
presence of eavesdroppers can compromise long-range secure communication.Comment: Submitted for journal publicatio
Wireless Secrecy in Large-Scale Networks
The ability to exchange secret information is critical to many commercial,
governmental, and military networks. The intrinsically secure communications
graph (iS-graph) is a random graph which describes the connections that can be
securely established over a large-scale network, by exploiting the physical
properties of the wireless medium. This paper provides an overview of the main
properties of this new class of random graphs. We first analyze the local
properties of the iS-graph, namely the degree distributions and their
dependence on fading, target secrecy rate, and eavesdropper collusion. To
mitigate the effect of the eavesdroppers, we propose two techniques that
improve secure connectivity. Then, we analyze the global properties of the
iS-graph, namely percolation on the infinite plane, and full connectivity on a
finite region. These results help clarify how the presence of eavesdroppers can
compromise secure communication in a large-scale network.Comment: To appear: Proc. IEEE Information Theory and Applications Workshop
(ITA'11), San Diego, CA, Feb. 2011, pp. 1-10, Invited Pape
Continuum Percolation in the Intrinsically Secure Communications Graph
The intrinsically secure communications graph (iS-graph) is a random graph
which captures the connections that can be securely established over a
large-scale network, in the presence of eavesdroppers. It is based on
principles of information-theoretic security, widely accepted as the strictest
notion of security. In this paper, we are interested in characterizing the
global properties of the iS-graph in terms of percolation on the infinite
plane. We prove the existence of a phase transition in the Poisson iS-graph,
whereby an unbounded component of securely connected nodes suddenly arises as
we increase the density of legitimate nodes. Our work shows that long-range
communication in a wireless network is still possible when a secrecy constraint
is present.Comment: Accepted in the IEEE International Symposium on Information Theory
and its Applications (ISITA'10), Taichung, Taiwan, Oct. 201
Techniques for Enhanced Physical-Layer Security
Information-theoretic security--widely accepted as the strictest notion of
security--relies on channel coding techniques that exploit the inherent
randomness of propagation channels to strengthen the security of communications
systems. Within this paradigm, we explore strategies to improve secure
connectivity in a wireless network. We first consider the intrinsically secure
communications graph (iS-graph), a convenient representation of the links that
can be established with information-theoretic security on a large-scale
network. We then propose and characterize two techniques--sectorized
transmission and eavesdropper neutralization--which are shown to dramatically
enhance the connectivity of the iS-graph.Comment: Pre-print, IEEE Global Telecommunications Conference (GLOBECOM'10),
Miami, FL, Dec. 201
When Does Relay Transmission Give a More Secure Connection in Wireless Ad Hoc Networks?
Relay transmission can enhance coverage and throughput, while it can be
vulnerable to eavesdropping attacks due to the additional transmission of the
source message at the relay. Thus, whether or not one should use relay
transmission for secure communication is an interesting and important problem.
In this paper, we consider the transmission of a confidential message from a
source to a destination in a decentralized wireless network in the presence of
randomly distributed eavesdroppers. The source-destination pair can be
potentially assisted by randomly distributed relays. For an arbitrary relay, we
derive exact expressions of secure connection probability for both colluding
and non-colluding eavesdroppers. We further obtain lower bound expressions on
the secure connection probability, which are accurate when the eavesdropper
density is small. By utilizing these lower bound expressions, we propose a
relay selection strategy to improve the secure connection probability. By
analytically comparing the secure connection probability for direct
transmission and relay transmission, we address the important problem of
whether or not to relay and discuss the condition for relay transmission in
terms of the relay density and source-destination distance. These analytical
results are accurate in the small eavesdropper density regime.Comment: Accepted for publication in IEEE Transactions On Information
Forensics and Securit
Percolation in the Secrecy Graph
The secrecy graph is a random geometric graph which is intended to model the
connectivity of wireless networks under secrecy constraints. Directed edges in
the graph are present whenever a node can talk to another node securely in the
presence of eavesdroppers, which, in the model, is determined solely by the
locations of the nodes and eavesdroppers. In the case of infinite networks, a
critical parameter is the maximum density of eavesdroppers that can be
accommodated while still guaranteeing an infinite component in the network,
i.e., the percolation threshold. We focus on the case where the locations of
the nodes and eavesdroppers are given by Poisson point processes, and present
bounds for different types of percolation, including in-, out- and undirected
percolation.Comment: 22 pages, 3 figure
Continuum AB percolation and AB random geometric graphs
Consider a bipartite random geometric graph on the union of two independent
homogeneous Poisson point processes in -space, with distance parameter
and intensities . We show for that if is
supercritical for the one-type random geometric graph with distance parameter
, there exists such that is supercritical (this was
previously known for ). For we also consider the restriction of this
graph to points in the unit square. Taking for fixed
, we give a strong law of large numbers as , for the
connectivity threshold of this graph
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