15,685 research outputs found
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
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
- …