11,094 research outputs found
INFORMATION THEORETIC SECRET KEY GENERATION: STRUCTURED CODES AND TREE PACKING
This dissertation deals with a multiterminal source model for
secret key generation by multiple network terminals with prior and
privileged access to a set of correlated signals complemented by
public discussion among themselves. Emphasis is placed on a
characterization of secret key capacity, i.e., the largest rate of
an achievable secret key, and on algorithms for key construction.
Various information theoretic security requirements of increasing
stringency: weak, strong and perfect secrecy, as well as different
types of sources: finite-valued and continuous, are studied.
Specifically, three different models are investigated.
First, we consider strong secrecy generation for a
discrete multiterminal source model. We discover a
connection between secret key capacity and a new
source coding concept of ``minimum information rate for signal dissemination,''
that is of independent interest in multiterminal data compression.
Our main contribution is to show for this discrete model
that structured linear codes suffice to generate a
strong secret key of the best rate.
Second, strong secrecy generation is considered for models with
continuous observations, in particular jointly Gaussian signals.
In the absence of suitable analogs of source coding notions for
the previous discrete model, new techniques are required for a
characterization of secret key capacity as well as for the design
of algorithms for secret key generation. Our proof of the secret
key capacity result, in particular the converse proof, as well as
our capacity-achieving algorithms for secret key construction
based on structured codes and quantization for a model with two
terminals, constitute the two main contributions for this second
model.
Last, we turn our attention to perfect secrecy generation for
fixed signal observation lengths as well as for their asymptotic
limits. In contrast with the analysis of the previous two models
that relies on probabilistic techniques, perfect secret key
generation bears the essence of ``zero-error information theory,''
and accordingly, we rely on mathematical techniques of a
combinatorial nature. The model under consideration is the
``Pairwise Independent Network'' (PIN) model in which every pair
of terminals share a random binary string, with the strings shared
by distinct pairs of terminals being mutually independent. This
model, which is motivated by practical aspects of a wireless
communication network in which terminals communicate on the same
frequency, results in three main contributions. First, the
concept of perfect omniscience in data compression leads to a
single-letter formula for the perfect secret key capacity of the
PIN model; moreover, this capacity is shown to be achieved by
linear noninteractive public communication, and coincides with
strong secret key capacity. Second, taking advantage of a
multigraph representation of the PIN model, we put forth an
efficient algorithm for perfect secret key generation based on a
combinatorial concept of maximal packing of Steiner trees of the
multigraph. When all the terminals seek to share perfect secrecy,
the algorithm is shown to achieve capacity. When only a subset of
terminals wish to share perfect secrecy, the algorithm is shown to
achieve at least half of it. Additionally, we obtain nonasymptotic
and asymptotic bounds on the size and rate of the best perfect
secret key generated by the algorithm. These bounds are of
independent interest from a purely graph theoretic viewpoint as
they constitute new estimates for the maximum size and rate of
Steiner tree packing of a given multigraph. Third, a particular
configuration of the PIN model arises when a lone ``helper''
terminal aids all the other ``user'' terminals generate perfect
secrecy. This model has special features that enable us to obtain
necessary and sufficient conditions for Steiner tree packing to
achieve perfect secret key capacity
Secret-key Agreement with Channel State Information at the Transmitter
We study the capacity of secret-key agreement over a wiretap channel with
state parameters. The transmitter communicates to the legitimate receiver and
the eavesdropper over a discrete memoryless wiretap channel with a memoryless
state sequence. The transmitter and the legitimate receiver generate a shared
secret key, that remains secret from the eavesdropper. No public discussion
channel is available. The state sequence is known noncausally to the
transmitter. We derive lower and upper bounds on the secret-key capacity. The
lower bound involves constructing a common state reconstruction sequence at the
legitimate terminals and binning the set of reconstruction sequences to obtain
the secret-key. For the special case of Gaussian channels with additive
interference (secret-keys from dirty paper channel) our bounds differ by 0.5
bit/symbol and coincide in the high signal-to-noise-ratio and high
interference-to-noise-ratio regimes. For the case when the legitimate receiver
is also revealed the state sequence, we establish that our lower bound achieves
the the secret-key capacity. In addition, for this special case, we also
propose another scheme that attains the capacity and requires only causal side
information at the transmitter and the receiver.Comment: 10 Pages, Submitted to IEEE Transactions on Information Forensics and
Security, Special Issue on Using the Physical Layer for Securing the Next
Generation of Communication System
The Capacity Region of the Source-Type Model for Secret Key and Private Key Generation
The problem of simultaneously generating a secret key (SK) and private key
(PK) pair among three terminals via public discussion is investigated, in which
each terminal observes a component of correlated sources. All three terminals
are required to generate a common secret key concealed from an eavesdropper
that has access to public discussion, while two designated terminals are
required to generate an extra private key concealed from both the eavesdropper
and the remaining terminal. An outer bound on the SK-PK capacity region was
established in [1], and was shown to be achievable for one case. In this paper,
achievable schemes are designed to achieve the outer bound for the remaining
two cases, and hence the SK-PK capacity region is established in general. The
main technique lies in the novel design of a random binning-joint decoding
scheme that achieves the existing outer bound.Comment: 20 pages, 4 figure
- …