4,914 research outputs found
Secret Key Agreement from Correlated Gaussian Sources by Rate Limited Public Communication
We investigate the secret key agreement from correlated Gaussian sources in
which the legitimate parties can use the public communication with limited
rate. For the class of protocols with the one-way public communication, we show
a closed form expression of the optimal trade-off between the rate of key
generation and the rate of the public communication. Our results clarify an
essential difference between the key agreement from discrete sources and that
from continuous sources.Comment: 9 pages, no figure, Version 2 is a published version. The results are
not changed from version 1. Explanations are polishe
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
A Lattice Coding Scheme for Secret Key Generation from Gaussian Markov Tree Sources
In this article, we study the problem of secret key generation in the
multiterminal source model, where the terminals have access to correlated
Gaussian sources. We assume that the sources form a Markov chain on a tree. We
give a nested lattice-based key generation scheme whose computational
complexity is polynomial in the number, N , of independent and identically
distributed samples observed by each source. We also compute the achievable
secret key rate and give a class of examples where our scheme is optimal in the
fine quantization limit. However, we also give examples that show that our
scheme is not always optimal in the limit of fine quantization.Comment: 10 pages, 3 figures. A 5-page version of this article has been
submitted to the 2016 IEEE International Symposium on Information Theory
(ISIT
Secret key generation from Gaussian sources using lattice hashing
We propose a simple yet complete lattice-based scheme for secret key
generation from Gaussian sources in the presence of an eavesdropper, and show
that it achieves strong secret key rates up to 1/2 nat from the optimal in the
case of "degraded" source models. The novel ingredient of our scheme is a
lattice-hashing technique, based on the notions of flatness factor and channel
intrinsic randomness. The proposed scheme does not require dithering.Comment: 5 pages, Conference (ISIT 2013
Key Capacity with Limited One-Way Communication for Product Sources
We show that for product sources, rate splitting is optimal for secret key
agreement using limited one-way communication at two terminals. This yields an
alternative proof of the tensorization property of a strong data processing
inequality originally studied by Erkip and Cover and amended recently by
Anantharam et al. We derive a `water-filling' solution of the
communication-rate--key-rate tradeoff for two arbitrarily correlated vector
Gaussian sources, for the case with an eavesdropper, and for stationary
Gaussian processes.Comment: 5 pages, ISIT 201
Compressed Secret Key Agreement: Maximizing Multivariate Mutual Information Per Bit
The multiterminal secret key agreement problem by public discussion is
formulated with an additional source compression step where, prior to the
public discussion phase, users independently compress their private sources to
filter out strongly correlated components for generating a common secret key.
The objective is to maximize the achievable key rate as a function of the joint
entropy of the compressed sources. Since the maximum achievable key rate
captures the total amount of information mutual to the compressed sources, an
optimal compression scheme essentially maximizes the multivariate mutual
information per bit of randomness of the private sources, and can therefore be
viewed more generally as a dimension reduction technique. Single-letter lower
and upper bounds on the maximum achievable key rate are derived for the general
source model, and an explicit polynomial-time computable formula is obtained
for the pairwise independent network model. In particular, the converse results
and the upper bounds are obtained from those of the related secret key
agreement problem with rate-limited discussion. A precise duality is shown for
the two-user case with one-way discussion, and such duality is extended to
obtain the desired converse results in the multi-user case. In addition to
posing new challenges in information processing and dimension reduction, the
compressed secret key agreement problem helps shed new light on resolving the
difficult problem of secret key agreement with rate-limited discussion, by
offering a more structured achieving scheme and some simpler conjectures to
prove
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