12 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
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
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
Separation of Reliability and Secrecy in Rate-Limited Secret-Key Generation
For a discrete or a continuous source model, we study the problem of
secret-key generation with one round of rate-limited public communication
between two legitimate users. Although we do not provide new bounds on the
wiretap secret-key (WSK) capacity for the discrete source model, we use an
alternative achievability scheme that may be useful for practical applications.
As a side result, we conveniently extend known bounds to the case of a
continuous source model. Specifically, we consider a sequential key-generation
strategy, that implements a rate-limited reconciliation step to handle
reliability, followed by a privacy amplification step performed with extractors
to handle secrecy. We prove that such a sequential strategy achieves the best
known bounds for the rate-limited WSK capacity (under the assumption of
degraded sources in the case of two-way communication). However, we show that,
unlike the case of rate-unlimited public communication, achieving the
reconciliation capacity in a sequential strategy does not necessarily lead to
achieving the best known bounds for the WSK capacity. Consequently, reliability
and secrecy can be treated successively but not independently, thereby
exhibiting a limitation of sequential strategies for rate-limited public
communication. Nevertheless, we provide scenarios for which reliability and
secrecy can be treated successively and independently, such as the two-way
rate-limited SK capacity, the one-way rate-limited WSK capacity for degraded
binary symmetric sources, and the one-way rate-limited WSK capacity for
Gaussian degraded sources.Comment: 18 pages, two-column, 9 figures, accepted to IEEE Transactions on
Information Theory; corrected typos; updated references; minor change in
titl