35,504 research outputs found
Perfectly Secure Index Coding
In this paper, we investigate the index coding problem in the presence of an
eavesdropper. Messages are to be sent from one transmitter to a number of
legitimate receivers who have side information about the messages, and share a
set of secret keys with the transmitter. We assume perfect secrecy, meaning
that the eavesdropper should not be able to retrieve any information about the
message set. We study the minimum key lengths for zero-error and perfectly
secure index coding problem. On one hand, this problem is a generalization of
the index coding problem (and thus a difficult one). On the other hand, it is a
generalization of the Shannon's cipher system. We show that a generalization of
Shannon's one-time pad strategy is optimal up to a multiplicative constant,
meaning that it obtains the entire boundary of the cone formed by looking at
the secure rate region from the origin. Finally, we consider relaxation of the
perfect secrecy and zero-error constraints to weak secrecy and asymptotically
vanishing probability of error, and provide a secure version of the result,
obtained by Langberg and Effros, on the equivalence of zero-error and
-error regions in the conventional index coding problem.Comment: 25 pages, 5 figures, submitted to the IEEE Transactions on
Information Theor
Perfectly Secure Steganography: Capacity, Error Exponents, and Code Constructions
An analysis of steganographic systems subject to the following perfect
undetectability condition is presented in this paper. Following embedding of
the message into the covertext, the resulting stegotext is required to have
exactly the same probability distribution as the covertext. Then no statistical
test can reliably detect the presence of the hidden message. We refer to such
steganographic schemes as perfectly secure. A few such schemes have been
proposed in recent literature, but they have vanishing rate. We prove that
communication performance can potentially be vastly improved; specifically, our
basic setup assumes independently and identically distributed (i.i.d.)
covertext, and we construct perfectly secure steganographic codes from public
watermarking codes using binning methods and randomized permutations of the
code. The permutation is a secret key shared between encoder and decoder. We
derive (positive) capacity and random-coding exponents for perfectly-secure
steganographic systems. The error exponents provide estimates of the code
length required to achieve a target low error probability. We address the
potential loss in communication performance due to the perfect-security
requirement. This loss is the same as the loss obtained under a weaker order-1
steganographic requirement that would just require matching of first-order
marginals of the covertext and stegotext distributions. Furthermore, no loss
occurs if the covertext distribution is uniform and the distortion metric is
cyclically symmetric; steganographic capacity is then achieved by randomized
linear codes. Our framework may also be useful for developing computationally
secure steganographic systems that have near-optimal communication performance.Comment: To appear in IEEE Trans. on Information Theory, June 2008; ignore
Version 2 as the file was corrupte
Perfectly Secure Steganography: Capacity, Error Exponents, and Code Constructions
An analysis of steganographic systems subject to the following perfect
undetectability condition is presented in this paper. Following embedding of
the message into the covertext, the resulting stegotext is required to have
exactly the same probability distribution as the covertext. Then no statistical
test can reliably detect the presence of the hidden message. We refer to such
steganographic schemes as perfectly secure. A few such schemes have been
proposed in recent literature, but they have vanishing rate. We prove that
communication performance can potentially be vastly improved; specifically, our
basic setup assumes independently and identically distributed (i.i.d.)
covertext, and we construct perfectly secure steganographic codes from public
watermarking codes using binning methods and randomized permutations of the
code. The permutation is a secret key shared between encoder and decoder. We
derive (positive) capacity and random-coding exponents for perfectly-secure
steganographic systems. The error exponents provide estimates of the code
length required to achieve a target low error probability. We address the
potential loss in communication performance due to the perfect-security
requirement. This loss is the same as the loss obtained under a weaker order-1
steganographic requirement that would just require matching of first-order
marginals of the covertext and stegotext distributions. Furthermore, no loss
occurs if the covertext distribution is uniform and the distortion metric is
cyclically symmetric; steganographic capacity is then achieved by randomized
linear codes. Our framework may also be useful for developing computationally
secure steganographic systems that have near-optimal communication performance.Comment: To appear in IEEE Trans. on Information Theory, June 2008; ignore
Version 2 as the file was corrupte
Weakly Secure Regenerating Codes for Distributed Storage
We consider the problem of secure distributed data storage under the paradigm
of \emph{weak security}, in which no \emph{meaningful information} is leaked to
the eavesdropper. More specifically, the eavesdropper cannot get any
information about any individual message file or a small group of files. The
key benefit of the weak security paradigm is that it incurs no loss in the
storage capacity, which makes it practically appealing.
In this paper, we present a coding scheme, using a coset coding based outer
code and a Product-Matrix Minimum Bandwidth Regenerating code (proposed by
Rashmi et al.) as an inner code, that achieves weak security when the
eavesdropper can observe any single storage node. We show that the proposed
construction has good security properties and requires small finite field size.Comment: Extended version of the paper accepted in NetCod 201
On the Secure DoF of the Single-Antenna MAC
A new achievability rate region for the secure discrete memoryless
Multiple-Access-Channel (MAC) is presented. Thereafter, a novel secure coding
scheme is proposed to achieve a positive Secure Degrees-of-Freedom (S-DoF) in
the single-antenna MAC. This scheme converts the single-antenna system into a
multiple-dimension system with fractional dimensions. The achievability scheme
is based on the alignment of signals into a small sub-space at the
eavesdropper, and the simultaneous separation of the signals at the intended
receiver. Tools from the field of Diophantine Approximation in number theory
are used to analyze the probability of error in the coding scheme.Comment: 5 Pages, Submitted to ISIT 201
Secure Multiterminal Source Coding with Side Information at the Eavesdropper
The problem of secure multiterminal source coding with side information at
the eavesdropper is investigated. This scenario consists of a main encoder
(referred to as Alice) that wishes to compress a single source but
simultaneously satisfying the desired requirements on the distortion level at a
legitimate receiver (referred to as Bob) and the equivocation rate --average
uncertainty-- at an eavesdropper (referred to as Eve). It is further assumed
the presence of a (public) rate-limited link between Alice and Bob. In this
setting, Eve perfectly observes the information bits sent by Alice to Bob and
has also access to a correlated source which can be used as side information. A
second encoder (referred to as Charlie) helps Bob in estimating Alice's source
by sending a compressed version of its own correlated observation via a
(private) rate-limited link, which is only observed by Bob. For instance, the
problem at hands can be seen as the unification between the Berger-Tung and the
secure source coding setups. Inner and outer bounds on the so called
rates-distortion-equivocation region are derived. The inner region turns to be
tight for two cases: (i) uncoded side information at Bob and (ii) lossless
reconstruction of both sources at Bob --secure distributed lossless
compression. Application examples to secure lossy source coding of Gaussian and
binary sources in the presence of Gaussian and binary/ternary (resp.) side
informations are also considered. Optimal coding schemes are characterized for
some cases of interest where the statistical differences between the side
information at the decoders and the presence of a non-zero distortion at Bob
can be fully exploited to guarantee secrecy.Comment: 26 pages, 16 figures, 2 table
New Results on Multiple-Input Multiple-Output Broadcast Channels with Confidential Messages
This paper presents two new results on multiple-input multiple-output (MIMO)
Gaussian broadcast channels with confidential messages. First, the problem of
the MIMO Gaussian wiretap channel is revisited. A matrix characterization of
the capacity-equivocation region is provided, which extends the previous result
on the secrecy capacity of the MIMO Gaussian wiretap channel to the general,
possibly imperfect secrecy setting. Next, the problem of MIMO Gaussian
broadcast channels with two receivers and three independent messages: a common
message intended for both receivers, and two confidential messages each
intended for one of the receivers but needing to be kept asymptotically
perfectly secret from the other, is considered. A precise characterization of
the capacity region is provided, generalizing the previous results which
considered only two out of three possible messages.Comment: Submitted to the IEEE Transactions on Information Theory, 11 pages, 5
figure
An Equivalence Between Secure Network and Index Coding
We extend the equivalence between network coding and index coding by Effros,
El Rouayheb, and Langberg to the secure communication setting in the presence
of an eavesdropper. Specifically, we show that the most general versions of
secure network-coding setup by Chan and Grant and the secure index-coding setup
by Dau, Skachek, and Chee, which also include the randomised encoding setting,
are equivalent
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