31 research outputs found
Strong Secrecy for Erasure Wiretap Channels
We show that duals of certain low-density parity-check (LDPC) codes, when
used in a standard coset coding scheme, provide strong secrecy over the binary
erasure wiretap channel (BEWC). This result hinges on a stopping set analysis
of ensembles of LDPC codes with block length and girth , for some
. We show that if the minimum left degree of the ensemble is
, the expected probability of block error is
\calO(\frac{1}{n^{\lceil l_\mathrm{min} k /2 \rceil - k}}) when the erasure
probability , where
depends on the degree distribution of the ensemble. As long as and , the dual of this LDPC code provides strong secrecy over a
BEWC of erasure probability greater than .Comment: Submitted to the Information Theory Workship (ITW) 2010, Dubli
Deterministic Constructions for Large Girth Protograph LDPC Codes
The bit-error threshold of the standard ensemble of Low Density Parity Check
(LDPC) codes is known to be close to capacity, if there is a non-zero fraction
of degree-two bit nodes. However, the degree-two bit nodes preclude the
possibility of a block-error threshold. Interestingly, LDPC codes constructed
using protographs allow the possibility of having both degree-two bit nodes and
a block-error threshold. In this paper, we analyze density evolution for
protograph LDPC codes over the binary erasure channel and show that their
bit-error probability decreases double exponentially with the number of
iterations when the erasure probability is below the bit-error threshold and
long chain of degree-two variable nodes are avoided in the protograph. We
present deterministic constructions of such protograph LDPC codes with girth
logarithmic in blocklength, resulting in an exponential fall in bit-error
probability below the threshold. We provide optimized protographs, whose
block-error thresholds are better than that of the standard ensemble with
minimum bit-node degree three. These protograph LDPC codes are theoretically of
great interest, and have applications, for instance, in coding with strong
secrecy over wiretap channels.Comment: 5 pages, 2 figures; To appear in ISIT 2013; Minor changes in
presentatio
Information-theoretic Physical Layer Security for Satellite Channels
Shannon introduced the classic model of a cryptosystem in 1949, where Eve has
access to an identical copy of the cyphertext that Alice sends to Bob. Shannon
defined perfect secrecy to be the case when the mutual information between the
plaintext and the cyphertext is zero. Perfect secrecy is motivated by
error-free transmission and requires that Bob and Alice share a secret key.
Wyner in 1975 and later I.~Csisz\'ar and J.~K\"orner in 1978 modified the
Shannon model assuming that the channels are noisy and proved that secrecy can
be achieved without sharing a secret key. This model is called wiretap channel
model and secrecy capacity is known when Eve's channel is noisier than Bob's
channel.
In this paper we review the concept of wiretap coding from the satellite
channel viewpoint. We also review subsequently introduced stronger secrecy
levels which can be numerically quantified and are keyless unconditionally
secure under certain assumptions. We introduce the general construction of
wiretap coding and analyse its applicability for a typical satellite channel.
From our analysis we discuss the potential of keyless information theoretic
physical layer security for satellite channels based on wiretap coding. We also
identify system design implications for enabling simultaneous operation with
additional information theoretic security protocols
Almost universal codes for fading wiretap channels
We consider a fading wiretap channel model where the transmitter has only
statistical channel state information, and the legitimate receiver and
eavesdropper have perfect channel state information. We propose a sequence of
non-random lattice codes which achieve strong secrecy and semantic security
over ergodic fading channels. The construction is almost universal in the sense
that it achieves the same constant gap to secrecy capacity over Gaussian and
ergodic fading models.Comment: 5 pages, to be submitted to IEEE International Symposium on
Information Theory (ISIT) 201
A Survey of Physical Layer Security Techniques for 5G Wireless Networks and Challenges Ahead
Physical layer security which safeguards data confidentiality based on the
information-theoretic approaches has received significant research interest
recently. The key idea behind physical layer security is to utilize the
intrinsic randomness of the transmission channel to guarantee the security in
physical layer. The evolution towards 5G wireless communications poses new
challenges for physical layer security research. This paper provides a latest
survey of the physical layer security research on various promising 5G
technologies, including physical layer security coding, massive multiple-input
multiple-output, millimeter wave communications, heterogeneous networks,
non-orthogonal multiple access, full duplex technology, etc. Technical
challenges which remain unresolved at the time of writing are summarized and
the future trends of physical layer security in 5G and beyond are discussed.Comment: To appear in IEEE Journal on Selected Areas in Communication
Coding for Cryptographic Security Enhancement using Stopping Sets
In this paper we discuss the ability of channel codes to enhance
cryptographic secrecy. Toward that end, we present the secrecy metric of
degrees of freedom in an attacker's knowledge of the cryptogram, which is
similar to equivocation. Using this notion of secrecy, we show how a specific
practical channel coding system can be used to hide information about the
ciphertext, thus increasing the difficulty of cryptographic attacks. The system
setup is the wiretap channel model where transmitted data traverse through
independent packet erasure channels with public feedback for authenticated ARQ
(Automatic Repeat reQuest). The code design relies on puncturing nonsystematic
low-density parity-check codes with the intent of inflicting an eavesdropper
with stopping sets in the decoder. Furthermore, the design amplifies errors
when stopping sets occur such that a receiver must guess all the channel-erased
bits correctly to avoid an expected error rate of one half in the ciphertext.
We extend previous results on the coding scheme by giving design criteria that
reduces the effectiveness of a maximum-likelihood attack to that of a
message-passing attack. We further extend security analysis to models with
multiple receivers and collaborative attackers. Cryptographic security is
enhanced in all these cases by exploiting properties of the physical-layer. The
enhancement is accurately presented as a function of the degrees of freedom in
the eavesdropper's knowledge of the ciphertext, and is even shown to be present
when eavesdroppers have better channel quality than legitimate receivers.Comment: 13 pages, 8 figure
Sparse graph codes for compression, sensing, and secrecy
Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 2010.Cataloged from student PDF version of thesis.Includes bibliographical references (p. 201-212).Sparse graph codes were first introduced by Gallager over 40 years ago. Over the last two decades, such codes have been the subject of intense research, and capacity approaching sparse graph codes with low complexity encoding and decoding algorithms have been designed for many channels. Motivated by the success of sparse graph codes for channel coding, we explore the use of sparse graph codes for four other problems related to compression, sensing, and security. First, we construct locally encodable and decodable source codes for a simple class of sources. Local encodability refers to the property that when the original source data changes slightly, the compression produced by the source code can be updated easily. Local decodability refers to the property that a single source symbol can be recovered without having to decode the entire source block. Second, we analyze a simple message-passing algorithm for compressed sensing recovery, and show that our algorithm provides a nontrivial f1/f1 guarantee. We also show that very sparse matrices and matrices whose entries must be either 0 or 1 have poor performance with respect to the restricted isometry property for the f2 norm. Third, we analyze the performance of a special class of sparse graph codes, LDPC codes, for the problem of quantizing a uniformly random bit string under Hamming distortion. We show that LDPC codes can come arbitrarily close to the rate-distortion bound using an optimal quantizer. This is a special case of a general result showing a duality between lossy source coding and channel coding-if we ignore computational complexity, then good channel codes are automatically good lossy source codes. We also prove a lower bound on the average degree of vertices in an LDPC code as a function of the gap to the rate-distortion bound. Finally, we construct efficient, capacity-achieving codes for the wiretap channel, a model of communication that allows one to provide information-theoretic, rather than computational, security guarantees. Our main results include the introduction of a new security critertion which is an information-theoretic analog of semantic security, the construction of capacity-achieving codes possessing strong security with nearly linear time encoding and decoding algorithms for any degraded wiretap channel, and the construction of capacity-achieving codes possessing semantic security with linear time encoding and decoding algorithms for erasure wiretap channels. Our analysis relies on a relatively small set of tools. One tool is density evolution, a powerful method for analyzing the behavior of message-passing algorithms on long, random sparse graph codes. Another concept we use extensively is the notion of an expander graph. Expander graphs have powerful properties that allow us to prove adversarial, rather than probabilistic, guarantees for message-passing algorithms. Expander graphs are also useful in the context of the wiretap channel because they provide a method for constructing randomness extractors. Finally, we use several well-known isoperimetric inequalities (Harper's inequality, Azuma's inequality, and the Gaussian Isoperimetric inequality) in our analysis of the duality between lossy source coding and channel coding.by Venkat Bala Chandar.Ph.D