265 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
Polar Coding for Secure Transmission and Key Agreement
Wyner's work on wiretap channels and the recent works on information
theoretic security are based on random codes. Achieving information theoretical
security with practical coding schemes is of definite interest. In this note,
the attempt is to overcome this elusive task by employing the polar coding
technique of Ar{\i}kan. It is shown that polar codes achieve non-trivial
perfect secrecy rates for binary-input degraded wiretap channels while enjoying
their low encoding-decoding complexity. In the special case of symmetric main
and eavesdropper channels, this coding technique achieves the secrecy capacity.
Next, fading erasure wiretap channels are considered and a secret key agreement
scheme is proposed, which requires only the statistical knowledge of the
eavesdropper channel state information (CSI). The enabling factor is the
creation of advantage over Eve, by blindly using the proposed scheme over each
fading block, which is then exploited with privacy amplification techniques to
generate secret keys.Comment: Proceedings of the 21st Annual IEEE International Symposium on
Personal, Indoor, and Mobile Radio Communications (PIMRC 2010), Sept. 2010,
Istanbul, Turke
Rate-Equivocation Optimal Spatially Coupled LDPC Codes for the BEC Wiretap Channel
We consider transmission over a wiretap channel where both the main channel
and the wiretapper's channel are Binary Erasure Channels (BEC). We use
convolutional LDPC ensembles based on the coset encoding scheme. More
precisely, we consider regular two edge type convolutional LDPC ensembles. We
show that such a construction achieves the whole rate-equivocation region of
the BEC wiretap channel.
Convolutional LDPC ensemble were introduced by Felstr\"om and Zigangirov and
are known to have excellent thresholds. Recently, Kudekar, Richardson, and
Urbanke proved that the phenomenon of "Spatial Coupling" converts MAP threshold
into BP threshold for transmission over the BEC.
The phenomenon of spatial coupling has been observed to hold for general
binary memoryless symmetric channels. Hence, we conjecture that our
construction is a universal rate-equivocation achieving construction when the
main channel and wiretapper's channel are binary memoryless symmetric channels,
and the wiretapper's channel is degraded with respect to the main channel.Comment: Working pape
The Wiretap Channel with Feedback: Encryption over the Channel
In this work, the critical role of noisy feedback in enhancing the secrecy
capacity of the wiretap channel is established. Unlike previous works, where a
noiseless public discussion channel is used for feedback, the feed-forward and
feedback signals share the same noisy channel in the present model. Quite
interestingly, this noisy feedback model is shown to be more advantageous in
the current setting. More specifically, the discrete memoryless modulo-additive
channel with a full-duplex destination node is considered first, and it is
shown that the judicious use of feedback increases the perfect secrecy capacity
to the capacity of the source-destination channel in the absence of the
wiretapper. In the achievability scheme, the feedback signal corresponds to a
private key, known only to the destination. In the half-duplex scheme, a novel
feedback technique that always achieves a positive perfect secrecy rate (even
when the source-wiretapper channel is less noisy than the source-destination
channel) is proposed. These results hinge on the modulo-additive property of
the channel, which is exploited by the destination to perform encryption over
the channel without revealing its key to the source. Finally, this scheme is
extended to the continuous real valued modulo- channel where it is
shown that the perfect secrecy capacity with feedback is also equal to the
capacity in the absence of the wiretapper.Comment: Submitted to IEEE Transactions on Information Theor
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