891 research outputs found
Universal secure rank-metric coding schemes with optimal communication overheads
We study the problem of reducing the communication overhead from a noisy
wire-tap channel or storage system where data is encoded as a matrix, when more
columns (or their linear combinations) are available. We present its
applications to reducing communication overheads in universal secure linear
network coding and secure distributed storage with crisscross errors and
erasures and in the presence of a wire-tapper. Our main contribution is a
method to transform coding schemes based on linear rank-metric codes, with
certain properties, to schemes with lower communication overheads. By applying
this method to pairs of Gabidulin codes, we obtain coding schemes with optimal
information rate with respect to their security and rank error correction
capability, and with universally optimal communication overheads, when , being and the number of columns and number of rows,
respectively. Moreover, our method can be applied to other families of maximum
rank distance codes when . The downside of the method is generally
expanding the packet length, but some practical instances come at no cost.Comment: 21 pages, LaTeX; parts of this paper have been accepted for
presentation at the IEEE International Symposium on Information Theory,
Aachen, Germany, June 201
Secret message capacity of a line network
We investigate the problem of information theoretically secure communication
in a line network with erasure channels and state feedback. We consider a
spectrum of cases for the private randomness that intermediate nodes can
generate, ranging from having intermediate nodes generate unlimited private
randomness, to having intermediate nodes generate no private randomness, and
all cases in between. We characterize the secret message capacity when either
only one of the channels is eavesdropped or all of the channels are
eavesdropped, and we develop polynomial time algorithms that achieve these
capacities. We also give an outer bound for the case where an arbitrary number
of channels is eavesdropped. Our work is the first to characterize the secrecy
capacity of a network of arbitrary size, with imperfect channels and feedback.
As a side result, we derive the secret key and secret message capacity of an
one-hop network, when the source has limited randomness
Coding against a Limited-view Adversary: The Effect of Causality and Feedback
We consider the problem of communication over a multi-path network in the
presence of a causal adversary. The limited-view causal adversary is able to
eavesdrop on a subset of links and also jam on a potentially overlapping subset
of links based on the current and past information. To ensure that the
communication takes place reliably and secretly, resilient network codes with
necessary redundancy are needed. We study two adversarial models - additive and
overwrite jamming and we optionally assume passive feedback from decoder to
encoder, i.e., the encoder sees everything that the decoder sees. The problem
assumes transmissions are in the large alphabet regime. For both jamming
models, we find the capacity under four scenarios - reliability without
feedback, reliability and secrecy without feedback, reliability with passive
feedback, reliability and secrecy with passive feedback. We observe that, in
comparison to the non-causal setting, the capacity with a causal adversary is
strictly increased for a wide variety of parameter settings and present our
intuition through several examples.Comment: 15 page
Centralized and Cooperative Transmission of Secure Multiple Unicasts using Network Coding
We introduce a method for securely delivering a set of messages to a group of
clients over a broadcast erasure channel where each client is interested in a
distinct message. Each client is able to obtain its own message but not the
others'. In the proposed method the messages are combined together using a
special variant of random linear network coding. Each client is provided with a
private set of decoding coefficients to decode its own message. Our method
provides security for the transmission sessions against computational
brute-force attacks and also weakly security in information theoretic sense. As
the broadcast channel is assumed to be erroneous, the missing coded packets
should be recovered in some way. We consider two different scenarios. In the
first scenario the missing packets are retransmitted by the base station
(centralized). In the second scenario the clients cooperate with each other by
exchanging packets (decentralized). In both scenarios, network coding
techniques are exploited to increase the total throughput. For the case of
centralized retransmissions we provide an analytical approximation for the
throughput performance of instantly decodable network coded (IDNC)
retransmissions as well as numerical experiments. For the decentralized
scenario, we propose a new IDNC based retransmission method where its
performance is evaluated via simulations and analytical approximation.
Application of this method is not limited to our special problem and can be
generalized to a new class of problems introduced in this paper as the
cooperative index coding problem
On Intercept Probability Minimization under Sparse Random Linear Network Coding
This paper considers a network where a node wishes to transmit a source
message to a legitimate receiver in the presence of an eavesdropper. The
transmitter secures its transmissions employing a sparse implementation of
Random Linear Network Coding (RLNC). A tight approximation to the probability
of the eavesdropper recovering the source message is provided. The proposed
approximation applies to both the cases where transmissions occur without
feedback or where the reliability of the feedback channel is impaired by an
eavesdropper jamming the feedback channel. An optimization framework for
minimizing the intercept probability by optimizing the sparsity of the RLNC is
also presented. Results validate the proposed approximation and quantify the
gain provided by our optimization over solutions where non-sparse RLNC is used.Comment: To appear on IEEE Transactions on Vehicular Technolog
Secret Communication over Broadcast Erasure Channels with State-feedback
We consider a 1-to- communication scenario, where a source transmits
private messages to receivers through a broadcast erasure channel, and the
receivers feed back strictly causally and publicly their channel states after
each transmission. We explore the achievable rate region when we require that
the message to each receiver remains secret - in the information theoretical
sense - from all the other receivers. We characterize the capacity of secure
communication in all the cases where the capacity of the 1-to- communication
scenario without the requirement of security is known. As a special case, we
characterize the secret-message capacity of a single receiver point-to-point
erasure channel with public state-feedback in the presence of a passive
eavesdropper.
We find that in all cases where we have an exact characterization, we can
achieve the capacity by using linear complexity two-phase schemes: in the first
phase we create appropriate secret keys, and in the second phase we use them to
encrypt each message. We find that the amount of key we need is smaller than
the size of the message, and equal to the amount of encrypted message the
potential eavesdroppers jointly collect. Moreover, we prove that a dishonest
receiver that provides deceptive feedback cannot diminish the rate experienced
by the honest receivers.
We also develop a converse proof which reflects the two-phase structure of
our achievability scheme. As a side result, our technique leads to a new outer
bound proof for the non-secure communication problem
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