120 research outputs found
Partial Strong Converse for the Non-Degraded Wiretap Channel
We prove the partial strong converse property for the discrete memoryless
\emph{non-degraded} wiretap channel, for which we require the leakage to the
eavesdropper to vanish but allow an asymptotic error probability to the legitimate receiver. We show that when the transmission rate is
above the secrecy capacity, the probability of correct decoding at the
legitimate receiver decays to zero exponentially. Therefore, the maximum
transmission rate is the same for , and the partial strong
converse property holds. Our work is inspired by a recently developed technique
based on information spectrum method and Chernoff-Cramer bound for evaluating
the exponent of the probability of correct decoding
Wiretap and Gelfand-Pinsker Channels Analogy and its Applications
An analogy framework between wiretap channels (WTCs) and state-dependent
point-to-point channels with non-causal encoder channel state information
(referred to as Gelfand-Pinker channels (GPCs)) is proposed. A good sequence of
stealth-wiretap codes is shown to induce a good sequence of codes for a
corresponding GPC. Consequently, the framework enables exploiting existing
results for GPCs to produce converse proofs for their wiretap analogs. The
analogy readily extends to multiuser broadcasting scenarios, encompassing
broadcast channels (BCs) with deterministic components, degradation ordering
between users, and BCs with cooperative receivers. Given a wiretap BC (WTBC)
with two receivers and one eavesdropper, an analogous Gelfand-Pinsker BC (GPBC)
is constructed by converting the eavesdropper's observation sequence into a
state sequence with an appropriate product distribution (induced by the
stealth-wiretap code for the WTBC), and non-causally revealing the states to
the encoder. The transition matrix of the state-dependent GPBC is extracted
from WTBC's transition law, with the eavesdropper's output playing the role of
the channel state. Past capacity results for the semi-deterministic (SD) GPBC
and the physically-degraded (PD) GPBC with an informed receiver are leveraged
to furnish analogy-based converse proofs for the analogous WTBC setups. This
characterizes the secrecy-capacity regions of the SD-WTBC and the PD-WTBC, in
which the stronger receiver also observes the eavesdropper's channel output.
These derivations exemplify how the wiretap-GP analogy enables translating
results on one problem into advances in the study of the other
The Sender-Excited Secret Key Agreement Model: Capacity, Reliability and Secrecy Exponents
We consider the secret key generation problem when sources are randomly
excited by the sender and there is a noiseless public discussion channel. Our
setting is thus similar to recent works on channels with action-dependent
states where the channel state may be influenced by some of the parties
involved. We derive single-letter expressions for the secret key capacity
through a type of source emulation analysis. We also derive lower bounds on the
achievable reliability and secrecy exponents, i.e., the exponential rates of
decay of the probability of decoding error and of the information leakage.
These exponents allow us to determine a set of strongly-achievable secret key
rates. For degraded eavesdroppers the maximum strongly-achievable rate equals
the secret key capacity; our exponents can also be specialized to previously
known results.
In deriving our strong achievability results we introduce a coding scheme
that combines wiretap coding (to excite the channel) and key extraction (to
distill keys from residual randomness). The secret key capacity is naturally
seen to be a combination of both source- and channel-type randomness. Through
examples we illustrate a fundamental interplay between the portion of the
secret key rate due to each type of randomness. We also illustrate inherent
tradeoffs between the achievable reliability and secrecy exponents. Our new
scheme also naturally accommodates rate limits on the public discussion. We
show that under rate constraints we are able to achieve larger rates than those
that can be attained through a pure source emulation strategy.Comment: 18 pages, 8 figures; Submitted to the IEEE Transactions on
Information Theory; Revised in Oct 201
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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