114 research outputs found
The Secrecy Capacity of Compound Gaussian MIMO Wiretap Channels
Strong secrecy capacity of compound wiretap channels is studied. The known
lower bounds for the secrecy capacity of compound finite-state memoryless
channels under discrete alphabets are extended to arbitrary uncertainty sets
and continuous alphabets under the strong secrecy criterion. The conditions
under which these bounds are tight are given. Under the saddle-point condition,
the compound secrecy capacity is shown to be equal to that of the worst-case
channel. Based on this, the compound Gaussian MIMO wiretap channel is studied
under the spectral norm constraint and without the degradedness assumption.
First, it is assumed that only the eavesdropper channel is unknown, but is
known to have a bounded spectral norm (maximum channel gain). The compound
secrecy capacity is established in a closed form and the optimal signaling is
identified: the compound capacity equals the worst-case channel capacity thus
establishing the saddle-point property; the optimal signaling is Gaussian and
on the eigenvectors of the legitimate channel and the worst-case eavesdropper
is isotropic. The eigenmode power allocation somewhat resembles the standard
water-filling but is not identical to it. More general uncertainty sets are
considered and the existence of a maximum element is shown to be sufficient for
a saddle-point to exist, so that signaling on the worst-case channel achieves
the compound capacity of the whole class of channels. The case of
rank-constrained eavesdropper is considered and the respective compound secrecy
capacity is established. Subsequently, the case of additive uncertainty in the
legitimate channel, in addition to the unknown eavesdropper channel, is
studied. Its compound secrecy capacity and the optimal signaling are
established in a closed-form as well, revealing the same saddle-point property.Comment: accepted for publication in IEEE Trans. Inf. Theor
Deep Learning for the Gaussian Wiretap Channel
End-to-end learning of communication systems with neural networks and
particularly autoencoders is an emerging research direction which gained
popularity in the last year. In this approach, neural networks learn to
simultaneously optimize encoding and decoding functions to establish reliable
message transmission. In this paper, this line of thinking is extended to
communication scenarios in which an eavesdropper must further be kept ignorant
about the communication. The secrecy of the transmission is achieved by
utilizing a modified secure loss function based on cross-entropy which can be
implemented with state-of-the-art machine-learning libraries. This secure loss
function approach is applied in a Gaussian wiretap channel setup, for which it
is shown that the neural network learns a trade-off between reliable
communication and information secrecy by clustering learned constellations. As
a result, an eavesdropper with higher noise cannot distinguish between the
symbols anymore.Comment: 6 pages, 11 figure
Secret-Key Generation Using Compound Sources and One-Way Public Communication
In the classical Secret-Key generation model, Common Randomness is generated
by two terminals based on the observation of correlated components of a common
source, while keeping it secret from a non-legitimate observer. It is assumed
that the statistics of the source are known to all participants. In this work,
the Secret-Key generation based on a compound source is studied where the
realization of the source statistic is unknown. The protocol should guarantee
the security and reliability of the generated Secret-Key, simultaneously for
all possible realizations of the compound source. A single-letter lower-bound
of the Secret-Key capacity for a finite compound source is derived as a
function of the public communication rate constraint. A multi-letter capacity
formula is further computed for a finite compound source for the case in which
the public communication is unconstrained. Finally a single-letter capacity
formula is derived for a degraded compound source with an arbitrary set of
source states and a finite set of marginal states
Wiretap Channels: Nonasymptotic Fundamental Limits
This paper investigates the maximal secret communication rate over a wiretap
channel subject to reliability and secrecy constraints at a given blocklength.
New achievability and converse bounds are derived, which are uniformly tighter
than existing bounds, and lead to the tightest bounds on the second-order
coding rate for discrete memoryless and Gaussian wiretap channels. The exact
second-order coding rate is established for semi-deterministic wiretap
channels, which characterizes the optimal tradeoff between reliability and
secrecy in the finite-blocklength regime. Underlying our achievability bounds
are two new privacy amplification results, which not only refine the existing
results, but also achieve stronger notions of secrecy.Comment: 53 pages, 3 figure
On the Continuity of the Secrecy Capacity of Compound and Arbitrarily Varying Wiretap Channels
The wiretap channel models secure communication between two users in the
presence of an eavesdropper who must be kept ignorant of transmitted messages.
The performance of such a system is usually characterized by its secrecy
capacity which determines the maximum transmission rate of secure
communication. In this paper, the issue of whether or not the secrecy capacity
is a continuous function of the system parameters is examined. In particular,
this is done for channel uncertainty modeled via compound channels and
arbitrarily varying channels, in which the legitimate users know only that the
true channel realization is from a pre-specified uncertainty set. In the former
model, this realization remains constant for the entire duration of
transmission, while in the latter the realization varies from channel use to
channel use in an unknown and arbitrary manner. These models not only capture
the case of channel uncertainty, but are also suitable for modeling scenarios
in which a malicious adversary jams or otherwise influence the legitimate
transmission. The secrecy capacity of the compound wiretap channel is shown to
be robust in the sense that it is a continuous function of the uncertainty set.
Thus, small variations in the uncertainty set lead to small variations in
secrecy capacity. On the other hand, the deterministic secrecy capacity of the
\emph{arbitrarily varying wiretap channel} is shown to be discontinuous in the
uncertainty set meaning that small variations can lead to dramatic losses in
capacity.Comment: 17 pages, 3 figures, final versio
On The Capacity of Broadcast Channels With Degraded Message Sets and Message Cognition Under Different Secrecy Constraints
This paper considers a three-receiver broadcast channel with degraded message
sets and message cognition. The model consists of a common message for all
three receivers, a private common message for only two receivers and two
additional private messages for these two receivers, such that each receiver is
only interested in one message, while being fully cognizant of the other one.
First, this model is investigated without any secrecy constraints, where the
capacity region is established, showing that the straightforward extension of
the K\"orner and Marton inner bound to the investigated scenario is optimal. In
particular, this agrees with Nair and Wang's result, which states that the idea
of indirect decoding - introduced to improve the K\"orner and Marton inner
bound - does not provide a better region for this scenario. Further, some
secrecy constraints are introduced by letting the private messages to be
confidential ones. Two different secrecy criteria are considered: joint secrecy
and individual secrecy. For both criteria, a general achievable rate region is
provided. Moreover, the joint and individual secrecy capacity regions are
established, if the two legitimate receivers are more capable than the
eavesdropper. The established capacity regions indicate that the individual
secrecy criterion can provide a larger capacity region as compared to the joint
one, because each cognizant message can be used as a secret key for the other
individual message. Further, the joint secrecy capacity is established for a
more general class of more capable channels, where only one of the two
legitimate receivers is more capable than the eavesdropper. This was done by
showing that principle of indirect decoding introduced by Nair and El Gamal is
optimal for this class of channels. This result is in contrast with the
nonsecrecy case, where the indirect decoding does not provide any gain
Secure Broadcasting Using Independent Secret Keys
The problem of secure broadcasting with independent secret keys is studied.
The particular scenario is analyzed in which a common message has to be
broadcast to two legitimate receivers, while keeping an external eavesdropper
ignorant of it. The transmitter shares independent secret keys of sufficiently
high rates with both legitimate receivers, which can be used in different ways:
they can be used as one-time pads to encrypt the common message, as fictitious
messages for wiretap coding, or as a hybrid of these. In this paper, capacity
results are established when the broadcast channels involving the three
receivers are degraded. If both legitimate channels are degraded versions of
the eavesdropper's channel, it is shown that the one-time pad approach is
optimal for several cases, yielding corresponding capacity expressions.
Alternatively, the wiretap coding approach is shown to be optimal if the
eavesdropper's channel is degraded with respect to both legitimate channels,
establishing capacity in this case as well. If the eavesdropper's channel is
neither the strongest nor the weakest, an intricate scheme that carefully
combines both concepts of one-time pad and wiretap coding with fictitious
messages turns out to be capacity-achieving. Finally we also obtain some
results for the general non-degraded broadcast channel.Comment: 18 pages, 5 figures, final versio
Finite-Blocklength Bounds for Wiretap Channels
This paper investigates the maximal secrecy rate over a wiretap channel
subject to reliability and secrecy constraints at a given blocklength. New
achievability and converse bounds are derived, which are shown to be tighter
than existing bounds. The bounds also lead to the tightest second-order coding
rate for discrete memoryless and Gaussian wiretap channels.Comment: extended version of a paper submitted to ISIT 201
Controllable Identifier Measurements for Private Authentication with Secret Keys
The problem of secret-key based authentication under a privacy constraint on
the source sequence is considered. The identifier measurements during
authentication are assumed to be controllable via a cost-constrained "action"
sequence. Single-letter characterizations of the optimal trade-off among the
secret-key rate, storage rate, privacy-leakage rate, and action cost are given
for the four problems where noisy or noiseless measurements of the source are
enrolled to generate or embed secret keys. The results are relevant for several
user-authentication scenarios including physical and biometric authentications
with multiple measurements. Our results include, as special cases, new results
for secret-key generation and embedding with action-dependent side information
without any privacy constraint on the enrolled source sequence.Comment: 15 page
Capacity Region Continuity of the Compound Broadcast Channel with Confidential Messages
The compound broadcast channel with confidential messages (BCC) generalizes
the BCC by modeling the uncertainty of the channel. For the compound BCC, it is
only known that the actual channel realization belongs to a pre-specified
uncertainty set of channels and that it is constant during the whole
transmission. For reliable and secure communication is necessary to operate at
a rate pair within the compound BCC capacity region. Therefore, the question
whether small variations of the uncertainty set lead to large losses of the
compound BCC capacity region is studied. It is shown that the compound BCC
model is robust, i.e., the capacity region depends continuously on the
uncertainty set
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