492 research outputs found
Strong Secrecy for Multiple Access Channels
We show strongly secret achievable rate regions for two different wiretap
multiple-access channel coding problems. In the first problem, each encoder has
a private message and both together have a common message to transmit. The
encoders have entropy-limited access to common randomness. If no common
randomness is available, then the achievable region derived here does not allow
for the secret transmission of a common message. The second coding problem
assumes that the encoders do not have a common message nor access to common
randomness. However, they may have a conferencing link over which they may
iteratively exchange rate-limited information. This can be used to form a
common message and common randomness to reduce the second coding problem to the
first one. We give the example of a channel where the achievable region equals
zero without conferencing or common randomness and where conferencing
establishes the possibility of secret message transmission. Both coding
problems describe practically relevant networks which need to be secured
against eavesdropping attacks.Comment: 55 page
On the minimal penalty for Markov order estimation
We show that large-scale typicality of Markov sample paths implies that the
likelihood ratio statistic satisfies a law of iterated logarithm uniformly to
the same scale. As a consequence, the penalized likelihood Markov order
estimator is strongly consistent for penalties growing as slowly as log log n
when an upper bound is imposed on the order which may grow as rapidly as log n.
Our method of proof, using techniques from empirical process theory, does not
rely on the explicit expression for the maximum likelihood estimator in the
Markov case and could therefore be applicable in other settings.Comment: 29 page
Secrecy Results for Compound Wiretap Channels
We derive a lower bound on the secrecy capacity of the compound wiretap
channel with channel state information at the transmitter which matches the
general upper bound on the secrecy capacity of general compound wiretap
channels given by Liang et al. and thus establishing a full coding theorem in
this case. We achieve this with a stronger secrecy criterion and the maximum
error probability criterion, and with a decoder that is robust against the
effect of randomisation in the encoding. This relieves us from the need of
decoding the randomisation parameter which is in general not possible within
this model. Moreover we prove a lower bound on the secrecy capacity of the
compound wiretap channel without channel state information and derive a
multi-letter expression for the capacity in this communication scenario.Comment: 25 pages, 1 figure. Accepted for publication in the journal "Problems
of Information Transmission". Some of the results were presented at the ITW
2011 Paraty [arXiv:1103.0135] and published in the conference paper available
at the IEEE Xplor
Equivalence between two-qubit entanglement and secure key distribution
We study the problem of secret key distillation from bipartite states in the
scenario where Alice and Bob can only perform measurements at the single-copy
level and classically process the obtained outcomes. Even with these
limitations, secret bits can be asymptotically distilled by the honest parties
from any two-qubit entangled state, under any individual attack. Our results
point out a complete equivalence between two-qubit entanglement and secure key
distribution: a key can be established through a one-qubit channel if and only
if it allows to distribute entanglement. These results can be generalized to
higher dimension for all those states that are one-copy distillable.Comment: 5 pages, REVTEX. Accepted version + added appendix. Proof of the main
result and discussion improved, conclusions unchange
The Bregman chord divergence
Distances are fundamental primitives whose choice significantly impacts the
performances of algorithms in machine learning and signal processing. However
selecting the most appropriate distance for a given task is an endeavor.
Instead of testing one by one the entries of an ever-expanding dictionary of
{\em ad hoc} distances, one rather prefers to consider parametric classes of
distances that are exhaustively characterized by axioms derived from first
principles. Bregman divergences are such a class. However fine-tuning a Bregman
divergence is delicate since it requires to smoothly adjust a functional
generator. In this work, we propose an extension of Bregman divergences called
the Bregman chord divergences. This new class of distances does not require
gradient calculations, uses two scalar parameters that can be easily tailored
in applications, and generalizes asymptotically Bregman divergences.Comment: 10 page
Distributions attaining secret key at a rate of the conditional mutual information
© International Association for Cryptologic Research 2015. In this paper we consider the problem of extracting secret key from an eavesdropped source pXY Z at a rate given by the conditional mutual information. We investigate this question under three different scenarios: (i) Alice (X) and Bob (Y) are unable to communicate but share common randomness with the eavesdropper Eve (Z), (ii) Alice and Bob are allowed one-way public communication, and (iii) Alice and Bob are allowed two-way public communication. Distributions having a key rate of the conditional mutual information are precisely those in which a “helping” Eve offers Alice and Bob no greater advantage for obtaining secret key than a fully adversarial one. For each of the above scenarios, strong necessary conditions are derived on the structure of distributions attaining a secret key rate of I(X: Y |Z). In obtaining our results, we completely solve the problem of secret key distillation under scenario (i) and identify H(S|Z) to be the optimal key rate using shared randomness, where S is the Gà cs-Körner Common Information. We thus provide an operational interpretation of the conditional Gà cs- Körner Common Information. Additionally, we introduce simple example distributions in which the rate I(X: Y |Z) is achievable if and only if two-way communication is allowed
Classical no-cloning theorem under Liouville dynamics by non-Csisz\'ar f-divergence
The Csisz\'ar f-divergence, which is a class of information distances, is
known to offer a useful tool for analysing the classical counterpart of the
cloning operations that are quantum mechanically impossible for the factorized
and marginality classical probability distributions under Liouville dynamics.
We show that a class of information distances that does not belong to this
divergence class also allows for the formulation of a classical analogue of the
quantum no-cloning theorem. We address a family of nonlinear Liouville-like
equations, and generic distances, to obtain constraints on the corresponding
functional forms, associated with the formulation of classical analogue of the
no-cloning principle.Comment: 6 pages, revised, published versio
Exponential lower bound on the highest fidelity achievable by quantum error-correcting codes
On a class of memoryless quantum channels which includes the depolarizing
channel, the highest fidelity of quantum error-correcting codes of length n and
rate R is proven to be lower bounded by 1-exp[-nE(R)+o(n)] for some function
E(R). The E(R) is positive below some threshold R', which implies R' is a lower
bound on the quantum capacity.Comment: Ver.4. In vers.1--3, I claimed Theorem 1 for general quantum
channels. Now I claim this only for a slight generalization of depolarizing
channel in this paper because Lemma 2 in vers.1--3 was wrong; the original
general statement is proved in quant-ph/0112103. Ver.5. Text sectionalized.
Appeared in PRA. The PRA article is typographically slightly crude: The LaTeX
symbol star, used as superscripts, was capriciously replaced by the asterisk
in several places after my proof readin
Spherical Code Key Distribution Protocols for Qubits
Recently spherical codes were introduced as potentially more capable
ensembles for quantum key distribution. Here we develop specific key creation
protocols for the two qubit-based spherical codes, the trine and tetrahedron,
and analyze them in the context of a suitably-tailored intercept/resend attack,
both in standard form, and a ``gentler'' version whose back-action on the
quantum state is weaker. When compared to the standard unbiased basis
protocols, BB84 and six-state, two distinct advantages are found. First, they
offer improved tolerance of eavesdropping, the trine besting its counterpart
BB84 and the tetrahedron the six-state protocol. Second, the key error rate may
be computed from the sift rate of the protocol itself, removing the need to
sacrifice key bits for this purpose. This simplifies the protocol and improves
the overall key rate.Comment: 4 pages revtex, 2 figures; clarified security analysis. Final version
for publicatio
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