277 research outputs found
The entropy of keys derived from laser speckle
Laser speckle has been proposed in a number of papers as a high-entropy
source of unpredictable bits for use in security applications. Bit strings
derived from speckle can be used for a variety of security purposes such as
identification, authentication, anti-counterfeiting, secure key storage, random
number generation and tamper protection. The choice of laser speckle as a
source of random keys is quite natural, given the chaotic properties of
speckle. However, this same chaotic behaviour also causes reproducibility
problems. Cryptographic protocols require either zero noise or very low noise
in their inputs; hence the issue of error rates is critical to applications of
laser speckle in cryptography. Most of the literature uses an error reduction
method based on Gabor filtering. Though the method is successful, it has not
been thoroughly analysed.
In this paper we present a statistical analysis of Gabor-filtered speckle
patterns. We introduce a model in which perturbations are described as random
phase changes in the source plane. Using this model we compute the second and
fourth order statistics of Gabor coefficients. We determine the mutual
information between perturbed and unperturbed Gabor coefficients and the bit
error rate in the derived bit string. The mutual information provides an
absolute upper bound on the number of secure bits that can be reproducibly
extracted from noisy measurements
Optimal symmetric Tardos traitor tracing schemes
For the Tardos traitor tracing scheme, we show that by combining the
symbol-symmetric accusation function of Skoric et al. with the improved
analysis of Blayer and Tassa we get further improvements. Our construction
gives codes that are up to 4 times shorter than Blayer and Tassa's, and up to 2
times shorter than the codes from Skoric et al. Asymptotically, we achieve the
theoretical optimal codelength for Tardos' distribution function and the
symmetric score function. For large coalitions, our codelengths are
asymptotically about 4.93% of Tardos' original codelengths, which also improves
upon results from Nuida et al.Comment: 16 pages, 1 figur
The fractional quantum Hall effect: Chern-Simons mapping, duality, Luttinger liquids and the instanton vacuum
We derive, from first principles, the complete Luttinger liquid theory of
abelian quantum Hall edge states. This theory includes the effects of disorder
and Coulomb interactions as well as the coupling to external electromagnetic
fields. We introduce a theory of spatially separated (individually conserved)
edge modes, find an enlarged dual symmetry and obtain a complete classification
of quasiparticle operators and tunneling exponents. The chiral anomaly on the
edge and Laughlin's gauge argument are used to obtain unambiguously the Hall
conductance. In resolving the problem of counter flowing edge modes, we find
that the long range Coulomb interactions play a fundamental role. In order to
set up a theory for arbitrary filling fractions we use the idea of a two
dimensional network of percolating edge modes. We derive an effective, single
mode Luttinger liquid theory for tunneling processes into the quantum Hall edge
which yields a continuous tunneling exponent . The network approach is
also used to re-derive the instanton vacuum or -theory for the plateau
transitions.Comment: 36 pages, 7 figures (eps
The problem of Coulomb interactions in the theory of the quantum Hall effect
We summarize the main ingredients of a unifying theory for abelian quantum
Hall states. This theory combines the Finkelstein approach to localization and
interaction effects with the topological concept of an instanton vacuum as well
as Chern-Simons gauge theory. We elaborate on the meaning of a new symmetry
( invariance) for systems with an infinitely ranged interaction
potential. We address the renormalization of the theory and present the main
results in terms of a scaling diagram of the conductances.Comment: 9 pages, 3 figures. To appear in Proceedings of the International
Conference "Mesoscopics and Strongly Correlated Electron Systems", July 2000,
Chernogolovka, Russi
(Mis-)handling gauge invariance in the theory of the quantum Hall effect II: Perturbative results
The concept of F-invariance, which previously arose in our analysis of the
integral and half-integral quantum Hall effects, is studied in 2+2\epsilon
spatial dimensions. We report the results of a detailed renormalization group
analysis and establish the renormalizability of the (Finkelstein) action to two
loop order. We show that the infrared behavior of the theory can be extracted
from gauge invariant (F-invariant) quantities only. For these quantities
(conductivity, specific heat) we derive explicit scaling functions. We identify
a bosonic quasiparticle density of states which develops a Coulomb gap as one
approaches the metal-insulator transition from the metallic side. We discuss
the consequences of F-invariance for the strong coupling, insulating regime.Comment: 26 pages, 7 figures; minor modifications; submitted to Phys.Rev.
(Mis-)handling gauge invariance in the theory of the quantum Hall effect I: Unifying action and the \nu=1/2 state
We propose a unifying theory for both the integral and fractional quantum
Hall regimes. This theory reconciles the Finkelstein approach to localization
and interaction effects with the topological issues of an instanton vacuum and
Chern-Simons gauge theory. We elaborate on the microscopic origins of the
effective action and unravel a new symmetry in the problem with Coulomb
interactions which we name F-invariance. This symmetry has a broad range of
physical consequences which will be the main topic of future analyses. In the
second half of this paper we compute the response of the theory to
electromagnetic perturbations at a tree level approximation. This is applicable
to the theory of ordinary metals as well as the composite fermion approach to
the half-integer effect. Fluctuations in the Chern-Simons gauge fields are
found to be well behaved only when the theory is F-invariant.Comment: 20 pages, 6 figures; appendix B revised; submitted to Phys.Rev.
Tardos fingerprinting is better than we thought
We review the fingerprinting scheme by Tardos and show that it has a much
better performance than suggested by the proofs in Tardos' original paper. In
particular, the length of the codewords can be significantly reduced.
First we generalize the proofs of the false positive and false negative error
probabilities with the following modifications: (1) we replace Tardos'
hard-coded numbers by variables and (2) we allow for independently chosen false
positive and false negative error rates. It turns out that all the
collusion-resistance properties can still be proven when the code length is
reduced by a factor of more than 2.
Second, we study the statistical properties of the fingerprinting scheme, in
particular the average and variance of the accusations. We identify which
colluder strategy forces the content owner to employ the longest code. Using a
gaussian approximation for the probability density functions of the
accusations, we show that the required false negative and false positive error
rate can be achieved with codes that are a factor 2 shorter than required for
rigid proofs.
Combining the results of these two approaches, we show that the Tardos scheme
can be used with a code length approximately 5 times shorter than in the
original construction.Comment: Modified presentation of result
Spamming the code offset method
We identify an inconsistency in Subjective Logic caused by the discounting operator ‘...’. We propose a new operator, ‘...’, which resolves all the consistency problems. The new algebra makes it possible to compute Subjective Logic trust values (reputations) in arbitrarily connected trust networks. The material presented here is an excerpt of [3]
Quantum Key Recycling with 8-state encoding (The Quantum One-Time Pad is more interesting than we thought)
Perfect encryption of quantum states using the Quantum One-Time Pad (QOTP) requires two classical key bits per qubit. Almost-perfect encryption, with information-theoretic security, requires only slightly more than 1. We slightly improve lower bounds on the key length. We show that key length n+2log1ε n+2log1ε suffices to encrypt n n qubits in such a way that the cipherstate’s L 1 L1 -distance from uniformity is upperbounded by ε ε . For a stricter security definition involving the ∞ ∞ -norm, we prove sufficient key length n+logn+2log1ε +1+1n log1δ +logln21−ε n+logn+2log1ε+1+1nlog1δ+logln21−ε , where δ δ is a small probability of failure. Our proof uses Pauli operators, whereas previous results on the ∞ ∞ -norm needed Haar measure sampling. We show how to QOTP-encrypt classical plaintext in a nontrivial way: we encode a plaintext bit as the vector ±(1,1,1)∕3 – √ ±(1,1,1)∕3 on the Bloch sphere. Applying the Pauli encryption operators results in eight possible cipherstates which are equally spread out on the Bloch sphere. This encoding, especially when combined with the half-keylength option of QOTP, has advantages over 4-state and 6-state encoding in applications such as Quantum Key Recycling (QKR) and Unclonable Encryption (UE). We propose a key recycling scheme that is more efficient and can tolerate more noise than a recent scheme by Fehr and Salvail. For 8-state QOTP encryption with pseudorandom keys, we do a statistical analysis of the cipherstate eigenvalues. We present numerics up to nine qubits
A capacity-achieving simple decoder for bias-based traitor tracing schemes
We investigate alternative suspicion functions for bias-based traitor tracing schemes, and present a practical construction of a simple decoder that attains capacity in the limit of large coalition size c. We derive optimal suspicion functions in both the Restricted- Digit Model and the Combined-Digit Model. These functions depend on information that is usually not available to the tracer – the attack strategy or the tallies of the symbols received by the colluders. We discuss how such results can be used in realistic contexts. We study several combinations of coalition attack strategy versus suspicion function optimized against some attack (another attack or the same). In many of these combinations the usual codelength scaling changes to a lower power of , e.g., . We find that the interleaving strategy is an especially powerful attack. The suspicion function tailored against interleaving is the key ingredient of the capacity-achieving construction
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