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 $\nu$ 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 $1/\nu$. The network approach is also used to re-derive the instanton vacuum or $Q$-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 ($\cal F$ 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

Asymptotic fingerprinting capacity in the combined digit model

We study the channel capacity of q-ary fingerprinting in the limit of large attacker coalitions. We extend known results by considering the Combined Digit Model, an attacker model that captures signal processing attacks such as averaging and noise addition. For q = 2 we give results for various attack parameter settings

Optimal attacks on qubit-based Quantum Key Recycling

Quantum Key Recycling (QKR) is a quantum-cryptographic primitive that allows one to re-use keys in an unconditionally secure way. By removing the need to repeatedly generate new keys it improves communication efficiency Skori and de Vries recently proposed a QKR scheme based on 8-state encoding (four bases). It does not require quantum computers for encryption/decryption but only single-qubit operations. We provide a missing ingredient in the security analysis of this scheme in the case of noisy channels: accurate bounds on the privacy amplification. We determine optimal attacks against the message and against the key, for 8-state encoding as well as 4-state and 6-state conjugate coding. We show that the Shannon entropy analysis for 8-state encoding reduces to the analysis of Quantum Key Distribution, whereas 4-state and 6-state suffer from additional leaks that make them less effective. We also provide results in terms of the min-entropy. Overall, 8-state encoding yields the highest capacity

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]