1,841 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
Quantum Quench in the Transverse Field Ising chain I: Time evolution of order parameter correlators
We consider the time evolution of order parameter correlation functions after
a sudden quantum quench of the magnetic field in the transverse field Ising
chain. Using two novel methods based on determinants and form factor sums
respectively, we derive analytic expressions for the asymptotic behaviour of
one and two point correlators. We discuss quenches within the ordered and
disordered phases as well as quenches between the phases and to the quantum
critical point. We give detailed account of both methods.Comment: 65 pages, 21 figures, some typos correcte
Asymptotic solutions of almost diagonal differential and difference systems
New methods for both asymptotic integration of the linear differential systems Y\u27(t) = [D( t) + R(t)]Y( t) and asymptotic summation of the linear difference systems Y(t + 1) = [D(t)+ R(t)]Y(t) are derived. The fundamental solution Y(t) = phi( t)[I+P(t)] for differential and difference systems is constructed in terms of a product. The first matrix function phi(t) is decided by the diagonal matrix D(t) and the second matrix I + P(t) is a perturbation of the identity matrix I. Another fundamental solution Y( t) = [I + Q(t)]phi( t) is also constructed for difference systems. Conditions are given on the matrix [D(t) + R( t)] that allow us to represent I + P( t) or Q(t) + I as an absolutely convergent resolvent series without imposing stringent conditions on R(t). In particular the analogs, in the setting of difference equations, of fundamental theorems of Levison and Hartman-Wintner are shown to follow from one and same theorem in this work
- …