15 research outputs found
Nonlocal Myriad Filters for Cauchy Noise Removal
The contribution of this paper is two-fold. First, we introduce a generalized
myriad filter, which is a method to compute the joint maximum likelihood
estimator of the location and the scale parameter of the Cauchy distribution.
Estimating only the location parameter is known as myriad filter. We propose an
efficient algorithm to compute the generalized myriad filter and prove its
convergence. Special cases of this algorithm result in the classical myriad
filtering, respective an algorithm for estimating only the scale parameter.
Based on an asymptotic analysis, we develop a second, even faster generalized
myriad filtering technique.
Second, we use our new approaches within a nonlocal, fully unsupervised
method to denoise images corrupted by Cauchy noise. Special attention is paid
to the determination of similar patches in noisy images. Numerical examples
demonstrate the excellent performance of our algorithms which have moreover the
advantage to be robust with respect to the parameter choice
Second Order Differences of Cyclic Data and Applications in Variational Denoising
In many image and signal processing applications, as interferometric
synthetic aperture radar (SAR), electroencephalogram (EEG) data analysis or
color image restoration in HSV or LCh spaces the data has its range on the
one-dimensional sphere . Although the minimization of total
variation (TV) regularized functionals is among the most popular methods for
edge-preserving image restoration such methods were only very recently applied
to cyclic structures. However, as for Euclidean data, TV regularized
variational methods suffer from the so called staircasing effect. This effect
can be avoided by involving higher order derivatives into the functional.
This is the first paper which uses higher order differences of cyclic data in
regularization terms of energy functionals for image restoration. We introduce
absolute higher order differences for -valued data in a sound way
which is independent of the chosen representation system on the circle. Our
absolute cyclic first order difference is just the geodesic distance between
points. Similar to the geodesic distances the absolute cyclic second order
differences have only values in [0,{\pi}]. We update the cyclic variational TV
approach by our new cyclic second order differences. To minimize the
corresponding functional we apply a cyclic proximal point method which was
recently successfully proposed for Hadamard manifolds. Choosing appropriate
cycles this algorithm can be implemented in an efficient way. The main steps
require the evaluation of proximal mappings of our cyclic differences for which
we provide analytical expressions. Under certain conditions we prove the
convergence of our algorithm. Various numerical examples with artificial as
well as real-world data demonstrate the advantageous performance of our
algorithm.Comment: 32 pages, 16 figures, shortened version of submitted manuscrip
Alternatives to the EM Algorithm for ML-Estimation of Location, Scatter Matrix and Degree of Freedom of the Student- Distribution
In this paper, we consider maximum likelihood estimations of the degree of
freedom parameter , the location parameter and the scatter matrix
of the multivariate Student- distribution. In particular, we are
interested in estimating the degree of freedom parameter that determines
the tails of the corresponding probability density function and was rarely
considered in detail in the literature so far. We prove that under certain
assumptions a minimizer of the negative log-likelihood function exists, where
we have to take special care of the case , for which
the Student- distribution approaches the Gaussian distribution. As
alternatives to the classical EM algorithm we propose three other algorithms
which cannot be interpreted as EM algorithm. For fixed , the first
algorithm is an accelerated EM algorithm known from the literature. However,
since we do not fix , we cannot apply standard convergence results for the
EM algorithm. The other two algorithms differ from this algorithm in the
iteration step for . We show how the objective function behaves for the
different updates of and prove for all three algorithms that it decreases
in each iteration step. We compare the algorithms as well as some accelerated
versions by numerical simulation and apply one of them for estimating the
degree of freedom parameter in images corrupted by Student- noise
Breaking Masked Implementations of the Clyde-Cipher by Means of Side-Channel Analysis
In this paper we present our solution to the CHES Challenge 2020, the task of which it was to break masked hardware respective software implementations of the lightweight cipher Clyde by means of side-channel analysis. We target the secret cipher state after processing of the first S-box layer. Using the provided trace data we obtain a strongly biased posterior distribution for the secret-shared cipher state at the targeted point; this enables us to see exploitable biases even before the secret sharing based masking. These biases on the unshared state can be evaluated one S-box at a time and combined across traces, which enables us to recover likely key hypotheses S-box by S-box.
In order to see the shared cipher state, we employ a deep neural network similar to the one used by Gohr, Jacob and Schindler to solve the CHES 2018 AES challenge. We modify their architecture to predict the exact bit sequence of the secret-shared cipher state. We find that convergence of training on this task is unsatisfying with the standard encoding of the shared cipher state and therefore introduce a different encoding of the prediction target, which we call the scattershot encoding. In order to further investigate how exactly the scattershot encoding helps to solve the task at hand, we construct a simple synthetic task where convergence problems very similar to those we observed in our side-channel task appear with the naive target data encoding but disappear with the scattershot encoding.
We complete our analysis by showing results that we obtained with a “classical” method (as opposed to an AI-based method), namely the stochastic approach, that
we generalize for this purpose first to the setting of shared keys. We show that the neural network draws on a much broader set of features, which may partially explain why the neural-network based approach massively outperforms the stochastic approach. On the other hand, the stochastic approach provides insights into properties of the implementation, in particular the observation that the S-boxes behave very different regarding the easiness respective hardness of their prediction
Attacks Against White-Box ECDSA and Discussion of Countermeasures
This paper deals with white-box implementations of the Elliptic Curve Digital Signature Algorithm (ECDSA): First, we consider attack paths to break such implementations. In particular, we provide a systematic overview of various fault attacks, to which ECDSA white-box implementations are especially susceptible. Then, we propose different mathematical countermeasures, mainly based on masking/blinding of sensitive variables, in order to prevent or at least make such attacks more difficult. We also briefly mention some typical implementational countermeasures and their challenges in the ECDSA white-box scenario. Our work has been initiated by the CHES challenge WhibOx Contest 2021, which consisted of designing and breaking white-box ECDSA implementations, so called challenges. We illustrate our results and findings by means of the submitted challenges and provide a comprehensive overview which challenge could be solved in which way. Furthermore, we analyze selected challenges in more details
Breaking Masked Implementations of the Clyde-Cipher by Means of Side-Channel Analysis: A Report on the CHES Challenge Side-Channel Contest 2020
In this paper we present our solution to the CHES Challenge 2020, the task of which it was to break masked hardware respective software implementations of the lightweight cipher Clyde by means of side-channel analysis. We target the secret cipher state after processing of the first S-box layer. Using the provided trace data we obtain a strongly biased posterior distribution for the secret-shared cipher state at the targeted point; this enables us to see exploitable biases even before the secret sharing based masking. These biases on the unshared state can be evaluated one S-box at a time and combined across traces, which enables us to recover likely key hypotheses S-box by S-box.In order to see the shared cipher state, we employ a deep neural network similar to the one used by Gohr, Jacob and Schindler to solve the CHES 2018 AES challenge. We modify their architecture to predict the exact bit sequence of the secret-shared cipher state. We find that convergence of training on this task is unsatisfying with the standard encoding of the shared cipher state and therefore introduce a different encoding of the prediction target, which we call the scattershot encoding. In order to further investigate how exactly the scattershot encoding helps to solve the task at hand, we construct a simple synthetic task where convergence problems very similar to those we observed in our side-channel task appear with the naive target data encoding but disappear with the scattershot encoding.We complete our analysis by showing results that we obtained with a “classical” method (as opposed to an AI-based method), namely the stochastic approach, thatwe generalize for this purpose first to the setting of shared keys. We show that the neural network draws on a much broader set of features, which may partially explain why the neural-network based approach massively outperforms the stochastic approach. On the other hand, the stochastic approach provides insights into properties of the implementation, in particular the observation that the S-boxes behave very different regarding the easiness respective hardness of their prediction