38,044 research outputs found
Manifold Learning Side-Channel Attacks against Masked Cryptographic Implementations
Masking, as a common countermeasure, has been widely utilized to protect cryptographic implementations against power side-channel attacks. It significantly enhances the difficulty of attacks, as the sensitive intermediate values are randomly partitioned into multiple parts and executed on different times. The adversary must amalgamate information across diverse time samples before launching an attack, which is generally accomplished by feature extraction (e.g., Points-Of-Interest (POIs) combination and dimensionality reduction). However, traditional POIs combination methods, machine learning and deep learning techniques are often too time consuming, and necessitate a significant amount of computational resources. In this paper, we undertake the first study on manifold learning and their applications against masked cryptographic implementations. The leaked information, which manifests as the manifold of high-dimensional power traces, is mapped into a low-dimensional space and achieves feature extraction through manifold learning techniques like ISOMAP, Locally Linear Embedding (LLE), and Laplacian Eigenmaps (LE). Moreover, to reduce the complexity, we further construct explicit polynomial mappings for manifold learning to facilitate the dimensionality reduction. Compared to the classical machine learning and deep learning techniques, our schemes built from manifold learning techniques are faster, unsupervised, and only require very simple parameter tuning. Their effectiveness has been fully validated by our detailed experiments
Masking Strategies for Image Manifolds
We consider the problem of selecting an optimal mask for an image manifold,
i.e., choosing a subset of the pixels of the image that preserves the
manifold's geometric structure present in the original data. Such masking
implements a form of compressive sensing through emerging imaging sensor
platforms for which the power expense grows with the number of pixels acquired.
Our goal is for the manifold learned from masked images to resemble its full
image counterpart as closely as possible. More precisely, we show that one can
indeed accurately learn an image manifold without having to consider a large
majority of the image pixels. In doing so, we consider two masking methods that
preserve the local and global geometric structure of the manifold,
respectively. In each case, the process of finding the optimal masking pattern
can be cast as a binary integer program, which is computationally expensive but
can be approximated by a fast greedy algorithm. Numerical experiments show that
the relevant manifold structure is preserved through the data-dependent masking
process, even for modest mask sizes
Out-of-sample generalizations for supervised manifold learning for classification
Supervised manifold learning methods for data classification map data samples
residing in a high-dimensional ambient space to a lower-dimensional domain in a
structure-preserving way, while enhancing the separation between different
classes in the learned embedding. Most nonlinear supervised manifold learning
methods compute the embedding of the manifolds only at the initially available
training points, while the generalization of the embedding to novel points,
known as the out-of-sample extension problem in manifold learning, becomes
especially important in classification applications. In this work, we propose a
semi-supervised method for building an interpolation function that provides an
out-of-sample extension for general supervised manifold learning algorithms
studied in the context of classification. The proposed algorithm computes a
radial basis function (RBF) interpolator that minimizes an objective function
consisting of the total embedding error of unlabeled test samples, defined as
their distance to the embeddings of the manifolds of their own class, as well
as a regularization term that controls the smoothness of the interpolation
function in a direction-dependent way. The class labels of test data and the
interpolation function parameters are estimated jointly with a progressive
procedure. Experimental results on face and object images demonstrate the
potential of the proposed out-of-sample extension algorithm for the
classification of manifold-modeled data sets
Nonlinear Supervised Dimensionality Reduction via Smooth Regular Embeddings
The recovery of the intrinsic geometric structures of data collections is an
important problem in data analysis. Supervised extensions of several manifold
learning approaches have been proposed in the recent years. Meanwhile, existing
methods primarily focus on the embedding of the training data, and the
generalization of the embedding to initially unseen test data is rather
ignored. In this work, we build on recent theoretical results on the
generalization performance of supervised manifold learning algorithms.
Motivated by these performance bounds, we propose a supervised manifold
learning method that computes a nonlinear embedding while constructing a smooth
and regular interpolation function that extends the embedding to the whole data
space in order to achieve satisfactory generalization. The embedding and the
interpolator are jointly learnt such that the Lipschitz regularity of the
interpolator is imposed while ensuring the separation between different
classes. Experimental results on several image data sets show that the proposed
method outperforms traditional classifiers and the supervised dimensionality
reduction algorithms in comparison in terms of classification accuracy in most
settings
A study of the classification of low-dimensional data with supervised manifold learning
Supervised manifold learning methods learn data representations by preserving
the geometric structure of data while enhancing the separation between data
samples from different classes. In this work, we propose a theoretical study of
supervised manifold learning for classification. We consider nonlinear
dimensionality reduction algorithms that yield linearly separable embeddings of
training data and present generalization bounds for this type of algorithms. A
necessary condition for satisfactory generalization performance is that the
embedding allow the construction of a sufficiently regular interpolation
function in relation with the separation margin of the embedding. We show that
for supervised embeddings satisfying this condition, the classification error
decays at an exponential rate with the number of training samples. Finally, we
examine the separability of supervised nonlinear embeddings that aim to
preserve the low-dimensional geometric structure of data based on graph
representations. The proposed analysis is supported by experiments on several
real data sets
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