SAFE-NET: Secure and Fast Encryption using Network of Pseudo-Random Number Generators

We propose a general framework to design a general class of random number generators suit- able for both computer simulation and computer security applications. It can include newly pro- posed generators SAFE (Secure And Fast Encryption) and ChaCha, a variant of Salsa, one of the four finalists of the eSTREAM ciphers. Two requirements for ciphers to be considered se- cure is that they must be unpredictable with a nice distributional property. Proposed SAFE-NET is a network of n nodes with external pseudo-random number generators as inputs nodes, several inner layers of nodes with a sequence of random variates through ARX (Addition, Rotation, XOR) transformations to diffuse the components of the initial state vector. After several rounds of transformations (with complex inner connections) are done, the output layer with n nodes are outputted via additional transformations. By utilizing random number generators with desirable empirical properties, SAFE-NET injects randomness into the keystream generation process and constantly updates the cipher’s state with external pseudo-random numbers during each iteration. Through the integration of shuffle tables and advanced output functions, extra layers of security are provided, making it harder for attackers to exploit weaknesses in the cipher. Empirical results demonstrate that SAFE-NET requires fewer operations than ChaCha while still producing a sequence of uniformly distributed random numbers

Revamped Differential-Linear Cryptanalysis on Reduced Round ChaCha

In this paper, we provide several improvements over the existing differential-linear attacks on ChaCha. ChaCha is a stream cipher which has $20$ rounds. At CRYPTO $2020$, Beierle et al. observed a differential in the $3.5$-th round if the right pairs are chosen. They produced an improved attack using this, but showed that to achieve a right pair, we need $2^5$ iterations on average. In this direction, we provide a technique to find the right pairs with the help of listing. Also, we provide a strategical improvement in PNB construction, modification of complexity calculation and an alternative attack method using two input-output pairs. Using these, we improve the time complexity, reducing it to $2^{221.95}$ from $2^{230.86}$ reported by Beierle et al. for $256$ bit version of ChaCha. Also, after a decade, we improve existing complexity (Shi et al: ICISC 2012) for a $6$-round of $128$ bit version of ChaCha by more than 11 million times and produce the first-ever attack on 6.5-round ChaCha$128$ with time complexity $2^{123.04}.

Boundary regularity for fully nonlinear integro-differential equations

We study fine boundary regularity properties of solutions to fully nonlinear elliptic integro-differential equations of order $2s$, with $s\in(0,1)$. We consider the class of nonlocal operators $\mathcal L_*\subset \mathcal L_0$, which consists of infinitesimal generators of stable L\'evy processes belonging to the class $\mathcal L_0$ of Caffarelli-Silvestre. For fully nonlinear operators $I$ elliptic with respect to $\mathcal L_*$, we prove that solutions to $I u=f$ in $\Omega$, $u=0$ in $\mathbb R^n\setminus\Omega$, satisfy $u/d^s\in C^{s+\gamma}(\overline\Omega)$, where $d$ is the distance to $\partial\Omega$ and $f\in C^\gamma$. We expect the class $\mathcal L_*$ to be the largest scale invariant subclass of $\mathcal L_0$ for which this result is true. In this direction, we show that the class $\mathcal L_0$ is too large for all solutions to behave like $d^s$. The constants in all the estimates in this paper remain bounded as the order of the equation approaches 2. Thus, in the limit $s\uparrow1$ we recover the celebrated boundary regularity result due to Krylov for fully nonlinear elliptic equations.Comment: To appear in Duke Math.

Next Order Asymptotics and Renormalized Energy for Riesz Interactions

We study systems of $n$ points in the Euclidean space of dimension $d \ge 1$ interacting via a Riesz kernel $|x|^{-s}$ and confined by an external potential, in the regime where $d-2\le s<d$. We also treat the case of logarithmic interactions in dimensions $1$ and $2$. Our study includes and retrieves all cases previously studied in \cite{ss2d,ss1d,rs}. Our approach is based on the Caffarelli-Silvestre extension formula which allows to view the Riesz kernel as the kernel of a (inhomogeneous) local operator in the extended space $\mathbb{R}^{d+1}$. As $n \to \infty$, we exhibit a next to leading order term in $n^{1+s/d}$ in the asymptotic expansion of the total energy of the system, where the constant term in factor of $n^{1+s/d}$ depends on the microscopic arrangement of the points and is expressed in terms of a "renormalized energy." This new object is expected to penalize the disorder of an infinite set of points in whole space, and to be minimized by Bravais lattice (or crystalline) configurations. We give applications to the statistical mechanics in the case where temperature is added to the system, and identify an expected "crystallization regime." We also obtain a result of separation of the points for minimizers of the energy

Analyticity of layer potentials and L2L^{2} solvability of boundary value problems for divergence form elliptic equations with complex L∞L^{\infty} coefficients

We consider divergence form elliptic operators of the form L=-\dv A(x)\nabla, defined in $R^{n+1} = \{(x,t)\in R^n \times R \}$, $n \geq 2$, where the $L^{\infty}$ coefficient matrix $A$ is $(n+1)\times(n+1)$, uniformly elliptic, complex and $t$-independent. We show that for such operators, boundedness and invertibility of the corresponding layer potential operators on $L^2(\mathbb{R}^{n})=L^2(\partial\mathbb{R}_{+}^{n+1})$, is stable under complex, $L^{\infty}$ perturbations of the coefficient matrix. Using a variant of the $Tb$ Theorem, we also prove that the layer potentials are bounded and invertible on $L^2(\mathbb{R}^n)$ whenever $A(x)$ is real and symmetric (and thus, by our stability result, also when $A$ is complex, $\Vert A-A^0\Vert_{\infty}$ is small enough and $A^0$ is real, symmetric, $L^{\infty}$ and elliptic). In particular, we establish solvability of the Dirichlet and Neumann (and Regularity) problems, with $L^2$ (resp. $\dot{L}^2_1)$ data, for small complex perturbations of a real symmetric matrix. Previously, $L^2$ solvability results for complex (or even real but non-symmetric) coefficients were known to hold only for perturbations of constant matrices (and then only for the Dirichlet problem), or in the special case that the coefficients $A_{j,n+1}=0=A_{n+1,j}$, $1\leq j\leq n$, which corresponds to the Kato square root problem

Elliptic theory for sets with higher co-dimensional boundaries

Many geometric and analytic properties of sets hinge on the properties of harmonic measure, notoriously missing for sets of higher co-dimension. The aim of this manuscript is to develop a version of elliptic theory, associated to a linear PDE, which ultimately yields a notion analogous to that of the harmonic measure, for sets of codimension higher than 1. To this end, we turn to degenerate elliptic equations. Let $\Gamma \subset \mathbb R^n$ be an Ahlfors regular set of dimension $d<n-1$ (not necessarily integer) and $\Omega = \mathbb R^n \setminus \Gamma$. Let $L = - {\rm div} A\nabla$ be a degenerate elliptic operator with measurable coefficients such that the ellipticity constants of the matrix $A$ are bounded from above and below by a multiple of ${\rm dist}(\cdot, \Gamma)^{d+1-n}$. We define weak solutions; prove trace and extension theorems in suitable weighted Sobolev spaces; establish the maximum principle, De Giorgi-Nash-Moser estimates, the Harnack inequality, the H\"older continuity of solutions (inside and at the boundary). We define the Green function and provide the basic set of pointwise and/or $L^p$ estimates for the Green function and for its gradient. With this at hand, we define harmonic measure associated to $L$, establish its doubling property, non-degeneracy, change-of-the-pole formulas, and, finally, the comparison principle for local solutions. In another article to appear, we will prove that when $\Gamma$ is the graph of a Lipschitz function with small Lipschitz constant, we can find an elliptic operator $L$ for which the harmonic measure given here is absolutely continuous with respect to the $d$-Hausdorff measure on $\Gamma$ and vice versa. It thus extends Dahlberg's theorem to some sets of codimension higher than 1.Comment: 122 page

Chipless RFID sensor systems for structural health monitoring

Ph. D. ThesisDefects in metallic structures such as crack and corrosion are major sources of catastrophic failures, and thus monitoring them is a crucial issue. As periodic inspection using the nondestructive testing and evaluation (NDT&E) techniques is slow, costly, limited in range, and cumbersome, novel methods for in-situ structural health monitoring (SHM) are required. Chipless radio frequency identification (RFID) is an emerging and attractive technology to implement the internet of things (IoT) based SHM. Chipless RFID sensors are not only wireless, passive, and low-cost as the chipped RFID counterpart, but also printable, durable, and allow for multi-parameter sensing. This thesis proposes the design and development of chipless RFID sensor systems for SHM, particularly for defect detection and characterization in metallic structures. Through simulation studies and experimental validations, novel metal-mountable chipless RFID sensors are demonstrated with different reader configurations and methods for feature extraction, selection, and fusion. The first contribution of this thesis is the design of a chipless RFID sensor for crack detection and characterization based on the circular microstrip patch antenna (CMPA). The sensor provides a 4-bit ID and a capability of indicating crack width and orientation simultaneously using the resonance frequency shift. The second contribution is a chipless RFID sensor designed based on the frequency selective surface (FSS) and feature fusion for corrosion characterization. The FSS-based sensor generates multiple resonance frequency features that can reveal corrosion progression, while feature fusion is applied to enhance the sensitivity and reliability of the sensor. The third contribution deals with robust detection and characterization of crack and corrosion in a realistic environment using a portable reader. A multi-resonance chipless RFID sensor is proposed along with the implementation of a portable reader using an ultra-wideband (UWB) radar module. Feature extraction and selection using principal component analysis (PCA) is employed for multi-parameter evaluation. Overall, chipless RFID sensors are small, low-profile, and can be used to quantify and characterize surface crack and corrosion undercoating. Furthermore, the multi-resonance characteristics of chipless RFID sensors are useful for integrating ID encoding and sensing functionalities, enhancing the sensor performance, as well as for performing multi-parameter analysis of defects. The demonstrated system using a portable reader shows the capability of defects characterization from a 15-cm distance. Hence, chipless RFID sensor systems have great potential to be an alternative sensing method for in-situ SHM.Indonesia Endowment Fund for Education (LPDP

Methods for Photoacoustic Image Reconstruction Exploiting Properties of Curvelet Frame

Curvelet frame is of special significance for photoacoustic tomography (PAT) due to its sparsifying and microlocalisation properties. In this PhD project, we explore the methods for image reconstruction in PAT with flat sensor geometry using Curvelet properties. This thesis makes five distinct contributions: (i) We investigate formulation of the forward, adjoint and inverse operators for PAT in Fourier domain. We derive a one-to-one map between wavefront directions in image and data spaces in PAT. Combining the Fourier operators with the wavefront map allows us to create the appropriate PAT operators for solving limited-view problems due to limited angular sensor sensitivity. (ii) We devise a concept of wedge restricted Curvelet transform, a modification of standard Curvelet transform, which allows us to formulate a tight frame of wedge restricted Curvelets on the range of the PAT forward operator for PAT data representation. We consider details specific to PAT data such as symmetries, time oversampling and their consequences. We further adapt the wedge restricted Curvelet to decompose the wavefronts into visible and invisible parts in the data domain as well as in the image domain. (iii) We formulate a two step approach based on the recovery of the complete volume of the photoacoustic data from the sub-sampled data followed by the acoustic inversion, and a one step approach where the photoacoustic image is directly recovered from the subsampled data. The wedge restricted Curvelet is used as the sparse representation of the photoacoustic data in the two step approach. (iv) We discuss a joint variational approach that incorporates Curvelet sparsity in photoacoustic image domain and spatio-temporal regularization via optical flow constraint to achieve improved results for dynamic PAT reconstruction. (v) We consider the limited-view problem due to limited angular sensitivity of the sensor (see (i) for the formulation of the corresponding fast operators in Fourier domain). We propose complementary information learning approach based on splitting the problem into visible and invisible singularities. We perform a sparse reconstruction of the visible Curvelet coefficients using compressed sensing techniques and propose a tailored deep neural network architecture to recover the invisible coefficients

Mining time-series data using discriminative subsequences

Time-series data is abundant, and must be analysed to extract usable knowledge. Local-shape-based methods offer improved performance for many problems, and a comprehensible method of understanding both data and models. For time-series classification, we transform the data into a local-shape space using a shapelet transform. A shapelet is a time-series subsequence that is discriminative of the class of the original series. We use a heterogeneous ensemble classifier on the transformed data. The accuracy of our method is significantly better than the time-series classification benchmark (1-nearest-neighbour with dynamic time-warping distance), and significantly better than the previous best shapelet-based classifiers. We use two methods to increase interpretability: First, we cluster the shapelets using a novel, parameterless clustering method based on Minimum Description Length, reducing dimensionality and removing duplicate shapelets. Second, we transform the shapelet data into binary data reflecting the presence or absence of particular shapelets, a representation that is straightforward to interpret and understand. We supplement the ensemble classifier with partial classifocation. We generate rule sets on the binary-shapelet data, improving performance on certain classes, and revealing the relationship between the shapelets and the class label. To aid interpretability, we use a novel algorithm, BruteSuppression, that can substantially reduce the size of a rule set without negatively affecting performance, leading to a more compact, comprehensible model. Finally, we propose three novel algorithms for unsupervised mining of approximately repeated patterns in time-series data, testing their performance in terms of speed and accuracy on synthetic data, and on a real-world electricity-consumption device-disambiguation problem. We show that individual devices can be found automatically and in an unsupervised manner using a local-shape-based approach