Related papers: Higher Order Differentiation over Finite Fields wi…
We discuss a new attack, termed a dimension or linear decomposition attack, on several known group-based cryptosystems. This attack gives a polynomial time deterministic algorithm that recovers the secret shared key from the public data in…
It is proved that for any finite dimensional representation of a prime order group over the field of rational numbers, polynomial invariants of degree at most $3$ separate the orbits. A result providing an upper degree bound for separating…
Deep neural network models are massively deployed on a wide variety of hardware platforms. This results in the appearance of new attack vectors that significantly extend the standard attack surface, extensively studied by the adversarial…
We consider a few modifications of the Big prime modular $\gcd$ algorithm for polynomials in $\Z[x]$. Our modifications are based on bounds of degrees of modular common divisors of polynomials, on estimates of the number of prime divisors…
Let $f$ be a polynomial of degree $d$ in $n$ variables over a finite field $\mathbb{F}$. The polynomial is said to be unbiased if the distribution of $f(x)$ for a uniform input $x \in \mathbb{F}^n$ is close to the uniform distribution over…
The inaccuracy of the classical magnetic field integral equation (MFIE) is a long-studied problem. We investigate one of the potential approaches to solve the accuracy problem: higher-order discretization schemes. While these are able to…
In this paper, we tackle the parametric complete multiplicity problem for a univariate polynomial. Our approach to the parametric complete multiplicity problem has a significant difference from the classical method, which relies on repeated…
We develop summation by parts (SBP) approach for generating high-order finite-difference schemes on the interval and propose new sets of schemes up to the 12th order. The coefficients of the schemes are governed by values of grid spacing…
Second-order polynomials generalize classical first-order ones in allowing for additional variables that range over functions rather than values. We are motivated by their applications in higher-order computational complexity theory,…
Consider an algorithm computing in a differential field with several commuting derivations such that the only operations it performs with the elements of the field are arithmetic operations, differentiation, and zero testing. We show that,…
We introduce and analyze a novel class of binary operations on finite-dimensional vector spaces over a field K, defined by second-order multilinear expressions with linear shifts. These operations generate polynomials whose degree increases…
Because of their interesting algebraic properties, several authors promote the use of generalized Reed-Solomon codes in cryptography. Niederreiter was the first to suggest an instantiation of his cryptosystem with them but Sidelnikov and…
Federated Learning (FL) has emerged as a leading paradigm for decentralized, privacy preserving machine learning training. However, recent research on gradient inversion attacks (GIAs) have shown that gradient updates in FL can leak…
In this paper, a higher order finite difference scheme is proposed for Generalized Fractional Diffusion Equations (GFDEs). The fractional diffusion equation is considered in terms of the generalized fractional derivatives (GFDs) which uses…
We bring in here a novel algebraic approach for attacking the McEliece cryptosystem. It consists in introducing a subspace of matrices representing quadratic forms. Those are associated with quadratic relationships for the component-wise…
Graph deep learning models, such as graph convolutional networks (GCN) achieve remarkable performance for tasks on graph data. Similar to other types of deep models, graph deep learning models often suffer from adversarial attacks. However,…
High-order finite-difference methods are commonly used in wave propagators for industrial subsurface imaging algorithms. Computational aspects of the reduced linear elastic vertical transversely isotropic propagator are considered. Thread…
Machine learning methods must be trusted to make appropriate decisions in real-world environments, even when faced with out-of-distribution (OOD) samples. Many current approaches simply aim to detect OOD examples and alert the user when an…
We present a novel approach for high-order accurate numerical differentiation on unstructured meshes of quadrilateral elements. To differentiate a given function, an auxiliary function with greater smoothness properties is defined which…
The concept of fractional order derivative can be found in extensive range of many different subject areas. For this reason, the concept of fractional order derivative should be examined. After giving different methods mostly used in…