Cube Attack is a successful case of Algebraic Attack. Cube Attack consists of two phases, linear equation extraction and solving the extracted equation system. Due to the high complexity of equation extraction phase in finding linear equations, we can extract nonlinear ones that could be approximated to linear equations with high probability. The probabilistic equations could be considered as l...

Quantum computing promises classically unparalleled benefits for various applications. Its properties are exploited in the Harrow-Hassidim-Lloyd (HHL) algorithm that, conjunction with quantum phase estimation, is capable of constructing states that proportional to solution linear equation systems and does so exponentially faster than fastest known classical algorithms. We explore this capabilit...

In this work, we give a product Nyström method for solving a Fredholm functional integral equation (FIE) of the second kind. With this method solving FIE reduce to solving an algebraic system of equations. Then we use some theorems to prove the existence and uniqueness of the system. Finally we investigate the convergence of the method.

This paper is a review of the authors’ results on the Dynamical Systems Method (DSM) for solving operator equation (*) F (u)= f . It is assumed that (*) is solvable. The novel feature of the results is the minimal assumption on the smoothness of F . It is assumed that F is continuously Fréchet differentiable, but no smoothness assumptions on F ′(u) are imposed. The DSM for solving equation (*) ...

The problem of synthesis stochastic sensitivity for equilibrium modes in nonlinear randomly forced dynamical systems with incomplete information is considered. We construct a feedback regulator that uses noisy data on some system state coordinates. For parameters the providing assigned sensitivity, quadratic matrix equation derived. Attainability reduced to solvability this equation. suggest co...

We formulate the problem of solving stochastic linear operator equations in a Bayesian Ganssian process (GP) framework. The solution is obtained in the spirit of a collocation method based on noisy evaluations of the target function at randomly drawn or deliberately chosen points. Prior knowledge about the solution is encoded by the covariance kernel of the GP. As in GP regression, analytical e...

in this paper, we propose a new method for solving the stochastic advection-diffusion equation of ito type. in this work, we use a compact finite difference approximation for discretizing spatial derivatives of the mentioned equation and semi-implicit milstein scheme for the resulting linear stochastic system of differential equation. the main purpose of this paper is the stability investigatio...

Several methods for solving efficiently the one-dimensional deconvolution problem are proposed. The problem is to solve the Volterra equation ku := ∫ t 0 k(t − s)u(s)ds = g(t), 0 ≤ t ≤ T . The data, g(t), are noisy. Of special practical interest is the case when the data are noisy and known at a discrete set of times. A general approach to the deconvolution problem is proposed: represent k = A(...