scholarly journals A new Modulo Addition with enhanced scalable security against algebraic attack

2021 ◽  
Author(s):  
Min Hsuan Cheng
Keyword(s):  
Algebraic Degree ◽  
Algebraic Equations ◽  
Algebraic Attack ◽  
Encryption Algorithms ◽  
Addition Modulo 2N ◽  
The Right ◽  
Inputs And Outputs

In recent years, Algebraic Attack has emerged to be an important cryptanalysis method in evaluating encryption algorithms. The attack exploits algebraic equations between the inputs and outputs of a cipher to solve for the targeted information. The complexity of the attack depends on the algebraic degree of the equations, the number of equations, and the probabilistic conditions employed. Addition Modulo 2n had been suggested over logic XOR as a mixing element to better defend against Algebraic Attack. However, it has been discovered that the complexity of the traditional Modulo Addition can be greatly reduced with the right equations and probabilistic conditions. The presented work introduces a new Modulo Addition structure that includes an Input Expansion, Modulo Addition, and Output Compaction. The security of the new structure is scalable and user-defined as the new structure increases the algebraic degree and thwarts the probabilistic conditions.

scholarly journals A new Modulo Addition with enhanced scalable security against algebraic attack

2021 ◽  
Author(s):  
Min Hsuan Cheng
Keyword(s):  
Algebraic Degree ◽  
Algebraic Equations ◽  
Algebraic Attack ◽  
Encryption Algorithms ◽  
Addition Modulo 2N ◽  
The Right ◽  
Inputs And Outputs

In recent years, Algebraic Attack has emerged to be an important cryptanalysis method in evaluating encryption algorithms. The attack exploits algebraic equations between the inputs and outputs of a cipher to solve for the targeted information. The complexity of the attack depends on the algebraic degree of the equations, the number of equations, and the probabilistic conditions employed. Addition Modulo 2n had been suggested over logic XOR as a mixing element to better defend against Algebraic Attack. However, it has been discovered that the complexity of the traditional Modulo Addition can be greatly reduced with the right equations and probabilistic conditions. The presented work introduces a new Modulo Addition structure that includes an Input Expansion, Modulo Addition, and Output Compaction. The security of the new structure is scalable and user-defined as the new structure increases the algebraic degree and thwarts the probabilistic conditions.

scholarly journals Transformation Method for Solving System of Boolean Algebraic Equations

Mathematics ◽  
2021 ◽  
Vol 9 (24) ◽  
pp. 3299
Author(s):  
Dostonjon Barotov ◽  
Aleksey Osipov ◽  
Sergey Korchagin ◽  
Ekaterina Pleshakova ◽  
Dilshod Muzafarov ◽  
...  
Keyword(s):  
Harmonic Polynomial ◽  
Optimization Methods ◽  
Optimization Method ◽  
Transformation Method ◽  
Polynomial Equations ◽  
Systems Of Equations ◽  
Algebraic Equations ◽  
Logical Operations ◽  
Dimensional Cube ◽  
The Right

: In recent years, various methods and directions for solving a system of Boolean algebraic equations have been invented, and now they are being very actively investigated. One of these directions is the method of transforming a system of Boolean algebraic equations, given over a ring of Boolean polynomials, into systems of equations over a field of real numbers, and various optimization methods can be applied to these systems. In this paper, we propose a new transformation method for Solving Systems of Boolean Algebraic Equations (SBAE). The essence of the proposed method is that firstly, SBAE written with logical operations are transformed (approximated) in a system of harmonic-polynomial equations in the unit n-dimensional cube Kn with the usual operations of addition and multiplication of numbers. Secondly, a transformed (approximated) system in Kn is solved by using the optimization method. We substantiated the correctness and the right to exist of the proposed method with reliable evidence. Based on this work, plans for further research to improve the proposed method are outlined.

The Green’S Function Solution of Right-Angle Plane Including a Semi-Cylindrical Canyon

2013 ◽  
Vol 275-277 ◽  
pp. 830-835
Author(s):  
Chun Xiang Zhao ◽  
Hui Qi
Keyword(s):  
Free Boundary ◽  
Green’S Function ◽  
Wave Field ◽  
Green's Function ◽  
Complex Function ◽  
Algebraic Equations ◽  
Function Solution ◽  
Out Of Plane ◽  
Stress Boundary Conditions ◽  
The Right

The Green’s function of a right-angle plane including semi-cylindrical canyon while bearing out-of-plane harmonic line source load on horizontal interface have been considered using the methods of complex function and image. Firstly, the wave field of right-angle plane was imaged half space, the scattering wave field, which satisfies the free stress boundary conditions of the right-angle plane on the vertical interface could be constructed. Secondly, a series of infinite algebraic equations be obtained to settle this problem by considering the stress free boundary condition of semi-cylindrical canyon. Finally, some examples for ground motion of a right-angle plane were given and discussed. Numerical results show that displacement of the horizontal surface is influenced by right-angle free boundary.

scholarly journals Solving Linear Programming Problems by Reducing to the Form with an Obvious Answer

2021 ◽  
Vol 28 (4) ◽  
pp. 434-451
Author(s):  
Gleb D. Stepanov
Keyword(s):  
Linear Programming ◽  
Simplex Method ◽  
Basic Solution ◽  
Algebraic Equations ◽  
Farkas Lemma ◽  
Second Stage ◽  
Positive Elements ◽  
Linear Algebraic Equations ◽  
The Matrix ◽  
The Right

The article considers a method for solving a linear programming problem (LPP), which requires finding the minimum or maximum of a linear functional on a set of non-negative solutions of a system of linear algebraic equations with the same unknowns. The method is obtained by improving the classical simplex method, which when involving geometric considerations, in fact, generalizes the Gauss complete exclusion method for solving systems of equations. The proposed method, as well as the method of complete exceptions, proceeds from purely algebraic considerations. It consists of converting the entire LPP, including the objective function, into an equivalent problem with an obvious answer. For the convenience of converting the target functional, the equations are written as linear functionals on the left side and zeros on the right one. From the coefficients of the mentioned functionals, a matrix is formed, which is called the LPP matrix. The zero row of the matrix is the coefficients of the target functional, $a_{00}$ is its free member. The algorithms are described and justified in terms of the transformation of this matrix. In calculations the matrix is a calculation table. The method under consideration by analogy with the simplex method consists of three stages. At the first stage the LPP matrix is reduced to a special 1-canonical form. With such matrices one of the basic solutions of the system is obvious, and the target functional on it is $ a_{00}$, which is very convenient. At the second stage the resulting matrix is transformed into a similar matrix with non-positive elements of the zero column (except $a_{00}$), which entails the non-negativity of the basic solution. At the third stage the matrix is transformed into a matrix that provides non-negativity and optimality of the basic solution. For the second stage the analog of which in the simplex method uses an artificial basis and is the most time-consuming, two variants without artificial variables are given. When describing the first of them, along the way, a very easy-to-understand and remember analogue of the famous Farkas lemma is obtained. The other option is quite simple to use, but its full justification is difficult and will be separately published.

Influence on Scattering of SH-Wave by Surface Ground Isosceles Triangular Hill in Right-Angle Plane with Circular Cavity

2010 ◽  
Vol 452-453 ◽  
pp. 529-532
Author(s):  
Guo Jing ◽  
Hui Qi ◽  
Jie Yang
Keyword(s):  
Boundary Conditions ◽  
Superposition Principle ◽  
Complex Function ◽  
Mirror Image ◽  
Circular Cavity ◽  
Algebraic Equations ◽  
Sh Wave ◽  
Polar Coordinate ◽  
The Right ◽  
Stress Free Boundary

The analytical solution to the problem of the scattering of SH-wave by isosceles triangular hill near the subsurface cavity in right-angle plane is given by using the idea of match up. Firstly, wave function was constructed by using the methods of complex function, multi-polar coordinate transformation and superposition principle, which satisfied the stress free boundary conditions at the free surfaces for the right-angle plane possessing a circular cavity. Secondly, transform the wave field from the right-angle plane to the half space by using the method of mirror image in order to obtain the total wave filed, which satisfied the boundary conditions. Finally, based on the conditions of the displacement continuity and stress continuity at the “common border” and the stress free condition at the subsurface cavity edge, a series of infinite algebraic equations were given and solved by truncation. Meanwhile, some examples and results are given and discussed.

On the Kronecker canonical form of a full row rank matrix pencil and applications

2019 ◽  
Author(s):  
Sophia D Karathanasi ◽  
Nicholas P Karampetakis
Keyword(s):  
Canonical Form ◽  
Matrix Pencil ◽  
Differential Algebraic Equations ◽  
Descriptor Systems ◽  
Algebraic Equations ◽  
Closed Form Solutions ◽  
Transformation Matrices ◽  
Rank Matrix ◽  
The Right ◽  
Kronecker Canonical Form

Abstract The Kronecker canonical form (KCF) of matrix pencils plays an important role in many fields such as systems control and differential–algebraic equations. In this article, we compute a finite and infinite Jordan chain and also a singular chain of vectors corresponding to a full row rank matrix pencil using an extended algorithm, first introduced by Jones (1999, Ph.D. Thesis, Department of Mathematics, Loughborough University of Technology, Loughborough, UK). The proposed method exploits these vectors forming the chains corresponding to the finite and infinite eigenvalues and to the right minimal indices of the pencil. This leads to the computation of two transformation matrices for obtaining under strict equivalence the KCF of the pencil. An application to the study of homogeneous linear rectangular descriptor systems is considered and closed form solutions are obtained in terms of these two transformation matrices. All the results are illustrated with an example.

scholarly journals Efficiency and/or Effectiveness in Managing Organizations

2020 ◽  
Vol 4 (2) ◽  
pp. p131
Author(s):  
Boushra W. Najar
Keyword(s):  
Organizational Effectiveness ◽  
Public Organization ◽  
Organizational Efficiency ◽  
Right Action ◽  
Organization Management ◽  
Effective Organization ◽  
The Right ◽  
Over Time ◽  
Inputs And Outputs

Does efficiency or effectiveness lead to successful organization management? Being efficient means investing as minimum resources as possible in order to get a desired result. Being effective by contrast means to achieve a desired result by using the right means or pursuing the right action. The question is not how to do this or that but rather, in what way the resources and efforts of a business should be directed to produce superior results rather than the usual efficient outcomes it can create. Organizational efficiency is the ratio between inputs and outputs in an organization. Organizational effectiveness is whether the organization fulfills its goals in doing the right thing. Concentrating on efficiency rather than effectiveness may limit an organization, so the argument of this article is that an organization should focus on effectiveness that is to pursue the right action. An effective organization is one that succeeds in adapting itself in place, time and content to a rapidly changing reality; such a business or public organization would succeeds over time in fulfilling and achieving its goals.

scholarly journals SYNTHESIS OF CONTROLLERS FOR NONLINEAR CONTROL OBJECTS ON BASIS OF NUMERICAL METHODS FOR SOLVING DIFFERENTIAL EQUATIONS

2018 ◽  
pp. 67-72
Author(s):  
Yu. P. Kornyushin ◽  
D. A. Akimenko ◽  
P. Yu. Kornyushin
Keyword(s):  
Differential Equations ◽  
Nonlinear Control ◽  
Dynamic Properties ◽  
Reference Signal ◽  
Reference Trajectory ◽  
Algebraic Equations ◽  
Entire Study ◽  
Right Hand ◽  
Study Interval ◽  
The Right

The algorithm of parametric synthesis of regulators for nonlinear control objects is presented in the article, in which knowledge of the real trajectory of the system motion is not required in an explicit form. The essence of the algorithm is as follows: the dynamic properties of the control system are always determined by the right-hand side of the system of differential equations written in the normal form of Cauchy. Depending on the values of the regulator parameters that are also included in the right-hand side, the system of equations may have one or another solution. If we substitute the reference trajectory into the scheme of numerical integration of differential equations describing the dynamics of the system, then at each step of integration it can be considered as a system of algebraic equations for the desired parameters of the regulator. For each discrete value of the reference signal, there is a set of desired regulator parameters from which the desired values are determined, for example, as weighted averages over the entire study interval, or, as some limiting values. In the proposed algorithm, in an implicit form, the criterion of optimality is the norm in the space of convergent numerical sequences.

Open Student Models

2011 ◽  
pp. 1541-1545
Author(s):  
Eshaa M. Alkhalifa
Keyword(s):  
Knowledge Transfer ◽  
Black Box ◽  
Student Response ◽  
Presentation Style ◽  
Student Knowledge ◽  
Student Models ◽  
The Right ◽  
Inputs And Outputs

When a student makes an error, the instructor wonders what possible misconception caused that error (Self, 1990) and attempts to correct it through altering the instruction method. Consequently, student models represent the system’s assumptions of learner knowledge and preferences without giving any guarantees that this model accurately reflects any of the information it contains. These models are utilized to present the right type of materials at the right point in time in the right presentation style (Fisher, 2001) in order to achieve optimal knowledge transfer. There are two main approaches followed when modeling student knowledge. The first attempts to delve into the cognitive workings of the student’s mind and tries to best explain how the results could be obtained. Some of those who followed this approach are Martin and Vahn Lehn (1995), Langley, Wogulis, and Ohlsson (1990), Ikeda, Kono, and Mizoguchi (1993), among others. The second approach assumes the process that occurs between the “inputs” and “outputs” that occur in a “black box” scenario. The researchers who adopt this presumption attempt to formulate a mapping between the situation and student response to that situation. Some of those who are following this type of modeling include Webb, Cumming, Richard, and Yum (1991) and Webb and Kuzmycz (1996).

The Ground Motion of Isosceles Triangular Hill in Right-Angle Plane Impacted by SH-Wave

2011 ◽  
Vol 121-126 ◽  
pp. 2363-2366
Author(s):  
Hui Qi ◽  
Jing Guo ◽  
Jie Yang
Keyword(s):  
Complex Function ◽  
Algebraic Equations ◽  
Sh Wave ◽  
Free Surfaces ◽  
Scattering Wave ◽  
The Common ◽  
Solution Region ◽  
The Right ◽  
Domain I ◽  
Stress Free Boundary

The analytical solution to the problem of the scattering of SH-wave by isosceles triangular hill in right-angle plane is given by using the methods of complex function and multiple coordinate. Firstly, the solution region is divided into two domains, where domain I involves isosceles triangular hill and a semi-circular bottom, domain II involves a semi-circular hollow in right-angle plane. And a standing wave function is constructed which satisfies the zero-stress conditions at the triangular wedges. In domain II, the scattering wave functions which satisfy the stress free boundary conditions at the free surfaces for the right-angle plane are constructed. Secondly, based on the conditions of the displacement continuity and stress continuity at the “common border” in the domains, a series of infinite algebraic equations are given and solved by truncation. Finally, some examples for amplitude of displacement on the surface are given. Numerical results show that amplitude of displacement on the surface is influenced by isosceles triangular hill.

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