Development of the mathematic model of disymmetric bigram cryptosystem based on a parametric solution family of multi-degree system of Diophantine equations✱

2020 ◽  
Author(s):  
Valeriy Osipyan ◽  
Kirill Litvinov
Keyword(s):  
Diophantine Equations ◽  
Mathematic Model ◽  
Parametric Solution

Development of the mathematic model of dissymmetric bigram cryptosystem based on parametric solution family of multi-degree system of Diophantine equations

2020 ◽  
Author(s):  
V. O. Osipyan
Keyword(s):  
Diophantine Equations ◽  
Mathematic Model ◽  
Parametric Solution

Предложен новый подход разработки дисимметричной биграммной криптосистемы (ДБК) на основе многопараметрических решений многостепенных систем диофантовых уравнений (МСДУ), обобщающий принцип построения криптосистем с открытым ключом. Вводится новое понятие равносильности числовых наборов или параметров заданной размерности и порядка. Описанные математические модели СЗИ демонстрируют потенциал применения МСДУ для разработки СЗИ с высокой степенью надёжности

scholarly journals Some diophantine problems concerning equal sums of integers and their cubes

2010 ◽  
Vol Volume 33 ◽  
Author(s):  
Ajai Choudhry
Keyword(s):  
Symmetric Solution ◽  
Diophantine Equations ◽  
Simple Solution ◽  
Parametric Solution ◽  
Quadratic Polynomials ◽  
Simultaneous Diophantine Equations ◽  
International Audience ◽  
Diophantine Problems ◽  
The Given ◽  
Complete Solutions

International audience This paper gives a complete four-parameter solution of the simultaneous diophantine equations $x+y+z=u+v+w, x^3+y^3+z^3=u^3+v^3+w^3,$ in terms of quadratic polynomials in which each parameter occurs only in the first degree. This solution is much simpler than the complete solutions of these equations published earlier. This simple solution is used to obtain solutions of several related diophantine problems. For instance, the paper gives a parametric solution of the arbitrarily long simultaneous diophantine chains of the type $x^k_1+y^k_1+z^k_1=x^k_2+y^k_2+z^k_2=\ldots=x^k_n+y^k_n+z^k_n=\ldots,~~k=1,3.$ Further, the complete ideal symmetric solution of the Tarry-Escott problem of degree $4$ is obtained, and it is also shown that any arbitrarily given integer can be expressed as the sum of four distinct nonzero integers such that the sum of the cubes of these four integers is equal to the cube of the given integer.

scholarly journals SYMMETRIC HOMOGENEOUS DIOPHANTINE EQUATIONS OF ODD DEGREE

2013 ◽  
Vol 09 (04) ◽  
pp. 867-876 ◽  
Author(s):  
M. A. REYNYA
Keyword(s):  
Diophantine Equations ◽  
Parametric Solution ◽  
Elementary Approach ◽  
Symmetric Form ◽  
Model Case ◽  
Parametric Solutions ◽  
Odd Degree

An elementary approach for finding non-trivial parametric solutions to homogeneous symmetric Diophantine equations of odd degree in sufficiently many variables is presented. The method is based on studying a model case of quintic symmetric Diophantine equations in six variables. We prove that every symmetric form of odd degree n ≥ 5 in 6 ⋅ 2n - 5 variables has a rational parametric solution depending on 2n-8 parameters. We also present a solution to a problem of Waring type: if F(x1,…, xN) is a symmetric form of odd degree n ≥ 5 in N = 6 ⋅ 2n-4 variables, then for any q ∈ ℚ the equation F(xi) = q has a rational parametric solution depending on 2n - 6 parameters.

A Calculation real abundance of gaseous elements of the comet PanSTARRS C/2011 S4

2020 ◽  
Vol 18 (45) ◽  
pp. 21-31
Author(s):  
Salman Zaidan Khalaf ◽  
Khaleel Abrahim ◽  
Imad Kassar Akeab
Keyword(s):  
Solar Wind ◽  
Physical Properties ◽  
Atomic Number ◽  
Mathematic Model ◽  
Emission Energy ◽  
X Ray ◽  
The Real

    X-ray emission contains some of the gaseous properties is produced when the particles of the solar wind strike the atmosphere of comet ISON and PanSTARRS Comets. The data collected with NASA Chandra X-ray Observatory of the two comets, C/2012 S1 (also known as Comet ISON) and C/2011 S4 (Comet PanSTARRS) are used in this study.    The real abundance of the observed X-ray spectrum elements has been extracted by a new simple mathematic model. The study found some physical properties of these elements in the comet’s gas such as a relationship between the abundance with emitted energy. The elements that have emission energy (2500-6800) eV, have abundance (0.1-0.15) %, while the elements that have emission energy (850-2500) eV and (6800-9250) eV have abundance (0.2-0.3) %.    The relation between interacted energy and atomic number is form two sets.  The interacted energy of each element is increased as the atomic number increased. This case has been seen in both comets

A Novel Control Scheme for PWM Boost Converter based on Sliding Mode Control using Particle Swarm Optimization

2020 ◽  
Vol 14 ◽  
Author(s):  
Gang Liu ◽  
Dong Qiu ◽  
Xiuru Wang ◽  
Ke Zhang ◽  
Huafeng Huang ◽  
...  
Keyword(s):  
Particle Swarm Optimization ◽  
Steady State ◽  
Sliding Mode ◽  
Particle Swarm ◽  
Mathematic Model ◽  
Absolute Error ◽  
Boost Converter ◽  
Sliding Mode Controller ◽  
Swarm Optimization ◽  
Steady State Performance

Background: The PWM Boost converter is a strongly nonlinear discrete system, especially when the input voltage or load varies widely, therefore, tuning the control parameters of which is a challenge work. Objective: In order to overcome the issues, particle swarm optimization (PSO) is employed for tuning the parameters of a sliding mode controller of a boost converter. Methods: Based on the analysis of the Boost converter model and its non-linear characteristics, a mathematic model of a boost converter with a sliding mode controller is built firstly. Then, the parameters of the Boost controller are adjusted based on the integrated time and absolute error (ITAE), integral square error (ISE) and integrated absolute error (IAE) indexes by PSO. Results: Simulation verification was performed, and the results show that the controllers tuned by the three indexes all have excellent robust stability. Conclusion: The controllers tuned by ITAE and ISE indexes have excellent steady-state performance, but the overshoot is large during the startup. The controller tuned by IAE index has better startup performance and slightly worse steady-state performance.

Secure Watermarking using Diophantine Equations for Authentication and Recovery

2015 ◽  
Vol 3 (2) ◽  
Author(s):  
Jayashree Nair ◽  
T. Padma
Keyword(s):  
Diophantine Equation ◽  
Diophantine Equations ◽  
Jpeg Compression ◽  
Authentication Scheme ◽  
Original Image ◽  
Invariant Features ◽  
Jpeg2000 Compression ◽  
Frequency Properties ◽  
Visual Authentication

This paper describes an authentication scheme that uses Diophantine equations based generation of the secret locations to embed the authentication and recovery watermark in the DWT sub-bands. The security lies in the difficulty of finding a solution to the Diophantine equation. The scheme uses the content invariant features of the image as a self-authenticating watermark and a quantized down sampled approximation of the original image as a recovery watermark for visual authentication, both embedded securely using secret locations generated from solution of the Diophantine equations formed from the PQ sequences. The scheme is mildly robust to Jpeg compression and highly robust to Jpeg2000 compression. The scheme also ensures highly imperceptible watermarked images as the spatio –frequency properties of DWT are utilized to embed the dual watermarks.

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