Transformation Method for Solving System of Boolean Algebraic Equations

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 polyn...

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Veröffentlicht in:Mathematics (Basel) Jg. 9; H. 24; S. 3299
Hauptverfasser: Barotov, Dostonjon, Osipov, Aleksey, Korchagin, Sergey, Pleshakova, Ekaterina, Muzafarov, Dilshod, Barotov, Ruziboy, Serdechnyy, Denis
Format: Journal Article
Sprache:Englisch
Veröffentlicht: Basel MDPI AG 01.12.2021
Schlagworte:
Algebra
algebraic cryptanalysis
Algorithms
Approximation
Boolean
Boolean algebra
Boolean polynomials
Codes
Cryptography
harmonic functions
logical operations
Mathematical analysis
Mathematics
Methods
Multiplication
Optimization
Optimization techniques
Polynomials
Real numbers
Rings (mathematics)
systems of Boolean algebraic equations
Transformations (mathematics)
ISSN:2227-7390, 2227-7390
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Zusammenfassung: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.
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ISSN:2227-7390
2227-7390
DOI:10.3390/math9243299