Mathematical Model of the Process of Raising Integers to an Arbitrary Power of a Natural Number in the System of Residual Classes

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dc.contributor.authorKrasnobayev, Victor
dc.contributor.authorYanko, Alina
dc.contributor.authorKovalchuk, Dmytro
dc.date.accessioned2023-11-22T11:41:07Z
dc.date.available2023-11-22T11:41:07Z
dc.date.issued2023
dc.description.abstractIt is known that the use of a non-positional number system in residual classes (SRC) in computer systems (CS) can significantly increase the speed of the implementation of integer arithmetic operations. The use of such properties of a non-positional number system in the SRC as independence, equality and low-bitness (low-digit capacity) of the residues that define the non-positional code data structure of the SRC provides high user performance for the implementation in the CS of computational algorithms consisting of a set of arithmetic (modular) operations. The greatest efficiency from the use of the SRC is achieved when the implemented algorithms consist of a set of arithmetic operations such as addition, multiplication and subtraction. There is a large class of algorithms and tasks (tasks of implementing cryptoalgorithms, optimization tasks, computational tasks of large dimension, etc.), where, in addition to performing integer arithmetic operations of addition, subtraction, multiplication, raising integers modulo and others in a positive numerical range, there is a need to implement the listed above arithmetic and other operations, in the negative numerical range. The need to perform these operations in a negative numerical range significantly reduces the overall efficiency of using the SRC as a number system of the CS. In this aspect, the lack of a mathematical model for the process of raising integers in the SRC in the negative numerical region makes it difficult to develop methods and procedures for raising integers to an arbitrary power of a natural number in the SRC, both in positive and negative numerical ranges. The purpose of the article is the synthesis of a mathematical model of the process of raising integers to an arbitrary power of a natural number in the SRC, both in positive and negative numerical ranges.uk
dc.format.pagerangePp. 5-14uk
dc.identifier.citationKrasnobayev, V. Mathematical Model of the Process of Raising Integers to an Arbitrary Power of a Natural Number in the System of Residual Classes / Victor Krasnobayev, Alina Yanko, Dmytro Kovalchuk // Theoretical and Applied Cybersecurity : scientific journal. – 2023. – Vol. 5, Iss. 2. – Pp. 5–14. – Bibliogr. 32 ref.uk
dc.identifier.doihttps://doi.org/10.20535/tacs.2664-29132023.2.278891
dc.identifier.orcid0000-0003-2876-9316uk
dc.identifier.urihttps://ela.kpi.ua/handle/123456789/62383
dc.language.isoukuk
dc.publisherIgor Sikorsky Kyiv Polytechnic Instituteuk
dc.publisher.placeKyivuk
dc.relation.ispartofTheoretical and Applied Cybersecurity: scientific journal, Vol. 5, No. 2uk
dc.subjectArtificial formuk
dc.subjectcomputer systemuk
dc.subjectmathematical inductionuk
dc.subjectmathematical modeluk
dc.subjectmethod for raising integersuk
dc.subjectpositional number systemuk
dc.subjectsystem of residual classesuk
dc.subject.udc004.02:519.87uk
dc.titleMathematical Model of the Process of Raising Integers to an Arbitrary Power of a Natural Number in the System of Residual Classesuk
dc.typeArticleuk

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Theoretical and Applied Cybersecurity: scientific journal, Vol. 5, No. 2