A Polynomial Composites and Monoid Domains as Algebraic Structures and their Applications

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Magdalena Jankowska
Magdalena Jankowska
2
Lukasz Matysiak
Lukasz Matysiak
1 Kazimierz Wielki University

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GJSFR Volume 21 Issue F3

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This paper contains the results collected so far on polynomial composites in terms of many basic algebraic properties. Since it is a polynomial structure, results for monoid domains come in here and there. The second part of the paper contains the results of the relationship between the theory of polynomial composites, the Galois theory and the theory of nilpotents. The third part of this paper shows us some cryptosystems. We find generalizations of known ciphers taking into account the infinite alphabet and using simple algebraic methods. We also find two cryptosystems in which the structure of Dedekind rings resides, namely certain elements are equivalent to fractional ideals. Finally, we find the use of polynomial composites and monoid domains in cryptology.

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No external funding was declared for this work.

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The authors declare no conflict of interest.

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No ethics committee approval was required for this article type.

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Magdalena Jankowska. 2021. \u201cA Polynomial Composites and Monoid Domains as Algebraic Structures and their Applications\u201d. Global Journal of Science Frontier Research - F: Mathematics & Decision GJSFR-F Volume 21 (GJSFR Volume 21 Issue F3): .

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GJSFR Volume 21 Issue F3
Pg. 93- 111
Journal Specifications

Crossref Journal DOI 10.17406/GJSFR

Print ISSN 0975-5896

e-ISSN 2249-4626

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GJSFR-F Classification: MSC 2010: 08A40
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v1.2

Issue date

July 2, 2021

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English

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This paper contains the results collected so far on polynomial composites in terms of many basic algebraic properties. Since it is a polynomial structure, results for monoid domains come in here and there. The second part of the paper contains the results of the relationship between the theory of polynomial composites, the Galois theory and the theory of nilpotents. The third part of this paper shows us some cryptosystems. We find generalizations of known ciphers taking into account the infinite alphabet and using simple algebraic methods. We also find two cryptosystems in which the structure of Dedekind rings resides, namely certain elements are equivalent to fractional ideals. Finally, we find the use of polynomial composites and monoid domains in cryptology.

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A Polynomial Composites and Monoid Domains as Algebraic Structures and their Applications

Magdalena Jankowska
Magdalena Jankowska Kazimierz Wielki University
Lukasz Matysiak
Lukasz Matysiak

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