A polynomial composites and monoid domains as algebraic structures and their applications
Abstract
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.
Keywords
Cite
@article{arxiv.2105.15145,
title = {A polynomial composites and monoid domains as algebraic structures and their applications},
author = {Magdalena Jankowska and Lukasz Matysiak},
journal= {arXiv preprint arXiv:2105.15145},
year = {2021}
}
Comments
22 pages. arXiv admin note: substantial text overlap with arXiv:2006.14948