2020/06/25 by Łukasz Matysiak, Matysiak, Lukasz · 1 citation
Computer Science · Mathematics · #Advanced Differential Equations and Dynamical Systems #Algebraic Geometry and Number Theory #Commutative Algebra (math.AC) #FOS: Mathematics #Polynomial and algebraic computation
paper · pdf · doi:10.48550/arxiv.2006.14948
openalex publication_date 2020/06/25 · openalex created_date 2020/07/02 · openalex updated_date 2026/07/28
In this paper I consider all possible properties from commutative algebra for polynomial composites and monoid domains. The aim is full characterization of these structures. I start with the examination of group, ring, modules properties, graded, but also the study of invertible elements, irreducible elements, ideals, etc. in these structures. In the second part of the work I give examples of the use of composites and monoid domains in cryptology. Each such polynomial is the sum of the products of the variable and the coefficient. And what if subsequent coefficient sets are appropriate cryptographic systems? Similarly, monoid domains can be a very good tool between encrypting and decrypting messages.