  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.
