Algebraic simplification and cryptographic motives

Algebraic simplification is considered from the general point of view. The main notion here is the so-called scheme of simplification due to the author. For a corepresented algebra simplificators are related to the standard basis (Gröbner basis, Gröbner–Shirshov basis) of the ideal of defining relations. We introduce as a main subject for study the class of algebras that may be obtained from ordered semigroup algebras by “deformation” in some sense. This class contains free associative algebras and universal enveloping algebras of Lie algebras. The main attention is paid to the latter algebras. Some possible applications to cryptography are given.