Construction of asymmetric cryptosystems using finite non-commutative algebraic groups

This article considers the work done to find a suitable group implementation for the creation of new cryptosystems which work is based on the use of finite non-commutative algebraic groups. In particular, some subgroup structures of matrix groups over finite fields are described, and one of the possible methods for representing of open texts as elements of the group is used. At the preliminary stage of the cryptosystem, the developed concept of generating keys is described, and recommendations are given for selecting the elements of the secret key. The structure and features of the cryptosystem under investigation are given, earlier studies and experiments that were carried out in this field are considered. To generate subgroups of the groups under study, it is proposed to use elementary transvections, in particular, long and short root unipotent elements. A classification of certain groups of the Chevalley type by types A
l
-D
l
is provided. Some assumptions are made concerning the possible improvement of reliability and speed of such cryptosystems based upon the finite non-commutative algebraic groups, as well as relating to the prospects of further research in this direction and minimizing or eliminating the shortcomings of this data encryption model.