Schemes of public distribution of a key based on a noncommutative operation

We study properties of two schemes of public distribution of a key suggested by V. M. Sidelnikov which are based on a noncommutative operation. As a noncommutative operation we consider the operations belonging to the family suggested by M. A. Cherepnev, namely, the operations in the rings of integers of cyclotomic fields based on the power residue symbol.
In the paper, a cryptanalysis of both schemes is performed for a particular noncommutative operation. We show that for an arbitrary operation of the mentioned above family the first scheme in not resistant. For the second scheme, we prove a theorem on the equivalence of its breaking to a solution of some problem of a computational algebraic number theory.