One of the approaches to form a cryptographically secure encryption range is the use of linear recurrent feedback registers based on primitive polynomials. The operational possibility of choosing the appropriate polynomial can provide the required degree of stability of the algorithm used. At present, primitive polynomials are known for sufficiently large powers, but usually these are the so-called sparse polynomials. To improve cryptographic strength, it is necessary to be able to quickly form new primitive polynomials of given degrees, which is the subject of this study