R.T. Mamedov, V.M. Fomichev

Mixing properties of some functions are investigated. These properties define usage efficiency of these functions in the subsystems that provide integrity and confidentiality of data in the information and telecommunication systems of high availability. A number of attributes of imperfectness are described and researched in the groups of vector space transformation. Sufficient conditions of triviality of triangularity attribute were obtained: there are no nonidentity triangular substitutions in the circular group of binary vector space, in the case of generating substitution has the cycles of odd-number length only. Optimization problem of sequential key search was reduced to determining the allowing set of fixations considering properties of equations set being solved. The article gives constructed transformations examples showing that sequential key search could be effectively applied to the equations systems with the perfect transformation at the left part allowing branching into some number of imperfectness transformations. All abovementioned emphasize the importance to continue researches of these classes of perfect transformation.