Information Theoretic Security - The problem of information security of critical information infrastructure objects in the conditions of openness is formulated. The concept of information infrastructure openness is analyzed. An approach to assessing the openness of an information system is presented. A set-theoretic model of information resources openness was developed. The formulation of the control problem over the degree of openness with restrictions on risk was carried out. An example of solving the problem of finding the coefficient of openness is presented.